SERIITR-252-3108 

UC Category: 262 

DE89000822 

Direct-Contact Condensers 

for Open-Cycle OTEC 

Applications 

Model Validation with Fresh Water 

Experiments for Structured Packings 

D. Bharathan 

B. K. Parsons 

J. A. Althof 

October 1988 

Prepared under Task No. OE713101 

Solar Energy Research Institute 

A Division of Midwest Research Institute 

1617 Cole Boulevard 

Golden, Colorado 80401-3393 

Prepared for the 

U.S. Department of Energy 

Contract No. DE-AC02-83CH10093 
TR-3108 

PREFACE 

This report describes the status of our direct-contact condenser model validation effort performed under the FY 1986 task entitled "Heat and Mass Transfer 

K~del." This task is a subset of an overall objective to develop a detailed, 

analytical computer model for various open-cycle ocean thermal energy conversion COC-OTEC) components. This report describes a complete set of process 

equations and an integration method for a one-dimensional, steady-state model 

of cocurrent and countercurrent condensers. Extensi ve sets of comparisons 

between experimental data and model predictions for structured packing in 

fresh water are provided. The report also summarizes results obtained in 

previ6us years that are pertinent to the model validation effort. 

The Pascal modeling code was developed and debugged on an IBM-AT computer 

using the Turbo Pascalm compiler. We have also run the code on available IBM 

personal computers. The condenser model represents the state of the art in 

direct-contact heat exchange for condensation for OC-OTEC applications. This 

is expected to provide a basis for optimizing OC-OTEC plant configurations. 

This model is an excellent tool for use in data reduction for the planned 

research activities with seawater at the Natural Energy Laboratory of Hawaii, 

for design and system evaluations for OC-OTEC, and for other low-temperature 

energy technologies. 

We would like to thank Andrew Trenka, Oceans Program leader, for his leadership and Terry Penney and David Johnson for their encouragement. The efforts 

of Ben Shelpuk, principal engineer, are also appreciated. Gratitude is 

expressed to Gene Winkler, Munters Corporation, and to Neil Yeoman, Koch Engineering Company, Inc., for providing valuable information on their companies' 

products. Critical reviews provided by Kenneth Bell, Oklahoma State University, Stillwater; Anthony Mills, University of California at Los Angeles; 

and G. B. Wallis, Dartmouth College, guided us in accomplishing our goals in 

this task. 

Approved for 

SOLAR ENERGY RESEARCH INSTITUTE 

Robert A. Stokes, Acting Director 

Solar Heat Research Division 

Desikan Bharathan, Senior'Engineer 
TR-3108 

SUMMARY 

Objective 

To develop analytical methods for evaluating the design and performance of 

advanced, high-performance heat exchangers that are reliable and costeffective for use in the open-cycle ocean thermal energy conversion (OC-DTEC) 

process. 

Discussion 

This report describes the progress made on validating a one-dimensional, 

steady-state analytical computer model of direct-contact condenser using 

structured packings based on extensive sets of fresh water experiments. The 

condenser model represents the state of the art 1n direct-contact heat 

exchange for condensation for DC-OTEC applications. This is expected to 

provide a basis for optimizing DC-OTEC plant configurations. Using the model, 

we examined two condenser geometries, a cocurrent and a countercurrent 

configuration. 

We developed a computer model for evaluating direct-contact condenser geometries and optimum flow parameters for DC-OTEC applications. Use of this 

model, however, was limited to structured packings. This report provides 

detailed validation results for important condenser parameters for cocurrent 

and countercurrent flows. With modifications this model can be used for other 

industrial applications as well. 

The model establishes the viability of packed-column geometries for use 1n 

OC-DTEC systems and illustrates the variations of condenser performance as 

geometric and flow parameters are altered. 

Conclusions 

We developed a one-dimensional, steady-state model that captures the heat, 

mass, and momentum processes in steam-water, direct-contact appl ications in 

the presence of noncondensable gases for both cocurrent and countercurrent 

condensers. The model also incorporates the mass transfer of dissolved gases 

in the coolant. Portable Turbo-PascalT.M computer codes for co current and 

countercurrent condensers were developed. These codes were exercised over a 

wide range of geometrical and condenser flow geometries to predict performances of tested condenser geometries. The predictions were compared with the 

experimental data to quantify deviations. 

Based on the comparisons and uncertainty overlap between the experimental data 

and predictions, the model is shown to predict critical condenser performance 

parameters with an uncertainty acceptable for general engineering design and 

performance evaluations. 

lV 
S5~1 TR-3108 

TABLE OF CONTENTS 

Nomenclature ......•.••....••.••.......•.••.........•.•....•.•.••..•...•.. X~11 

1.0 

2.0 

3.0 

4.0 

Introduction •••••••••••••••••••••••••••••••••••••••••••••••••••••••• 

1.1 

1.2 

1.3 

1.4 

1.5 

Objective and Goal •••••••••••••••••••••.•••••••••••••.••.•••••• 

Approach •••••••.••.•.....•..•.•••..••....••.......••.•.•••....• 

Scope and Limitation ••••••••••••••••••••••••••.•••••••••••••••• 

Background ••........•....••.•.••••.......•••......••...•..••••• 

Report Organization •••••••••••••• .............................. 

Model Description ••••••••••••••••••••••••••••••••••••••••••••••••••• 

2.1 

2.2 

2.3 

2.4 

Condenser •••••••••••••••••••••••••••••••••••••••••••• 

Interface Temperature ••••••.••.•••••••.••••••••••••••••• 

Cocurrent 

2.1.1 

2.1.2 

2.1.3 

2.1.4 

Transfer Fluxes •••••••.•..•••••••••••.•••••••••••••••••• 

Process Equations ••••••••••••••••••••••••••••••••••••••• 

Equilibrium Calculations .•••••..••••...•••••..•••••••.•• 

Countercurrent Condenser ••••••••••••••••••••••••••••••••••••••• 

2.2.1 Differences in Countercurrent Operation ••••••••••••••••• 

2.2.2 

2.2.3 

Process Equations •••••••••••••••••••• 

Equilibrium Calculations ••••••••••••• 

Structured Packings •••.•.••••.•••••••.•••••.•••••••••..•••••••• 

2.3.1 Geometry Definitions ••••••••••.••••.•.•••••••••••••••••• 

2.3.2 Transfer Correlations ••••••••••••.•••••••••••••.••••••.• 

Integration Scheme ••••••.••••••••••••.•••..••••••••••••.••••••• 

Experimental Details •.•••••••.••••.••••••••••••••.••••••••.••••••••• 

3.1 

3.2 

3.3 

3.4 

Facility •••••.••••••••..•••.••••••••••••••••.•••••••••.••••••.. 

Instrumentation •••••••••••••••••••••••.•••.••••••••.•••.••••••• 

Condenser Test Models ......................................... Test Procedure ••••••••••••••••••••••••••••••••••••••••••••••••• 

Model Validation ••••••••••••••••.••••••••••.•.•••••••••••••••••••••• 

4.1 

4.2 

4.3 

Cocurrent Condenser •••.•••••••••••••••••••.•••••••••••••••••••• 

4. 1 • 1 AX. Pac king ••••••••••••••••••••.••••••••••••••••••••••••• 

4.1.2 Plasdek 19060 Packing ••••••••••••••••••••••••••••••••••• 

4.1.3 

4.1.4 

4X Packing •••••••.•••••••••••••••••.••••••••••••••••.••• 

Free Jets ••••••••••••••••••••••••••••••••••••••••••••••• 

4.1.5 Summary of Cocurrent Condenser Findings ••••••••••••••••• 

Countercurrent Condenser ••••••••••••••••••••••••••••••••••••••• 

4.2.1 

4.2.2 

4.2.3 

4.2.4 

4.2.5 

~ Packing •..••.•••••••••••.••.•.•....••.•.•.•...••...•• 

Plasdek 19060 Packing •••••••••••••••..•••.••••••••••.••• 

3X Packing ••••••••••.••••.••••••••••.•••••••••.••••••••• 

Plasdek 27060 Packing •••••••••.••.••••••••••••••.••••••• 

Summary of Countercurrent Condenser Findings •••••••••••• 

Summary •••••••••••••••••••••••••••••••••••••••••••••••••••••••• 

v 

1 

4 

5 

7 

8 

11 

13 

13 

13 

15 

15 

18 

18 

18 

18 

20 

20 

20 

22 

28 

31 

31 

31 

34 

37 

39 

40 

41 

42 

43 

44 

47 

48 

48 

51 

51 

53 

53 

56 
TR-3108 

5.0 

6.0 

7.0 

TABLE OF CONTENTS (Concluded) 

Numerical Results and Parametric Studies •••••••••••••••••••••••••••• 

5.1 

5.2 

Cocurrent Condenser ••••..•..••.•••••••.••••••••••••••.••••••••• 

5.1.1 

5.1.2 

5.1.3 

Condensation Process •••••••••••••••••••••••••••.•••••.•. 

Influence of Packing Geometry ••••••••••••••••••••••••••• 

Influence of Flow Parameters •••••••••••••••••••••••••••• 

Countercurrent Condenser •••••••••••••••••••••••••••••.••••••••• 

5.2.1 

5.2.2 

5.2.3 

Condensation Process ••••.•••••...••••••••••.•••.•••••••• 

Influence of Packing Geometry ••••••••••••••••••••••••••• 

Influence of Flow Parameters •••••••••••••••••••••••••••• 

Conclusions and Recommendations ••••••••••••••••••••••••••••••••••••• 

6.1 

6.2 

Conclusions ..••.•..•..•.••.••.•.•.••••..••.••••••..••......•••. 

Recommendations •••••••••••••••••••.••...•••.••••..••••••.••..•• 

References 

57 

57 

57 

61 

64 

72 

72 

78 

81 

85 

85 

87 

90 

Nomenclature for Appendices •••••••••••••••••••••••••••••••••••••••••••• o. 93 

Appendix A Experimental Facility and Instrumentation •••••••••••••••••••• 95 

Appendix B Measurement Uncertainties and Their Propagation •••••••••••••• 112 

Appendix C Relative Ranking of Tested Contact Devices ••••••••••••••••••• 122 

Appendix D Data Tables for Experiments Using Structured Packings •••••••• 132 

Appendix E Data Tables for Countercurrent Condenser Geometries Other 

Than Structured Packing •.••••••••••••••••••••••.•...••••••••• 163 

Appendix F Computer Program Listings ••••••..•••.••••.•.••••••••••••••••• 189 

Appendix G Equilibrium Calculations •••••••••••••••••••••••••••••..••.••• 246 

Appendix H Water, Steam, and Air Properties ••••••••••••••••••••••••••••• 250 

Selected Distribution List ••••••••••••••••••••••..••••••••••••••••••••••• 255 

Vl 
TR-3108 

LIST OF FIGURES 

1-1 Schematic of an open-cycle ocean thermal energy 

converSl.on system.................................................. 1 

1-2 Diagram of desalinated water production scheme using direct contact 

1-3 

condenser. • . • • • • . • • • . • . • • • . • • • . • . • . . . . • • • • • . . . . • • . • . . • . . . . • . . . . . • . • 2 

Schematic of barometric direct-contact condenser subsystem 

indicating steam and noncondensable gas mixture flow through 

cocurrent and countercurrent sections using structured packings •••• 3 

1-4 Relative performance comparison of a few tested countercurrent 

condenser configurations........................................... 6 

2-1 Representation of temperature distribution in coolant, gas, and 

interface during condensation: condensing steam flux and 

noncondensable mass flux........................................... 14 

2-2 A slice of a cocurrent direct-contact condenser indicating the 

modeling variables for one-dimensional flow........................ 16 

2-3 A slice of a countercurrent direct-contact condenser indicating 

the modeling variables for one-dimensional flow.................... 19 

2-4 Structured sheet packing.~ ••••••••••••••••••••••••••••••••••••••••• 21 

2-5 Structured packing geometry definition ••••••••••••••••••••••••••••• 21 

2-6 Liquid film flow on an inclined structured packing geometry........ 23 

3-1 Heat- and mass-transfer laboratory flow loop schematic ••••••••••••• 32 

3-2 Schematic of cocurrent condenser test article arrangement •••••••••• 35 

3-3 Schematic of countercurrent condenser test article arrangement..... 35 

4-1 Comparison of condensed steam for AX packing in co current flow..... 41 

4-2 Comparison of pressure loss for AX packing in cocurrent flow ••••••• 42 

4-3 Comparison of condensed steam for 19060 packing in cocurrent 

flow........ ............................. .......................... 43 

4-4 Comparison of pressure loss for 19060 packing in cocurrent flow •••• 44 

4-5 Comparison of condensed steam for 4X packing in cocurrent flow ••••• 45 

4-6 Comparison of pressure loss for 4X packing in cocurrent flow ••••••• 45 

4-7 Free-falling jets in cocurrent configuration ••••••••••••••••••••••• 46 

V~~ 
4-8 

4-9 

4-10 

4-11 

4-12 

4-13 

4-14 

4-15 

4-16 

4-17 

5-1 

TR-3108 

LIST OF FIGURES (Continued) 

Comparison of measured condensed steam for a cocurrent condenser 

with and without 19060 packing ••••••••••••••••••••••••••••••••••••• 

Comparison of measured pressure loss for a cocurrent condenser 

with and without 19060 packing ••••••••••••••••••••••••••••••••••••• 

Flooding limits for countercurrent condensers using the 

46 

47 

correlation of Wallis (1969) ••••••••••••••••••••••••••••••••••••••• 50 

Comparison of condensed steam predictions with data for type AX 

packing in countercurrent flow ••••.••••.•••••..••••••••••••••.••..• 50 

Comparison of pressure loss for AX packing in countercurrent 

flow .•••••..•••.•.•.•...•••....••..•..........•...••....•...•.•...• 51 

Pressure loss comparison for 19060 packing in countercurrent 

flow ..•••....••••••.•.•.•••.•••.••.•..••.••... III •• •••••••••••••••••• 52 

Comparison of condensed steam for 3X packing in countercurrent 

flow ...•.••....••.•••..•••....•..•...........••....•....... 0 ••••••• 52 

Comparison of pressure loss for 3X packing in countercurrent 

flow ..•••....••.•.•••.•.•••.•••.....•.•.•...••..•.••........••••..• 53 

Comparison of condensed steam for 27060 packing in countercurrent 

flow...... ....... ....................... ....... .................... 54 

Comparison of pressure loss for 27060 packing in countercurrent 

flow ...••.•.••.•.••..•.•.•....•..••.••...•.•...•.••....•.•....••... 54 

Variations of temperatures within the condenser versus 

downstream distance in cocurrent flow •••••••••••••••••••••••••••••• 58 

5-2 Variations of pressure loss, interfacial steam flux, and inert 

content in steam within the condenser versus downstream distance 

in cocurrent flow ••••.••••.••••••••••...•••••.••••••••••••••.•••.•• S9 

5-3 Process path 1n co current condensation ••••••••••••••••••••••••••••• 60 

5-4 Influence of effective area fraction on cocurrent condenser 

perf ormance ••••.••.••.•••.•.....•.••.••••••••••••.•••.••• 0 • 0 ••••• 0 62 

5-5 Influence of packing size on cocurrent condenser performance ••••••• 63 

5-6 Influence of packing height-to-base ratio on cocurrent condenser 

perf ormance •••• 0 •••••• 0 ••••••••••••••••• 0 •••••••••••••••••• 0 • • • • • • • 64 

5-7 Influence of channel inclination on cocurrent condenser 

performance •.••...•.•..•.•.••.....••••.•••.•..••..•••.•••.....••... 65 
5-8 

5-9 

5-10 

5-11 

5-12 

5-13 

5-14 

TR-3108 

LIST OF FIGURES (Continued) 

Influence gas loading on cocurrent condenser performance ••••••••••• 

Influence of Jakob number varied via water flow rate on cocurrent 

condenser performance at G = 0.6 kg/m2 s ••••••••••••••••••••••••••• 

Influence of Jakob number varied via water flow rate on cocurrent 

condenser performance at G = 0.4 kg/m2 s ••••••••••••••••••••••••••• 

Co current condenser operating diagram •....•••.....•.•....•..••.• ~ •• 

Influence of Jakob number varied v~a inlet steam temperature on 

cocurrent condenser performance at G = 0.6 kg/m2 s ••••••••••••••••• 

Influence of Jakob number varied v~a inlet steam temperature on 

co current condenser performance at G = 0.4 kg/m2 s ••••••••••••••••• 

Variations of temperatures within the condenser versus 

downstream distance ~n countercurrent f1 ow ••••••••••••••••••••••••• 

66 

69 

70 

71 

73 

74 

75 

5-15 Variations of pressure loss, interfacial steam flux, and inert 

content in steam within condenser versus downstream distance in 

countercurrent flow •••••••••••••••••••••••••••••••••••••••••••••••• 76 

5-16 Steam and inert gas mixture process path in countercurrent flow.... 77 

5-17 Influence of effective area fraction on countercurrent condenser 

performance........................................................ 78 

5-18 Influence of packing size on countercurrent condenser performance.. 79 

5-19 Influence of packing height-to-base ratio on countercurrent 

condenser performance •••.••••••••••••••••••.•••••.••••••••••.•••••• 80 

5-20 Influence of channel inclination on countercurrent condenser 

perf ormance. • • . • . • . • • • . • . . . • . • . . . . . • • • . . • • . . . • • • • . . • • • . . . • • • . . • . • • • 81 

5-21 Influence of gas loading on countercurrent condenser performance ••• 82 

5-22 Influence of Jakob number varied via water flow on countercurrent 

condenser performance.............................................. 83 

A-I Heat- and mass-transfer laboratory test chamber: condenser, left; 

evaporator, right •••••••.•••••••••••••••••••••••••••••••••••••••••• 96 

A-2 Vacuum test chamber with end caps rolled back...................... 98 

A-3 Water piping and an end view of the test chamber ••••••••••••••••••• 98 

IX 
TR-3108 

LIST OF FIGURES (Concluded) 

A-4 Schematic of laboratory p1p1ng ••••••••••••••••••••••••••••••••••••• 99 

A-S Temperature measurement system ••••••••••••••••••••••••••••••••••••• 102 

A-6 Typical water temperature measurement RTD installation ••••••••••••• 105 

A-7 Summary curve of 20 step-linearized solutions for probe 

temperature calculations ••••.••••••••••••.••••••••••••••••••••••••• 106 

A-8 Wet-bulb steam temperature measurement probe ••••••••••••••••••••••• 109 

B-1 Comparison of measured and calculated steam outlet temperature 

for co current packing 19060 •••••••••••••••••••••••••••••••••••••••• lIS 

C-l Countercurrent condenser ••••••••••••.•.••.•••..••••••.•••••••••••.. 124 

C-2 Spiral screen, condenser configuration 1 ••••••••••••••••••••••••••• 126 

C-3 Baffle plate, disc donut, condenser configurations 2 through 4 ••••• 126 

C-4 Spiral rubber mat, condenser configuration S ••••••••••••••••••••••• 126 

C-S Munters packing, condenser configurations 6 and 7 •••••••••••••••••• 126 

C-6 Condenser configuration 8 with random packing •••••••••••••••••••••• 128 

C-7 Performance of countercurrent disc-donut baffle condensers ••••••••• 129 

C-8 Relative performance comparisons of countercurrent condenser 

configurations ••••••••••••••••••••••••••••••••••••••••••••••••••••• 130 

x 
TR-3108 

LIST OF TABLES 

2-1 Comparison of Correlation Data Base with Experimental Condenser 

Entrance Conditions ••••••••••••••••••••••••••.••••••••••••••••••••• 26 

2-2 Correlations for SERI Direct-Contact Condenser Model ••••••••••••••• 29 

3-1 SERI Direct-Contact Laboratory Capabilities •••••••••••••••••••••••• 33 

3-2 Summary of Uncertainties in Primary Measurements ••••••••••••••••••• 33 

3-3 Estimated Uncertainties in Derived Quantities for Packing 19060 •••• 34 

3-4 Geometry Comparisons of the Tested Packings •••••••••••••••••••••••• 36 

3-5 Tested Range for Cocurrent Condensers •••••••••••••••••••••••••••••• 38 

3-6 Tested Range for Countercurrent Condensers ••••••••••••••••••••••••• 38 

4-1 Cocurrent Condenser Comparison Summary ••••••••••••••••••••••••••••• 48 

4-2 Countercurrent Condenser Comparison Summary •••••••••••••••••••••••• 55 

5-1 Condenser Parameters ••••••••••••••••••••••••••••••••••••••••••.•••• 57 

6-1 Comparison of the Influence of Rate Deaeration on a Two-Stage 

Condenser •••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 88 

A-I SERI Low-Temperature Heat- and Mass-Transfer Laboratory 

Capabilities ••••••••••••••••••••••••••••••••••••••••••••••••••••••• 97 

A-2 Heat- and Mass-Transfer Laboratory Hardware Model Numbers and 

Specifications ••••••••••••••••••••••••••••••••••••••••••••••••••••• 97 

A-3 P1atinum-Resistance--Temperature-Detector Specifications ••••••••••• 102 

A-4 Typical Calibration Data for RTD ••••••••••••••••••••••••••••••••••• 103 

A-5 Summary of Uncertainties in Primary Measurements ••••••••••••••••••• 110 

B-1 Countercurrent Derived Parameter Uncertainty Estimates 

19060 Packing •••••••••••••••••••••••••••••••••••••••••••••••••••••• 117 

B-2 Primary Uncertainties ••••••••••••.•.••••••••••••••.••••••••••••••.• 118 

B-3 Uncertainties in Countercurrent Condenser Experimental Results ••••• 119 

B-4 Uncertainties in Cocurrent Condenser Experimental Results •••••••••• 120 

B-5 Cocurrent Derived Parameter Uncertainty Estimates 19060 Packing •••• 121 
TR-3l08 

LIST OF TABLES (Concluded) 

C-l Summary of Countercurrent Condenser Configurations ••••••••••••••••• 125 

D-l Co current Condenser Data for AX Packing •••••••••••••••••••••••••••• 132 

D-2 Cocurrent Condenser Data for 19060 Packing ••••••••••••••••••••••••• 134 

D-3 Cocurrent Condenser Data for 4X Packing •••••••••••••••••••••••••••• 136 

D-4 Cocurrent Condenser Data for Falling Jets •••••••••••••••••••••••••• 138 

D-5 Countercurrent Condenser Data for AX Packing ••••••••••••••••••••••• 140 

D-6 Countercurrent Condenser Data for 19060 Packing •••••••••••••••••••• 143 

D-7 Countercurrent Condenser Data for 3X Packing ••••••••••••••••••••••• 149 

D-8 Countercurrent Condenser Data for 27060 Packing •••••••••••••••••••• 152 

E-l Countercurrent Condenser Data for Configuration 1 with Spiral 

Metal Screen ••••.•......•......•••.••.••.•.•••......••.....••..•... 164 

E-2 Countercurrent Condenser Data for Configuration 2 with Three 

Pairs of Baffles ••••••••••••••••••••••••••••••••••••••••••••••••••• 167 

E-3 Countercurrent Condenser Data for Configuration 3 with Two 

Pairs of Baffles ••••••••••••••••••••••••••••••••••••••••••••••••••• 169 

E-4 Countercurrent Condenser Data for Configuration 4 with One Pair 

of Baffles ••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 171 

E-5 Countercurrent Condenser Data for Configuration 5 with Spiral 

Matted Screen ••.••...•..•...••.•..••••••..•....•.•....••......•..•• 172 

E-6 Countercurrent Condenser Data for Configuration 8 with Random 

Packing ...••.•..•.••.•..•..••....•.•.....••.•••......••••.•.•• 0 •••• 177 

F-l Cross Reference of Computer Program Variables •••••••••••••••••••••• 238 
A 

A 

Ackf 

Ackh 

af 

a p 

B 

C 

Fr 

f 

G 

g 

He 

h 

h 

hfg 

Ja 

J 

k 

L 

Le 

~ 

M 

condenser cross-sectional area (m2 ) 

lumped pressure loss coefficient (Eq. 2-34) 

Ackermann friction correction factor 

Ackermann heat-transfer correction factor 

effective area fraction 

available surface area per unit volume (l/m) 

packing base dimension (m) 

pressure loss coefficient ~n packing (Eq. 2-34) 

contact loss in area 

dimensionless steam flux 

specific heat (kJ/kg K) 

diffusivity of inert gas ~n water (m2/s) 

diameter (m) 

liquid Froude number (Eq. 2-33) 

friction factor 

TR-3l08 

gas loading of steam-inert mixture on planform condenser area 

(kg/m2 s) 

gravitational acceleration (m/s2) 

Henry's Law constant for dissolved inerts (Pa) 

heat-transfer coefficient [used with subscripts L or G] (kW/m2 K) 

height of packing cross section (m) 

latent heat of condensation (kJ/kg) 

Jakob number (Eq. 4-1) 

superficial velocity (m/s) 

mass-transfer coefficient (kg/m2 s) 

liquid loading based on planform condenser area (kg/m2 s) 

Lewis number (Eq. 2-14) 

packing stack length (m) 

molecular weight 

mass flow rate (kg/s) 

~Because of the large number of variables appearing ~n this report, some symbols are used to represent more than one variable. However, care was taken to 

use them in widely differing contexts to minimize possible misinterpretation 

and confusion. In addition, a separate nomenclature appears after Section 7.0 

for the symbols used in the appendices. 

x~~~ 
Nu 

n 

P 

P 

pp 

t.p 

Pr 

Q 

q 

q 

R 

Re 

S 

S' 

Sc 

Sh 

T 

u 

v 

w 

x 

y 

z 

Greek 

r 

e: 

NOMENCLATURE (Continued) 

Nusse1t number 

Manning roughness coefficient 

static pressure (Pa) 

pressure (Pa) 

partial pressure (Pa) 

pressure drop (Pa) 

Prandtl number 

condenser heat load (kW) 

TR-3108 

heat transferred per unit mass flow per unit length (K/m) 

(Eqs. 2-12, 2-13) 

gas dynamic pressure (Eq. 2-34) 

universal gas constant (kJ/kg K) 

Reynolds number 

slant height of packing cross section (m) 

distance over which liquid renewal occurs (m) 

Schmidt number 

Sherwood number 

temperature (OC, K) 

packing sheet thickness (m) 

effective gas velocity (m/s) 

effective liquid film velocity (m/s) 

gas velocity (m/s) 

condenser vent fraction 

interfacial mass transfer flux (kg/m2 s) 

inert gas mass fraction 

inert gas mole fraction 

coordinate along the condenser 

modified flow surface inclination from horizontal (deg) 

liquid film flow per unit surface area in unit length of packing 

(kg/m s) 

changes in property 

void fraction of the packing 

condenser water effectiveness 

liquid film thickness (m) 

XlV 
8 

J..l 

p 

NOMENCLATURE (Concluded) 

packing channel inclination from horizontal (deg) 

dynamic viscosity (kg/m s) 

density (kg/m3 ) 

shear stress (Pa) 

Subscripts and Superscripts 

b 

c 

eq 

ex,x 

f 

G,g 

1. 

int 

L 

max 

o,out 

S 

s 

sat 

w 

wet 

* 

bulk 

condensed 

equilibrium, equivalent 

exhaust 

liquid 

gas or steam and inert gas mixture 

inert 

interface 

liquid 

maximum 

outlet, outside column 

based on slant height S 

steam 

saturation 

water 

wetted conditions 

equilibrium 

xv 

TR-3108 
TR-3108 

1.0 INTRODUCTION 

This report summarizes extensive work carried out at the Solar Energy Research 

Institute (SERI) in developing direct-contact condensers for use in the 

Claude-cycle ocean thermal energy conversion systems. The primary focus of 

the effort was to develop a numerical model of the condenser and to determine 

how well this model predicts the behavior observed in the parallel experimental program using structured packings as the gas-liquid contacting device. 

We also provide detailed descriptions on the study's background, previous work 

in this field, the numerical model, the experimental facility and instrumentation, and the uncertainties in primary and derived parameters. Full sets of 

measurements made at SERI and their corresponding predictions yielded by the 

model accompany this report. 

Figure 1-1 shows a schematic of an open-cycle (Claude-cycle) ocean thermal 

energy conversion (OC-OTEC) power system. Warm seawater (about 2S0C) enters 

the evaporator section of a vacuum chamber. Pressure in the evaporator is 

maintained sufficiently low to produce steam. This is done by operating below 

the vapor pressure at the incoming surface water temperature. Water droplets 

carried by the wet steam are removed in a mist eliminator. The steam expands 

through a turbine between the evaporator and the condenser section of the 

chamber. Cold seawater (about SOC), pumped from a depth of about 1000 m, is 

used as the heat sink in the condenser. The turbine is mechanically linked to 

a generator that yields net power after providing the power required to pump 

the warm and cold water streams and to remove noncondensable gases released in 

the vacuum chamber. 

Direct-contact 

evaporator 

Di rect-contact 

condenser subsystem 

Surface 

To inert gas removal 

Desalinated water 

Figure 1-1. Schematic of an open-cycle ocean thermal energy 

conversion system 

1 
TR-3l08 

Dissolved gases in warm and cold water may corne out of solution in the evaporator and condenser. Unless removed, these gases will accumulate in the condenser section of the vessel, blanketing the condensing surfaces and decreasing the condensation efficiency. Additional pumping power, therefore, must be 

expended to remove these gases and to maintain suitable operating pressure in 

the condenser. The condenser can be direct contact, surface, or a combination 

of both. A surface condenser can yield desalinated water as a by-product. 

An alternative method for desalinated water production from the open cycle 

uses a direct-contact desalinated water condenser in a pump-around loop 

together with a desalinated water/seawater heat exchanger. A schematic of the 

use of a direct-contact condenser for desalinated water production is shown in 

Figure 1-2. In this method, the circulating, warmed desalinated water 

discharge from the condenser is cooled in a heat exchanger using the cold 

seawater. The attractiveness for this approach arises from the ability of the 

direct-contact condenser to handle low-density stearn efficiently wi thout a 

large pressure loss within a compact volume. However, it requires using a 

water/water heat exchanger and a desalinated water circulating pump. 

Preliminary estimates show that this type of a system may be less expensive 

compared with a large volume surface condenser. However, the relative costeffectiveness of the surface condenser or a direct-contact condenser system 

for desalinated water production from an OTEC plant requires further study. 

This report focuses on the boxed area in Figure 1-1, enclosing the directcontact condenser subsystem. This condenser system, because of its barometric 

placement and system integration constraints, consists of two stages to keep 

Desalinated 

water "'-

circulating "-

loop 

Spent 

steam 

from 

turbine 

Direct 

contact 

condenser 

Cold 

seawater 

SoC 

Water/water 

heat 

exchanger 

Cold 

seawater 

return 

Desalinated 

I--.... --water 

production 

Noncondensable 

-----I ....... gas removal system 

Figure 1-2. Diagram of desalinated water production scheme using directcontact condenser 

2 
TR-3108 

plant volume and water pumping power low. Figure 1-3 illustrates the steam 

flow through the stages. In the first stage, the steam and noncondensable gas 

mixture flows downward in a co current mode along with the seawater. About 70% 

to 80% of the incoming steam is condensed here. The remaining steam then 

flows into a countercurrent condenser against the downward cooling water flow. 

This stage condenses most of the remaining steam and thereby concentrates the 

noncondensable gases to the maximum extent possible. The outgoing uncondensed 

steam and noncondensable gases are then removed by an exhaust vacuum pumping 

system. 

Typically, in an open-cycle plant, the steam flow to be condensed ranges from 

10 to 20 kg/s per MWe gross output at temperatures from 9° to 13°C with the 

higher flow rate corresponding to the higher temperature (Parsons, Bharathan, 

and Althof 1987). Because of the progressive condensation of steam, the mass 

fraction of noncondensable gases in the steam can vary· from 0-.5% up to 40% 

within the condenser. 

To exhaust 

compressors 

Drain 

water level 

.. 

Enriched I 

inert gases I 

I 

I 

I 

Structured 

Countercurrent region Cocurrent region 

. 

t 

Water inlet 

Figure 1-3. Schematic of barometric direct-contact condenser subsystem 

indicating steam and noncondensable gas mixture flow through 

cocurrent and countercurrent sections using structured packings 

3 
TR-3108 

Because the temperature difference between the warm and cold water used in 

OTEC is small, the condenser must handle large quantities of cold seawater on 

the order of 2-4 m3/s per MWe of gross power (Parsons, Bharathan, and Althof 

1987). We estimate the overall water pumping head losses to be about 5 m in 

the cold-water hydraulic loop, which consists of the intake pipe (extending to 

a depth of about 1 km below sea level), the distribution manifold, the discharge pipe, and perhaps a predeaerating system. Nominally, a free-fall of 

2 m is available for the seawater in the condenser. Each meter of additional 

head loss in the condenser can reduce the available power up to 6%. 

In addition to removing spent steam, the condenser must efficiently remove 

noncondensable gases. These gases accumulate at the condenser because they 

desorb from the resource waters and because atmospheric air leaks into the 

vacuum system. Thus, the condenser performance is closely coupled to that of 

the noncondensable-gas removal (NCGR) system. The gas mixture exhausted 

through the NCGR system consumes a parasitic power of typically 10% to 15% of 

the gross power (Parsons, Bharathan, and Althof 1987). 

The noncondensable gas removal system and the condenser performances are 

closely interrelated. The capacity of the NCGR system will dictate the back 

pressure and, thus, the condenser operating pressure. On the other hand, the 

effectiveness of the condenser in reducing the partial pressure of steam in 

the exhaust gas mixture and its gas-side pressure loss will affect the capacity of the removal system. Although it is difficult to separate the condenser 

and the noncondensable gas removal system requirements, from a system point of 

view, the key condenser design parameters are 

• Low liquid-side pressure loss 

• Low vapor-side pressure loss 

• High condenser effectiveness 

• Minimal degradation caused by the presence of noncondensable gases 

• Simple liquid inlet and exit manifolds 

• Simple gas exhaust manifold designs to concentrate the noncondensable gases 

• Small volume 

• Immunity to plant motion for floating platforms or to tides for shore-based 

plants 

• Low cost of fabrication 

• Low susceptibility to corrosion and biofouling 

• Uniform liquid and gas loadings. 

1.1 Objective and Goal 

The objective of this study is to develop an engineering data base and to validate analytical methods to design and evaluate the performance of advanced, 

high-performance heat exchangers that are reliable and cost-effective for use 

in an OC-OTEC process. 

The specific goal is to establish quantitatively the extent to which the 

developed numerical condenser model captures the observed behavior in the 

4 
S=~II~ -: 

TR-3108 

experiments over an extensive set of data that covers a large portion of the 

expected condenser operating range for an OC-OTEC system. 

1.2 Approach 

Our approach in the engineering development of direct-contact condensers 

included the following steps: 

1. Investigate experimentally a variety of likely condenser configurations 

such as commonly used gas-liquid contacting devices to establish their 

relative performance. 

2. Evaluate and choose a device according to its performance as a condenser, 

its ease of integration into an OTEC system, and its commercial availability in terms of its geometry, material choices for seawater use, and 

cost. 

3. Develop a numerical model for the chosen condenser configurations that 

captures the physical phenomena occurring within the condenser, with the 

goal of predicting key condenser performance parameters. 

4. Establish the validity of the model by comparing the predictions with 

experimental observations for a variety of contactor geometries for the 

chosen device. 

5. Generate parametric results to provide guidance in selecting suitable 

geometries as well as flow conditions for potential OTEC design options. 

Experimental work carried out at SERI was aimed at addressing research issues 

on heat exchangers for the open cycle. For investigating evaporation and condensation at low pressures, an experimental facility using fresh water was 

commissioned in 1979 (see Section 3.0 and Appendix A). This facility allows 

us to quickly and efficiently investigate various heat exchanger configurations under controlled test conditions and to avoid unwanted external influences related to field-site operation. This well instrumented facility yields 

minimal uncertainties in the derived heat-exchanger performance parameters as 

well (see Appendix B). The fresh water results from this facility provide a 

firm technical basis for selecting prototype test articles for seawater testing. By properly accounting for seawater's varied physical properties, we 

anticipate being able to transfer fresh water results to seawater. This 

assumption will be tested using seawater at the experimental facility described in the following paragraph. 

We investigated a variety of evaporator configurations in the early 1980s 

using this facility (Bharathan and Penney 1984). Screening the configuration 

with fresh water in this facility resulted in the selection of the spout evaporator as the preferred geometry for seawater tests. Ongoing experiments with 

seawater at the u.s. Department of Energy's (DOE) Seacoast Test Facility (STF) 

at the Natural Energy Laboratory of Hawaii substantially confirm the earlier 

findings obtained using fresh water. 

We tested various direct-contact condenser configurations at this facility, 

including contactors using random and structured packings. Their performance 

was evaluated relative to their efficiency in cooling water usage and in 

handling the noncondensable gases present in steam. Typical test results for 

a countercurrent condenser are shown in Figure 1-4. The plot shows the water 

5 
0.8 Random packing - w 

r.!l 

(f) 

CD 

c 0.6 

CD 

.::: 

(3 

2 

Qi 

'- 0.4 CD 

co 

S 

0.2 

o.o~ ______ ~ ______ ~ ______ ~ ______ ~ ____ ~ 

0.0 0.2 0.4 0.6 0.8 1.0 

Vent fraction, V 

Figure 1-4. Relative performance comparison of a few tested 

countercurrent condenser configurations 

TR-3108 

effectiveness g against a vent fraction V. The effectiveness represents the 

cooling water temperature rise as a fraction of the available temperaturedriving potential. The vent fraction represents the ratio of volumetric 

exhaust flow for an ideal condenser to that of an actual condenser. From 

these definitions, we can see that for a good condenser configuration we 

should aim to achieve high values for both the effectiveness and the vent 

fraction. Typical test results for three condenser configurations, namely, 

baffles, randomly packed media, and structured packings, are shown in Figure 1-4. Among these and all other tested configurations, we found that the 

structured packings yielded the highest effectiveness and vent fraction at 

similar test conditions. These results indicate that for a direct-contact 

condenser, the structured packings yield the best performance among all tested 

configurations. A more detailed description of these test results and the 

evaluation of relative ranking of tested configurations are provided 1n 

Appendix C. 

Based on these early experimental results, we narrowed our choice of gasliquid contact media to structured packings. With the structured packing as 

the preferred configuration for the direct-contact condensers, we expanded the 

scope of our study to further experimentation, modeling, and validation 

efforts confined to this type of packing as summarized in this report. 

The results from the fresh water facility provide the basis for selecting test 

articles and operating conditions for the planned seawater tests at the STF. 

We were encouraged in using such a basis because our ongoing seawater 

experiments successfully substantiate the fresh water investigations on 

evaporation conducted earlier at this facility. The utility of the SERI fresh 

water facil i ty in efficiently and cost-effectively screening configurations 

6 
TR-3108 

and in conducting detailed investigations of low-temperature heat and mass 

transfer phenomena cannot be overemphasized. 

1.3 Scope and Limitation 

Despite an ambitious scope, practical considerations limited our experimental 

investigations to five basic configurations: falling jets, spirally screened 

passages, disc-donut baffles, and random and structured packings. Results of 

our studies with jets were reported earlier by Bharathan et ale (1982). All 

other results are included in this report. Tabular data for structured 

packing are provided in Appendix D; data for other configurations are in 

Appendix E. Because of earlier experiments, we quickly narrowed our choice of 

a contacting device to structured packings. The ready commercial availability 

of these packings, commonly used in cooling towers and distillation and 

absorption applications in chemical engineering, also provided a substantial 

reason for choosing them. These packings are available in a wide variety of 

geometries and materials, so specific needs for an OTEC condenser can be 

readily met. 

Based on the choice of structured packing as the appropriate contacting 

device, we chose to model the condensation process occurring within these for 

both co current and countercurrent configurations. Presently, we model co current and countercurrent condenser modules as separate ent~t~es; in other 

words, they are not interconnected. The computer algorithms to capture the 

physical process are written in the Turbo-Pascal~* language (version 3.0). 

Suitable process transfer correlations for performance predictions for these 

geometries were not available in the open literature until the recent works of 

Bravo, Rocha, and Fair (1985 and 1986) at the University of Texas in Austin. 

We used transfer correlations provided by Bravo. Based on available experimental data, we made suitable modifications to the liquid-side transfer correlations for turbulent liquid films on inclined surfaces. An effective surface 

area fraction was introduced that represents the ratio of the packing's active 

surface to the total available geometric area. Although the surface area and 

heat-transfer coefficient are treated separately for the sake of modeling, 

such a separation is difficult to make based on the available experimental 

data; therefore, these quantities should be viewed as the product of the 

available area and the appropriate transfer coefficient rather than as 

individual quantities. 

In this report, we supply extensive sets of comparisons of the analytical 

results with available fresh water experimental data. Currently, only experimental data on inlet and outlet condi tions for condensers of a specified 

geometry and length are available. Thus, these comparisons indicate the overall correctness of the model. 

Uncertainty overlaps between the predictions and the data indicate that the 

predictions agree with the data within generally acceptable engineering 

*Turbo-Pascal~ is the trade name of a 

national, Inc., Scotts Valley, Calif. 

cient error-tracking capability, ease 

speeds on personal computers. 

programming language by Borland InterWe chose this language for its effiof use, and compilation and execution 

7 
TR-3l08 

uncertainties for performance predictions of heat exchangers. Thus, the validated model provides firm technical basis for design, optimization, and performance predictions of direct-contact condensers using structured packings. 

We also conducted detailed parametric studies of the validated model (Section 5.0). These parameters were generally categorized as geometric and flow 

parameters. For some of these, we identified clear-cut, optimum choices based 

on predicted results. To select others, evaluations based on system optimization are required to yield the "best" cost or performance for an overall 

plant. 

1.4 Background 

In direct-contact condensation, a subcooled liquid stream enters a chamber 

holding the vapor to be condensed. The resistances to heat transfer consist 

in a series of a gas phase, an interfacial, and a liquid phase. In the 

absence of noncondensable impuri ty gases in the vapor, the gas-phase and 

interfacial resistances are small compared with the liquid-phase resistance. 

The heat-transfer mechanism can be described in two parts: as the molecular 

crossover mass transfer from the vapor to the interface and as the accompanying transfer of heat to the bulk liquid from the interface at an intermediate 

temperature. The overall transfer rate is governed by the molecular transport 

within the liquid and the differential rate of molecular crossing at the 

interface. For water at DTEC temperatures, the resistance to heat transfer at 

the interface is extremely small compared with the resistance on the liquid 

side (Maa 1967). For simple liquid geometry, such as films or uniform droplets, we can readily predict the heat-transfer resistance. Thus, the rate of 

condensation for simple geometries can be evaluated when the resistance 

resides primarily on the liquid side. 

Seawater contains dissolved gases of which mostly nitrogen and oxygen will be 

released in the vacuum chamber of an DC-DTEC plant. These gases affect plant 

performance by raising the condenser pressure, degrading the performance of 

the condenser, and requiring compression power for their removal. 

Analyzing direct-contact condensation is complicated because these noncondensable gases are present in the condensing vapor. Since the coolant acts as a 

sink, the gases are drawn to the exposed liquid interface by the condensing 

steam. Accumulating gases adjacent to the interface blanket the condensing 

surfaces. Therefore, the vapor must diffuse through the gaseous barrier 

before condensing, causing the gas-side resistance to increase significantly. 

To maintain satisfactory condensation efficiency, the accumulating gases must 

be continuously removed and exhausted. 

For combined heat and mass transfer, Colburn and Hougen (1934) proposed a 

method to account for liquid-side heat-transfer resistance and gas-side massand heat-transfer resistances. Their approach treats the vapor flow from a 

mixture of vapor and noncondensable gas as diffusion through a stagnant film. 

They adopted a trial and error method to determine an intermediate interface 

temperature. Ackermann (1937) later derived multiplicative factors for evaluating transfer rates to account for high vapor fluxes toward the interface. 

Bras (1953) showed that the vapor does not remain at saturation as it flows 

through the condenser. Depending on the relative magnitude of vapor-side 

8 
TR-3108 

heat- and mass-transfer rates, the vapor may become subcooled or superheated. 

At relatively low diffusional rates, subcooling may cause fog to form in the 

flowing vapor stream. 

A vast amount of literature exists on condensation related to surface condensers. Subjects range from a fundamental investigation of accommodation 

coefficients (see, for example, Mills and Seban [1967]) to two-dimensional 

analytical modeling of vapor flow through a complex array of tube bundles (see 

Johnson, Vanderp1aats, and Marlo [1980]). It is beyond the scope of this work 

to provide a detailed summary of the surface-condenser literature. A succinct 

summary of condensation heat-transfer may be found in Metre (1973), Webb and 

Wanniarachchi (1980), and Butterworth and Hewitt (1978). For DC-DTEC, Panchal 

and Bell (1984) provide a theoretical analysis of surface condensers. 

Direct-contact condensation differs from surface condensation 1n that an 

impermeable surface separating the coolant and the condensate is absent. 

Modeling the direct-contact condenser is similar to modeling a surface conderiser except for the difficulty in defining an appropriate geometry and 

available surface area for the vapor-liquid interface. Turbulence level, 

back-mixing and recirculation, and instabilities at the interface result in 

large uncertainties in estimated transfer coefficients and available interfacial area for condensation. 

Literature in the area of direct-contact condensation is scant. No comprehensi ve treatments are available for direct-contact applications for designing 

and analyzing industrial and power systems, such as those available for surface condensers. Sideman and Moalem-Mason (1982) provide a brief review of 

the majority of earlier works on this subject. Since the vapor-liquid interface geometry plays a major role in direct-contact condensation, they categorize the earlier works according to the available interface, such as freeliquid interface (including jets, films, and drops), bubble columns, and other 

contacting devices (such as packed beds and baffle trays). 

Well-defined interfaces are amenable to analytical modeling. When the liquidside heat-transfer resistance 1S dominant relative to the gas-side resistances, analytical models for cylindrical jets (Kutateladze 1959), planar jets 

(Hasson, Luss, and Peck 1964), fan sprays (Hasson, Luss, and Peck 1964), droplets (Kulic, Rhodes, and Sullivan 1975), and falling films (Dukler 1960) are 

available. For more complicated geometries, such as in spray nozzles or 

packed columns where the interfacial area is complicated, little modeling 

effort is reported. However, many industrial vapor-liquid contacting devices 

use the more complex geometries because of their inherently higher contacting 

efficiency. 

Four general classifications exist for direct-contact gas (or vapor) to liquid 

heat-transfer processes: simple gas cooling, gas cooling with vaporization, 

gas cooling with partial condensation, and gas cooling with total condensation. These processes are complex, and each of them is described by a separate set of relations. Direct-contact heat exchange has traditionally been 

accomplished in one of the following devices: baffle tray columns, spray 

chambers, packed columns, cross-flow tray columns, or pipeline contactors. 

Design methods for each of them were summarized by Fair (1961 and 1972). The 

most common techniques used in industrial applications are the liquid spray 

column and the baffle-plate column. Fa:lr compared these devices and showed 

9 
TR-3l08 

that the typical performance given 1n number of transfer units (NTU) is only 

about 1, yielding 60%-70% condenser effectiveness. This value is so low 

because of back-mixing, and in baffle columns there is also a large gas-side 

pressure drop. This is a particular disadvantage for OTEC applications where 

minimizing parasitic power consumption is of prime importance. 

In addition to liquid-spray and baffle-plate columns, packed columns have been 

used in applications that require a large rate of heat and mass transfer per 

unit volume. Until recently, the packings or inserts commonly used in the 

columns were randomly distributed and thus created a complex flow pattern with 

a relatively large pressure loss. In the past decade or so, however, new 

types of packings have been introduced in the United States. They, unlike the 

classical, randomly placed packing elements, are fitted in an ordered and 

structured manner in the column to carefully match its size and operation. 

These structured packings show excellent performance characteristics. In particular, they yield a relatively low ratio of pressure drop to heat- or masstransfer coefficient per unit volume (Bravo, Rocha, and Fair 1985 and 1986). 

Although the cost per unit volume of structured packings is higher than that 

of classical packings such as Berl saddles and Pall rings, their favorable 

efficiency and pressure drop characteristics make these packings preferable 

for many applications, especially when operating in a vacuum such as an OTEC 

condenser. These new packings also provide a means of continually redistributing the liquid flow, while supplying a relatively straightforward flow path 

for the vapor, which significantly reduces the pressure drop. These packings, 

made of plastic sheets, have been used for some time in cooling towers; but 

recent improvements in manufacturing have made these packings available in the 

form of gauze or wire-mesh sheets. These surfaces allow vapor-to-liquid contact on both sides and also provide for uniform liquid distribution due to 

capillary action, even at low liquid loadings. Structured gauze packings 

increase the residence time of the liquid, and available data show that the 

entire area of the packing is effective in mass transfer. These highperformance packings were developed in Europe, and, unfortunately, performance 

data are largely proprietary, although some design equations for gauzestructured packings were recently published by Bravo, Rocha, and Fair (1985) 

over a limited range of operating parameters. 

SERI began a research program in 1983 to better understand the mode of operation of various packings for direct-contact heat and mass transfer and to provide experimental data for developing a predictive model. SERI experiments 

show that structured packing offers an attractive geometry for condenser 

applications. 

Direct-contact condensers have potential for use in many process applications 

as well as in power plants. One of the main reasons for the limited use of 

direct-contact condensers is that engineers do not have reliable design and 

performance prediction methods. Condensers are difficult to analyze for the 

following reasons: 

• Vapor loading and heat and mass flux decrease continuously as vapor condenses. The vapor's velocity in a direct-contact device varies appreciably 

with the distance traveled because of continuous condensation; hence, the 

average values of heat- or mass-transfer coefficients used for design are 

usually not accurate. 

10 
TR-3l08 

• The latent heat of condensation is high, caus~ng a great ratio of liquid-tovapor mass flux (not typical in mass transfer applications); and little 

experimental data are available for that range of liquid loadings. 

• For use with seawater, noncondensable gases are present, and their effects 

on the gas mass-transfer rates are difficult to predict quantitatively. 

• Finally, in many practical situations, the flow changes from turbulent to 

laminar, and such a transition is not well understood in general and is difficult to quantify under condensation conditions. 

For these reasons, the widely used NTU design methodology will generally not 

suffice (Kreith and Bohn 1986; Sherwood, Pigford, and Wilke 1975) because the 

,transfer coefficients are not uniform as this approach assumes. Hence, it is 

necessary to integrate the rate of transfer numerically along the path of the 

vapor. 

The first attempts to model a direct-contact condenser of falling-film geometry for OC-OTEC applications are reported by Wassel et al. (1982). Their 

model treated the condensation process rigorously and included pressure and 

temperature recovery terms resulting from the condensation reducing the velocity of the vapor-gas mixture. They investigated the effect of spacing plates 

20 to 60 mm apart in a cocurrent condenser. They also varied flow rates and 

temperatures over a limited range to establish the trends of condenser performance variations. Wassel illustrated that 

• For steam-water condensation when air is present at low pressures, condensation tends to superheat the incoming steam. 

• Decreases ~n steam velocity provide sizable temperature and pressure 

recover~es. 

• Considerable differences exist among available 

Choosing an appropriate correlation necessitates 

mental program. 

transfer correlations. 

an accompanying experiIn an article presenting design methods for gas-to-liquid direct-contact heat 

transfer, Fair (1961) noted that design information was based on proprietary 

art instead of solid engineering know-how. This situation was reconfirmed in 

the National Science Foundation (NSF)-sponsored workshop "Direct-Contact Heat 

Transfer," held at SERI (Kreith and Boehm 1988). Consequently, these directcontact heat- and mass-transfer devices have not been widely used for heat 

exchange despite the fact that they are simple, potentially economical, and 

able to handle fluids that would otherwise cause excessive fouling, corrosion, 

or mechanical stresses in conventional equipment. 

1.5 Report Organization 

In this report, we introduce the problem, describe the numerical model, and 

summarize the experimental details. We then provide validation attempts and 

results of parametric studies. The first five appendices provide more 

detailed descriptions of the experimental facility and instrumentation, performance parameters, uncertainties in the reported experimental data, and a 

first-cut evaluation of various tested contacting devices and their tabulated 

data. The last three appendices list the computer program codes, discuss the 

11 
TR-3108 

assumptions made ln the equilibrium calculations used for assessing performance, and describe how we evaluated the physical properties of water and 

steam. 

12 
TR-3108 

2.0 MODEL DESCRIPTION 

This section describes the 

gas mixture as it flows 

detailed numerical codes 

iteration schemes for the 

basic modeling equations for the coolant and vaporthrough the condenser. Appendix F provides the 

for integrating the process equations and other 

cocurrent and countercurrent condensers. 

2.1 Cocurrent Condenser 

For cocurrent condensation, we developed process equations 

dimensional, steady-state model. These equations follow the 

Butterworth and Hewitt (1977), as Wassel et al. (1982) originally 

OTEC condensers, and assume the following: 

for a oneapproach of 

proposed for 

• The two-phase flow is in the separated flow regime (when gas and liquid are 

separated by a well-defined continuous interface) with the steam and water 

flowing downward by gravity. 

• The coolant and condensate are well mixed so their temperature and dissolved 

inert gas content are identical. 

• The interfacial steam flux is governed by combined heat- and mass-transfer 

processes (in the liquid and vapor, respectively), as modeled by the 

Colburn-Hougen (1934) approach. 

• Suitable corrections on all vapor-side transfer rates and 

ture the effects of high interfacial fluxes are modeled 

priate Ackermann (1937) factors. Similar corrections 

transfer rates are negligible. 

friction to capusing the approfor liquid-side 

• Diffusion of steam through the inert gas and steam mixture is modeled using 

the stagnant film theory (Sherwood, Pigford, and Wilke 1975). 

• Steam and inert gases are well mixed with an identical temperature, nominally denoted by Ts (i.e., TG = Ti = Ts ). 

• The flux of inert gas des orbed from the coolant water stream is small 

compared with the condensing steam flux throughout the condenser, i.e., 

(w. « w ). 1 S 

• Desorption of inert gas from the coolant is controlled by diffusion and does 

not disturb the free interface between the steam and the coolant. 

• For structured packings, the effective transfer area for heat and mass is 

expressed as afa , where af is the effective area fraction, assumed to lie 

in a range 0 < a~ ~ 1, and a

p 

is the total available surface area per unit 

volume. 

2.1.1 Interface Temperature 

Using the stagnant-film theory, the condensing steam flux w

s

' as indicated ln 

Figure 2-1, can be expressed ast 

tThe term 

liquid. 

(2-1) 

is considered positive when steam flows from the vapor to the 

13 
where 

Coolant 

water 

~ Condensing 

steam 

flux Ws 

Interface 

Noncondensable gas 

absorption/desorption 

Figure 2-1. Representation of temperature distribution in coolant, gas, and 

interface during condensation: 

condensing steam flux and nonconsensable mass flux 

kG = the vapor-side mass-transfer coefficient (kg/m2 s) 

= the steam mole fractions 

interface, respectively. 

~n the bulk mixture 

TR-3108 

and at the 

The heat flux to the coolant consists of two parts: sensible heat transferred 

from the gas mixture and latent heat caused by condensation. Using the 

Colburn-Hougen equation (1934), the interfacial steam flux and heat flux can 

be related to the interface temperature Tint as 

where 

= the liquid-side and gas-side 

respectively, (kW/m2 K) 

heat 

(2-2) 

transfer coefficients, 

= the latent heat of .condensation evaluated at the interface 

temperature (kJ/kg) 

TL,Tint,TG = the liquid, interface, and gas temperatures, respectively. 

The term Ackh represents the Ackermann correction factor for heat transfer to 

account for high interfacial flux defined as 

where 

Co 

Ackh = 1 - exp (-Co) , 

Co = wsCps/hG 

and Cp = the specific heat capacity of the steam (kJ/kg K). 

s 

14 

(2-3) 
TR-3108 

Equations 2-1, 2-2, and 2-3 allow us to iteratively evaluate the interface 

temperature Tint' provided we know the transfer coefficients hL' hG' and kG. 

2.1.2 Transfer Fluxes 

Inert gas desorption from the coolant is primarily controlled by diffusion 

resistance in the liquid film. Inert gas flux from the coolant w· IS 

expressed as+ 1 

(2-4) 

where 

kL = the liquid-side mass transfer coefficient (kg/m2 s) 

x,x* = the inert gas mass fraction in the bulk coolant and the equilibrium 

value at the partial pressure of inert gas In the bulk mixture, 

respectively. 

The equilibrium value for the dissolved inert gas In the coolant IS assumed to 

be governed by Henry's Law, such that 

y* = 

where 

PPi 

He 

y* = the inert gas mole fraction in equilibrium 

PPi = the partial pressure of inert gas In the bulk mixture (Pa) 

(2-5) 

He = Henry's Law constant, which may be a function of coolant temperature 

(Pa). 

2.1.3 Process Equations 

Process equations are derived from mass, momentum, and energy balances across 

a slice of the cocurrent condenser as shown in Figure 2-2. 

2.1.3.1 Mass Balances 

The following mass balances were used to develop process equations: 

Steam flow: 

(2-6) 

+Inert gas flux absorbed by the coolant IS considered posive here. 

15 
TR-3108 

{m,T,y,p} {m,T,x} {m,T,x} 

Steam Steam 

and Conden Coolant 

inert gases Inert sate water 

f 

dz 

~ 

~ Transfer 

processes ! ~ Heat 

mass and = fn {L,G,y, p, T,geometry} 

Figure 2-2. A slice of a cocurrent direct-contact condenser indicating the 

modeling variables for one-dimensional flow 

Inert gas 1n steam and inert gas mixture: t 

Coolant flow (condensate 1S added): 

Inert gas dissolved 1n the coolant: 

d • 

dz (mi ,L) = 

2.1.3.2 Momentum and Energy Balances 

-w'afa A 1 P 

Similarly, the following momentum and energy balances were used: 

Condenser heat load: 

dQ - h (T' T )afa A dz - L 1nt - L P 

Water temperature: 

Temperature and pressure of the steam and inert gas mixture are 

as follows: 

2 2 

1 + 

u u -L u --- (pu) , CpGT pCpG dz CpG pCpG 

= 

2 2 

pu 1 - E- dp -u(pu) I - T. a T RT dz 1nt p 

(2-7) 

(2-8) 

(2-9) 

(2-10) 

2-11) 

interrelated 

(2-12 & 

2-13) 

tDouble subscripts in all of the following equations, i, sand i ,L, refer to 

inert gas in steam and inert gas in liquid, respectively. 

16 
where 

(pu)' = rate of change of gas loading, ~~ 

q/GpG = interfacial heat transfer per unit mass 

flow rate, per unit length, divided by GpG (K/m) 

hG(Ackh)(TG - Tint) exp (-Go) afap 

= G GpG 

and 

'intap = the frictional term expressed as 

= iPG(UGeff ± uLeff )2 

where 

f[(Ackf)afap + (1 - af)ap ] (N/m3), 

u = UGeff = effective gas velocity (m/s), 

UGeff ± ULeff = gas relative velocity (m/s) 

f = friction factor 

Ackf = Ackermann correction factor for high mass 

as 

Ackf = (2ws /Gf) / [1 - exp (-2ws /Gf)] 

G = superficial gas loading (kg/s m2 ) • 

TR-3108 

fluxes, expressed 

Note that for the frictional term, the ineffective fraction of the available 

surface· area (1 - af) also contributes to pressure loss. The Ackermann correction is applied only where mass transfer occurs (i.e., over the fractional 

area afa , assuming all contribution to pressure loss occurs via interfacial 

shear). p Other contributions to friction that may arise from form drag are 

assumed to be negligible. 

Equations 2-6 through 2-13 can be integrated along the length of the condenser 

to arrive at variations of steam, inert, and coolant properties under steadystate conditions. Note that these equations allow us to evaluate the steam 

and inert gas mixture partial pressures and temperature independently. Steam 

is normally expected to enter the cocurrent condenser at saturated conditions. However, depending on the relative magnitudes of the vapor-side heatand mass-transfer rates, the vapor may become supersaturated (forming fog) or 

superheated. For typical OC-OTEG operating conditions, the Lewis number 

Pr Le =-Sc ' (2-14) 

representing the ratio of mass to heat-transfer rates, generally ranges around 

2. For Le > 1, the steam and inert gas mixture superheats as it goes through 

the condenser because of a dominating mass-transfer rate (Bras 1953; Sherwood, 

Pigford, and Wilke 1975). 

17 
TR-3l08 

2.1.4 Equilibrium Ca1cu1ations+ 

To evaluate a maximum possible performance of a cocurrent condenser, we 

calculated an equilibrium outlet condition assuming the following: 

• Steam and water exiting from the condenser are in equilibrium. 

• Dissolved inert gas level in the exiting coolant is again in equilibrium at 

the partial pressure of inert gases 1.n the exiting steam and inert gas 

mixture. 

• Vapor pressure loss through the condenser 1.S nonexistent. 

These assumptions allow us to evaluate the equilibrium exit conditions iterati vely and provide a measure to compare performance in an actual condenser 

wi th the maximum condenser performance achieved in an ideal condenser (see 

Appendix G). 

2.2 Countercurrent Condenser 

A slice of a countercurrent condenser is shown in Figure 2-3. All assumptions 

used for the cocurrent condenser also apply to the countercurrent condenser. 

We evaluated the steam-water interface temperature and steam and inert fluxes 

using the Colburn-Hougen approach described earlier. 

2.2.1 Differences in Countercurrent Operation 

Initial conditions in a countercurrent condenser are usually specified as flow 

properties for liquid at the top and for gas at the bottom. The integration 

scheme, however, requires that liquid and vapor properties be specified at one 

end of the condenser so the calculation can proceed through the full length of 

the unit from beginning to end. In this study, the integration proceeded from 

the bottom, requiring an initial guess of the coolant temperature, flow rate, 

and dissolved inert gas content exiting the condenser at the bottom. Calculations presented here reflect this reversal. These estimates are updated 

iteratively to match the calculated coolant inlet conditions at the top with 

the specified values (within an acceptable tolerance). Our experience indicates four to five iterations are necessary for coolant inlet temperatures to 

agree within ±O.OloC. 

2.2.2 Process Equations 

The equations for countercurrent flow are essentially similar to the cocurrent 

flow except that the liquid flows in the negative z direction. Integration is 

carried out from the bottom of the condenser. 

2.2.2.1 Mass Balances 

The following mass balances were used to develop process equations for 

countercurrent flow. 

+Note that these equilibrium calculations are not "rate-limited," and thus they 

project the outlet conditions should the heat and mass transfer rates or the 

condenser length be infinite. 

18 
TR-3108 

{m,T,xl {m,T,xl 

Steam 

Steam Conden- and Inert gases 

Seawater 

inert gases sate 

I 

dz 

~ t Transfer 

rocesses ~ ~ {m,T,Y,pl p 

Heat 

mass and 

momentum 

= fn {L,G,Y,P,T,geometry} 

Figure 2-3. A slice of a countercurrent direct-contact condenser indicating 

the modeling variables for one-dimensional flow 

Steam flow: 

Inert gas in steam and inert gas mixture: 

~z (mi,s) = wiafapA 

Coolant £low (condensate 1S subtracted): 

d (mL) = d (ms ) dz dz 

Inert gas dissolved in the coolant: 

d . d 

dz (mi,L) = (mi,s) dz 

2.2.2.2 Momentum and Energy Balances 

Similarly, the following momentum and energy balances were used: 

Condenser heat load: 

dQ - h (T· T )afa A dz - L 1nt - L P 

Water temperature (decreases with z): 

dTL 

dz = -

1 dQ 

Tit. C dz· 

L PL 

(2-15) 

(2-16) 

(2-17) 

(2-18) 

(2-19) 

(2-20) 

Derivatives of temperature and pressure of the steam-inert gas mixture are the 

same as given in Eqs. 2-12 and 2-13. 

19 
TR-3l08 

These equations allow us to integrate along the condenser's length if we estimate water temperature, flow rate, and dissolved inert gas content in the 

water at the outlet. Iterations are required to match the exact water flow 

conditions at the top of the condenser. 

2.2.3 Equilibrium Calculations* 

To evaluate the maximum performance of an ideal countercurrent condenser, we 

calculated the equilibrium assuming 

• Water exiting the condenser ~s ~n equilibrium with the steam entering from 

the bottom. 

s Dissolved inert gas in the water is also in equilibrium with the partial 

pressure of inert gases in the entering mixture at the bottom. 

s The steam and inert gas mixture exiting from the top of the condenser ~s ~n 

equilibrium with the incoming water. 

s The incoming water is deaerated to an extent corresponding to its 

equilibrium level with the steam and inert gas mixture at the top. 

A detailed calculation procedure ~s provided in Appendix G. 

2.3 Structured Packings 

2~3.l Geometry Definitions 

The used structured packings are made of adjacent layers of corrugated sheets 

bound together. The sheets may be made of metallic or plastic solid sheets or 

gauze (wire mesh) sheets. Figure 2-4 shows a structured packing material 

tested in this study. The orientation of adjacent corrugated sheets is shown 

in Figure 2-5. The cross-section of the upflowing vapor channel alternates 

between triangle and diamond shapes. 

The vapor flow channel is at an angle 8 of 60 deg from the horizontal. This 

arrangement causes the vapor and liquid flowing between adjacent sheets to 

periodically redistribute within the bed. The base of the triangle is denoted 

by B, height by h, and slanted side by 5. 

Following Bravo, Rocha, and Fair (1985), an equivalent hydraulic diameter for 

the vapor flow d

eq 

can be defined as four times the flow area per unit 

perimeter: 

deq = Bh (B ! 25 + ;5) (2-21) 

taken as the arithmetic mean of hydraulic diameters of triangular and diamondshaped passages. The available surface area per unit volume of the packing, 

as approximated by Bravo, Rocha, and Fair, is 4/deq (11m). 

For packings made of solid sheets, the contact area (normally the glued or 

welded area between sheets) between adjacent sheets represents a loss ~n 

*Note that these equilibrium calculations are not rate limited. 

20 
S=~I 

Figure 2-4. Structured sheet packing (Courtesy: 

Munters Corporation) 

Peak 

Valley 

Right-left mixing between sheets T 

Flow 

channel 

Flow channel arrangement 

T S h 

1 

14-B-+l 

Triangular 

cross section 

h 

1 

r 

(/0 

Diamond or squareshaped cross section 

Flow channel cross section 

Figure 2-5. Structured packing geometry definition 

21 

TR-3108 
TR-3108 

available area. The thickness of the sheet causes a small but finite reduction in the available volume and void fraction. 

Thus, the void fraction is estimated as 

g = 1 - 4t/d

eq , 

where t is the sheet thickness (m). 

If a contact loss is expressed as a percentage of total available area CLos~' 

then we may use a better approximation for the available surface area per un~t 

volume as 

(l/m) • (2-22) 

2.3.2 Transfer Correlations 

The transfer correlations adopted in this study follow the approach of Bravo, 

Rocha, and Fair (1985). However, modifications were introduced in the liquidside relations to accommodate high liquid loadings (L - 30 kg/m2 s versus 2.8 

for Bravo). 

2.3.2.1 Liquid-side Correlations 

Mass Transfer. The liquid moves down by gravity as a film along the flow 

channel. For gauze-packing capillary action spreads the liquid into thin 

films (even at low liquid rates) to cover almost the entire available packing 

surface area. For packings made of solid sheets, however, only a fraction af 

(0 < af < 1) of the available packing area may be effective in the transfer 

process. The liquid flows as a film on a surface inclined vertically, as 

shown in Figure 2-6, as opposed to a vertical surface. Considering that the 

liquid flow on the inclined surface is equivalent to an "open-channel" flow, 

Manning's formula (see, for example, John and Haberman 1980) can be used to 

estimate the effective liquid-film thickness and velocity for water flow. For 

an inclined smooth surface, the water velocity can be expressed as 

0.820 ~2/3 (. )1/2 ULeff = u s~n a n (m/ s) , 

where 

a = modified inclination of the surface from horizontal 

n = Manning roughness coefficient (= 0.010 for smooth surfaces), 

o = film thickness (m). 

Using a value of 0.010 for n for smooth surfaces, we see that 

(2-23) 

(2-24) 

where r ~s the water flow per unit surface area in unit length of packing 

r = PLULeffo = L/afap (kg/m s). Here L ~s the superficial liquid loading 

(kg/m2 s). 

22 
Figure 2-6. Liquid film flow on an inclined structured packing geometry 

TR-3108 

Note that Eqs. 2-23 and 2-24 are in dimensional form, given here in metric 

units. These equations are valid only for turbulent water flow. Universal 

dimensionless correlations for turbulent flow on an inclined plane are not 

available in the literature for use with other liquids. 

The typical distance over which liquid renewal occurs ~s the slanted side S 

modified by the inclination 8 of the corrugation, or S' where 

[( B )2 2]1/2 S' = + h 2 cos 8 (2-25) 

and 

sln a = B/(2S' cos 8) • (2-26) 

The local liquid-side mass-transfer coefficient, based on the penetration 

theory of Higbie (1935) and as used by Bravo, Rocha, and Fair (1985), then can 

be expressed as 

(2-27) 

where 

DL = a~r diffusivity in water (m2/s) 

23 
ULeff = effective liquid film velocity (m/s) 

S' = distance over which liquid renewal occurs (m) 

kL = liquid-side mass-transfer coefficient (kg/m2 s). 

TR-3l08 

The expression in Eq. 2-27 differs from that of Bravo, Rocha, and Fair in that 

ULeff is based on a turbulent water flow on an inclined plane rather than 

laminar flow on a vertical surface; and the renewal distance is S', which is 

dependent on 8, as opposed to Bravo's shorter distance S, which is independent 

of 8. 

These differences can be justified in that in all of Bravo's cases, " ••• the 

liquid-side resistance did not play a significant role in the overall mass 

transfer resistance, II and, thus, the magnitude of the liquid-side resistance 

as formulated by Bravo possesses a larger degree of uncertainty. 

Heat Transfer. The local liquid-side heat-transfer coefficient was evaluated 

using the Chilton-Colburn (1934) analogy: 

hL __ (SCL)2/3 

kLCpL PrL 

where 

hL = liquid-side heat-transfer coefficient (kW/m2 K) 

kL = liquid-side mass-transfer coefficient (kg/m2 s) 

CpL = specific heat of liquid (kJ/kg K) 

SCL = liquid Schmidt number 

PrL = liquid Prandtl number. 

2.3.2.2 Gas-side Correlations 

Mass Transfer. The local gas-side mass-transfer coefficient 

extensive earlier investigations of wet-wall columns. Following 

and Fair (1985), the gas Sherwood number is expressed as 

ShG = O.0338(ReG)4/5(ScG)1/3 , 

where 

the Sherwood number, ShG = kGdeq/PGDG' 

(2-28) 

1.S based on 

Bravo, Rocha, 

(2-29) 

the gas Reynolds number, ReG = deqPG (UGeff ± ULeff)/~G' 1.S based on a 

relative velocity, and 

the gas Schmidt number, SCG = ~G/PGDG' 

Here, kG represents the gas-side mass-transfer coefficient (kg/m2 s), DG 1.S 

the gas diffusivity (m2/s), and ~G is the gas dynamic viscosity (kg/m s). 

24 
TR-3108 

The effective gas velocity UGeff is dependent on the superficial gas loading G 

(kg/m2 s), the void fraction of the packing 8, and the flow channel inclination a, as 

G 

UGe ff = -p-G----:,..--~a • 8 S1.n (2-30) 

The valid range for Eq. 2-29, which Bravo, Rocha, and Fair verified for 

structured packings, is 220 < Re < 2000 and 0.37 < Sc < 0.78 (given in 

Table 2-1). Based on previous studies, Sherwood, Pigford, and Wilke (1975) 

claimed a valid range of 3000 < Re <40,000 and 0.5 < Sc < 3. Thus, we expect 

this expression to be valid at a typical parameter range for an OTEC directcontact condenser inlet of 800 < Re < 4000 and Sc ~ 0.44 (shown in the lower 

part of Table 2-1). 

Heat Transfer. The local gas-side heat-transfer coefficient 1.S evaluated 

using the Chilton-Colburn (1934) analogy: 

hG __ (SCG)2/3 

kGCpG PrG ' (2-31) 

where 

hG = gas-side heat-transfer coefficient (kW/m2 K) 

CpG = specific heat of gas (kJ/kg K) 

SCG = gas Schmidt number 

PrG = gas Prandtl number. 

Gas Friction. The local gas friction is modeled based on the study of Bravo, 

Rocha, and Fair (1986) who compiled 6p measurements for long stacks of structured packing where six to ten individual layers were arranged so that 

successive layers are rotated by 90 deg in a horizontal plane. They express 

the pressure loss in such a stack under dry conditions 6po' as 

(2-32) 

where ReS is a gas Reynolds number based on length S as PG UGeff s/~G' and L 

is the total packed length. For an irrigated packing, the increase due to 

liquid flow was accounted for as 

(2-33) 

where Fr 1.S the liquid Froude number, U~eff/ gdeq , and C3 is a dimensionless 

constant with a value in the range of 3 to 7.5, depending upon the packing 

chosen. 

Consider a single stack of packing. If we denote entrance and exit loss coefficients lumped together by A and the frictional coefficient within the 

packing in laminar flow by C/ReS' then we may write the dry pressure loss for 

the single stack as 

25 
Table 2-1. Comparison of Correlation Data Base with Experimental Condenser Entrance Conditions 

System 

o/p Xylenes 

o/p Xylenes 

o/p Xylenes 

o/p Xylenes 

o/p Xylenes 

olp Xylenes 

o/p Xylenes 

o/p Xylenes 

EB/Styrene 

EB/Styrene 

EB/Styrene 

EB/Styrene 

Meth/Ethanol 

Meth/Ethanol 

Glycols 

Glycols 

Steam-Air 

Steam-Air 

Steam-Air 

Steam-Air 

Packing 

Pr'?ssure Dia. 

(mm Hg) (m) 

730 

730 

300 

300 

100 

100 

16 

16 

100 

100 

50 

50 

760 

760 

10 

10 

12 

12 

12 

12 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.00723 

0.0267 

0.0267 

0.0355 

0.0355 

Liquid 

Loading 

(kg/m2s) 

0.41 

2.75 

0.39 

2.57 

0.29 

1.77 

0.24 

0.96 

0.35 

1.93 

0.26 

1.47 

0.45 

2.68 

0.23 

0.54 

14.8 

59 

14.8 

59 

Source: Bravo, Rocha, and Fair 1985 

Vapor 

Loading 

(kg/m2s) 

0.41 

2.75 

0.39 

2.57 

0.29 

1.77 

0.24 

0.96 

0.35 

1.93 

0.26 

1.47 

0.45 

2.68 

0.23 

0.54 

0.2 

0.8 

0.2 

0.8 

Liquid Va por 

DensijY DensijY 

(kg/m) (kg/m) 

765 

765 

791 

791 

819 

819 

849 

849 

828 

828 

842 

842 

756 

756 

1010 

1010 

1000 

1000 

1000 

1000 

3.100 

3.100 

1.400 

1.400 

0.480 

0.480 

0.090 

0.090 

0.480 

0.480 

0.260 

0.260 

1.200 

1.200 

0.080 

0.030 

0.012 

0.012 

0.012 

0.012 

Liquid 

Viscosity 

(kg/~s) 

(10 ) 

0.23 

0.23 

0.28 

0.28 

0.38 

0.38 

0.51 

0.51 

0.39 

0.39 

0.47 

0.47 

0.45 

0.45 

2.80 

2.80 

1.15 

1.15 

1.15 

1.15 

Vapor 

Viscosity 

(kg/~s) 

(10 ) 

8.8 

8.8 

8.2 

8.2 

7.6 

7.6 

6.9 

6.9 

7.7 

7.7 

7.4 

7.4 

8.5 

8.5 

9.6 

9.6 

8.6 

8.6 

8.6 

8.6 

6.0 

6.0 

4.5 

4.5 

3.0 

3.0 

2.0 

2.0 

3.6 

3.6 

2.8 

2.8 

4.0 

4.0 

5.0 

5.0 

4.05 

4.05 

8.80 

8.80 

43.10 

43.10 

119.00 

119.00 

23.40 

23.40 

43.00 

43.00 

9.10 

9.10 

420.00 

420.00 

2.4 1661.00 

2.4 1661.00 

2.4 1661.00 

2.4 1661.00 

Vapor 

Re Vapor 

Vapor 

Sherwood 

(UL-ignored) Sc Number 

426.8 

2862.5 

435.7 

2870.9 

349.5 

2133.3 

318.6 

1274.4 

416.4 

2296.0 

321.8 

1819.6 

484.9 

2888.1 

219.5 

515.3 

786.7 

3146.7 

1046.0 

4183.9 

0.701 3.82 

0.701 17.49 

0.666 3.81 

0.666 

0.367 

0.367 

0.644 

0.644 

0.686 

0.686 

0.662 

0.662 

0.778 

0.778 

0.762 

0.762 

0.431 

0.431 

0.431 

0.431 

17.23 

2.62 

11.15 

2.94 

8.90 

3.71 

14.56 

2.99 

11.94 

4.38 

18.24 

2.30 

4.56 

5.30 

16.05 

6.65 

20.16 

Remarks 

Total Reflux 

Total Reflux 

Total RefluX 

Total RefluX 

Total RefluX 

Total Reflux 

Total Reflux 

Total RefluX 

Total RefluX 

Total Reflux 

Total Reflux 

Total Reflux 

Total RefluX 

Total Reflux 

Total Reflux 

Total Reflux 

Entrance Conditions 

Entrance Conditions 

Entrance Conditions 

Entrance Conditions 

U8 

III 

;\II 

--~ 

I I 

~-" 

H 

~ 

I 

VJ 

...... 

o 

00 
TR-3108 

where t is a single stack length, and q is the dynamic pressure of the gas. 

If an interstack loss coefficient, caused by entrance and exit effects and by 

rotations occurring in the region between two adjacent stacks, is denoted by 

B, then for a stack of n layers, the dry pressure loss is 

(~p/q) = A + (n - l)B + (C/Res)(nt/deq) • (2-34) 

If A 1S of the order of B, we may approximate this expression as 

(2-35) 

Note that in Eq. 2-35, the first term is a constant dependent on the number of 

layers of packing but independent of the layer's length. 

Expressing Eq. 2-32 in a similar form, we get 

(2-36) 

where the first term is multiplied by the layer length as well. There is an 

inconsistency in the lip expression as provided by Bravo, Rocha, and Fair 

(1986). The inconsistency arises because the term that represents entrance 

and exit losses is multiplied by the layer length. However, as long as the 

same number of layers is used in other applications, Eq. 2-36 should yield 

pressure losses within ±15%, as demonstrated by Bravo, Rocha, and Fair (1986). 

For our condenser study experiments, we used a maximum of only two layers of 

packing. If we assume that in Bravo's studies, an eight-layer stack was used 

on the average, then the entrance and exit loss coefficients for our case 

should be B = 0.342 x 2/8 = 0.0855. Thus an appropriate expression for the 

dry pressure loss for a two-stack condenser may be 

lIPo/q = 0.0855 + (185.4/ReG)(L/deq ) • (2-37) 

Although these arguments are speculative, our initial attempts to model lip 

using Eq. 2-32 yielded predictions that were a factor of two higher than their 

corresponding measurements. For lack of justifiable data, we chose to model 

~p as follows. 

For the model predictions provided in this report we used an approximate 

expression for the "local friction" coefficient as 

f = 0.171 + (92.7/ReG) (2-38) 

in the Darcy-Weisbach equation as 

~p = f ~ q • (2-39) deq 

Equations 2-38 and 2-39 yields a 50% smaller ~p for a two~stack layer than 

Eq. 2-32 for a multiple-stack layer. 

27 
TR-3l08 

The correction for increase in 6p due to liquid flow as in Eq. 2-33 yielded a 

negative frictional loss at high liquid loadings in the condenser (as opposed 

to lower liquid loadings investigated by Bravo, Rocha, and Fair [1986]). This 

correction for irrigated packings was not used in this study. 

All correlation schemes are summarized in Table 2-2. 

2.4 Integration Scheme 

The process equations described in Section 2.2 were integrated using a fourthorder Runge-Kutta integration scheme. For cocurrent flow, integration proceeded along the superficial direction of steam and water flow. Because the 

conditions at the inlet to the condenser were known (an initial value problem), the procedure for integration was straightforward. 

We assumed the packing was available at the entry into the condenser; no 

special treatment was made for the water distribution system and the accompanying liquid free-fall. We assumed the condenser packing was available 

until the end of the condenser length as well. Water free-fall into a drain 

pool was not modeled separately. 

A description of the steps of the integration process follows. 

• Evaluate the fundamental properties (namely, 

mutual diffusivity, and thermal conductivity) 

mixture and the liquid-inert solution 

mixture density, 

of the steam and 

viscosity, 

inert gas 

• Based on the local flow rates at the beginning of the step, evaluate the 

effective liquid and gas mixture velocities 

• Predict the local Nusselt and Sherwood numbers based on the chosen correlations using the local values of the liquid and gas Reynolds, Prandtl, and 

Schmidt numbers 

• Evaluate an interfacial temperature, based on the local heat- and masstransfer coefficients, using the Colburn-Hougen equation in an iterative 

manner that uses the ZEROIN subroutine outlined by Forsythe, Malcolm, and 

Moler (1977) 

• Use the interface temperature to calculate a series of derivatives of the 

local state variables 

• Based on the local derivatives, determine the state conditions at the end of 

the step. 

For co current flow, we integrated either to a specified condenser length or to 

a length at which the local steam saturation temperature is O.02°C above the 

water temperature. For countercurrent flow, the inlet conditions specified 

for water and steam corresponded to the top and bottom of the condenser, 

respectively (a boundary-value problem). Thus, to match conditions at either 

end of the condenser, we implemented an iterative scheme. We chose to integrate the process equations from the bottom of the condenser. A set of state 

values for the water at the bottom were estimated. Integration proceeded to 

the top, up to the specified condenser length, in a manner similar to that 

used for cocurrent flow. We then compared the calculated water conditions at 

the top to the specified water inlet conditions (temperature, flow rate, and 

28 
S=~I 

Table 2-2. Correlations for SERl Direct-Contact Condenser Model 

Liquid Side 

Mass transfer (for water) 

= 

= 

0.820 ~2/3 (. )1/2 u Sl.n a 

n 

With n = 0.010, 

= [ r ]3/5 

82p 1/2 L (sin a) 

S' = [(B/2 cos 8)2 + h2]1/2 

sl.n a = B/(2S' cos 8) 

r = L/afap 

Heat transfer 

hL (SCL)2/3 (kLC ) = 

PL PrL 

Gas Side 

Mass transfer 

where Re = 

Heat transfer 

Friction (Darcy-Weisbach formulation) 

f = 

= 

0.171 + 92.7 /ReS 

ReS/deq 

(m/s) 

(m) 

(m) 

(kg/m s) 

+Dimensional equations using Mannings formula for open-channel 

flow given here for water in Sl units. n = 0.010 for smooth 

surface. 

TR-3108 

§Use relative velocity, + for countercurrent flow, - for cocurrent. 

29 
TR-3108 

dissolved level of inert gas in water). Based on the magnitude of these differences, we estimated new sets of bottom water conditions and repeated the 

integration. This procedure was repeated iteratively following a modified 

scheme similar to ZEROIN (Forsythe et ale 1977). Iterations were performed 

until the calculated and specified water temperatures at the top of the condenser differ to within ±O.Oloe. For typical countercurrent condenser operating conditions, we required a series of four iterations for convergence. 

We found that an integration step size of 1 mm was suitable for most cases. 

Step sizes much less than 1 mm were tried but yielded the same results. However, at low levels of noncondensable gases and near the top of the countercurrent condenser, when the derivatives of steam mass flow or temperature and 

pressures are large, we reduced the step size to 0.25 mm. 

At the end of the calculations, we printed summaries of condenser outlet conditions and stored them on diskettes for later use. 

30 
TR-3108 

3.0 EXPERIMENTAL DETAILS 

The experiments described in this report were performed ln SERI's Low Temperature Heat- and Mass-Transfer Laboratory in Golden, Colo. The purpose of the 

laboratory is to investigate and improve methods of transferring heat and mass 

under small driving potentials that often exist when the sun is the energy 

source. 

Although other processes could be investigated, the primary thrust was to 

examine direct-contact evaporators and condensers for OC-OTEC. The emphasis 

of the research in the lab was to simultaneously increase the transfer rates 

of the direct-contact heat exchangers and decrease the size and water flow 

requirements. These objectives are reflected in the design of the research 

facility. 

3.1 Facility 

A heat rate of up to 300 kW is transferred to the closed warm-water loop 

through a shell-and-tube heat exchanger. The exchanger receives heat from 

another closed loop fired by natural-gas boilers. The cold-water loop removes 

heat by routing the flow through vapor-compression chillers. Warm water flows 

through an evaporator in one end of the chamber, and cold water flows through 

a condenser at the other end, as shown in Figure 3-1. Heat and mass are 

exchanged by evaporation of the warm water and direct-contact condensation of 

the vapor in the cold water. 

The pressure in the O-ring-sealed vacuum chamber is maintained by a threestage compressor train consisting of a booster, a rotary-vane pump, and a 

liquid-ring vacuum pump. Inert gases, which affect heat- and mass-transfer 

rates, can be added to the steam through gas mass flow meters to examine the 

effect of vacuum leaks and desorbed gases that may evolve from natural seawater in OTEC systems. The concentration of these noncondensable gases in the 

vapor is measured at the vacuum exhaust or at other points in the test chamber 

with a gas mass spectrometer. A solenoid-operated butterfly valve in the line 

between the vacuum tank and the compressor train allows us to vary the venting 

rate and seal the tank under vacuum for leak tests and inactive periods. 

Table 3-1 summarizes the facility's capabilities. 

3.2 Instrumentation 

We monitor all temperatures using platinum resistance thermometers (Rosemount 

Model 785-01N-0900). We take steam temperature measurements with a wet-bulb 

arrangement to arrive at local saturation values. Water flow rates are 

measured using two 3-in. turbine flow meters (Flow Technology, Inc., Model 

FT-96C3000-LJC). We monitor the inert gas injection rate using a gas mass 

flow controller (Tylan Model FC262, 0 to 50 and 0 to 150 Standard L/min). The 

vacuum exhaust volumetric flow was fixed by the first stage rotary blower 

(Kinney, Model MB 2000) over an inlet pressure range of 10 to 1500 Pa. We 

measure pressures in the test cell using absolute pressure gauges (MKS Instruments, Model 222BHS-A-0-IOO). Differential pressures are measured using t.P 

transducers (MKS Instruments, Model 221BD). Instruments were calibrated at 

SERI's in-house calibration facility or at the manufacturer's facilities. 

31 
TR-3108 

Fill/drain ...... -c:><:::r--Fill/drain 

Dissolved 

O2 man itor ,.....-----'----c:-=:::t---t Heat 

Chillers 

Filter 

Makeup 

line 

Water 

pumps 

Filter 

Boiler 

pump 

Boiler 

Strainer 

Cold loop Warm loop Static 

mixer 

Cold 

water 

inlet ........... _____ ....I.---, Inert gas 

.--C><J---l~ .. ~---injection 

6-in. flow 

meter 

Test Chamber 

~--~-------~ 

To vacuum ~-O<J----' 

exhaust system 

Straightener 

port 

Warm 

water 

inlet 

Straightener 

6-in. flow 

meter 

Figure 3-1. Heat- and mass-transfer laboratory flow loop schematic 

We took extreme care to assure that the instruments were properly installed to 

avoid external influences in test results. Detailed sets of uncertainty 

analyses were conducted to identify error sources and minimize their influences. Table 3-2 summarizes the estimates of uncertainties in the primary 

measurements. 

Further details on the facility, instrumentation, and uncertainty are also 

provided in Appendix A. 

32 
TR-3l08 

Uncertainties in the primary measurements affect the derived parameters such 

as the gas loading, Jakob number, inert gas inlet concentration, percentage of 

steam condensed, and pressure loss, as listed in data tables provided in 

Appendices D and E. We conducted detailed propagation analyses using the 

method of Kline and McClintock (1953). Table 3-3 summarizes the typical 

uncertainties in these derived quanti ties for a particular tested packing 

(19060). 

Table 3-1. SERI Direct-Contact Laboratory Capabilities 

Testing Condition 

Heat input 

Heat rejection 

Temperature 

Flow rate 

Vacuum pressure 

Leak rate 

Vent capacity 

Warm-Water Loop 

0-300 kW 

3°-30°C 

SO kg/s 

700 Pa 

0.5 mg/s 

0.57 m3/s 

Cold-Water Loop 

0-300 kW 

3°-30°C 

SO kg/s 

700 Pa 

0.5 mg/s 

0.57 m3/s 

Table 3-2. Summary of Uncertainties 1n 

Primary Measurements 

Condenser Inlet Conditions 

Steam temperature 

Total pressure 

Inert gas flow 

Water temperature 

Water flow rate 

Condenser Outlet Conditions 

Steam temperature 

Water temperature 

Pressure loss 

Exhaust Pump Conditions 

Steam temperature (dry bulb) 

Total pressure 

Volumetric flow 

33 

±0.02°C 

±0.5% 

±2.0% 

±O.OloC 

±l.O% 

+0.02°C 

±O.OloC 

±lO Pa 

or 10% 

20o-0°C 

±0.5% 

±3.0% 
Table 3-3. Estimated Uncertainties in Derived Quantities 

for Packing 19060 

Derived 

Parameter 

Gas loading 

Jakob number 

Inlet inert mass fraction 

Outlet inert mass fraction 

Effectiveness 

Percentage condensed 

Inlet pressure 

Outlet pressure 

3.3 Condenser Test Models 

Cocurrent 

Condenser 

Error 

Range (%) 

2.4-2.7 

1.8-2.0 

2.3-5.5 

3.4-5.0 

0.17-0.75 

1. 7-5.0 

0.12-0.14 

0.38-0.93 

Countercurrent 

Condenser 

Error 

Range (%) 

2.4-2.6 

1.8-2.0 

2.3-2.5 

2.0-4.5 

0.19-0.70 

1.7-2.0 

0.12-0.20 

0.40-0.94 

TR-3108 

Figure 3-2 shows a schematic of the cocurrent condenser test set-up. The 

steam and inert-gas mixture enters the top of the condenser and flows downward. Cooling water flows onto a distributor on top and is allowed to flow 

freely onto a metallic screen. With the screen, water is distributed as 

evenly as practical over the contact medium. The warmed water from the 

condenser is collected in a drain pool. Noncondensable gases and uncondensed 

steam from the bottom of the condenser are routed to the vacuum exhaust 

pumps. 

Figure 3-3 illustrates the test arrangement in countercurrent flow. The steam 

and inert-gas mixture enters the condenser from the bottom of a cylindrical 

enclosure. The water enters the condenser similarly to that for the cocurrent 

flow. A water distribution plate on top of the condenser allows uncondensed 

steam and inert gases to escape to the exhaust system. 

We tested five different structured packings in either the cocurrent or 

countercurrent condenser configuration or both. Table 3-4 summar~zes the 

relevant geometric characteristics of the tested packings. The AX packing was 

made of stainless steel wire mesh with 0.16-mm-diameter strands. This packing 

possesses the largest available surface area per volume of all tested packings 

(250 m2 jm3 ). The stack length for the AX packing was 0.18 m. All other 

packings were sheet-type packings. The articles 19060 and 27060 were made of 

o .40-mm-thick polyethylene sheets and are commonly used as cooling tower 

fill. For these packings, we tested individual stacks of 0.61-m lengths. 

Packings 3X and 4X were made of 0.38-mm stainless steel sheet metal that was 

rippled and perforated with approximately 3-mm-diameter holes in a square 

pitch with a center-to-center spacing of 11 mm. The stack length for the 3X 

and 4X was 0.30 m. Two stacks rotated at 90 deg about a vertical axis were 

used to make up the required overall length. 

34 
Steam and inert Steam and inert 

gas m ixtu re \.l~;;:::;:;::;;;:F~~~;::;;,-J. 

inlet 

screen 

Vacuum 

exhaust 

~ Water drain 

Figure 3-2. Schematic of cocurrent condenser 

test article arrangement 

gas mixture 

inlet 

Vacuum exhaust 

Water ~~:r-=,;;;:;;;:t. t:;!:~:=t dis t rib u tor 

I-'r~....,.....,.-,I plate 

Steam and inert 1T:"Tr"'i-T-'...,....~ 

Water 

inlet 

Water drain 

pool 

gas mixture 

inlet 

Figure 3-3. Schematic of countercurrent condenser test article arrangement 

35 

TR-3108 
Base Height 

Packing (mm) (mm) 

Identifier B h 

AX 26.0 13.0 w 

19060§ 0- 48.3 19.1 

3X 50.8 25.4 

27060§ 73.0 27.2 

4X 94.0 47.0 

+Quoted by manufacturers. 

§Packings 19060 and 27060 

Engineering Company. 

Table 3-4. Geometry Comparisons of the Tested Pac kings 

Sheet Surface Equi- Void 

Thick- Inc1i- Contact Area per valent Frac- Tested Water 

ness nation Loss Volume Diameter tion Packing Free-fall 

(mm) (deg) (%) (1/m)+ (mm) (%) Length Length 

t e CLoss a p deq e: (m) (m) 

0.32 60 0.0 250.0 14.6 91.2 0.36 1.08 

0.40 60 13.6 138.0 23.3 93.5 0.61 0.80 

0.38 60 0.0 133.0 28.5 94.7 0.61 0.80 

0.40 60 5.9 106.0 33.9 95.5 0.61 0.80 

0.38 60 0.0 73.7 52.7 97.1 0.61 1.08 

are products of Munter's Corporation; packings AX, 3X, and 4X are products of Koch 

t-3 

~ 

I 

w 

...... 

o 

00 

III 

III 

N 

-
TR-3l08 

The packings used and the entire range of tested parameters for the cocurrent 

condenser are summarized in Table 3-S. A similar range for countercurrent 

flow is summarized in Table 3-6. A compilation of test data together with 

predictions for the structured packings is provided in Appendix D. 

In addition to structured packings, other gas-liquid contactors were also 

tested in a countercurrent configuration. The results of these tests clearly 

showed the superiority of using structured packings as the gas-liquid contacting medium. Appendix C provides a summary of the relative comparisons of the 

tested media, and Appendix E tabulates the test data for devices other than 

structured packings when used in a countercurrent condenser. 

3.4 Test Procedure 

The test procedure for both co current and countercurrent condensers was essentially the same. The test cell was evacuated to the lowest possible pressure 

with the vacuum butterfly valve fully open and all vacuum pumps running. We 

established warm and cold water flow rates and deaerated the water to approximately 20 ppb of dissolved oxygen. We turned on the chiller and boiler to 

select the desired thermal transfer rate. Atmospheric air at a selected 

airflow rate was introduced into the test cell as noncondensable gas. We 

adjusted the boiler and chiller controls to operate the condenser at a steadystate cold-water inlet temperature of nominally SoC. The steam inlet 

temperature floated up or down to its steady-state level, depending on the 

condenser performance and the vacuum exhaust venting rate. A series of 

10 measurements averaged over IS-minute intervals was taken at steady state. 

At this point, we closed the vacuum butterfly valve slightly to increase the 

condenser pressure. We then corrected the heat inputs to the next steadystate operating condition and collected the next set of data. Gradually 

closing the valve forced the steam inlet temperature to increase and more 

steam to condense in the condenser. As we closed the butterfly valve, we 

typically collected a series of seven data points at the fixed water flow 

rate, heat rate, and noncondensable gas injection rate. For other series, the 

injected noncondensable gases, cooling water flow rate, or the heat rate may 

be varied. 

37 
Table 3-5. Tested Range for Cocurrent Condensers III 

III 

Packing Number Tsi T . G Ja X· . N 

Wi 11 - (kg/m2s) - Identifier of Points (0 C) (OC) (---) (% ) Remarks I II 

~-~ 

AX 51 11.02 4.54 0.203 0.864 0.500 Single stack of 

14.02 5.51 0.268 1.361 1.311 0.18 m length 

19060 48 8.50 4.76 0.15 0.95 0.06 Single stack of 

18.09 6.84 0.65 1.40 0.89 0.61 m length 

4X 37 9.84 4.03 0.187 0.843 0.487 Two stacks of 

14.58 5.59 0.528 1.389 0.744 0.30 m length each 

Falling 61 13.05 4.76 0.14 1.93 0.47 Water fall length 

Jets 21.95 5.49 0.34 3.37 2.38 of 0.8 m 

w 

00 

Table 3-6. Tested Range for Countercurrent Condensers 

Packing Number Tsi T . Wi G Ja X· . 11 

Identifier of Points (0 C) (OC) (kg/m2s) (---) (% ) Remarks 

AX 60 10.11 4.45 0.015 0.967 2.93 Two stacks of 

16.92 5.81 0.304 13.4 33.3 0.18 m length each 

19060 209 9.92 4.64 0.15 1.02 0.35 Single stack of 

20.14 5.55 0.41 2.80 2.46 0.61 m length 

3X 37 9.38 4.10 0.05 1.0 2.50 Two stacks of 

13.54 5.74 0.45 10.52 24.8 0.30 m length each 

H 

27060 246 8.63 4.56 0.15 0.99 0.32 Single stack of ~ 

I 

21.15 5.68 0.42 3.18 2.45 0.61 m length w 

..... 

0 

00 
S=~I TR-3108 

4.0 MODEL VALIDATION 

We developed the condenser model to provide guidance to a preferred design and 

to allow a designer to incorporate conservatism by overdesign to assure 

condenser performance. A common engineering practice to overcome prediction 

uncertainties is to include a margin of safety in the design. In general, 

uncertainties in predictive models decrease as the technology matures. 

Current validation efforts for the direct-contact condenser attempt to establish that the model (1) captures the physical trends observed in the experiments over the entire range of test variables and geometries, (2) provides 

predictions that are comparable to the observations, and (3) possesses 

uncertainties of similar magnitude to those in the data. 

The following approach is pursued in the remaining sections to validate the 

condenser model. For each tested packing, we generated a series of predictions at the condenser inlet conditions that corresponded to those of the 

experimental data. The predictions and experimental results are compared in 

graphs and tables. 

We provide significant trends of performance measures with independent varlables wherever they can be clearly illustrated. We illustrate the deviations 

between predictions and experiments with the independent parameters and 

explain their underlying causes. We characterize the performance measures for 

a particular geometry by the condensed steam (expressed as a percentage) and 

by its overall pressure loss. The deviations for the entire data set for a 

particular packing are quantified as an average and a standard deviation of 

the condensed steam (expressed as a percentage of the incoming steam) and the 

pressure loss. The independent variables in each set are the steam inlet 

saturation temperature Tsi , the gas loading G, the Jakob number Ja, and the 

inert gas content in the incoming steam Xii expressed as a mass percentage. 

Here, the Jakob number for the condenser is defined as 

(4-1) 

where ffiwi and msi represent the incoming water and steam mass flow rates 

(kg/ s), respectively; Twi and Tsi represent the incoming water and steam 

saturation temperatures (OC), respectively; C

pw 

is an average specific heat 

capacity of water (kJ/kg K); and h fg is an average latent heat of condensation 

fqr steam (kJ/kg). 

The scope of the comparisons focuses on illustrating the similar trends 

between the model and the experiments and quantifying the deviations. However, notable differences exist between the model and experiments with respect 

to their underlying assumptions and method of implementation, as discussed in 

the following paragraphs. 

We used only fresh water in the experiments. The water was consistently 

deaerated to 20 ppb of dissolved oxygen for all of the tests. With steam condensation, deaeration from the coolant does not occur to the extent that it 

may occur in seawater. 

39 
TR-3108 

In the experiments, we treated the condenser as a black box. Only measurements to characterize incoming and outgoing steam and water were made. We did 

not provide instrumentation to map out variations of process variables through 

the condenser. We simulated the presence of inert gas in stearn by dispersing 

atmospheric air into the stearn generated in the evaporator section of the test 

cell. The homogeneity of the mixture was verified using mass spectral traces 

at various locations. 

Finite lengths of free-fall (distance between water distributor and the top of 

the packing) were required to distribute the water onto the condenser packing 

and to drain it from the packing. A pool of drained water settled in a pool 

below the condenser. These spaces on top and bottom of the packing, although 

devoid of packing, did allow a certain amount of condensation to take place. 

We did not attempt to isolate contributions from these spaces. 

We tested the cocurrent jet condenser as a single-stage condenser 1n the 

experiments. The vacuum exhaust system could remove, at most, 14% of the 

uncondensed steam from this condenser (at a minimal noncondensable gas injection rate and stearn flow). Although for OTEC applications a cocurrent section 

may condense 70% to 80% of the incoming stearn. In some of these experiments, 

the cocurrent section condensed 80% to 98% of the incoming stearn because there 

was no second-stage condenser, causing the data to be confined to large Jakob 

numbers. 

The limitations of the numerical model are as follows. We assume the incoming 

stearn contacts the water and begins condensing as soon as it enters the packing. The water distribution manifold and free water streams are not accounted 

for. We assume the packing extended to the height where the cooling water 

first contacts the stearn. Draining streams of water from the bottom of the 

packing are not modeled. 

The transfer correlations used in the numerical model possess uncertainties 

because of the nature of the empirical data upon which they were based. They 

apply to fully developed flows; whereas in short, efficient packings, there 

generally is not an adequate length for the flow to develop. Thus, they do 

underpredict the transfer rates where entrance effects persist. 

The effective area over which transfer takes place is an interfacial area 

between the two phases and, 1n general, 1S difficult to define. After 

comparing the model with the data, we found that this area is comparable to 

the total geometric area of the packing. For generating comparable model 

results for the experimental data, we assumed that this area fraction af 

remains constant through the length of the condenser, although in practice 

this fraction may decrease continuously with decreased gas loading and 

increased steam condensation. 

4.1 Cocurrent Condenser 

We tested three different packings, namely, AX, 19060, and 4X and free-falling 

water jets in a cocurrent configuration. 

40 
TR-3108 

4.1.1 AX Packing 

The AX packing is made of stainless steel wire mesh (0.16 mm diameter). This 

gauze packing yields an effective transfer area equal to the total available 

area in mass transfer applications (Bravo, Rocha, and Fair 1985; and Meier 

1979). This packing possesses the highest surface area per volume a p of 

250 m2 /m3 and the lowest equivalent diameter of 14.6 mm of all the tested 

packings. For the tests, we introduced a short stack of 0.18-m length in a 

water free-fall of 1.08 m. 

Figure 4-1 illustrates a comparison of condensed steam between the data and 

the predictions, plotted versus Jakob number. The data are for an inert 

level, X •• of 0.55. The Jakob number varies from 0.87 to 1.4. For all the 

data, th~1gas loading is nominally 0.26 kg/m2 s. 

At this inert gas concentration, we note that the condensed steam data 

increases with increasing Ja. The predictions show similar trends. For 

Ja < 0.97, the predictions match the data extremely well. For 0.97 < Ja < 1.1, 

the data lie approximately 2% above the predictions. For even higher Ja, the 

data lie about 3% higher than the predictions. The cause for this deviation 

with increasing Ja is that the free-falling water jets contribute to an 

increase in condensation in the experiments. The model does not consider the 

free-fall contributions. Similar trends were observed at a higher inert gas 

concentration of 1.2% as well. 

E 

co 

Q) 

-

en 

"0 

Q) 

en 

c: 

Q) 

"0 

c: 

o 

o 

100r-------------------------------------o 

Xii = 0.55% • Data ---- Model I I 

.( 

_ •• to 

95 "" 

90 I85 I-

.. 

-. 

r e ",,/" 

- ,/ 

/' 

/" 

/' 

f/ 

80~--~1.---~----~--~~--~-----L--~ " I • I I I 

0.8 1 1.2 1.4 

Jakob number 

Figure 4-1. Comparison of condensed steam for AX 

packing in cocurrent flow 

41 
TR-3108 

For the entire data set of 51 points, the model underpredicts condensed steam 

by less than 1.4% with a standard deviation of 1.5% of steam. The experimental data possess an uncertainty of ±2%, as illustrated. In this and all the 

remaining figures illustrating the data, uncertainty estimates are indicated 

as vertical bars around a typical data point. 

Figure 4-2 illustrates the comparison of pressure loss between data and predictions. The model predicts pressure losses with the same trend as the data, 

but about 5 Pa higher than the data. Measured pressure loss is estimated to 

possess an uncertainty of ±10 Pa. Thus the predictions fall well within the 

uncertainty range of the data. 

We tried to test this packing at higher gas loadings. In general, at 

G > 0.3 kg/m2 s the AX packing was observed to be overloaded, with dramatic 

increases in the measured pressure loss. Considering the low packing equivalent diameter, this limit is similar to a flooding limit in countercurrent 

flow (see Section 4.2.1) but somewhat higher in cocurrent applications. This 

particular gauze packing is unable to handle liquid loads higher than about 

25 kg/m2 s without the water bridging the gaps and causing significant 

resistance to the steam flow. 

4.1.2 P1asdek 19060 Packing 

This packing made of 0.4-mm-thijk polyethylene sheets possesses a surface area 

per unit volume a of 138 m2 /m and an equivalent diameter d of 23.3 mm. A 

single stack of cf.61-m length was introduced in the cocurreRt configuration 

with a water free-fall height of 0 ... 8 m. 

«l 

a.. 

(/) 

(/) 

.Q 

<1> 

.... 

::::l 

(/) 

(/) 

<1> 

.... 

c.. 

"0 

<1> 

.... 

::::l 

(/) 

(l) 

<1> 

~ 

20 '" 0 

..... 

0 

c;; 

0 

Cl 

-': 

III 

10 

10 20 

Predicted pressure loss (Pa) 

Figure 4-2. Comparison of pressure loss for AX 

packing in cocurrent flow 

42 
TR-3l0B 

Figure 4-3 illustrates the comparison of condensed steam between the model and 

the data for a Jakob number range of O.B to 1.5. six different data sets at 

varied levels of G and X·· are included. To preserve clarity in the figure, 

only a faired line repr~~senting the predictions is shown in this figure. 

Detailed data set comparisons are provided in the tables in Appendix D. For 

Ja < 1.2 the predictions follow the data quite well, with a maximum deviation 

of less than 3% and well within the experimental uncertainty. For Ja > 1.2, 

the model overpredicts the data by as much as 4% at low G and Xii levels. 

Figure 4-4 compares pressure losses. Over the tested range, measured values 

are larger than the predictions by as much as 35 Pa. The model indicates a 

trend that is different from the data. Tests with this packing were conducted 

early in the program when we encountered some difficulty in the 6p measurement 

because water was clogging the pressure transducer connecting lines. This 

problem was later resolved by using larger diameter lines and maintaining a 

warmer constant temperature at the transducers. 

The differing trend between the model and the data may be attributed to the 

measurement difficulties encountered for this set of data. Despite this discrepancy, considering the low mean value of the 6p data of around 50 Pa and 

the uncertainty in the data of ±10 Pa, the comparison between the data and the 

model is reasonable. 

4.1.3 4X Packing 

The 4X packing we used was made with rippled and perforated stainless steel 

sheets. This packing possesses the highest equivalent diameter dp of 52.7 mm 

and the lowest a of 74 m2 /m3 of all packings tested. Two indiv~dual stacks 

of 0.3 m length tere introduced in an overall condenser free-fall height of 

1.1 m. 

100 '" ;:: 

- Data 0 

.J N 

Faired modeJ 0 CJ 

.;; 

co 

95 

~ ~ --: -.,. "'_1' E 

ttl 

<ll 

"C 

-

<ll 

CIl 90 :.:--. CIl 

- c: 

<ll 

"C 

c: 

0 

() 

85 

, - 80~ __ ~ ____ ~ ____ ~ __ ~~ __ ~ ____ ~ __ -J 

0.8 1.4 

Jakob number 

Figure 4-3. Comparison of condensed steam for 19060 

packing in co current flow 

43 
100 

-co 

0... 

C/) 

C/) 

0 

Q.) 

lo-

:J 

C/) 

C/) 

Q.) 

loa. 40 

"0 

Q.) 

lo-

:J 

C/) 

co 

Q.) 

::?! 

~--------------------------------------------~8 r •• .. 

/ 

~ " . .. 

/ 

/ • 

• , 

/ 

I 

20 40 60 

Predicted pressure loss (Pa) 

80 

... 

o 

N 

o 

<!) 

<I: 

Ol 

100 

Figure 4-4. Comparison of pressure loss for 19060 

packing in cocurrent flow 

TR-310B 

Because of its Iowa, this packing exhibited the largest influence of water 

free-fall. Predictio~s of condensed steam using the actual packing length of 

0.61 m yielded about 9% lower values than did the experiments. Thus, we 

decided to include the contribution of the free-fall in the predictions by 

adopting the overall free-fall length of 1.1 m for the packing. Figure 4-5 

illustrates the comparison of condensed steam at five levels of gas loading. 

Again, only a fa ired line through predictions is shown to preserve clarity. 

The predictions follow trends similar to the data. For Ja < 1.5, the predictions fall well within the experimental uncertainty. For Ja > 1.5, the model 

underpredicts the data by as much as 3%. 

Figure 4-6 illustrates the comparison of pressure loss plotted versus Jakob 

number again at five levels of gas loading. The agreement between data and 

predictions is excellent and is well within the experimental uncertainty. 

4.1.4 Free Jets 

A series of tests were conducted with the packing removed from the cocurrent 

condenser. Water flowed onto the distributor plate (described in Section 3.3) 

and fell to the bottom pool O.B m below. This configuration (shown ~n 

Figure 4-7) was not backed by a second-stage condenser. We included the data 

obtained for this configuration to illustrate the improvement obtained with 

the packing. We did not try to model the jets here. 

Figure 4-B illustrates the experimental data taken with and without the 

presence of packing 19060 in the cocurrent configuration. The data for freefalling jets lie in a range of 1.B < Ja < 3.4. For an equivalent amount condensed, the introduction of the packing shifts the Jakob number range to less 

44 
-::R 

~ 

E 

co 

CD 

-(IJ 

"0 

CD 

(IJ 

c:: 

CD 

"0 

c:: 

0 

0 

100 

• Data 

Model I· · 

• 

95 

.. 

•• 90 

85 

80~ __ ~~ __ ~ ____ ~ ____ ~ __ ~ ____ ~ __ ~ 

0.8 1.2 

Jakob number 

1.4 

Figure 4-5. Comparison of condensed steam for 4X 

packing in cocurrent flow 

50~--------------------------------------~ 

10 

0.52 

0.4 

\ 

• Data 

-Model 

G (kg/m2 s) 

~~---..a\ 0.25 

O~ __ ~~ __ ~~ __ ~ ____ ~ ____ ~ ____ ~ ____ ~ 

0.8 1.2 

Jakob number 

1.4 

Figure 4-6. Comparison of pressure loss for 4X 

packing in cocurrent flow 

45 

TR-3108 
S=~I TR-3108 

than 1.4. The free-jet data exhibit 

large sensitivity to both the gas 

loading and inert gas concentration 

(see data tables in Appendix D). This 

type of sensitivity is significantly 

reduced by using a packing as the 

contact medium. 

These results also illustrate that 

the steam condenses mostly within the 

packing. The method of liquid distribution, as long as the distribution is reasonably uniform, is immaterial to the modeling approach as 

formulated. 

Figure 4-7. Free-falling jets 

in cocurrent configuration 

Figure 4-9 illustrates the measured 

pressure losses with and without 

packing. Presence of packing results 

in higher pressure losses confined to 

much lower Jakob numbers. Of course, 

with a proper choice of packing, the 

increase in pressure loss can be minimized while the Jakob number can be 

reduced to a m1nlmum possible to 

achieve equivalent performance from a 

co current condenser. 

100r---------------------------------~ 

E 

co 

(]) 

95 

en 90 

"0 

(]) 

.. 00 

c:: 

(]) 

"0 

c:: 

o 

() 85 

Entire data range 

with 19060 packing 

. Data range 

without packing 

80~ __ ~ ____ ~----~----~ ____ ~ __ ~~ 

0.8 1.2 2.4 

Jakob number 

2.8 3.2 

Figure 4-8. Comparison of measured condensed steam 

for a cocurrent condenser with and 

without 19060 packing 

46 

!?i 

.... 

o 

N 

o 

(!l 

.( 

III 
co 

Cl... 

CIl 

CIl 

.2 

(].) 

:.... 

:::l 

CIl 

CIl 

(].) 

:.... 

Cl. 

"0 

(].) 

:.... 

:::l 

CIl 

co 

(].) 

::2: 

100~------------------------------------------~o :!: 

50 

1.2 

Entire data range 

with 19060 packing 

1.6 

Data range 

without packing 

/ at varied G 

",..""".......:. and Xii 

2 2.4 2.8 

Jakob number 

3.2 

o 

~ 

" .;: 

<Xl 

Figure 4-9. Comparison of measured pressure loss for 

a cocurrent condenser with and without 

19060 packing 

4.1.5 Summary of Co current Condenser Findings 

TR-3108 

From the discussions of the data on co current condensers presented in Section 4.1, the following findings result: 

• Introducing a packing as a contact medium substantially reduces the water 

flow requirement as expressed by the Jakob number. The packing also causes 

higher condenser pressure losses. Selecting a condenser configuration 

requ~res a trade-off between the Jakob number and pressure loss to minimize 

both. 

• We tested three structured packings with a wide range of surface areas per 

volume and presented their experimental data. 

• The gauze packing with a low d limited an acceptable gas loading to less 

than 0.3 kg/m2 s for OC-OTEC ope~ating conditions. 

• We tested the packing with the largest dp of 52.7 mm at gas loadings of up 

to 0.52 kg/m2 s. 

• The packing with the lowest a exhibited the largest influence of water 

free-fall. We obtained more Kccurate predictions for these experimental 

data using the total water free-fall length rather than the actual packing 

length. 

• Table 4-1 summarizes the deviations between predictions and experiments. 

The average and standard deviations of the differences in condensed steam 

are less than 3%; these deviations are comparable to a measurement uncertainty of ±2%. 

47 
TR-3108 

Table 4-1. Co current Condenser Comparison Summary 

Deviation (Prediction-Experiment) 

Condensed Steam (%) Pressure Loss (Pa) 

Number 

Packing of Std. Std. 

Identifier Points Average Deviation Average Deviation 

AX 51 -1.4 1.5 4.0 0.6 

19060 48 2.8 2.4 -17.6 10.4 

4X 37 -1.1 1.3 -0.1 1.2 

Experimental 2.0 10.0 

Uncertainty 

• The average and standard deviations of the differences in pressure loss are 

less than 3 Pa for AX and 4X packings. The data for 19060 exhibit larger 

differences of -18 Pa on the average and 11 Pa on standard deviation. The 

deviations for 19060 packing are well above those for the rest of the packings. As mentioned earlier, the experimental values of ~p for this packing 

are perhaps in question because of the waterlogged ~p transducer lines during some of the ~p measurements. However, in general the ~p differences in 

terms of their average and standard deviations are comparable to an estimated measurement uncertainty of ±10 Pa. 

4.2 Countercurrent Condenser 

Four different structured packings, AX, 19060, 3X, and 27060, were tested ~n 

countercurrent flow. 

4.2.1 AX Packing 

For the tests, two short stacks of 0.18 m length were introduced in a water 

free-fall length of 0.8 m. This condenser was used as a second-stage condenser in a two-stage configuration. Because of this arrangement, we achieved a 

wide range of inlet parameters for the tests. 

Flooding is a common limitation in countercurrent gas-liquid contactors. This 

packing, possessing the smallest equivalent diameter, was more prone to flooding at lower gas loading than others tested. Using dp ' we estimated the 

flooding limits using the correlations proposed by Wallis (1969) for circular 

tubes in turbulent flow as+ 

.* 1/2 (Jg) + 

.* 1/2 (Jf) = 0.7 , (4-2) 

+Commonly available flooding correlations for random packings are not directly 

applicable to the regular ~eometry found in structured packings. 

48 
TR-3l0B 

where 

.*2 = Pgjg2/ilPgd Jg 

.~:2 

Jf = pd~/ ilpgd 

jg,f = superficial gas and liquid velocities (m/s) 

Pg,f = gas and liquid densities (kg/m3 ) 

ilp = Pf - Pg 

g = gravitational acceleration (m/s 2 ) 

d = tube diameter (m) • 

Figure 4-10 illustrates the flooding limits for stearn and water flow at typical OTEe conditions for three different de values. An acceptable liquid 

loading L is plotted versus the gas loadin~ G. The limit of acceptable L 

decreases monotonically with increasing G. This limit increases with increasing tube diameter. 

Also shown in this figure are two lines of constant Jakob number. These lines 

represent straight lines with L proportional to G. A countercurrent condenser 

may operate at Ja ~ 1.2; a cocurrent may operate at Ja ~ O.B. 

The intersection of the constant Ja line with the flooding limit represents 

acceptable maximum allowable gas and liquid loadings for a particular packing. 

This figure shows that for a 20-rnrn-diameter tube, an allowable limit gas loading of G is ~0.32 kg/m2 s. 

The flow geometry in structured packings is different from that of circular 

tubes. We used this figure, however, to help select experimental conditions 

and estimate flooding envelopes. 

The AX packing with an e~uivalent diameter d of 14.7 rnrn could not accept gas 

loadings over 0.25 kg/m s without substanrial increase in vapor pressure 

losses. 

Figure 4-11 illustrates the comparison of 

and measurements for G < 0.25 kg/m2 s. 

experimental data over the entire range. 

0.9% with a standard deviation of 2%. 

condensed stearn between predictions 

The predictions lie close to the 

On the average, the difference is 

Figure 4-12 shows the comparison of pressure-loss predictions and the data. 

The comparison in this figure is not very good. The differences between predictions and measurements average 2 Pa but with a large standard deviation of 

6 Pa. This standard deviation is comparable to the uncertainty in the ilp 

measurement of ±10 Pa. 

49 
60 

50 

-en 

N 

E 40 "-

OJ 

~ 

OJ 

c: 30 

"0 

co 

o 

10 

deq = 

(mm) 

oc-__ ~ ____ ~ __ ~~ __ ~ __ ~~ __ ~ __ ~ __ ~ 

'" 0 

.... 

0 

c;; 

0 

(!) 

.;: 

al 

o 0.2 0.4 0.6 0.8 

Gas loading (kg/m2 s) 

Figure 4-10. Flooding limits for countercurrent 

condensers using the correlation 

of Wallis (1969) 

100r-----------------------------------~ 

95 

-

~ 

e..... 90 

E 

co 

Q) 

en 

"0 

Q) 

en 

c: 

Q) 

"0 

c: 

o () 75 

"0 

Q) 

... 

;;; 70 co 

Q) 

2 

65 

• Data 

Model 

• • 

60 ____ ~ __ ~ ____ +_--~ __ ~~ __ ~ __ ~ __ __ 

60 70 80 90 100 

Predicted condensed steam (%) 

Figure 4-11. Comparison of condensed steam predictions with data for AX packing 

in countercurrent flow 

50 

TR-3108 
55'1 1*1 

40 r----------------------------------------------,~ ~ I ~ 

35 (!) 

<: • III • • -co 30 a.. • C/) 

C/) • 

.2 25 Q) 

'-

:::I 

C/) 

C/) 20 Q) 

'-

Q. • 

"0 

Q) 15 '- • :::I 

C/) 

co 

Q) 10 ~ 

5 

0 

0 10 20 30 40 

Predicted pressure loss (Pa) 

Figure 4-12. Comparison of pressure loss for AX 

packing in countercurrent flow 

4.2.2 P1asdek 19060 Packing 

TR-3108 

A single stack length of 0.61 m was introduced in a water free-fall length of 

0.8 m. For this packing, we compared an extensive set of 209 data points. 

The differences between predictions and measurements for the condensed steam 

yielded an average of 0.1% and a standard deviation of 0.8%. 

For the pressure loss, 

shown in Figure 4-13. 

The differences yielded 

4.2.3 3X Packing 

comparison between experiments and predictions are 

The predictions follow the measurements quite well. 

an average of 1 Pa with a standard deviation of SPa. 

The 3X packing used here is similar to the 4X described earlier, with a surface area a p of 133 m2 /m3 and a diameter dp of 28.S mm. Two stacks, each 

0.30-m long, were placed in a water free-fall length of 0.8 m. 

Because of its larger equivalent diameter, some condensation occurred in the 

free-falling water jets as it did with the 4X packing. Therefore, we did comparisons using two lengths, namely, the packing length of 0.61 m and a total 

free-fall length of 0.8 m. 

Figure 4-14 shows the condensed steam comparison. Predictions for ~ = 0.61 m 

and ~ = 0.8 m are included. The experimental data generally fall within the 

two predictions. The differences between the predictions (at ~ = 0.8 m) and 

the data yield an average of 1.1% with a standard deviation of 1.S%. 

S1 
S=~II_I 

50 co 

0 

.... 

0 

" 0 

c.? 

.l: 

CD 

40 ~ 

ell 

0... 

(Jl 

(Jl 

.2 30 Q) 

.... 

::::l 

(Jl 

(Jl 

Q) 

.... 

Q. 20 "0 

Q) 

.... 

::::l 

(Jl 

ell 

Q) 

~ 10 

Predicted pressure loss (Pa) 

Figure 4-13. Pressure loss comparison for 19060 

packing in countercurrent flow 

E 

co 

Q) 

u:; 

"0 

Q) 

(Jl 

c 

Q) 

"0 

C 

o 

() 

"0 

Q) 

'-

::::l 

(Jl 

co 

Q) 

2 

100r---------------------------------------~~ 

Q, = O.S ----'~ 

Q, = 0.61 m 

90 

SOL-__________________ ~ __________________ _ 

.... 

o 

N 

o 

c.? 

.l: 

III 

SO 90 100 

Predicted condensed steam !%) 

at Q, = 0.61 m 

Figure 4-14. Comparison of condensed steam for 

3X packing in countercurrent flow 

52 

TR-3108 
TR-310B 

Figure 4-15 shows the comparison of pressure loss with ~ = O.B m. The pressure 

loss is insensitive to length in the range of ~ = 0.61 to O.B m. The experimental data exhibit large scatter around the predictions. The differences 

between predictions and data yield an average 2 Pa, but with a large standard 

deviation of 12 Pa. The ~p measurements possess an uncertainty of ±10 Pa. 

4.2.4 Plasdek 27060 Packing 

This packing possessed the highest equivalent diameter of the packings tested 

in countercurrent flow. A single stack length of 0.61 m was placed in a water 

free-fall length of 0.8 m. 

Figure 4-16 shows the comparison of condensed steam between the data and predictions using the full water free-fall length of O.B m. The differences 

between predictions and data yield an average of -0.6% with a standard deviation of 0.7%, well within the experimental uncertainty of ±2%. 

Figure 4-17 shows the pressure loss comparison for this packing, demonstrating 

excellent comparison between data and predictions. The difference between 

predictions and data yields an average of 3.6 Pa with a standard deviation of 

3.4 Pa, well within the ~p measurement uncertainty of ±lO Pa. 

4.2.5 Summary of Countercurrent Condenser Findings 

Our investigation of using structured packing in a countercurrent condenser 

resulted in the following accomplishments and findings: 

• We tested four different geometries for the packing with widely varied surface areas per unit volume. 

60 

50 

-co 

0.. CtJ 0 C/) 40 0 C/) 

.2 0 Q) 0 .... 0 

:J 

C/) 

30 C/) 

Q) 

Db .... 0 0.. CI 

"0 0 0 Q) 0 .... 

:J 

C/) 0 co 

Q) 

~ 

10 

0 

0 20 40 60 

Predicted pressure loss (Pa) 

Figure 4-15. Comparison of pressure loss for 3X 

packing in countercurrent flow 

53 
-:f2. 99 0 

E 

ro 

Q) 

en 

1:J 98 Q) 

en 

c 

Q) 

1:J 

C 

0 

(,) 97 1:J 

Q) 

'-

::::l 

en 

ro 

Q) 96 ~ 

o 0 

o 

8 

o o 

o 

o 

o 0 

o 0 

o 

o 

o 

o 

95 ~ ____ ~ ______ ~ ______ ~ ______ ~ ____ ~ 

95 

Predicted condensed steam (%) 

Figure 4-16. Comparison of condensed steam for 

27060 packing in countercurrent flow 

60~------------------------------------~ 

50 

-ro 

0-

~ 40 

o 

Q) 

'-

~ 30 en 

Q) 

'-

a. 

1:J 

~ 20 ::::l 

en 

ro 

Q) 

~ 

10 

O~ ____ ~~ ____ ~ ____ ~ ______ ~ ____ ~ ______ ~ 

o ~ W 

Predicted pressure loss (Pa) 

Figure 4-17. Comparison of pressure loss for 

27060 packing in countercurrent flow 

54 

TR-3108 
S5~1 < : TR-3108 

• The packing with the smallest dp of 14.7 mm exhibited a flooding limit of 

acceptable gas loading of 0.25 kg/m2 s. We also observed a similar capacity 

limit in cocurrent flow for this packing. 

• A maximum gas loading of up to 0.45 kg/m2 s was included in the tests. None 

of the other tested packings showed a flooding capaci ty limit over the 

tested loadings. 

• The packings with the largest diameter d exhibited the most influence of 

water free-fall; in other words, contribu~ions to condensation in the water 

free-fall areas outside the packing could not be ignored in the predictions. A simple but heuristic method of accounting for this contribution is 

to treat the condenser as if the packing extended all through the water 

free-fall area. With this approach, we achieved excellent comparisons 

between the model and data. 

• The model exhibited most of the trends observed in the experiments for all 

tested packings. Some discrepancies in the pressure loss comparisons are 

attributed to measurement difficulties. 

• Table 4-2 summarizes comparisons between predictions and measurements. For 

the tested 548 data points, the condensed steam predicted by the model differs from the data by less than 1.2% on the average, with a standard deviation of less than 2%. This deviation is comparable to the experimental 

uncertainty of ±2% in the measurements. 

• The model predictions of pressure loss differ from the data by less than 

4 Pa on the average; the standard deviation of the differences is less than 

6 Pa for three packings. For the tests with the 3X packing, considerably 

higher scatter in ~p measurements resulted in a standard deviation of the 

differences of 12.3 Pa. In general, the average and standard deviations of 

the ~p differences are comparable to the ~p measurement uncertainty of 

±10 PaD 

Packing 

Identifier 

AX 

19060 

3X 

27060 

Experimental 

Uncertainty 

Table 4-2. Cocurrent Condenser Comparison Summary 

Deviation (Prediction-Experiment) 

Condensed Steam (%) Pressure Loss (Pa) 

Number 

of Std. Std. 

Points Average Deviation Average Deviation 

60 0.9 1.9 2.2 6.0 

209 0.1 0.8 1.0 5.1 

33 1.1 1.5 1.9 12.3 

246 -0.6 0.7 3.6 3.4 

2.0 10.0 

55 
TR-3108 

4.3 Swmnary 

The validation efforts described in this section show that (1) the model captures the physical trends observed in the experiments over the entire range of 

test variables, geometries, and condenser configuration; (2) the model provides predictions comparable to the observations; and (3) the deviations 

between predictions and measurements are of comparable magnitude to the uncertainty in the measurements. Given the experimental data and their accuracies, 

no further effort is called for to improve the analysis and verification. 

Based on the entire sets of comparisons provided in this section, we find that 

the model provides predictions that differ from measurements well within 

acceptable limits for engineering design of direct-contact condensers. Hence, 

we conclude that this model is validated over the entire range of tested 

parameters reported here for both cocurrent and countercurrent condensers. 

These conclusions are based on fresh water results with injection of noncondensable gases into the steam. We anticipate extension of these results to 

seawater in the near future. 

56 
TR-310B 

5.0 NUMERICAL RESULTS AND PARAMETRIC STUDIES 

This section addresses the results of using the validated model over a wide 

range of geometric and flow parameters to show performance sensitivities and 

their potential effect on an overall OC-OTEC system. To illustrate the influence of key parameters on the condenser performance and to identify the best 

condenser configuration, we conducted two series of parametric studies for the 

co current and countercurrent condensers. The parameters are broadly categorized as geometric and flow. Table 5-1 lists the parameters studied. The 

model carried out calculations until the steam saturation temperature 

approached the cooling water temperature within O.OZoC. The condenser performance was characterized by the following three parameters: percentage of 

incoming steam condensed, the vapor pressure loss (Pa), and the length of the 

required condenser. This section presents the results for both a cocurrent 

condenser and a countercurrent condenser. 

5.1 Co current Condenser 

The co current condenser, as the first stage of the condenser subsystem, will 

condense 70% to 90% of the incoming steam. To use the cooling water effectively, we need to limit the water flow into this condenser to yield a Jakob 

number of less than one. Also, since the steam saturation temperature and the 

water temperature approach each other in cocurrent flow, we need to keep the 

pressure loss from reducing the steam saturation temperature significantly 

within the condenser. 

5.1.1 Condensation Process 

Detailed cocurrent condenser numerical results are shown in 

through 5-3. We used a Jakob number of O.B for the simulations. 

for area fraction af of one. 

Figures 5-1 

Results are 

Figure 5-1 illustrates how the temperatures vary with condenser length. Water 

temperature increases monotonically from an inlet value of 5°C to the steam 

saturation temperature at a condenser length of 0.75 m. The steam and inert 

gas mixture comes in at a saturation temperature of lZoC. The saturation temperature of this gas mixture decreases continuously with length. The steam, 

Table 5-1. 

Geometric 

Packing base B 

Packing height h 

Channel inclination e 

Effective area fraction af 

Condenser Parameters 

Flow 

Steam 

Gas loading G 

Inlet gas temperature+ Tsi 

Inlet inert gas content Xii 

Water§ 

Jakob number, Ja 

+Incoming steam was assumed to be saturated. 

§For all the studies, water inlet temperature was assumed to be 5°C. 

57 
TR-3108 

13 

Dry-bulb 

Saturation Superheat 

- 10 

() 

e..... 

Q) 

..... B 50 mm ::::l 

- 9 CIl h 50 mm ..... 

Q) 

0.. 

E 

B 60 deg 

at 1.0 - Q) 

I- 8 

G 0.4 kg/m2 s 

Xii 1.0 % 

Tsi 12.0 °C 

Ja 0.8 -

TWi 5.0 °C 

5~----~----~------~----~------~----~----~----~ o 0.2 0.4 

Condenser length (m) 

0.6 

Figure 5-1. Variations of temperatures within the condenser versus 

downstream distance in cocurrent flow 

0.8 

however, superheats through the process, attaining approximately 0.5°C superheat at the condenser length of 0.75 m. 

Also shown in this figure is the variation of the vapor-liquid interface temperature. At any length, the relative value of the interface temperature with 

respec~ to the water and saturation values indicates the relative magnitude of 

the liquid or the gas-side resistance to condensation. Generated with an 

inlet inert gas concentration of 1%, the interface temperature lies close to 

the saturation temperature at all lengths, indicating that the resistance is 

dominated by the liquid side. The condensation process was essentially complete at a length of 0.74 m. Approximately 74% of the incoming steam was 

condensed at this point. 

Figure 5-2 shows the variations of the condensing steam flux w (kg/m2 s), the 

static pressure loss lip (Pa), and the inert gas mass pe;centage in the 

steam. The steam flux decreases monotonically with length, reaching negligible values at the end. The pressure loss increases with length. At 0.4 m, 

almost 70% of the overall pressure loss has occurred. Note that the 

calculation abruptly stops at a length of 0.74 m. If the steam were allowed 

58 
55'1 1*1 

B 40 h 

e 

af 

35 

G 

Xii 

30 Tsi 

~ Ja ~ Twi -E _C\J 

t\l E t\l 25 Q.. 2 -~ (/) 

(/) Ol C (/) ~.-

0-- - c CD x CD "- :::l _ 

:::l:;:: C 

~ E 8 

CD t\l (/) 0: CD t\l 

enOl 15 -

"-CD 

C 

10 

5 

50 

50 

60 

1.0 

0.4 

1.0 

12.0 

0.8 

5.0 

0.2 

mm 

mm 

deg 

kg/m2 s 

% 

°C 

°C 

Interfacial steam flux 

0.4 

Condenser length (m) 

TR-3108 

~ 0 

N 

0 

(!) 

"= CD 

Inert gas mass percent 

0.6 0.8 

Figure 5-2. Variations of pressure loss, interfacial steam flux, and inert 

content in steam within the condenser versus downstream 

distance in cocurrent flow 

to flow through this packing for longer lengths (about 36% of the steam 

remains uncondensed), the saturation pressure of the steam would continue to 

decrease due to friction and eventually drop below the saturation pressure of 

the water. At excessive condenser lengths this condition will result in the 

water reevaporating, which is contrary to the basic process of condensation. 

Reevaporation will occur only in the cocurrent condenser with excessive pressure loss, thus lowering the steam partial pressure to values below the 

water's saturation pressure. To avoid reevaporation, the cocurrent condenser 

length must be limited to values less than those required for thermal equilibrium between steam and water, accounting for all causes of pressure 

losses. Thus, pressure loss in the cocurrent flow plays a key role in the 

condensation process and hardware design. 

Figure 5-2 also shows variations of inert-gas mass content of steam X., which 

increases monotonically from an inlet value of 1% to approximately 3%.~ 

59 
TR-3108 

Figure 5-3 shows the process of the steam and inert gas mixture a 

pressure-verslls-temperature diagram.. The saturat ion 1 ioe divides the steam 

into subcooled and superheated regions.. The also shows how the sta ic 

pressure of the mixture and part pressure of steam along the process 

path (along the condenser length). Both of these decrease 

continuously.. The temperature of the mixture however, ses init ly 

and then decreases" The ini tial increase occurs partly from the decreas 

gas mixture velocity caused by condensation and partly from ctional 

heating. The temperature eventually decreases as the heat transfers from the 

mixture to the water It The steam entering the condenser at saturation is 

driven into the superheated region as condensation proceeds in the 

condenser. For all conditions numerically simulated in this study, fog (vapor 

entering the subcooled region) never formed .. 

-ca 

D-

..lie:: 

-(I) 

lo... 

::J 

(/) 

(/) 

(I) 

lo... 

a.. 

B 50 

h 50 

8 60 

at 1.0 

G 0.4 

1.44 Xii 1.0 

Tsi 12.0 

Ja 0.8 

Twi 5.0 

1.42 

Subcooled 

region 

1.40 

1.38 

1.36 

1.34 pressure 

1.32 

mm 

mm 

deg 

kg/m2 s 

% 

°C 

°C 

Superheated 

region 

\\",0. 

\\0'" ,'3- c:,~'\.\}. 

pressure 

pressure 

1.30 L-_-'-__ ..I..-_--I __ .......I.-__ ..I..-.._--L. __ -'--_---" __ -"-_........i 

11.5 11.7 11.9 12.1 

Steam and inert gas mixture temperature (OC) 

Figure 5-3. Process path in cocurrent condensation 

60 
TR-3108 

5.1.2 Influence of Packing Geometry 

Geometric parameters that influence condenser performance include effective 

area fraction, packing size, packing height, and channel inclination 

(Table 5-1). Among these geometric parameters, channel inclination 8 and the 

effective area fraction af influenced condenser performance the most. 

5.1.2.1 Effective Area Fraction 

This fraction is the ratio of the active heat- and mass-transfer area to total 

available packing surface area. Although our experiments suggest that all of 

the area is active, under some circumstances only part of the area may be 

active in the transfer process. 

A larger af causes the liquid to spread over a larger surface, thus decreasing 

liquid-film velocity and the corresponding heat-transfer coefficient. 

Although this aspect may be detrimental, increased af also provides more surface area for the stearn to condense. In general, we find that larger af 

increases the overall condenser performance. 

Figure 5-4 depicts the results of increasing the effective surface area fraction af from 0.1 to 1.0. For this series we used the packing geometry for 

packing 19060, and the condenser length was fixed at 0.8 m. With increasing 

af' the percentage of condensed steam increased smoothly from a value of about 

45% at af = 0.1 to a maximum value of 86% at af = 1. The condenser pressure 

loss decreases continuously with increasing af' dramatically decreasing from 

nearly 150 Pa at af = 0.15 down to 35 Pa at af = 1. Because pressure loss in 

cocurrent flow reduces the condenser driving potential, a large value for af 

in cocurrent flow is beneficial. However, variation in af within the range of 

0.6 to 1.0 does not alter the condenser performance significantly. Thus, a 

packing with an assured af in the neighborhood of 0.8 or more is desirable for 

cocurrent flow. 

5.1.2.2 Packing Size (Base and height varied together) 

We investigated the influence of packing size by varying the packing base from 

10 to 120 rom and maintaining a height-to-base ratio of 0.35. 

Figure 5-5 shows the influence of varying packing size <af = 1). The important features of this figure are that the condensed stearn exhibits a max~mum 

and the pressure loss a minimum at a packing base value of 45 rom. However, 

the maximum and minimum are shallow; a variation between 30 to 70 rom results 

in a less than 1% change in condensed stearn and 4% change in the pressure 

loss. From this figure we also see that the required condenser length 

increases and the available surface area per unit volume decreases with 

increased packing size. 

These findings suggest that at any cocurrent condenser inlet conditions, 

although an optimum packing size may be identified, condenser performance 

reductions of less than 5% may be expected when size deviates from an optimum 

by as much as 30%. Larger sizes will allow for higher acceptable gas loadings 

with minimal bop. 

. 61 
_'Cf2. - co- e:.E 

(f) co (f) Q) 

.2 00 

Q)"O 

:.... Q) :::J (f) 

(f) C (f) Q) 

Q)"O 

:.... C 

c.. 0 

u 

150 

100 

50 

B 

h 

8 

at 

G 

Xii 

Tsi 

Ja 

Twi 

} Packing 

19060 

60 

varied 

0.4 

1.0 

12.0 

1.0 

5.0 

-

-

deg 

-

kg/m2 s 

% 

°C 

-

°C 

Condensed 

steam 

TR-3l08 

O.~----~--~----~----~----~-----L----~----~----~--~ o 0.2 0.4 0.6 0.8 1.0 

Effective area fraction, at 

Figure 5-4. Influence of effective area fraction on cocurrent condenser 

performance 

5.1.2.3 Packing Height 

The packing height of the experimentally tested articles ranged from 0.3 

to 0.4 times their base dimension. To identify any significant influence of 

this height in relation to base, we conducted a study with the base set at 

50 mm and varied the height from 0.1 to 1.2 times the base. 

Figure 5-6 shows the results of this height variation. With increasing 

height-to-base (his) ratio, the condensed steam percentage increases, and the 

pressure loss decreases. The required condenser length is again found to 

increase, and the surface area per unit volume decreases. No clear-cut maximum or minimum was found over the range of his investigated. Thus the his 

ratio should be .chosen based on a trade-off between the vapor pressure loss 

and the required condenser length. At an his ratio of 1, changes of ±10% in 

this ratio result in less than a 10% change in the condenser length and pressure loss. Hence, for the remaining set of co current parametric studies 

presented in this section, the ratio of his was set to 1 (unless stated 

otherwise). 

62 
5=~1 TR-3108 

B varied mm 

h 0.35B mm 

180 8 60 deg 

af 1.0 

160 G 0.6 kg/m2 s 

Xii 1.0 % 

E Tsi 12.0 °C 

....... Ja 1.0 

-Q) 

TWi 5.0 °C 

~ E E 

e......-O::J 120 ctl_-

EQ...!:o Pressure loss ctS- ...... > Q) CJ) Cl~ 

-CJ)c:c: 

CJ) 0 Q) 100 ::::l '0-- '- Q) Q) "- Q) CJ) '- Q) a. c: ::::l CJ) Q) CJ) c: ctl Condensed steam 'O~Q) Q) 80 c:,-'O '-

o a. c: ctl 

o 8 Q) 

(.) 

.E 

'- 60 ::::l 

CJ) 

'0 

c: 

ctl 40 1/4 x surface area 

per volume 

O~--~--~~--~--~----~--~----~--~----~--~--~ 

10 30 50 70 90 110 

Packing base (mm) 

Figure 5-5. Influence of packing size on cocurrent condenser performance 

5.1.2.4 Channel Inclination 

The channel inclination 8 from the horizontal for all the experimentally 

tested articles was 60 deg. Figure 5-7 shows the influence of this angle as 

it varies from 20 deg to 85 deg. Other packing parameters, namely, base and 

height, were fixed at 50 mmand 17.5 mm, respectively, resulting in a surface 

area per unit volume of 168 m2 jm3 • A clear-cut maximum in the condensed steam 

and a minimum in the pressure loss occur at 8 = 60 deg. The condenser length 

increased with increasing 8. At low values of 8, because of the accompanying 

large pressure losses, only short condenser lengths are needed. At 

8 > 60 deg, the pressure loss and the required condenser length increase 

simultaneously. 

Thus, for cocurrent condensers with this packing geometry, optimum performance 

occurs at a channel inclination angle of 60 deg. A deviation of ±5 deg from 

this optimum, however, results in a less than 2% change in the condensed steam 

and a less than 5% change in the pressure loss. 

63 
TR-310B 

B 50 mm 

150 h varied mm 

8 60 deg 

af 1.0 

G 0.6 kg/m2 s 

Xii 1.0 % 

Tsi 12.0 °C 

E Ja 1.0 ....... Twi 5.0 °C 

Condensed steam 

Pressure loss 

0.1 0.3 0.5 0.7 

1/4 x surface area 

per volume 

0.9 

Packing height-to-base ratio 

1.1 

Figure 5-6. Influence of packing height-to-base ratio on cocurrent 

condenser performance 

5.1.3 Influence of Flow Parameters 

Flow parameters that influence condenser performance include gas loading, 

inert gas content, Jakob number, and inlet gas temperature. To determine the 

effects of flow parameters on cocurrent condensation, we fixed the condenser 

packing geometry at a base and height = 50 mm, 8 = 60 deg, and af = 1. 

5.1.3.1 Gas Loading 

The condenser gas loading G is defined as the incoming steam and inert mixture 

flow rate per unit planform area of the condenser. The term "gas loading" is 

used in the conventional sense as found in chemical engineering literature. 

Figure 5-B illustrates the influence of G on cocurrent condensers at three 

different inlet inert gas percentages x·· (0.1%, 0.5%, and 1%) and at a water 

f1 . 11 . . ow rate correspond1ng to a Jakob number of O.B. Shown are var1at10ns of 

64 
S=~II*I TR-3108 

'" B 50 ~ mm 0 

'" h 17.5 mm 0 

(!) 

() varied deg .i: 

co 

af 1.0 

G 0.6 kg/m2 s 

Xii 1.0 % 

Tsi 12.0 °C 

160 Ja 1.0 

Twi 5.0 °C 

140 

120 

Condensed steam 

o~----~------~------~------~------~------~----~ 20 40 60 

Channel inclination, e (deg) 

80 

Figure 5-7. Influence of channel inclination on cocurrent condenser 

performance 

condensed steam percentage, pressure loss, and required condenser length.+The 

pressure loss increases nearly quadratically with increasing gas loading. 

Higher levels of inert gases result in higher pressure losses. The percentage 

of condensed steam decreases with increasing gas loading. Since the Jakob 

number is 0.8, the maximum possible value of 80% for condensed steam 

+The pressure loss and condenser length have been scaled by dividing by 2 to 

show salient features and preserve clarity in this figure. 

65 
TR-3108 

B 50 mm 

h 50 mm 

8 60 deg 

af 1.0 

100 G varied kg/m2 s 

Xii 0.1,0.5,1.0 % 

Tsi 12.0 °C 

Ja 0.8 

Twi 5.0 °C 

80 

Condensed steam 

20 

r Increasing Xii 

O~----~----~------~----~------~----~----~----~ 0.2 0.4 0.6 0.8 1.0 

Gas loading (kg/m2 s) 

Figure 5-8. Influence gas loading on co current condenser performance 

is approached at low gas loadings. Increased levels of inert gas in the stearn 

reduce the amount of stearn condensed. 

An important feature shown in this figure is the variation of required condenser length. The required length reaches a maximum at gas loadings that 

range from 0.4 to 0.6 kg/m2 s and then decreases with increasing G. We reach 

the maximum at lower values of G as the inert gas content Xii is increased. 

At gas loadings beyond the maximum length, the pressure loss ~ncurred during 

the initial lengths decreases the stearn saturation pressure enough to overcome 

the benefits of increasing the downstream length. As indicated earlier, 

lengths greater than those required would result in reevaporation and must be 

avoided. 

66 
TR-3108 

5.1.3.2 Inert Gas Content 

An inert gas content Xii in the turbine exhaust steam on the order of 0.1% or 

less is typical of OTEC systems that can predeaerate incoming water (Parsons, 

Bharathan, and Althof 1985). The gas content X .. may reach 0.5% in systems 

h + u... t at do not predeaerate the water. For the parametrl.c studl.es, three specific values for Xii were chosen: 9.1%, 0.5%, and 1.0%. The results of this 

study are included l.n Figure 5-8. The influences of increased X.· over this . h 1 % l.l. range are to l.ncrease t e condenser pressure oss by about 7 and to decrease 

the condensed steam by 5%. The required condenser length increases with 

increasing Xii for gas loadings of up to 0.5 kg/m2 s. At higher gas loadings, 

the influence of Xii on required length is minimal. 

Other results (not shown) to determine the optimum condenser geometry for 

cocurrent condensers with X·· from 0.1% to 0.5% indicated that a base value 

from 20 to 30 inm yields th€l.lowest pressure losses, with base = height and 

af = 1, at Ja = 0.8, and a gas loading of 0.6 kg/m2 s. Decreasing the gas 

loading to 0.4 kg/m2 s resulted in a larger base dimension from 40 to 50 mrn. 

5.1.3.3 Jakob Number 

The Jakob number for the condenser is defined as 

where 

mwi ,msi 

Twi,Tsi 

= incoming water and steam mass flow rates (kg/s), respectively 

= incoming water and steam saturation te~peratures (OC), 

respectively 

C

pw 

= average specific heat capacity of water (kJ/kg K)§ 

h fg = average latent heat of condensation for steam (kJ/kg)§. 

(5-1) 

A Jakob number of 1 represents the minimum water flow required to condense 

100% of the incoming steam flow given certain inlet water and steam saturation 

inlet temperatures. Conversely, it can also represent a minimum required 

steam inlet saturation temperature to condense all the steam for a given water 

flow rate and its inlet temperature. 

Note that two dimensionless parameters make up the Jakob number: ~wi/~si' a 

ratio of cooling water to incoming steam flow rate, and Cpw(Tsi - Twi)/hfg , a 

ratio of the potential sensible heat capacity of the water to the latent fieat 

of condensation. Thus, the Jakob number can be altered by varying either of 

these quantities. 

+These values include an estimated atmospheric al.r leakage into the vacuum 

enclosure. 

§For this study, Cpw = 4.186 kJ/kg K, and h fg = 2470 kJ/kg. 

67 
TR-3108 

For the following discussions, we define two other dimensionless quantities. 

The water effectiveness €w is expressed as 

which represents the ratio of actual water temperature rise to a maximum possible. An uncondensed steam percentage is defined as the percentage of steam 

that remains uncondensed in a particular condenser stage and, thus, must be 

handled by downstream equipment (a next-stage condenser or vacuum exhaust 

pumps). An ideal condenser subsystem with no pressure loss and no noncondensable gases present operates most effectively at Ja = 1. From the definitions, 

it follows that €w = 1, and uncondensed steam = O. 

At Jakob numbers other than unity, ideal condenser operational limits are 

established as follows 

• For Ja > 1, €w = l/Ja, and uncondensed steam % = a 

• For Ja < 1, €w = 1.0, and uncondensed steam % = 100 (1 - Ja). 

These cri teria yield the asymptotes that bracket a condenser performance ln 

Figures 5-9 through 5-13. 

For a real condenser subsystem, the presence of noncondensab1e gases requires 

a finite amount of uncondensed steam to be purged from the system. Pressure 

losses through the condenser hardware cause reductions in the steam saturation 

temperature from an inlet value and thus limit the sensible &T that the cooling water can take up. This loss reduces the water effectiveness to values 

less than unity. 

Because the .cocurrent condenser represents the first stage of the condenser 

subsystem, only part of the incoming steam needs to be condensed here. Thus, 

for this condenser, operating at a local Jakob number of less than unity is 

possible and desirable if a water effectiveness close to unity should be 

approached for the overall condenser subsystem. 

We varied the Jakob number from 0.4 to 1.2 by changing the water flow rate in 

the cocurrent condenser (Figure 5-9). For this figure, we fixed Tsi and T . 

at 12° and 5°C, respectively, and assumed a gas loading G of 0.6 kg/m2 ~: 

Asymptotes for €w and uncondensed steam bracketing the condenser performance 

are also shown. Uncondensed steam decreases with increasing Ja, and is always 

higher than that given by the asymptote. The pressure loss through the condenser increases slightly with Ja in the range of 0.4 to 0.6, and then begins 

to decrease with further increases in Ja. The required condenser length 

increases with Ja up to a Ja of 1.0 because more of the steam is condensed at 

higher Ja. Water effectiveness increases with decreasing Ja, reaching an 

almost constant value of 0.85 for Ja < 0.8. Note that the predicted €w values 

are always lower than the corresponding ideal asymptotic limits. An upper 

limit on €w of 0.85 results primarily from the vapor pressure losses on the 

order of 85 Pa at the assumed gas loading of 0.6 kg/m2 s. 

Figure 5-10 illustrates the features of Figure 5-9 at a reduced gas loading 

value of 0.4 kg/m2 s. Note that the condenser pressure losses were reduced by 

more than 50% from the previous figure to values of around 35 PaD The reduced 

68 
B 50 mm 

h 17.5 mm 

e 60 deg 

af 1.0 

G 0.6 kg/m2 s 

Xii 1.0 % 

Tsi 12.0 °C 

Ja varied 

120 TWi 5.0 °C 

Asymptote for Ew 

100 -------------------- --' ..... ' ...... 

TR-3l08 

............ 

F==-------==============~ ____ ~~:__,~----~E~w~----___ ....... " 

, 

20 

" , ....... 

"""' .............. 

....... ....... 

Asymptote for ~, 

uncondensed ............ 

steam ..... , ' ...... OL-----------~------------~--------~~----------~ 0.4 

Figure 5-9. 

0.6 0.8 

Jakob number 

1.0 1.2 

Influence of Jakob number varied via water flow rate on cocurrent condenser performance at G = 0.6 kg/m2 s 

pressure losses result in e: > 0.90 for Ja < 0.90. Both e: and uncondensed 

steam are closer to their c~rresponding asymptotes at this Yower gas loading 

of 0.4 kg/m2 s. 

For Figures 5-9 and 5-10, the assumed packing geometry was close to optimum. 

Thus, for cocurrent flow, to achieve a water effectiveness of over 85%, the 

gas loading should be limited to less than 0.6 kg/m2 s at an inert inlet concentration x.· of 1%. Lowering the X·· from 1.0% to 0.5% will allow either . ~~ • . .~:t. • h~gher gas load~ngs at a f~xed e: w or h~gher e:w at a f~xed G. 

69 
B 50 mm 

h 17.5 mm 

8 60 deg 

af 1.0 

G 0.4 kg/m2 s 

X·· .11 1.0 % 

Tsi 12.0 °c 

Ja varied 

120 TWi 5.0 °c 

Asymptote for water effectiveness 

100 --------------------

20 

"-

" " Asymptote for """ 

uncondensed steam " . "-

"-

"-

" " '" 

TR-3l08 

.6.p 

Uncondensed 

______ ____________ __________ ........ ____________ 

0.4 0.6 0.8 

Jakob number 

1.0 1.2 

Figure 5-10. Influence of Jakob number varied via water flow rate on cocurrent condenser performance at G = 0.4 kg/m2 s 

Figure 5-11 illustrates the effect of water flow rate on the condensation process in co current flow. This figure shows condenser heat load fer unit planform area versus steam and water temperatures at G = 0.6 kg/m s. An ideal 

condenser performance is depicted by an outer envelope, typical of condensation in the presence of inert gases. Lines of constant Jakob numbers 

originate at zero heat load and water inlet temperature. Low Jakob numbers 

represent low water flows. The intersection of a constant Jakob number line 

with the ideal envelope shows the outlet water and steam temperatures and the 

heat load taken by an ideal condenser. For the ideal envelope, we can achieve 

70 
TR-3108 

Ideal 

1.4 

Actual 

condenser 

~ 1.2 envelope 

~~ ct=> 

ylQ ". 

~ 

':)~ 1/ "'C)<O 

..-.. 1.0 CV ". '" E ". ,,;- / 1:0<0 

~ C). 

e. ,,9 / ,\C) 

~ C). 

"0 C). / co 0.8 ~' ..Q 

- ~"'~ /"'<.3 co 

Q) 

.!: c)"':- C)!><CO .... 

Q) 

~"''i>/ ", .• 0 

en 

c 

Q) 

"0 

c 

0 <;,/ () B 50 mm /(). ~<;, h 50 mm (). 

e 60 deg b./ (). 

af 1.0 / 0'2.6 ..- . 

G 0.6 kg/m2 s ..----..-o.~ 

Xii 1.0 % _o:\S 

0.2 Tsi 12.0 °C 

___ 0.2 

Ja varied 

Twi 5.0 °C 

0.0 

5 8.5 12 

Temperature (0 C) 

Figure 5-11. Cocurrent condenser operating diagram 

outlet water temperatures as high as the steam inlet temperature if Ja is from 

0.1 to 0.8. (At higher Ja, sensible cooling of the steam and inert gas m~xture begins to take place.) 

However, for an actual condenser, the outlet water temperature is considerably 

lower because of vapor pressure losses. In a range of Ja = 0.4 to 0.8, essentially a constant water outlet temperature is achieved for a real condenser. 

For Ja < 0.4, higher water outlet temperatures result; for Ja > 0.8, outlet 

water temperature begins to decrease. 

The Jakob number can also be varied with inlet steam saturation temperature 

for the co current condenser by holding the ratio m ./m . constant (at 84.3) W1 Sl 

71 
TR-3108 

and varying the steam inlet temperature. Figure 5-12 illustrates the variation of the condenser performance with ,Jakob number from 0~4 to 1.2 for two 

levels of Xii (0.1% and 1.0%) and G = 0.6 kg/m2 s. The differences between 

Figure 5-9 and Figure 5-12 are: 6p increases dramatically with decreasing 

steam inlet temperature and the Jakob number, causing €w to reach a maximum at 

Ja ~ 1; and uncondensed steam and €w deviate farther from their corresponding 

asymptotes as Ja decreases. 

A similar set of features is seen for G = 0.4 kg/m2 s in Figure 5-13. However, because of a lower 6p at lower G, deviations from the asymptotes in this 

figure are smaller. 

This series of parametric studies provides a designer with guidelines for 

choosing cocurrent condenser packing geometry and operating conditions. From 

the results reported, we can estimate performance parameters at design conditions and the penalties associated with deviations in parameters from chosen 

values. For optimal design, however, the condenser model should be incorporated into an overall system study to identify appropriate design choices. 

5.2 Countercurrent Condenser 

The countercurrent condenser, the second stage of the condenser subsystem, 

condenses the leftover steam flow from the first co current stage and concentrates the inert gases to the maximum extent possible before exhausting 

them. We expect this second stage will handle approximately 10%-30% of the 

total steam flow. Since the counterflow operation is generally more efficient, performance does not suffer as significantly in this stage from vapor 

pressure loss as in the first stage. Despite varying pressure losses, because 

the water temperature decreases in the direction of steam flow, more than 98% 

of the incoming steam is condensed in this stage. Thus, the minimum required 

water flow for this stage always corresponds to a Jakob number greater than 

one. 

5.2.1 Condensation Process 

Figure 5-14 illustrates detailed numerical results of steam condensation in 

counterflow in the presence of inert gases. Results are for packings with the 

effective area fraction af = 1. Figure 5-14 also shows the variation of various temperatures with condenser length. The condenser length is measured 

beginning at the bottom (the condenser bottom is on the left.). In this 

figure, the condenser is 0.37 m high. The steam and inert gas mixture enters 

the condenser from below at a nominally saturated condition of 12°C. Cooling 

water at 5°e corresponding to a Ja of 1.1 enters from the top. (Because 

numerical integration was carried out from the bottom, a series of iterations 

are required to match the cooling water temperature at any given height. 

Details of the integration and iteration processes may be found ln 

Appendix F.) The water temperature rises continuously from the inlet value to 

approximately 11.3°e as it reaches the bottom. 

The saturation temperature of steam decreases continuously; the rate of 

decrease is gradual in the first part of the condenser over lengths less than 

0.27 m, where most of the steam condenses. Farther from the inlet, the gas 

begins cooling with a sharp decrease in the saturation temperature. The drybulb temperature of the gas increases in the first part of the condenser, 

72 
TR-3108 

50 mm 

h 50 

8 60 

af 1.0 

G 0.6 kg/m2 s 

Xii 0.1,1.0 % 

varied °C 

Ja varied 

TWi 5.0 °C 

Steam inlet 1I'ornn,r:'>I"'!!,'I'. 

7.8 9.2 10.6 12.0 13.4 

120----------------------------~--------------~-------------

80 

40 

t Increasing Xii 

"-"-,,-

" , 

, 

, ........ ........ 

Asymptote for "-

uncondensed steam "'-

"-

, 

Asymptote for water 

effectiveness 

, 

-----............ 

"-", ....... ........ ....... 

' ..... " 

OL-__________ -L ____________ ~ __________ '~ ______ ======~ 

0.4 0.6 0.8 

Jakob Number 

1.0 1.2 

Figure 5-12. Influence of Jakob number varied via inlet steam temperature 

on cocurrent condenser performance at G = 0.6 kg/m2 s 

73 
TR-3108 

B 50 mm 

h 50 mm 

8 60 deg 

af 1.0 -

G 0.4 kg/m2 s 

Xii 0.1,1.0 % 

Tsi varied °C 

Ja varied - TWi 5.0 °C 

Steam inlet temperature (0 C) 

7.8 9.2 10.6 12.0 13.4 120r-------------~------------T_------------__ ------------_ 

80 

40 

Asym ptote for water effectiveness 

-------------- ------~ 

Uncondensed 

steam 

"" 

I 

" "'-

"-

" " "-

Asymptote for '" "-

uncondensed steam " 

" "-

" 

----------------"" 

t Increasing Xii "" 

........ 

" '~ ...... 

" " O~ ____________ ~ ______________ ~ ____________ ~W-____________ ~ 

0.4 0.6 0.8 

Jakob Number 

1.0 1.2 

Figure 5-13. Influence of Jakob number varied via inlet steam temperature 

on cocurrent condenser performance at G = 0.4 kg/m2 s 

74 
5='1,*, TR-3l08 

B 25 mm 

h 25 mm 

e 60 deg 

af 1.0 

13 G 0.4 kg/m2 s 

Xii 1.0 % 

Dry bulb Tsi 12.0 °C 

12 Ja 1.1 

5.0 °C 

11 

-

0 

10 

~ 

Q) 

.... 

::l 

- 9 ctS 

.... 

Q) 

c.. 

E 

Q) 

I- 8 

5 

0 0.1 0.2 0.3 0.4 

Bottom 

Condenser length (m) 

Figure 5-14. Variations of temperatures within the condenser versus 

downstream distance in countercurrent flow 

resulting from decreasing gas 

ature drops sharply 1n the 

cooling. 

velocity and frictional heating. This temperlatter part of the condenser because of gas 

Also shown in Figure 5-14 is the variation of the gas-liquid interface temperature. This temperature decreases continuously with length, following the 

water temperature. Again, the relative value of this interface temperature to 

the water and saturation temperatures indicates the relative value of gas- or 

liquid-side resistance to condensation. Near the bottom of the condenser, the 

interface temperature is close to the saturation value, implying a liquidside-controlled process. As more steam condenses through the length, the 

interface temperature moves closer to the water temperature, indicating a 

75 

'" '" .... 

0 

N 

0 

(!) 

.0: 

CD 
dominant gas-side resistance. 

incoming steam was condensed. 

TR-3108 

At the top of the condenser, nearly 99% of the 

Figure 5-15 shows the variations of the interfacial steam flux w (kg/m2 s), 

the pressure loss 6p (Pa), and inert gas mass percentage in steam~ The steam 

flux increases gradually from the bottom of the condenser, reaches a maximum 

midway, and then begins to decrease at the top. This maximum occurs because 

the largest driving temperature potential occurs somewhere in the middle of 

the condenser in countercurrent flow. The pressure loss increases monotonically with length. Initially, the rise in pressure loss is high; this rate 

is maintained almost halfway through the condenser. In the latter half, however, the pressure loss does not ~ncrease as rapidly. 

B 

h 

f) 

af 

60 G 

Xii 

Tsi 

Ja 

50 Twi 

40 

30 

20 

10 

25 

25 

60 

1.0 

0.4 

1.0 

12.0 

1.1 

5.0 

mm 

mm 

deg 

kg/m2 s 

% 

°C 

°C 

Interfacial 

Pressure loss 

Inert gas 

mass 

percent 

OLO~==~=====OI.1==::::==~-0~.2----~-----=0.L3::~~~t--~0.4 

Bottom Top Condenser length (m) 

Figure 5-15. Variations of pressure loss, interfacial steam flux, and 

inert content in steam within condenser versus downstream 

distance in countercurrent flow 

76 
TR-3108 

The inert gas mass concentration in the steam increases with condenser length 

as the steam progressively condenses. This increase is gradual in the first 

half of the condenser; the latter half concentrates the inert gases by a great 

amount, starting from almost the initial inlet value of 1% to an outlet concentration of 45%. The counterflow arrangement is efficient in achieving a 

high concentration of noncondensable gases and, thus, is best suited as the 

last stage of the condenser subsystem to reduce the load on the inert gas 

removal system. In fact, the counterflow arrangement is the most efficient, 

and if the turbine exhaust steam can be routed directly into a countercurrent 

condenser without other penalties, it should be considered. 

Figure 5-16 shows the countercurrent condensation of the steam and inert gas 

mixture state diagram, including static pressure, partial pressure of steam, 

and saturation pressure versus temperature. The saturation line splits this 

figure into subcooled and superheated regions. The gas mixture entering the 

condenser quickly goes into the superheated region. The static pressure 

decreases slightly initially and remains essentially constant in the latter 

half of the condenser. The steam partial pressure decreases continuously 

until it reaches a value corresponding to the water inlet saturation temperature. The steam and inert gas mixture, however, remains superheated by about 

1.5°C as it exits the condenser. 

1.5 

1.4 

1.3 

-

g: 1.2 .:.::: 

-

~ :::l 

CI) 

CI) 

~ 1.1 

0.. 

1.0 

0.9 

Subcooled 

region 

Partial 

pressure 

of inert gases 

Static pressure 

Superheated 

region 

B 

h 

e 

af 

G 

Xii 

Tsi 

Ja 

Twi 

pressure 

of steam 

25 

25 

60 

1.0 

0.4 

1.0 

12.0 

1.1 

5.0 

mm 

mm 

deg 

kg/m2 s 

% 

°C 

°C 

O.8~----~----~------~----~------~----~----~----~ 5 7 9 11 13 

Steam and inert gas mixture temperature (0C) 

Figure 5-16. Steam and inert gas mixture process path in countercurrent flow 

77 
TR-310B 

5.2.2 Influence of Packing Geometry 

5.2.2.1 Effective Area Fraction 

Experimental results suggest all surface area ~s effective for the tested 

packings in countercurrent flow. Figure 5-17 shows the influence of af as it 

varies from 0.1 to 1.0 for a fixed countercurrent packing length of O.B m. 

With increasingly higher effective fraction, the condensed steam increases 

monotonically, and the accompanying pressure loss decreases from a high value 

of 120 Pa down to 50 Pa. Changes in both of these quant i ties, when af is 

around O.B, are gradual. 

5.2.2.2 Packing Size 

We investigated packing size variation (base and height varied together) by 

varying the base dimension over 10 to 50 mm and holding a height-to-base ratio 

of 1.0. Calculations were continued to a condenser length where the steam 

saturation temperature was 0.02°e higher than the water inlet temperature. 

This condition, in effect, resulted in condensing almost a constant 98.8% of 

incoming steam for all cases. The results of packing size variation are shown 

~n Figure 5-18. The required condenser length, as expected, increases almost 

130 B 50 mm 

h 50 mm 

B 60 deg 120 af varied 

G 0.4 kg/m2 s 

110 Xii 1.0 % 

Tsi 12.0 °C 

- Ja 1.1 ~ 100 Condensed steam ~ TWi 5.0 °C 

caE 

Cl... to - Q) 

~(j) 90 

0"0 

- Q) Q) (/) 

'- C ::J Q) 

(/)"0 80 (/) C" 

~ 0 

Cl... (.) 

"0 

C 

to 70 

60 

50 

Effective area fraction, af 

Figure 5-17. Influence of effective area fraction on countercurrent 

condenser performance 

78 
S=~I TR-3108 

B varied mm 

150 h = B mm 

e 60 deg 

af 1.0 

130 G 0.4 kg/m2 s 

Xii 1.0 % 

Tsi 12.0 °C 

E Ja 1.1 .£ 110 -CIl..c Twi 5.0 °C 

CL- _ Ol 

00 c:: oo~ 

o lo.. 90 - Q) 

Q) 00 lo.. c:: ::J Q) 00"0 

~ c:: lo.. 0 

CL u 70 "0 

c:: Pressure loss CIl 

50 

30 

10~--------~--------~~--------~--------~--------~ 

10 30 50 

Packing base dimension (mm) 

Figure 5-18. Influence of packing size on countercurr~nt condenser 

performance 

linearly with the packing base dimension. The pressure loss shows a gradual 

minimum at a base of 25 mm. The variation of pressure loss over the entire 

range of base variation is less than 10%. Of course, larger packing size will 

allow for larger gas loadings without flooding. 

5.2.2.3 Packing Height 

The results of a parametric study varying the packing height-to-base (hiB) 

ratio from 0.1 to 1.2 at a base of 25 mm are shown in Figure 5-19 as plots of 

pressure loss, required condenser length, and surface area per volume versus 

the hiB ratio. Again in all cases, over 98.8% of the incoming steam was condensed. As expected, the required condenser length increases and surface area 

per volume decreases with increasing hiB ratio. The pressure loss decreases 

monotonically with increasing hiB ratio within the range investigated. As in 

co current flow, we could not find a clear-cut choice for the hiB ratio. A 

trade-off between vapor pressure loss and required condenser length on a 

system level must be made for an appropriate choice of hiB ratio. 

79 
TR-3108 

100 

1/4 x surface area 

per volume 

B 

h 

() 

af 

G 

Xii 

Tsi 

Ja 

Twi 

25 mm 

varied mm 

60 deg 

1.0 

0.4 kg/m2 s 

1.0 % 

12.0 °C 

1.1 

5.0 °C 

o~--~----~----~--~----~----~--~----~--~~--~--~ 

0.1 0.3 0.5 0.7 0.9 1.1 

Packing height-to-base ratio 

Figure 5-19. Influence of packing height-to-base ratio on countercurrent 

condenser performance 

5.2.2.4 Channel Inclination 

'" '" ,.. 

0 

N 

0 

(!) 

<I: 

co 

Varied channel inclinations provided the most significant influence on 

countercurrent flow as well. Figure 5-20 shows pressure loss and required 

condenser length. In all cases, over 96% of the incoming steam was 

condensed. The pressure loss exhibits a pronounced minimum at 8 = 65 deg. 

Variation of Llp over 55 ::; 8 ::; 70 is within 6% of the minimum value. The 

required condenser length also exhibited a rather flat minimum, which occurred 

over e values of 35 to 45 deg. At e = 60 deg, the required length was 6% over 

its m~n~mum. Since vapor pressure loss is a premium for OTEC applications, a 

channel inclination from 55 to 70 deg is clearly preferred for achieving 

optimum condenser performance. 

80 
TR-3l08 

100 

80 

E 

_u 

C1l ~ 60 

Q...L:; 

~c, en C o~ .... Q) Q) 

.... en :J C en Q) 

~ -g 40 

Q.. 0 

U 

"0 

C 

C1l 

20 

Length 

B 

h 

B 

af 

G 

Xii 

Tsi 

Ja 

Twi 

25 mm 

25 mm 

varied deg 

1.0 

0.4 kg/m2 s 

1.0 % 

12.0 °C 

1.1 

5.0 °C 

O~----~------~------~-------L------~------~----~ 20 40 60 80 

Channel inclination. B (deg) 

Figure 5-20. Influence of channel inclination on countercurrent condenser 

performance 

5.2.3 Influence of Flow Parameters 

In the following studies, the packing geometry was fixed at base B = 25 mm, 

height h = 25 mm, e = 60 deg, and af = 1.0. 

5.2.3.1 Gas Loading 

Figure 5-21 shows the influence of increasing gas loading G. The pressure 

loss increases monotonically with G, while the condensed steam remains close 

to 100% for G up to 0.55 kg/m2 s and then begins to drop off sharply because 

of increasing pressure losses. The required condenser length lncreases 

gradually for G up to 0.5 kg/m2 s and then shows a somewhat steeper increase 

for G up to 0.65 kg/m~ s, reaching a maximum of slightly over 1 m here. At 

higher gas loadings, because of large condenser pressure losses, the required 

length of the condenser begins to decrease. The results in this figure im~ly 

that gas loading perhaps should be limited to a maximum value of 0.65 kg/m s 

in practical situations at OTEC conditions. 

81 

o 

;: 

o 

N 

o 

(!) 

.i: 

CD 
200 B 25 mm 

h 25 mm 

e 60 deg 

180 Bj 1.0 

160 

G varied kg/m2 s 

Xii 1.0 % 

Tsi 12.0 °C 

E 140 

Ja 1.1 

TWi 5.0 °C <..l ~ - cf. _..c: 

-E ~ 0, 120 _ c: 

m (/)~ Condensed steam -(/) ... (/) 0 <1l 

~- (/) 100r------------------------------------t--------~~ __ <1l <1l c: (/) ... <1l c:::J~ 

<1l ~ c: ~ <1l 0 80 § 0.. <..l 

o -g 

co 60 

40 

20 

Condenser 

length 

TR-3108 

O--------~--------~--------~--------~--------~------~ 0.1 0.3 0.5 

Gas loading (kg/s m2) 

Figure 5-21. Influence of gas loading on countercurrent condenser 

performance 

5.2.3.2 Inert Gas Content 

0.7 

Increased levels of inert gas in the incoming steam resulted in an increase in 

the required condenser length and also a corresponding increase in the vapor 

pressure loss. We investigated inert gas content at three levels: X·· = 1%, 

3%, and 5%. The following section describes the combined effects Jl Jakob 

number and Xii" 

5.2.3.3 Jakob number 

The Jakob number was parametrically varied via water flow rate at a fixed T . 

and T . of 12°C and SoC, respectively. Figure 5-22 shows the influence ~t 

variel~Jakob number. Since over 98% of the steam is condensed for Ja > 1 in 

countercurrent flow, the water effectiveness can be related to the Jakob 

number simply as £ = 0.98/Ja. Shown in this figure are variations of pressure loss and a required condenser length for three levels of X .. : 1%, 3%, . . ~~ 1 and 5%. Increases ~n Jakob number cause decreases ~n both pressure oss and 

82 
TR-3108 

E 

~ 

100 

80 

co £ 60 a.. 0l -c 

~~ 

o .... - Q) Q) (J) 

.... C :J Q) (J)\::l 

(J) C 

~ 0 40 

a.. u 

\::l 

C 

('(l 

20 

\ 

\ 

"-

"-........ 

B 25 mm 

h 25 mm 

8 60 deg 

at 1.0 -

G 0.4 kg/m2 s 

Xii (%) Xii 1,3,5 % 

Tsi 12.0 °C 

Ja varied -

TWi 5.0 °C 

------- -------- -- ---

--.--.--

....... _ 1 

------- ------

---Length 

---t..p 

O~----------~----------~----------~----------~----------~ 1 1.2 1.4 

Jakob number 

Figure 5-22. Influence of Jakob number varied V1a water flow on 

countercurrent condenser performance 

'" '" .... 

o 

N 

o 

" .J: 

<Xl 

condenser length. Higher levels of X.. increase both of these quantities. 

Operating at conditions equivalent to a

1

}akob number of 1.2 is common in many 

mass transfer processes 1n the chemical industry. Operation at higher Ja 

results 1n inefficient use of cooling water. Despite somewhat increased 

requirements for vapor pressure loss and condenser length, the OTEC condenser 

is expected to operate over a Jakob number range of 1.05 to 1.15 to efficiently use cold water. 

The countercurrent parametric studies presented provide results for prelim1nary design choices. Critical choices in parameters such as channel 

83 
TR-3108 

inclination, gas loading, and Jakob number are required to assure optimum 

condenser subsystem performance. Choices on other parameters may be less 

critical. Detailed systems analyses should be pursued to arrive at design 

trade-offs on all the condenser choices as well as other components for a proto typical DTEC system. 

84 
TR-3l08 

6.0 CONCLUSIONS AND RECOMMENDATIONS 

6.1 Conclusions 

This work focuses on establishing the feasibility of direct-contact condensers 

for DG-DTEG applications. We examined a large number of potential packing 

materials and identified structured packing as the most suitable for the 

cocurrent and countercurrent stages of the condenser. We also achieved 

significant progress in the areas of model development, experimental investigation, model validation, and parametric studies. Under each category, the 

following paragraphs summarize the approach taken and describe the major 

achievements. These conclusions are based on fresh water tests with injection 

of noncondensible gases into steam. We anticipate extending these results to 

seawater in the near future. 

Model Development 

• We present a model for one-dimensional flow of steam condensing on water in 

the presence of a noncondensable gas in steam and water for cocurrent and 

countercurrent flow. 

• For flow through structured packings, the model uses established correlations for gas- and liquid-side heat and mass transfer. For liquid flow, we 

consider turbulent water film flow over an inclined plane. 

• For gas flow through one to two layers of packings, we used the friction 

correlation developed by Bravo, Rocha, and Fair (1986) in a Darcy-Weisbach 

formulation (see Table 2-2). 

• Because we evaluate heat, mass, and momentum transfers independently in the 

model, we show the vapor process path deviating from the saturat ion line 

during condensation and entering a superheated region. 

• We model the evolution of inert gas from the coolant during condensation as 

a diffusional process. 

• We implemented numerical schemes for integrating the process differential 

equations. 

• For countercurrent flow, we implemented efficient iteration schemes to match 

calculated water conditions with specified inlet water conditions. 

• We coded the cocurrent and countercurrent models in Turbo-Pascalm language 

so the program can be used on a standard IBM personal computer or other 

compatible computer. 

Experimental Investigations 

• We tested four different co current condenser geometries and presented the 

results in tables over a wide range of cocurrent condenser operating condi tions that bracket expected conditions for DTEG applications as can be 

simulated with the facility. 

• For countercurrent condensers, we tested four different structured packings 

and presented their results. The experimental data allowed us to establish 

flooding limits for the tested packing with the lowest equivalent diameter. 

85 
TR-3108 

• We tabulated extensive test results for evaluating experimental repeatability, consistency, and uncertainties. We estimated uncertainties for the 

measured parameters • 

.. For countercurrent condenser geometries not using structured packings, we 

provide entire sets of observed measurements in Appendix E. We provide 

comparisons of tests with and without structured packings to illustrate the 

advantages of using structured packings. 

Model Validation 

.. We provide extensive sets of comparisons between model predictions and 

experimental data for condensers using structured packings. 

• The model follows a majority of the significant trends observed in the 

experiments. Some discrepancies exist in pressure loss comparisons, as 

discussed below • 

.. The model predictions yielded condensed steam with an average deviation of 

less than 2.8% and standard deviation of less than 2.4%, as compared with 

the laboratory data for the tested structured packings. 

• The predictions for gas pressure loss yielded an average deviation of less 

than 4 Pa with a standard deviation of less than 6 Pa; exceptions to these 

are test data with 3X packing in countercurrent flow where the standard 

deviation is 12.3 Pa and test data for 19060 packing in cocurrent flow with 

an average deviation of -17 Pa and a standard deviation of 10.4 Pa. These 

discrepancies are small compared with the gas pressure losses in the condenser. We believe the discrepancies were caused by the pressure measurement lines becoming clogged with water during some of the experiments • 

.. With the noted exceptions, the model provides performance estimates of condensers well wi thin an uncertainty acceptable for engineering des ign of 

direct-contact condensers. For a two-stage condenser with a ±2% uncertainty 

in condensed steam for either stage at a design condition of 80% and 98% 

condensed steam in cocurrent and countercurrent stages, respect i vely, the 

resulting uncertainty in the overall condensed steam is less than ±0.5%. A 

designer may opt to use a third stage to reduce this uncertainty even more 

at the expense of 2% additional water usage, if desired. 

The shortcomings of the present model lie primarily in choosing a formulation 

for a local gas friction coefficient. Similar drawbacks in the experimental 

data lie in the large uncertainty and possible errors in 6p measurements. 

Parametric Studies 

.. For cocurrent and countercurrent condensers, we present detailed sets of 

parametric studies with geometrical and flow parameters. These results provide guidance in selecting suitable packing and operating conditions for a 

particular application. 

• The pressure loss in the condenser can be maintained low by choosing a channel inclination e in a range of 55 ~ e ~ 70 deg. Increasing packing size 

allows higher admissible gas loadings but requires longer lengths to condense a given amount. The maximum amount condensed is insensitive to the 

86 
base dimension in the range of 

height = 0.35 times base) and in 

current flow (with height = base) • 

TR-3108 

45 < B < 90 mm for co current flow {with 

the range of 30 < B < 60 mm for counter-

• For optimum use of condenser length, the maximum allowable inlet gas loading 

for cocurrent flow is limited to less than 0.6 kg/m2 s for co current flow 

and perhaps to 0.5 kg/m2 s for countercurrent flow. These limits arise 

because of increasing ~p with increased available condenser length. 

For the proposed seawater tests of direct-contact condensers at the heat and 

mass transfer scoping test apparatus, the major uncertainty in the condenser 

performance resides in the rate at which the dissolved gases may come out of 

solution within the condenser. Phenomena other than that modeled here, such 

as nucleation, may come into play. For three assumptions on the rate of 

deaeration (which are designed to bracket performance in seawater), Table 6-1 

summarizes the predictions of condenser performance via condensed steam and 

pressure losses. We expect to see about 1% difference in the condensed steam; 

the pressure loss difference under the worst condition of immediate gas 

release from the coolant is a 16-Pa increase. Thus, the expected performance 

differences for seawater use are minimal and within the predictive capability 

of the model. However, confirming this finding will have to await the 

completion of the proposed tests. 

6.2 Recommendations 

Based on the present study, the following future efforts are recommended for 

developing direct-contact condensers for OC-OTEC. 

• The two separate codes for the cocurrent and countercurrent stages should be 

combined to form an integral condenser code. This integration will allow 

identification of appropriate geometry and flow conditions for both stages 

in an optimal manner. 

• The fresh water properties used in the model should be supplemented with 

seawater properties such as viscosity, density, and most importantly, boiling point elevation or vapor pressure reduction. The phenomena of independent absorption and desorption of oxygen and nitrogen in cold seawater may 

require treating noncondensable gases as two individual species. 

• The model could be improved further by (1) using a formulation for turbulent 

film flow over inclined planes that might be expressed in a dimensionless 

form for use with liquids other than water and (2) a phenomenological model 

of condensation occurring in free-fall regions above and below the packing. 

• Entrance and exit losses should be treated in the model as they occur 

instead of being lumped together as a local gas friction :oefficient. Additionally, adequate care must be exercised in future tests to prevent the ~p 

measurement lines from becoming waterlogged to reduce the overall IIp measurement uncertainty. 

• Integrated staged-condenser designs identified for maximum performance in 

seawater should be fabricated and tested within the scope of the future 

experimental plan. Cooling water distribution manifold designs that result 

in minimum water and steam pressure losses must be pursued. Uniform gas and 

liquid distributions for cocurrent condensers require further study. 

87 
co 

co 

Table 6-1. Comparison of the Influence of Rate Deaeration on a Two-Stage Condenseri 

Fresh Water, 

no gas liberation 

Freshwater,~ 

gradual gas 

li beration 

Fresh water, 

immediate gas 

liberation 

Inert Gas 

In In 

Steam 

(%) 

0.35 

0.35 

0.70 

Water 

(ppm) 

o 

17 

o 

Cocurrent 

Condenser 

Condensed Pressure 

Steam (%) Loss (Pa) 

73 .83 45.45 

73.35 46.20 

72 .03 50.59 

iAssumed inlet conditions are: Tsi = 12.5°C; Twi = 5.0°C; 

Countercurrent§ 

Condenser 

Condensed Pressure 

Steam (%) Loss (Pa) 

98.13 43.8 

94.79 54.9 

94.79 54.9 

Gas Loading = 0.5 kg/m2 ~ (for cocurrent stage); 

= 0.4 kg/m2 s (for countercurrent stage). 

Jakob number = 0.8 for cocurrent and 1.2 for countercurrent stage. 

§Immediate gas release in a countercurrent stage does not affect its performance. 

~Assumed gas diffusivity in water 1S ten times the normal level. 

Overall 

Condenser 

Condensed Pressure 

Steam (%) Loss (Pa) 

99.5 89.3 

98.6 101.1 

98.5 105.5 

III 

III 

N 

.... -~ 

I J 

< -' 

., 

~ 

I 

w 

...... 

o 

00 
TR-3l08 

Many potential applications exist for direct-contact condensers. The presented design method may be modified to analyze condensers for other applications. Mass transfer processes occurring in the many gas-liquid contactors 

can again be modeled using the present approach with suitable modifications. 

This study evaluates the suitability of structured packings for use in OTEC 

direct-contact condensers. At OTEC conditions, these packings can accept gas 

loadings in a range of 0.4 to 0.55 kg/m2 s, translating to a heat rejection 

capacity of 1 to 2 MW t /m3 of packing volume. Typical volumetric heat-transfer 

coefficient ranges from 150 to 300 kW/m3 K. For any power rating, analytical 

results indicate that the turbine exhaust steam can be condensed by l-m-high 

condensers at water-flow rates of less than 10% over a thermodynamically 

required minimum with gas venting requirements of not over 10% of a thermodynamically required minimum. These results significantly reduce the coldwater flow rate and pumping power requirement and increase the costeffectiveness of OC-OTEC as a renewable energy resource. 

89 
TR-3108 

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90 
TR-3108 

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TR-3108 

Wassel, A. T., D. C. Bugby, A. F. Mills, and J. L. Farr, Jr., Science 

Applications, Inc., 1982 (Feb.), Design Methodology for Direct-Contact 

Fallin Film Eva orators and Condensers for 0 en-C cle Ocean Thermal Ener 

Conversion, SERI STR-25l-2256, Golden, CO: Solar Energy Research Institute. 

Webb, R. L., and A. S. Wanniarachchi, 1980, "The Effects of Noncondensable 

Gases in Water Chiller Condensers--Literature Survey and Theoretical 

Predictions," ASHRAE Transactions, Vol. 80, pp. 142-159. 

92 
D 

d 

E 

Gr 

h 

K 

r 

Sol 

V 

V 

Greek 

NOMENCLATURE FOR APPENDICES~ 

tube diameter (m) 

probe diameter (m) 

enthalpy rate (kW) 

Grashof number 

enthalpy (kJ/kg) 

pressure loss coefficient 

convective mass-transfer coefficient (m/s) 

contribution of kinetic energy (App. H) 

thermal conductivity (W/m K) 

probe length (m) 

packing stack length (m) 

vapor momentum 

volumetric flow rate (m3/s) 

RTD probe resistance (Q) 

recovery factor 

solubility (mole air/mole water) 

condenser vent fraction 

velocity (m/s) 

e coefficient of thermal expansion (I/K) 

E condenser effectiveness 

E' effective emissivity 

T shear stress (Pa) 

a surface tension (N/m) 

a Stefan-Boltzmann constant 

Subscripts and Superscripts 

adi adiabatic 

atm atmospheric 

D tube diameter 

d probe diameter 

e exhaust 

~See Nomenclature on page xiii for additional symbols. 

93 

TR-3l08 
TR-3l08 

NOMENCLATURE FOR APPENDICES (Concluded) 

In inlet 

id ideal (equilibrium conditions) 

nc natural convection 

p probe, pressure 

r radiative 

tip probe tip 

94 
TR-3l08 

APPENDIX A EXPERIMENTAL FACILITY AND INSTRUMENTATION 

A.I Introduction 

The experiments described here were performed in SERI's Low Temperature Heatand Mass-Transfer Laboratory in Golden, Colo. The laboratory, recently moved 

to a permanent location, allows us to investigate and improve methods of 

transferring heat and mass under the small driving potentials that often exist 

when the sun is the energy source. 

Our primary thrust was to examine direct-contact evaporators and condensers 

for OC-OTEC. The driving force for OTEC systems is a near 20°C temperature 

difference between warm surface tropical seawater and cold seawater pumped 

from depths of approximately 1000 m. Direct-contact devices are attractive 

since the liquid and vapor are not separated by a solid barrier. A solid 

barrier, such as those used in conventional surface condensers, adds to the 

thermal resistance that reduces heat transfer and overall performance. 

Increased transfer rates can lower component and overall system costs. For a 

fixed thermal load, lower resistance to heat-transfer results in smaller and 

less costly heat exchangers and containment vessels. Increased heat exchanger 

effectiveness also reduces the required liquid flow rate. The cost of the 

piping and pumps is proportional to the flow rate; therefore, seawater 

requirements affect the cost of OTEC systems because the seawater system cost 

is a large portion of the total cost. In addition, reducing the seawater flow 

lowers the power requirements of the pumps and condenser exhaust system. 

Because this power is subtracted from the gross generator output, lowering the 

seawater flow requirement increases the net available power. 

The thrust of our laboratory research is to understand the direct-contact 

heat-exchange mechanism and to simultaneously increase the transfer rates and 

decrease size and water flow requirements. These objectives are reflected in 

the research facility's design. 

A.2 Capabilities of the Facility 

A.2.I General 

A heat rate of up to 300 kW is transferred to the closed warm-water loop 

through a shell-and-tube heat exchanger. Another closed loop fired by natural 

gas boilers provides heat to the exchanger. The cold-water loop removes heat 

by routing the flow through vapor compression chillers. The warm- and coldwater loops exchange heat and mass in an evacuated test cell. Warm water 

flows through an evaporator in one end of the chamber, and cold water flows 

through a condenser at the other end, as shown in Figure A-I. Heat and mass 

are exchanged by evaporation of the warm water and direct-contact condensation 

of the vapor on the cold water. 

The pressure in the O-ring-sealed vacuum chamber is maintained by a threestage compressor train consisting of a booster, a rotary vane pump, and a 

liquid-ring vacuum pump. Inert gases, which affect heat- and mass-transfer 

rates, can be added to the steam through flowmeters to examine the effect 

vacuum leaks and desorbed gases that may evolve from using seawater have on 

95 
TR-3I08 

Figure A-I. Heat- and mass-transfer laboratory test chamber: condenser, 

left; evaporator, right 

condenser performance. We can measure the concentration of these noncondensable gases in the vapor at the vacuum exhaust or other points in the test 

chamber with a gas mass spectrometer. A solenoid butterfly valve in the line 

between the vacuum tank and the compressor train allows us to vary the venting 

rate and to seal the tank under vacuum for leak tests and inactive periods. 

Table A-I summarizes the facility's capabilities. 

A.2.2 Hardware 

This section documents the hardware specifications at the time of the reported 

tests. We modified the laboratory slightly when we moved it to its permanent 

location, particularly the piping lengths, but replication tests indicate the 

changes had no measurable effect on experimental results. Table A-2 lists the 

model numbers and other hardware specifications. Figures A-2 and A-3 show the 

laboratory in its former location. 

96 
A.2.2.1 Flow Loops 

Table A-i. SERI Low-Temperature 

Heat- and Mass-Transfer 

Laboratory Capabilities 

Parameters 

Heat rate 

Water temperature 

Water flow 

Threshold vacuum 

pressure 

Vent capacity 

Inert gas injection 

Chamber leak rate 

Units 

0-300 kW 

3-30°C 

0-50 kg/s 

700 Pa 

0-0.57 m3/s 

0-200 L/min 

0.5 mg/s 

TR-3108 

The water flow loops are constructed of carbon steel Schedule-40 plpe. Most 

of the pipes on the high pressure side of the pumps have a nominal pipe diameter of 6 in. The pipes that drain the test section on the suction side are 

approximately 8 in. in diameter. Pipes to the chillers and the separate 

boiler loop are 4-in. lines. Near the end of the tests on the countercurrent 

condenser geometries, we replaced a portion of the 6-in. pipe with a 3-in. 

pipe downstream of the pumps. This replacement accommodates 3-in. turbine 

flowmeters, which increased the accuracy of our measurements at lower flow 

rates over the previous 6-in. flowmeter (see Section A-4). All of the pipe 

connections, such as to valves and bends, are sealed with O-rings to minimize 

air leakage into the system. The capacity of the cold-water loop, approximately 4 m3 , is large because of the long piping run to the outside 

chillers. The capacity of the warm-water loop is near 1 m3 • 

Included in the lines are static mixers, flow straighteners, turbine flowmeters, and numerous valves to control flow rate and water routing. 

Figure A-4 shows the layout. The water circulation pumps are located in a pit 

3 m below the laboratory floor to ensure adequate suction head. The bearings 

of the centrifugal pumps have double mechanical seals and a stuffing box that 

is flooded with water to minimize air leakage. 

Table A-2. Heat- and Mass-Transfer Laboratory Hardware Model Numbers 

and Specifications 

Hardware 

Cold water pump 

Warm water pump 

Chiller 

Boiler 

WW heat exchanger 

Lobed blower 

Rotary compressor 

Liquid-ring pump 

Manufacturer 

Cornell 

Ingersol-Rand 

McQuay 

Hydrotherm 

Young 

Kinney 

Kinney 

Kinney 

97 

Model 

4RFB-6 

6x5xl0 HC 

ALR-llOAD 

MR-1800 B 

HF-802-ER-IP 

MB 2000 

KT 500 

KLRC-75 

Remarks 

40-hp electric motor 

20-hp electric motor 

Vapor compression 

Natural gas 

Shell and tube 

10-hp electric motor 

30-hp electric motor 

3-hp electric motor 
TR-3108 

Figure A-2. Vacuum test chamber with end caps rolled back 

Figure A-3. Water piping and an end view of the test chamber 

98 
TR-310B 

Fill/drain r---C><t-Fill/drain 

Chillers 

Filter 

Cold loop 

Cold 

water 

Dissolved 

O2 mon itor ,..------'----t::I<Jt---t 

3-in. flow 

meters 

Makeup 

line 

Water 

pumps 

Filter 

Warm loop 

in let,..-..... _____ --L---. Inert gas 

Boiler 

pump 

Boiler 

Strainer 

Static 

mixer 

.---C><l---l~ ""'E-----injection 

port Straightener 

6-in. flow 

meter 

Test Chamber 

~ __ ~ _____ -J 

To vacuum ~-O<1--""" 

exhaust system 

Straightener 

Warm 

water 

inlet 

6-in. flow 

meter 

Figure A-4. Schematic of laboratory piping 

A.2.2.2 Test Chamber 

The test cell is a carbon steel horizontal cylinder 1.B m long and 1.5 m in 

diameter with two clamp-on hemispherical end caps. The end caps are mounted 

on trolleys that can be rolled away from the cylinder. The evaporator and 

condenser modules with their water inlet manifolds and instrumentation are 

mounted directly on the end caps for easy fabrication and removal of the t~st 

articles. Two reservoirs under the heat exchanger sections of the test cell 

allow us to collect the warm and cold discharge waters separately. The test 

cell is equipped with four glass ports, two on top for lighting and two on one 

side for viewing and photographing. 

99 
TR-3108 

Two cold-water inlet pipes enter the test chamber, one on the lower part of 

the end cap and the other on the upper part. The warm-water inlet is on the 

upper part of the end cap. In addition to the water inlets and drains, SlX 

2.s-in. pipes through the end caps are used for instrumentation wiring. 

Because the system operates under vacuum, the closed water loops contain low 

levels of dissolved oxygen. Low oxygen levels along with a standard practice 

of keeping the test chamber sealed under vacuum during inactive periods limits 

corrosion of the test cell interior. 

A.2.2.3 Chiller and Boiler 

The chiller is composed of two independent refrigerant loops with two compressors each. There is one 2s-hp compressor and three 3s-hp compressors resulting in a total capacity of around 135 tons of cooling. Various combinations 

of compressor units are used to achieve stepwise steady-state heat rates from 

around 75 to 300 kW. 

A natural-gas-fired boiler supplies hot water to the heat exchanger in the 

experimental warm-water loop. The boiler has six independently controlled 

units with a capacity of around 56 kW each. A butterfly valve in the gas 

supply line for three of the units allows us to vary the heat rate continuously to match the cooling rate of the chillers and achieve steady-state conditions in the test chamber. 

A.2.2.4 Inert Gas Injection System 

Two Tylan mass flow controllers are used to control and measure the rate of 

inert gas added to the tank. Plumbing allows us to use either bottled gas or 

ambient alr. Continuously variable gas flow rates from 0 to 200 standard litres per minute are possible. Coupled with the steam production of the 

evaporator, these flow rates allow us to test the full range of possible inert 

gas level s in the steam entering the condenser that are typical for OTEC 

systems. 

A.2.2.s Vacuum Exhaust System 

The test cell is evacuated by a three-stage gas exhaust system consisting of a 

lobe blower, an oil-sealed rotary vane compressor, and a liquid-ring vacuum 

pump in series. The nominal venting capacity of the system is 0.57 m3 /s. A 

butterfly valve in the 8-in. line between the tank and the vacuum system 

induces a pressure drop that allows us to vary the actual venting rate at the 

tank continuously. A threshold pressure of 700 Pa can be attained in the test 

cell. At operating pressure the air leakage into the cell is less than 

0.5 mg/s (0.4 atmospheric cubic centimeters per second). The three stages of 

the vacuum system are water cooled. The gas passes through a separator to 

remove sealing and lubrication oil entrained in the exhaust before being 

vented to ambient. A noise-suppression curtain suspended from the ceiling 

reduces the noise level in the laboratory. 

A.3 Facility Changes after Relocation 

Most of the experimental facility description previously presented applies to 

the existing hardware at the permanent location. This subsection describes 

the minor changes. 

100 
TR-3l08 

The laboratory is now in its own independent single-level building. The 

boiler that supplies heat to the evaporator loop is in an attached room. The 

chiller that supplies cold water to the condenser is now on a pad directly 

outside the laboratory building. Relocating this equipment resulted in 

shorter water supply lines. The current warm- and cold-water capacity has not 

been measured, but we estimate that both loops are currently under 1 m3 • This 

change does not affect steady-state experimental results but does affect the 

response time to changes in operating conditions between runs. 

The compressed air supply in the new facility has a smaller capacity than that 

provided in the earlier facility. Therefore, supply pressure fluctuates more 

than it did when air was taken from a large building system. This change, 

however, does not affect the experiments when inert gas enters the chamber 

because air is introduced through mass flow controllers (see 

Section A.4.2.2). These controllers deliver constant mass flow under the current pressure fluctuations. 

The pump pit in the new building is 1 m deeper (4 m total) than the one at the 

previous location. This change results in less cavitation at the pump intake 

at low tank pressures and should not affect experimental results. 

A.4 Instrumentation 

This section presents an overview of the available instrumentation at the 

laboratory. We categorize the instrumentation in terms of the primary quantity to be measured, such as pressure, temperature, and flow. We discuss 

appropriate installation effects of probes and overall uncertainties in the 

primary measurements. 

A.4.1 Temperature 

Measuring the temperature is critical for OTEC processes because we are dealing with very low temperature differences; for example, about 3°C for the evaporator. To arrive at acceptable uncertainty in the measured evaporator or 

condenser effectiveness, the temperatures of the heat-exchange fluids must be 

measured within an uncertainty limit of a few millikelvins. The overall 

uncertainty of the temperature measuring system is affected by a variety of 

factors such as the choice of the probe, its calibration, installation, and 

environment. 

We quickly narrowed our initial choice of a probe down to platinum-resistance 

temperature detectors (RTD) because of their stable resistance-temperature 

relationship, inherently low measurement uncertainty of approximately 1 mK 

(O'Brien and Miller 1983), ruggedness, and reasonable cost. After reviewing 

various commercially available RTD probes, we chose the Rosemount 

Model 78S-0IN-0900 as the primary temperature sensor for all applications ln 

the laboratory. Table A-3 summarizes the specification of this probe as 

quoted by the manufacturers. 

Each RTD is connected in a four-wire ohm configuration to a digital voltmeter 

(HP model 34S6A) via a 20-channel relay mul t iplexer card housed in a data 

acquisition and control unit (HP model 3497A). A schematic of the temperature 

measurement system is shown in Figure A-S. We modified the relay multiplexer 

internally to allow four contact closures for the four-wire ohm measurement. 

Two relay cards allow us to monitor 20 RTD channels. 

101 
Table A-3. Platinum-Resistance--TemperatureDetector Specifications 

Resistance at oOe 

Sensitivity 

Lead wire configuration 

Range 

Repeatability over range 

Stability over range (1 year) 

Response time (water, 1 m/s) 

Material of construction 

100 Q 

0.0038S/ oe 

4-wire 

-200° to 660 0 e 

±o.osoe 

±0.2Soe 

5.0 s 

316SS 

TR-3108 

Two specific channels monitor the system measurement uncertainty continuously 

during tests. One channel was connected to a 4-wire ohm short circuit to 

monitor the zero-offset of the voltmeter. We used a second channel to monitor 

the voltmeter calibration by connecting a precision 100-Q resistor (Guideline 

Model 9330, calibrated 9/10/81, at 2S oe, 10 rnA test current, 100.0004 Q 

±0.0003 Q, temperature-coefficient, -0.0001 Q/K, stability, 0.001 Q/yr) housed 

in an insulated isothermal enclosure kept at room temperature within the 

laboratory. We continually monitored these two channels during the course of 

the experiments to apply appropriate corrections to the indicated ohm readings 

of the RTD probes. 

We performed a separate series of tests to estimate the uncertainty in the 

4-wire ohm measurement of the system using the above two channels. For these 

tests, the operation of the voltmeter was set for shifted 4-wire ohm function 

Digital 

voltmeter 

(HP 3456A) 

----

IEEE 488 

Data 

acquisition 

computer 

Data 

acquisition 

control unit 

(HP 3497A) 

Four-wire 

shielded cable ! 

(Trompeter Electronics TW-78-2) 

20-channel 

relay 

multiplexer 

(HP 44421 A) 

Platinum RTD 

(Rosemount 78-S) 

Figure A-S. Temperature measurement system 

102 
TR-3108 

with Auto-Zero, with the measurement taken over 10 power-line cycles, typical 

of the conditions during the operation of the experiment. A current of 1 rnA 

is applied to the unknown resistor during the measurement. The standard 

deviation in the 100-U resistance measurement over one month of tests was 

0.000223 U with a maximum deviation of 0.003526 U. Thus, the uncertainty in 

the ohm measurement is 30 = 0.000669 U. For 100-U platinum RTDs with a 

resistance-temperature coefficient of 0.385 U/K, the uncertainty in the temperature measurement is estimated to be 1.74 mK. 

Before installing the apparatus, we calibrated the RTDs using controlled temperature water bath facilities available at the SERI calibration laboratory. 

The calibration bath temperature is reproducible within ±5 mK in the calibration range of 0° to 40°C. The temperature was monitored using a high-purity, 

glass-enclosed platinum resistance RTD with its accuracy traceable to NBS 

standards. We measured the resistance of the calibrated probes within an 

uncertainty of ±1 mU. A typical set of calibration data for a particular RTD 

is shown in Table A-4. The calibration data were then fitted to yield temperature as a function of the measured resistance as 

T = a + bR + cR2 , (A-l) 

where T is the temperature in °c and R is the resistance in ohms. For each 

RTD, the predicted temperature differed from the calibration temperature to 

within ±2 mK (see Table A-4). 

Table A-4. Typical Calibration Data for RTD 

RTD+ 

Bath Probe Predicted 

Observation Temperature Resistance Temperature Residual~ 

No. (OC) R (OC) (OC) 

1 25.001 109.822 24.999 0.001 

2 30.002 111. 765 30.003 -0.001 

3 35.001 113.702 34.999 0.001 

4 40.001 115.638 40.001 -0.000 

5 19.999 107.877 19.999 -0.000 

6 15.012 105.933 15.0lD 0.002 

7 10 .001 103.979 10.003 -0.002 

8 5.007 102.026 5.007 -0.000 

9 0.005 100.067 0.004 0.001 

+Serial No 185225 

~Rounded to three-digit fractions. 

103 
TR-3108 

The combined effect of calibration errors and measurement-system errors 1n the 

temperature measurement is estimated to be less than 7 mK. 

The installation and environment of the RTD have the largest influence in 

determining the overall measurement uncertainty. Because these influences 

vary widely with the fluid media properties and the surroundings, we treat 

them separately for water and steam temperature measurements. 

A.4.1.1 Water Temperature 

In fluid appl ications, the probe faces a complex heat-transfer effect where 

the convective heat transfer between the fluid is balanced against radiative 

transfer between the probe, the fluid, and the surrounding and the simultaneous conductive heat transfer between the sensor and its support. Self 

heating because of the passage of measurement current introduces addi tional 

heat generated within the sensor that must be considered in estimating an 

"effective" sensor temperature. Benedict (1977) provides an excellent treatment of the problem with practical guidelines for evaluating various effects 

and avoiding installation errors. 

It is inherently clear that for obtaining least error, the dominant mode of 

heat transfer must be c.onvecti ve transfer between the fluid and the probe. 

Worst-case errors result when the fluid velocity is low and the difference in 

the temperature of the probe and its environment is large. 

Consider a typical water temperature measurement RTD installation as shown in 

Figure A-6. (Approximate dimensions of the probe, of diameter d, and the flow 

pipe are also included in this figure.) For a worst case, the water temperature is assumed to be at SoC; the surrounding ambient air is at 2SoC. The 

emissivity of the wall surrounding the probe is assumed to be unity. Assuming 

a low water flow rate of 5 kg/s, the flow Reynolds number around the probe is 

1180. Assuming a nominal Prandtl number for water of 10, we can estimate the 

convective Nusse1t number as 

Nu = 0.193 Re~.618PrO.31 = 31 • (A-2) 

With the thermal conductivity for water k = 0.57 W/m K, the convective heattransfer coefficient hc 1S 

kNu / 2 hc = --d-- = 2783 W m K. (A-3) 

Estimating an "effective" radiative heat-transfer coefficient requ1res estimating the pipe wall temperature. 

To estimate pipe wall temperature, we estimate the natural convective air-side 

heat-transfer coefficient using (Kreith and Bohn 1986) 

1/4 NUD = 0.53(GrDPr) , (A-4) 

where 

GrD (A-5) 

104 
Sensor tip 

(12.7 mm long) 

1+-------230 mm-------i~ 

Figure A-6. Typical water temperature measurement RTD installation 

TR-3108 

With the pipe diameter D = 165 mm, at standard atmospheric conditions, and 

T - Too = 20 K, we get 

GrD (1.225)2 9.81(3.5 x 10-3 ) 20(0.165)3 = ~----~--~--~------~~~--~----~- (1. 789 x 10-5 )2 

7 = 1.45 x 10 . (A-6) 

Then, for air, using Pr = 0.7, we get NUD = 29.9 • 

For air, with k = 26.24 x 10-3 W/m K, the effective heat-transfer coefficient 

~s 

26.24 x 10-3 

= 29.9 x 0.165 = 4.76 W/m2 K . (A-7) 

The approximate heat-transfer coefficient through the steel wall of 

thickness t is 

ks 

h =-

s t 

= 51.9 W/m2 K = 8.1 kW/m2 K • 

0.0064 m (A-8) 

For water flow through the pipe, the effective convective heat-transfer 

coefficient ~s 

ReD = 27,870; Nu = 220; hc = 1.67 kW/m2 K • (A-9) 

With these assumptions, we estimate an inner wall temperature of 5.07°C. 

lOS 
TR-3108 

The radiative heat-transfer coefficient between the probe and its environment 

is approximated as 

where 

a = the Stefan-Boltzmann constant, 5.67 x 10-8 W/m2 K4 

Tp,Tw = estimated probe and wall temperatures (K) 

E' = effective emissivity, approximated by (Benedict 1977) 

E' = 

T4. T4 

( adl - W) Ep 1 - Efl T4 _ T4 

P w 

(A-10) 

(A-ll) 

For T and T of 60 and SoC, respectively, we get hr '" 49 W/m2 K. Using 

Figur~ A-7 (B~nedict 1977, p. 248), we estimate 

1.0 

0.1 \ (') 

'" n:I n:I I 

a. ~ 0.01 j-:' ~ 

II 

>-

0.001 ::: 

1= 

lI-

~-

hcTadi + hrTw 

hc + hr 

\ ~ 

~ K "'-

"' '" . 

~ ........... I t', 

en 

;:: 

~ 

'" o 

<!l 

.( 

m 

0.0001 

o 2 4 6 8 10 12 14 16 18 20 22 

x = [

(he + hr)Ol [ L2 J 

k J 0 2 - d2 

Source: Benedict 1984 

Figure A-7. Summary curve of 20 step-linearized 

solutions for probe temperature calculations. Limits of 

variables (0 < E < 1), (0 < E < 1), (1 < k < 20), 

(1 < hc < 1000),w(2 in. < L < l~ in.), (1/16 in. < D < 2 in.), 

(0 < d < 1/4 in.), (70°F < T < l200°F) 

106 
TR-3l08 

The abscissa x, defined as 

x = [(he +Khr)O] [02 ~2d2] 

= [2.832 x 0.00635] [ 9 in. 2 ] = 

0.0519 0.875 in.2 0.25 in. 2 115.2. (A-12 ) 

This yields an ordinate value of <0.0001; i.e., if 

< 0.0001 Ttip - 5.0012 

= 0.0688 < 0.0001 , 

Thus, errors in the water temperature measurement because of installation 

effects are negligible. 

For continuous operation with a 1 rnA sensing current, self-heating generates 

100 ~w. Assuming this heat 1S lost by convection only, the probe temperature 

rise may be estimated as 

Q 100 x 10-6 

6T = -- = = 0.14 x 10-3 K • hc~d~ 2783 x 253.3 x 10-6 (A-13 ) 

Thus, an overall error in the water temperature measurement is estimated to be 

less than ±0.01 K. 

A.4.1.2 Steam Temperature 

The uncertainties in the temperature measurement, because of calibration and 

measurement system errors, are once again less than 7 mK. Installation 

effects, however, are considerably larger than for water, as we shall note 

below. 

Consider a worst-case steam temperature measurement with an assumed nominal 

saturated steam temperature of 5°C and a steam flow rate of 0.06 kg/s through 

the vacuum vessel of 1.52 m diameter, corresponding to a steam velocity of 

4.8 m/s. The probe Reynolds number is then 

Re = pVd = ( ___ 1 __ ) 4.84 (0.00635 ) = 25 47 

d ~ 147.2 8.2 x 10-6 •• (A-14) 

Note that this Reynolds number is extremely low. 

The mean Nusselt number can be expressed as Nu = 0.821ReO• 385 x 1.lPrO•3l 

(O'Brien and MilJef8~983). ~tth a steam Prandtl number of 0.82, we see that 

Nu = 0.903(25.5)· (0.82)0. = 2.95. 

The corresponding conductive heat-transfer coefficient is 

h -_ kNu 2.95(1.85 x 10-2 ) _- 8 61 wi 2 K 

C d = 0.00635 . m (A-15) 

107 
The stagnation temperature at the probe may be calculated as 

V2 

=T+ru-' 

p 

where r ~s the recovery factor, r = (Pr)1/2 , for laminar flow. 

Then, the adiabatic steam stagnation temperature ~s 

2 

Tadi = 5 + (O.B2)1/2 4.B4 = 5.0057°C 

21.B6 x 103 

The effective radiative heat-transfer coefficient may be calculated as 

hr = ae:' 

Assuming Tw = 25°C, and e:' ~ 1, we get hr = 5.43 W/m2 K • 

TR-310B 

(A-16) 

(A-17 ) 

(A-IB) 

(A-19) 

Assuming that the probe is completely immersed in steam, we can neglect conduction through the probe. In this case, the probe tip temperature can be 

calculated as 

Tt" = hrTw + hcTadi = 5.43(25) + B.6l(5.006) = 12 740C ~p hr + hc 5.43 + B.61 •• (A-20) 

Error in dry-bulb steam temperature measurement can be quite high. 

Now consider the case of the steam saturation temperature measurement using a 

wet bulb where the probe tip is covered by a wick constantly kept wet by the 

internal wicking action from a reservoir contairiing water. 

The typical wet-bulb probe schematic is shown in Figure A-B. The convective 

heat transfer to the probe is now enhanced by heat transfer associated with 

mass transfer in the form of evaporation or condensation. Neglecting radial 

temperature distribution within the probe, we may write a heat balance equation for the probe as 

where 

= mass-transfer coefficient 

= mole fraction of steam in bulk 

= the mole fraction of steam at the interface temperature 

temperature). 

We can estimate Kc using the Colburn-Hougen analogy from hc as 

hc __ (SC)2/3 

KcPCp Pr , giving us Kc = 1.41 m/s. 

(A-2l) 

Ts (probe 

(A-22) 

Solving Eq. 3-21 iteratively then yields a probe surface temperature of 

Ts ~ 5.0l o C. 

lOB 
Probe 

Radiation 

/ 

Convective ......--- heat transfer 

Heat transfer 

....... 1---associated with 

mass transfer 

Wet wick 

Figure A-B. Wet-bulb steam temperature measurement probe 

~ 

TR-3108 

Thus, the error in steam saturation 

temperature measurement using a wet 

bulb, because of installation effect, 

1S significantly smaller than that 

for the corresponding dry-bulb measurement. Therefore, for all steam 

temperature measurements in the laboratory, we adopted wet-bulb probes. 

We estimated the overall system error 

in steam saturation temperature measurement to be less than ±0.02 K. 

A.4.2 Flow Measurement 

Next to temperature, flow measurement 

1S critical in achieving the overall system energy balance ln the 

laboratory. 

A.4.2.l Water Flow Measurement 

We measured the cold- and warm-water 

flow rates going into the heat 

exchangers using two 3-in. turbine 

flowmeters (Flow Technology Inc., 

Model FT-96C3000-LJC(s)}. We calibrated the response of the flowmeter 

as the number of turbine revolutions per unit volumetric fluid displacement 

(e.g., pulses/gal). The flowmeter output is in the form of a scaled 0-5-V 

pulse per turbine revolution. The manufacturers calibrated the meters regularly once a year. The calibration was repeatable within ±0.2% over the 

course of five years of operation. 

The elapsed time between pulses is measured using an electronic counter (Fluke 

Model 7260A), time-averaged to yield less than 0.1% error in the overall time 

measurement. 

Sources of error ln flow rate measurement arise from errors in estimating the 

cal ibrat ion "constant" and in measuring the elapsed time between pulses. 

Error 1n the water-flow measurement is estimated to be ±1% over the flow rate 

range of 5 to 15 kg/so 

A.4.2.2 Inert Gas Injection Rate 

Inert gas used in the investigation is compressed a1r available from the common laboratory utility line. For the tests, we injected gas into the vacuum 

chamber in the vapor space above the evaporator. The gas flow was monitored 

using two mass-flow controllers (Tylan Model FC262, 0-50 and 0-150 Std. 

L/min). Depending upon the requirement, we used either one or both of the 

controllers. The accuracy of the gas flow injection measurement is ±2% of the 

full-scale reading as quoted by the controller manufacturers. This specification translates into an uncertainty of ±0.02.g/s for injection rates of less 

than 1 gis, ±0.06 g/s for injection rates of up to 3 g/s and ±0.08 g/s for the 

maximum injection rate of approximately 4.1 g/s. 

109 
Table A-S. Summary of Uncertainties 

in Primary Measurements 

Condenser inlet conditions 

Steam temperature 

Total pressure 

Inert gas flow 

Water temperature 

Water flow rate 

Condenser outlet conditions 

Steam temperature 

Water temperature 

Pressure loss 

Exhaust pump conditions 

Steam temperature (dry bulb) 

Total pressure 

Volumetric flow 

±0.02°C 

±0.5% 

±2.0% 

±O.OloC 

±1.0% 

±0.02°C 

±O.OloC 

flO Pa 

or ±10% 

+20-0°C 

±0.5% 

±7% 

TR-3108 

A.4.2.3 Exhaust Volumetric Flow 

Inert gas and uncondensed steam are 

exhausted from the vacuum exhaust 

pumps as described earlier. The volumetric flow upstream of the firststage rotary blower 1S constant 

within ±3% over a range of inlet 

pressures from 1000 Pa to 3000 PaD 

We verified this constant volumetric 

flow rate by injecting known amounts 

of inert gas into the vacuum system 

under dry (completely void of water 

spots) conditions and by measuring 

the pressure and temperature of the 

gas upstream of the blower inlet. 

The measurements indicate that the 

volumetric flow of th1 blower 

remained constant at 0.56 m /s within 

±3% over an inlet pressure and temperature ranges of 1000 to 3000 Pa, 

and 6° to 27°C, respectively. We 

then inferred the volumetric flow of 

the exhaust gases just downstream of 

the condenser by correcting the volumetric flow upstream of the blower for 

pressure and temperature changes in the exhaust gas between the two stations. 

We estimate overall uncertainty in the inferred volumetric flow downstream of 

the condenser to be ±7%. The large uncertainty in this measurement arises 

primarily because of uncertainties in estimating 6p between the two stations. 

A.4.3 Pressure 

For these tests, we measured absolute pressure of the steam at three different 

locations; namely, above the evaporator, at the condenser outlet and at the 

vacuum pump inlet. Three absolute pressure transducers (MKS, Inc., model 

222BHS-A-0-IOO, O-IOO-mm Hg range) were used with three digital indicators. 

Errors in absolute pressure measurement arise from calibration errors, zeroshifts of the transducers, and reading errors. As quoted by the manufacturers, the overall error in the absolute pressure measurement is estimated to 

be ±O.5% of the reading over the tested range of 1000 to 3000 Pa of absolute 

pressure. 

We also used two differential pressure transducers to measure pressure losses 

in the steam flow. One of these was connected across the condenser packing to 

yield losses from condenser inlet to the vapor outlet. The second transducer 

measured the pressure difference between the condenser inlet to the inert gas 

exit location above the vacuum chamber. 

Errors in the differential pressure measurement arise from calibration errors, 

zero-shifts, and reading errors. Large zero-shift turned out to be a severe 

problem with these transducers. To compensate for zero-drift errors, all zero 

readings were recorded both at the beginning and end of each test run. The 

differential pressure readings were corrected using an average zero-reading 

110 
TR-3108 

for each run. Estimated errors in the differential pressure measurements are 

large, about ±10 Pa or ±10% of the quoted results, whichever is larger. 

A.4.4 Summary 

Table A-5 summarizes the uncertainties in the primary measurements. These 

uncertainties are then carried forward to provide uncertainty estimates for 

the deduced or inferred quantities such as water effectiveness and modified 

vent fraction. Analyses for inferring uncertainties in the deduced quantities 

are provided in Appendix B and summarized in Section 3.2. 

A.5 References 

Benedict, R. P., 1984, 

surements, New York: 

Fundamentals of Temperature, Pressure, and Flow MeaKreith, F., 

New York: 

John Wiley & Sons. 

and M. Bohn, 1986, 

Harper and Row. 

Principles of Heat Transfer, 4th ed., 

O'Brien, B., and S. Miller, 1983 (Nov.) "Thermocouples, RTDs Can Boost Temperature Measurement Accuracy," Ind. R&D, Vol 25. No. 11, pp. 96-100. 

111 
TR-3l08 

APPENDIX B MEASUREMENT UNCERTAINTIES AND THEIR PROPAGATION 

In this appendix we discuss experimental measurements and the parameters we 

used to describe condenser performance. We discuss the primary data taken for 

each of the condenser configurations, such as temperature and pressure, and 

define the derived parameters. In addition, we present the uncertainties or 

errors in the numerical values of these derived quantities arising from the 

primary measurement errors discussed in Appendix A. 

B.l Primary Data Measurements 

At every test condition, the raw experimental data include temperatures, flow 

rates, and pressures. We measured temperatures with platinum RTDs as discussed in Appendix A. We measured steam saturation temperatures at the top 

and bottom of the test articles using cotton wicks for wetting. At the 

bottom, we placed the RTD nominally 0.2 m above the water drain pool, which 

eliminated direct splashing of the temperature probe. The upper steam temperature probe was placed around 0.15 m above the water distribution plate for 

similar reasons. In both cases, the end of the wick trailed directly in the 

water resulting in full wetting. Water inlet and outlet temperatures were 

measured by probes placed in the inlet and drain piping just upstream and 

downstream of the test article. We measured the water flow rate by a turbinetype flow meter placed in the inlet piping. Inert gas injection ports were 

located near an upper corner of the tank on the evaporator side to allow the 

gas to fully mix with the steam before the mixture entered the condenser. 

We took three primary gas pressure measurements, the inlet pressure, the pressure drop through the test article, and the exhaust pressure at the vacuum 

pump inlet. In the first and last measurement points, we used absolute pressure transducers but measured the pressure drop with a differential instrument. Experiments varied the inert gas injection rate, the heat removal rate 

(reflected in varying water flow rate because inlet water temperature was 

nearly constant), and volumetric venting rate (achieved by closing the butterfly valve in the line between the condenser exit and the exhaust vacuum 

pump). The measured data are presented in Appendices D and E for all performed tests along with performance parameters. 

B.2 Consistency of Data 

The experimental data have a definite uncertainty associated with the measurements. These intrinsic uncertainties result in inconsistencies in redundant 

data. For our applications, these inconsistencies can be significant because 

of the small driving forces and pressure drops. To minimize confusion, we 

chose a set of nonredundant data as the baseline results and derived other 

results from them. We tried several schemes for eliminating data inconsistencies with varying results. The following scheme resulted in good agreement 

between derived and measured results and minimized errors in computing 

condenser performance parameters. 

The primary measurements are inlet steam temperature Tsi '. inlet water temperature T ., outlet water temperature T 0' water flow rate mw' inert gas flow • Wi W 

rate mi , pressure drop in the condenser ~p, and the temperature and pressure 

at the vacuum exhaust Tex and Pex ' respectively. The following procedure 

112 
TR-3l08 

finds the inlet and outlet absolute pressure and the outlet steam temperature 

from these values. 

We assume the steam 1S saturated, and saturation pressure can be calculated 

using the following equation: 

Psat(T) = A exp [8 - C/(T + D)] + E , in Pascals for T in °c , (8-1) 

where A = 161.7574, B = 18.4779, C = 4026.976, D = 234.738, and E = 3.73835. 

Therefore, the partial pressure of steam at the inlet is 

(B-2) 

The amount of steam condensed can be found from a heat balance, assuming the 

sensible heat content of the inert gas and the condensed steam is small 

compared with the latent heat of condensation: 

(B-3) 

where C is an average specific heat of water, nominally 4.186 kJ/kg °c, and 

hfg is E~ average heat of vaporization, nominally 2470 kJ/kg. 

We made an initial guess of the steam flow rate at the condenser outlet of 

ro so = rosc/lO. The total inlet steam flow rate 1S then 

msi = msc + mso • (B-4) 

The steam outlet mole fraction is found as 

Yso = (B-5) 

We guessed a new outlet flow rate by using the measurements made at the 

exhaust pump. First, we used the mole fraction of steam at the condenser exit 

to find the partial pressure of steam at the exhaust (at this point the steam 

is no longer saturated): 

PPsx = PexYso , (B-6) 

where P ex is the measured exhaust pressure. The steam outlet mass flow is 

then found using a known exhaust volumetric flow rate Qex as 

The variable 

calculations 

outlet steam 

R~ is the gas constant for steam. The process 

uS1ng Eqs. B-4 through B-7 is continued until the 

mass flow rate converges within 10-4%. 

(B-7) 

of making 

condenser 

Other condenser parameters are calculated as follows. 

fraction is 

The inlet steam mole 

113 
TR-3108 

Ysi = (B-8) 

The total inlet pressure 1S now inferred as 

(B-9) 

The total outlet pressure is found using the measured pressure drop 

(B-10) 

Outlet steam partial pressure 1S found from this and the calculated mole 

fraction 

The outlet steam temperature is found by using an 1nverse of Eq. B-1, as 

T 

so 

c 

= B - ~n[(P - E)/A] - D 

= T (pp ). sat so 

(B-11 ) 

(B-12) 

(B-13 ) 

For establishing the consistency of the data, in Figure B-1, the calculated 

T is compared with the measured T for the cocurrent condenser tests using 

19860 packing. Variations are mini~al and within the derived uncertainty of 

the calculations (presented in Section B.4). Similar variations are found for 

all experimental data sets. The following condenser performance parameter 

calculations use the derived absolute pressures and steam outlet temperatures 

to avoid inconsistencies because of measurement redundancies and errors. 

These inconsistencies are well within the derived error bands presented in 

Section B.4. 

B.3 Condenser Performance Parameters 

The data analysis presented here uses several common heat exchanger parameters 

as well as several less common parameters that we found to be particularly 

useful in understanding the performance of direct-contact devices for OC-OTEC 

applications. 

Effectiveness 

Effectiveness 1S defined as the ratio of the actual heat-transfer rate to the 

maximum possible heat-transfer rate. This parameter varies from zero to one 

with a value of one indicating a perfect device, such as an infinitely long 

countercurrent heat exchanger. For a condenser with noncondensable gases in 

the vapor, the maximum possible heat transfer is if the water outlet temperature is equal to the steam inlet temperature. Assuming a constant liquid 

specific heat and low condensate to coolant flow ratios, the effectiveness E 

can be defined as 

(B-14) 

114 
U 0 

-

Q) 

..... 

::J 

-co 

..... 

Q) 

a. 

E 

Q) 

-

E 

co 

Q) 

iii 

-

Q) 

-::J 

0 

"'0 

Q) 

..... 

::J 

(f) 

co 

Q) 

~ 

Figure B-1. 

20 M 

0 "" 

N 

0 

C!) 

..i: 18 CD 

16 

14 

10 

8 

8 10 12 14 16 18 20 

Calculated outlet steam temperature (0 C) 

Comparison of measured and calculated steam outlet 

temperature for cocurrent packing 19060 

TR-3l08 

This definition does not account for heat exchanger geometry. In a cocurrent 

condenser where the streams flow in the same direction, the maximum possible 

heat transfer results in equal vapor and liquid outlet temperatures. It is 

possible to find this equilibrium outlet temperature T* from a heat balance: 

(B-15) 

The maximum amount of steam that can be condensed for a given set of conditions, msc,max (where Tso = Two), is a function of the inert flow rate, inlet 

steam temperature, and condenser pressure. We have assumed no pressure drop 

in the condenser for these ideal calculations. The solution method is as 

follows: for a guessed T 0' the outlet steam partial pressure is found using 

Eq. B-2. The outlet iner1 gas partial pressure and known mass flow rate can 

then be used to determine the amount of steam condensed: 

P = Psat(Tsi)/(l - Yii) (B-16) 

PPio = P - Psat(Tso) (B-1?) 

mso = (Ms/Mi)mi (1 - P/PPio) (B-18) 

msc = msi - mso (B-19) 

The amount of steam condensed is then used in the heat balance of Eq. B-15. 

These equations are solved iteratively until Tso and Two agree. 

115 
TR-3108 

A modified effectiveness E* can then be defined that considers that the 

maximum possible temperature difference Ln a countercurrent geometry is less 

than Tsi - Twi: 

Mass Fractions 

Two - Twi 

T~'( - Twi (B-20) 

Inlet and outlet inert mass fractions are easily found from mass flow rates 

Gas Loading 

Xii = ~i/(~i + ~si) 

Xio = ~i/(~i + ~so) 

(B-21) 

(B-22) 

The gas loading is simply the inlet steam and inert gas mixture flow divided 

by the cross-sectional area: 

(B-23) 

Area represents the cross-sectional area of the gas-liquid contacting device. 

Percentage of Steam Condensed 

The percentage of steam condensed LS on a mass basis 

Jakob Number 

A Jakob number LS defined as 

Ja = ~Cpw(Tsi - Twi) 

msihfg 

B.4 Derived Parameter Error Analysis 

(B-24) 

(B-25) 

The uncertainty in the primary measurements discussed in Appendix A has a 

definite effect on the certainty of derived condenser performance parameters. It is possible to estimate these derived parameter uncertainties. 

This section presents error estimates for both cocurrent and countercurrent 

experimental tests with 19060 packing; errors are similar for the other 

packing media. 

The method for estimating the propagation of errors, as well as the errors 

associated with the primary variables, is taken from Kline and McCl intock+. 

Table B-1 shows the error ranges for the 19060 packing Ln countercurrent 

+K1ine, S. J., and F. A. McClintock, 1953 (Jan.), "Describing Uncertainties in 

Single-Sample Experiments," Mechanical Engineering, Vol. 75, No.1, pp. 3-8. 

116 
TR-3108 

tests. Briefly, the errors are estimated as the sum of the squares of the 

partial derivatives of the equations with respect to the primary variables 

times the errors in the primary variables. For example, if a derived 

parameter Y is a function of other variables A, B, and C: 

Y = f(A,B,C), 

and the error estimates of A, B, and C are known and represented by ~A, ~B, 

and ~C, respectively, the error of derived parameter Y with approximately the 

same confidence level is 

(B-26) 

This error estimation 1S commonly used and gives a good estimate of the actual 

errors. As an example, the error in effectiveness defined in Eqs. B-14 is 

computed as 

AE = {( ATwo )2 

Tsi - Twi 

+ [(Two - Tsi)ATWij2 

( T . - T .)2 S1 W1 

+ [(Twi - Two)~TSij2}~ • 

(Tsi - Twi)2 

(B-27 ) 

The relative error can be found by dividing by the actual value of computed 

effectiveness as (AE/E). 

This process assumes that the functional form of Eq. B-26 is correct. Errors 

resulting from assumptions in the equations are not included. In our case, 

the only assumptions affecting the analysis are that the sensible heat capacity of the vapor and condensate is negligible compared with the latent heat 

Table 8-1. Countercurrent Derived Parameter 

Uncertainty Estimates 19060 Packing 

Derived Parameter 

Gas loading 

Jakob number 

Inlet inert mass fraction 

Outlet inert mass fraction 

Effectiveness 

Percentage condensed 

Inlet pressure 

Outlet pressure 

ll7 

Error Range (%) 

2.4-2.6 

1.8-2.0 

2.3-2.5 

2.0-4.5 

0.2-0.7 

1.7-2.0 

0.1-0.2 

0.4-0.9 
TR-3l08 

of condensation, that the ideal gas law holds (used for volumetric flow 

calculations), and that the curve fits for saturation temperature and pressure 

are accurate (standard deviation for our data ranges was 0.3%). 

The pr~mary uncertainties in the experimental measurements are presented in 

Appendix A. Table B-2 presents these values again along with the uncertainties in several other parameters used in the analysis. 

It can be seen that the derived uncertainty depends on the value of the experimentally measured variables. We computed the errors for every experimental 

condition along with the derived results. We also computed uncertainties for 

every parameter in intermediate calculations. Tables B-3 and B-4 show the 

complete results of the error analysis for a data point for each of the 

countercurrent and cocurrent tests using 19060 packing. The range of relative 

error for all the experimental data with these configurations are presented ~n 

Table B-5 for cocurrent flow and Table B-1 for countercurrent flow. 

Table B-2. Primary Uncertainties 

Temperature 

Water inlet 

Water outlet 

Steam inlet 

Steam outlet 

Exhaust 

Pressure 

Condenser inlet 

Condenser differential 

Exhaust 

Flow rates 

Water 

Inert gas 

Other 

Exhaust volumetric flow 

(0.5668 m3/s) 

Water specific heat 

(4.186 kJ/kg °C) 

Heat of vaporization 

(2470 kJ/kg) 

Column diameter 

(0.6096 m in 8 cases) 

Supply pipe diameter 

(0.1524 m) 

118 

O.Ol°C 

O.OloC 

0.02°C 

0.02°C 

10.00°C 

0.5% 

10 Pa or 10% 

0.5% 

1.0% 

2.0% 

3.0% 

0.5% 

0.6% 

1.0% 

0.5% 
TR-3108 

The only parameter with large errors is the pressure loss. These errors are 

the result of the large uncertainty in the pressure drop measurement. For 

these tests, the measured vapor pressure drop is very low, usually between 

2 and 20 Pa. The error in the pressure drop is 10 Pa. 

Table B-3. Uncertainties 1n Countercurrent Condenser Experimental Results 

Parameter 

Measured Parameters 

Steam inlet temperature 

Steam outlet temperature 

Water inlet temperature 

Water outlet temperature 

Steam exhaust temperature 

Inert mass flow rate 

Water mass flow rate 

Total inlet pressure 

Pressure drop 

Exhaust pressure 

Input Parameters 

Exhaust volumetric flow 

Heat of vaporization 

Water specific heat 

Value 

283.07 

281.82 

278.18 

282.54 

297.39 

0.3450 x 10-3 

0.6140 x 10 

1153.00 

11.14 

437.23 

0.56680 

2470.00 

4.18600 

Intermediate Calculated Results 

Cross-section area 

P sat (TSI) 

Ps t (TSOC) 

Ex~aust steam partial 

pressure 

Steam flow in 

Steam flow out 

Steam condensed 

Inlet gas constant 

Outlet gas constant 

0.27386 

1221.08 

1071.09 

385.28 

0.4696 x 10-1 

0.1591 x 10-2 

0.4537 x 10-1 

460.75 

440.80 

Intermediate Calculated Results 

Steam inlet p 

Gas inlet velocity 

Calculated Results 

Total inlet pressure 

Total outlet pressure 

Steam outlet temperature 

Steam loading 

0.9346 x 10-2 

18.347 

1226.66 

1215.52 

281.13 

0.1715 

119 

Units 

K 

K 

K 

K 

K 

kg/s 

kg/s 

Pa 

Pa 

Pa 

m3/s 

kJ/kg 

kJ/kg °c 

m2 

Pa 

Pa 

Absolute 

Error 

0.020 

0.020 

0.010 

0.010 

10.000 

0.6900 x 10-5 

0.6140 x 10-1 

5.765 

10.000 

2.186 

0.0170040 

14.8200 

0.020930 

0.00584 

1.64 

10.96 

Pa 2.99 

kg/s 0.59863 x 10-3 

kg/s 0.72751 x 10-4 

k~/s 0.59418 x 10-3 

Pa-m /kg-C 0.06 

Pa-m3/kg-C 2.84 

kg/m3 

m/s 

Pa 

Pa 

K 

kg/m2 s 

0.12537 x 10-4 

0.45648 

1.65 

10.14 

0.150 

0.00426 

Relative 

Error 

0.00007 

0.00007 

0.00004 

0.00004 

0.03363 

0.02000 

0.01000 

0.00500 

0.89767 

0.00500 

0.03000 

0.00600 

0.00500 

0.02132 

0.00134 

0.01024 

0.00776 

0.01275 

0.04573 

0.01310 

0.00013 

0.00645 

0.00134 

0.02488 

0.00135 

0.00834 

0.00053 

0.02484 
TR-3108 

Table 8-3. Uncertainties 1n Countercurrent Condenser Experimental Results 

(Cone! uded) 

Absolute Relative 

Parameter Value Units Error Error 

Fraction condensed 0.9661 0.0177 0.01828 

Jakob number 1. 0836 0.0201 0.01856 

Inlet inert mass fraction 0.7293 x 10-2 0.1717 x 10-3 0.02354 

Outlet inert mass fraction 0.1782 0.7309 x 10-2 0.04102 

Inlet inert mole fraction 0.4548 x 10-2 0.1074 x 10-3 0.02361 

Outlet inert mole fraction 0.1188 0.5226 x 10-2 0.04398 

Inlet steam mole fraction 0.9955 0.1074 x 10-3 0.00011 

Outlet steam mole fraction 0.8812 0.5233 x 10-2 0.00594 

Effectiveness (water) 0.8916 0.00419 0.00470 

Inlet volumetric flow 5.02969 m3/s 0.06402 0.01273 

Outlet volumetric flow 0.19738 m3 /s 0.00774 0.03919 

Table 8-4. Uncertainties 1n Cocurrent Condenser Experimental Results 

Parameter 

Measured Parameters 

Steam inlet temperature 

Steam outlet temperature 

Water inlet temperature 

Water outlet temperature 

Steam exhaust temperature 

Inert mass flow rate 

Water mass flow rate 

Total inlet pressure 

Pressure drop 

Exhaust pressure 

Input Parameters 

Value 

284.15 

283.99 

278.42 

282.86 

295.28 

0.3100 x 10-4 

0.5760 x 10 

1318.00 

16.50 

1284.09 

Exhaust volumetric flow 0.56680 

Equilibrium outlet temperature 283.37 

Water specific heat 4.18600 

Intermediate Calculated Results 

Cross-section area 

P sat (TSI) 

P t (TSOC) 

Ei~aust steam partial 

pressure 

0.27386 

1312.40 

1291.74 

1279.45 

120 

Units 

K 

K 

K 

K 

K 

kg/s 

kg/s 

Pa 

Pa 

Pa 

Pa 

Absolute 

Error 

0.020 

0.020 

0.010 

0.010 

10.000 

0.6200 x 10-6 

0.5760 x 10-1 

6.590 

10.000 

6.420 

0.0170040 

0.020 

0.020930 

0.00584 

1. 75 

10.96 

6.40 

Relative 

Error 

0.00007 

0.00007 

0.00004 

0.00004 

0.03387 

0.02000 

0.01000 

0.00500 

0.60606 

0.00500 

0.03000 

0.00007 

0.00500 

0.02132 

0.00133 

0.00783 

0.00500 
TR-3108 

Table 8-4. Uncertainties 1n Cocurrent Condenser Experimental Results 

(Concluded) 

Parameter Value 

Steam flow in 0.4866 x 10-1 

Steam flow out 0.5321 x 10-2 

Steam condensed 0.4334 x 10-1 

Inlet gas constant 461.47 

Outlet gas constant 460.91 

Intermediate Calculated Results 

Steam inlet () 

Gas inlet velocity 

Calculated Results 

0.1001 x 10-1 

17.757 

Units 

kg/s 

kg/s 

kfls 

Pa-m Ikg 

Pa-m3/kg 

kg/m3 

m/s 

Pa 

Pa 

K 

°c 

°c 

Absolute 

Error 

0.61662 x 10-3 

0.24221 x 10-3 

0.56701 x 10-3 

0.01 

0.10 

0.13309 x 10-4 

0.44110 

Total inlet pressure 

Total outlet pressure 

Steam outlet temperature 

Steam loading 

1312.92 

1296.42 

283.91 

0.1777 

0.8907 

1.1494 

kg/m2 s 

1.65 

10.14 

0.118 

0.00441 

0.0162 

0.0211 

0.1506 x 10-4 

Fraction condensed 

Jakob number 

Inlet inert mass fraction 

Outlet inert mass fraction 

Inlet inert mole fraction 

Outlet inert mole fraction 

Inlet steam mole fraction 

Outlet steam mole fraction 

Effectiveness (water) 

Inlet volumetric flow 

Outlet volumetric flow 

0.6366 x 10-3 

0.5792 x 10-2 

0.3960 x 10-3 

0.3610 x 10-2 

0.9964 

0.9996 

0.7749 

4.86331 

0.54024 

0.2863 x 10-3 

0.9372 x 10-5 

0.1788 x 10-3 

0.1789 x 10-3 

0.9372 x 10-5 

0.00324 

0.06192 

0.02481 

Table 8-5. Cocurrent Derived Parameter 

Uncertainty Estimates 

19060 Packing 

Derived 

Parameter 

Gas loading 

Jakob number 

Inlet inert mass fraction 

Outlet inert mass fraction 

Effectiveness 

Percentage condensed 

Inlet pressure 

Outlet pressure 

121 

Error 

Range (%) 

2.4-2.7 

1.8-2.0 

2.3-5.5 

3.4-5.0 

0.17-0.75 

1. 7-5.0 

0.12-0.14 

0.38-0.93 

Relative 

Error 

0.01267 

0.04552 

0.01308 

0.00001 

0.00021 

0.00133 

0.02484 

0.00133 

0.00783 

0.00041 

0.02481 

0.01821 

0.01835 

0.02366 

0.04946 

0.02367 

0.04954 

0.00018 

0.00001 

0.00418 

0.01273 

0.04593 
TR-3108 

APPENDIX C RELATIVE RANKING OF TESTED CONTACT DEVICES 

C.I Direct-Contact Design Considerations 

Several physical factors influence the design of direct-contact condensers. 

In selecting our test articles, we looked at 1 iquid-vapor interfacial area, 

liquid renewal, inert gas influences, liquid and vapor pressure drops, and 

other factors. 

Vapor-liquid interfacial area affects the overall transfer process rates. 

Gas- and liquid-phase heat- and mass-transfer coefficients, which are defined 

per unit area, are relatively insensitive to packing characteristic diameter 

(typical published correlations include an exponent of less than one for the 

Reynolds number). Therefore, maximizing the liquid-gas interfacial area 

results in the largest overall heat- and mass-transfer rates. Increasing the 

interfacial area usually means decreasing the characteristic packing dimension 

and results in smaller, more contorted vapor passageways that cause a larger 

frictional vapor pressure drop. In DTEC systems where the overall driving 

potential is only around 20°C, condenser vapor pressure drop should be minimized so the turbine can extract more energy. The trade-offs between increasing pressure drop and increasing condensation efficiency falls into the 

systems analysis area. We used a preliminary systems analysis to guide the 

design for the test articles described in this section. These results showed 

that pressure drops between 0 and 200 Pa were acceptable; that around 75%-90% 

of the steam should be condensed in the cocurrent section; and that the maximum possible of the remaining steam should be condensed in the second-stage 

countercurrent section. 

For open-cycle OTEC conditions, the transfer coefficients in the gas and 

liquid phases are of the same magnitude. High heat-transfer rates associated 

with direct-contact processes result in quick warming of the coolant surface. To maintain high transfer rates, the liquid surface needs to be renewed 

with the cooler liquid either by turbulent mixing within the liquid or by bulk 

remixing. Renewal of the liquid interface temperature is an obvious design 

feature of the test articles. 

Inert gases affect the performance of direct-contact condensers in several 

ways. First, the presence of inert gases lowers the bulk steam partial pressure, which is the driving force for mass transfer. Second, the inert gases 

are carried by bulk vapor flow to the coolant surface, and a gradient of noncondensable gases builds up. The diffusion of steam through this gradient is 

reflected by an increase in the gas-side resistance to mass transfer. 

Finally, the inert gases must be continuously removed from the condenser to 

prevent pressure buildup. Removing the inert gases from all portions of the 

condenser is a major design consideration. Any pockets where inert gases are 

allowed to build up are ineffective and reduce the overall effectiveness of 

the device. Inactive areas can be prevented by designs that do not allow 

local vapor veloci ties to drop and by intell igent placement of the exhaust 

intake. The first two effects are examined experimentally by controlling the 

inert gas content in the inlet steam. We discuss the effects of our exhaust 

system on the experimental conditions in Sections C.4 and C.S. The location 

122 
TR-3108 

of the exhaust intake and the vapor velocities in our experiments ensure that 

the effects of localized noncondensable-gas buildup are minimized or 

eliminated. 

All other factors being equal, a condenser with lower vapor and liquid pressure drop is desirable, especially in OC-OTEC applications. As previously 

mentioned, any reduction in condenser vapor pressure drop allows the turbine 

to extract a larger amount of useful energy. The 1 iquid pressure drop is a 

function of the frictional losses in the water piping, the height of the contacting device, and the height of the water distribution and collection systems. The pressure drop must be overcome by pumps, and the power required to 

run the pumps reduces the electric energy available from the complete power 

system. In OTEC systems this is especially critical since the turbinegenerator requires around 1600 kg/s of cold water per megawatt of electricity 

produced. Every meter of liquid head loss in the condenser results l.n a 

reduction of around 2% in the net power delivery of the system. 

Other factors to consider in designing the test articles are cost of materials 

and fabrication; modularity or ability to scale up to larger units; biofouling 

potential, which may be low for all cases because of low oxygen content in 

deep, cold seawater (Panchal et al. 1984); and potential maintenance problems. 

C.2 Existing Contact Devices 

Direct-contact devices are used extensively in chemical process industries. 

Direct-contact separators include many familiar types of hardware such as 

absorbers, strippers, distillation columns, and liquid extractors where mass 

exchange is the primary purpose. Cooling tower, flasher, and direct-contact 

condenser processes include heat and mass transfer. Many of the same principles apply for all the devices. For example, most designs incorporate methods 

for increasing interfacial area. Some of the designs suitable for our application of condensation are baffle trays (both segmental and disc-donut), spray 

columns, packed columns, tray columns, and pipeline contactors. Most of these 

designs can be used in cocurrent and countercurrent flow geometries. Several 

are also amenable to cross-flow. Literature on the performance and design of 

these devices are mainly limited to mass transfer alone. A review of the 

material available on direct-contact heat transfer was done by Fair (1961, 

1972). Most of the methods and experiments described in those articles and in 

applications are limited to conditions where the sensible and latent loads are 

of nearly equal magnitude. Little data are available for conditions where the 

latent load is the majority of the heat duty. 

Another factor of deviation from routine applications is the possibility of 

high levels of noncondensable gases in the steam. If seawater deaeration is 

not used upstream of the heat exchangers, the steam entering the condenser may 

have inert gas mass fractions near 0.2%. For the high-performance condensers 

considered in OC-OTEC applications, the inert gas mass fraction will increase 

up to 50% through the condenser stages. These levels of inert gases are much 

greater than those usually encountered in conventional power-plant surface 

condensers. The geometries we selected for this report are the next logical 

progression l.n developing direct-contact condensers for open-cycle 

applications. 

123 
C.3 Test Configurations 

C.3.! General 

To ascertain the relative merits 

among configurations, we tested a set 

of eight different methods of gasliquid contact in countercurrent 

flow. The first seven condenser test 

sections have several common features. We used a central l27-mm 1D 

PVC pipe to supply cold water to the 

unit. The pipe was centrally located 

as shown in the cross sections of 

Figure C-l. A cylindrical enclosure 

was used to contain the steam and 

water flow. 

For the countercurrent tests, outlet 

gas venting was through a centrally 

located l52-mm {inside diameter} pipe 

mounted nominally 0.2 m above the top 

of the water delivery pipe. The 

first four countercurrent condenser 

Steam 

and inert 

gas 

mixture 

inlet 

Figure C-l. 

TR-3l08 

Vacuum exhaust 

~~~=l:;~~' Water I: ~~ distributor 

..,....:..r+r"" plate 

Steam 

and inert 

gas 

mixture 

,.,. ...... -~ inlet 

Water Water drain 

inlet pool 

Countercurrent condenser 

configurations did not use a water distribution plate. Water exiting the distribution pipe cascaded freely onto the spiral screen or onto the first baffle 

plate. The last three countercurrent geometries used a water distribution 

plate located 25 mm below the outlet of the cold-water pipe. The plate was 

0.61 m in diameter and made of Plexiglas®. Water flowed downward through 

9.5-mm-diameter holes dri lled on a square pi tch of 25 mm. Six 70-mm-long, 

70-mm {inside diameter} plastic tubes mounted on the plate allowed upward 

vapor escape. For the eighth configuration, a 50-mm nozzle located nominally 

100 mm above the packing was used to distribute the water. 

C.3.2 Countercurrent Test Article Designs 

Table C-l describes the eight test-article configurations tested. Performance 

figures for all of the configurations were measured and calculated in countercurrent flow. Configurations 7 and 8 were tested in cocurrent flow as well. 

Figures C-2 through C-6 show the different condenser types. The first configuration is an innovative design with relatively unrestricted spiral vapor flow 

paths to minimize pressure drop, yet the screens renew the water surface temperatures by mixing and distributing the water evenly through the holes. The 

baffle plates of configuration 2 through 4 are a common contactor design that 

is simple to construct and has features that make it of interest for OTEC 

applications such as simple vapor paths. Configuration 5 is a variation of 

configuration 1 but is easier to construct. The water falls more freely downward without following the screw spirals because of a larger void area in the 

rubber screen. 

Configuration 7 uses a commercial structured packing used for contacting 

devices. Corrugated plastic sheets are attached with angles of 60 deg between 

124 
TR-3108 

Table C-l. Summary of Countercurrent Condenser Configurations 

Configuration 

1 

2 

3 

4 

5 

6 

7 

8 

Description 

Spiral 

screen 

Three 

baffles 

Two 

baffles 

One 

baffle 

Spiral 

rubber 

Hunters 

pack 

27060 

Hunters 

pack 

19060 

Jaeger 

Tri-Pack 

no. 1 

Length (m) 

0.61 

0.58 

0.58 

0.58 

0.78 

0.78 

0.78 

0.18,0.36, 

0.66 

125 

Diameter (m) Remarks 

0.46 Perforated metal 

screens with 4.7 mm 

diam. holes, triangular pitch of 6.4 mm, 

triple lead screw 

spiral with pitch of 

20 cm. 

0.61 Disc-donut baffles 

with 50% steam 

blockage and 20 cm 

spacing. 

0.61 

0.61 

0.61 

0.61 

0.61 

0.64 

Same as 2 except 

bottom disc and donut 

was removed. 

Same as 3 except 

bottom disc and donut 

was removed. 

Rubber screen with 

7.1 mm holes at 

10.7 mm pitch, 6 lead 

screw spiral with 

60-cm pitch. 

Commercial cooling 

tower fill polyethylene PLASdek 

27060,surf~ce area 

ratio 98 m 1m3 

Same as 6 with 

smaller corrugation 

height PLASdek 19060, 

surface ~rea ratio 

138 m2 /m 

Random packing polypropylene surface 

area ratio 157 m2 /m3 , 

equivalent diameter 

50 mm, 98% void 
Figure C-2. Spiral screen, condenser configuration 1 

Figure C-4. Spiral rubber mat, condenser configuration S 

a) 

<t) 

,-

s: 

'" 0 

y 

C126 

TR-3108 

Figure C-3. Baffle plate, disc 

donut, condenser configurations 2 

through 4 

Figure C-S. Hunters packing, condenser configurations 6 and 7 

:.n 

4-' 

r-

'" '" a 

C 

o. 
TR-3108 

adjacent sheets. The resulting matrix has relatively simple vapor flow areas, 

and the interfacial surface area is large. Dimples on the sheets promote 

liquid mixing. Configuration 8 used random packings (Jaeger Tri-Pack no. lot 

nominal 50 mm diameter) wi th an active surface area per volume of 157m2 imj 

and made of polypropylene. This packing was dumped into a 0.64-m-diameter 

cylinder. We used three different packing depths, 0.18, 0.36, and 0.66 m, in 

the tests. 

These test articles are not meant to be all inclusive of the options available 

for OTEC direct-contact condensers. Other geometries may be included 1n 

future tests. 

c.4 Performance Measures 

The relative performance of the tested condenser configurations 1S quantified 

by two parameters: a water effectiveness € and a vent fraction V. Considering that in a gas-liquid contact device, we aim to maximize the heat- and 

mass-transfer rates at a minimum pressure loss penalty, the above two parameters allow us to quantify the efficiency with which these two objectives are 

met in a device. Both of these parameters are defined to illustrate the deviation of a countercurrent condenser from its potentially maximum possible 

performance. 

The water effectiveness € 1S defined as 

(C-l) 

and represents the efficiency with which the available temperature difference 

potential is used. An ideal countercurrent condenser can operate at a m1n1mum 

water flow (corresponding to a Jakob number of unity) and yield £ = 1, in the 

absence of noncondensable gas. 

An ideal condenser, again, incurs no pressure loss. If p. and P represent . h d'l 11 0 • the stat1c pressures at t e con enser 1n et and out et, then for an 1deal 

condenser we have Pi = Pot. This condenser also reduces the partial pressure 

of the outgoing vapor to the minimum possible, in other words, to a saturation 

value at the coolant inlet temperature. In our case, this condition results 

1n 

(C-2) 

and causes a minimum amount of vapor to be carried away from the condenser by 

the venting system designed to remove the noncondensable gases. 

tRecovery of kinetic energy from the incoming vapor may result 1n P > p., but 

o 1 this effect is currently ignored. 

127 
Figure C-6. Condenser configuration 8 with random packing 

TR-3108 

The volume flow rate requirement Q 

for the venting system is then inversely proportional to the partial 

pressure of noncondensable gases at 

the exi t and is proportional to the 

gas absolute temperature 

1 PPio - 0:: --. Q Tio (C-3) 

For the ideal condenser, we may write 

the volume flow requirement as 

1 [Pi - Psat(Twi)] 

(Twi + 273.15) (C-4) 

The venting volume flow requirement 

increases for an actual condenser. 

Because of incomplete condensation 

within a finite length, the outgoing 

vapor does not come to equilibrium 

with the incoming water, in other 

words, Tso >,Twi • This results in 

lower partial pressure for the noncondensable gases at the exit. In 

addition the exit static pressure is reduced by lip, the incurred pressure 

loss. Thus, for the actual condenser, we write 

1 

- 0:: 

Q 

[Pi - lip - Psat (Tso)] 

(Tso + 273.15) 

Here Tso is the saturation temperature of the outgoing steam. 

Now the condenser vent fraction is defined as 

v = = 

(C-5) 

(C-6) 

We note that E = 1 and V = 1 represent the maximum ideal performance we may 

expect from the condenser. The condenser effectiveness E provides a measure 

of the heat- and mass-transfer efficiencies and V a measure of the pressure 

loss penalty. 

For the tested condenser configurations, we find that as E approaches one, V 

tends to be much smaller than one and vice versa. An efficient operating 

point lies where both E and V approach unity; this point must be found based 

on a study of overall system trade-offs. 

128 
TR-3l0B 

C.S Relative Performance 

The relative performance of the various tested condenser configurations are 

compared in a plot of water effectiveness versus vent fraction at similar gas 

loadings and noncondensable gas concentrations. For the disc and donut baffle 

contactors (configur~tions 2 through 4 of Table C-l), measured performances at 

0.35 < G < 0.45 kg/m sand 0.7 < X .. < 2.0 are shown in Figure C-7. For each 

h h h 11 . . geometry, t e test data s ow t at as E increases, V decreases and Vice versa. 

The top righthand corner of this figure wi th E = I and V = 1 represents an 

ideal condenser with possible maximum performance. The farther away from this 

corner a condenser performance falls, the worse it is. Within the set of data 

shown for the three configurations, the single pair disc-donut baffle yields 

the lowest performance, limited to a region of E < 0.6 and V < 0.4. Using a 

second pair of baffles improves the performance considerably, expanding the 

operating range to E < 0.7 and V < 0.65. For the tests with three pairs of 

baffles, the improvement in performance from the two pairs is only minimal. 

The three pairs allow operation at a vent fraction of up to 0.75. For the 

entire set of data for these types of contactors, the performance was limited 

to E and V less than about O.B. 

Similar comparisons of performance configurations 1, 5, 6, and B of Table C-l 

are shown in Figure C-B. Features similar to those shown in Figure C-7 are 

seen here as well. All sets of data in this figure yield performance measures 

higher than those for the disc-donut baffles shown in Figure C-7. Increasingly 

better performance was observed with the configurations in the following 

sequence: spiral screen, random packing, spiral mat, and structured packing. 

The data range for the random packing is limited to V < 0.4; although the data 

for rubber mat and random packing appear to be equivalent in this figure, the 

random packings yielded substantially higher vapor pressure loss (see tables 

'" 

CIl 

CIl 

Q.l 

1.0r-------------------------------------~ 

0.8 !-

~ 0.6!- > 

'0 

2 

-Q.l 

0.2 !-

Baffles 

o 1 pair 

1::. 2 pair 

• 3 pair 

0~ __ 1~~1 __ ~1 ___ ~1 __ 1~~1 __ ~1 ___ ~1 __ ~1_J 

o 0.2 0.4 0.6 0.8 1.0 

Figure C-7. Performance of countercurrent disc-donut baffle condensers 

129 
0.3 0 Spiral screen no. 1 - 0 Spiral mat no. 5 

0.2 !'" • 27060 packing no. 6 

0.1 I- ~ Random packing data range 

0 I 1 I I I I I I I 

0 0.2 0.4 0.6 0.8 

Vent fraction, V 

Figure C-8. Relative performance comparisons of countercurrent 

condenser configurations 

TR-3108 

ln Appendix E). Among the four sets of data shown for 0.35 < G < 0.5 kg/m2 s 

ln Figure C-8, the use of structured packing as the gas-liquid contactor 

yields the highest performance, with E falling in the range of 0.7 < E < 0.95 

for a vent fraction of up to V = 0.95. 

Entire test data for the structured packings are tabulated in Appendix D. The 

data for configurations not using structured packings, namely, configurations 

1 through 5 and 8 listed in Table C-l are provided in Appendix E. 

Early test results, such as shown in Figures C-7 and C-8, guided us to identify the structured packings as the most promising method for steam-water 

contact in a direct-contact condenser application and allowed us to concentrate our mOdeling efforts for condensers using structured packings. 

C.6 References 

Fair, J. R., 1961 (Aug.), "Design of Direct-Contact Gas Coolers," Petroleum 

and Chemical Engineer, Vol. 2, pp. 203-210. 

Fair, J. R., 1972 (June), "Designing Direct-Contact Coolers/Condensers," 

Chemical Engineering, Vol. 2, pp. 91-100. (See also, "Process Heat Transfer 

by Direct Fluid Phase Contract," Chemical Engineering Progress Symposium 

serles no. 118, Vol. 68, pp 1-11, 1972.) 

Panchal, C. B., and Bell, K. J., 1984, Theoretical Analysis of Condensation in 

the Presence of Noncondensable Gases as A lied to 0 en C cle OTEC 

Condensers, ASME paper 84-WA Sol-27, New York: American of 

Mechanical Engineers. 

130 
TR-3108 

APPENDIX D DATA TABLES FOR EXPERIMENTS USING STRUCTURED PACKINGS 

A complete set of experimental data and model predictions for structured packings are provided in the accompanying tables. Cocurrent test data are 

contained in Tables D-1 through D-4 for AX, 19060, 4X packings, and for freefalling jets, respectively. Tables D-5 through D-8 contain data for countercurrent condensers using AX, 19060, 3X, and 27060 packings , respectively. 

Details of the packing geometry may be found in Section 3.0. 

Most of the tables have 10 columns. Column 1 refers to a serial number. 

Column 2, labeled T i' represents the measured saturation temperature of the 

incoming steam and rnert gas mixture in degrees Celsius. The uncertainty in 

this measurement is ±0.02°C. Column 3, labeled T i' represents the measured 

water inlet temperature in degrees Celsius with an ~ncertainty of ±O.Ol°C. 

Column 4, labeled G, is the condenser gas loading defined as the entire mass 

flow rate of the steam and inert gas mixture divided by the planform area of 

the condenser. This quantity is expressed in kilograms per square meter per 

second and possesses an uncertainty of ±2.5% of the measured value. 

Column 5, labeled Ja, is the Jakob number, defined in Eq. 4-1, with an uncertainty of ±1.9%. Column 6, labeled X .. , is the inert gas mass concentration . .. 11 . 1n the 1ncom1ng steam expressed as a percentage of the total steam and 1nert 

gas mixture flow. This quantity 1S estimated to possess an uncertainty of 

±2.4% of the quoted value. 

Column 7 represents the amount of steam condensed within the contactor 

expressed as a percentage of the incoming steam flow with an uncertainty of 

±1.9% of the incoming steam flow. Column 8 represents the measured overall 

condenser pressure loss (static pressure difference between inlet and outlet 

gas streams) expressed in Pascals with an uncertainty of ±10 Pa or ±10% of the 

quoted value, whichever is greater. Columns 9 and 10 represent the predicted 

condensed steam and pressure loss directly comparable to columns 7 and 8, 

respectively. 

Columns 11 and 12, where present, show a second set of comparisons of predictions made that assume the packing extends the full free-fall height of water. 

A list of minimum, maximum, average, and standard deviation for each column is 

provided at the end of each table. Also provided are the average and standard 

deviation of the difference between model prediction (length is specified) and 

the experimental data for condensed steam and pressure loss. 

Note that Table D-4 for free-falling jets does not contain any predictions. 

131 
55'1 1

111 

TR-3108 

Table D-1. Cocurrent Condenser Data for AX Packing 

--------------------------------------------------------------------------- Measured Model <1=0.1811) 

Cond- Press- Cond- Pressensed ure ensed ure 

No Tsi Twi G Ja Xii Steall Loss Steaa Loss 

(C) (C) kg/sJR"2 (") (%) (Pa) (") (Pa) 

---------------------------------------------------------------------------

1 12.89 5.24 0.266 0.864 0.508 80.68 11.04 81.25 14.70 

2 12.84 5.12 0.268 0.879 0.500 81.88 12.02 82.32 14.64 

3 13.03 5.44 0.259 0.892 0.519 82.69 9.97 82.96 13.72 

4 12.87 5.09 0.261 0.895 0.517 83.03 9.21 83.27 13.90 

5 12.67 5.25 0.252 0.898 0.532 82.97 9.34 83.12 13.57 

6 12.40 5.00 0.248 0.906 0.540 83.41 9.75 83.47 13.44 

7 12.69 5.16 0.253 0.907 0.531 83.72 9.88 83.71 13.44 

8 12.70 5.26 0.249 0.907 0.538 83.63 9.38 83.62 13.24 

9 12.25 4.86 0.248 0.908 0.541 83.54 9.74 83.55 13.52 

10 12.50 5.05 0.246 0.908 0.548 83.72 8.83 83.62 13.19 

11 12.79 5.44 0.242 0.916 0.553 84.17 8.87 83.98 12.67 

12 13.23 5.13 0.265 0.920 0.510 85.10 10.06 84.93 13.41 

13 12.80 5.51 0.239 0.923 0.561 84.55 8.82 84.22 12.40 

14 12.35 4.80 0.246 0.923 0.548 84.81 9.11 84.46 13.08 

15 13.04 4.93 0.263 0.925 0.513 85.40 8.97 85.17 13.40 

16 13.50 5.31 0.263 0.931 0.513 85.94 8.57 85.55 12.95 

17 12.73 4.98 0.250 0.933 0.539 85.67 8.81 85.16 12.89 

18 12.48 5.25 0.231 0.948 0.581 85.83 7.89 85.24 11.92 

19 13.73 5.29 0.262 0.964 0.515 88.31 7.83 87.16 12.32 

20 11.02 4.97 0.267 0.969 0.507 85.02 13.53 84.53 16.58 

21 12.49 5.17 0.228 0.969 0.588 87.20 6.95 86.13 11.52 

22 11.08 4.98 0.267 0.975 0.503 85.41 13.52 84.90 16.37 

23 11.16 5.05 0.267 0.976 0.503 85.40 13.18 84.94 16.28 

24 11.15 5.08 0.263 0.984 0.511 85.73 12.73 85.16 15.93 

25 12.16 4.95 0.253 0.985 0.531 87.44 9.37 86.69 13.42 

26 11.28 5.29 0.260 0.987 0.518 85.78 12.71 85.18 15.56 

27 11.10 5.11 0.257 0.994 0.522 86.09 12.98 85.39 15.49 

28 11.04 4.98 0.260 0.995 0.517 86.19 12.33 85.53 15.70 

29 11.08 4.97 0.259 1.008 0.518 86.97 11.81 86.02 15.43 

30 12.49 5.19 0.249 1.011 0.540 88.72 8.47 87.59 12.69 

31 12.72 5.11 0.227 1.014 0.590 89.64 6.46 87.85 10.94 

32 12.48 5.31 0.244 1.018 0.553 88.98 8.36 87.61 12.34 

33 12.31 5.25 0.235 1.035 0.572 89.59 7.36 87.91 11.89 

34 12.13 5.15 0.230 1.043 0.584 89.82 7.25 87.98 11.69 

35 12.12 5.13 0.227 1.059 0.593 90.41 7.67 88.33 11.39 

36 12.13 5.22 0.223 1.065 0.604 90.48 7.20 88.33 11.15 

37 11.47 4.96 0.261 1.066 0.514 89.86 10.38 88.16 14.52 

38 11.93 5.07 0.220 1.070 0.612 90.73 6.85 88.37 11.11 

39 11. 73 5.12 0.259 1.090 0.519 90.85 9.40 88.78 13.93 

40 13.20 4.94 0.227 1.100 0.591 93.41 5.76 90.31 10.01 

41 12.23 5.09 0.215 1.136 0.627 92.85 5.87 89.78 10.25 

42 12.64 5.14 0.213 1.204 0.630 94.71 5.43 90.95 9.63 

132 
TR-3108 

Table D-1. eocurrent Condenser Data for AX Packing (Concluded) 

Measured Model (1=0.18a) 

Cond- Press- Cond- PressHo Tsi 

43 

44 

45 

46 

47 

48 

49 

50 

51 

(e) 

12.37 

13.63 

12.91 

12.81 

14.22 

12.29 

12.88 

12.60 

12.98 

Kiniaum: 

Twi G 

(e) kg/sa A 2 

5.06 

4.70 

5.05 

5.04 

4.54 

4.86 

5.09 

5.28 

4.98 

0.257 

0.223 

0.212 

0.257 

0.219 

0.239 

0.241 

0.209 

0.203 

Ja 

1.210 

1.212 

1.271 

1.289 

1.335 

1.075 

1.122 

1.211 

1.361 

Xii 

(") 

0.522 

0.602 

0.635 

0.523 

0.612 

1.116 

1.110 

1.277 

1.311 

ensed 

Steaa 

(") 

94.65 

95.97 

95.91 

96.23 

97.32 

87.70 

89.84 

90.94 

93.88 

11.02 4.54 0.203 0.864 0.500 80.68 

Kaxiaum: 

ure 

Loss 

(Pa) 

7.47 

4.98 

5.45 

6.47 

4.22 

9.61 

9.02 

7.11 

6.11 

ensed 

Steaa 

(") 

91.26 

92.16 

91.84 

92.33 

93.41 

85.01 

86.31 

86.58 

88.64 

4.22 81.25 

14.22 5.51 0.268 1.361 1.311 97.32 13.53 93.41 

Average: 

12.42 5.10 0.245 1.023 0.599 87.90 8.90 86.48 

Standard Deviation: 

0.74 0.18 0.018 0.124 0.182 4.16 2.32 

Di£ference Between Predictions and Experiaent: 

Condensed Steam (,,) 

Pressure Loss (Pa) 

No. of Standard 

Points Average Deviation 

133 

51 

51 

-1.40 

4.00 

1.50 

0.60 

2.82 

ure 

Loss 

(Pa) 

12.42 

9.07 

9.15 

11.66 

8.24 

13.95 

13.22 

11.31 

10.19 

8.24 

16.58 

12.85 

1.96 
55'1'*' TR-3108 

Table D-2. Cocurrent Condenser Data for 19060 Packing 

--------------------------------------------------------------------------- Measured Model (l=0.6la) 

Cond- Press- Cond- Pressensed ure ensed ure 

No Tsi Twi G Ja Xii Steaa Loss Steaa Loss 

(C) (C) kg/sa A

2 00 (") (Pa) (") CPa) 

---------------------------------------------------------------------------

1 11.00 5.27 0.178 1.144 0.064 89.05 16.50 97.14 4.61 

2 11.10 5.47 0.169 1.179 0.067 89.77 14.39 96.96 4.20 

3 11.11 5.45 0.167 1.200 0.068 90.69 13.71 96.97 4.09 

4 11.13 5.46 0.162 1.241 0.070 91.69 11.79 96.85 3.85 

5 11.21 5.45 0.156 1.304 0.072 92.98 11.23 96.75 3.55 

6 11.29 5.40 0.154 1.354 0.074 93.98 10.13 96.67 3.40 

7 13.40 5.20 0.243 1.204 0.078 90.54 17.81 97.70 5.92 

8 13.62 5.35 0.239 1.236 0.079 91.38 15.14 97.62 5.61 

9 8.50 4.96 0.223 1.238 0.085 92.71 27.49 97.32 10.43 

10 13.84 5.43 0.236 1.267 0.080 92.15 14.29 97.58 5.36 

11 8.73 5.07 0.224 1.274 0.085 93.72 24.28 97.47 10.07 

12 13.90 5.49 0.230 1.299 0.082 93.09 12.46 97.49 5.10 

13 9.00 5.20 0.226 1.311 0.084 94.96 19.98 97.45 9.59 

14 13.80 5.47 0.220 1.339 0.086 93.82 9.85 97.43 4.81 

15 9.24 5.35 0.222 1.367 0.086 95.97 16.93 97.37 8.85 

16 17.98 4.99 0.367 1.231 0.096 91.65 20.38 98.13 8.27 

17 17.88 5.05 0.358 1.241 0.099 92.19 17.91 98.08 8.01 

18 16.94 4.76 0.342 1.243 0.103 91.60 19.77 98.09 7.97 

19 17.86 5.21 0.347 1.266 0.102 92.65 15.66 98.04 7.64 

20 17.82 5.09 0.338 1.305 0.105 93.36 14.02 98.00 7.28 

21 18.09 4.92 0.337 1.354 0.105 94.18 13.14 97.95 6.98 

22 10.94 5.34 0.321 1.359 0.110 94.05 41.62 98.05 13.80 

23 10.93 5.22 0.322 1.378 0.110 94.80 40.54 98.07 13.65 

24 14.28 5.05 0.648 1.110 0.630 88.69 88.94 91.50 56.80 

25 14.40 5.04 0.644 1.130 0.630 89.23 88.60 92.16 54.54 

26 14.63 5.08 0.646 1.150 0.630 89.86 86.10 92.75 52.95 

27 15.01 5.25 0.649 1.170 0.620 90.75 82.91 93.36 50.90 

28 15.40 5.18 0.646 1.230 0.630 92.30 78.07 94.45 47.11 

29 13.93 5.60 0.510 0.950 0.790 82.64 78.17 84.53 44.89 

30 14.24 5.84 0.511 0.960 0.790 82.94 63.07 85.26 43.52 

31 14.42 5.79 0.514 0.980 0.790 84.01 65.38 86.55 42.10 

32 14.73 5.76 0.512 1.020 0.790 86.27 57.27 88.73 38.82 

33 14.96 5.79 0.507 1.050 0.800 87.97 49.53 89.97 36.46 

34 15.46 6.04 0.508 1.070 0.800 89.37 41.22 90.82 34.62 

35 16.51 6.84 0.509 1.100 0.790 90.87 20.47 91.86 31.63 

36 13.96 5.11 0.519 1.190 0.780 92.76 63.87 92.74 38.11 

37 14.18 5.29 0.522 1.190 0.780 92.88 63.94 92.76 37.95 

38 14.10 5.22 0.516 1.210 0.780 93.05 62.55 93.08 37.00 

134 
TR-3l08 

Table 0-2. Cocurrent Condenser Data for 19060 Packing (Concluded) 

No 1si 1wi G 

(C) (C) kg/s .... 2 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

14.49 

14.56 

14.68 

15.35 

13.40 

12.97 

13.05 

13.36 

13.48 

13.99 

Kini.u.: 

5.33 

5.32 

5.30 

5.08 

5.72 

5.35 

5.34 

5.53 

5.32 

5.56 

8.50 4.76 

Maxi.ulI: 

18.09 6.84 

Average: 

13.73 5.36 

Standard Deviation: 

2.40 0.34 

0.523 

0.518 

0.518 

0.514 

0.463 

0.461 

0.456 

0.459 

0.451 

0.452 

0.15 

0.65 

0.39 

0.15 

Ja 

1.230 

1.250 

1.270 

1.400 

1.080 

1.080 

1.110 

1.110 

1.180 

1.220 

0.95 

1.40 

1.20 

0.11 

0.770 

0.780 

0.780 

0.790 

0.870 

0.880 

0.890 

0.880 

0.890 

0.890 

Measured Model (1=0.61.) 

Cond- Press- Cond- Pressensed 

Stea. 

00 

93.46 

93.93 

94.26 

96.37 

89.13 

88.86 

89.57 

90.12 

92.11 

93.03 

ure 

Loss 

(Pa) 

63.27 

61.76 

60.17 

55.61 

64.53 

63.64 

61.77 

60.55 

57.85 

58.78 

ensed 

Stea. 

(") 

93.57 

93.82 

94.12. 

95.46 

89.08 

88.89 

89.82 

90.03 

91.80 

92.64 

ure 

Loss 

(Pa) 

36.18 

35.11 

34.40 

30.48 

36.85 

37.81 

36.09 

35.47 

32.38 

30.60 

0.06 82.64 9.85 84.53 3.40 

0.89 96.37 88.94 98.13 56.80 

0.45 91.36 42.02 94.23 24.08 

0.35 3.00 25.78 3.76 17.26 

Difference Between Predictions and Experiaent: 

Condensed Steaa <,,> 

Pressure Loss (Pa) 

No. of Standard 

Points Average Deviation 

135 

48 2.80 2.40 

48 -17.60 10.40 
S=~II*I TR-3l08 

Table D-3. Cocurrent Condenser Data for 4X Packing 

--------------------------------------------------------------------------- Meaaured Model (1=1.0811) 

Cond- Press- Cond- Pressensed ure ensed ure 

No Tsi Twi G Ja Xii Steall Loss Steall Loss 

(C) (C) kg/slll"2 (l'<) (l'<) (Pa) (l'<) (Pa) 

---------------------------------------------------------------------------

1 11.95 4.57 0.266 0.843 0.504 80.32 12.27 80.53 12.73 

2 11.36 5.29 0.227 0.847 0.590 79.40 10.81 79.72 10.86 

3 12.31 4.83 0.267 0.847 0.502 80.66 12.20 80.97 12.39 

4 12.55 4.81 0.275 0.847 0.487 80.86 12.57 81.17 12.67 

5 12.80 5.02 0.273 0.856 0.492 81.50 11.70 81.93 12.14 

6 13.30 5.49 0.269 0.865 0.498 82.25 11.07 82.70 11.32 

7 11.45 5.39 0.220 0.867 0.607 80.80 10.23 81.14 10.00 

8 11.66 5.51 0.219 0.880 0.610 81.77 10.04 82.12 9.60 

9 11.81 5.58 0.217 0.899 0.616 83.26 9.37 83.40 9.13 

10 9.84 4.03 0.193 0.947 0.692 85.41 8.73 85.16 8.38 

11 10.42 4.55 0.191 0.977 0.701 87.17 8.04 86.52 7.77 

12 10.92 4.13 0.187 1.141 0.713 93.49 7.09 91.69 6.34 

13 12.43 5.08 0.394 0.905 0.680 82.13 25.50 81.91 27.13 

14 12.30 4.95 0.394 0.907 0.681 82.16 25.97 81.99 27.31 

15 12.43 5.13 0.387 0.914 0.694 82.77 24.50 82.40 26.09 

16 12.64 5.27 0.387 0.921 0.693 83.29 24.08 82.94 25.43 

17 12.67 5.21 0.381 0.946 0.704 85.01 23.27 84.39 23.95 

18 13.13 4.93 0.378 1.048 0.710 90.96 18.91 89.12 20.41 

19 12.06 4.99 0.451 0.979 0.744 84.95 38.25 83.62 36.52 

20 12.32 5.09 0.452 0.999 0.743 86.47 36.21 84.78 35.10 

21 12.36 4.93 0.455 1.016 0.737 87.67 35.61 85.75 34.51 

22 12.29 4.60 0.458 1.045 0.733 89.44 34.44 87.09 33.84 

23 13.10 5.12 0.458 1.079 0.732 91.23 31.65 88.54 30.93 

24 13.21 4.82 0.457 1.137 0.734 93.60 28.13 90.27 29.03 

25 13.67 4.72 0.464 1.196 0.724 95.40 26.32 91.73 27.56 

26 14.58 4.23 0.462 1.389 0.726 97.78 22.33 94.25 23.17 

27 13.26 5.13 0.502 0.933 0.668 83.41 40.71 82.87 40.36 

28 13.40 5.26 0.498 0.942 0.674 84.18 41.03 83.44 38.99 

29 13.30 5.03 0.496 0.963 0.676 85.55 39.29 84.67 37.86 

30 13.27 5.21 0.496 1.060 0.675 90.35 36.16 88.07 35.92 

31 14.45 4.29 0.500 1.175 0.671 95.68 27.42 92.43 28.69 

32 14.54 4.94 0.504 1.223 0.665 96.33 27.39 92.65 29.29 

33 13.82 5.20 0.528 0.916 0.636 82.65 43.19 82.46 42.52 

34 13.70 5.23 0.519 0.917 0.647 82.69 43.53 82.37 41. 72 

35 12.91 5.13 0.518 0.965 0.647 84.66 45.47 83.76 43.88 

36 13.10 5.29 0.514 0.975 0.652 85.66 44.92 84.39 42.18 

37 13.49 5.59 0.514 0.987 0.652 86.62 42.18 85.17 40.45 

136 
TR-3108 

Table D-3. Cocurrent Condenser Data for 4X Packing (Concluded) 

Measured Model <1=1.08.) 

Cond- Pressensed ure 

No Tsi Twi G Ja Xii Stesa Loss 

(C) (C) kg/sa"2 (%) <%) (Pa) 

Miniaua: 

9.84 4.03 0.187 0.843 0.487 79.40 7.09 

Maxiaua: 

14.58 5.59 0.528 1.389 0.744 97.78 45.47 

Average: 

12.67 4.99 0.388 0.982 0.657 86.15 25.69 

Standard Deviation: 

1.04 0.38 0.116 0.122 0.074 5.01 12.55 

Difference Between Predictions and Experiaent: 

Condensed Steaa (%) 

Pressure Loss (Pa) 

No. of Standard 

Points Average Deviation 

137 

37 

37 

-1.10 

-0.10 

1.30 

1.20 

Cond- Pressensed ure 

Steaa Loss 

00 (Pa) 

79.72 6.34 

94.25 43.88 

85.08 25.57 

3.81 12.04 
$5'1 1*1 TR-3108 

Table D-4. Cocurrent Condenser Data for Falling Jets 

----------------------------------------------------------- Measured 

Cond- Pressensed ure 

No Tsi Twi G Ja Xii Steaa Loss 

(C) (C) kg/s ..... 2 ("> ("> (Pa) 

-----------------------------------------------------------

1 14.08 5.41 0.155 1.999 0.604 85.08 3.96 

2 13.95 5.16 0.151 2.080 0.618 86.13 3.53 

3 14.43 4.91 0.157 2.174 0.597 87.92 3.15 

4 14.91 4.84 0.161 2.242 0.582 89.74 3.29 

5 16.08 4.93 0.171 2.326 0.546 91.56 1.84 

6 16.86 5.14 0.169 2.481 0.554 93.13 2.09 

7 17.91 5.38 0.173 2.582 0.541 94.57 1.82 

8 16.53 5.11 0.173 2.344 1.608 84.78 3.78 

9 17.25 5.10 0.178 2.430 1.570 86.19 3.71 

10 17.79 5.20 0.179 2.496 1.557 87.83 2.46 

11 18.57 5.35 0.179 2.611 1.554 89.26 2.56 

12 19.03 5.43 0.179 2.687 1.557 90.87 2.26 

13 13.35 5.15 0.187 2.048 0.503 88.18 6~10 

14 13.46 5.25 0.181 2.119 0.520 89.30 4.60 

15 13.51 5.30 0.177 2.164 0.532 90.42 3.77 

16 13.46 5.36 0.165 2.292 0.571 91.39 3.69 

17 13.44 5.27 0.155 2.448 0.604 92.59 2.66 

18 13.60 5.14 0.151 2.621 0.624 93.86 2.32 

19 14.03 5.00 0.145 2.909 0.649 95.34 1.71 

20 18.66 5.49 0.226 2.050 0.690 86.40 6.03 

21 17.89 5.39 0.206 2.133 0.758 87.01 5.30 

22 17.61 5.37 0.197 2.189 0.793 87.44 4.26 

23 17.56 5.21 0.191 2.268 0.816 88.53 3.17 

24 17.91 5.08 0.188 2.398 0.830 89.89 3.75 

25 18.45 4.85 0.192 2.488 0.812 91.66 2.99 

26 19.06 4.79 0.196 2.569 0.798 92.89 2.41 

27 20.66 5.09 0.236 2.308 1.961 85.84 6.36 

28 20.94 5.22 0.230 2.395 2.010 86.99 5.26 

29 21.14 5.37 0.220 2.507 2.100 87.76 4.52 

30 21.36 5.39 0.216 2.584 2.136 88.83 4.17 

31 21.50 5.40 0.208 2.706 2.217 89.59 2.95 

32 21.74 5.47 0.202 2.811 2.282 90.37 2.44 

33 21.95 5.42 0.194 2.979 2.378 91.38 1.93 

34 15.72 4.91 0.242 2.086 0.647 89.53 6.94 

35 16.02 5.02 0.238 2.151 0.655 90.34 5.38 

36 16.26 5.10 0.234 2.220 0.666 91.30 4.61 

37 16.53 5.12 0.230 2.308 0.678 92.23 4.48 

138 
S5~1'_' TR-3108 

Table D-4. Cocurrent Condenser Data for Falling Jets (Cone! uded) 

----------------------------------------------------------- Measured 

Cond- Pressensed ure 

No lsi Twi G Ja Xii Stea. Loss 

(C) (C) kg/s ..... 2 (") (") (Pa) 

-----------------------------------------------------------

38 16.78 5.15 0.224 2.413 0.696 93.18 4.20 

39 17.12 5.17 0.219 2.545 0.714 94.12 2.93 

40 17.56 5.12 0.215 2.694 0.726 95.08 2.80 

41 18.20 5.06 0.208 2.944 0.751 96.12 1.97 

42 14.49 5.31 0.154 2.800 1.809 87.54 5.10 

43 14.57 5.14 0.149 2.984 1.871 88.92 3.86 

44 15.04 4.90 0.151 3.145 1.837 90.57 3.94 

45 15.87 4.76 0.155 3.369 1.794 92.50 3.71 

46 13.06 5.12 0.320 1.927 0.489 93.45 15.89 

47 13.05 4.94 0.316 1.992 0.495 94.07 14.60 

48 13.17 4.87 0.313 2.055 0.499 94.60 14.14 

49 13.36 4.79 0.314 2.116 0.498 95.29 10.85 

50 13.73 4.86 0.313 2.197 0.500 95.86 11.32 

51 14.37 4.92 0.323 2.265 0.484 96.61 10.53 

52 14.79 5.02 0.314 2.410 0.498 97.20 8.92 

53 15.31 5.00 0.311 2.571 0.504 97.75 8.19 

54 15.58 5.12 0.336 2.064 0.466 92.55 11.53 

55 15.76 5.10 0.335 2.109 0.468 93.19 10.50 

56 16.03 5.19 0.329 2.180 0.475 93.73 9.47 

57 16.31 5.11 0.332 2.235 0.472 94.59 8.45 

58 16.68 5.16 0.323 2.362 0.485 95.36 7.68 

59 17.04 5.10 0.326 2 •. 420 0.479 96.08 7.30 

60 17.49 5.07 0.320 2.567 0.489 96.72 6.52 

61 18.32 5.06 0.310 2.830 0.505 97.54 5.69 

IUni.ulII: 

13.05 4.76 0.14 1.93 0.47 84.78 1.71 

Kaxi.u.: 

21.95 5.49 0.34 3.37 2.38 97.75 15.89 

Average: 

16.51 5.13 0.22 2.42 0.94 91.46 5.35 

Standard Deviation: 

2.44 0.19 0.06 0.31 0.59 3.45 3.37 

-----------------------------------------------------------

139 
S=~II*I TR-3108 

Table 0-5. Countercurrent Condenser Data for AX Packing 

--------------------------------------------------------------------------- Measured Model <1=0.36.) 

Cond- Press- Cond- Pressensed ure ensed ure 

No Tsi Twi G Ja Xii Steam Loss Steam Loss 

(C) (C) kg/sJA"2 (%) (%) (Pa) (%) (Pa) 

---------------------------------------------------------------------------

1 11.29 5.63 0.100 1.062 6.225 89.88 6.85 89.90 12.45 

2 11.34 5.63 0.076 1.427 8.102 89.33 5.87 88.90 8.63 

3 12.30 5.23 0.074 3.667 8.276 91.70 5.76 91.80 6.93 

4 11.48 5.29 0.068 4.727 8.941 89.97 7.47 89.93 7.17 

5 11.27 5.81 0.093 1.087 12.496 81.82 7.11 81.22 15.06 

6 10.89 5.56 0.061 1.615 17.830 78.19 6.11 78.14 10.00 

7 11.40 5.63 0.056 1.957 10.701 86.61 5.43 86.99 6.55 

8 11.32 5.61 0.043 2.524 13.518 83.49 5.45 84.65 5.44 

9 10.81 5.38 0.027 3.803 19.832 77.50 5.44 79.32 4.20 

10 12.04 4.99 0·944 6.094 13.066 87.58 4.98 88.46 5.00 

11 11.34 5.25 0.048 6.583 12.232 86.90 6.47 87.09 5.81 

12 11.59 4.83 0.029 8.907 18.674 83.04 4.22 84.36 4.11 

13 10.67 5.27 0.046 2.191 22.515 74.11 5.58 75.86 8.01 

14 10.58 5.25 0.040 2.461 24.822 71.95 5.45 74.37 7.23 

15 10.23 5.31 0.031 2.941 29.966 67.25 4.89 69.82 6.26 

16 10.26 5.34 0.027 3.433 33.286 65.59 4.52 68.26 5.68 

17 10.11 4.95 0.015 6.391 30.433 69.50 4.87 72.09 3.10 

18 10.89 4.45 0.018 13.368 26.564 76.94 3.49 79.22 3.33 

19 11.58 5.68 0.115 0.967 5.461 86.03 7.25 90.32 15.83 

20 11.52 5.71 0.107 1.028 5.861 88.60 7.67 90.37 13.46 

21 11.50 5.75 0.104 1.039 6.004 89.55 7.20 90.18 12.98 

22 11.96 5.46 0.144 1.730 4.416 94.91 6.95 94.12 13.15 

23 12.13 5.39 0.116 2.222 5.418 94.09 6.46 93.60 10.25 

24 10.98 5.18 0.130 2.300 4.850 93.90 10.38 92.97 12.72 

25 11.20 5.34 0.117 2.598 5.393 93.34 9.40 92.53 11.36 

26 11.89 5.62 0.121 0.968 9.944 81.66 9.02 84.60 19.47 

27 16.92 5.13 0.141 6.111 10.526 94.21 15.43 94.08 11.48 

28 12.37 5.72 0.189 1.344 3.395 95.03 8.87 95.05 18.10 

29 12.36 5.80 0.182 1.380 3.522 95.33 8.82 94.86 17.28 

30 11.94 5.06 0.184 1.393 3.502 93.25 20.28 95.21 17.49 

31 12.64 5.19 0.189 1.473 3.409 95.49 16.75 95.83 16.38 

32 12.31 5.24 0.177 1.497 3.646 94.97 15.86 95.31 15.86 

33 10.76 5.30 0.185 1.534 3.472 93.51 12.73 93.70 20.09 

34 12.01 5.54 0.161 1.535 3.958 95.32 7.89 94.45 15.03 

35 10.89 5.51 0.182 1.540 3.529 93.74 12.71 93.51 19.71 

36 13.08 5.57 0.182 1.543 3.537 96.11 13.35 95.80 15.10 

37 10.70 5.33 0.176 1.582 3.633 94.03 12.98 93.41 19.06 

140 
TR-3108 

Table D-5. Countercurrent Condenser Data for AX Packing (Continued) 

--------------------------------------------------------------------------- Measured Model <1=0.36a> 

Cond- Press- Cond- Pressensed ure ensed ure 

No Tsi Twi G Ja Xii Steaa Loss Steaa Loss 

(C) (C) kg/s .... 2 (") (") (Pa) (") (Pa) 

---------------------------------------------------------------------------

38 10.64 5.19 0.177 1.595 3.623 94.26 12.33 93.55 19.08 

39 10.66 5.18 0.166 1.710 3.844 94.40 11.81 93.42 17.47 

40 13.28 5.55 0.151 1.922 4.241 96.06 8.58 95.49 11.78 

41 1~.06 5.54 0.184 1.360 8.284 90.99 35.30 89.69 23.51 

42 16.57 5.15 0.161 5.195 9.350 94.62 18.50 94.28 13.16 

43 12.66 5.72 0.220 1.204 2.926 89.40 9.97 95.58 22.36 

44 12.28 5.53 0.211 1.221 3.046 90.25 9.34 95.32 21.74 

45 12.49 5.33 0.218 1.232 2.974 89.30 33.13 95.76 21.66 

46 11.99 5.29 0.203 1.264 3.170 92.15 9.75 95.22 20.68 

47 11.85 5.14 0.201 1.277 3.197 93.23 9.74 95.22 20.45 

48 12.09 5.32 0.197 1.283 3.274 89.94 27.44 95.20 19.61 

49 12.30 5.55 0.201 1.286 3.201 94.40 9.38 95.27 19.81 

50 12.30 5.45 0.203 1.293 3.174 93.72 9.88 95.40 19.85 

51 12.84 5.39 0.194 1.434 3.323 95.79 16.22 95.88 16.82 

52 10.79 5.28 0.192 1.494 3.347 91.81 13.18 93.89 20.98 

53 10.70 5.20 0.192 1.498 3.350 91.88 13.52 93.87 21.09 

54 13.02 5.75 0.204 1.188 7.525 86.17 37.02 89.34 28.27 

55 12.92 5.58 0.204 1.203 7.546 88.79 37.97 89.49 28.16 

56 15.93 4.92 0.210 3.803 7.348 95.60 18.94 94.83 17.53 

57 16.07 5.16 0.198 4.049 7.757 95.24 24.33 94.59 16.50 

58 15.73 5.40 0.304 2.462 5.188 96.49 33.73 95.36 27.13 

59 15.68 5.32 0.290 2.582 5.417 96.43 30.49 95.28 25.67 

60 15.84 5.15 0.250 3.104 6.243 96.09 24.36 95.11 21.27 

Kiniaua: 

10.11 4.45 0.015 0.967 2.926 65.59 3.49 68.26 3.10 

Kaxiaulft: 

16.92 5.81 0.304 13.368 33.286 96.49 37.97 95.88 28.27 

Average: 

12.17 5.37 0.142 2.545 8.705 89.19 12.75 90.12 14.91 

Standard Deviation: 

1.63 0.26 0.071 2.184 7.611 7.65 8.97 7.06 6.61 

141 
Table D-5. 

No Tsi 

(C) 

TR-3l08 

Countercurrent Condenser Data for AX Packing (Concluded) 

Measured Model 

Cond- Press- Condensed ure ensed 

Twi G Ja Xii Steall Loss Steaa 

(C) kg!sJII .... 2 00 00 (Pa) (%) 

Difference Between Predictions and Experiaent: 

Condensed SteaM (%) 

Pressure Loss (Pa) 

No. of Standard 

Points Average Deviation 

142 

60 

60 

0.90 

2.20 

1.90 

6.00 

<1=0.3611) 

Pressure 

Loss 

(Pa) 
5='11*1 TR-3108 

Table D-6. Countercurrent Condenser Data for 19060 Packing 

--------------------------------------------------------------------------- Measured Hodel 0=0.6111) 

eond- Press- eond- Pressensed ure ensed ure 

No 1si 1wi G Ja Xii Steaa Loss Steaa Loss 

(e) (e) kg/s."'2 (") (") (Pa) (") (Pa) 

---------------------------------------------------------------------------

1 9.93 5.19 0.175 1.018 0.357 96.02 13.97 98.87 20.75 

2 9.93 5.27 0.172 1.018 0.364 95.93 13.56 98.96 18.61 

3 9.93 5.19 0.177 1.018 0.354 96.04 14.66 98.91 20.82 

4 9.98 5.30 0.172 1.029 0.364 96.55 11.71 99.12 16.65 

5 9.93 5.25 0.170 1.034 0.368 97.22 10.13 99.08 16.70 

6 9.97 5.27 0.168 1.055 0.373 97.85 8.34 99.22 14.32 

7 9.98 5.26 0.167 1.067 0.373 98.33 7.37 99.28 12.85 

8 10.03 5.28 0.165 1.079 0.378 98.62 6.16 99.27 12.28 

9 9.98 5.22 0.163 1.097 0.384 98.87 4.98 99.32 10.17 

10 10.04 5.16 0.161 1.141 0.389 99.17 2.90 99.34 9.07 

11 9.98 4.98 0.175 1.063 0.713 96.31 11.04 98.22 15.59 

12 10.02 5.09 0.174 1.074 0.717 96.26 12.61 98.30 13.55 

13 9.92 5.03 0.170 1.080 0.730 96.24 11.14 98.29 13.29 

14 10.17 5.13 0.174 1.082 0.717 97.23 8.47 98.41 12.83 

15 10.20 5.11 0.174 1.094 0.720 97.77 6.59 98.47 12.37 

16 10.26 5.09 0.172 1.123 0.728 98.21 5.24 98.56 11.39 

17 10.35 5.20 0.166 1.160 0.755 98.47 3.83 98.56 10.64 

18 10.49 5.11 0.166 1.212 0.755 98.66 2.32 98.70 9.66 

19 11.16 5.11 0.153 1.484 0.819 98.85 0.58 98.92 6.25 

20 10.02 5.00 0.173 1.095 1.081 96.65 8.78 97.37 13.27 

21 10.27 5.17 0.174 1.098 1.074 96.48 8.22 97.48 12.94 

22 10.05 5.07 0.170 1.111 1.100 96.59 8.21 97.32 13.10 

23 10.22 5.14 0.169 1.119 1.106 97.15 6.51 97.41 12.62 

24 10.46 5.09 0.172 1.164 1.087 97.78 5.90 97.78 11.31 

25 11.32 5.08 0.165 1.409 1.127 98.43 1.43 98.35 8.44 

26 10.71 5.07 0.186 1.127 1.337 96.88 8.21 97.02 14.59 

27 10.52 5.22 0.174 1.159 1.430 96.90 6.74 96.82 12.20 

28 10.48 5.29 0.168 1.177 1.481 96.80 5.89 96.63 12.20 

29 10.89 5.19 0.178 1.189 1.393 97.39 6.09 97.21 12.20 

30 11.07 5.24 0.178 1.216 1.395 97.59 5.02 97.33 11.63 

31 11.20 5.27 0.175 1.260 1.419 97.75 4.13 97.50 10.11 

32 11.06 4.90 0.183 1.269 1.692 97.26 5.45 96.97 11.57 

33 11.44 4.96 0.184 1.349 1.685 97.65 3.40 97.30 10.57 

34 11.48 5.22 0.166 1.400 1.497 97.93 2.05 97.64 9.20 

35 10.54 4.81 0.166 1.312 1.856 97.11 2.87 96.41 11.30 

36 10.59 4.91 0.162 1.334 1.908 97.01 2.28 96.39 10.24 

37 11. 79 5.07 0.180 1.422 1.720 97.78 2.70 97.41 10.00 

38 11.48 5.10 0.180 1.488 2.061 97.25 16.14 96.59 10.86 

143 
S5~1'*' TR-3108 

Table D-6. Countercurrent Condenser Data for 19060 Packing (Continued) 

--------------------------------------------------------------------------- Measured Model <1=0.61.) 

Cond- Press- Cond- Pressensed ure ensed ure 

No Tsi Twi G Ja Xii StealR Loss Steallll Loss 

(C) (C) kg/s .... 2 00 (") (Pa) (") (Pa) 

---------------------------------------------------------------------------

39 11.50 5.17 0.176 1.501 2.097 97.19 14.17 96.48 10.94 

40 12.20 5.21 0.173 1.534 1.791 97.86 1.94 97.57 8.62 

41 12.53 5.25 0.172 1.603 1.800 97.98 1.21 97.72 8.22 

42 12.19 4.93 0.170 1.606 2.174 97.58 1.53 97.12 8.95 

43 12.38 4.97 0.169 1.659 2.186 97.64 2.14 97.19 8.74 

44 11.28 4.89 0.176 1.785 2.099 97.24 13.36 96.68 10.43 

45 11.29 4.90 0.173 1.821 2.135 97.19 15.21 96.73 9.55 

46 11. 74 5.50 0.160 1.474 2.311 96.87 1.62 96.18 9.40 

47 11.15 4.91 0.152 1.542 2.418 96.88 0.26 96.14 8.78 

48 11.15 4.95 0.150 1.571 2.459 96.81 0.79 96.05 8.81 

49 12.06 5.20 0.157 1.651 2.345 97.23 1.30 96.69 8.60 

50 11.33 5.14 0.155 2.227 2.381 96.79 13.21 96.44 8.05 

51 11.37 5.25 0.151 2.267 2.441 96.67 13.56 96.29 8.14 

52 11.96 5.30 0.249 1.022 0.379 96.83 26.40 99.06 29.50 

53 11.90 5.14 0.249 1.033 0.378 96.86 26.40 99.26 26.38 

54 11.87 5.03 0.253 1.034 0.372 96.91 26.87 99.31 26.21 

55 11.96 4.97 0.256 1.048 0.368 97.28 25.95 99.43 23.93 

56 12.07 4.97 0.259 1.054 0.364 97.67 25.89 99.48 23.42 

57 12.19 4.99 0.258 1.065 0.365 98.06 23.84 99.50 21.69 

58 12.30 4.96 0.258 1.081 0.365 98.49 21.64 99.57 19.22 

59 12.42 5.00 0.261 1.092 0.361 98.79 20.70 99.59 18.20 

60 12.86 5.25 0.258 1.127 0.365 99.08 17.09 99.63 15.42 

61 13.01 5.33 0.258 1.137 0.365 99.21 15.34 99.64 14.83 

62 13.13 5.37 0.252 1.178 0.374 99.46 10.36 99.65 12.55 

63 12.63 5.40 0.256 1.068 0.731 97.08 21.95 98.68 21.55 

64 12.55 5.47 0.250 1.073 0.750 97.59 19.10 98.64 20.29 

65 12.26 4.98 0.259 1.076 0.723 97.25 26.44 98.76 21.14 

66 12.24 4.99 0.261 1.078 0.717 97.26 31.66 98.75 21.22 

67 12.33 5.37 0.243 1.081 0.770 97.88 16.12 98.65 18.53 

68 12.12 5.32 0.235 1.095 0.796 98.09 14.83 98.58 18.06 

69 12.15 5.10 0.238 1.137 0.786 98.55 13.30 98.79 16.09 

70 12.37 5.01 0.233 1.203 0.803 98.89 9.77 98.96 13.07 

71 12.99 4.80 0.237 1.303 0.788 99.13 8.57 99.17 11. 73 

72 13.25 5.50 0.267 1.106 1.049 97.44 21.42 98.22 20.31 

73 12.72 5.39 0.251 1.111 1.116 97.45 18.56 98.01 18.81 

74 13.24 5.54 0.265 1.112 1.058 97.44 20.69 98.24 18.96 

75 12.59 5.28 0.250 1.113 1.121 97.47 18.92 98.00 18.98 

76 12.48 4.92 0.255 1.122 1.096 97.51 17.82 98.11 19.76 

144 
55'1 1*1 TR-3108 

Table D-6. Countercurrent Condenser Data for 19060 Packing (Continued) 

--------------------------------------------------------------------------- Measured Model <l=0.6h) 

Cond- Press- Cond- Pressensed ure ensed ure 

No Tsi Twi G Ja Xii Steaa Loss Steaa Loss 

(C) (C) kg/sa A

2 (") (") (Pa) (") (Pa) 

---------------------------------------------------------------------------

77 12.48 5.18 0.266 1.135 1.053 97.66 20.97 98.10 20.72 

78 12.55 4.95 0.254 1.140 1.104 97.92 15.80 98.25 17.52 

79 12.46 5.16 0.262 1.149 1.069 97.62 22.14 98.15 19.00 

80 12.69 5.01 0.247 1.171 1.134 98.22 13.54 98.28 16.61 

81 11.62 5.23 0.249 1.177 1.127 97.79 20.09 97.67 19.31 

82 11.57 5.27 0.242 1.195 1.159 97.73 19.99 97.67 17.72 

83 12.86 4.99 0.249 1.197 1.126 98.45 12.38 98.40 15.64 

84 11.54 5.11 0.259 1.215 1.083 97.87 21.61 97.81 19.87 

85 11.48 5.07 0.254 1.235 1.104 97.84 22.12 97.86 18.20 

86 11.05 5.07 0.245 1.278 1.142 97.88 21.71 97.58 18.69 

87 11.07 5.19 0.239 1.290 1.170 97.82 20.39 97.53 17.43 

88 10.98 5.24 0.239 1.343 1.171 97.81 19.12 97.50 17.14 

89 11.00 5.30 0.234 1.363 1.195 97.77 18.20 97.52 15.77 

90 10.99 5.17 0.252 1.373 1.111 97.93 22.51 97.68 17.74 

91 13.72 5.04 0.240 1.380 1.168 98.88 7.18 98.74 11.69 

92 11.02 5.26 0.245 1.399 1.144 97.86 21.99 97.66 16.36 

93 14.16 4.98 0.238 1.468 1.177 98.98 5.78 98.87 10.79 

94 11.01 5.28 0.246 1.476 1.139 97.88 20.53 97.64 17.05 

95 11.00 5.33 0.243 1.545 1.153 97.85 19.69 97.69 15.56 

96 10.90 5.18 0.244 1.652 1.149 97.91 13.81 97.78 15.13 

97 10.85 5.23 0.234 1.857 1.197 97.81 17.85 97.74 13.80 

98 12.88 4.76 0.264 1.185 1.410 97.90 17.97 97.85 17.95 

99 12.92 5.34 0.238 1.188 1.564 97.65 11.92 97.46 16.26 

100 12.88 4.78 0.262 1.192 1.420 97.87 18.83 97.84 17.80 

101 13.10 5.10 0.248 1.217 1.499 98.12 10.17 97.77 16.20 

102 13.29 5.10 0.245 1.249 1.516 98.25 9.54 97.92 14.40 

103 13.81 5.11 0.262 1.265 1.770 97.97 14.16 97.57 16.32 

104 13.60 5.11 0.247 1.308 1.504 98.44 8.06 98.07 14.31 

105 14.04 5.07 0.249 1.359 1.493 98.63 7.02 98.28 13.23 

106 14.67 5.12 0.238 1.523 1.563 98.74 5.23 98.47 11.13 

107 13.82 5.17 0.258 1.274 1.800 97.93 14.35 97.51 16.33 

108 13.73 5.35 0.241 1.314 1.926 97.83 10.20 97.36 14.43 

109 13.88 5.29 0.238 1.362 1.945 98.01 8.60 97.49 13.83 

110 14.75 5.06 0.267 1.372 2.083 98.09 12.86 97.54 15.65 

111 14.79 5.00 0.269 1.378 2.065 98.10 13.79 97.60 15.45 

112 14.82 5.34 0.280 1.383 1.987 98.17 14.75 97.54 16.47 

113 14.83 5.41 0.276 1.384 2.015 98.15 13.22 97.49 16.57 

114 14.20 5.33 0.228 1.465 2.034 98.11 7.08 97.61 12.16 

115 14.43 5.25 0.227 1.523 2.036 98.23 6.73 97.75 11.70 

116 14.60 5.14 0.234 1.543 1.983 98.36 6.04 97.94 11.28 

145 
55'1 1*1 TR-3108 

Table D-6. Countercurrent Condenser Data for 19060 Packing (Continued) 

--------------------------------------------------------------------------- Measured Model <1=0.6111) 

Cond- Press- Cond- Pressensed ure ensed ure 

No Tsi Twi G Ja Xii SteaM Loss SteaM Loss 

(C) (C) kg/sJII A

2 (%) (%) (Pa) (%) (Pa) 

---------------------------------------------------------------------------

117 13.99 5.18 0.254 1.568 2.184 98.08 7.47 97.29 14.20 

118 14.46 5.30 0.273 1.648 2.038 98.21 11.86 97.57 14.92 

119 14.45 5.23 0.277 1.650 2.010 98.24 13.73 97.58 15.77 

120 14.87 5.12 0.223 1.660 2.078 98.39 5.89 98.00 10.15 

121 14.35 5.20 0.263 1.948 2.111 98.15 10.84 97.63 13.66 

122 14.36 5.22 0.259 1.975 2.143 98.12 11.00 97.59 13.69 

123 14.22 4.96 0.255 2.153 2.177 98.11 10.51 97.63 13.62 

124 14.39 5.25 0.262 2.220 2.121 98.11 10.97 97.68 13.37 

125 14.41 5.30 0.255 2.279 2.182 98.05 11.06 97.65 12.61 

126 14.35 5.21 0.255 2.403 2.182 98.06 10.59 97.69 12.56 

127 14.38 5.23 0.255 2.405 2.181 98.06 11.27 97.69 12.53 

128 14.44 5.21 0.249 1.418 2.226 97.99 9.62 97.30 14.29 

129 14.10 4.94 0.245 1.425 2.262 97.99 7.90 97.22 14.67 

130 14.40 5.09 0.252 1.428 2.199 98.03 10.12 97.39 14.15 

131 14.23 5.16 0.237 1.455 2.338 97.89 8.27 97.17 13.64 

132 14.06 5.40 0.233 1.669 2.378 97.89 6.96 97.11 12.55 

133 14.34 5.40 0.236 1.734 2.344 97.95 8.98 97.26 12.89 

134 14.25 5.26 0.236 1.741 2.349 97.98 8.78 97.27 12.92 

135 14.03 5.25 0.252 1.805 2.203 98.04 9.12 97.36 13.68 

136 13.95 5.12 0.248 1.834 2.234 98.01 6.56 97.35 13.72 

137 14.10 4.89 0.250 1.931 2.223 98.12 9.68 97.55 13.20 

138 14.09 4.86 0.243 1.994 2.277 98.08 8.88 97.55 12.39 

139 14.21 5.01 0.248 2.211 2.236 98.06 10.78 97.59 12.88 

140 14.37 5.26 0.252 2.538 2.205 98.05 4.97 97.66 12.55 

141 14.39 5.30 0.251 2.546 2.213 98.03 9.97 97.66 12.54 

142 14.38 5.31 0.247 2.694 2.244 98.00 10.81 97.63 12.56 

143 14.41 5.43 0.243 2.715 2.288 97.95 10.25 97.59 11.87 

144 14.39 5.30 0.253 2.785 2.197 98.04 6.97 97.70 12.42 

145 14.40 5.31 0.252 2.802 2.205 98.02 9.97 97.69 12.43 

146 16.05 5.32 0.377 1.061 0.663 97.48 42.43 99.14 31.80 

147 16.10 5.08 0.389 1.063 0.642 97.56 44.11 99.20 32.92 

148 16.72 5.45 0.386 1.083 0.969 97.72 33.01 98.71 30.46 

149 16.80 5.43 0.389 1.088 0.961 97.73 34.65 98.79 29.21 

150 16.54 5.16 0.392 1.089 0.955 97.83 36.54 98.78 29.63 

151 16.62 5.16 0.395 1.089 0.947 97.82 36.54 98.82 29.32 

152 16.65 4.81 0.404 1.101 0.926 97.86 38.94 98.92 29.36 

153 15.83 4.94 0.403 1.108 0.930 98.05 37.70 98.75 31.59 

154 16.81 4.87 0.403 1.109 0.929 98.05 36.73 98.97 28.21 

155 15.92 5.00 0.401 1.109 0.934 98.00 38.20 98.75 31.37 

146 
S5~1'*' TR-3l08 

Table D-6. Countercurrent Condenser Data for 19060 Packing (Continued) 

--------------------------------------------------------------------------- Measured Model (1=0.6111) 

Cond- Press- Cond- Pressen sed ure ensed ure 

No Tsi Twi G Ja Xii Stea. Loss Stea. Loss 

(C) (C) kg/s .... 2 (%) (%) CPa) (") (Pa) 

---------------------------------------------------------------------------

156 15.02 4.81 0.413 1.120 0.907 98.30 42.69 98.59 35.40 

157 16.94 4.93 0.400 1.124 0.937 98.31 33.72 98.99 27.31 

158 17.06 4.90 0.405 1.134 0.925 98.53 31.07 99.06 26.24 

159 15.14 5.15 0.393 1.139 0.951 98.19 41.04 98.61 30.82 

160 14.69 5.22 0.406 1.150 0.923 98.32 44.60 98.45 35.54 

161 14.61 5.19 0.400 1.156 0.934 98.32 43.84 98.49 33.38 

162 17.30 4.92 0.402 1.160 0.932 98.77 28.26 99.13 24.29 

163 13.77 5.36 0.370 1.186 1.010 98.40 36.26 98.18 30.81 

164 13.69 5.34 0.366 1.192 1.021 98.38 37.00 98.13 31.15 

165 13.66 5.13 0.395 1.214 0.947 98.52 44.41 98.31 32.99 

166 13.53 5.22 0.379 1.229 0.987 98.48 41.43 98.22 31.42 

167 13.11 5.18 0.371 1.266 1.007 98.53 37.05 98.14 30.09 

168 13.14 5.32 0.364 1.271 1.028 98.49 37.14 98.11 28.74 

169 13.32 5.47 0.389 1.277 0.960 98.56 41.95 98.15 32.68 

170 13.44 5.44 0.391 1.293 0.956 98.56 43.59 98.23 31.76 

171 12.89 5.37 0.368 1.373 1.016 98.56 27.10 98.09 28.98 

172 12.81 5.35 0.357 1.397 1.045 98.53 28.97 98.07 27.33 

173 12.96 5.17 0.390 1.412 0.959 98.64 42.51 98.29 30.22 

174 12.52 5.01 0.363 1.527 1.030 98.60 36.08 98.24 25.80 

175 12.47 5.04 0.358 1.532 1.042 98.59 29.97 98.19 26.10 

176 12.65 5.20 0.369 1.563 1.012 98.60 37.78 98.24 26.68 

177 17.42 5.16 0.407 1.126 1.222 98.01 35.12 98.57 28.53 

178 17.42 5.25 0.401 1.130 1.241 97.97 34.55 98.56 27.31 

179 17.56 5.15 0.395 1.180 1.571 98.24 26.73 98.21 26.27 

180 17.57 5.32 0.391 1.183 1.587 98.23 27.42 98.19 25.22 

181 18.28 5.26 0.399 1.230 1.863 98.35 25.90 98.03 24.53 

182 18.30 5.22 0.404 1.230 1.839 98.37 26.36 98.07 24.37 

183 17.88 5.26 0.383 1.253 1.936 98.42 22.31 97.94 22.96 

184 17.87 5.07 0.388 1.254 1.915 98.45 23.36 97.96 23.91 

185 17.58 5.21 0.405 1.258 1.834 98.58 23.73 97.95 25.36 

186 17.61 5.26 0.408 1.264 1.821 98.59 23.75 97.91 26.55 

187 18.89 5.14 0.400 1.293 2.146 98.45 21.53 97.91 23.14 

188 18.86 5.26 0.391 1.297 2.208 98.40 20.99 97.85 22.27 

189 18.99 4.85 0.386 1.360 1.920 98.88 16.44 98.37 20.12 

190 16.88 5.06 0.384 1.392 1.930 98.69 22.01 97.89 22.97 

191 16.85 5.16 0.373 1.408 1.986 98.66 19.73 97.83 22.03 

192 19.60 4.96 0.382 1.424 1.940 99.00 15.22 98.52 17.92 

193 16.75 4.96 0.402 1.445 1.847 98.77 22.51 97.95 24.66 

194 16.67 4.83 0.399 1.453 1.859 98.77 22.50 97.95 24.66 

195 20.14 4.64 0.388 1.491 1.913 99.15 13.87 98.68 17.37 

196 16.75 5.36 0.381 1.546 1.947 98.69 19.14 97.86 22.31 

147 
TR-3l08 

Table D-6. Countercurrent Condenser Data for 19060 Packing (Concluded) 

--------------------------------------------------------------------------- Measured Model <1=0.611\) 

Cond- Press- Cond- Pressensed ure ensed ure 

No Tsi Twi G Ja Xii Steaa Loss Steaa Loss 

(C) (C) kg/Sll"2 00 00 (Pa) 00 (Pa) 

---------------------------------------------------------------------------

197 16.63 5.19 0.377 1.566 1.965 98.70 18.36 97.87 22.33 

198 16.64 5.31 0.384 1.662 1.929 98.71 18.08 97.93 21.82 

199 16.63 5.26 0.384 1.670 1.929 98.71 17.56 97.94 21.76 

200 16.79 5.40 0.404 1.768 1.837 98.71 20.46 98.04 22.88 

201 16.80 5.55 0.398 1.776 1.866 98.69 19.97 97.96 23.08 

202 16.56 5.14 0.372 1.826 1.993 98.67 17.80 97.98 20.41 

203 16.55 5.18 0.367 1.836 2.020 98.65 16.66 97.93 20.54 

204 16.64 5.29 0.385 1.975 1.926 98.68 16.78 98.01 21.77 

205 16.64 5.32 0.374 2.030 1.982 98.65 16.92 98.03 19.89 

206 16.56 5.01 0.402 2.033 1.846 98.75 18.60 98.14 22.29 

207 16.59 5.14 0.394 2.044 1.883 98.73 18.97 98.12 21.42 

208 16.57 5.16 0.391 2.252 1.897 98.70 14.97 98.13 21.17 

209 16.57 5.28 0.369 2.263 2.010 98.63 16.09 98.04 19.71 

IHnillul'A: 

9.92 4.64 0.150 1.018 0.354 95.93 0.26 96.05 6.25 

Kaxiaull: 

20.14 5.55 0.413 2.802 2.459 99.46 44.60 99.65 35.54 

Average: 

13.50 5.16 0.273 1.412 1.413 97.98 17.07 98.03 18.10 

Standard Deviation: 

2.42 0.17 0.084 0.384 0.621 0.67 11.14 0.74 6.87 

Difference Between Predictions and Experiaent: 

----------------------------------------------- No. of Standard 

Points Average Deviation 

Condensed Steall (%) 209 0.10 1.00 

Pressure Loss (Pa) 209 0.80 5.10 

148 
In 

Table D-7. Countercurrent Condenser Data for 3X Packing III 

N - ------------------------------------------------------------------------------------------- Measured Hodel <1=0.6la) Kodel <1=0.80a) 

I I .. '-' 

Cond- Press- Cond- Press- Cond- Pressen sed ure ensed ure ensed ure 

No Tsi Twi G Ja Xii Steaa Loss Steaa Loss Steaa Loss 

(C) (C) kg/s,."'2 (,,) (,,) (Pa) (,,) (Pa) (") (Pa) 

-------------------------------------------------------------------------------------------

1 9.72 4.20 0.060 3.584 9.935 87.58 7.09 86.25 4.36 87.88 5.08 

2 13.29 5.10 0.091 6.942 15.408 86.64 27.39 86.22 6.81 88.23 7.95 

3 11.34 4.40 0.050 10.520 24.813 78.33 22.33 79.13 4.86 80.87 5.92 

4 11.33 5.57 0.197 1.159 3.260 91.13 10.04 91.34 17.18 94.12 18.88 

5 11.46 5.65 0.179 1.280 3.568 93.12 9.37 91.65 13.85 94.13 15.07 

....... 6 9.38 4.10 0.139 1.483 4.557 92.22 8.73 89.99 11.14 92.42 12.25 

.j:-. 

\0 7 9.90 4.62 0.121 1.717 5.216 91.87 8.04 89.54 8.95 91.80 9.92 

8 12.40 5.14 0.168 2.578 7.324 92.67 18.91 89.46 12.55 91.91 13.88 

9 12.48 5.29 0.198 2.781 7.763 91.50 31.65 88.25 16.64 91.03 18.39 

10 12.43 4.98 0.144 3.958 10.358 89.59 28.13 87.30 11.40 89.80 12.88 

11 12.57 4.89 0.105 5.584 13.671 87.03 26.32 86.02 8.20 88.26 9.48 

12 13.54 4.33 0.106 7.162 13.512 89.70 27.42 88.84 7.41 90.73 8.54 

13 11.14 5.44 0.209 1.081 3.082 88.76 10.23 90.77 20.56 93.85 23.09 

14 12.53 5.10 0.248 1.101 2.602 92.12 11.70 93.89 21.55 96.27 23.59 

15 13.02 5.56 0.235 1.165 2.742 93.95 11.07 94.20 17.91 96.36 19.30 

16 12.19 5.42 0.281 1.439 4.517 93.48 23.27 89.67 28.17 92.89 30.58 

17 11.81 5.09 0.276 1.862 5.683 92.25 35.61 88.31 28.48 91.57 30.98 

18 11. 72 4.76 0.238 2.234 6.535 92.21 34.44 88.46 22.48 91.47 24.58 

19 12.72 5.34 0.236 2.261 6.581 92.80 36.16 89.15 20.49 92.04 22.37 

20 12.00 5.28 0.347 1.154 3.691 89.10 25.50 88.63 46.00 92.49 51.47 

21 11.87 5.15 0.346 1.161 3.701 89.34 25.97 88.68 45.87 92.52 51.24 

22 11.99 5.33 0.328 1.209 3.894 90.58 24.50 88.88 40.35 92.59 44.59 I-i 

::0 

23 12.20 5.47 0.319 1.259 4.006 92.02 24.08 89.25 36.81 92.82 40.34 I 

w 

24 12.44 5.29 0.391 1.411 4.071 90.96 45.47 89.25 49.23 92.87 53.34 ....... 

0 

O:J 
III 

III 

N 

Table D-1. Countercurrent Condenser Data for 3X Packing (Continued) -I I .-'_7 

------------------------------------------------------------------------------------------- Measured Model <1=0.61a) Model <1=0.80.) 

Cond- Press- Cond- Press- Cond- Pressensed ure ensed ure en sed ure 

No Tsi Twi G Ja Xii Steaa Loss Steaa Loss Steaa Loss 

(C) (C) kg/s .... 2 00 (%) (Pa) (%) (Pa) (%) (Pa) 

-------------------------------------------------------------------------------------------

25 11.53 5.15 0.335 1.467 4.740 89.85 38.25 87.44 42.28 91.23 46.16 

26 12.63 5.45 0.363 1.528 4.373 92.25 44.92 89.50 41.58 92.93 44.86 

27 12.95 5.29 0.388 1.638 4.111 94.00 41.03 90.67 42.77 93.86 45.75 

...... 28 11. 78 5.25 0.301 1.660 5.241 91.60 36.21 87.93 33.61 91.42 36.57 VI 

0 29 13.02 5.74 0.339 1.662 4.675 93.35 42.18 89.75 35.34 93.01 38.06 

30 12.84 5.07 0.353 1.821 4.501 94.61 39.29 90.86 35.84 93.86 38.34 

31 12.80 5.17 0.410 1.539 3.894 93.14 40.71 90.54 48.37 93.84 51.81 

32 13.39 5.31 0.451 1.582 3.555 92.40 43.19 91.47 52.46 94.61 55.81 

33 13.27 5.34 0.442 1.587 3.625 92.21 43.53 91.24 51.51 94.42 54.87 

HinilRulR: 

9.38 4.10 0.050 1.081 2.602 78.33 7.09 79.13 4.36 80.87 5.080 

Haxiau.: 

13.54 5.74 0.451 10.520 24.813 94.61 45.47 94.20 52.46 96.36 55.810 

Average: 

12.11 5.13 0.254 2.441 6.339 90.98 27.36 89.17 26.82 92.06 29.271 

Standard Deviation: 

0.99 0.40 0.112 2.104 4.586 2.99 12.29 2.57 15.42 2.78 16.552 

o-'j 

ll=I 

I 

w 

..... 

0 

CXl 
No Tsi ....... (C) VI 

....... 

Table D-7. Countercurrent Condenser Data for 3X Packing (Concluded) 

Measured Model <1=0.61111> 

Cond- Press- Cond- Pressen sed ure ensed ure 

Twi G Ja Xii Steaa Loss Steaa Loss 

(C) kg/s .... 2 00 (~) (Pa) (~) (Pa) 

Difference Between Predictions (1=0.8111) and Experilllent: 

Condensed Steaa (~) 

Pressure Loss (Pa) 

No. of Standard 

Points Average Deviation 

33 

33 

1.10 

1.90 

1.50 

12.30 

Model 

Condensed 

Steaa 

(~) 

(1=0.80111) 

Pressure 

Loss 

(Pa) 

III 

III 

N -

-

-' 

I I 

'-~ 
Table D-8. Countercurrent Condenser Data for 27060 Packing In 

UI 

N - ------------------------------------------------------------------------------------------- I I .-

Measured Model <1=0.61JR) Model <1=0.80.) "_ r 

Cond- Press- Cond- Press- Cond- Pressen sed ure ensed ure ensed ure 

No Tsi Twi G Ja Xii SteaM Loss SteaM Loss SteaM Loss 

(C) (C) kg/Sl'AA2 (%) (%) (Pa) (%) (Pa) (%) (Pa) 

-------------------------------------------------------------------------------------------

1 9.81 5.34 0.172 0.988 0.365 95.94 8.78 94.74 16.06 96.64 23.12 

2 10.16 5.52 0.191 0.995 0.330 96.33 13~01 94.94 18.40 96.90 26.28 

3 9.79 5.32 0.165 1.011 0.379 96.36 8.32 95.99 13.48 98.16 17.68 

4 9.86 5.25 0.170 1.028 0.368 97.18 7.28 96.68 13.08 98.73 15.95 

5 9.95 5.22 0.172 1.046 0.365 97.72 6.60 97.26 12.24 99.04 14.02 

6 10.21 5.24 0.175 1.066 0.357 98.42 6.56 97.88 11.28 99.26 12.35 ...... 

\on 7 10.43 5.33 0.177 1.080 0.354 98.89 4.74 98.15 10.72 99.34 11.51 N 8 10.55 5.38 0.173 1.117 0.362 99.16 2.56 98.54 9.11 99.39 9.53 

9 9.90 5.33 0.165 1.041 0.758 96.12 7.05 94.49 11.67 97.29 13.73 

10 9.91 5.29 0.184 1.054 0.681 96.53 11. 73 94.63 13.78 97.46 16.08 

11 9.88 5.33 0.180 1.059 0.696 96.59 11.32 94.65 13.17 97.46 15.21 

12 9.92 5.18 0.168 1.059 0.745 96.76 6.55 95.09 11.34 97.68 12.95 

13 10.03 5.15 0.170 1.082 0.736 97.35 5.76 95.64 10.79 97.98 11.99 

14 10.19 5.13 0.173 1.097 0.724 97.97 4.84 96.04 10.51 98.19 11.51 

15 10.28 5.01 0.197 1.098 0.947 97.12 11.18 94.38 13.52 97.23 15.08 

16 10.85 5.68 0.196 1.102 0.952 97.01 10.64 94.30 12.99 97.18 14.47 

17 9.90 5.21 0.181 1.138 1.029 97.08 9.92 93.90 11.84 96.81 13.02 

18 9.98 5.30 0.179 1.154 1.043 96.94 9.41 94.01 11.35 96.86 12.40 

19 9.85 5.30 0.197 1.194 0.949 97.33 12.14 94.08 13.11 96.95 14.23 

20 9.82 5.40 0.190 1.207 0.983 97.19 11.56 93.94 12.35 96.82 13.37 

21 9.50 4.97 0.179 1.212 1.045 97.10 11.55 94.15 11.16 96.88 12.04 

22 9.44 5.13 0.167 1.233 1.118 96.99 10.44 93.84 10.05 96.60 10.83 

23 9.38 5.39 0.182 1.301 1.027 97.15 11.13 93.60 11.51 96.48 12.35 ~ 

~ 

24 9.36 5.48 0.174 1.322 1.075 97.13 10.20 93.42 10.71 96.30 11.48 I 

w 

25 9.11 5.24 0.159 1.329 1.170 96.85 9.28 93.36 9.36 96.16 10.04 ..... 

0 

00 
Table D-8. Countercurrent Condenser Data for 27060 Packing (Continued) 

------------------------------------------------------------------------------------------- ~ ~ 

Measured Model (1=0 .. 61.) Nodel (1=0 .. 80M) 

Cond- Press- Cond- Press- Cond- Pressensed ure ensed ure en sed ure 

No Tsl Twi G Ja Xii Steam Loss SteaM Loss SteaM Loss 

(C) (C) kg/sJl A 2 (%) C,,) (Pa) (%) CPa) (%) (Pa) 

-------------------------------------------------~-----~~--~---------~---------~-----~--~--

26 9.01 5 .. 09 o. 1 .. 332 1.150 96.82 9 .. 64 93 .. 49 9.62 96.27 10 .. 31 

27 9 13 S .. 19 0.181 1 .. 368 1.032 97 .. 21 12 .. 35 93 .. 78 11.18 96 .. 54 11 .. 93 

28 9.15 5 .. 24 0 .. 177 1 387 1.057 97 .. 21 11 .. 40 93 .. 76 10.71 96 .. 49 11 .. 42 

29 Sa9S 5.04 0.188 1 .. 411 0,,992 97 .. 41 12.47 93 .. 97 11 .. 14 96.67 12 48 

30 9.08 5 .. 16 0~186 1 .. 411 1.002 97 .. 23 13 .. 29 93.95 11 .. 47 96 .. 64 12.19 

31 9.11 5.40 o 168 1 546 1.108 97 .. 07 2 .. 69 93 .. 17 9.52 96 .. 36 10 .. 10 I-' 32 8890 5 .. 10 0 .. 180 1 566 1 .. 040 97.29 11 .. 77 94.06 10 .. 55 96.60 11.16 Vl 

w 33 8.95 5 .. 19 0 .. 178 1 567 1 .. 052 97 .. 10 11 .. 12 93 .. 97 10 .. 39 96 .. 53 11 .. 00 

34 9.07 5 .. 42 0.162 1 570 1 .. 152 96 .. 81 10 .. 49 93 .. 62 9.04 96 .. 21 9 .. 61 

35 8a80 5 03 0 .. 178 1 .. 707 1 .. 048 97 .. 34 12 .. 92 94.29 10 .. 07 96 .. 68 10 .. 61 

36 8 .. 74 4 .. 95 0.178 1 .. 724 1 .. 050 91 .. 33 1 .. 69 94 34 10.04 96 .. 10 10.58 

37 8 .. 63 4 .. 92 0 .. 160 1 .. 799 1 .. 166 97 .. 00 10 .. 98 94 .. 12 8 .. 57 96 .. 44 9 .. 06 

38 10 .. 62 5 .. 21 0 .. 181 1 .. 128 1.374 96 .. 92 5,,78 93.30 11.29 96 .. 37 12 .. 44 

39 10 .. 60 5 10 o 199 1 156 1.248 97 .. 31 9 13 93 .. 73 12 .. 74 96 .. 70 13.92 

40 10.69 5.22 o 197 18160 1 .. 261 97 .. 30 9 .. 64 93.12 12 .. 44 96 .. 68 13.57 

41 10.76 5.37 o 169 1.186 1.466 97.23 3.89 93 .. 68 9 .. 45 96.49 10.24 

42 10369 5 .. 32 0.169 1.199 1.471 97 .. 34 3 .. 50 93 .. 70 9 .. 41 96 .. 49 10 .. 18 

43 11~O5 5 .. 41 0.191 1 .. 221 1.621 97 .. 39 7 .. 54 92 .. 98 11.33 96 .. 06 12 .. 27 

44 10 94 5 .. 42 0 .. 184 1 .. 237 1.678 97.27 6 .. 84 92.S4 10 .. 13 95.92 11 .. 60 

45 10.79 4,,93 0.178 1 238 1 .. 739 97.18 4 24 93.28 10.00 96 .. 19 10 .. 78 

46 10 .. 64 5,,30 0.156 1 270 1 .. 588 91 .. 27 2 .. 09 93.89 7 .. 97 96.49 8 .. 55 

47 10 .. 88 4 .. 95 0.173 1.281 1.789 97919 3 .. 61 93.52 9.23 96.29 9 .. 91 

48 10 .. 59 5 .. 20 0 .. 152 1,,306 1.626 97.42 1 .. 98 94.06 7.51 96,,55 8 .. 03 

49 10 62 5 .. 02 0 .. 153 1 .. 362 1.623 97 .. 52 1.58 94 .. 49 7 .. 26 96.80 7.73 1-3 

IX' 

50 10.78 4.82 0.163 1 .. 368 1.519 97 .. 81 2820 95 .. 05 7.64 97.21 8.09 I w 

51 8.71 5 .. 06 0.151 1 .. 871 1.233 96 .. 90 10,,28 93.99 7.81 96.27 8 .. 28 ..... 

0 

CX) 
Table D-8. Countercurrent Condenser Data for 27060 Packing (Continued) 

Measured Model <1=0. 61JR) Model <1=0.80a) 

Cond- Press- Cond- Press- Cond- Pressensed ure en sed ure ensed ure 

No Tsi Twi G Ja Xii Steaa Loss Steaa Loss Steaa Loss 

(C) (C) kg/sill'" 2 (%) (%) (Pa) (%) (Pa) (%) (Pa) 

52 11.52 5.31 0.194 1.333 1.913 97.43 6.38 93.11 10.64 96.05 11.39 

53 11.55 5.31 0.192 1.346 1.925 97.48 6.30 93.20 10.36 96.10 11.08 

54 11.08 5.03 0.165 1.364 1.869 97.39 1.93 93.88 8.12 96.44 8.66 

55 11.32 5.02 0.163 1.443 1.895 97.57 1.94 94.33 7.53 96.69 8.00 

56 11.64 5.34 0.182 1.449 2.039 97.30 5.88 93.43 9.15 96.16 9.75 

...... 57 11.65 5.36 0.180 1.461 2.053 97.35 5.95 93.45 8.96 96.16 9.55 VI 

.p. 58 11.49 4.96 0.165 1.491 1.871 97.70 1.31 94.69 7.37 96.93 7.81 

59 11.35 4.91 0.184 1.557 2.013 97.46 3.97 93.84 9.08 96.41 9.63 

60 11.76 4.95 0.164 1.564 1.885 97.85 1.39 95.06 6.95 97.14 7.36 

61 11.45 5.07 0.182 1.568 2.031 97.30 4.23 93.79 8.90 96.35 9.45 

62 11.98 4.90 0.163 1.601 1.896 97.90 1.39 95.33 6.65 97.31 7.03 

63 11.54 5.27 0.180 1.798 2.054 97.22 4.21 93.96 ·8.44 96.40 8.94 

64 11.56 5.34 0.176 1.828 2.099 97.27 4.22 93.89 8.17 96.32 8.66 

65 11.50 5.22 0.184 1.881 2.012 97.35 4.60 94.11 8.62 96.49 9.12 

66 11.62 5.42 0.180 1.903 2.061 97.31 4.70 93.98 8.34 96.38 8.84 

67 11.34 4.90 0.187 2.039 1.982 97.51 4.37 94.45 8.66 96.71 9.14 

68 11.39 5.00 0.185 2.061 2.005 97.42 4.58 94.38 8.52 96.65 9.01 

69 11.43 5.13 0.178 2.482 2.078 97.31 4.44 94.49 7.90 96.64 8.36 

70 11.49 5.27 0.177 2.586 2.084 97.28 4.08 94.47 7.81 96.60 8.27 

71 11.60 5.25 0.176 1.353 2.106 97.17 3.57 93.16 9.00 96.00 9.64 

72 11.74 5.20 0.172 1.414 2.146 97.30 2.05 93.54 8.34 96.21 8.90 

73 11.99 5.31 0.167 1.488 2.210 97.37 2.18 93.79 7.66 96.33 8.16 

74 12.18 5.21 0.166 1.558 2.219 97.48 1.89 94.22 7.26 96.59 7.72 

75 12.39 5.25 0.168 1.581 2.200 97.63 1.81 94.43 7.20 96.74 7.64 

76 12.59 5.19 0.171 1.604 2.159 97.75 1.68 94.74 7.15 96.95 7.58 

In 

III 

N -

If

-~ 

I ) 

, - ' 

1-3 

:::0 

I 

w 

...... 

0 

00 
In 

Table D-8. Countercurrent Condenser Data for 27060 Packing (Continued) In 

N - ------------------------------------------------------------------------------------------- [ I .. '-' Measured Model <1=0.6b) Model <1=0.80.) 

Cond- Press- Cond- Press- Cond- Pressenaed ure enaed ure ensed ure 

No Tai Twi G Ja Xii Stea. Loss Stea. Loss Stea. Loss 

(C) (C) kg/sRI"'2 00 (") (Pa) (") (Pa) (") CPa) 

-------------------------------------------------------------------------------------------

77 12.91 5.20 0.174 1.640 2.120 97.87 2.05 95.08 7.03 97.19 7.44 

78 11.14 4.67 0.173 1.795 2.131 97.38 4.83 94.09 8.05 96.46 8.54 

79 11.13 4.83 0.158 1.915 2.334 96.99 4.12 93.79 7.12 96.16 7.58 

80 11.31 5.03 0.163 2.417 2.270 97.00 4.23 94.21 7.11 96.38 7.56 

81 11.38 5.10 0.172 2.461 2.155 97.20 3.79 94.36 7.59 96.53 8.05 

82 11.37 5.20 0.156 2.482 2.364 96.96 3.55 94.02 6.73 96.21 7.17 

I-' 83 11.34 5.04 0.169 2.490 2.188 97.23 4.28 94.37 7.41 96.51 7.86 U1 

U1 84 11.43 5.19 0.171 2.560 2.166 97.24 5.01 94.36 7.50 96.51 7.95 

85 11.51 5.32 0.169 2.698 2.181 97.19 4.04 94.38 7.33 96.49 7.78 

86 11.46 5.31 0.161 2.951 2.296 96.93 3.93 94.30 6.88 96.38 7.32 

87 11.22 4.85 0.170 3.037 2.177 97.25 4.22 94.68 7.36 96.68 7.80 

88 11.40 5.24 0.156 3.063 2.368 96.95 4.01 94.26 6.61 96.32 7.05 

89 11.24 4.94 0.160 3.182 2.312 96.97 4.27 94.51 6.81 96.51 7.25 

90 12.26 5.14 0.264 1.027 0.357 97.11 26.16 96.98 22.70 99.00 27.94 

91 12.26 5.05 0.267 1.030 0.353 97.54 24.04 97.10 22.81 99.07 27.72 

92 12.36 5.12 0.268 1.044 0.352 97.89 23.45 97.47 21.43 99.27 24.78 

93 12.45 5.10 0.268 1.051 0.351 98.21 21.94 97.71 20.54 99.37 23.23 

94 12.57 5.19 0.262 1.068 0.360 98.56 20.61 98.06 18.14 99.46 19.80 

95 12.68 5.19 0.261 1.077 0.360 98.83 19.80 98.25 17.15 99.51 18.47 

96 12.76 5.20 0.268 1.078 0.352 99.10 17.28 98.25 17.90 99.52 19.29 

97 12.92 5.34 0.257 1.119 0.366 99.36 14.19 98.67 14.36 99.58 15.00 

98 13.07 5.24 0.253 1.168 0.372 99.52 11.00 98.98 12.15 99.63 12.52 

99 12.52 5.08 0.269 1.050 0.696 97.35 21.86 95.75 20.53 98.26 23.81 ~ :::tl 

100 12.66 5.20 0.265 1.069 0.707 97.61 20.69 96.13 18.70 98.46 21.03 I 

w 

101 12.67 5.14 0.265 1.071 0.706 97.96 19.01 96.22 18.50 98.51 20.73 I-' 

0 

ex> 
Table D-8. Countercurrent Condenser Data for 27060 Packing (Continued) UI 

III 

N - ------------------------------------------------------------------------------------------- Measured Model 

I I .. "- " <1=0.61111 } Model <1=0.801l} 

eond- Press- eond- Press- eond- Pressensed ure ensed ure ensed ure 

No Tsi Twi G Ja Xii Stea. Loss Stea. Loss Steall Loss 

(e> (e) kg/slll"2 (%) 00 (Pa) (%) (Pa) (%) (Pa) 

-------------------------------------------------------------------------------------------

102 12.70 5.15 0.263 1.094 0.713 98.40 18.18 96.53 17.18 98.64 18.81 

103 12.82 5.18 0.261 1.110 0.718 98.63 16.76 96.76 16.13 98.74 17.44 

104 12.96 5.16 0.261 1.134 0.719 98.90 15.08 97.06 15.11 98.86 16.13 

105 13.24 5.17 0.255 1.207 0.734 99.15 11.70 97.60 12.56 99.04 13.13 

106 13.98 5.09 0.243 1.393 0.770 99.33 5.68 98.32 9.11 99.26 9.40 

....... 107 12.52 4.80 0.298 1.085 0.940 97.82 19.76 94.77 23.21 97.66 26.17 VI 

0'\ 108 10.34 4.96 0.203 1.091 0.922 97.12 11.48 94.41 14.28 97.27 16.01 

109 12.74 4.95 0.268 1.093 1.047 97.70 20.05 95.07 18.25 97.77 20.25 

110 10.85 5.51 0.203 1.097 0.923 97.00 11.19 94.45 13.77 97.30 15.37 

111 12.55 5.02 0.287 1.099 0.977 97.76 18.51 94.82 21.18 97.67 23.60 

112 12.08 4.93 0.290 1.109 0.968 97.88 18.27 94.52 22.40 97.48 24.95 

113 12.84 5.14 0.262 1.113 1.070 97.87 18.02 95.23 16.87 97.84 18.48 

114 12.08 4.96 0.285 1.119 0.984 97.87 17.49 94.63 21.33 97.53 23.59 

115 12.93 5.04 0.263 1.122 1.068 98.13 16.57 95.46 16.46 97.97 17.92 

116 13.06 5.07 0.261 1.153 1.075 98.43 14.79 95.79 15.30 98.12 16.43 

117 11.45 5.02 0.268 1.160 1.048 97.92 17.81 94.29 19.52 97.25 21.31 

118 11.44 4.98 0.268 1.160 1.047 97.86 19.18 94.33 19.48 97.27 21.26 

119 11.20 4.95 0.275 1.187 1.019 98.03 17.71 94.27 20.42 97.24 22.17 

120 11.20 4.97 0.273 1.191 1.029 98.03 16.81 94.27 20.09 97.23 21.78 

121 11.03 5.06 0.270 1.214 1.036 98.00 19.75 94.12 19.81 97.11 21.41 

122 11.05 5.11 0.270 1.218 1.038 98.03 19.46 94.10 19.77 97.10 21.35 

123 11.00 5.24 0.276 1.236 1.017 98.05 17.00 93.95 20.64 97.01 22.27 

124 10.93 5.22 0.269 1.241 1.040 98.05 16.61 93.94 19.74 96.98 21.27 

125 10.63 5.13 0.263 1.308 1.065 97.95 18.57 94.01 18.63 96.96 19.89 J--3 

::0 

126 10.60 5.04 0.265 1.311 1.055 98.08 19.24 94.12 18.77 97.03 20.01 I 

w 

127 10.43 4.91 0.275 1.344 1.020 98.13 16.65 94.18 19.93 97.07 21.18 ....... 0 

00 
In 

Table D-8. Countercurrent Condenser Data for 27060 Packing (Continued) In 

AI -

If ------------------------------------------------------------------------------------------- I I 

Measured Model <1=0.6h) Model <1=0.801l> ~-~ 

Cond- Press- Cond- Press- Cond- Pressensed ure ensed ure en sed ure 

Ho Tsi Twi G Ja Xii Steall Loss Steall Loss Stea. Loss 

(C) (C) kg/s .... 2 (") (") (Pa) (") (Pa) (,,) (Pa) 

-------------------------------------------------------------------------------------------

128 10.50 5.02 0.271 1.355 1.034 98.15 17.08 94.19 19.26 97.06 20.45 

129 10.51 5.17 0.268 1.393 1.044 98.11 19.38 94.15 18.69 97.01 19.80 

130 10.52 5.19 0.269 1.394 1.041 98.09 20.15 94.13 18.82 97.00 19.94 

131 10.30 5.02 0.269 1.456 1.041 98.14 18.64 94.27 18.56 97.05 19.58 

132 10.36 5.06 0.270 1.456 1.037 98.07 18.69 94.30 18.58 97.07 19.60 

133 10.41 5.23 0.267 1.499 1.051 98.11 18.57 94.25 18.05 97.01 19.01 

...... 134 10.45 5.30 0.264 1.507 1.063 98.04 15.80 94.22 17.65 96.98 18.59 V1 

-.I 135 10.33 ·5.20 0.264 1.572 1.063 98.08 18.14 94.36 17.38 97.04 18.25 

136 10.37 5.28 0.257 1.595 1.089 98.06 18.91 94.36 16.48 97.01 17.30 

137 12.05 5.09 0.238 1.115 1.175 97.43 14.34 94.58 15.47 97.38 17.02 

138 12.09 4.98 0.241 1.117 1.164 97.40 14.71 94.73 15.59 97.48 17.11 

139 11.92 5.03 0.249 1.141 1.124 97.52 16.75 94.72 16.39 97.47 17.86 

140 11.80 4.94 0.249 1.141 1.124 97.62 16.01 94.68 16.54 97.45 18.03 

141 11.24 5.20 0.230 1.188 1.214 97.59 13.42 94.10 14.91 96.99 16.14 

142 11.24 5.10 0.234 1.194 1.198 97.60 14.52 94.25 15.17 97.09 16.38 

143 11.27 5.26 0.244 1.203 1.147 97.68 15.86 94.15 16.34 97.06 17.65 

144 11.32 5.24 0.244 1.212 1.148 97.70 17.13 94.29 16.06 97.14 17.29 

145 10.92 5.43 0.226 1.272 1.237 97.57 14.32 93.82 14.38 96.73 15.41 

146 10.88 5.34 0.228 1.273 1.227 97.66 14.55 93.89 14.56 96.79 15.59 

147 11.01 5.44 0.242 1.284 1.156 97.70 17.82 94.01 15.86 96.91 16.96 

148 10.95 5.33 0.244 1.284 1.149 97.75 17.97 94.07 16.08 96.95 17.19 

149 10.58 5.20 0.246 1.392 1.138 97.82 18.71 94.19 15.94 96.96 16.89 

150 10.38 5.02 0.230 1.393 1.217 97.71 14.69 94.12 14.40 96.86 15.26 

151 10.65 5.33 0.242 1.399 1.160 97.81 17.94 94.10 15.48 96.89 16.40 ~ 

l:O 

152 10.36 5.10 0.219 1.423 1.274 97.66 14.91 94.05 13.21 96.76 14.00 I 

w 

153 10.44 5.31 0.229 1.497 1.224 97.74 16.02 94.08 13.93 96.78 14.71 ..... 

0 

(Xl 
In 

Table D-8. Countercurrent Condenser Data for 27060 Packing (Continued) III 

N 

-

II I I ------------------------------------------------------------------------------------------- '-. Measured Hodel <1=0. 611ft) Model <1=0.80a> 

Cond- Press- Cond- Press- Cond- Pressen sed ure ensed ure en sed ure 

No Tsi Twi G Ja Xii Steaa Loss Steaa Loss Steaa Loss 

(C) (C) kg/sJR"2 00 00 (Pa) (") (Pa) (") (Pa) 

-------------------------------------------------------------------------------------------

154 10.44 5.32 0.228 1.498 1.225 97.69 16.51 94.09 13.83 96.78 14.60 

155 10.44 5.28 0.238 1.533 1.176 97.73 18.80 94.26 14.61 96.91 15.39 

156 10.20 5.07 0.225 1.612 1.243 97.73 16.69 94.33 13.21 96.88 13.90 

157 10.17 5.08 0.221 1.636 1.268 97.72 15.89 94.28 12.83 96.82 13.50 

158 10.25 5.13 0.238 1.675 1.175 97.83 18.39 94.50 14.21 97.01 14.90 

159 10.07 4.95 0.226 1.687 1.240 97.84 1.96 94.44 13.17 96.92 13.82 ..... 160 10.18 5.06 0.233 1.704 1.199 97.83 18.60 94.53 13.68 97.00 14.34 VI 

00 161 10.12 5.06 0.218 1.716 1.283 97.67 15.32 94.37 12.38 96.84 13.01 

162 13.16 5.11 0.261 1.152 1.427 97.90 15.45 94.48 15.98 97.31 17.33 

163 13.22 5.09 0.258 1.179 1.442 98.15 13.76 94.73 15.08 97.43 16.21 

164 14.11 5.33 0.273 1.196 1.699 98.05 12.55 94.23 15.76 97.12 16.94 

165 13.39 5.10 0.256 1.215 1.456 98.31 12.62 95.04 14.12 97.59 15.06 

166 14.24 5.40 0.262 1.242 1.768 98.22 10.57 94.48 14.03 97.22 14.97 

167 13.60 4.98 0.257 1.257 1.446 98.57 11.29 95.47 13.33 97.82 14.10 

168 14.06 5.03 0.249 1.348 1.494 98.68 9.54 95.97 11.45 98.06 12.01 

169 14.84 5.14 0.261 1.390 1.781 98.62 6.59 95.47 11.98 97.77 12.58 

170 14.90 4.90 0.253 1.495 1.472 98.95 6.81 96.73 10.14 98.46 10.56 

171 16.19 4.90 0.286 1.496 1.303 99.22 7.17 97.31 10.91 98.84 11.30 

172 14.46 5.36 0.255 1.312 1.819 98.36 8.32 94.88 12.56 97.42 13.28 

173 14.34 5.09 0.262 1.342 2.122 98.05 8.51 94.12 13.60 96.93 14.42 

174 14.36 5.26 0.258 1.357 2.154 98.00 8.58 94.03 13.27 96.86 14.07 

175 14.39 5.21 0.257 1.366 2.164 98.03 9.18 94.11 13.07 96.90 13.85 t-3 

176 14.79 5.33 0.255 1.376 1.815 98.51 7.54 95.30 11.76 97.65 12.38 ::0 

I 

177 14.07 5.07 0.258 1.438 2.154 98.09 7.16 94.16 13.14 96.90 13.88 w 

..... 178 14.11 5.19 0.254 1.443 2.186 98.03 6.91 94.09 12.83 96.85 13.56 0 

00 
In 

Table D-8. Countercurrent Condenser Data for 27060 Packing (Continued) III 

N 

-

" ------------------------------------------------------------------------------------------- I I 

Measured Model <1=0.61a) Model <1=0.801R) ,_ 7 

Cond- Press- Cond- Press- Cond- Pressen sed ure ensed ure en sed ure 

No Tsi Twi G Ja Xii StealR Loss StealR Loss StealR Loss 

(C) (C) kg/slR"2 (%) (%) (Pa) (%) (Pa) (%) (Pa) 

-------------------------------------------------------------------------------------------

179 15.28 5.05 0.253 1.508 1.833 98.75 5.61 95.94 10.48 98.00 10.96 

180 15.49 5.11 0.254 1.563 2.185 98.48 5.81 95.25 10.82 97.57 11.36 

181 14.04 5.35 0.259 1.642 2.145 98.06 5.48 94.31 12.75 96.93 13.42 

182 14.02 5.32 0.255 1.663 2.180 98.07 0.69 94.31 12.42 96.92 13.06 

183 15.89 4.89 0.242 1.683 1.914 98.83 4.21 96.44 8.89 98.25 9.28 

184 16.62 4.99 0.255 1.750 2.177 98.74 4.70 96.05 9.50 98.05 9.93 ...... 185 13.89 5.16 0.260 1.891 2.133 98.14 5.46 94.64 12.41 97.10 13.01 \J1 

\0 186 13.90 5.24 0.253 2.171 2.193 98.04 5.52 94.77 11.64 97.13 12.20 

187 14.64 5.31 0.252 1.415 2.200 98.12 8.31 94.33 12.18 97.02 12.88 

188 14.81 5.25 0.252 1.458 2.202 98.22 7.72 94.57 11.79 97.16 12.43 

189 15.02 5.20 0.252 1.490 2.201 98.31 7.41 94.80 11.42 97.30 12.02 

190 13.95 5.15 0.251 1.589 2.210 98.04 6.79 94.26 12.29 96.90 12.95 

191 13.96 5.14 0.252 1.589 2.206 98.03 6.29 94.27 12.35 96.91 13.01 

192 16.13 5.08 0.251 1.697 2.216 98.57 4.56 95.72 9.79 97.84 10.25 

193 13.80 5.04 0.245 1.879 2.263 98.03 5.14 94.54 11.42 97.01 12.00 

194 13.80 5.06 0.238 1.916 2.328 97.99 4.98 94.51 10.92 96.97 11.48 

195 13.96 5.30 0.251 1.943 2.214 98.03 5.78 94.57 11. 71 97.03 12.30 

196 13.89 5.24 0.245 2.092 2.260 97.96 6.02 94.66 11.19 97.05 11.74 

197 13.91 5.28 0.241 2.135 2.304 97.97 4.72 94.63 10.90 97.01 11.45 

198 13.84 5.15 0.252 2.196 2.206 98.07 1.49 94.78 11.58 97.14 12.14 

199 13.77 5.12 0.234 2.448 2.367 97.91 4.51 94.78 10.31 97.07 10.84 

200 13.80 5.09 0.247 2.490 2.243 98.04 5.82 94.95 11.06 97.20 11.60 

201 13.83 5.27 0.226 2.507 2.448 97.82 4.23 94.69 9.80 96.98 10.32 

202 13.76 5.04 0.245 2.512 2.266 97.95 2.19 94.94 10.95 97.19 11.49 . t-3 

~ 

203 13.85 5.27 0.238 2.640 2.331 97.86 5.23 94.86 10.47 97.11 11.00 I 

w 

204 13.86 5.26 0.238 2.648 2.325 97.92 4.87 94.89 10.44 97.13 10.97 ...... 

0 

00 
In 

Table Ir8. Countercurrent Condenser Data for 27060 Packing (Continued) In 

N - ------------------------------------------------------------------------------------------- II I J 

~-~ 

Measured Model <1=0.611R) Model <1=0.80.) 

Cond- Press- Cond- Press- Cond- Pressensed ure en sed ure ensed ure 

No Tsi Twi G Ja Xii Stea. Loss Stea. Loss Stea. Loss 

(C) (C) kg/s .... 2 (%) (%) (Pa) (%) (Pa) (%) (Pa) 

-------------------------------------------------------------------------------------------

205 13.76 5.11 0.240 2.777 2.307 97.93 4.86 94.99 10.55 97.19 11.08 

206 13.77 5.13 0.236 2.821 2.350 97.95 1.59 94.96 10.30 97.16 10.82 

207 14.69 5.12 0.389 1.020 0.322 97.49 39.45 96.56 40.37 98.75 52.34 

208 14.70 5.20 0.389 1.020 0.321 97.49 38.81 96.52 40.49 98.72 52.65 

209 14.65 5.10 0.383 1.040 0.652 97.73 33.70 95.39 34.88 98.13 41.94 I-' 

0- 210 16.43 5.16 0.375 1.042 0.995 98.80 23.05 95.26 27.76 98.03 32.38 

0 211 14.76 5.25 0.378 1.051 0.660 97.69 34.31 95.66 32.60 98.31 38.23 

212 16.50 5.45 0.382 1.064 0.978 97.67 28.67 95.46 27.34 98.17 31.02 

213 15.04 4.95 0.390 1.083 0.958 98.07 31.27 95.05 31.12 97.92 35.09 

214 15.02 4.92 0.391 1.084 0.956 98.08 31.66 95.06 31.24 97.93 35.20 

215 16.87 5.26 0.371 1.027 1.008 99.04 20.79 95.18 27.33 97.95 32.65 

216 17.18 5.41 0.359 1.064 1.040 99.26 14.27 95.94 22.50 98.42 25.20 

217 15.58 5.48 0.354 1.066 1.054 97.83 26.23 95.00 25.66 97.86 29.17 

218 15.52 5.28 0.359 1.073 1.038 98.07 25.18 95.17 25.90 97.97 29.21 

219 15.63 5.21 0.354 1.102 1.054 98.34 24.95 95.64 23.38 98.21 25.68 

220 15.32 4.56 0.396 1.146 1.255 98.38 27.64 94.91 28.31 97.77 30.77 

221 15.24 4.73 0.382 1.155 1.302 98.35 27.55 94.85 26.51 97.71 28.72 

222 15.98 5.16 0.366 1.169 1.020 98.53 25.53 96.35 21.58 98.56 22.97 

223 14.38 5.25 0.357 1.231 1.391 98.42 25.58 94.40 24.21 97.36 25.91 

224 14.30 5.10 0.360 1.235 1.381 98.40 25.85 94.47 24.53 97.40 26.22 

225 13.97 5.10 0.373 1.307 1.334 98.56 28.77 94.55 25.73 97.43 27.27 

226 14.00 5.25 0.363 1.318 1.371 98.49 28.90 94.50 24.42 97.38 25.85 

227 13.73 5.39 0.363 1.434 1.371 98.51 26.25 94.56 23.83 97.37 25.04 J-3 

lx:I 

228 13.69 5.34 0.362 1.441 1.373 98.52 26.21 94.60 23.67 97.38 24.85 I 

VJ 

229 13.42 5.25 0.373 1.696 1.332 98.61 28.86 94.99 23.52 97.56 24.46 I-' 

0 

00 
1ft 

Table D-8. Countercurrent Condenser Data for 27060 Packing (Continued) In 

N 

-

If ------------------------------------------------------------------------------------------- I I 

Measured Model (1=0.6b) Model (1=0.80.) '- ~ 

Cond- Press- Cond- Press- Cond- Pressen sed ure ensed ure en sed ure 

No Tsi Twi G Ja Xii Stea. Loss Stea. Loss Stea. Loss 

(C) (C) kg/sa"2 00 (~) (Pa) (~) (Pa) (~) (Pa) 

-------------------------------------------------------------------------------------------

230 13.49 5.36 0.367 1.709 1.355 98.58 29.01 94.97 22.75 97.54 23.67 

231 16.95 5.21 0.350 1.155 2.114 98.42 16.04 93.61 21.03 96.88 22.84 

232 17.21 4.82 0.361 1.201 2.053 98.59 15.91 94.26 20.50 97.28 21.95 

233 15.79 5.14 0.371 1.206 1.672 98.43 22.12 94.20 23.86 97.26 25.61 

234 15.73 5.03 0.369 1.209 1.681 98.44 22.73 94.25 23.58 97.28 25.29 

235 I-' 21.15 4.91 0.372 1.228 1.990 99.25 8.32 95.92 15.22 98.31 16.05 0- 236 17.67 4.78 0.356 1.270 2.082 98.75 14.08 94.78 18.26 97.57 19.33 I-' 

237 19.43 4.83 0.351 1.294 2.108 99.06 9.30 95.55 15.18 98.03 15.97 

238 18.34 4.80 0.356 1.294 2.080 98.89 12.58 95.15 17.01 97.79 17.92 

239 17.72 5.30 0.392 1.330 2.215 98.51 19.38 94.01 22.06 97.10 23.34 

240 17.69 5.23 0.389 1.346 2.217 98.54 20.13 94.11 21.57 97.15 22.78 

241 13.08 4.66 0.352 1.688 1.410 98.61 25.34 95.12 21.40 97.61 22.26 

242 13.10 4.77 0.340 1.729 1.463 98.57 23.67 95.08 20.07 97.55 20.88 

243 16.08 5.13 0.409 1.112 1.220 98.24 30.83 94.68 30.17 97.68 33.35 

244 15.95 5.27 0.400 1.117 1.245 98.23 28.66 94.59 29.19 97.61 32.20 

245 17.69 5.45 0.424 1.191 1.755 98.44 25.80 94.15 27.09 97.29 29.16 

246 17.72 5.54 0.422 1.195 1.763 98.43 26.00 94.14 26.77 97.29 28.79 

Miniau.: 

8.63 4.56 0.151 0.988 0.321 95.94 0.69 92.84 6.61 95.92 7.03 

Haxiau.: 

21.15 5.68 0.424 3.182 2.448 99.52 39.45 98.98 40.49 99.63 52.65 t-'3 

::.0 

Average: I 

w 

12.37 5.15 0.244 1.455 1.418 97.83 12.54 94.76 14.77 97.27 16.12 ...... 

0 

00 
Table D-8. Countercurrent Condenser Data for 27060 Packing (Concluded) 

Keasured Kodel <1=0.61a) 

Cond- Press- Cond- Pressensed ure en sed ure 

No Tsi Twi G Ja Xii Steal! Loss SteaM Loss 

(C) (C) kg/s .... 2 (") 00 (Pa) (") (Pa) 

Standard Deviation: 

2.29 0.17 0.069 0.444 0.590 0.63 8.31 1.11 6.35 

Difference Between Predictions (1=0.8.) and Experi.ent: 

Condensed Steam (") 

Pressure Loss (Pa) 

No. of Standard 

Points Average Deviation 

246 

246 

-0.60 

3.60 

0.70 

3.40 

Kodel <1=0.80.) 

Cond- Pressen sed ure 

SteaM Loss 

(") (Pa) 

0.81 7.53 

lit 

IU 

N -

-

-' 

I I 

"- ' 

I-cl 

i':l 

I 

W 

..... 

o 

CIO 
TR-3l08 

APPENDIX E DATA TABLES FOR COUNTERCURRENT CONDENSER GEOMETRIES OTHER THAN 

STRUCTURED PACKING 

This appendix provides a complete set of experimental data for countercurrent 

condensers not using structured packing. Their geometries are described and 

performances are evaluated in Appendix C. 

Table E-l contains the data for spiral screen configuration 1 in Table C-l. 

Tables E-2 through E-4 contain the data for di sc-donut baffle contactors, 

configurations 2 through 4. Table E-S contains data for configuration S. 

Table E-6 summarizes the data for configuration 8 using random packings tested 

at three different packing fill depths. 

All the tables contain 9 columns. Column 1 refers to a serial number. 

Column 2, labeled T i' represents the measured saturation temperature of the 

incoming steam and inert gas mixture in degrees Celsius; the uncertainty in 

this measurement is ±0.02°C. Column 3, labeled T i' represents the measured 

water inlet temperature in degrees Celsius with an wuncertainty of ±O.OloC. 

Column 4, labeled G, is the condenser gas loading defined as the entire mass 

flow rate of the steam and inert gas mixture divided by the flow planform area 

of the condenser; this quantity is expressed in kg/m2 s and possesses an 

uncertainty of ±2. 5% of the measured value. Column 5, labeled Ja, is the 

Jakob number with an uncertainty of ±1.9%. 

Column 6, labeled X. i' is the inert gas mass concentration ln the incoming 

steam expressed as la percentage of the total steam and inert gas mixture 

flow. This quantity is estimated to possess an uncertainty of ±2.4% of the 

quoted value. 

Column 7 represents the amount of steam condensed within the contactor 

expressed as a percentage of the incoming steam flow with an uncertainty of 

±l. 9% of the incoming steam flow. Column 8 represents the measured overall 

condenser pressure loss (static pressure difference between inlet and outlet 

gas streams) expressed in Pascals, with an uncertainty of ±10 Pa or ±10% of 

the quoted value, whichever is greater. Column 9 refers to the vent fraction 

of Eq. C-6 and possesses an uncertainty of less than 10%. 

163 
5='1'11, TR-3108 

Table E-l. Countercurrent Condenser Data for Configuration 1 

with Spiral Metal Screen 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi T . W1. G Ja x· . 1.1. Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

1 15.98 5.90 0.331 2.346 3.307 93.34 63.20 0.876 

2 15.47 5.67 0.314 2.363 2.913 93.09 60.77 0.849 

3 14.87 4.98 0.329 2.307 2.245 93.79 75.54 0.837 

4 14.28 5.41 0.379 1.793 1.469 94.41 167.16 0.634 

5 14.23 5.66 0.384 1.699 0.971 94.36 169.80 0.589 

6 14.02 5.69 0.386 1.614 0.485 94.35 196.14 0.504 

7 14.56 6.06 0.450 1. 394 0.415 94.99 171.75 0.640 

8 14.62 5.92 0.458 1.419 0.407 95.08 236.21 0.510 

9 14.66 5.86 0.447 1.476 0.418 94.96 230.71 0.541 

10 14.68 5.73 0.450 1.493 0.415 95.07 140.45 0.692 

11 14.64 5.39 0.443 1.561 0.843 95.17 188.53 0.607 

12 14.74 5.35 0.449 1.552 0.832 95.18 248.06 0.560 

13 14.85 5.26 0.459 1.560 0.813 95.34 171. 59 0.646 

14 15.30 5.30 0.460 1.616 1.214 95.34 240.00 0.611 

15 15.38 5.44 0.461 1.598 1.212 95.30 210.95 0.637 

16 15.83 5.58 0.446 1. 708 1.668 95.13 170.26 0.717 

17 15.95 5.64 0.447 1. 706 1.664 95.12 144.67 0.748 

18 15.74 5.53 0.466 1.631 1.597 95.35 191.45 0.674 

19 16.21 5.36 0.454 1.776 2.036 95.27 140.17 0.770 

20 16.95 5.45 0.446 1.902 2.476 95.10 115.52 0.808 

21 8.98 5.03 0.219 1.476 0.854 90.81 92.27 0.582 

22 9.02 5.10 0.209 1.513 0.894 90.31 91.83 0.589 

23 9.71 4.69 0.219 1.896 1.695 91.02 44.02 0.781 

24 9.75 4.75 0.210 1.944 1. 765 90.60 41.09 0.793 

25 10.79 4.27 0.217 2.446 2.543 91.16 25.53 0.894 

26 10.79 4.38 0.204 2.579 2.699 90.54 24.16 0.899 

27 10.30 4.48 0.220 2.166 2.096 91.18 34.53 0.850 

28 10.39 4.65 0.207 2.269 2.226 90.52 30.97 0.866 

29 9.46 4.96 0.219 1.662 1.272 90.88 72.34 0.716 

30 9.08 5.29 0.223 1.370 0.420 90.76 144.01 0.398 

31 9.09 5.26 0.228 1.372 0.411 91.02 144.58 0.163 

32 15.58 5.53 0.498 1.539 0.750 95.28 451.02 0.326 

33 15.55 5.54 0.497 1.534 0.751 95.32 442.16 0.357 

34 15.44 5.78 0.487 1.513 1.528 95.51 235.63 0.653 

35 15.46 5.78 0.490 1.501 1.519 95.53 230.37 0.666 

36 16.38 5.56 0.471 1. 758 2.350 95.40 115.65 0.820 

37 16.40 5.60 0.454 1. 798 2.432 95.23 113.85 0.827 

38 17.05 5.10 0.460 1.990 2.821 95.42 92.61 0.861 

39 17 .08 5.16 0.457 2.005 2.838 95.38 95.96 0.860 

164 
5=~1'*' TR-3108 

Table E-l. Countercurrent Condenser Data for Configuration 1 

with Spiral Ketal Screen (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. T . Sl T . WI G Ja X .. 

11 Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

40 15.66 5.54 0.468 1.628 1.978 95.39 158.23 0.769 

41 15.62 5.43 0.491 1.606 1.888 95.65 153.52 0.769 

42 15.27 5.50 0.484 1.544 1.153 95.44 338.77 0.516 

43 15.28 5.54 0.481 1.546 1.159 95.40 339.63 0.475 

44 15.09 5.58 0.483 1.505 0.386 94.94 475.77 0.188 

45 15.11 5.61 0.479 1.512 0.391 94.88 475.20 0.184 

46 14.99 4.76 0.494 1.622 0.474 95.42 472.72 0.257 

47 14.92 4.75 0.497 1.602 0.472 95.49 469.29 0.244 

48 14.87 4.77 0.487 1.632 0.959 95.67 367.28 0.449 

49 14.94 4.77 0.487 1.638 0.958 95.65 369.78 0.457 

50 15.08 4.87 0.502 1.590 1.455 95.92 193.66 0.710 

51 15.15 4.99 0.493 1.612 1.481 95.81 192 .44 0.686 

52 15.49 4.96 0.504 1.634 1.607 95.89 173.74 0.731 

53 15.71 4.95 0.510 1.646 1.587 95.94 177 .44 0.736 

54 15.93 5.12 0.501 1.682 1.163 95.70 349.36 0.505 

55 15.94 5.17 0.500 1.673 1.163 95.69 352.72 0.519 

56 15.34 5.18 0.506 1.552 0.694 95.48 450.89 0.303 

57 15.24 5.22 0.488 1.587 0.719 95.32 436.53 0.325 

58 14.89 5.24 0.496 1.508 0.236 95.18 514.17 0.144 

59 14.92 5.18 0.502 1.513 0.234 95.25 524.72 0.145 

60 14.84 5.18 0.485 1.533 0.724 95.35 425.25 0.342 

61 14.80 5.08 0.483 1.545 0.727 95.35 423.01 0.316 

62 14.80 5.05 0.492 1.532 0.714 95.51 362.29 0.420 

63 14.89 5.10 0.492 1.537 0.713 95.44 367.99 0.415 

64 15.06 5.52 0.493 1.487 0.712 95.55 107.05 0.781 

65 15.02 5.46 0.501 1.470 0.701 95.63 104.21 0.776 

66 15.16 5.57 0.477 1.526 0.735 95.15 412.81 0.362 

67 15.16 5.65 0.480 1.513 0.732 95.15 412.47 0.370 

68 14.66 5.56 0.494 1.419 0.711 95.58 232.17 0.616 

69 14.57 5.56 0.488 1.407 0.720 95.54 223.28 0.600 

70 14.44 5.51 0.489 1.399 0.718 95.59 140.21 0.741 

71 14.55 5.74 0.477 1.411 0.735 95.42 138.75 0.720 

72 11.25 5.29 0.173 2.597 3.298 88.02 11.87 0.900 

73 11.28 5.29 0.171 2.633 3.326 87.93 12.03 0.902 

74 14.31 4.31 0.146 5.149 7.454 86.51 62.94 0.881 

75 14.30 4.25 0.148 5.123 7.384 86.65 65.19 0.862 

76 16.62 5.39 0.160 5.737 8.657 86.85 31.36 0.936 

77 16.64 5.40 0.162 5.716 8.590 86.96 28.83 0.939 

165 
55'1,*, TR-3108 

Table E-l. Countercurrent Condenser Data for Configuration 1 

with Spiral Metal Screen (Concluded) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi T . 

W1 G Ja x· . 11 Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

78 13.27 5.99 0.438 1.342 0.143 94.78 447.21 0.088 

79 13.24 5.96 0.436 1.340 0.144 94.77 450.86 0.125 

80 13 .50 5.67 0.430 1.450 0.436 94.81 445.19 0.192 

81 13.49 5.64 0.433 1.446 0.434 94.84 448.71 0.202 

82 14.15 5.42 0.429 1.628 1. 733 95.11 142.45 0.742 

83 14.18 5.44 0.434 1.624 1. 710 95.15 142.56 0.754 

84 16.98 5.15 0.471 1.994 2.721 95.57 98.88 0.863 

85 16.96 5.25 0.470 1.991 2.721 95.54 99.23 0.865 

86 17.50 6.38 0.414 2.790 3.092 94.59 106.82 0.859 

87 17.37 6.16 0.422 2.745 3.026 94.77 107.39 0.863 

88 13 .03 5.43 0.390 1.507 0.481 94.41 344.24 0.232 

89 12.57 5.70 0.374 1.827 0.501 94.40 276.69 0.391 

90 11. 71 5.50 0.364 2.050 0.515 94.40 234.89 0.392 

91 12.07 5.53 0.364 1.972 0.515 94.37 249.52 0.404 

92 12.88 5.26 0.384 1. 776 0.488 94.63 314.28 0.361 

93 14.48 5.57 0.418 1.397 0.449 94.08 380.30 0.150 

94 14.60 5.97 0.399 1.419 0.937 93.92 305.09 0.375 

95 13.64 5.73 0.360 1.944 1. 037 94.12 184.77 0.590 

96 12.48 5.28 0.353 2.255 1.057 94.27 157.55 0.657 

97 12.88 5.38 0.355 2.562 1.052 94.28 167.34 0.634 

98 13 .06 5.20 0.383 2.057 0.974 94.72 188.02 0.612 

99 13.19 5.32 0.385 1.587 0.970 94.56 229.93 0.520 

100 16.63 5.78 0.512 1.612 0.731 95.06 471. 86 0.304 

101 15.52 6.01 0.454 1.608 0.823 94.84 388.39 0.313 

102 15.58 5.66 0.464 1.641 0.806 95.27 285.01 0.535 

103 15.54 5.62 0.473 1.617 0.790 95.37 246.96 0.584 

104 15.54 5.64 0.477 1.600 0.785 95.37 254.95 0.581 

105 15.83 5.92 0.461 1.632 0.812 94.37 113.98 0.535 

------------------------------------------------------------------

166 
S5'l1,1f, 

TR-3108 

Table E-2. Countercurrent Condenser Data for Configuration 2 

with Three Pairs of Baffles 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi T . 

W1 G Ja X .. 

11 Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

1 12.89 4.98 0.198 2.088 1.874 92 .37 160.52 0.618 

2 12.89 5.09 0.193 2.119 1.924 92.11 128.22 0.677 

3 10.78 5.64 0.201 1.328 0.311 92.21 242.20 0.206 

4 10.79 5.69 0.196 1.352 0.319 91.99 237.14 0.248 

5 12.30 5.18 0.191 1.939 1.622 92.03 152.16 0.629 

6 12.29 5.20 0.186 1.979 1.664 91.83 158.12 0.624 

7 11.11 5.48 0.1.98 1.462 0.632 92.18 215.47 0.344 

8 11.06 5.49 0.195 1.461 0.640 92 .07 203.56 0.388 

9 11. 70 5.02 0.195 1.793 1.275 92.31 156.62 0.605 

10 11. 73 5.08 0.189 1.833 1.313 92.04 170.67 0.583 

11 11.37 5.33 0.189 1.643 0.987 91.92 191.75 0.496 

12 11.37 5.33 0.189 1.643 0.987 91 .• 92 191.75 0.496 

13 11.41 5.17 0.200 1.611 0.933 92.43 195.60 0.441 

14 15.98 4.91 0.378 1.477 0.660 96.07 565.32 0.329 

15 16.01 4.91 0.381 1.467 0.655 96.10 589.30 0.306 

16 17.18 4.90 0.378 1.626 1.317 96.00 474.78 0.507 

17 17.20 4.91 0.379 1.637 1.315 96.01 491.82 0.497 

18 18.06 5.23 0.375 1.704 1.978 95.76 318.79 0.663 

19 18.05 5.14 0.383 1.693 1.938 95.88 318.41 0.666 

20 18.76 5.27 0.376 1.775 2.340 95.68 274.62 0.705 

21 18.79 5.23 0.381 1. 771 2.313 95.74 255.38 0.721 

22 17.80 5.26 0.377 1.633 1.645 95.84 455.98 0.549 

23 17.78 5.41 0.371 1.654 1.670 95.74 455.72 0.541 

24 16.16 5.06 0.362 1.526 1.030 95.81 481.65 0.444 

25 16.16 5.12 0.360 1.534 1.037 95.76 481.09 0.445 

26 15.26 4.98 0.362 1.396 0.346 95.87 633.96 0.216 

27 15.34 5.01 0.364 1.393 0.345 95.90 638.38 0.214 

28 18.15 4.78 0.341 2.570 2.601 95.53 242.15 0.751 

29 18.48 4.89 0.329 3.225 2.684 95.41 321.49 0.715 

30 19.34 6.90 0.420 1.447 0.890 95.88 758.79 0.303 

31 18.32 6.09 0.419 1.445 0.893 96.07 656.54 0.380 

32 18.26 6.29 0.402 1.473 0.931 95.86 663.11 0.370 

33 17.04 5.01 0.396 1.504 0.943 96.14 576.79 0.410 

34 17.08 5.16 0.391 1.511 0.955 96.06 560.96 0.422 

35 15.74 3.96 0.389 1.520 0.960 96.36 477.51 0.454 

36 15.71 4.25 0.371 1.547 1.008 96.11 458.40 0.469 

37 18.21 3.93 0.391 1.831 2.245 96.16 240.68 0.728 

38 18.24 4.03 0.389 1.844 2.234 96.15 225.89 0.743 

39 18.97 5.43 0.386 1. 737 2.261 95.72 275.45 0.704 

167 
Table E-2. Countercurrent Condenser Data for Configuration 2 

with Three Pairs of Baffles (Concluded) 

Cond- Pressensed ure Vent 

S.No. T . SI T . WI G Ja x· . 11 Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

40 18.76 5.22 0.386 1. 718 2.273 95.78 244.75 0.727 

41 19.71 5.88 0.403 1.688 2.165 95.84 350.20 0.680 

42 19.67 5.79 0.408 1.685 2.163 95.91 366.47 0.671 

43 20.86 6.91 0.406 1.654 2.137 95.58 490.06 0.609 

44 20.77 6.82 0.409 1.659 2.163 95.62 457.45 0.628 

168 

TR-3108 
55'1,*, 

TR-3108 

Table E-3. Countercurrent Condenser Data for Configuration 3 

with Two Pairs of Baffles 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi T . 

W1 G Ja x· . 11 Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

1 13.15 4.75 0.166 2.566 2.227 90.73 84.87 0.600 

2 13 .18 4.71 0.174 2.499 2.127 91.15 84.14 0.597 

3 10.39 5.37 0.179 1.436 0.350 91.25 98.00 0.183 

4 10.35 5.35 0.178 1.439 0.352 91.23 128.60 0.083 

5 12.63 4.97 0.176 2.232 1. 760 91.19 86.60 . 0.550 

6 12.62 5.00 0.169 2.285 1.828 90.86 79.29 0.571 

7 11.12 5.37 0.185 1.575 0.674 91.47 115.60 0.264 

8 11.17 5.47 0.179 1.628 0.699 91.13 112.06 0.272 

9 12.19 5.38 0.166 2.076 1.491 90.54 72 .35 0.562 

10 12.18 5.32 0.171 2.029 1.452 90.79 85.20 0.539 

11 11.64 5.47 0.175 1. 788 1.064 90.98 73.08 0.457 

12 11.62 5.43 0.177 1.778 1.055 91.06 91. 74 0.406 

13 15.85 4.93 0.356 1.583 0.700 95.66 495.06 0.262 

14 15.93 4.90 0.350 1.630 0.713 95.46 450.66 0.302 

15 16.21 4.81 0.367 1.596 1.354 95.50 199.64 0.546 

16 16.24 4.96 0.358 1.622 1.388 95.32 186.96 0.558 

17 18.53 5.39 0.384 1. 746 1.929 95.27 147.65 0.624 

18 18.55 5.47 0.367 1.804 2.017 95.02 148.01 0.620 

19 19.51 5.21 0.365 1.999 2.415 94.90 135.62 0.645 

20 19.54 5.24 0.365 1.989 2.410 94.86 148.90 0.631 

21 17.44 5.31 0.364 1.687 1. 704 95.14 174.92 0.576 

22 17.51 5.38 0.354 1. 717 1. 748 94.97 167.76 0.585 

23 16.67 5.45 0.362 1. 575 1.031 95.57 417.49 0.420 

24 16.59 5.40 0.364 1.566 1.026 95.59 408.93 0.387 

25 15.46 5.40 0.362 1.413 0.345 95.23 471.48 0.144 

26 15.41 5.39 0.358 1.415 0.349 95.18 465.59 0.170 

27 17.15 4.63 0.460 1.369 0.272 96.57 788.31 0.119 

28 17.42 4.59 0.475 1.359 0.263 96.69 807.25 0.108 

29 18.07 4.21 0.470 1.480 0.531 97.06 845.04 0.244 

30 18.09 4.24 0.460 1.502 0.544 96.98 847.51 0.244 

31 18.77 4.63 0.469 1.508 0.797 96.93 785.31 0.325 

32 18.72 4.49 0.473 1.507 0.792 97.00 768.88 0.326 

33 18.76 4.46 0.466 1.534 1.072 96.90 630.08 0.439 

34 18.79 4.42 0.466 1.540 1.071 96.90 650.23 0.425 

35 19.23 4.32 0.465 1.611 1.339 96.83 564.23 0.491 

36 19.26 4.33 0.461 1.611 1.348 96.80 551.54 0.488 

37 19.74 4.21 0.464 1.677 1.604 96.76 501.86 0.540 

38 19.69 4.25 0.460 1.672 1.616 96.72 492.75 0.540 

39 20.09 4.22 0.455 1. 743 1.949 96.53 378.45 0.598 

169 
S=~II_I TR-3108 

Table E-3. Countercurrent Condenser Data for Configuration 3 

with Two Pairs of Baffles (Concluded) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. T . SI T . 

WI G Ja x· . 11 Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

40 20.12 4.15 0.460 1. 732 1.928 96.62 402.68 0.594 

41 20.02 4.85 0.463 2.032 1.901 96.72 401.47 0.634 

42 19.98 4.91 0.461 2.032 1.921 96.70 388.49 0.643 

43 20.34 5.29 0.444 2.530 2.007 96.66 467.98 0.622 

44 20.33 5.21 0.450 2.512 1.987 96.70 464.66 0.629 

45 19.61 5.04 0.482 1.071 0.519 .95.06 452.31 0.154 

46 19.60 5.00 0.477 1.082 0.525 94.98 477.07 0.137 

47 19.60 5.00 0.477 1.082 0.525 94.98 477.07 0.137 

48 21.22 5.40 0.457 1.207 1.092 94.45 336.64 0.299 

49 21.22 5.34 0.466 1.196 1.071 94.48 358.72 0.275 

SO 21.82 5.36 0.468 1.228 1.591 94.31 167.30 0.376 

51 21.80 5.37 0.471 1.228 1.580 94.38 169.42 0.383 

52 22.70 5.19 0.476 1.295 1.881 94.25 123.75 0.421 

53 22.68 5.18 0.477 1.297 1.876 94.25 122.28 0.419 

54 22.35 5.38 0.471 . 1.222 1.322 94.30 325.02 0.302 

55 22.40 5.37 0.495 1.225 1.257 94.19 361.77 0.217 

56 20.15 5.72 0.436 1.151 0.859 93.83 230.66 0.209 

57 20.06 5.79 0.431 1.150 0.869 93.81 265.86 0.193 

58 18.90 5.26 0.458 1.045 0.273 94.83 498.50 0.058 

59 18.87 5.33 0.454 1.048 0.276 94.79 485.80 0.077 

60 13.77 5.79 0.143 2.057 2.573 88.15 30.25 0.610 

61 13.61 5.70 0.147 1.989 2.512 88.51 42.29 0.590 

62 9.38 5.26 0.123 1.263 0.508 87.40 60.15 0.093 

63 9.42 5.25 0.121 1.285 0.515 87.20 43.70 1.237 

64 13.08 5.63 0.149 1.861 2.070 88.67 51.28 0.524 

65 13.05 5.59 0.154 1.820 2.007 89.05 53.95 0.519 

66 10.75 5.79 0.128 1.438 0.977 87.27 58.50 0.294 

67 10.68 5.77 0.129 1.417 0.965 87.45 57.28 0.294 

68 12.23 5.18 0.156 1.691 1.586 89.47 58.07 0.455 

69 12.32 5.26 0.157 1.679 1.578 89.44 26.51 0.514 

70 11.64 5.94 0.134 1.565 1.388 87.57 37.38 0.440 

71 11.63 5.89 0.135 1.574 1.375 87.76 54.03 0.402 

------------------------------------------------------------------

170 
5=~11_1 TR-3108 

Table E-4. Countercurrent Condenser Data for Configuration 4 

with One Pair of Baffles 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. T . 

S1 

T . 

W1 G Ja x .. 

11 Steam Loss Fraction 

(C) (C) (kg/m2s) (% ) (%) (Pa) 

------------------------------------------------------------------

1 15.91 5.52 0.180 2.982 2.051 88.11 19.58 0.391 

2 15.94 5.62 0.171 3.115 2.162 87.53 15.97 0.407 

3 10.86 5.41 0.171 1.654 0.366 89.52 21.11 0.080 

4 10.85 5.46 0.165 1.680 0.379 89.14 21.16 0.085 

5 14.75 5.05 0.182 2.770 1.698 88.82 17.94 0.390 

6 11.36 4.81 0.169 2.022 0.740 89.53 15.27 0.230 

7 13.01 5.21 0.191 2.112 0.979 89.89 15.52 0.278 

8 17.00 4.80 0.374 1.653 0.677 93.51 40.40 0.259 

9 17.06 4.91 0.365 1.672 0.694 93.29 44.16 0.262 

10 20.03 4.95 0.364 2.096 1.366 92 .43 22.59 0.319 

11 20.03 4.76 0.374 2.072 1.331 92 .67 28.37 0.327 

12 22.75 4.90 0.377 2.394 1.965 91. 75 35.56 0.350 

13 22.78 4.91 0.381 2.365 1.945 91.83 19.11 0.360 

14 24.22 5.49 0.381 2.470 2.280 91.11 18.79 0.359 

15 21.51 5.40 0.346 2.310 1. 793 91.49 22.44 0.358 

16 21.49 5.20 0.355 2.271 1. 748 91. 72 28.50 0.358 

17 19.02 5.55 0.360 1.847 1.036 92.53 31.53 0.288 

18 19.01 5.65 0.349 1.883 1.069 92 .30 23.47 0.297 

19 15.32 5.41 0.345 1.419 0.364 93.38 65.86 0.183 

20 15.31 5.34 0.344 1.428 0.364 93.37 65.28 0.189 

------------------------------------------------------------------

171 
S5~lr_r 

TR-3108 

Table E-S. Countercurrent Condenser Data for Configuration S 

with Spiral Matted Screen 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. T . 

Sl 

T . 

W1 G Ja x· . 11 Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

1 9.90 5.47 0.165 1.192 1.130 91.19 40.38 0.559 

2 9.86 5.40 0.165 1.200 1.129 91.25 40.92 0.565 

3 9.53 5.05 0.172 1.091 0.725 91.35 44.53 0.335 

4 12.08 5.75 0.174 1.532 2.127 91. 71 40.46 0.807 

5 9.54 5.05 0.176 1.084 0.712 91.48 44.55 0.323 

6 12.05 5.70 0.176 1.496 2.096 91.87 40.48 0.811 

7 9.85 5.02 0.177 1.229 1.056 92.08 40.67 0.618 

8 10.59 5.08 0.177 1.300 1.052 92.27 40.43 0.756 

9 9.82 4.96 0.179 1.221 1.043 92.20 41.51 0.615 

10 10.06 4.90 0.179 1.281 1.041 92 .38 40.04 0.701 

11 10.89 4.84 0.180 1.502 1.038 92.60 36.59 0.818 

12 10.05 4.86 0.181 1.280 1.030 92.48 39.54 0.701 

13 10.82 4.77 0.182 1.500 1.025 92.72 37.03 0.816 

14 10.40 5.16 0.188 1.171 0.993 92.33 42.96 0.603 

15 10.34 5.14 0.189 1.149 0.989 92.14 44.61 0.498 

16 10.34 5.13 0.191 1.147 0.978 92 .21 44.85 0.492 

17 11.11 4.92 0.192 1. 352 1.612 92.82 43.30 0.752 

18 10.59 4.85 0.195 1.230 1.274 92.77 42.87 0.649 

19 11.12 4.94 0.195 1.342 1.586 92.92 42.27 0.753 

20 13 .99 5.16 0.196 2.003 0.952 92.98 34.42 0.879 

21 10.55 4.83 0.197 1.218 1.262 92.82 43.97 0.635 

22 13 .93 5.07 0.199 1.988 0.942 93.10 34.16 0.879 

23 15.55 5.24 0.205 2.081 1.812 92.43 16.18 0.798 

24 12.64 5.32 0.212 1.419 1.173 93.26 27.32 0.817 

25 11.82 5.06 0.214 1.301 1.164 93.33 30.06 0.762 

26 11.48 4.98 0.216 1.245 1.152 93.30 31.16 0.696 

27 11.19 5.07 0.217 1.166 1.149 92.96 35.06 0.550 

28 11.24 4.95 0.217 1.196 1.149 93.15 33.12 0.614 

29 12.75 5.38 0.219 1.384 1.698 92.98 15.70 0.720 

30 15.06 5.53 0.219 1.789 1.692 92.90 15.87 0.796 

31 10.67 4.78 0.220 1.117 0.851 92.90 37.56 0.397 

32 10.67 4.78 0.220 1.117 0.851 92.90 37.56 0.397 

33 10.75 4.77 0.221 1.131 0.847 93.04 37.12 0.449 

34 10.75 4.77 0.221 1.131 0.847 93.04 37.12 0.449 

35 12.63 5.52 0.222 1.319 1.675 92.93 21.69 0.669 

36 13 .12 5.19 0.227 1.445 1.639 93.32 22.01 0.733 

37 11.08 4.76 0.230 1.151 0.815 93.40 36.78 0.520 

38 11.08 4.76 0.230 1.151 0.815 93.40 36.78 0.520 

172 
S5~1'_' TR-3108 

Table E-5. Countercurrent Condenser Data for Configuration 5 

with Spiral Matted Screen (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. T . s~ 

T . W~ 

G Ja x· . ~~ 

Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

39 14.63 5.38 0.233 1.630 0.803 93.78 25.15 0.855 

40 13.38 5.10 0.236 1.445 0.532 93.92 26.28 0.821 

41 13 .38 5.10 0.236 1.445 0.532 93.92 26.28 0.821 

42 11.11 5.09 0.236 1.051 0.531 92.31 42.05 0.045 

43 11.11 5.09 0.236 1.051 0.531 92 .31 42.05 0.045 

44 11.45 5.12 0.237 1.096 0.529 93.14 37.86 0.415 

45 11.45 5.12 0.237 1.096 0.529 93.14 37.86 0.415 

46 11.58 5.ll 0.237 1.118 0.528 93.48 35.86 0.555 

47 11.58 5.ll 0.237 1.118 0.528 93.48 35.86 0.555 

48 14.51 5.47 0.238 1.559 1.564 93.50 17.63 0.782 

49 11.20 5.02 0.239 1.065 0.524 92.72 40.10 0.175 

50 11.20 5.02 0.239 1.065 0.524 92.72 40.10 0.175 

51 11.15 5.01 0.241 1.057 0.520 92.59 41.98 0.093 

52 11.15 5.01 0.241 1.057 0.520 92.59 41.98 0.093 

53 1l.63 4.86 0.241 1.177 0.777 93.87 35.01 0.640 

54 11.63 4.86 0.241 1.177 0.777 93.87 35.01 0.640 

55 11.32 5.04 0.242 1.074 0.518 93.03 39.51 0.293 

56 11.32 5.04 0.242 1.074 0.518 93.03 39.51 0.293 

57 12.40 5.19 0.242 1.234 0.773 93.97 32.62 0.745 

58 12.40 5.19 0.242 1.234 0.773 93.97 32.62 0.745 

59 12.20 5.05 0.244 1.203 0.513 94.09 32.86 0.750 

60 12.20 5.05 0.244 1.203 0.513 94.09 32.86 0.750 

61 13.32 5.46 0.244 1.332 0.767 94.03 29.83 0.813 

62 13.78 5.ll 0.253 1.414 1.474 93.95 23.25 0.741 

63 11.22 5.23 0.332 1.402 0.752 95.51 72.03 0.531 

64 11.37 5.50 0.332 1.433 0.751 95.47 69.83 0.547 

65 11.30 5.44 0.333 1.424 0.749 95.48 74.08 0.528 

66 11.19 5.18 0.334 1.390 0.745 95.55 72.28 0.524 

67 11.55 5.37 0.335 1.349 0.743 95.40 74.01 0.481 

68 11. 70 5.35 0.337 1.264 0.739 95.34 72.39 0.458 

69 11.26 4.93 0.339 1.327 0.736 95.56 73.74 0.486 

70 12.67 5.19 0.339 1.142 0.736 94.94 74.32 0.361 

71 16.29 5.54 0.340 1.877 2.176 95.36 49.79 0.774 

72 12.62 5.13 0.340 1.141 0.733 95.02 74.10 0.378 

73 11.55 5.34 0.341 1.335 0.732 95.48 75.26 0.483 

74 11.28 4.93 0.342 1.320 0.729 95.60 74.17 0.482 

75 13.69 5.57 0.344 1.901 1.447 95.76 43.49 0.839 

173 
55'1 1*1 

TR-3108 

Table E-5. Countercurrent Condenser Data for Configuration 5 

with Spiral Matted Screen (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.Na. Tsi T . 

W1 G Ja X .. 

11 Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

76 16.03 5.19 0.347 2.531 2.138 95.72 38.02 0.834 

77 16.01 5.14 0.347 2.538 2.136 95.73 50.08 0.819 

78 16.04 5.19 0.347 2.311 2.135 95.66 48.47 0.804 

79 12.28 5.28 0.347 1.184 0.718 95.21 78.96 0.377 

80 13.68 5.53 0.347 1.886 1.431 95.82 31.97 0.841 

81 16.24 5.41 0.349 1.853 2.124 95.50 49.41 0.772 

82 16.07 5.17 0.350 2.090 2.119 95.68 49.92 0.798 

83 17.01 5.50 0.350 1.480 2.115 95.16 51.81 0.714 

84 16.11 5.25 0.350 2.294 2.116 95.69 48.74 0.807 

85 16.05 5.12 0.352 2.080 2.107 95.72 49.40 0.802 

86 13.70 5.38 0.353 1. 746 1.409 95.89 54.31 0.791 

87 16.94 5.34 0.353 1.495 2.096 95.24 51.25 0.711 

88 12.28 5.24 0.353 1.179 0.706 95.30 79.68 0.378 

89 15.97 4.90 0.354 1.973 2.093 95.90 49.46 0.826 

90 13.63 5.34 0.354 1.816 1.404 95.94 54.07 0.823 

91 13.63 5.34 0.354 1.820 1.405 95.93 53.59 0.816 

92 16.01 4.98 0.354 1.977 2.091 95.89 49.48 0.827 

93 16.25 5.51 0.354 2.151 2.091 95.75 49.91 0.828 

94 14.69 4.97 0.355 1.230 1.402 95.53 60.11 0.665 

95 13.71 5.39 0.356 1. 731 1.400 95.91 54.68 0.790 

96 16.38 5.47 0.356 1. 710 2.081 95.61 19.50 0.817 

97 14.69 4.97 0.356 1.232 1.396 95.57 60.04 0.670 

98 13.81 5.42 0.357 1.561 1.393 95.84 56.47 0.758 

99 13.86 5.47 0.358 1.564 1.392 95.82 56.09 0.755 

100 13.66 5.21 0.358 1.672 1.391 95.94 55.65 0.795 

101 17.27 5.37 0.359 1.504 1.386 95.94 107.82 0.817 

102 16.33 5.35 0.359 1.694 2.064 95.67 51.21 0.779 

103 15.48 5.B7 0.361 1.193 1.379 95.25 115.28 0.568 

104 15.54 5.64 0.361 1.225 1.377 95.55 112.80 0.651 

105 16.07 5.48 0.362 1.316 1.375 95.79 110.68 0.732 

106 13.94 5.07 0.362 1.376 1.373 95.B9 58.45 0.755 

107 13.69 5.21 0.363 1.658 1.373 96.00 55.71 0.800 

lOB 16.24 5.47 0.363 2.107 2.044 95.85 50.20 0.823 

109 14.21 5.00 0.363 1.313 1.371 95.78 61.14 0.693 

110 12.26 5.31 0.363 1.210 0.687 95 .• 44 81.22 0.383 

111 15.39 5.69 0.363 1.190 1.372 95.34 115.41 0.570 

112 12.30 5.35 0.363 1.204 0.687 95.44 82.00 0.386 

174 
55'11*' TR-3108 

Table E-5. Countercurrent Condenser Data for Configuration 5 

with Spiral Matted Screen (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi T . W~ 

G Ja X .. 

~~ 

Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

113 16.06 5.46 0.363 1.319 1.370 95.82 110.22 0.736 

114 13 .96 5.11 0.364 1.083 0.685 94.74 76.60 0.284 

115 13.76 5.20 0.365 1.490 1.366 95.91 58.01 0.731 

116 15.58 5.58 0.365 1.236 1.362 95.55 113.24 0.634 

117 13.99 5.11 0.366 1.079 0.682 94.74 76.73 0.275 

118 14.17 4.95 0.366 1.299 1.362 95.83 60.92 0.693 

119 13.72 5.14 0.366 1.491 1.360 95.95 57.93 0.758 

120 14.03 5.42 0.366 1.393 1.360 95.77 59.83 0.699 

121 16.28 5.47 0.366 2.273 2.027 95.89 52.23 0.823 

122 14.40 4.90 0.366 1.263 1.360 95.72 60.93 0.661 

123 13.98 5.06 0.367 1.365 1.357 95.92 59.33 0.730 

124 19.32 5.29 0.367 1.675 2.018 95.85 45.26 0.860 

125 19.27 5.26 0.368 1.668 2.012 95.87 44.76 0.861 

126 16.30 5.52 0.369 2.257 2.007 95.91 9.66 0.870 

127 14.02 5.38 0.370 1.377 1.347 95.82 61.42 0.693 

128 17.21 5.13 0.370 1.469 1.344 96.10 108.30 0.817 

129 14.35 4.82 0.370 1.259 1.345 95.80 61.32 0.663 

130 19.15 5.17 0.371 1.698 1.343 96.10 46.48 0.891 

131 13.96 5.49 0.372 1.096 0.671 94.85 36.80 0.350 

132 16.59 5.08 0.373 1.598 1.990 95.67 52.86 0.731 

133 16.58 5.06 0.374 1.612 1.986 95.69 53.91 0.734 

134 16.85 5.13 0.374 1.388 1.984 95.84 54.26 0.784 

135 15.44 4.99 0.376 1.173 1.323 95.53 61.93 0.614 

136 16.84 5.10 0.379 1.385 1.960 95.91 53.74 0.787 

137 19.12 5.09 0.380 1.675 1.310 96.20 46.64 0.889 

138 18.21 4.71 0.380 1.455 2.322 96.03 50.49 0.824 

139 18.16 4.76 0.380 1.451 2.325 96.02 50.39 0.822 

140 15.93 5.27 0.381 1.152 1.308 95.42 61.66 0.608 

141 15.42 4.92 0.382 1.164 1.306 95.58 61.96 0.606 

142 15.96 5.31 0.382 1.150 1.305 95.42 61.24 0.610 

143 20.46 5.21 0.382 1. 774 1.941 96.00 43.95 0.870 

144 13.78 5.19 0.384 1.083 0.649 95.06 81.62 0.268 

145 13.04 5.12 0.385 1.140 0.649 95.42 87.16 0.315 

146 20.45 5.18 0.387 1. 750 1.915 96.04 43.50 0.868 

147 16.98 5.23 0.388 1.462 1.912 95.81 55.26 0.741 

148 18.47 5.46 0.388 1.472 1.912 95.96 49.14 0.829 

149 13.04 5.10 0.388 1.134 0.642 95.44 88.13 0.305 

150 15.64 5.61 0.389 1.051 0.642 94.26 71.58 0.200 

175 
5='1 1

111 

TR-3108 

Table E-5. Countercurrent Condenser Data for Configuration 5 

with Spiral Matted Screen (Concluded) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. T . 

Sl 

T . 

W1 G Ja x· . 11 Steam Loss Fraction 

(C) (C) (kg/m2s) (%) (%) (Pa) 

------------------------------------------------------------------

151 18.44 5.49 0.389 1.469 1.909 95.96 50.31 0.828 

152 15.64 5.64 0.389 1.046 0.642 94.25 72.10 0.198 

153 17.39 4.96 0.391 1.298 1.898 95.96 55.23 0.770 

154 17.44 5.03 0.391 1.300 1.897 95.95 55.03 0.770 

155 16.49 4.67 0.395 1.218 1.571 95.90 59.86 0.697 

156 15.19 5.07 0.400 1.064 0.625 94.81 76.19 0.259 

157 17.54 5.20 0.400 1.295 1.857 95.63 55.57 0.679 

158 17.62 5.30 0.401 1.293 1.851 95.62 55.85 0.679 

159 15.16 4.99 0.401 1.058 0.622 94.86 76.10 0.265 

160 16.80 4.81 0.402 1.452 1.846 96.04 56.11 0.735 

161 16.45 4.58 0.406 1.211 1.531 96.01 60.59 0.693 

162 15.23 4.87 0.407 1.067 0.613 94.99 75.40 0.289 

163 15.20 4.87 0.408 1.068 0.612 95.03 75.39 0.294 

164 17.25 5.62 0.409 1.100 1.220 95.17 63.01 0.526 

165 15.41 5.13 0.409 1.053 0.611 94.66 78.96 0.194 

166 15.36 5.07 0.409 1.051 0.611 94.75 79.07 0.217 

167 16.93 5.40 0.412 1.164 0.605 96.07 61.28 0.737 

168 16.95 5.42 0.414 1.155 0.603 96.07 60.60 0.733 

169 15.41 5.07 0.414 1.047 0.603 94.76 80.40 0.203 

170 17.18 5.34 0.418 1.091 1.193 95.30 65.02 0.522 

171 15.66 4.95 0.418 1.075 0.597 95.15 76.23 0.336 

172 15.75 4.99 0.418 1.077 0.597 95.16 77 .07 0.345 

173 16.42 5.37 0.421 1.088 0.593 95.61 69.98 0.541 

174 15.42 5.02 0.424 1.037 0.589 94.84 80.97 0.191 

175 16.41 5.37 0.425 1.089 0.588 95.67 69.98 0.550 

176 18.48 5.33 0.425 1.210 1. 751 95.17 60.16 0.544 

177 16.16 5.23 0.425 1.079 0.587 95.34 74.20 0.420 

178 18.45 5.30 0.426 1.203 1. 747 95.18 59.39 0.540 

179 16.10 5.16 0.426 1.077 0.586 95.39 73.71 0.427 

180 16.17 4.89 0.427 1.082 0.877 95.29 73.74 0.398 

181 16.12 4.81 0.427 1.081 0.876 95.29 74.12 0.391 

182 16.65 5.00 0.443 1.030 0.564 94.45 80.43 0.135 

183 16.61 4.97 0.443 1.031 0.564 94.50 79.67 0.144 

184 17.89 4.69 0.460 1.083 1.085 95.37 122.43 0.397 

185 18.02 4.80 0.460 1.085 1.085 95.37 122.95 0.400 

------------------------------------------------------------------

176 
55'1 1*1 TR-3l08 

Table E-6. Countercurrent Condenser Data for Configuration 8 

with Random Packing 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja Xii Steam Loss Fraction 

(C) (C) (kg/m2 s) (%) (%) (Pa) 

------------------------------------------------------------------

Packing Depth 18 em. 

1 11.64 5.14 0.243 1.141 0.892 90.74 43.87 0.133 

2 10.41 5.25 0.243 1.118 0.891 90.53 l31. 97 0.171 

3 11. 76 5.16 0.245 1.156 1. 758 90.57 43.57 0.257 

4 11.06 5.02 0.245 1.052 0.885 89.90 95.87 0.144 

5 11.59 5.15 0.248 1.110 1.734 90.00 56.37 0.263 

6 11.09 5.05 0.248 1.085 0.873 90.15 116.17 0.144 

7 10.82 4.99 0.249 1.103 0.872 90.41 125.47 0.151 

8 11.62 5.23 0.249 1.099 0.872 90.12 53.47 0.l34 

9 11.24 5.06 0.250 1.056 0.868 90.02 106.87 0.140 

10 10.36 5.05 0.250 1.143 1. 721 90.83 123.77 0.330 

11 11.58 5.17 0.251 1.094 1. 716 89.93 65.17 0.264 

12 11.19 4.93 0.251 1.068 0.866 90.10 93.17 0.139 

l3 10.62 5.07 0.251 1.113 1. 715 90.60 113.87 0.313 

14 11.21 4.91 0.251 1.073 1.7l3 90.11 97.87 0.272 

15 10.92 5.15 0.252 1.091 1.711 90.37 105.17 0.298 

16 10.63 4.95 0.252 1.116 0.862 90.74 137.27 0.156 

17 11.18 5.14 0.252 1.077 1.706 90.19 98.77 0.282 

18 11.32 5.01 0.252 1.072 1.706 90.07 97.37 0.270 

19 11.18 4.80 0.253 1.080 1. 700 90.22 92.77 0.270 

20 11.63 5.21 0.254 1.080 0.854 90.03 68.37 0.l33 

21 11.67 5.22 0.255 1.081 1.686 89.99 74.27 0.261 

22 11.36 4.93 0.256 1.076 0.849 90.20 87.37 0.135 

23 11.55 5.07 0.256 1.081 0.847 90.12 79.47 o .l33 

24 11.07 4.82 0.257 1.030 0.423 90.51 115.97 0.071 

25 11.81 5.29 0.259 1.075 1.660 90.05 87.57 0.257 

26 10.56 5.22 0.261 1.l35 0.045 91.58 342.87 0.009 

27 10.61 4.77 0.262 1.102 0.045 91.49 193.97 0.008 

28 10.92 4.72 0.263 1.060 0.415 90.95 l38.17 0.072 

29 10.54 4.94 0.263 1.120 0.045 91.63 349.87 0.009 

30 11.44 4.92 0.264 1.049 0.413 90.57 129.27 0.067 

31 11.38 5.03 0.264 1.020 0.045 90.61 l32.07 0.007 

32 11.70 5.00 0.266 1.070 0.410 90.54 69.37 0.065 

33 11.69 4.86 0.266 1.089 0.409 90.88 58.97 0.064 

34 11. 70 5.09 0.266 1.054 0.409 90.40 80.57 0.065 

35 11.45 4.88 0.267 1.046 0.409 90.63 122.77 0.066 

177 
S=~II_I TR-3108 

Table E-6. Countercurrent Condenser Data for Configuration 8 

with Random Packing (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja xii Steam Loss Fraction 

(C) (C) (kg/m2 5) (%) (%) (Pa) 

------------------------------------------------------------------

36 10.84 4.78 0.267 1.085 0.409 91.28 154.57 0.074 

37 11.42 4.89 0.267 1.039 0.044 90.58 86.27 0.007 

38 11.41 4.96 0.267 1.026 0.044 90.55 98.67 0.007 

39 10.49 5.06 0.267 1.137 0.408 91. 72 182.87 0.083 

40 11.21 5.01 0.268 1.084 0.044 91.26 193.27 0.008 

41 11. 73 5.12 0.268 1.047 0.407 90.43 91. 77 0.065 

42 11.43 4.98 0.268 1.020 0.044 90.65 117.67 0.007 

43 10.78 4.89 0.269 1.104 0.406 91.50 171. 97 0.076 

44 11. 56 5.11 0.269 1.018 0.044 90.73 143.07 0.007 

45 10.71 5.04 0.270 1.120 0.404 91.63 180.97 0.079 

46 11.61 4.92 0.270 1.053 0.404 90.65 116.87 0.065 

47 11.49 4.95 0.270 1.029 0.044 90.74 129.27 0.007 

48 11. 76 5.05 0.271 1.051 0.402 90.56 106.47 0.064 

49 11. 56 5.06 0.272 1.061 0.044 91.08 181. 97 0.007 

50 11. 71 5.04 0.273 1.038 0.043 90.91 166.87 0.007 

51 13 .37 4.81 0.366 1.172 0.444 93.40 329.47 0.072 

52 13 .81 5.08 0.367 1.137 0.445 93.09 311.57 0.070 

53 15.02 4.88 0.374 1.161 0.438 93.58 76.47 0.059 

54 14.51 5.24 0.374 1.118 0.435 92.84 314.37 0.064 

55 15.01 5.02 0.383 1.115 0.427 92.55 132.27 0.059 

56 15.10 4.95 0.386 1.124 0.421 92.92 338.07 0.057 

57 15.18 5.16 0.387 1.107 0.422 92.43 166.37 0.058 

58 15.36 5.23 0.391 1.109 0.420 92.63 276.47 0.057 

59 15.38 5.23 0.391 1.111 0.417 92.46 204.57 0.057 

60 15.42 5.20 0.392 1.116 0.417 92.57 251.27 0.056 

61 15.08 4.91 0.394 1.106 0.074 93.24 409.37 0.010 

62 14.80 4.85 0.394 1.125 0.074 93.47 425.97 0.011 

63 15.25 5.20 0.394 1.091 0.074 92.47 167.27 0.010 

64 15.51 5.18 0.395 1.120 0.416 92.81 330.27 0.056 

65 15.53 5.24 0.395 1.115 0.414 92.73 304.97 0.056 

66 14.61 5.03 0.395 1.144 0.074 93.66 437.17 0.011 

67 15.27 5.10 0.395 1.100 0.074 93.15 403.17 0.010 

68 13.78 4.90 0.396 1.222 0.073 94.28 472.07 0.012 

69 15.23 5.03 0.397 1.101 0.073 93.16 393.27 0.010 

70 15.24 5.00 0.398 1.102 0.073 93.10 371.07 0.010 

71 14.31 5.02 0.399 1.167 0.073 93.94 455.67 0.011 

178 
5='1,*, TR-3108 

Table E-6. Countercurrent Condenser Data for Configuration 8 

with Random Packing (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja Xii Steam Loss Fraction 

(C) (C) (kg/m2 s) (%) (%) (Pa) 

------------------------------------------------------------------

72 15.39 5.23 0.399 1.090 0.073 92 .59 235.97 0.010 

73 15.30 5.03 0.400 1.101 0.073 93.03 355.77 0.010 

74 15.39 5.10 0.401 1.099 0.073 92 .90 327.17 0.010 

75 15.46 5.18 0.401 1.096 0.072 92.76 292.27 0.010 

Packing Depth 36 cm. 

1 10.74 5.14 0.244 1.001 0.048 90.64 343.04 0.009 

2 10.63 4.88 0.247 1.015 0.048 90.88 350.04 0.009 

3 10.74 4.91 0.253 1.028 0.047 91.14 200.74 0.008 

4 10.56 4.86 0.254 1.037 0.046 91.36 202.64 0.009 

5 10.37 5.35 0.255 1.090 0.046 91.59 216.94 0.010 

6 10.24 5.31 0.255 l.ll9 0.428 91.66 208.44 0.091 

7 10.28 5.40 0.255 1.102 0.046 91.68 220.84 0.010 

8 10.70 5.34 0.256 1.056 0.046 91.39 212.44 0.009 

9 10.59 5.35 0.258 1.066 0.046 91.56 217.74 0.009 

10 10.38 5.13 0.259 1.ll0 0.420 91. 71 214.74 0.086 

II 10.89 5.26 0.260 1.059 0.045 91.46 221. 74 0.009 

12 11. 70 5.45 0.261 1.023 0.418 92.00 81.44 0.069 

13 10.74 4.94 0.261 1.058 0.045 91.61 223.64 0.008 

14 11.25 5.11 0.262 1.002 0.417 90.89 135.84 0.072 

15 11.48 5.25 0.267 0.997 0.409 90.94 151.54 0.070 

16 11.48 5.13 0.267 1.016 0.408 91.00 132.24 0.069 

17 11.39 4.82 0.267 1.052 1.613 91.24 171.74 0.263 

18 11.44 4.94 0.268 1.040 1.610 91.20 171 .14 0.264 

19 11.15 4.85 0.268 1.059 1.610 91.45 183.64 0.276 

20 10.51 4.84 0.268 1.101 0.407 92.06 226.64 0.080 

21 11.67 5.32 0.269 1.010 0.406 90.96 171. 34 0.068 

22 10.76 4.92 0.269 1.086 0.406 91.89 224.34 0.071 

23 10.31 4.82 0.269 1.199 0.809 92.41 244.74 0.166 

24 11.47 4.97 0.269 1.033 1.602 91.23 175.94 0.264 

25 11.64 5.14 0.271 1.020 0.403 91.17 201. 54 0.066 

26 11.68 5.24 0.271 1.017 0.402 91.12 186.54 0.067 

27 10.71 4.97 0.272 1.166 0.802 92.22 244.14 0.156 

28 11.94 5.44 0.272 1.020 0.401 91.51 102.04 0.066 

29 11.30 4.98 0.272 1.092 0.799 91. 72 224.94 0.138 

30 11.22 5.11 0.272 1.059 0.400 91.67 222.04 0.072 

179 
5='11*1 TR-3108 

Table E-6. Countercurrent Condenser Data for Configuration 8 

with Random Packing (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja Xii Steam Loss Fraction 

(C) (C) (kg/m2 s) (%) (%) (Pa) 

------------------------------------------------------------------

31 11. 71 5.16 0.273 1.025 0.400 91.26 119.54 0.066 

32 11.28 4.93 0.274 1.047 0.398 91.66 216.74 0.069 

33 11.48 4.98 0.274 1.071 0.795 91.59 215.64 0.134 

34 11.12 5.19 0.274 1.134 0.793 92 .01 237.64 0.148 

35 11. 79 5.12 0.275 1.039 0.793 91.28 196.74 0.129 

36 11.90 5.21 0.275 1.042 0.792 91.24 207.24 0.127 

37 11.10 4.84 0.275 1.087 1.568 91.87 204.24 0.279 

38 11. 71 5.02 0.275 1.039 0.789 91.35 185.24 0.129 

39 11.15 5.00 0.276 1.111 0.790 91.99 234.94 0.143 

40 11.92 5.12 0.277 1.052 1.560 91.28 173.64 0.249 

41 11.69 4.97 0.277 1.039 0.787 91.39 176.84 0.129 

42 10.85 5.25 0.278 1.175 1.554 92.29 232.14 0.310 

43 12.04 5.13 0.278 1.064 1.554 92.26 105.24 0.246 

44 11.05 4.94 0.278 1.114 1.552 92.09 217.64 0.285 

45 10.87 5.01 0.280 1.151 1.544 92 .32 230.44 0.299 

46 11.98 5.13 0.280 1.048 1.544 91.38 157.44 0.247 

47 10.95 4.95 0.280 1.132 1.544 92.24 224.04 0.291 

48 11.80 4.97 0.280 1.045 0.778 91.46 168.84 0.127 

49 12.02 5.12 0.281 1.050 1.536 91.48 146.84 0.245 

50 12.36 5.31 0.282 1.071 0.773 92.69 104.34 0.121 

51 12.08 5.13 0.282 1.054 1.531 91.64 132.94 0.243 

52 12.02 5.06 0.284 1.049 0.767 91.53 160.04 0.123 

53 12.20 5.20 0.286 1.048 0.762 91.61 141.14 0.122 

54 13.85 5.31 0.339 1.075 1.283 92.66 215.84 0.189 

55 13.88 4.95 0.340 1.123 1.279 94.18 161.14 0.185 

56 13.77 5.07 0.340 1.092 1.279 93.23 190.94 0.188 

57 14.46 5.23 0.341 1.155 2.533 94.32 123.24 0.345 

58 13.97 5.14 0.343 1.103 2.526 92.78 288.34 0.360 

59 13.79 5.06 0.343 1.126 2.520 92.96 302.84 0.366 

60 13.51 5.15 0.344 1.155 2.516 93.22 308.94 0.385 

61 13.87 4.81 0.345 1.125 2.509 92.98 309.74 0.354 

62 13.36 5.12 0.345 1.080 0.634 93.09 344.44 0.100 

63 13.73 5.09 0.347 1.142 2.497 93.16 317.34 0.371 

64 13.12 5.00 0.349 1.126 0.629 93.48 370.64 0.103 

65 14.04 4.78 0.350 1.133 2.474 93.10 301.64 0.347 

66 14.49 5.25 0.351 1.127 2.466 93.67 195.24 0.342 

67 13.04 5.15 0.354 1.161 0.622 93.73 387.94 0.107 

180 
S=~I[*[ TR-3108 

Table E-6. Countercurrent Condenser Data for Configuration 8 

with Random Packing (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja xii Steam Loss Fraction 

(C) (C) (kg/m2 s) (%) (%) (Pa) 

------------------------------------------------------------------

68 14.19 5.26 0.355 1.071 0.622 92.99 368.94 0.091 

69 14.51 5.15 0.355 1.127 2.436 93.21 241. 54 0.336 

70 14.35 4.93 0.356 1.134 2.434 93.15 288.64 0.337 

71 14.30 5.11 0.357 1.103 1.223 93.01 372.34 0.172 

72 14.05 4.97 0.357 1.084 0.616 93.10 365.14 0.090 

73 14.17 5.18 0.357 1.072 0.610 93.04 377 .14 0.089 

74 14.22 4.98 0.358 1.105 1.220 93.08 354.74 0.173 

75 14.43 5.24 0.358 1.093 0.617 94.19 186.24 0.089 

76 15.27 5.06 0.359 1.213 1.800 94.66 74.64 0.229 

77 14.39 5.24 0.362 1.076 0.613 93.27 226.94 0.089 

78 14.18 4.92 0.362 1.091 0.610 93.18 364.34 0.088 

79 14.64 5.27 0.363 1.106 1.201 93.00 323.64 0.167 

80 13.88 5.11 0.363 1.174 1.197 93.60 408.74 0.183 

81 14.22 5.06 0.363 1.142 1.200 93.39 406.04 0.174 

82 14.82 5.53 0.363 1.094 1.199 92.91 278.54 0.167 

83 14.40 4.97 0.364 1.112 1.198 93.18 353.64 0.169 

84 14.39 5.23 0.364 1.073 0.605 93.02 271.14 0.088 

85 14.37 5.04 0.365 1.090 0.603 93.13 350.84 0.087 

86 13.77 4.88 0.365 1.175 1. 772 93.73 391. 54 0.272 

87 14.19 4.99 0.365 1.145 1. 769 93.46 387.54 0.258 

88 14.43 5.17 0.366 1.079 0.603 93.07 318.04 0.087 

89 13.34 4.94 0.366 1.232 1.189 94.04 421.94 0.196 

90 13.54 4.83 0.366 1.220 1. 764 93.97 402.14 0.280 

91 14.59 5.06 0.367 1.104 0.888 93.18 391.44. 0.124 

92 14.58 4.83 0.368 1.133 1. 756 93.35 387.74 0.241 

93 14.72 5.02 0.368 1.125 1. 755 93.24 402.74 0.239 

94 14.45 4.80 0.368 1.119 0.885 93.33 388.94 0.124 

95 14.32 4.98 0.368 1.081 0.442 93.37 414.74 0.064 

96 14.27 4.87 0.369 1.087 0.088 93.53 459.44 0.013 

97 14.63 4.91 0.370 1.119 1. 749 93.35 397.54 0.242 

98 12.85 5.09 0.370 1.206 0.087 94.30 453.44 0.016 

99 15.08 5.23 0.370 1.132 1.746 94.33 217.44 0.237 

100 14.18 5.00 0.371 1.104 0.439 93.58 431.74 0.066 

101 13.94 5.15 0.371 1.122 0.439 93.73 432.14 0.069 

102 13.73 5.20 0.372 1.144 0.439 93.88 435.14 0.072 

103 14.44 4.97 0.372 1.084 0.437 93.43 427.84 0.063 

181 
5=~1'*' TR-3108 

Table E-6. Countercurrent Condenser Data for Configuration 8 

with Random Packing (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja Xii Steam Loss Fraction 

(C) (C) (kg/m2 s) (%) (%) (Pa) 

------------------------------------------------------------------

104 14.41 4.95 0.372 1.083 0.087 93.50 453.74 0.013 

105 14.12 5.00 0.372 1.109 0.087 93.76 475.74 0.013 

106 14.73 5.13 0.373 1.096 0.435 94.53 206.94 0.062 

107 13 .06 4.82 0.374 1.192 0.086 94.34 471.84 0.015 

108 14.58 5.10 0.374 1.078 0.087 93.38 437.34 0.012 

109 13.87 5.12 0.375 1.145 0.085 93.99 483.34 0.014 

110 14.47 4.81 0.376 1.096 0.433 93.50 425.64 0.062 

III 14.90 4.82 0.376 1.143 1. 720 93.46 402.74 0.232 

112 15.03 5.18 0.376 1.119 0.867 94.16 260.04 0.119 

113 14.78 4.82 0.376 1.128 0.867 93.45 399.04 0.119 

114 14.77 5.27 0.376 1.074 0.086 93.25 422.64 0.012 

115 14.96 5.59 0.376 1.057 0.086 92.94 363.94 0.012 

116 14.72 5.13 0.377 1.084 0.431 93.80 252.54 0.062 

117 15.16 5.25 0.377 1.122 1.714 93.61 282.94 0.233 

118 14.91 5.45 0.378 1.064 0.086 93.12 397. 54 0.012 

119 15.09 5.01 0.378 1.137 1. 709 93.44 374.44 0.230 

120 15.03 5.12 0.379 1.114 0.859 93.56 314.74 0.118 

121 15.18 5.11 0.379 1.130 1.706 93.48 325.44 0.229 

122 14.74 5.14 0.380 1.078 0.431 93.31 321.04 0.062 

123 14.62 4.83 0.380 1.098 0.429 93.52 420.24 0.061 

124 14.99 4.96 0.381 1.123 0.858 93.47 377.54 0.117 

125 14.82 5.12 0.382 1.083 0.427 93.33 360.64 0.061 

126 15.32 5.29 0.382 1.119 0.854 93.30 455.04 0.114 

127 14.80 4.97 0.383 1.095 0.425 93.43 398.04 0.060 

128 15.36 5.15 0.384 1.133 0.850 93.44 492.24 0.112 

129 14.84 5.25 0.385 1.061 0.075 93.27 387.14 0.01l 

130 14.78 5.13 0.385 1.067 0.075 93.25 360.54 0.01l 

131 15.13 5.13 0.386 1.158 0.846 93.66 502.34 0.115 

132 14.16 5.07 0.386 1.286 0.844 94.34 519.94 0.132 

133 14.91 5.26 0.386 1.192 0.843 93.85 510.54 0.120 

134 14.35 4.97 0.387 1.246 0.842 94.22 517.44 0.127 

135 15.06 5.32 0.389 1.066 0.075 93.36 426.24 0.011 

136 15.05 5.26 0.390 1.070 0.075 93.34 307.74 0.011 

137 14.96 5.12 0.390 1.075 0.075 93.29 356.04 0.011 

138 15.08 5.05 0.391 1.095 0.074 93.82 534.84 0.010 

139 13.75 4.91 0.391 1.186 0.074 94.49 521.24 0.012 

140 14.35 4.95 0.391 1.138 0.074 94.21 534.14 0.01l 

182 
S='II*~ TR-3108 

Table E-6. Countercurrent Condenser Data for Configuration 8 

with Random Packing (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja Xii Steam Loss Fraction 

(C) (C) (kg/m2 s) (%) , (%) (Pa) 

------------------------------------------------------------------

141 14.94 5.16 0.392 1.112 0.074 93.94 542.34 0.011 

142 15.21 5.28 0.392 1.079 0.074 93.52 469.24 0.010 

143 15.15 5.11 0.393 1.092 0.074 93.77 524.74 0.010 

144 14.25 5.15 0.393 1.158 0.074 94.28 529.44 0.012 

145 15.22 5.19 0.394 1.086 0.074 93.67 505.84 0.010 

146 13.71 5.10 0.394 1.204 0.074 94.54 522.34 0.013 

147 18.80 4.86 0.486 1.228 0.903 95.87 83.54 0.102 

148 18.12 5.23 0.489 1.184 1.784 94.62 697.44 0.218 

149 17.82 5.31 0.490 1.207 1.779 94.80 701.04 0.227 

150 18.46 5.12 0.490 1.161 1. 778 94.47 695.54 0.209 

151 18.23 5.02 0.496 1.130 0.437 94.56 744.34 0.053 

152 18.78 5.25 0.497 1.163 1. 755 95.74 411.24 0.207 

153 18.10 4.76 0.499 1.138 0.444 94.63 730.04 0.054 

154 18.46 4.99 0.501 1.149 0.874 95.74 449.64 0.106 

155 18.81 5.27 0.502 1.152 1.740 94.85 519.14 0.205 

156 18.50 5.23 0.503 1.121 0.436 94.58 779.24 0.052 

157 18.94 5.33 0.503 1.155 1. 732 94.51 592.74 0.201 

158 18.61 5.13 0.504 1.145 0.870 94.78 548.84 0.104 

159 18.42 4.90 0.506 1.137 0.427 94.55 722.94 0.052 

160 18.77 5.26 0.506 1.143 0.868 94.50 615.04 0.103 

161 19.11 5.43 0.507 1.155 1. 721 94.44 646.24 0.199 

162 18.46 4.87 0.508 1.138 0.433 94.54 692.24 0.052 

163 16.85 5.09 0.508 1.214 0.433 95.42 761.84 0.063 

164 18.63 5.05 0.508 1.136 0.431 95.73 446.44 0.052 

165 18.96 5.34 0.510 1.143 0.859 94.45 662.24 0.100 

166 18.30 4.81 0.510 1.126 0.435 94.81 780.74 0.053 

167 18.58 4.86 0.511 1.143 0.430 94.53 665.34 0.051 

168 19.33 5.45 0.513 1.158 1.701 94.43 686.54 0.194 

169 19.17 5.37 0.514 1.148 0.853 94.43 710.94 0.098 

170 17.50 5.32 0.514 1.181 0.428 95.25 779.44 0.060 

171 18.72 4.99 0.514 1.135 0.426 94.76 561.54 0.051 

172 19.43 5.33 0.516 1.168 1.692 94.48 736.44 0.190 

173 18.78 4.94 0.516 1.139 0.426 94.55 633.64 0.051 

174 18.82 5.28 0.516 1.116 0.062 94.52 771.34 0.007 

175 18.24 5.06 0.516 1.137 0.062 95.14 878.64 0.008 

176 19.23 5.32 0.517 1.151 0.849 94.48 743.64 0.097 

183 
S='II*~ TR-3108 

Table E-6. Countercurrent Condenser Data for Configuration 8 

with Random Packing (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja Xii Steam Loss Fraction 

(C) (C) (kg/m2 s) (%) (%) (Pa) 

------------------------------------------------------------------

177 18.79 5.29 0.518 1.109 0.062 94.77 837.64 0.007 

178 18.75 5.24 0.518 1.109 0.062 94.71 811.54 0.007 

179 19.28 4.99 0.520 1.177 1.680 94.71 777 .94 0.190 

180 18.26 4.93 0.520 1.149 0.423 95.05 813.94 0.054 

181 18.89 5.24 0.521 1.115 0.062 94.50 758.54 0.007 

182 19.29 5.31 0.521 1.148 0.842 94.57 789.14 0.097 

183 18.13 5.33 0.524 1.155 0.421 95.14 807.34 0.056 

184 18.69 4.92 0.524 1.120 0.061 95.07 899.54 0.007 

185 18.87 5.18 0.524 1.111 0.061 94.92 871.84 0.007 

186 17.26 5.12 0.525 1.276 0.061 95.76 893.44 0.009 

187 19.29 5.51 0.526 1.112 0.061 94.23 693.34 0.007 

188 18.14 5.10 0.527 1.170 0.061 95.41 903.74 0.008 

189 17.88 5.26 0.527 1.198 0.061 95.51 899.44 0.008 

190 19.17 5.37 0.527 1.113 0.061 94.39 747.14 0.007 

191 17.58 5.11 0.528 1.235 0.061 95.67 900.64 0.008 

192 17.58 5.11 0.528 1.235 0.061 95.67 900.64 0.008 

193 19.38 5.27 0.529 1.142 0.831 94.76 840.84 0.096 

194 18.35 5.27 0.531 1.160 0.060 95.35 906.44 0.008 

195 19.28 5.42 0.532 1.163 0.826 94.90 855.74 0.097 

196 18.19 5.00 0.534 1.243 0.824 95.49 864.64 0.107 

197 17.89 5.10 0.536 1.294 0.820 95.64 866.64 0.112 

198 19.11 5.47 0.536 1.185 0.818 95.09 875.14 0.099 

Packing Depth 66 cm. 

1 10.75 5.10 0.233 1.027 1.843 90.85 205.74 0.309 

2 10.73 5.03 0.233 1.041 1.842 91.50 175.74 0.310 

3 10.93 5.31 0.233 1.022 1.841 90.76 217.04 0.306 

4 10.68 5.02 0.233 1.027 1.841 90.94 199.34 0.311 

5 10.66 4.96 0.234 1.033 1.835 91.15 191.94 0.310 

6 10.91 5.12 0.235 1.045 0.925 92.27 134.94 0.155 

7 11.37 5.49 0.238 1.048 1.363 92.18 121.24 0.221 

8 10.84 5.08 0.240 1.022 0.907 91.58 185.34 0.155 

9 10.59 5.32 0.240 1.069 0.907 91.31 240.74 0.168 

10 11.31 5.51 0.240 1.023 1.349 91.37 181.44 0.223 

11 10.89 5.13 0.241 1.016 0.904 91.23 207.04 0.154 

12 10.89 4.93 0.241 1.048 1.342 91.26 243.04 0.221 

184 
55'1 1*1- TR-3108 

Table E-6. Countercurrent Condenser Data for Configuration 8 

with Random Packing (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja Xii Steam Loss Fraction 

(C) (C) (kg/m2 s) (%) (%) (Pa) 

------------------------------------------------------------------

13 11.34 5.51 0.242 1.021 1.336 91.21 197.94 0.221 

14 11.05 5.23 0.243 1.019 0.893 91.07 228.24 0.150 

15 ll.41 5.46 0.246 1.027 1.320 91.10 216.14 0.216 

16 11.15 5.16 0.246 1.037 0.884 9l.27 252.74 0.146 

17 11.32 5.30 0.246 1.039 1.315 91.13 237.34 0.215 

18 10.94 4.93 0.251 1.064 0.864 91. 70 268.34 0.147 

19 11.19 4.88 0.262 1.015 0.083 91.98 287.54 0.014 

20 11.66 5.41 0.267 0.983 0.081 91.51 227.54 0.014 

21 12.18 5.29 0.268 1.077 0.407 93.00 72.34 0.063 

22 11.01 5.04 0.270 1.056 0.080 92.32 298.04 0.015 

23 10.92 4.89 0.271 1.062 0.080 92.31 287.44 0.015 

24 11.85 5.42 0.272 0.998 0.043 91.55 243.64 0.007 

25 11.52 4.93 0.272 1.026 0.043 92.21 314.74 0.007 

26 ll.49 4.87 0.272 1.026 0.080 92.10 292.34 0.013 

27 11. 77 5.28 0.274 1.000 0.043 91.80 236.44 0.007 

28 11. 74 5.19 0.274 1.006 0.079 92.00 236.14 0.013 

29 11.54 5.12 0.274 1.050 0.397 92.26 311.14 0.068 

30 11.65 4.99 0.275 1.024 0.043 92.09 303.24 0.007 

31 11.93 5.42 0.275 0.998 0.043 91.67 267.14 0.007 

32 11.35 5.10 0.278 1.073 0.043 92.57 330.84 0.008 

33 ll.87 5.16 0.278 1.019 0.078 92.00 287.34 0.013 

34 12.01 5.33 0.278 1.015 0.042 91.90 293.14 0.007 

35 11.57 5.02 0.279 1.054 0.391 92.34 290.54 0.067 

36 11.96 5.11 0.279 1.028 0.391 92.59 239.94 0.063 

37 10.93 4.71 0.279 1.068 0.078 92.56 292.34 0.014 

38 11.45 5.29 0.280 1.047 0.042 92.27 257.74 0.008 

39 ll.47 5.32 0.280 1.044 0.042 92.17 271.04 0.008 

40 12.03 5.19 0.280 1.032 0.389 92.07 281.94 0.063 

41 11. 76 5.09 0.280 1.048 0.389 92.27 285.14 0.065 

42 11.48 5.32 0.280 1.046 0.042 92.23 288.24 0.008 

43 ll.37 5.10 0.281 1.064 0.042 92.49 315.94 0.008 

44 11.68 5.16 0.281 1.042 0.077 92.56 246.34 0.013 

45 11.50 5.23 0.282 1.061 0.042 92.37 305.24 0.008 

46 12.26 5.36 0.282 1.024 0.387 92.34 247.24 0.062 

47 11.16 4.85 0.283 1.069 0.077 92.52 290.24 0.014 

48 11.49 5.17 0.283 1.069 0.077 93.05 247.14 0.014 

49 12.18 5.25 0.284 1.025 0.385 92.16 268.74 0.062 

185 
55'1 1

_ 

TR-3108 

Table E-6. Countercurrent Condenser Data for Configuration 8 

with Random Packing (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja Xii Steam Loss Fraction 

(C) (C) (kg/m2 s) (%) (%) (Pa) 

------------------------------------------------------------------

50 12.30 5.47 0.284 1.014 0.076 91.88 286.14 0.012 

51 11.85 4.83 0.284 1.027 0.021 92.50 343.54 0.003 

52 11.32 4.98 0.285 1.066 0.076 92.48 277 .24 0.014 

53 11. 70 4.93 0.286 1.056 0.021 92.66 351.84 0.003 

54 11.80 4.77 0.286 1.026 0.021 92.41 326.44 0.003 

55 10.89 4.83 0.287 1.129 0.021 93.15 344.84 0.004 

56 11.63 5.23 0.289 1.059 0.020 92.66 330.44 0.004 

57 11.62 5.20 0.290 1.060 0.020 92.61 320.54 0.004 

58 12.23 5.28 0.290 1.023 0.102 92.59 260.04 0.017 

59 12.20 5.23 0.290 1.023 0.102 92.35 274.04 0.017 

60 12.70 5.19 0.291 1.107 2.356 92.58 307.54 0.347 

61 11.51 5.00 0.294 1.048 0.020 92.72 312.94 0.004 

62 12.27 5.23 0.294 1.021 0.100 92.37 292.54 0.016 

63 12.39 5.32 0.295 1.021 0.100 92.31 306.34 0.016 

64 12.61 5.41 0.296 1.013 0.020 92.18 329.54 0.003 

65 12.23 4.93 0.296 1.055 0.100 92.79 371. 94 0.016 

66 12.43 4.90 0.297 1.078 1.168 92.76 351.64 0.179 

67 11.42 4.78 0.297 1.058 0.020 92.88 308.24 0.004 

68 12.66 4.93 0.298 1.114 2.301 92.83 335.44 0.340 

69 12.52 5.35 0.298 1.003 0.020 92.19 313.54 0.003 

70 12.56 5.39 0.299 1.026 0.099 92.40 328.64 0.016 

71 12.43 4.83 0.299 1.081 1.157 92.85 340.94 0.178 

72 12.61 5.31 0.299 1.041 0.099 92.57 358.94 0.016 

73 12.03 4.79 0.301 1.020 0.020 92.60 312.04 0.003 

74 12.47 4.90 0.302 1.071 0.098 92.95 395.44 0.015 

75 13.14 5.47 0.303 1.082 1.699 92.98 299.24 0.253 

76 12.64 5.14 0.303 1.055 0.078 92.73 376.74 0.012 

77 12.79 5.32 0.306 1.043 0.077 92.55 340.24 0.012 

78 12.71 5.21 0.307 1.047 0.077 92.67 359.54 0.012 

79 12.89 5.48 0.307 1.032 0.077 92.48 317.94 0.012 

80 12.91 5.22 0.307 1.062 0.569 92.81 371.94 0.087 

81 12.80 4.88 0.308 1.097 1.127 93.22 344.14 0.170 

82 12.80 5.10 0.308 1.062 0.566 92.99 356.44 0.088 

83 13.28 5.37 0.308 1.098 1.670 92.84 348.34 0.244 

84 12.67 4.69 0.309 1.111 2.223 93.69 316.14 0.335 

85 12.85 4.92 0.309 1.100 2.221 93.39 323.44 0.333 

186 
S5~1[_J- TR-3108 

Table E-6. Countercurrent Condenser Data for Configuration 8 

with Random Packing (Continued) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja Xii Steam Loss Fraction 

(C) (C) (kg/m2 s) (%) (%) (Pa) 

------------------------------------------------------------------

86 13.06 5.35 0.309 1.059 0.563 92.82 391.04 0.085 

87 13.12 4.96 0.309 1.128 1.664 93.04 393.34 0.240 

88 12.76 4.99 0.311 1.066 0.562 93.39 336.34 0.088 

89 13.14 5.12 0.311 1.098 1.117 93.89 306.54 0.166 

90 12.78 4.64 0.312 1.122 2.203 93.89 320.14 0.329 

91 12.79 4.92 0.312 1.075 0.559 93.94 309.04 0.087 

92 12.88 5.19 0.314 1.037 0.125 93.08 324.54 0.020 

93 13.27 5.11 0.314 1.107 1.104 93.08 416.74 0.160 

94 13.14 5.25 0.321 1.041 0.123 93.03 357.34 0.019 

95 13.27 5.21 0.322 1.058 0.122 93.05 401.14 0.019 

96 13.27 5.22 0.323 1.054 0.122 93.05 385.94 0.019 

97 13.32 5.18 0.323 1.067 0.122 93.17 433.04 0.018 

98 13.35 5.09 0.325 1.079 0.121 93.36 462.24 0.018 

99 15.69 5.02 0.389 1.171 1.846 94.48 647.04 0.237 

100 15.89 5.00 0.391 1.188 2.401 94.83 619.04 0.304 

101 16.21 5.22 0.392 1.194 2.352 95.29 460.84 0.294 

102 15.95 5.06 0.392 1.188 2.312 95.01 600.64 0.294 

103 16.06 5.11 0.393 1.192 2.411 95.27 550.74 0.305 

104 15.90 5.04 0.393 1.184 2.373 94.64 650.04 0.301 

105 15.99 5.20 0.393 1.169 1.222 95.32 411.84 0.158 

106 15.74 4.88 0.394 1.180 1.825 94.66 650.34 0.234 

107 15.85 4.97 0.394 1.183 2.313 94.73 634.04 0.295 

108 15.88 5.03 0.395 1.175 1.819 94.89 620.84 0.234 

109 15.94 5.05 0.395 1.179 1.818 95.19 591. 24 0.234 

110 15.82 4.94 0.395 1.177 1.817 94.78 640.34 0.234 

III 15.89 5.18 0.396 1.154 1.213 94.83 610.34 0.158 

112 15.90 5.30 0.397 1.143 1.211 94.60 616.44 0.159 

113 16.07 5.46 0.397 1.139 1.211 94.39 638.54 0.157 

114 15.94 5.18 0.397 1.160 1.210 95.18 581.24 0.158 

115 16.03 5.05 0.397 1.184 1.810 95.39 499.04 0.232 

116 16.38 5.29 0.405 1.168 1.186 94.48 719.64 0.148 

117 17.99 4.94 0.472 1.198 0.052 95.35 991.64 0.006 

118 17.99 5.01 0.472 1.177 0.108 95.32 975.04 0.013 

119 18.28 5.26 0.473 1.176 0.070 95.20 991.14 0.008 

120 17.99 4.83 0.474 1.188 0.113 95.35 978.64 0.013 

121 18.06 4.95 0.475 1.196 0.052 95.35 993.14 0.006 

187 
55'1'*' TR-3108 

Table E-6 .. Countercurrent Condenser Data for Configuration 8 

with Random Packing (Concluded) 

------------------------------------------------------------------ Cond- Pressensed ure Vent 

S.No. Tsi Twi G Ja Xii Steam Loss Fraction 

(C) (C) (kg/m2 s) (%) (%) (Pa) 

------------------------------------------------------------------

122 18.33 5.19 0.476 1.180 0.069 95.22 993.64 0.008 

123 18.07 4.82 0.476 1.190 0.103 95.36 979.94 0.012 

124 18.76 5.01 0.478 1.228 0.506 95.44 983.54 0.057 

125 18.17 4.89 0.478 1.188 0.112 95.35 974.04 0.013 

126 18.39 5.29 0.479 1.169 0.069 95.65 905.64 0.008 

127 18.29 5.15 0.479 1.187 0.051 95.24 982.24 0.006 

128 18.17 5.03 0.479 1.189 0.051 95.32 988.14 0.006 

129 18.44 5.21 0.480 1.181 0.069 95.21 990.74 0.008 

130 18.40 5.30 0.480 1.167 0.069 95.38 921.14 0.008 

131 18.87 5.10 0.480 1.227 0.504 95.73 961.34 0.057 

l32 18.46 5.14 0.481 1.183 0.051 95.20 986.84 0.006 

133 18.53 5.30 0.481 1.175 0.069 95.17 976.24 0.008 

134 18.72 5.41 0.482 1.180 0.108 95.98 858.24 0.013 

l35 18.46 5.33 0.482 1.164 0.069 95.18 948.24 0.008 

136 18.35 4.97 0.482 1.188 0.103 95.34 977.74 0.012 

l37 18.50 5.10 0.483 1.1S4 0.110 95.32 965.14 0.013 

138 18.59 5.24 0.484 1.178 0.051 95.1S 975.74 0.006 

139 18.64 5.31 0.485 1.177 0.105 95.35 951.24 0.012 

140 lS.78 5.25 0.485 1.192 0.498 96.16 752.94 0.058 

141 lS.78 5.37 0.486 1.182 0.051 95.34 956.34 0.006 

------------------------------------------------------------------

188 
TR-3108 

APPENDIX F COMPUTER PROGRAM LISTINGS 

This appendix lists the computer codes, written in PASCAL, used for condenser 

modeling. We used the commercially available PASCAL computer program compiler 

code Turbo-Pascalm (version 3.0) to run the codes. The code can be run on any 

IBM or compatible personal computer. 

The first part of the list is for modeling a co current condenser; the second 

part is for modeling a countercurrent operation. Brief explanations and comments are included in the listings. A detailed table of the variables and 

their descriptions follows in Table F-l. 

189 
PROGRAM Cocurrent_Condenser; 

{$U+} { User Interrupt enabled } 

{ This algorithm contains routines which model a cocurrent direct 

contact condenser with a packed column geometry for use in an open 

cycle ocean thermal energy conversion (OTEC) system. Packings 

modelled are of the structured type. Details of the modeling and 

the accompanying study can be found in this report (SERI/TR-252-3108). 

This version is set up to run with the TURBO-Pascal compiler (version 

3.0, Borland International Inc.) on an IBM or compatible 

personal computer. 

CONST 

TYPE 

VAR 

In case of you may find errors or problems 1n using this code, 

please contact the authors at SERI: 

1617 Cole Boulevard 

Golden, Colorado, 80401 

Tel: (303)-23l-1000 

*********************** 

Main Routine --Cocond-- version 871015, Revisions 10-15-87 ... ~****;':··k*'";':** .. k*** .. k*'";,':*;':***** ----------------------------------} 

{ Physical Constants } 

Molwts=18.015;, Mo1wti=28.97; 

G=9.8l; Sigma=0.072; 

{ Water Saturation Pressure Curve Fit Constants} 

pl=161.75743l78; p2=18.4779l1547; p3=4026.97587317; 

p4=234.73842369; p5=3.73834517667; 

{ Water Viscosity Curve Fit Constants} 

anl=241.4; an2=0.382809486; an3=0.2162830218; 

{ Accuracy Tolerance Limit for Integration } 

To1=le-12; 

{ Mathematical Constants } 

Pi=3.1415927; 

Neqn=11 { Number of Equations to be Integrated }; 

Nseg=200 {Number of Segments the condenser is divided into }; 

State = 

Lab1e = 

Vector = 

Istep 

Nrun,Seria1 

ARRAY [ 1 •• 11] of Real; 

String[20]; 

ARRAY[1..20] of Real; 

Cond Len,Pckdia,C S Area,Saperv,Cor1iq,Corgas, 

Corfrc,Void,Theta~SIna1pha 

Run Lable 

Xin~Velin,Pstgin,Tstgin,Super_In 

190 

Integer; 

Integer; 

Real; 

String[15]; 

Real; 

TR-3108 
X,X Est,Tdew,Xend Real; 

Kliq,Muliq,Gpliq,Prliq,Scliq,Rholiq,Diffaw Real; 

Lhtc,Lmtc,Ghtc,Gmtc,Frcgas,Frcliq,Rel,Reg Real; 

Tsurf,Ovhtc,Ovrntc,SteamFlux,Gzero,Cht1,Ght2,Ght3, 

Ackerh,Ackf Real; 

Xeq,Veleq,Pstgeq,Tstgeq,Supreq Real; 

Temp,Press,Volw,Vols,Enthw,Enths Real; 

Y,Yin,Yeqlbm,Y Est,Prime,Yprime State; 

Filein,Filot1,Filot2 Lable; 

Geometry String[4]; 

Form6,Form7 Char; 

InFile,OutFilel,OutFile2,OutFile3 Text; 

TgasDB,Tsat,Tliq Real; 

Ptotal,Satpr,ppsteam Real; 

Xmass,Ymole Real; 

AirMu,AirK,AirGp Real; 

StmMu,StmK,StmGp Real; 

StmRho,StmDiff Real; 

MixMu,MixK,MixGp,MixPr,MixSc,MixMwt,MixRho Real; 

Phi12,Phi21 Real; 

MixEnth,Enthliq Real; 

I Integer; 

Epsilon,Tol1,T,Tolzer,Tolerance Real; 

Tot In Enth,Wat In Enth,Gas In Enth Real; 

U_B~lk~Gamma,A,Mach - - Real; 

Tzbyt,Pzbyp Real; 

Vel_Eqlbm,Super_Eqlbm,X_Eqlbm Real; 

Mom_In,Vel_In,K_E_In Real; 

T_Stg_In,T_Dew_In,P_Stg_In Real; 

T_Stg_Eq,P_Stg_Eq Real; 

Yacob,PpmIn Real; 

Gas Load,Xinprc Real; 

RhoUb Real; 

Step,Afraction,Xfinal Real; 

Base,Height,Side,Apgeom,Sprime Real; 

Wateff,Cond prc,Pdrop,Nusselt Gas Real; 

U G Eff,U L-Eff - Real; 

Iprint,Setflag Boolean; 

{ A TURBO-Pascal support file } 

TYPE 

RegPack = 

RECORD { register pack Used in MSDos call } 

AX, BX, CX, DX, BP, SI, DI, DS, ES, Flags: Integer; 

END; 

TimeStr = 

VAR 

String(8) ; DateStr = String[ 10] ; 

RecPack RegPack; 

Gtime,Cdate String[IO); 

FUNCTION Time: Timestr; 

{ returns the current time In string format HH:MM:SS } 

VAR 

Hour,Min,Sec,Frac : String[2]; 

191 

TR-3108 
BEGIN 

WITH RecPack DO 

BEGIN AX := $2COO ; MsDos(RecPack) 

AX := hi(CX); Str(AX,Hour); 

IF AX < 10 THEN Insert(' ',Hour, 1); 

AX := lo(CX); Str(AX,Min ); 

IF AX < 10 THEN Insert('O',Min ,1); 

AX := hi(DX); Str(AX,Sec ); 

IF AX < 10 THEN Insert('O',Sec ,1); 

AX := lo(DX); Str(AX,Frac); 

IF AX < 10 THEN Insert('O',Frac,l); 

Time := Hour + I:' + Min + I:' + Sec; 

{+ '.' + Frac} 

END; 

END; 

FUNCTION Date: DateStr; 

{ returns the current date in string format : MM/DD/YYYY } 

VAR 

Year: String[4] ; Month,Day : String[2] 

BEGIN 

WITH RecPack DO 

BEGIN 

AX := $2A shl 8 ; MsDos(Recpack); 

AX := DX shr 8; Str(AX,Month); 

IF AX < 10 THEN Insert(' ',Month,I); 

AX := DX mod 256; Str(AX,Day); 

IF AX < 10 THEN Insert('O',Day ,1); 

Str (CX,Year); 

Date := Month + 'I' + Day + 'I' + Year; 

END; 

END; 

PROCEDURE MachineAccuracy; 

{ Calculates the smallest discernable real number 

for the machine } 

BEGIN 

END; 

Epsilon:=1.0; 

REPEAT 

Epsilon:=Epsilon/2.0; 

Tolerance:=1.0 + Epsilon; 

UNTIL (Tolerance< =1.0); 

FUNCTION InertMasstoMoleFraction(xm: Real): Real; 

{ Converts inert mass fraction to mole fraction } 

BEGIN 

InertMasstoMoleFraction:=xm/Molwti/(xm/Molwti+(l-xm)/Molwts); 

END; 

FUNCTION InertMoletoMassFraction(yml: Real): Real; 

{ Converts inert mole fraction to mass fraction } 

BEGIN 

192 

TR-3108 
InertMoletoMassFraction:=ym1*Molwti/(yml*Mo1wti+(1-yml)*Molwts); 

END; 

FUNCTION SatTemperature(Satpr: Real): Real; 

{ Returns saturation temperature (C) as a function of 

saturation pressure (Pa) } 

VAR 

ak 

BEGIN 

IF (Satpr>p5) THEN 

BEGIN 

ak:=(Satpr-p5)/p1; 

SatTemperature:=p3/(p2-ln(ak»-p4; 

END else 

SatTemperature:=-270.l5; 

END { SatTemperature }; 

FUNCTION SatPressure(SatT: Real): Real; 

{ Returns saturation pressure as a function of 

saturation temperature (C) } 

BEGIN 

SatPressure:=pl*exp(p2-p3/(SatT+p4»+p5; 

END { SatPressure }; 

FUNCTION Henry(Twater: Real): Real; 

real; 

{ Returns Henry's Law constant for air solubility in 

fresh water in (Pa/Mole Fraction) of Dissolved Air as a 

function of Twater in Celcius. Curve fit from 0 to 40 C, 

Taken from data in the Saline Water Conversion Engineering 

Data Book, M.W. Kellogg Company, Office of Water Research 

and Technology, PB-250 907, October 1975, p136. } 

VAR 

sol : real; 

BEGIN 

TR-3108 

sol:=(2.3333 + Twater*( -0.05425579 + Twater*0.00623618»/100000.0; 

Henry:=101325.0/sol; 

END { Henry}; 

FUNCTION MixtureEnthalpy(TmixDB,IMF: Real): Real; 

{ Returns mixture enthalpy (kJ/kg) as function of gas 

mixture temperature (C), and inert mass fraction} 

BEGIN 

MixtureEnthalpy:=(1-IMF)*(2501.6+1.866*TmixDB)+ 

IMF*1.005*TmixDB; 

END { MixtureEnthalpy }; 

FUNCTION LiquidEnthalpy(Tw: Real): Real; 

{ Returns water enthalpy (kJ/kg) as a function of 

water temperature (C) } 

BEGIN 

LiquidEnthalpy:=4.186*Tw; 

END { LiquidEnthalpy }; 

PROCEDURE AirTransProp(Tair: Real); 

193 
{ Air Transport Properties as functions of temperature Tair (K)} 

BEGIN 

AirK:=26.464e-4*exp(1.S*ln(Tair»/ 

(Tair+24S.4*exp«-12.0/Tair)*ln(lO.O»); 

{ Thermal Conductivity in (W/mK)} 

AirMu:=1.4SSe-6*exp(l.S*ln(Tair»/(Tair+110.4); 

{ Dynamic Viscosity in (kg/ms) } 

AirCp:=l.OOS; 

{ Specific Heat in (kJ/kg.K)} 

END { AirTransProp}; 

PROCEDURE SteamTransProp(Tstm: Real); 

{ Steam Transport Properties as functions of temperature (K)} 

BEGIN 

StmK:=(1.S2+0.006*(Tstm-273.1S»/lOO; 

{ Thermal Conductivity in (W/mK)} 

StmMu:=(S.02+0.04*(Tstm-273.1S»*1.Oe-6; 

{ Dynamic Viscosity in (kg/ms) } 

StmCp:=1.SS4+0.00077S*(Tstm-273.1S); 

{ Specific Heat in (kJ/kg.K)} 

END { SteamTransProp}; 

PROCEDURE MixTransProp(TDB,Pt,IMF: Real); 

{Given TDB = Dry-Bulb Steam Temperature in Celcius. 

VAA 

Pt = Total Mixture Pressure in Pascals. 

IMF = Inert Gas Mass Fraction.} 

Tabs,Gmolfr 

BEGIN 

Real; 

Tabs:=TDB+273.1S; 

AirTransProp(Tabs); 

SteamTransProp(Tabs); 

{ Calculate Mixture Properties, Wilke's Method 

{ Section 9-S, p410, Reid et. al., 

The properties of Gases and Liquids, McGraw Hill, 1977.} 

Gmolfr:=InertMasstoMoleFraction(IMF); 

StmDiff:=2.91S*exp(1.7S*ln(Tabs/313.0»/Pt; 

{ Diffusivity in (m*m/s), pSS7, Reid et. al., 

The properties of Gases and Liquids, McGraw Hill, 1977.} 

MixMwt:=l/(IMF/Molwti+(l.O-IMF)/Molwts); 

MixCp:=IMF*AirCp+(l.O-IMF)*StmCp; 

MixRho:=Pt*MixMwt/(S314.3*Tabs); 

Phi12:=sqr(1.O+exp(O.2S*ln(Molwti/Molwts»*sqrt(Stmmu/AirMu» 

/sqrt(S.O+S.O*Molwts/Molwti); 

Phi21:=sqr(1.O+exp(O.2S*ln(Molwts/Molwti»*sqrt(AirMu/Stmmu» 

/sqrt(S.O+S.O*Molwti/Molwts); 

MixMu:=(l.O-Gmolfr)*Stmmu/«l.O-Gmolfr)+Gmolfr*Phi12)+ 

Gmolfr*AirMu/(Gmolfr+(1.O-Gmolfr)*Phi21); 

Phi12:=sqr(l.O+exp(O.2S*ln(Molwti/Molwts»*sqrt(StmK/AirK» 

/sqrt(S.O+S.O*Molwts/Molwti); 

Phi21:=sqr(1.O+exp(O.2S*ln(Molwts/Molwti»*sqrt(AirK/StmK» 

/sqrt(S.O+S.O*Molwti/Molwts); 

MixK:=(1.O-Gmolfr)*StmK/«l.O-Gmolfr)+Gmolfr*Phi12)+GmoIfr*AirK/ 

(Gmolfr+(l.O-Gmolfr)*Phi21); 

194 

TR-310S 
MixPr:=1000.0*MixCp*MixMu/MixK; 

MixSc:=MixMu/(MixRho*StmDiff); 

END { MixTransProp }; 

PROCEDURE WaterTransProp(WaterTemp: Real); 

{ as function of temperature, WaterTemp in Celcius } 

VAR 

DeIRho,enl,en2 

BEGIN 

: real; 

DeIRho:=-O.69224607+WaterTemp* 

(-O.OOI75714+WaterTemp*O.00557l43); 

IF (WaterTemp< 11.85) THEN DeIRho:=O.O; 

Rholiq:=lOOO.O-DeIRho; 

{ Specific Heat in (kJ/kg.K) } 

CpLiq:=(4217044.18+WaterTemp* 

(-3504.246+WaterTemp*(lI3.l74+ 

WaterTemp*(-1.309»»/I.Oe6; 

{ Dynamic Viscosity in (kg/m.s) } 

enl:=an2/«WaterTemp+273.15)/647.3-an3); 

en2:=exp(enl*ln(lO.O»; 

Muliq:=anl*en2*1.Oe-7; 

{ Thermal Conductivity of Fresh Water ~n (W/m.K) } 

Kliq:=O.569+0.00l575*WaterTemp; 

{ Prandtl Number } 

Prliq:=lOOO.O*Cpliq*Muliq/Kliq; 

{ Schmidt Number } 

Scliq:=372.7*(sqr(muliq)/(watertemp+273.15»/(2.7Ie-9); 

{ Derived from oxygen diffusivity in water, 

p576, Reid et. al., 

The properties of Gases and Liquids, McGraw Hill, 1977.} 

END { WaterTransProp }; 

PROCEDURE PackingCharacteristics; 

{ Calculates Structured Packing Characteristics, given 

Base, Height, and angle of inclination Theta; All length 

dimensions are in meters; Theta is in degrees; } 

V~ 

Sheet,Contactloss 

BEGIN 

: Real; 

Base:=O.050; 

Height:=Base*l.OO; 

Theta:=60.0; 

Side:=Sqrt(Sqr(Base/2) + Sqr(Height»; { slant length} 

Sprime:=Sqrt(Sqr(Base/(2.0*Cos(Theta*Pi/180.0»+Sqr(Height»); 

{ distance over which liquid renewal occurs } 

Sinalpha:=Base/(2.0*Sprime*Cos(Theta*Pi/180.0»; 

{ Sine of angle of inclination of liquid flow with 

respect to horizontal } 

Pckdia:=Base*Height*(1/(Base+2*Side) + 1/(2*Side»; 

{ Equivalent Packing diameter} 

Sheet:=O.381/1000.0; 

{ Packing sheet thickness } 

Void:=1.O-4.0*Sheet/Pckdia; 

{ Packing void fraction } 

195 

TR-3108 
END; 

Contactloss:=O.O; {%} 

{ loss of area due to contact between adjacent sheets } 

ApGeom:=(1.O-Contactloss/100.O)*4.0*Void/Pckdia; 

{ Total available geometric area per volume (l/m) } 

FUNCTION Equil Pressure Balance(OneFrac: Real): Real; 

{function-used by ~eroin to find equilibrium conditions 

at the condenser exit. } 

VM 

BEGIN 

Mom_Out,OneCompFlow,TwoCompFlow 

K E Term,K E Term New 

Ine;t_Out_Eqlbm,Stm_Out_Eqlbm 

TwoFrac,TwoFracnew 

T Eqlbm,Ysoeq,Poutl,Pout2,Pp Inert 

XIw,Yiw,X_Out_Eqlbm -

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

{total inlet inert in (water+steam) is TwoCompFlow, 

total inlet (water+steam) is OneCompFlow} 

OneCompFlow:=Yin[l]+Yin[4]; 

TwoCompFlow:=Yin[3]+Yin[6]; 

TR-3l08 

{TwoFrac is ratio of outlet inerts in water to total inlet inerts, and 

OneFrac is ratio of steam at outlet to total inlet water flow} 

{first guess of inert Release and 

steam kinetic energy at the outlet} 

TwoFrac:=Yin[6]/TwoCompFlow; 

K_E_Term_New:=O.O; 

REPEAT 

K E Term:=K E Term New; 

{Iteration loop fo; equilibrium temperature} 

{energy balance for equilibrium temperature 

with the above assumptions} 

T Eqlbm:=(Tot In Enth-K E Term-OneCompFlow*OneFrac*250l.3)/ 

- (OneCompFlow*4:l86+ 

TwoCompFlow*1.006+ 

OneCompFlow*OneFrac*(1.866-4.l86»; 

{outlet equilibrium saturation pressure and 

steam flow using above temperature and 

saturated steam properties} 

PpSteam:=SatPressure(T Eqlbm); 

Stm_Out_Eqlbm:=OneFrac*OneCompFlow; 

TwoFracnew:=TwoFrac; 

REPEAT 

TwoFrac:=TwoFracnew; 

{iteration loop for equilibrium gas 

Release and pressure outlet inert flow 

in steam with the assumed Release and 

steam outlet mole fraction} 

Inert Out Eqlbm:=(l.O-TwoFrac)*TwoCompFlow; 

Ysoeq:=Stm Out Eqlbm/Molwts/ 

(Stm-Out-Eqlbm/Molwts+Inert Out Eqlbm/Molwti); 

{total outlet equilibrium pressure and 

inert partial pressure} 

196 
Pout1:=PpSteam/Ysoeq; 

Pp Inert:=Poutl-PpSteam; 

{inert gas Release using inert 

partial pressure and Henry's law} 

Yiw:=Pp Inert/Henry(T Eqlbm); 

Xiw:=Yi;*Molwti/(Yiw*Molwti+(1.0-Yiw)*Molwts); 

{find new TwoFrac and iterate to get correct gas Release 

for the assumed temperature} 

TwoFracnew:=Xiw*Yin[l]/TwoCompFlow; 

UNTIL (abs«TwoFrac-TwoFracnew)/TwoFracnew)< 1e-3); 

{using above gas Release find outlet gas mixture properties} 

X Out Eq1bm:=Inert Out Eqlbm/(Inert Out Eq1bm+Stm Out Eqlbm); 

MixTransProp(T Eqlbm,Pout1,X Out EqIbm); --

{find gas outlet velocity and kinetic energy term, 

check for kinetic energy convergence} 

U Bulk:=(Stm Out Eqlbm+Inert Out Eqlbm)/Mixrho/C S Area; 

K-E Term New;=(Stm Out Eqlbm+Inert Out Eqlbm) --

- - - *Sqr(U B~lk)/(2.0*1000.0); 

UNTIL (abs«K E Term New-K E Term)/K E Term New)< 1e-3); 

{go back and re;ise temperat~re calc~lation} 

{find new outlet pressure, pressure difference 

is zero function for zeroin} 

Mom Out:=(Stm Out Eqlbm+Inert Out Eqlbm)*U Bulk/C S Area; 

Pout2:=Yin[7]+Mom=In-Mom_Out;- - - - -

Equil_Pressure_Balance:=Poutl-Pout2; 

{stagnation equilibrium conditions 

from compressible gas equations} 

Gamma:=Mixcp/(Mixcp-S.3143/Mixmwt); 

A:=Sqrt(Gamma*S214.3/Mixmwt*(T Eqlbm+273.l5»; 

Mach:=U Bulk/A; -

Tzbyt:=(l.O+(Gamma-l.O)*Sqr(Mach)/2.0); 

Pzbyp:=Exp«Gamma/(Gamma-1.0»*Ln(Tzbyt»; 

T Stg Eq:=(T Eq1bm+273.15)*Tzbyt-273.15; 

P-Stg-Eq:=Po~t1*Pzbyp; 

{set array of equilibrium conditions} 

Yeqlbm[l]:=Yin[l]+Yin[4]-Stm Out Eqlbm; 

Yeqlbm[2]:=4.1S6*(T Eqlbm-Yin[S])*Yin[l]; 

Yeqlbm[3]:=Yin[l]*Xiw; 

Yeqlbm[4]:=Stm Out Eqlbm; 

Yeqlbm[5]:=T Eqlbm; 

Yeqlbm[6]:=Inert Out Eqlbm; 

Yeqlbm[7]:=Pout1; -

Yeqlbm[S]:=T Eqlbm; 

Yeqlbm[9]:=PpSteam; 

Yeqlbm[lO]:=le5; 

Yeqlbm[ll]:=O.O; 

Vel Eqlbm:=U Bulk; 

Super Eqlbm:;O.O; 

X Eqlbm:=le20; 

END { Equil_Pressure_Balance }; 

FUNCTION Colburn_Hougen(Tinterface: Real): Real; 

197 

TR-310S 
V~ 

{ evaluates the Colburn Hougen equation at any 

assumed interface temperature, Tinterface in Celcius 

that lies between the steam saturation temperature and 

water temperature } 

Stmlfr,Xbulk,Ybulk 

BEGIN 

: Real; 

{ Find steam properties at the interface temperature and 

Steam Mole fraction at the interface and bulk } 

Stmlfr:=SatPressure(Tinterface)/Y Est(7]; 

Xbulk:=Y Est[4]/(Y Est(4]+Y Est[6T); 

Ybulk:=Xbulk/Molwts/(Xbulk/Molwts+(l.O-Xbulk)/Molwti); 

{ Steam flux in kg/s/m~2 } 

SteamFlux:=-Gmtc*ln«l.O-Ybulk)/(l.O-Stmlfr»; 

{ Ackermann correction factors for high mass flux 

to heat and friction, Ref: Butterworth and Hewitt: 

TR-3l08 

Two-phase Flow and Heat Transfer, Oxford University Press, 1978 } 

Czero:=SteamFlux*StmCp/Ghtc; 

Ackerh:=Czero/(l.O-exp(-Czero»; 

RhoUb:=(Y Est[4]+Y Est[6])/C S Area; 

Ackf:=2.0*SteamFlu~/(RhoUb*F;cgas)/ 

(1.O-exp(-2.0*SteamFlux/(RhoUb*Frcgas»); 

{ Liquid and Gas Side heat balance - via Colburn Hougen equation. 

If interface temperature and coefficients are correct, the 

function value of Colburn-Hougen=ZERO } 

Chtl:=Lhtc*(Tinterface-Y Est(8]); 

Cht2:=Ghtc*Ackerh*(Y EstTS]-Tinterface); 

Enths:=MixtureEnthalpy(Tinterface,O); 

Enthw:=LiquidEnthalpy(Tinterface); 

Cht3:=(Enths-Enthw)*SteamFlux; 

Colburn_Hougen:=Chtl-Cht2-Cht3; 

END { Colburn_Hougen}; 

PROCEDURE CocurrentZeroin (ax,bx: Real;Flag:Lable;V~ Tint: Real); 

V~ 

{ finds value of x at which a nonlinear function f(x)=O; 

this procedure was adopted from Forsythe et al, 

Computer Methods for Mathematical Computations, 

Prentice-Hall, 1977, Chapter 7. } 

a,b,c,d,e,fa,fb,fc 

p,q,r,s,Xm 

Real; 

Real; 

BEGIN 

IF (Flag='inter') THEN 

BEGIN 

a:=ax+le-6; 

b:=bx-le-6; 

fa:=Colburn Hougen(a); 

fb:=Colburn-Hougen(b); 

END ELSE -

BEGIN 

a:=ax; 

b:=bx; 

198 
VAR 

{ evaluates the Colburn Hougen equation at any 

assumed interface temperature, Tinterface in Celcius 

that lies between the steam saturation temperature and 

water temperature } 

Stmlfr,Xbulk,Ybulk 

BEGIN 

: Real; 

{ Find steam properties at the interface temperature and 

Steam Mole fraction at the interface and bulk } 

Stmlfr:=SatPressure{Tinterface)/Y Est[7]; 

Xbulk:=Y Est[4]/(Y Est[4]+Y Est[6]); 

Ybulk:=Xbulk/Molwts/{Xbulk/Molwts+(l.O-Xbulk)/Molwti); 

{ Steam flux in kg/s/m~2 } 

SteamFlux:=-Gmtc*ln{(1.0-Ybulk)/(l.0-Stmlfr»; 

{ Ackermann correction factors for high mass flux 

to heat and friction, Ref: Butterworth and Hewitt: 

TR-3108 

Two-phase Flow and Heat Transfer, Oxford University Press, 1978 } 

Czero:=SteamFlux*StmCp/Ghtc; 

Ackerh:=Czero/(1.0-exp{-Czero»; 

RhoUb:=(Y Est[4]+Y Est[6])/C S Area; 

Ackf:=2.0*SteamFlui/(RhoUb*F;cgas)/ 

(1.0-exp(-2.0*SteamFlux/(RhoUb*Frcgas»); 

{ Liquid and Gas Side heat balance - via Colburn Hougen equation. 

If interface temperature and coefficients are correct, the 

function value of Colburn-Hougen=ZERO } 

Cht1:=Lhtc*(Tinterface-Y Est[8]); 

Cht2:=Ghtc*Ackerh*(Y Est[S]-Tinterface); 

Enths:=MixtureEnthalpy{Tinterface,O); 

Enthw:=LiquidEnthalpy(Tinterface); 

Cht3: =(Enths-Enthw »"SteamFlux; 

Colburn_Hougen:=Chtl-Cht2-Cht3; 

END { Colburn_Hougen}; 

PROCEDURE CocurrentZeroin (ax,bx: Real;Flag:Lable;VAR Tint: Real); 

VAR 

{ finds value of x at which a nonlinear function f{x)=O; 

this procedure was adopted from Forsythe et aI, 

Computer Methods for Mathematical Computations, 

Prentice-Hall, 1977, Chapter 7. } 

a,b,c,d,e,fa,fb,fc 

p,q,r,s,Xm 

Rea~; 

Real; 

BEGIN 

IF (Flag='inter') THEN 

BEGIN 

a:=ax+le-6; 

b:=bx-1e-6; 

fa:=Colburn Hougen{a); 

fb:=Colburn=Hougen(b); 

END ELSE 

BEGIN 

a:=ax; 

b:=bx; 

198 
END; 

c:=a; 

fa:=Equil Pressure Balance(a); 

fb:=Equil=Pressure=Balance(b); 

fc:=fa; 

d:=b-a; 

e:=d; 

{ convergence test } 

Toll:=2.0*Epsilon*abs(b)+0.S*Tol; 

Xm:=O.S*(c-b); 

WHILE (abs(Xm»Toll) AND 

BEGIN 

(fb< >0.0) AND 

(fb*(fc/abs(fc»< 0.0) DO 

IF (abs(fc)< abs(fb» THEN 

BEGIN 

END; 

a:=b; 

b:=c; 

c:=a; 

fa:=fb; 

fb:=fc; 

fc:=fa; 

Xm:=O.S"~(c-b) ; 

Toll:=2.0*Epsilon*abs(b)+0.S*Tol; 

IF (abs(e)< Toll) AND (abs(fa)< =abs(fb» THEN 

BEGIN { bisect } 

d:=Xm; 

e:=d; 

END ELSE 

BEGIN 

{ is quadratic interpolation possible } 

IF (a=c) THEN 

BEGIN 

{ linear interpolation } 

s:=fb/fa; 

p: =2. O'''"Xm*s ; 

q:=1.0-s; 

END ELSE 

BEGIN 

END; 

{ inverse quadratic interpolation } 

q:=fa/fc; 

r:=fb/fc; 

s:=fb/fa; 

p:=s*(2.0*Xm*q*(q-r)-(b-a)*(r-l.0»; 

q:=(q-l.O)*(r-l.O)*(s-l.O); 

{ adjust signs } 

IF (p>O.O) THEN q:=-q; 

p:=abs(p); 

{ is interpolation acceptable } 

IF «2.0*p)< (3.0*Xm*q-abs(Toll*q») AND 

(p< abs(O.S*e*q» THEN 

BEGIN 

199 

TR-3l08 
END; 

e:=d; 

d:=p/q; 

END ELSE 

BEGIN 

END; 

{ bisection } 

d:=Xm; 

e:=d; 

{ Complete Step } 

a:=b; 

fa:=fb; 

IF (abs(d»Toll) THEN b:=b+d; 

IF (abs(d)< =Toll) THEN b:=b+Toll*Xm/abs(Xm); 

IF (Flag='inter') THEN fb:=Colburn Hougen(b) ELSE 

fb:=Equil Pressure Balance(b); 

IF «fb*(fc/abs(fc»»O.O) THEN - -

BEGIN 

END; 

c:=a; 

fc:=fa; 

d:=b-a; 

e:=d; 

{ convergence test } 

Toll:=2.0*Epsilon*abs(b)+0.S*Tol; 

Xm: =0. S'i~( c-b); 

END { While }; 

Tint:=b; 

END { CocurrentZeroin }; 

PROCEDURE CocurrentEquilibrium; 

VAR 

{finds equilibrium outlet conditions (infinite length) 

for the cocurrent condenser} 

Op Flag,Zero Flag 

T Tol -

Terml,Term2,Term3 

OneFrac,Lolimit,Hilimit 

Lable; 

Real; 

Real; 

Real; 

BEGIN 

{set temperature tolerance and 

operating conditions to Superheat} 

T Tol:=le-3; 

Op Flag:='Super'; 

{find steam and liquid properties 

at the inlet (assummed to be saturated)} 

Tdew:=SatTemperature(Yin[9]); 

{check for Superheat or saturated conditions} 

IF (abs(Tdew-Yin[S]»T_Tol) THEN 

BEGIN 

Writeln (OutFilel,' inlet conditions super saturated', 

, or equilibrium Superheated.', 

END ELSE 

BEGIN 

'***** calculations aborted **~~*t); 

200 

TR-3108 
END; 

IF (abs«Tdew-Yin[S]»< T Tol) THEN 

BEGIN 

END; 

Op Flag:='Satur'; 

Tdew:=Yin[S]; 

Super_In:=O; 

{calculate inlet gas Mixture properties} 

Xmass:=Yin(6]/(Yin(6]+Yin[4]); 

MixTransProp(Yin(S],Yin(7],Xmass); 

{calculate inlet stagnation temperature 

and pressure using compressible gas equations} 

Gamma:=Mixcp/(Mixcp-8.3143/Mixmwt); 

Vel In:=(Yin[4]+Yin[6])/C S Area/Mixrho; 

A:=Sqrt(Gamma*8314.3/Mixm;t*(Yin[S]+273.lS»; 

Mach:=Vel In/A; 

Tzbyt:=(l:0+(Gamma-l.0)*Sqr(Mach)/2.0); 

Pzbyp:=Exp«Gamma/(Gamma-1.0»*Ln(Tzbyt»; 

T Stg In:=(Yin[S]+273.lS)*Tzbyt-273.l5; 

P-Stg-In:=Yin[7]*Pzbyp; 

{Inlet gas enthalpy} 

Gas In Enth:=(Yin[6]+Yin[4])*MixtureEnthalpy(Yin[5],Xmass); 

{water-inlet enthalpy, total inlet enthalpy, 

and inlet momentum flux} 

Enthw:=LiquidEnthalpy(Yin[8]); 

Wat In Enth:=Yin[l]*Enthw+Yin[3]*AirCp*Yin[8]; 

K E-In:=(Yin[6]+Yin[4])*Sqr(Vel In)/(2*1000.0); 

Tot-In Enth:=Wat In Enth+Gas In-Enth+K E In; 

Mom-In:=(Yin[4]+Yin[6])*Vel In/C S Area;-

{check for saturatated equilibri;m-conditions, 

i.e. there is adequate water flow to cool the steam 

down to saturation conditions at the outlet} 

WaterTransProp(Yin[8]); 

Terml:=Yin[4]*StmCp*(Yin[S]-Tdew); 

Term2:=Yin[6]*AirCp*(Yin[S]-Tdew); 

Term3:=Yin[l]*Cpliq*(Tdew-Yin[8])+ 

Yin[3]*AirCp*(Tdew-Yin[8]); 

IF «Terml+Term2»Term3) THEN 

Writeln (Con,' inlet conditions super saturated', 

, or equilibrium Superheated.', 

'***** calculations aborted *****') 

Else 

BEGIN 

END; 

{find equilibrium conditions 

using zero in function solver} 

Zero Flag:='equil'; 

Hilimit:=Yin[4]/(Yin(4]+Yin[l]); 

Lolimit:=HiLimit/lOOO.O; 

CocurrentZeroin (Lolimit,Hilimit,Zero_Flag,OneFrac); 

END { CocurrentEquilibrium }; 

PROCEDURE FileSetup; 

201 

TR-3l08 
{ sets up input and output files for the calculations } 

BEGIN 

{ Interactive reading of input and output file names } 

Form6:=Char(012); 

Form7:=Char(012); 

{ Writeln('Input File Name??? 

- (EG. A:Cctml.Doc ','-- 20 characters max)'); 

ReadLn (Kbd,Filein); 

Writeln('First Output File Name??? - (EG. C:Tape6.0ut)'); 

ReadLn (Kbd,Filotl); 

Writeln('Second Output File Name??? - (EG. C:Tape7.0ut)'); 

ReadLn (Kbd,Filot2);} 

Assign (InFile, 'd:coinput.par'); 

Assign (OutFilel,'d:CoTape6.out'); 

Assign (OutFile2,'d:CoTape7.out'); 

Assign (OutFile3,'d:CoTape8.out'); 

IF (Filotl='Lst') THEN Form6:='l'; 

IF (Filot2='Lst') THEN Form7:='l'; 

Reset (InFile); 

Rewrite(OutFilel); 

Rewrite(OutFile2); 

Rewrite(OutFile3); 

{ Read the number of condenser runs to be made 

from the first line of the input file } 

Readln (Infile); 

Readln (InFile,Nrun); 

END { FileSetup }; 

PROCEDURE Cocurrentinput; 

VAR 

{This procedure contains the input and output routines 

for the direct contact condenser routine -cocond-. 

Input routine for cocurrent condenser reads from the InFile 

assigned earlier.} 

Verbage 

Ipos 

BEGIN 

String(80); 

Integer; 

{initialize condenser starting length to zero} 

Xin:=O.O; 

{Verbage is a dummy character variable which reads comment 

lines in the input file} 

Readln (InFile,Run Lable,Serial,T Dew In,Yin[8), 

Gas Load,Yacob,Xinprc); - -

Ipos:=Pos('-8',Run Lable); 

Delete(Run Lable,1~Ipos-7); 

Ipos:=pos(T-8',Run Lable); 

Delete(Run Lable,Ipos+3,lS); 

Insert{""~Run Lable,l); 

Insert{ "" ,Run-Lable,ll); 

Writeln (CON,R~n Lable,T Dew In:lO:2,Yin[8]:10:2, 

Gas Load:lO:4,Y~cob:lO:4,Xinprc:lO:4); 

Geometry:='P~ck'; 

202 

TR-3108 
{ Multiplicative correction factors for the heat and 

mass transfer correlations for the liquid, heat and 

mass transfer correlations for the gas, and friction 

factor for the gas, respectively} 

Cond Len:=2.000; {Condenser overall length (m) } 

PpmIn:=14.0; { ppm of dissolved gas in liquid at entry} 

Super In:=O.O; {Superheat of the vapor at entry} 

{input calculations} 

C S Area:=l.O; {flow superficial cross sectional area (m~2)} 

yIn(4):=Gas Load*C S Area; 

Yin[1):=Yacob*Yin[4)*2470.0/(4.186*(T Dew In-Yin[8]»; 

Yin[3]:=Yin[1]*PpmIn*1.Oe-6; --

Yin[6]:=Yin[4]*Xinprc/lOO.O; 

Yin[2]:=0.O; 

Yin[lO]:=O.O; 

Yin[ll]:=O.O; 

Yin[S):=T_Dew_In+Super In; 

Afraction:=l.O; 

{ effective area fraction of the packing } 

PackingCharacteristics; 

Saperv:=Afraction*Apgeom; 

{ effective surface area per unit volume (l/m)} 

END { Cocurrentinput }; 

PROCEDURE Co_Transfer_Coefficients; 

{ This routine calculates the gas friction coefficient, 

the liquid heat and mass transfer coefficients, and 

the gas heat and mass transfer coefficients given 

local flow conditions and geometry. For 

the liquid, only turbulent flow is considered. } 

Chlen 

Diff,K L 

GammaL~Delta,Lload,Reside 

U G 

BEGIN 

{ 

liquid-Side coefficients 

------------------------} 

{ Find liquid properties } 

WaterTransProp(Y Est[8); 

{ Liquid ReynoldTs number} 

Lload:=Y Est[l)/C S Area; 

GammaL:=Lload/Saperv; 

Rel:=4.0*GammaL/Muliq; 

{ Turbulent flow coefficient } 

203 

Real; 

Real; 

Real; 

Real; 

TR-3108 
Delta:=Exp(0.6*Ln(GammaL/(Rholiq*82.0*Sqrt(Sinalpha»»; 

{ Liquid film thickness for turbulent flow on an inclined plane, 

Manning Formula, p312 of John Haberman, Introduction to 

Fluid Mechanics, Prentice-Hall, 1980 } 

U L Eff:=GammaL/(Rholiq*Delta); 

DIff:=(Muliq/Rholiq)/Scliq; 

K L:=2.0*Sqrt(Diff*U L Eff/(Pi*Sprime»; 

{-Higbie's Penetration-Theory} 

Lmtc:=Rholiq*K L; {liquid-side mass transfer coefficient} 

TR-3108 

{ Heat transfe; coefficient is found using Chilton-Colburn analogy} 

Lhtc:=Lmtc*Cpliq*Exp«2.0/3.0)*Ln(Scliq/Prliq»; 

{ ------------------------------

Gas-Side transfer coefficients 

------------------------------ } 

{ Evaluations for Structured Packing flow characteristics 

are based on Bravo, Rocha, and Fair, Mass Transfer in 

Gauze Packings, Hydrocarbon Processing, January 1985, 

pp. 91-95. DB 7/28/86} 

{ Find gas Mixture properties } 

Xmass:=Y Est[6]/(Y Est[4]+Y Est[6]); 

MixTransProp(Y Est[5],Y Est[7],Xmass); 

{ Compute mass-flux and-dimensionless numbers} 

RhoUb:=(Y Est[4]+Y Est[6])/C S Area; 

U G:=RhoUb/MixRho;-U G Eff:=U C/Sin(Theta*Pi/180); 

{-Note Relative velocity is used here, according to Bravo } 

Reg: =MixRho~~(U G Eff-abs (U L Eff) )*Pckdia/Mixmu; 

{ for cocurrent flow} - -

{ If Relative velocity based Reynolds number goes below 5, 

then set flag for discontinuing calculations } 

IF (Reg< 5.0) THEN 

BEGIN 

END; 

Setflag: =true; 

Xfinal:=X; 

Nussel t Gas: =0. 0338-::Exp( O. 8-k Ln(Reg» 

- *Exp(0.333*Ln(Mixpr»; {Bravo} 

{ Equivalent to Eqs. 2-29 and 2-31 in text} 

Ghtc:=Nusselt Gas*Mixk/Pckdia/1000.0; 

{ Mass transfer coefficient is found using Chilton-Colburn analogy} 

Gmtc:=Ghtc*Exp«2.0/3.0)*Ln(Mixpr/Mixsc»/MixCp; 

{ -------------------------

Gas friction coefficients 

------------------------- } { Note:-- Gas Reynolds Number Based on Side, per Bravo } 

{ for friction evaluations, Correlations of Bravo is used} 

{ Liquid Froude number corrections as in Bravo are not used here.} 

204 
Reside:=Reg*Side/Pckdia; { Side Reynolds Number} 

Frcgas :=0 .171 +92. 7*Pckdia/ (Reg>':Side); 

END { Co Transfer Coefficients }; 

PROCEDURE CocurrentDerivatives; 

VAR 

BEGIN 

{ This subroutine computes the first derivatives 

of the differential equations given the length 

and the values of the variables. An explanation 

of the variables is given above in the main routine. } 

a11,a12,a2l,a22,b1,b2 

Molair,Molest 

Dmlsdx,Dmladx,Dppadx 

Count 

Real; 

Real; 

Real; 

Integer; 

IF «setflag=true) OR 

(Y_Est[9]< =(l.0+SatPressure(Y_Est[8]»» THEN 

BEGIN 

FOR Count:=l TO 11 DO Yprime[Count]:=O.O; 

IF (Setflag=False) THEN 

BEGIN 

Xfinal:=x; 

setflag:=true; 

END; 

END Else 

BEGIN 

{ Compute heat and mass transfer coefficients for use 

in the differential equations. Call Transfer 

Coefficients to initialize. } 

Co Transfer Coefficients; 

Tdew:=SatTemperature(Y Est[9]); 

{ CocurrentZeroin iteratively solves the Colburn-Hougen 

equation for the interface conditions and correct 

transfer coefficients. } 

CocurrentZeroin (y Est[8],Tdew,'inter',Tsurf); 

{find stearn and water properties} 

Xmass:=Y Est[6]/(Y Est[6]+Y Est[4]); 

MixTransProp(Y Est[S],Y Est[7],Xmass); 

WaterTransProp(Y Est[8]); 

{ Solve for overall heat and mass transfer coefficients 

using the interface temperature (Tsurf). } 

Ovhtc:=Lhtc*(Tsurf-Y_Est[8])/(Y_Est[S]-Y_Est[8]); 

Ovrntc:=Lmtc; 

{ Compute first derivatives of all variables } 

205 

TR-3108 
Yprime[l]:=SteamFlux*C S Area*Saperv; 

Yprime[2]:=Lhtc*Saperv*C-S Area*(Tsurf-Y Est[8]); 

Yprime[3]:=-Lmtc*C S Area*Saperv* -

(y Est[3]/Y Est[l]-(Y Est[7]-Y Est[9])/ 

(Henry(Y Est[8]»*Mol~ti/Molwts); 

Yprime[4]:=-Yprime[1]; 

Yprime[6]:=-Yprime[3]; 

{ Matrix solution needed for calculations of 

steam temperature and total pressure derivatives } 

RhoUb:=(Y Est[6]+Y Est[4])/C S Area; 

U Bulk:=RhoUb/(Void*MixRho*SIn(Theta*Pi/180.0»; 

all:=l.O+U Bulk*U Bulk/(IOOO.O*MixCp*(273.1S+Y Est[S]»; 

a22:=I.O-U-Bulk*U-Bulk/(8314.3/Mixmwt*(273.1S+Y Est[S]»; 

aI2:=-U Bulk*U Bulk/(MixRho*IOOO.O*MixCp*8314.37 

MIxmwt*(273.IS+Y Est[S]»; 

a21:=MixRho*U Bulk*U B~lk/(273.IS+Y Est[5]); 

bl:=-Cht2*exp(-Czero)*Saperv*C S Area/(MixCp)/ 

(y Est[4]+Y Est[6])-U Bulk*(Yprime[4]/C S Area)/ 

(MIxRho*MixCp*IOOO.O); - -

TR-3108 

b2:=-U Bulk*Yprime[4]/C S Area-O.5*MixRho*Sqr(U Bulk-abs(U L Eff»* 

Apgeom*Frcgas* - - - - -

(Afraction*Ackf+I.O-Afraction); 

{ Note Apgeom used here instead of Saperv, to account for 

friction associated with the ineffective mass transfer 

areas as well. } 

Yprime[S]:=(a22*bl-aI2*b2)/(all*a22-a12*a21); 

Yprime[7]:=(all*b2-a21*bl)/(all*a22-aI2*a21); 

{ Molar flow rates needed for calculating 

steam partial pressure derivative} 

Molair:=Y Est[6]/Molwti; 

Molest:=Y-Est[4]/Molwts; 

Dmladx:=Yprime[6]/Molwti; 

Dmlsdx:=Yprime[4]/Molwts; 

Dppadx:=Molair/(Molair+Molest)*Yprime[7]+ 

Y Est[7]*«(Molair+Molest)*DmladxMolair*(Dmladx+Dmlsdx»/(Sqr(Molair+Molest»); 

Yprime[9]:=Yprime[7]-Dppadx; 

Yprime[8]:=Yprime[2]/(Y Est[l]*Cpliq); 

Yprime[lO]:=Yprime[8]/(Y Est[S]-Y Est[8]); 

Yprime[ll]:=O.O; - -

END {if}; 

{ save derivatives for printing} 

Prime:=Yprime; 

END { CocurrentDerivatives }; 

PROCEDURE CocurrentOutAdd(Nline,Nseg: Integer); 

VM 

{ Additional cocurrent detailed output including 

dimensionless numbers and individual coefficients 

as a function of condenser length are generated here 

and recorded onto the file OutFile2.} 

Vout : Vector; 

206 
BEGIN 

{print label, header, and initial conditions on first call} 

IF (Nline=O) THEN Writeln(OutFile2,Form6,Run Lable); 

IF (Nline=O) THEN Writeln(OutFile2,Cdate,' '~Ctime); 

{re-solve for ackerman heat transfer Correlation} 

Ackerh:=Czero/(l.O-exp{-Czero»); 

{load and print output matrix} 

IF (Nline< 100) THEN 

BEGIN 

END; 

Vout[I]:=X; 

Vout[2]:=Rel; 

Vout[3]:=Reg; 

Vout[4]:=PrLiq; 

Vout[5]:=Mixpr; 

Vout[6]:=ScLiq; 

Vout[7]:=Mixsc; 

Vout[8]:=Lhtc; 

Vout[9]:=Ghtc*1000.0; 

Vout[10]:=Lmtc*1000.0; 

Vout[ll]:=Gmtc*lOOO.O; 

Vout[12]:=Ackerh; 

Vout[13]:=Ackf; 

Vout[14]:=SteamFlux*1000.0; 

Vout[15]:=Tdew; 

Vout[16]:=Prime[5]; 

Vout[17]:=Nusselt Gas; 

Vout[18]:=Prime[9]; 

Vout[19]:=Frcgas; 

FOR i:=l TO 19 DO Write{ OutFile2, Vout[i]:10,' I); 

Writeln(OutFile2); 

IF{Nline=100) THEN 

BEGIN 

END; 

Writeln{OutFile2); 

FOR i:=1 TO 18 DO Write( OutFile2, 999.9:10,' I); 

Writeln(OutFile2); 

Writeln(OutFile2); 

END { CocurrentOutAdd} 

PROCEDURE CocurrentOutput(Nline,Nseg: Integer); 

VAR 

{Output routine for co current condenser model. 

Prints detailed results as a function of condenser 

length and a summary of actual and equilibrium 

outlet conditions on the file OutFilel. } 

Vout 

Tstago,Pstago,Superht 

Ploss,Poten 

Effweq,Effw 

207 

Vector; 

Real; 

Real; 

Real; 

TR-3108 
BEGIN 

{print header, label, and inlet conditions 

for the first call} 

IF (Nline=O) THEN 

BEGIN 

Cdate:='"'+date+'" '; 

Ctime:='"'+time+'" '; 

Writeln(OutFilel,Form6,Run Lable); 

Writeln(OutFilel ,Cdate,' '-;-Ctime); 

{ Write inlet conditions } 

Vout[l]:=Xin; 

Vout[2]:=Yin[1]/C S Area; 

Vout[3]:=Yin[4]/C-S-Area; 

Vout[4]:=Yin[3]*le67(Yin[1]+Yin[3]); 

Vout[S]:=(Yin[6]*100.O)/(Yin[6]+Yin[4]); 

Vout[6]:=Yin[S]; 

Vout[7]:=Tsurf; 

Vout[S] :=Yin[S]; 

Vout[9]:=Super In; 

Vout[10):=Yin[7); 

Vout[11):=Yin[9]; 

Vout[12):=SatPressure(Yin[S]); 

Vout[13):=O.0; 

Vout[14]:=Yin[10]; 

Vout[lS]:=Yin[2]/C S Area; 

Vout[16]:=(1.O-Yin[4]/Yin[4])*100.0; 

Vout[17]:=Vel In; 

Vout[18]:=0.0; 

Vout[19]:=0.0; 

FOR i:=l TO 19 DO Write(OutFilel, Vout[i]:lO,' '); 

Writeln(OutFilel); 

CocurrentOutAdd(Nline,Nseg); 

END ELSE 

IF (Nline< 100) THEN 

BEGIN 

{set output conditions} 

Tdew:=SatTemperature(Y[9]); 

{find stagnation temperature and pressure conditions} 

U Bulk:=(Y[4]+Y[6])/C S Area/Mixrho; 

G;mma:=Mixcp/(Mixcp-8:3I43/Mixmwt); 

A:=Sqrt(Gamma*S314.3/Mixmwt*(Y[S]+273.1S»; 

Mach:=U Bulk/A; 

Tzbyt:=(1.0+(Gamma-l.0)*Sqr(Mach)/2.0); 

Pzbyp:=Exp(Gamma/(Gamma-l.O)*Ln(Tzbyt»; 

Tstago:=Y[S]*Tzbyt; 

Pstago:=Y[7]*Pzbyp; 

Superht:=Y[S]-Tdew; 

{define a "pressure loss" Term which includes momentum} 

Ploss:=Yin[7]-Y[7]+(Mom In-(Y[4]+Y[6])*U Bulk/C S Area); 

{set output array and p;int intermediate-results}-

Vout[l]:=X; 

Vout[2]:=Y[1]/C_S_Area; 

208 

TR-310S 
END; 

Vout[3]:=Y[4]/c S Area; 

Vout[4]:=Y[3]*le67(Y[1]+Y[3]); 

Vout[S]:=(Y[6]*100.0)/(Y[6]+Y[4]); 

Vout[6]:=Y[S]; 

Vout[7]:=Tsurf; 

Vout[8]:=Y[8]; 

Vout[9]:=Superht; 

Vout[10]:=Y[7]; 

Vout[ll] :=Y[9]; 

Vout[12]:=SatPressure(Y[S]); 

Vout[13]:=Ploss; 

Vout[14]:=Y[10]; 

Vout[lS]:=Y[2]/C S Area; 

Vout[16]:=(1.0-Y[4]/Yin[4])*100.0; 

Vout[17]:=U Bulk; 

Vout[18]:=O-;htc; 

Vout[19]:=Ovmtc*1000.0; 

Pdrop:=Yin[7]-Y[7]; 

FOR i:=l TO 19 DO Write(OutFile1, Vout[i]:ll,' I); 

Writeln(OutFile1); 

CocurrentOutAdd(Nline,Nseg); 

IF(Nline=lOO) THEN 

BEGIN 

END; 

{**** Last two lines of output ****} 

Writeln(OutFile1); 

{ Equilibrium Conditions } 

Vout[1]:=999.9; 

Vout[2]:=Yeqlbm[1]/C S Area; 

Vout[3]:=Yeqlbm[4]/C-S-Area; 

Vout[4]:=Yeqlbm[3]*le67(Yeq1bm[1]+Yeqlbm[3]); 

Vout[S]:=(Yeqlbm[6]*100.0)/(Yeqlbm[6]+Yeqlbm[4]); 

Vout[6]:=Yeqlbm[S]; 

Vout[7] :=0.0; 

Vout[8]:=Yeqlbm[8]; 

Vout[9]:=0.0; 

Vout[10]:=Yeqlbm[7]; 

Vout[ll]:=Yeqlbm[9]; 

Vout[l2]:=SatPressure(Yeqlbm[S]); 

Vout[13]:=0.0; 

Vout[14]:=Yeqlbm[10]; 

Vout[lS]:=Yeqlbm[2]/C S Area; 

Vout[16]:=(1.0-Yeqlbm[4]/Yin[4])*100.0; 

Vout[l7]:=Vel Eqlbm; 

Vout[18]:=999:-9; 

Vout[19]:=999.9; 

FOR i:=l TO 19 DO Write(OutFile1, Vout[i]:ll,' I); 

Writeln(OutFi1e1); 

CocurrentOutAdd(Nline,Nseg); 

END {CocurrentOutput }; 

209 

TR-3108 
PROCEDURE Runga(h,xO: Real; YO:State); 

{ Fourth-order Runge-Kutta integration scheme } 

VAR 

k1,k2,k3,k4 : State; 

BEGIN 

X Est:=xO; Y Est:=YO; 

CocurrentDerlvatives; 

IF (Iprint AND (xO=O.O)) THEN CocurrentOutput(0,40); 

FOR i:=1 TO Neqn DO 

BEGIN 

END; 

k1[i):=h*Yprime[i); 

Y_Est[i]:=YO[i)+k1[i]/2; 

X Est:=X Est+h/2; 

CocurrentDerivatives; 

FOR i:=1 TO Neqn DO 

BEGIN 

END; 

k2[i):=h*Yprime[i); 

Y_Est[i]:=YO[i]+k2[i)/2; 

CocurrentDerivatives; 

FOR i:=1 TO Neqn DO 

BEGIN 

END; 

k3[i):=h*Yprime[i); 

Y_Est[i]:=YO[i)+k3[i); 

X Est:=X Est+h/2; 

CocurrentDerivatives; 

FOR i:=1 TO Neqn DO 

BEGIN 

k4[i):=h*Yprime[i]; 

Y[i]:=YO[i)+(k1[i)+2*k2[i)+2*k3[i)+k4[i))/6; 

END; 

X:=XO+h; 

END { Runga }; 

PROCEDURE Cocurrent Main; 

VAR 

BEGIN 

{ This Main procedure sets up inputs, then calls 

other calculation procedures, updates monitor 

display and then Ends calculations. It is repeated 

for every run case. } 

Ix 

Stmlfr 

Mlfrar,Mlfrst 

FOR Ix:=1 TO Nrun DO 

BEGIN 

FOR i:=1 TO 11 DO 

BEGIN 

END; 

Y[ i] :=0; 

Yin[ i) : =0; 

Integer; 

Real; 

Real; 

210 

TR-3108 
X:=O; 

Xin:=O; 

{ Read the condenser initial values of most of the 

variables for the modeling differential equations 

by calling subroutine cinput. 

The differential equation variables are as follows: 

Y[l):=water flow rate (kg/s) 

Y[2):=condenser heat load (kW) 

Y[3):=dissolved gas flow rate (kg/s) 

Y[4):=steam flow rate (kg/s) 

Y[S):=steam temperature (C) 

Y[6):=inert gas mass flow rate (kg/s) 

Y[7):=condenser pressure (Pa) ** calculated ** 

Y[8):=water temperature (C) 

Y[9):=partial pressure of the steam (Pa) ** calculated ** 

Y[lO):=ntu 

Y[ll):=fog flow rate (kg/s) ** not used ** } 

Cocurrentinput; 

{ Solve for remaining initial values of 

integration variables } 

Stmlfr:=(Yin[4)/Molwts/(Yin[4)/Molwts+Yin[6)/Molwti»; 

Yin[9):=SatPressure(Yin[S)-Super In); 

Yin[7):=Yin[9)/Stmlfr; -

Tdew:=Yin[S)-Super In; 

{ save initial val~es of variables ~n an array 

Yin and length as Xin } 

Y:=Yin; 

X:=Xin; 

{ Set initial heat, mass and friction 

coefficients to zero } 

Lhtc:=O.O; Lmtc:=O.O; Ghtc:=O.O; Gmtc:=O.O; 

Frcgas:=O.O; Frcliq:=O.O; 

{ Find equilibrium conditions at the condenser 

outlet (infinite length or residence time).} 

CocurrentEquilibrium; 

{ Check for saturation of cold water with a~r 

at atmospheric pressure at the inlet 

using Henry's law, print a warning if 

supersaturated.} 

Mlfrst:=10132S.0/Henry(Y[S); 

Mlfrar:=Y[3)*Molwts/(Y[1)*Molwti); 

IF (Mlfrar>Mlfrst) THEN Writeln(lst,Mlfrar,Mlfrst, 

, specified inlet dissolved air Mole fraction',Mlfrar, 

I saturation inlet dissolved air Mole fraction',Mlfrst, 

'***** check inlet conditions --- supersaturated *****'); 

{ Set the integration Step size } 

Step:=Cond_Len/Nseg; 

Istep:=O; 

Xend:=Xin; 

Xfinal:=Cond_Len; 

211 

TR-3108 
Setflag:=False; 

REPEAT 

IF (Setflag) THEN Step:=Cond_Len-Xend; 

Xend:=Xend+Step; 

Runga(Step,X,Y); 

{ Monitor print statements to check progress } 

Wateff:=(Y[8]-Yin[8])/(Yin[S]-Yin[8]); 

Cond prc:=(Yin[4]-Y[4])*100.0/Yin[4]; 

Pdrop:=Yin[7]-Y[7]; 

Writeln(CON,Xend:6:3,Y[8]:6:2,Tsurf:6:2,Tdew:6:2, 

Cond_prc:6:2,Pdrop:7:2, 

U G Eff:6:2,U L Eff:6:2, 

Reg:6:l,MixSc:6:2,Nusselt Gas:6:2, 

Y[6]:10:6); -

IF (abs(x-Cond Len)< O.OOS) THEN 

Writeln(lst,Run Lable:20,Serial:S,Yin[S]:10:2, 

xfinal:lO:2,Y[8]:10:2, 

Cond prc:lO:2,Pdrop:lO:2, 

Tdew:10:2,Base:8:4, 

Saperv:lO:2,Yacob:lO:4); 

IF (abs(x-Cond Len)< O.OOS) THEN 

Writeln(OutFile3,Run Lable:20,Serial:S, 

Yin[S]:11:4,xfinal:ll:4, 

Y[8]:11:4,Cond prc:ll:4, 

Pdrop:ll:4,Tdew:ll:4,Base:8:4, 

Saperv:lO:2,Yacob:10:4); 

Tdew:=SatTemperature(Y[9]); 

{ Succesful integration, increment length 

and print intermediate results} 

Istep:=Istep+l; 

IF (Iprint) THEN CocurrentOutput(Istep,Nseg); 

{ Final length reached, go on to next set of conditions} 

UNTIL (Xend>=Cond_Len); 

IF (Iprint) THEN CocurrentOutput(lOO,lOO); 

END { Run-for-do loop }; 

END { Procedure Cocurrent Main }; 

BEGIN 

END. 

FileSetUp; 

Machineaccuracy; 

Iprint:=False; {Printing to Files not opted} 

Write(lst,chr(27),chr(49»; 

Co current Main; 

Close(OutFilel); 

Close(OutFile2); 

Close(OutFile3) ; 

212 

TR-3l08 
TR-3108 

PROGRAM Countercurrent_Condenser; 

{$U+} { User Interrupt enabled.} 

{ This program contains routines which model a Countercurrent 

direct contact condenser using structured packings for use in open 

cycle ocean thermal energy conversion (OTEC). Details of the modeling 

and the accompanying study can be found in this report (SERI/TR-252-3108). 

This version is set up to run with the TURBO-Pascal compiler (version 

3.0, Borland International Inc.) on an IBM or compatible personal 

computer. 

In case of you may find errors or problems 1n using this code, 

please contact the authors at SERI: 

1617 Cole Boulevard 

Golden, Colorado, 80401 

Tel: (303)-231-1000 

*********************** 

Main Routine --CCcond-- version 871015, Revisions 10-15-87 

 ~~** *"I~*****"#':*"#': .. k***** ----------------------------------} 

CONST 

TYPE 

VAR 

{ Physical Constants } 

Molwts=18.0l5; Molwti=28.97; 

G=9.8l; Sigma=0.072; 

{ Water saturation pressure curve-fit Constants } 

pl=161.75743178; p2=18.477911547; p3=4026.97587317; 

p4=234.73842369; p5=3.738345l7667; 

{ Water viscosity curve-fit Constants} 

an1=24l.4; an2=0.382809486; an3=0.2162830218; 

{ integration and numerical error tolerance } 

Tol=le-12; 

{ Mathematical Constant } 

Pi=3.1415927; 

Neqn=11 { Number of equations to be integrated }; 

Nseg=400 { Number of segments the condenser is divided into. }; 

State = 

Lable = 

Vector = 

Istep 

Nrun,Serial 

ARRAY [ 1. .11] of Real; 

String[20]; 

ARRAY [ 1..20] of Real; 

Cond Len,Pckdia,C S Area,Saperv,Corliq,Corgas, 

Corfrc,Theta,Void~SInalpha 

Run Lable 

Xin~Velin,Pstgin,Tstgin,Super_In 

X,X Est,Tdew,Xend 

Kliq,Muliq,Cpliq,Prliq,Scliq,Rholiq,Diffaw 

Lhtc,Lmtc,Ghtc,Gmtc,Frcgas,Frcliq,Rel,Reg 

213 

Integer; 

Integer; 

Real; 

String[15]; 

Real; 

Real; 

Real; 

Real; 
Tsurf,Ovhtc,Ovmtc,SteamF1ux,Czero,Cht1,Cht2,Cht3, 

Ackerh,Ackf 

Xeq,Veleq,Pstgeq,Tstgeq,Supreq 

Temp,Press,Vo1w,Vols,Enthw,Enths 

Y,Ytop,Ybot,Yeqlbm,Y Est,Prime,Yprime 

Filein,Filot1,Filot2-

Geometry 

Form6,Form7 

InFile,OutFile1,OutFile2,OutFile3 

TgasDB,Tsat,Tliq 

Ptotal,Satpr,Ppsteam 

Xmass,Ymole 

AirMu,AirK,AirCp 

StmMu,StmK,StmCp 

StmRho,StmDiff 

MixMu,MixK,MixCp,MixPr,MixSc,MixMwt,MixRho 

Phil2,Phi21 

MixEnth,Enthliq 

I,Iguess 

Epsilon,Tol1,T,Tolzer,Tolerance 

Tot In Enth,Wat In Enth,Gas In Enth 

U_B~lk~Gamma,A,Mach - -

Tzbyt,Pzbyp 

Vel_Eqlbm,Super_Eqlbm,X_Eqlbm 

Mom_In,Vel_In,K_E_In 

T_Stg_In,T_Dew_In,P_Stg_In 

T_Stg_Eq,P_Stg_Eq 

Mom Out,K E Out 

Vel=Out,Gas=Out_Enth 

Yacob,PpmIn 

Gas Load,Xinprc 

RhoUb,U L Eff,Nusselt Gas 

Step,Afraction -

Base,Height,Side,Apgeom,Sprime 

Wateff,Cond prc,Pdrop,Xfinal 

Convergence~Setflag,Iprint 

{ A TURBO-Pascal support file } 

TYPE 

RegPack = 

RECORD { register pack Used in MSDos call } 

Real; 

Real; 

Real; 

State; 

Lable; 

String[4] ; 

Char; 

Text; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Integer; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Real; 

Boolean; 

AX, BX, CX, DX, BP, SI, DI, DS, ES, Flags: Integer; 

END; 

TimeStr = 

VAR 

String[8] ; DateStr = String[ 10] ; 

RecPack RegPack; 

Ctime,Cdate String[10]; 

FUNCTION Time: Timestr; 

{ returns the current time 1n string format HH:MM:SS } 

VAR 

Hour,Min,Sec,Frac : String[2]; 

BEGIN 

WITH RecPack DO 

214 

TR-3108 
BEGIN AX := $2COO ; MsDos(RecPack) 

AX := hi(CX); Str(AX,Hour); 

IF AX < 10 THEN Insert(' ',Hour,l); 

AX := lo(CX); Str(AX,Min ); 

IF AX < 10 THEN Insert('O',Min ,1); 

AX := hi(DX); Str(AX,Sec ); 

IF AX < 10 THEN Insert('O',Sec ,1); 

AX := lo(DX); Str(AX,Frac); 

IF AX < 10 THEN Insert('O',Frac,l); 

Time := Hour + ':' + Min + ':' + Sec; 

{+ '.' + Frac} 

END; 

END; 

FUNCTION Date: DateStr; 

{ returns the current date 1n string format : MM/DD/yyyy } 

VM 

Year: String[4] ; Month,Day : String[2] 

BEGIN 

WITH RecPack DO 

BEGIN 

AX := $2A shl 8 ; MsDos(Recpack); 

AX := DX shr 8; Str(AX,Month); 

IF AX < 10 THEN Insert(' ',Month,l); 

AX := DX mod 256; Str(AX,Day); 

IF AX < 10 THEN Insert('O',Day ,1); 

Str (CX,Year); 

Date := Month + 'I' + Day + 'I' + Year; 

END; 

END; 

PROCEDURE MachineAccuracy; 

{ Calculates the smallest discernable real number 

for the machine } 

BEGIN 

END; 

Epsilon:=l.O; 

REPEAT 

Epsilon:=Epsilon/2.0; 

Tolerance:=l.O + Epsilon; 

UNTIL (Tolerance<=l.O); 

FUNCTION InertMasstoMoleFraction(xm: Real): Real; 

{ Converts inert mass fraction to mole fraction } 

BEGIN 

InertMasstoMoleFraction:=xm/Molwti/(xm/Molwti+(l-xm)/Molwts); 

END; 

FUNCTION InertMoletoMassFraction(yml: Real): Real; 

{ Converts inert mole fraction to mass fraction } 

BEGIN 

InertMoletoMassFraction:=yml*Molwti/(yml*Molwti+(l-yml)*Molwts); 

215 

TR-3108 
END; 

FUNCTION SatTemperature(Satpr: Real): Real; 

{ Returns saturation temperature (C) as a function of 

saturation pressure (Pa) } 

VAA 

ak 

BEGIN 

IF (Satpr>p5) THEN 

BEGIN 

ak:=(Satpr-p5)/p1; 

SatTemperature:=p3/(p2-ln(ak»-p4; 

END else 

SatTemperature:=-270.15; 

END { SatTemperature }; 

FUNCTION SatPressure(SatT: Real): Real; 

{ Returns saturation pressure as a function of 

saturation temperature (C) } 

BEGIN 

SatPressure:=pl*exp(p2-p3/(SatT+p4»+p5; 

END { SatPressure }; 

FUNCTION Henry(Twater: Real): Real; 

real; 

{ Returns Henry's Law constant for air solubility in 

fresh water in (Pa/Mole Fraction) of Dissolved Air as a 

function of Twater in Celcius. Curve fit from 0 to 40 C, 

Taken from data in the Saline Water Conversion Engineering 

Data Book, M.W. Kellogg Company, Office of Water Research 

and Technology, PB-250 907, October 1975, p136. } 

VAA 

sol : real; 

BEGIN 

TR-3108 

sol:=(2.3333 + Twater*( -0.05425579 + Twater*0.00623618»/100000.0; 

Henry:=101325.0/sol; 

END { Henry}; 

FUNCTION MixtureEnthalpy(TmixDB,IMF: Real): Real; 

{ Returns mixture enthalpy (kJ/kg) as function of gas 

mixture temperature (C), and inert mass fraction} 

BEGIN 

MixtureEnthalpy:=(1-IMF)*(250l.6+l.866*TmixDB)+ 

IMF*1.005*TmixDB; 

END { MixtureEnthalpy }; 

FUNCTION LiquidEnthalpy(Tw: Real): Real; 

{ Returns water enthalpy (kJ/kg) as a function of 

water temperature (C) } 

BEGIN 

LiquidEnthalpy:=4.186*Tw; 

END { LiquidEnthalpy }; 

PROCEDURE AirTransProp(Tair: Real); 

{ Air Transport Properties as functions of temperature Tair (K)} 

216 
BEGIN 

AirK:=26.464e-4*exp(1.5*ln(Tair»/ 

(Tair+245.4*exp«-12.0/Tair)*ln(lO.O»); 

{ Thermal Conductivity in (W/mK)} 

AirMu:=1.458e-6*exp(1.5*ln(Tair»/(Tair+l10.4); 

{ Dynamic Viscosity in (kg/ms) } 

AirCp:=1.005; 

{ Specific Heat in (kJ/kg.K)} 

END { AirTransProp}; 

PROCEDURE SteamTransProp(Tstm: Real); 

{ Steam Transport Properties as functions of temperature (K)} 

BEGIN 

StmK:=(1.82+0.006*(Tstm-273.15»/IOO; 

{ Thermal Conductivity in (W/mK)} 

StmMu:=(8.02+0.04*(Tstm-273.15»*1.Oe-6; 

{ Dynamic Viscosity in (kg/ms) } 

StmCp:=1.854+0.000775*(Tstm-273.15); 

{ Specific Heat in (kJ/kg.K)} 

END { SteamTransProp}; 

PROCEDURE MixTransProp(TDB,Pt,IMF: Real); 

{Given TDB = Dry-Bulb Steam Temperature in Celcius. 

VAR 

Pt = Total Mixture Pressure in Pascals. 

IMF = Inert Gas Mass Fraction.} 

Tabs,Gmolfr 

BEGIN 

Real; 

Tabs:=TDB+273.l5; 

AirTransProp(Tabs); 

SteamTransProp(Tabs); 

{ Calculate Mixture Properties, Wilke's Method 

{ Section 9-5, p4l0, Reid eta al., 

The properties of Gases and Liquids, McGraw Hill, 1977.} 

Gmolfr:=InertMasstoMoleFraction(IMF); 

StmDiff:=2.9IS*exp(l.75*ln(Tabs/3l3.0»/Pt; 

{ Diffusivity in (m*m/s), p557, Reid eta al., 

The properties of Gases and Liquids, McGraw Hill, 1977.} 

MixMwt:=l/(IMF/Molwti+(I.O-IMF)/Molwts); 

MixCp:=IMF*AirCp+(I.O-IMF)*StmCp; 

MixRho:=Pt*MixMwt/(S3l4.3*Tabs); 

PhiI2:=sqr(l.O+exp(O.25*ln(Molwti/Molwts»*sqrt(Stmmu/AirMu» 

/sqrt(S.O+S.O*Molwts/Molwti); 

Phi2l:=sqr(l.O+exp(O.25*ln(Molwts/Molwti»*sqrt(AirMu/Stmmu» 

/sqrt(S.O+S.O*Molwti/Molwts); 

MixMu:=(l.O-Gmolfr)*Stmmu/«l.O-Gmolfr)+Gmolfr*Phi12)+ 

Gmolfr*AirMu/(Gmolfr+(l.O-Gmolfr)*Phi2l); 

Phil2:=sqr(l.O+exp(O.25*ln(Molwti/Molwts»*sqrt(StmK/AirK» 

/sqrt(S.O+S.O*Molwts/Molwti); 

Phi2l:=sqr(1.O+exp(O.25*ln(Molwts/Molwti»*sqrt(AirK/StmK» 

/sqrt(S.O+S.O*Molwti/Molwts); 

MixK:=(1.O-Gmolfr)*StmK/«l.O-Gmolfr)+Gmolfr*Phil2)+GmoIfr*AirK/ 

(Gmolfr+(1.0-Gmolfr)*Phi21); 

MixPr:=lOOO.O*MixCp*MixMu/MixK; 

217 

TR-3108 
MixSc:=MixMu/(MixRho*StmDiff); 

END { MixTransProp }; 

PROCEDURE WaterTransProp(WaterTemp: Real); 

{ as function of temperature, WaterTemp in Celcius } 

VAR 

DeIRho,enl,en2 : real; 

BEGIN 

DeIRho:=-O.69224607+WaterTemp* 

(-O.00175714+WaterTemp*O.00557143); 

IF (WaterTemp<11.85) THEN DeIRho:=O.O; 

Rholiq:=lOOO.O-DeIRho; 

{ Specific Heat in (kJ/kg.K) } 

CpLiq:=(4217044.18+WaterTemp* 

(-3504.246+WaterTemp*(113.174+ 

WaterTemp*(-1.309»»/1.Oe6; 

{ Dynamic Viscosity in (kg/m.s) } 

enl:=an2/«WaterTemp+273.15)/647.3-an3); 

en2:=exp(enl*ln(lO.O»; 

Muliq:=anl*en2*1.Oe-7; 

{ Thermal Conductivity of Fresh Water ~n (W/m.K) } 

Kliq:=O.569+0.001575*WaterTemp; 

{ Prandtl Number } 

Prliq:=lOOO.O*Cpliq*Muliq/Kliq; 

{ Schmidt Number } 

Scliq:=372.7*(sqr(muliq)/(watertemp+273.15»/(2.71e-9); 

{ Derived from oxygen diffusivity in water, 

p576, Reid et. al., 

The properties of Gases and Liquids, McGraw Hill, 1977.} 

END { WaterTransProp }; 

PROCEDURE PackingCharacteristics; 

VAR 

{ Calculates packing characteristics given 

base,height,and angle of inclination Theta} 

Sheet,Contactloss Real; 

[ all calculations in meters.} 

BEGIN 

Base:=O.025; 

Height:=Base; 

Theta:=60.0; {degrees} 

Side:=Sqrt(Sqr(Base/2) + Sqr(Height»; 

Sprime:=Sqrt(Sqr(Base/(2*Cos(Theta*Pi!180.0»+Sqr(Height»); 

Sinalpha:=Base/(2*Sprime*Cos(Theta*Pi/180.0»; 

Pckdia:=Base*Height*(1/(Base+2*Side) + 1/(2*Side»; 

Sheet:=O.381/1000.0; 

Void:=1.O-4.0*Sheet!Pckdia; 

Contactloss:=O.O {%}; 

Apgeom:=(1.O-Contactloss!lOO.O)*4.0*Void!Pckdia; 

END { PackingCharacteristics }; 

FUNCTION Colburn Hougen(Tinterface: Real): Real; 

{ Tinterface in Celcius } 

218 

TR-3l08 
VM 

BEGIN 

Stmlfr,Xbulk,Ybulk,Cfric : Real; 

{ Find steam properties at the interface temperature and 

Steam Mole fraction at the interface and bulk } 

Stmlfr:=SatPressure(Tinterface)/Y Est[7]; 

Xbulk:=Y Est[4]/(Y Est[4]+Y Est[6]); 

Ybulk:=Xbulk/Molwts/(Xbulk/Molwts+(l.O-Xbulk)/Molwti); 

{ Steam flux in kg/s/mA2 } 

IF (Stmlfr>l.O) THEN Stmlfr:=1.0-1.Oe-12; 

IF (Ybu1k>1.0) THEN Ybulk :=1.0-1.Oe-12; 

SteamFlux:=-Gmtc*ln«l.O-Ybulk)/(l.O-Stmlfr»; 

TR-3108 

{ Ackerman correction factors for high mass flux to heat and friction, 

Ref. Butterworth and Hewitt: Two-phase flow and heat transfer} 

Czero:=SteamFlux*StmCp/Ghtc; 

Ackerh:=Czero/(l.O-exp(-Czero»; 

RhoUb:=(Y Est[4]+Y Est[6])/C S Area; 

Cfric:=2.0*SteamFl~x/(RhoUb*Frcgas); 

IF (Cfric<1.Oe-6) THEN Ackf:=Cfric/(1.0-exp(-1.Oe-6» 

ELSE Ackf:=Cfric/(l.O-exp(-Cfric»; 

{ Liquid and Gas Side heat balance - via Colburn Hougen equation. 

IF interface temperature and coefficients are correct, the 

function value of Colburn-Hougen=ZERO } 

Cht1:=Lhtc*(Tinterface-Y Est[8]); 

Cht2:=Ghtc*Ackerh*(Y EstTS]-Tinterface); 

Enths:=MixtureEnthalpy(Tinterface,O); 

Enthw:=LiquidEnthalpy(Tinterface); 

Cht3:=(Enths-Enthw)*SteamFlux; 

Colburn_Hougen:=Cht1-Cht2-Cht3; 

END { Colburn_Hougen}; 

PROCEDURE CountercurrentZeroin (ax,bx: Rea1;Flag:Lable;VM Tint: Real); 

VM 

a,b,c,d,e,fa,fb,fc 

p,q,r,s,Xm 

BEGIN 

IF (Flag='inter') THEN 

BEGIN 

END; 

c:=a; 

a:=ax+1e-6; 

b:=bx-1e-6; 

fa:=Colburn Hougen(a); 

fb:=Colburn=Hougen(b); 

fc:=fa; 

d:=b-a; 

e:=d; 

{ convergence test } 

Tol1:=2.0*Epsilon*abs(b)+0.S*Tol; 

Xm:=O.S*(c-b); 

WHILE (abs(Xm»Tol1) AND 

(fb< >0.0) AND 

Real; 

Real; 

219 
(fb*(fc/abs(fc»< 0.0) DO 

BEGIN 

IF (abs(fc)< abs(fb» THEN 

BEGIN 

END; 

a:=b; 

b:=c; 

c:=a; 

fa:=fb; 

fb:=fc; 

fc:=fa; 

Xm:=0.5*(c-b); 

Toll:=2.0*Epsilon*abs(b)+0.5*Tol; 

IF (abs(e)< Toll) AND (abs(fa)< =abs(fb» THEN 

BEGIN { bisect } 

d:=Xm; 

e:=d; 

END ELSE 

BEGIN 

END; 

{ is quadratic interpolation possible } 

IF (a=c) THEN 

BEGIN 

{ linear interpolation } 

s:=fb/fa; 

p: =2. Oi~Xmi~s; 

q:=1.0-s; 

END ELSE 

BEGIN 

END; 

{ inverse quadratic interpolation } 

q:=fa/fc; 

r:=fb/fc; 

s:=fb/fa; 

p:=s*(2.0*Xm*q*(q-r)-(b-a)*(r-l.0»; 

q:=(q-!.O)*(r-l.O)*(s-l.O); 

{ adjust signs } 

IF (p>O.O) THEN q:=-q; 

p:=abs(p); 

{ is interpolation acceptable } 

IF «2.0*p)< (3.0*Xm*q-abs(Toll*q») AND 

(p< abs(0.5*e*q» THEN 

BEGIN 

e:=d; 

d:=p/q; 

END ELSE 

BEGIN 

END; 

{ bisection } 

d:=Xm; 

e:=d; 

{ Complete Step } 

a:=b; 

fa:=fb; 

220 

TR-3l08 
IF (abs(d»Tol1) THEN b:=b+d; 

IF (abs(d)< =Tol1) THEN b:=b+Tol1*Xm/abs(Xm); 

fb:=Colburn Hougen(b); 

IF «fb*(fc7abs(fc»»O.O) THEN 

BEGIN 

END; 

c:=a; 

fc:=fa; 

d:=b-a; 

e:=d; 

{ convergence test } 

Tol1:=2.0*Epsilon*abs(b)+O.S*Tol; 

Xm:=O.S"~(c-b) ; 

END { While }; 

Tint:=b; 

END { CountercurrentZeroin }; 

PROCEDURE CCEquilibrium; 

VAR 

{ finds equilibrium outlet conditions (infinite length) 

for the Countercurrent condenser} 

Op_Flag,Zero_Flag 

T Tol 

T;o,Tso,Ppii,Xiwi,Yiwi,Ppio 

Xiwo,Yiwo,Sphwi,Sphwo,Pcout,Pcoutnew 

Xso,Yso,Desorbi,Mio,Xio,Yio 

Mwi,Mso,Msc,Mionew 

Lable; 

Real; 

Real; 

Real; 

Real; 

Real; 

BEGIN 

{set temperature tolerance and 

operating conditions to Superheat} 

T Tol:=le-3; 

Op Flag:='Super'; 

{ find steam and liquid properties 

at the inlet (assumed to be saturated)} 

Tdew:=SatTemperature(Ybot[9]); 

{check for Superheat or saturated conditions} 

IF «Tdew-Ybot[S]»T_Tol) THEN 

BEGIN 

Writeln (OutFilel,' inlet conditions super saturated', 

'*":~b~* calculations aborted **~b~*'); 

END ELSE 

BEGIN 

END; 

IF (abs«Tdew-Ybot[S]»< T Tol) THEN 

BEGIN 

END; 

Op Flag:='Satur'; 

Tdew:=Ybot[S]; 

Super_In:=O; 

{calculate inlet gas Mixture properties} 

Xmass:=Ybot[6]/(Ybot[6]+Ybot[4]); 

MixTransProp(Ybot[S],Ybot[7],Xmass); 

221 

TR-3108 
{calculate inlet stagnation temperature 

and pressure using compressible gas equations} 

Gamma:=Mixcp/(Mixcp-8.3l43/Mixmwt); 

Vel In:=(Ybot[4]+Ybot[6])/C S Area/Mixrho; 

A:=Sqrt(Gamma*83l4.3/Mixmwt*(Ybot[S]+273.lS»; 

Mach:=Vel In/A; 

Tzbyt:=(1:O+(Gamma-l.O)*Sqr(Mach)/2.0); 

Pzbyp:=Exp«Gamma/(Gamma-l.O»*Ln(Tzbyt»; 

T Stg In:=(Ybot[S]+273.lS)*Tzbyt-273.lS; 

P-Stg-In:=Ybot[7]*Pzbyp; 

{Inlet gas enthalpy} 

Gas In Enth:=(Ybot[6]+Ybot[4])*MixtureEnthalpy(Ybot[S],Xmass); 

{water-inlet enthalpy, total inlet enthalpy, 

and inlet momentum flux} 

Enthw:=LiquidEnthalpy(Ytop[8]); 

Wat In Enth:=Ytop[l]*Enthw+Ytop[3]*AirCp*Ytop[8]; 

K E-In:=(Ybot[6]+Ybot[4])*Sqr(Vel In)/(2*lOOO.O); 

Tot-In Enth:=Wat In Enth+Gas In Enth+K E In; 

Mom=In:=(Ybot[4]+Ybot[6])*VeI_In/C_S_Area; 

TR-3l08 

{By definition for equilibrium water outlet temp=steam inlet temp; 

water outlet inert content corresponds to steam inlet inert content; 

steam outlet inert content corresponds to water inlet inert content; 

pressure loss is zero; water flow is minimum required; 

solve for both water and steam outlet properties and 

minimum water flow;} 

Two:=Tdew; Tso:=Ytop[8]; 

Ppii:=Ybot[7]-Ybot[9]; 

Yiwo:=Ppii/Henry(Two); 

Xiwo:=InertMoletoMassFraction(Yiwo); 

Sphwo:=LiquidEnthalpy(Two)+Xiwo*AirCp*Two; 

Mom_Out:=O.O; 

REPEAT 

Pcout:=Ybot[7] + Mom In - Mom Out; 

Yso:=SatPressure(Tso)/Pcout; 

Yio:=l.O-Yso; 

Xio:=InertMoletoMassFraction(Yio); 

Xso:=l.O-Xio; 

Desorbi:=O.O; 

REPEAT 

Mio:=Ybot[6] + Desorbi; 

Xio:=l.O - Xso; 

Mso:=Mio*Xso/Xio; 

Msc:=Ybot[4] - Mso; 

MixTransProp(Tso,Pcout,Xio); 

Vel Out:=(Mso+Mio)/MixRho/C S Area; 

K E-Out:=(Mso+Mio)*Sqr(Vel Out)/2000.0; 

Mom-Out:=(Mso+Mio)*Vel Out7C S Area; 

Gas-Out Enth:=(Mso+Mio)*MixtureEnthalpy(Tso,Xio); 

{ fInd top dissolved gas in water} 

Ppio:=Pcout*(l.O-Yso); 

Yiwi:=Ppio/Henry(Ytop[8]); 

Xiwi:=InertMoletoMassFraction(Yiwi); 

222 
Sphwi:=LiquidEnthalpy(Ytop[S])+Xiwi*AirCp*Ytop[S]; 

{ find required waterflow and released gas } 

YEqlbm[2]:=(Gas In Enth - Gas Out Enth + 

K E-In- - K E Out-- Msc*Sphwo); 

Mwi:=YEqlbm[2]/(Sphwo --Sphwi); 

Desorbi:=Mwi*(Xiwi-Xiwo); 

TR-310S 

{ find new outlet gas flow and repeat until convergence } 

Mionew:=Ybot[6] + Desorbi; 

UNTIL (Abs«Mionew-Mio)/Mio)< 1.Oe-S); 

{ find new outlet pressure till convergence } 

Pcoutnew:=Ybot[7]+ Mom In -Mom Out; 

UNTIL (Abs«Pcoutnew-Pcout)7pcout)<-l.Oe-S); 

{ Now save equilibrium values for later use } 

{stagnation equilibrium conditions 

from compressible gas equations} 

Gamma:=Mixcp/(Mixcp-S.3143/Mixmwt); 

A:=sqrt(Gamma*S214.3/Mixmwt*(Tso+273.lS»; 

Mach:=Vel Out/A; 

Tzbyt:=(l:0+(Gamma-l.0)*Sqr(Mach)/2.0); 

Pzbyp:=Exp«Gamma/(Gamma-l.O»*Ln(Tzbyt»; 

T_Stg_Eq:=(Tso+273.1S)*Tzbyt-273.1S; 

P Stg Eq:=Pcout*Pzbyp; 

{set array of equilibrium conditions} 

Yeqlbm[l]:=Mwi+Msc; 

Yeqlbm[3]:=Xiwo*(Yeqlbm[l]); 

Yeqlbm[4]:=Mso; 

Yeqlbm[S]:=Tso; 

Yeqlbm[6]:=Mio; 

Yeqlbm[7]:=Pcout; 

Yeqlbm[S]:=Two; 

Yeqlbm[9]:=Pcout*Yso; 

Yeqlbm[lO]:=leS; 

Yeqlbm[ll]:=O.O; 

Vel Eqlbm:=Vel Out;; 

Super_Eqlbm:=O:O; 

X_Eqlbm:=le20; 

END { CCEquilibrium }; 

PROCEDURE FileSetup; 

BEGIN 

{ Interactive reading of input and output file names } 

Form6:=Char(012); 

Form7:=Char(012); 

{ Writeln('Input File Name??? 

- (EG. A:Cctml.Doc ','-- 20 characters max)'); 

ReadLn (Kbd,Filein); 

Writeln('First Output File Name??? - (EG. C:Tape6.0ut)'); 

ReadLn (Kbd,Filotl); 

Writeln('Second Output File Name??? - (EG. C:Tape7.0ut)'); 

ReadLn (Kbd,Filot2);} 

Assign (InFile, 'd:CCinput.par'); 

223 
Assign (OutFilel,'d:CCTape6.out'); 

Assign (OutFile2,'d:CCTape7.out'); 

Assign (OutFile3,'d:CCTape8.out'); 

IF (Filotl='lst') THEN Form6:='l'; 

IF (Filot2='lst') THEN Form7:='l'; 

Reset (InFile); 

Rewrite(OutFilel); 

Rewrite(OutFile2); 

Rewrite(OutFile3); 

{ Read the number of condenser runs to be 

from the first line of the input file } 

Readln (Infile); 

Readln (InFile,Nrun); 

Afraction:=l.O; 

PackingCharacteristics; 

Saperv:=Afraction*Apgeom; 

made 

END { FileSetup }; 

PROCEDURE Countercurrentinput; 

VAR 

{ This procedure contains the input routines 

for the direct contact condenser routine 

Input routine for Countercurrent condenser reads from 

the file CCinput.par. } 

Verbage 

Ipos 

BEGIN 

String[80]; 

Integer; 

{initialize condenser starting length to zero} 

Xin:=O.O; 

{read run label and Correction factors to Correlations 

Verbage is a dummy character variable which reads comment 

lines in the input file} 

Readln (InFile,Run Lable,Serial,T Dew In,Ytop[8], 

Gas Load,Yacob,Xinprc); - -

Ipos:=Pos('-8',Run Lable); 

Delete(Run Lable,l:Ipos-7); 

Ipos:=pos(T-8',Run Lable); 

Delete(Run Lable,Ipos+3,lS); 

Insert{ "":Run Lable, 1); 

Insert( "" ,Run-Lable,ll); 

Geometry:='Pack'; 

Cand Len:=2.000; 

PpmIn:=l4.0; { Note: If PpmIn<PpmInmin for efficient operation 

then PpmIn will be reset to PpmInmin } 

Super In:=O.O; 

{input calculations} 

C S Area:=l.O; 

Ybot[4]:=Gas Load*C S Area; 

Ytop[l]:=Yacob*Ybot[4T*2470.0/(4.l86*(T_Dew_In-Ytop[8]»; 

224 

TR-3l08 
Ytop[3):=Ytop[l)*PpmIn*l.Oe-6; 

Ybot[6):=Ybot[4)*Xinprc/lOO.O; 

Ybot[2):=O.O; 

Ybot[lO):=O.O; 

Ybot[ll):=O.O; 

Ybot[S):=T_Dew_In+Super_In; 

END { Countercurrent input }; 

PROCEDURE CC_Transfer_Coefficients; 

{ This routine calc~lates the gas friction coefficient, 

the liquid heat and mass transfer coefficients, and 

TR-3l08 

the gas heat and mass transfer coefficients given local conditions. 

Both laminar and turbulent flow for the gas is considered. 

VAR 

For the liquid only turbulent flow is incorporated. } 

Diff,K L 

GammaL~Delta,Lload,Reside 

U_G,U_G_Eff 

Real; 

Real; 

Real; 

BEGIN 

{ 

liquid-Side coefficients 

------------------------} { Find liquid properties } 

WaterTransProp(Y Est[8); 

{ Liquid Reynolds number } 

Lload:=Y Est[l)/C S Area; 

GammaL:=Lload/Saper~; 

Rel:=4.0*GammaL/Muliq; 

{ Liquid film thickness } 

Delta:=Exp(O.6*Ln(GammaL/(Rholiq*82.0*Sqrt(Sinalpha»»; 

{ Turbulent flow over an inclined plane, 

Manning Formula, p3l2 of John Haberman} 

U L Eff:=GammaL/(Rholiq*Delta); 

DIff:=(Muliq/Rholiq)/Scliq; 

K L:=2.0*Sqrt(Diff*U L Eff/(Pi*Sprime»; 

{-Liquid-side mass t~ansfer coefficient } 

Lmtc:=Rholiq*K L; 

{ Heat transfe~ coefficient is found using Chilton-Colburn 

Lhtc:=Lmtc*Cpliq*Exp«2.0/3.0)*Ln(Scliq/Prliq»; 

{ 

Gas-Side transfer coefficients 

------------------------------ } 

{ Correlations from Bravo } 

{ Find gas Mixture properties } 

Xmass:=Y Est[6)/(Y Est[4)+Y Est[6); 

MixTransProp(Y Est[5],y Est(7),Xmass); 

{ Compute mass-flux and-dimensionless numbers } 

RhoUb:=(Y Est[4]+Y Est[6)/C S Area; 

U_G:=RhoUb/MixRho;-U_G_Eff:=U_G/Sin(Theta*Pi/l80); 

225 

analogy } 
{ Note Relative velocity is used here, according to Bravo } 

Reg:=MixRho*(U G Eff+abs(U L Eff»*Pckdia/Mixmu; 

{ Countercurrent-flow} --

Nusselt Gas:=O.0338*Exp(O.8*Ln(Reg» 

TR-3l08 

- *Exp(O.333*Ln{Mixpr» { Bravo/Structured Packings}; 

{ Equivalent to Eqs. 2-29 and 2-31 in text} 

Ghtc:=Nusselt Gas*Mixk/Pckdia/lOOO.O; 

Gmtc:=Ghtc*Exp«2.0/3.0)*Ln{Mixpr/Mixsc»/MixCp; 

{ -------------------------

gas friction coefficients 

------------------------- } 

{ Note:-- Gas Reynolds Number Based on Side, per Bravo } 

{ for friction evaluations alone, Correlations of Bravo} 

{ Liquid Froud number corrections as in bravo are not used.} 

Reside:=Reg*Side/Pckdia; { side Reynolds Number} 

Frcgas:=O.171+92.7/{Reside); 

END { CC_Transfer_Coefficients }; 

PROCEDURE CountercurrentDerivatives; 

VM 

BEGIN 

{ This subroutine computes the first derivatives 

of the differential equations given the length 

and the values of the variables. An explanation 

of the variables is given above in the main routine. } 

all,a12,a2l,a22,bl,b2 

Molair,Molest 

Dmlsdx,Dmladx,Dppadx 

Count 

IF ({Setflag=True) OR 

Real; 

Real; 

Real; 

Integer; 

{Y_Est[9]< =(1.O+SatPressure(Y_Est[8]»» THEN 

BEGIN 

FOR Count:=l TO 11 DO Yprime[Count]:=O.O; 

IF (Setflag=False) THEN 

BEGIN 

Xfinal:=x; 

Setflag:=True; 

END; 

END ELSE 

BEGIN 

{ Compute heat and mass transfer coefficients for use 

in differential equations. Call Transfer Coefficients 

to initialize. } 

226 
CC Transfer Coefficients; 

{ Zeroin iteratively solves the Colburn-Hougen equation 

for interface conditions and correct transfer 

coefficients. } 

Tdew:=SatTemperature(Y Est[9]); 

CountercurrentZeroin (Y Est[8],Tdew,'inter',Tsurf); 

{find steam and water p;operties} 

Xmass:=Y Est[6]/(Y Est[6]+Y Est[4]); 

MixTransProp(Y Est[S],Y Est[7],Xmass); 

WaterTransProp(Y Est[8]); 

{ Solve for overall heat and mass transfer 

coefficients using the interface temperature (Tsurf). } 

Ovhtc:=Lhtc*(Tsurf-Y_Est[8])/(Y_Est[S]-Y_Est[8]); 

Ovrntc:=Lmtc; 

{ Compute first derivatives of the variables } 

Yprime[l]:=-SteamFlux*C S Area*Saperv; 

Yprime[2]:=Lhtc*Saperv*C S Area*(Tsurf-Y Est[8]); 

Yprime[3]:=Lmtc*C S Area*Saperv*(Y Est[3T/y Est[l]-

(y Est[7T-y Est[9])/ - -

(Henry(Y Est[ 8]) )>':Molwti/Molwts); 

Yprime[4]:=Yprime[lT; 

Yprime[6]:=Yprime[3]; 

{ Matrix solution is needed for calculating the 

steam temperature and total pressure derivatives } 

RhoUb:=(Y Est[6]+Y Est[4])/C S Area; 

U Bulk:=RhoUb/(Void*MixRho*SIn(Theta*Pi/l80.0»; 

all:=l.O+U Bulk*U Bulk/(lOOO.O*MixCp*(273.lS+Y Est[S]»; 

a22:=1.O-U-Bulk*U-Bulk/(8314.3/Mixmwt*(273.lS+Y Est[5]»; 

al2:=-U Bulk*U Bulk/(MixRho*lOOO.O*MixCp*8314.37 

MIxmwt~'(273 .1S+Y Est [5] »; 

a2l:=MixRho*U Bulk*U B~lk/(273.15+Y Est[5]); 

bl:=-Cht2*exp(-Czero)*Saperv*C S Area/ 

(MixCp)/(Y Est[4]+Y Est[6T)-

-U Bulk*(Yprime[4]/C S Area)/ 

(MIxRho*MixCp*lOOO.O);-

b2:=-U Bulk*Yprime[4]/C S Area-O.5*MixRho* 

Sqr(U Bulk+abs(U L-Eff»* Apgeoiii*Frcgas~~ --

(Afraction*Ackf+(l.O-Afraction»; 

{ Note Apgeom used here instead of Saperv to 

account for friction contribution from 

ineffective mass transfer area as well.} 

Yprime[5]:=(a22*bl-al2*b2)/(all*a22-a12*a2l); 

Yprime[7]:=(all*b2-a2l*bl)/(all*a22-al2*a21); 

{ Molar flow rates needed for steam partial pressure } 

Molair:=Y Est[6]/Molwti; 

Molest:=Y-Est[4]/Molwts; 

Dmladx:=Yprime[6]/Molwti; 

Dmlsdx:=Yprime[4]/Molwts; 

Dppadx:=Molair/(Molair+Molest)*Yprime[7]+ 

Y Est [7 ]*( «Molair+Molest ) >':DmladxMolair*(Dmladx+Dmlsdx»/(Sqr(Molair+Molest»); 

Yprime[9]:=Yprime[7]-Dppadx; 

Yprime[8]:=-Yprime[2]/(Y_Est[l]*Cpliq); 

227 

TR-3l08 
Yprime[10]:=-Yprime[8]/(Y Est[S]-Y Est[8]); 

Yprime[ll]:=O.O; -

END {if}; 

{ save derivatives for printing} 

Prime:=Yprime; 

END { CountercurrentDerivatives }; 

PROCEDURE CountercurrentOutAdd(Nline,Nseg: Integer); 

VAR 

{ Additional Countercurrent detailed output including 

dimensionless numbers and individual coefficients 

as a function of condenser length are generated here 

and printed in file OutFile2. } 

Vout 

BEGIN 

Vector; 

{print label, header, and initial conditions on first call} 

IF (Nline=O) THEN Writeln(OutFile2,Form6,Run Lable); 

IF (Nline=O) THEN -

Writeln(OutFile2,Cdate,' ',Ctime,' Iteration ',Iguess); 

{re-solve for ackerman heat transfer Correlation} 

Ackerh:=Czero/(1.0-exp(-Czero»; 

{load and print output matrix} 

IF (Nline< 100) THEN 

BEGIN 

Vout[l]:=X; 

Vout[2]:=Rel; 

Vout[3]:=Reg; 

Vout[4] :=Prliq; 

Vout[5]:=Mixpr; 

Vout[6] :=Scliq; 

Vout[7]:=Mixsc; 

Vout[8]:=Lhtc; 

Vout[9]:=Ghtc*1000.0; 

Vout[lO]:=Lmtc*lOOO.O; 

Vout[ll]:=Gmtc*lOOO.O; 

Vout[12]:=Ackerh; 

Vout [13] : =Ackf; 

Vout[14]:=SteamFlux*1000.0; 

Vout[15]:=Tdew; 

Vout[16]:=Prime[S]; 

Vout[17]:=Prime[7]; 

Vout[18]:=Nusselt Gas; 

Vout[19]:=Frcgas;-

FOR i:=1 TO 19 DO Write(OutFile2,Vout[i] :10,' '); 

Writeln(OutFile2); 

END; 

IF(Nline=100) THEN 

BEGIN 

Writeln(OutFile2); 

FOR i:=1 TO 18 DO Write(OutFile2,999.9:10,, '); 

Writeln(OutFile2); 

Writeln(OutFile2); 

228 

TR-3108 
S=~I 

END; 

END { CountercurrentOutAdd} 

PROCEDURE CountercurrentOutput(Nline,Nseg: Integer); 

VAR 

{ Output routine for Countercurrent condenser model 

Prints detailed results as a function of condenser 

length and a summary with actual and equilibrium 

outlet conditions on the file OutFilel. } 

Vout 

Tstago,Pstago,Superht 

Ploss,Poten 

Effweq ,Effw 

{print header, label, and inlet 

for the first call} 

Vector; 

Real; 

Real; 

Real; 

conditions 

BEGIN 

IF (Nline=O) THEN 

BEGIN 

Cdate:=""+date+'" '; 

Ctime:=""+time+'" '; 

Writeln(OutFilel,Form6,Run Lable); 

Writeln(outfilel,Cdate,' ':Ctime,' Iteration ',Iguess); 

{ write inlet conditions } 

Vout[l]:=Xin; 

Vout[2]:=Ybot[1]/C S Area; 

Vout[3]:=Ybot[4]/C-S-Area; 

Vout[4]:=Ybot[3]*le67(Ybot[1]+Ybot[3]); 

Vout[S]:=(Ybot[6]*100.0)/(Ybot[6]+Ybot[4]); 

Vout[6]:=Ybot[S]; 

Vout[7]:=Tsurf; 

Vout[8]:=Ybot[8]; 

Vout[9]:=Super In; 

Vout[lO]:=Ybot[7]; 

Vout[11]:=Ybot[9]; 

Vout[12]:=SatPressure(Ybot[S]); 

Vout[13]:=O.0; 

Vout[14]:=Ybot[10]; 

Vout[lS]:=Ybot[2]/C S Area; 

Vout[16]:=(1.O-Ybot[4]/Ybot[4])*lOO.O; 

Vout[17]:=Ve1 In; 

Vout[18]:=O.0; 

Vout[19]:=O.0; 

FOR i:=l TO 19 DO Write(OutFi1e1, Vout[i]:lO,' I); 

Write1n(OutFi1e1); 

CountercurrentOutAdd(N1ine,Nseg); 

END ELSE IF (Nline< 100) THEN 

BEGIN 

{set output conditions} 

Tdew:=SatTemperature(Y[9]); 

{find stagnation temperature and pressure conditions} 

U_Bulk:=(Y[4]+Y[6])/C_S_Area/Mixrho; 

229 

TR-3l08 
END; 

Gamma:=Mixcp/(Mixcp-8.3l43/Mixmwt); 

A:=sqrt(Gamma*83l4.3/Mixmwt*(Y[5]+273.l5»; 

Mach:=U Bulk/A; 

Tzbyt:=(1.0+(Gamma-l.0)*Sqr(Mach)/2.0); 

Pzbyp:=Exp(Gamma/(Gamma-l.O)*Ln(Tzbyt»; 

Tstago:=Y[5]*Tzbyt; 

Pstago:=Y[7]*Pzbyp; 

Superht:=Y[S]-Tdew; 

{define a "pressure loss" Term which includes momentum} 

Ploss:=Ybot[7]-Y[7]+(Mom In-(Y[4]+Y[6])*U Bulk/C S Area); 

{set output array and print intermediate results} -

Vout[l]:=X; 

Vout[2]:=Y[l]/C S Area; 

Vout[3]:=Y[4]/C-S-Area; 

Vout[4]:=Y[3]*le6!(Y[l]+Y[3]); 

Vout[S]:=(Y[6]*100.0)/(Y[6]+Y[4]); 

Vout[6]:=Y[S] ; 

Vout[7]:=Tsurf; 

Vout[8]:=Y[8]; 

Vout[9]:=Superht; 

Vout[lO] :=Y[7]; 

Vout[ll] :=Y[9]; 

Vout[12]:=SatPressure(Y[5]); 

Vout[13] :=Ploss; 

Vout[14]:=Y[lO]; 

Vout[lS]:=Y[2]/C S Area; 

Vout[16]:=(1.0-Y[4]/Ybot[4])*100.0; 

Vout[17]:=U Bulk; 

Vout[18]:=O~htc; 

Vout [ 19] : =Ovrntc": 1000.0; 

Pdrop:=Ybot[7]-Y[7]; 

FOR i:=l TO 19 DO Write(OutFilel,Vout[i]:ll,' '); 

Writeln(OutFilel); 

CountercurrentOutAdd(Nline,Nseg); 

IF(Nline=lOO) THEN 

BEGIN 

{**** Last two lines of output ****} 

Writeln(OutFilel); 

{ Equilibrium Conditions } 

Vout[l]:=999.9; 

Vout[2]:=Yeqlbm[l]/C S Area; 

Vout[3]:=Yeqlbm[4]/C-S-Area; 

Vout[4]:=Yeqlbm[3]*le6!Yeqlbm[l]; {approx} 

Vout[S]:=(Yeqlbm[6]*100.0)/(Yeqlbm[6]+Yeqlbm[4]); 

Vout[6]:=Yeqlbm[S]; 

Vout[7] :=0.0; 

Vout[8]:=Yeqlbm[8]; 

Vout[9):=0.O; 

Vout[10]:=Yeqlbm[7]; 

Vout[11]:=Yeqlbm(9); 

Vout[12]:=SatPressure(Yeqlbm[S]); 

Vout[13] :=0.0; 

230 

TR-3l08 
END; 

Vout[14]:=Yeqlbm[10]; 

Vout[15]:=Yeqlbm[2]/C S Area; 

Vout[16]:=(1.0-Yeqlbm[4]/Ybot[4])*100.0; 

Vout[17]:=Vel Eqlbm; 

Vout[18]:=999:9; 

Vout[19]:=999.9; 

FOR i:=l TO 19 DO Write(OutFile1,Vout[i]:11,' 

Writeln(OutFile1); 

CountercurrentOutAdd(Nline,Nseg); 

END {CountercurrentOutput }; 

PROCEDURE Runga(h,xO: Real;YO:State); 

{ Integration Routine } 

VAR 

BEGIN 

k1,k2,k3,k4 State; 

X Est:=xO; 

Y-Est:=YO; 

CountercurrentDerivatives; 

, ) ; 

IF «xO=O.O) AND Convergence) THEN CountercurrentOutput(O,40); 

FOR i:=l TO Neqn DO 

BEGIN 

END; 

k1[i]:=h*Yprime[i]; 

Y_Est[i]:=YO[i]+k1[i]/2; 

X Est:=X Est+h/2; 

Counterc~rrentDerivatives; 

FOR i:=l TO Neqn DO 

BEGIN 

END; 

k2[i]:=h*Yprime[i]; 

Y_Est[i]:=YO[i]+k2[i]/2; 

CountercurrentDerivatives; 

FOR i:=l TO Neqn DO 

BEGIN 

END; 

k3[i]:=h*Yprime[i]; 

Y_Est[i]:=YO[i]+k3[i]; 

X Est:=X Est+h/2; 

Counterc~rrentDerivatives; 

FOR i:=l TO Neqn DO 

BEGIN 

k4[i]:=h*Yprime[i]; 

Y[i]:=YO[i]+(k1[i]+2*k2[i]+2*k3[i]+k4[i])/6; 

END; 

X:=XO+h; 

END { Runga }; 

PROCEDURE March; 

VAR 

231 

TR-3108 
Increment 

Stepflag 

BEGIN 

Y:=Ybot; 

X:=Xin; 

: Real; 

: Boolean; 

{set initial heat, mass and friction coefficients to zero} 

Lhtc:=O.O; Lmtc:=O.O; Ghtc:=O.O; Gmtc:=O.O; 

Frcgas:=O.O; Frcliq:=O.O; 

Istep:=O; Xend:=Xin; Xfinal:=Cond_Len; Setflag:=False; 

Step:=Cond_len/Nseg; 

Stepflag:=False; 

Window(l,l7,80,2S); 

GotoXY(l, 1) ; 

REPEAT 

Increment:=Step; 

Xend:=Xend+Increment; 

IF «Xend>Cond Len) OR «Cond Len-Xend)< 2.0*Step) 

OR (Setflag~True» THEN 

BEGIN 

Xend:=Cond_Len; 

Increment:=Cond_Len-X; 

END; 

Runga(Increment,X,Y); 

Wateff:=(Y[8]-Ytop[8])/(Ybot[S]-Ytop[8]); 

Cond prc:=(Ybot[4]-Y[4])*100.0/Ybot[4]; 

Pdrop:=Ybot[7]-Y[7]; 

Writeln(Iguess:2,Xend:6:3,Y[8]:6:2,Tsurf:6:2, 

Tdew:6:2,Wateff:8:4, 

Cond prc:6:2,Pdrop:6:2, I " 

Reg: 7' : 1 , I I, Y [ 4 ] : 6 : 3 , I I, 

Y[6] :8:6, t I ,Y[3] :8:6); 

Tdew:=SatTemperature(Y[9]); 

{ succesful integration, increment length 

and print intermediate results} 

Istep:=Istep+l; 

IF (Convergence AND Iprint) THEN 

CountercurrentOutput(Istep,Nseg); 

IF (convergence AND (x=Cond_Len» THEN 

BEGIN 

Writeln(lst,Run Lable:20,Serial:S,Iguess:3, 

Ybot[5]:Io:2,Xfinal:l0:2,Y[8]:lO:2, 

Ybot[8]:lO:2,Cond prc:lO:2,Pdrop:lO:2, 

Tdew:lO:2,Gas Load:6:2,Saperv:lO:4); 

Writeln(OutFile3,Run-Lable:20,Serial:5,Iguess:3, 

Ybot[5]:11:4,Xfinal:ll:4,Y[8]:ll:4, 

Ybot[8]:11:4,Cond prc:ll:4,Pdrop:ll:4, 

Tdew:ll:4,Gas Load:6:2,Saperv:lO:4); 

IF (Convergence AND Iprint) THEN 

CountercurrentOutput(lOO,lOO); 

232 

TR-3l08 
END; 

{final length reached, go on to next set of conditions} 

IF «Stepflag=False) AND (Cond_prc>97.0» THEN 

BEGIN 

Step:=Step!4.0; 

Stepflag: =True; 

END; 

UNTIL (Xend>=Cond_Len); 

Window(1,1,80,20); 

GotoXY(1,Iguess+2); 

Writeln(Con,Run Lable:lS,Iguess:4,Y[1]:8:2, 

Ybot[1]:8:2,Y[8]:8:2,Ybot[8]:8:2, 

Y[3]:12:8,Ybot[3]:12:8,' ',Convergence:l); 

END { March }; 

PROCEDURE Iterate(VAR a,b,c,fa,fb,fc,new : Real; Tol: Real; 

VAR Converged: Boolean); 

VAR 

{ note: tolerance set on fb for temperature only } 

d,e 

p,q,r,s 

Xm,ToI2 

Real; 

Real; 

Real; 

BEGIN 

Converged:=False; 

d:=b-a; 

e:=d; 

{ convergence test } 

To12:=2.0*Epsilon*abs(b); 

Xm:=O.S*(c-b); 

IF (abs(fb)< Tol) THEN Converged:=True; 

IF «abs(Xm»ToI2) AND 

BEGIN 

(fb< >0.0) AND 

(fb>':(fc!abs(fc»< 0.0» THEN 

IF (abs(fc)< abs(fb» THEN 

BEGIN 

END; 

a:=b; 

h:=c; 

c:=a; 

fa:=fb; 

fb:=fc; 

fc:=fa; 

Xm:=O.S*(c-b); 

ToI2:=2.0*Epsilon*abs(b); 

IF (abs(e)< To12) AND (abs(fa)< =abs(fb» THEN 

BEGIN { bisect } 

d:=Xm; 

e:=d; 

233 

TR-3l08 
END ELSE 

BEGIN 

END; 

{ is quadratic interpolation possible } 

IF (a=c) THEN 

BEGIN 

{ linear interpolation } 

s:=fb/fa; 

p: =2. O'''"Xm*s; 

q:=l.O-s; 

END ELSE 

BEGIN 

END; 

{ inverse quadratic interpolation } 

q:=fa/fc; 

r:=fb/fc; 

s:=fb/fa; 

p: =s*( 2. O*Xm'~q*( q-r )-( b-a )"'~( r-l. 0» ; 

q:=(q-l.O)*(r-l.O)*(s-l.O); 

{ adjust signs } 

IF (p>O.O) THEN q:=-q; 

p:=abs(p); 

{ is interpolation acceptable } 

IF «2.0*p)< (3.0*Xm*q-abs(To12*q») AND 

(p< abs(O.S*e*q» THEN 

BEGIN 

e:=d; 

d:=p/q; 

END ELSE 

BEGIN 

END; 

{ bisection } 

d:=Xm; 

e:=d; 

{ Complete Step } 

IF (abs(d»To12) 

IF (abs(d)< =To12) 

a:=b; 

THEN new:=b+d; 

THEN new:=b+To12*(Xm/abs(Xm»; 

fa:=fb; 

IF (abs(fb)< =Tol) 

END { IF }; 

THEN Converged:=True; 

END { Iterate }; 

PROCEDURE CountercurrentMain; 

{repeat the procedure from here on for every run} 

VAR 

Ix,J 

Stmlfr 

Ppiomax,Ytop3min 

Xa,Xb,Xc,Fxa,Fxb,Fxc,Xnew 

Ind 

Tolerance 

Stop 

Integer; 

Real; 

Real; 

ARRAY [1 •• 3] of Real; 

ARRAY [1 •• 3] of Integer; 

ARRAY [1 •• 3] of Real; 

Boolean; 

234 

TR-3108 
LABEL 

BEGIN 

FOR Ix:=l TO Nrun DO 

BEGIN 

FOR i:=l TO 11 DO 

BEGIN 

Y[i]:=O; 

Ybot[i]:=O; 

END; 

X:=O; 

Xin:=O; 

Quit; 

{read the condenser initial values of most of the 

variables in the modeling differential equations 

by calling subroutine cinput. The variables are 

as follows: 

Y[l]:=water flow rate (kg/s) 

Y[2]:=condenser heat load (kW) 

Y[3]:=dissolved gas flow rate (kg/s) 

Y[4]:=steam flow rate (kg/s) 

Y[5]:=steam temperature (C) 

Y[6]:=inert gas mass flow rate (kg/s) 

Y[7]:=condenser pressure (Pa) ** calculated ** 

Y[8]:=water temperature (C) 

Y[9]:=partial pressure of the steam (Pa) ** calculated ** 

Y[lO]:=ntu 

Y[ll]:=fog flow rate (kg/s) ** not used **} 

Countercurrentinput; 

{ Solve for remaining initial values of 

integration variables} 

Stmlfr:=(Ybot[4]/Molwts/(Ybot[4]/Molwts+Ybot[6]/Molwti)); 

Ybot[9]:=SatPressure(Ybot[5]-Super In); 

Ybot[7]:=Ybot[9]/Stmlfr; -

Tdew:=Ybot[5]-Super_In; 

{ determine a minimum deaeration level practical for 

incoming water; below this we could be wasting energy } 

Ppiomax:=Ybot[7]-SatPressure(Ytop[8]); 

Ytop3min:=Ytop[1]*InertMoletoMassFraction 

(Ppiomax/Henry(Ytop[8])); 

IF (Ytop[3]< Ytop3min) THEN Ytop[3]:=Ytop3min; 

CCEquilibrium; 

{set the input parameters for the 

integration routine} 

Step:=Cond_Len/Nseg; 

Iguess:=l; 

Convergence:=False; 

Stop:=False; 

Clrscr; 

235 

TR-3108 
Window(1,1,80,20); 

Writeln(con,' Run Id " 'Iter',' WF-Top ',' WF-Bot ' 

, Tw-Top ',' Tw-Bot " 

, Iw-Top ',' Iw-Bot '); 

Writeln(con,Run Lable:15,' -- ':4,Ytop[1]:8:2,'--des.--':8, 

Ytop[8]:8:2,'--des.--':8,Ytop[3]:12:8, 

, desired. ':12); 

TR-3l08 

{ outlet condition guessing game for Countercurrent operation } 

{ first try } 

Ind[l]:=l; Tolerance[l]:=O.O; 

Ind[2]:=3; Tolerance[2]:=O.O; 

Ind[3]:=8; Tolerance[3]:=O.03; { on top water temperature} 

{ convergence is determined when calculated water 

temperature on top matches the specified water 

inlet temperature within the specified tolerance 

limit. Only water temperature is used for testing 

convergence. Other tolerances for top water flow 

rate, Tolerance[l], and top water dissolved alr 

content, Tolerance[2] are set to zero.} 

Xa[l]:=Ytop[l]+l.OO*Ybot[4]; 

{ first guess of bottom water flow rate } 

Xa(2]:=Ytop(3]; 

{ first guess of bottom air flow rate dissolved in water } 

Xa(3]:=Ytop[8]+Ybot[4]*l.OO*2470.0/(4.l86*Ytop[l]); 

{ first guess of bottom water temperature } 

IF (Xa[3]>=Tdew) THEN Xa[3]:=Tdew-O.l; 

FOR J:=l TO 3 DO Ybot[Ind[J]]:=Xa[J]; 

March; 

FOR J:=l TO 3 DO Fxa[J]:=Y[Ind[J]]-Ytop[Ind[J]]; 

{ second try } 

Iguess:=2; 

Xb(l]:=Ytop[l]; 

{ second guess of bottom water flow rate } 

Xb(2]:=Ytop[3]-S.O*(Y[3]-Ybot[3]); 

{ second guess of bottom air flow rate dissolved in water} 

Xb[3]:=Ytop[8]+Ybot[4]*O.600*2470.0/(4.l86*Xb[l]); 

{ second guess of bottom water temperature } 

{ the second guesses may be altered to narrow limits 

on bottom water flow rate, dissolved air content, and 

water temperatures suitably and aid in faster 

convergence on iterations.} 

FOR J:=l TO 3 DO Ybot[Ind[J]]:=Xb[J]; 

March; 

FOR J:=l TO 3 DO Fxb[J]:=Y[Ind[J]]-Ytop[Ind[J]]; 

{ Begin iterations to achieve convergence } 

Xc:=Xa; Fxc:=Fxa; Xnew:=Xa; 

WHILE «NOT Convergence) AND (Iguess< 24» DO 

BEGIN 

Iguess:=Iguess+l; 

FOR J:=l TO 3 DO 

BEGIN 

Iterate(Xa[J],Xb[J],Xc[J],Fxa[J],Fxb[J],Fxc[J], 

Xnew[J],Tolerance[J],Convergence); 

END {for}; 

236 
Quit: 

Xb:=Xnew; 

FOR J:=l TO 3 DO Ybot[Ind[J]]:=Xb[J]; 

Writeln('Ybot 1,3,8 ',Ybot[1]:6:2, 

Ybot[3]:12:8,Ybot[B]:10:4); 

Writeln(' Convergence' ,convergence); 

March; 

FOR J:=l TO 3 DO 

BEGIN 

Fxb[J]:=Y[Ind[J]]-Ytop[Ind[J]]; 

IF (Fxb[J]*(Fxc[J]/abs(Fxc[J]» > 0.0) THEN 

BEGIN 

Xc [ J] : =Xa [J1 ; 

Fxc[J]:=Fxa[J]; 

END { if }; 

END {for} 

END { While }; 

IF (NOT Convergence) THEN Writeln(OutFile3,Run Lable:25, 

'" No Convergence, go to next run" '); 

IF (NOT Convergence) THEN Writeln(lst,Run Lable:25, 

'" No Convergence, gO' to next run" '); 

END { Run-for-do loop }; 

END { Procedure CountercurrentMain }; 

{ Beginning of Main Program } 

BEGIN 

FileSetUp; 

Machineaccuracy; 

Iprint:=True; 

CountercurrentMain; 

Close(OutFilel) ; 

Close(OutFile2); 

Close(OutFile3); 

Close(Lst); 

END { CCcond }. 

237 

TR-310B 
Variable 

a 

Abs 

. Ackerh 

Ackf 

Afraction 

AirCp 

AirK 

Table F-l. 

AirMu 

Airtransprop 

Ak 

Apgeom 

Ax 

b 

Base 

Bx 

c 

Cccond 

Ccequilibrium 

Ccinput 

Cdate 

Cfric 

Char 

Cht 

Clrscr 

Cocond 

Coinput 

Colburn-Hougen 

Con 

Cond-Len 

Cond-Prc 

Const 

Contactloss 

Cos 

CountercurrentOutAdd 

CountercurrentOutput 

CpLiq 

Ctime 

Cx 

Czero 

C-S-Area 

d 

Datestr 

Datetime 

DelRho 

Cross Reference of Computer Program Variables 

Description 

lower limit of x in ZEROIN 

absolute value 

Ackermann correction factor for heat transfer 

Ackermann correction factor for friction 

fractional area effective in mass transfer 

specific heat of air 

thermal conductivity of air 

dynamic viscosity of air 

procedure for air transport property 

calculations 

variable in SatTemperature Procedure 

geometric transfer area per volume of the 

packing 

register addressed in DATETIME functions 

upper limit of x in ZEROIN 

base dimension of the packing 

register addressed in DATETIME functions 

intermediate value of x in ZEROIN 

program countercurrent condenser 

countercurrent equilibrium calculations 

procedure 

countercurrent input procedure 

date in string format 

term for Ackermann friction correction 

character variable 

terms in the Colburn-Hougen equation 

screen clear procedure 

program cocurrent condenser 

co current condenser input procedure 

value of the Colburn-Hougen equation 

console screen monitor 

length of the condenser 

percentage of condensed steam 

numerical constants 

percent of lost area due to sheet contact 

cosine of the angle 

output procedure for the countercurrent 

condenser 

output procedure for the countercurrent 

condenser 

specific heat of the liquid 

time in string format 

register addressed in DATETIME functions 

non-dimensional steam flux 

condenser cross sectional area 

domain of x in ZEROIN 

date in string format 

current date and time evaluation procedure 

water density correction term 

238 

TR-3108 

Units 

kJ/kg K 

W/m K 

kg/m s 

11m 

m 

m 

% 

% 

kJ/kg K 
TR-3108 

Table F-l. Cross Reference of Computer Program Variables (Continued) 

Variable 

Delta 

Derivatives 

Di 

Diffaw 

Dmladx 

Dmlsdx 

Dppadx 

Ds 

Dx 

e 

Effw 

Effweq 

En 

Enthliq 

Enths 

Enthw 

Epsilon 

Equil-Pressure-Balance 

Es 

Exp 

Fa 

Fb 

Fc 

Filesetup 

Frcgas 

Frcliq 

Fxa 

Fxb 

Fxc 

G 

Gamma 

Gammal 

Gas-In-Enth 

Gas-Load 

Gas-Out-Enth 

Ghtc 

Gmolfr 

Gmtc 

Gotoxy 

h 

Height 

Henry 

Hilimit 

I 

Iguess 

Imf 

Increment 

Description 

liquid film thickness 

derivative evaluation procedure 

register addressed in DATETIME functions 

diffusivity of air in water 

derivative of air molar flow 

derivative of steam molar flow 

derivative of the partial pressure of air 

register addressed in DATETIME functions 

register addressed in DATETIME functions 

domain of x in ZEROIN 

water effectiveness 

water effectiveness at equilibrium 

water viscosity evaluation constants 

enthalpy of the liquid 

enthalpy of the steam 

enthalpy of water 

lowest discernable real number 

function for co current equilibrium 

calculations 

register addressed in DATETIME functions 

exponential function 

value of f(x) at x=a 1n ZEROIN 

value of f(x) at x=b 1n ZEROIN 

value of f(x) at x=c 1n ZEROIN 

set up procedure for input and output files 

gas friction factor 

liquid friction factor 

value of f(x) at x=a in ITERATE 

value of f(x) at x=b in ITERATE 

value of f(x) at x=c in ITERATE 

gravitational acceleration 

ratio of specific heats for steam-air mixture 

liquid-film flow per unit length 

enthalpy of the incoming steam-air mixture 

steam-air mixture loading 

enthalpy of the outgoing steam-air mixture 

gas-side heat transfer coefficient 

inert gas 

gas-side mass transfer coefficient 

a TURBO-pascal procedure 

increment in x in integration procedure 

condenser packing height 

procedure for estimating dissolved air in 

water 

upper limit of steam to total water flow 

integer counter 

integer counter for the number of guesses 

inert gas mole fraction 

step size for integration 

239 

Units 

m 

m2/s 

mole/s m 

mole/s m 

Pals 

kJ/kg 

kJ/kg 

kJ/kg 

Pa 

kg/m s 

kW 

kg/s m2 

kW 

kW/m2 K 

kg/m2 s 

m 

m 

m 
TR-3108 

Table F-l. Cross Reference of Computer Program Variables (Continued) 

Variable 

InertMasstoMoleFract 

InertMoletoMassFract 

Inert-Out-Eqlbm 

Infile 

Insert 

Ipos 

Iprint 

Istep 

Iter 

Ix 

J 

K 

Kbd 

Kliq 

K-E-In 

K-E-Out 

K-E-Term 

K-E-Term-New 

K-l 

Lable 

Lhtc 

LiquidEnthalpy 

Lload 

Lmtc 

Ln 

Lolimit 

Lst 

Mach 

MachineAccuracy 

Mio 

Mionew 

MixCp 

MixEnth 

MixK 

MixMu 

MixMwt 

MixPr 

MixRho 

MixSc 

MixTransProp 

MixtureEnthalpy 

Mlfrar 

Description 

function to convert inert mass to mole 

fraction 

function to convert inert mole to mass 

fraction 

inert gas flow at equilibrium 

input file 

TURBO-pascal procedure 

integer variable 

boolean variable to set file outputs 

integration step counter 

iteration counter 

run number counter 

counter 

counter 

key board designation 

thermal conductivity of liquid 

kinetic energy of the incoming steam-gas 

mixture 

kinetic energy of the outgoing steam-gas 

mixture 

kinetic energy term 

kinetic energy term 

liquid-side mass transfer coefficient 

run identification label 

liquid-side heat transfer coefficient 

enthalpy of the liquid 

liquid loading 

liquid-side mass transfer coefficient 

natural logarithmic function 

lower limit of steam to total water flow 

line printer designation 

Mach number 

function to calculate the machine accuracy 

mass flow rate of outgoing inert gas 

revised mass flow rate of outgoing inert gas 

specific heat of the steam-air mixture 

enthalpy of the steam-air mixture 

thermal conductivity of the steam-air mixture 

dynamic viscosity of the steam-air mixture 

molecular weight of the steam-air mixture 

Prandtl number of the steam-air mixture 

density of the steam-air mixture 

Schmidt number of the steam-air mixture 

function to calculate transport 

properties of the steam-gas mixture 

enthalpy of the steam-air mixture 

mole fraction of air 

240 

Units 

kg/s 

W/m K 

kW 

kW 

kW 

kW 

m/s 

kW/m2 K 

kJ~kg 

kg/m s 

kg/m2 s 

kg/s 

kg/s 

kJ/kg K 

kJ/kg 

W/m K 

kg/m s 

kJ/kg 
TR-3108 

Table F-l. Cross Reference of Computer Program Variables (Continued) 

Variable 

Mlfrst 

Molair 

Molest 

Molwti 

Molwts 

Mom-In 

Mom-Out 

Msc 

Mso 

MuLiq 

Mwi 

Neqn 

Nline 

Nrun 

Nseg 

Ntu 

Nusselt-Gas 

Onecompflow 

Onefrac 

Op-Flag 

Outfile 

Ovhtc 

Ovrntc 

p 

PackingCharacteristics 

Pckdia 

Pcout 

Pcoutnew 

Pdrop 

Phi 

Pi 

Ploss 

Poten 

Pout 

Pp 

Ppii 

Ppio 

Ppiomax 

Ppmin 

Ppminmin 

Ppsteam 

Pp-Inert 

Prime 

Prliq 

Pstago 

Description 

mole fraction of steam 

molar air flow rate 

molar steam flow rate 

molecular weight of the inert gas 

molecular weight of steam 

momentum of the incoming steam-gas mixture 

momentum of the outgoing steam-gas mixture 

mass flow of steam condensed 

mass flow of steam out 

dynamic viscosity of the liquid 

mass flow rate of incoming water 

number of equations to be integrated 

counter for line printer 

number of runs to be processed 

number of segments the condenser 1S divided 

into 

number of transfer units 

gas-side Nusselt number 

total component one (water+steam) flow rate 

fraction of steam outlet flow to total water 

flow 

indicator for inlet superheat or saturation 

output file designation 

overall heat transfer coefficient 

overall mass transfer coefficient 

variable in ZEROIN 

function to calculate packing 

geometric charateristics 

equivalent packing diameter 

condenser outlet pressure 

revised condenser outlet pressure 

condenser static pressure loss 

terms for gas mixture property evaluations 

mathematical constant 3.141527 ••• 

condenser total pressure loss 

temperature driving potential 

condenser outlet pressure 

partial pressure 

Units 

mole/s 

mole/s 

Pa 

Pa 

kg/s 

kg/s 

kg/m s 

kg/s 

m 

Pa 

Pa 

Pa 

Pa 

C 

Pa 

Pa 

Pa 

Pa 

partial pressure of incoming inert gas 

partial pressure of outgoing inert gas 

maximum partial pressure of outgoing inert 

level of dissolved gas in incoming water 

minimum level of dissolved gas in incoming 

gas Pa 

water 

partial pressure of steam 

partial pressure of inert gas 

derivative of the state variable 

Prandtl number of the liquid 

stagnation pressure at outlet 

241 

Pa 

Pa 

Pa 

Pa 

(varied) 

Pa 
Table F-l. 

Variable 

Pstgeq 

Pstgin 

Pt 

Ptotal 

Pzbyp 

P-Stg-Eq 

P-Stg-In 

q 

r 

Reg 

ReI 

Reside 

Rholiq 

Rhoub 

Run-Lable 

s 

Saperv 

Satpr 

SatPressure 

Satt 

SatTemperature 

Satur 

Seliq 

Setflag 

Sheet 

Side 

Sigma 

Sin 

Sinalpha 

Sol 

Sphwi 

Sphwo 

Sprime 

Sqr 

Sqrt 

State 

Steamflux 

SteamTransProp 

Step 

Stepflag 

StmCp 

StmDiff 

StmK 

Stmlfr 

StmMu 

TR-3l08 

Cross Reference of Computer Program Variables (Continued) 

Description 

stagnation pressure at outlet at equilibrium 

stagnation pressure at inlet 

static (total = sum of partials) pressure 

static (total = sum of partials) pressure 

stagnation to static pressure ratio 

stagnation pressure at outlet at equilibrium 

stagnation pressure at inlet 

variable in ZEROIN 

variable in ZEROIN 

gas Reynolds number 

liquid Reynolds number 

gas Reynolds number, based on side 

liquid density 

gas mass flux 

run identification label 

variable in ZEROIN 

effective surface area per volume of the 

packing 

steam saturation pressure 

steam saturation pressure function 

steam saturation temperature 

steam saturation temperature function 

saturated inlet indicator 

liquid Schmidt number 

flag for discontinuing calculations 

packing sheet thickness 

packing side dimension 

water surface tension 

sine function 

sine of liquid film plane angle w.r.to 

horizontal 

air solubility in water 

enthalpy of inlet water and dissolved a1r 

mixture 

enthalpy of outlet water and dissolved air 

mixture 

liquid renewal distance 

square function 

square-root function 

variable type 

interfacial steam flux 

procedure for steam transport properties 

integration step size 

flag for decreased step Slze 

specific heat of steam 

diffusivity of steam 1n steam-gas mixture 

thermal conductivity of steam 

steam mole fraction 

dynamic viscosity of steam 

242 

Units 

Pa 

Pa 

Pa 

Pa 

Pa 

Pa 

11m 

Pa 

Pa 

C 

C 

m 

m 

N/m 

Pa 

kJ 

kJ 

m 

m 

kJ~kg K 

m Is 

W/m K 

kglm s 
Table F-l. 

Variable 

StmRho 

Stm-Out-Eqlbm 

Super 

SuperHeat 

Superht 

Super-Eqlbm 

Super-In 

SuprEq 

Tabs 

Tair 

Tdb 

Tdew 

Temp 

Term 

Tgasdb 

Theta 

Time 

Timestr 

Tint 

Tinterface 

Tliq 

Tmixdb 

Tol 

Tolerance 

Tolzer 

Tot-In-Enth 

Tsat 

Tso 

Tstago 

Tstgeq 

Tstgin 

Tstm 

Tsurf 

Tw 

Twater 

Two 

Twocompflow 

Twofrac 

Twofracnew 

Tzbyt 

T-Dew-In 

TsTago 

T-Stg-Eq 

T-Stg-In 

T-Tol 

TR-3108 

Cross Reference of Computer Program Variables {Continued} 

Description 

steam density 

steam exhaust flow at equilibrium 

superheated inlet indicator 

steam superheat 

steam superheat 

steam superheat at equilibrium {=O} 

steam superheat at inlet 

steam superheat at equilibrium {=O} 

absolute temperature 

air temperature 

dry-bulb temperature 

dew point temperature 

temperature 

terms in equilibrium calculations 

gas dry-bulb temperature 

packing flow channel inclination from 

horizontal 

time in string format 

time in string format 

interface temperature 

interface temperature 

liquid temperature 

gas dry-bulb temperature 

convergence tolerance 

convergence tolerance criteria 

convergence tolerance in ZEROIN 

total inlet enthalpy 

saturation temperature 

steam outlet temperature 

gas outlet stagnation temperature 

gas outlet stagnation temperature at 

equilibrium 

gas inlet stagnation temperature 

steam temperature 

interface temperature 

water temperature 

water temperature 

water outlet temperature 

total component two {air 1n water&steam} flow 

rate 

ratio of outlet inerts to total inert flow 

revised ratio of outlet inerts to total inert 

flow 

stagnation to static temperature ratio 

inlet dew point temperature 

gas outlet stagnation temperature 

stagnation temperature at equilibrium 

inlet stagnation temperature 

tolerance on temperature 

243 

Units 

kg/m3 

kg/s 

°c 

°c 

°c 

°c 

°c 

K 

°c 

°c 

°c 

°c 

kW 

°c 

(deg) 

kg/s 
Table F-l. 

Variable 

U-bulk 

U-g 

U-g-eff 

U-L-eff 

Veleq 

Velin 

Vel-Eqlbm 

Vel-In 

Vel-Out 

Verbage 

Void 

Vols 

Volw 

Vout 

Wateff 

Waterflow 

Watertemp 

Watertransprop 

Wat-In-Enth 

X 

Xa 

Xb 

Xbulk 

Xc 

Xend 

Xeq 

Xfinal 

Xin 

Xinprc 

Xio 

Xiw 

Xiwi 

Xiwo 

Xm 

Xmass 

Xnew 

Xso 

X-Eqlbm 

X-Est 

X-Out-Eqlbm 

Y 

Yacob 

Ybot 

TR-3l08 

Cross Reference of Computer Program Variables (Continued) 

Description 

effective.velocity in condenser 

column 

bulk gas superficial velocity in condenser 

column 

effective gas velocity in packing channel 

effective liquid film velocity 

gas outlet superficial velocity at 

equilibrium 

gas inlet superficial velocity 

gas outlet superficial velocity at 

equilibrium 

gas inlet superficial velocity 

gas outlet superficial velocity 

string variable to read in comments 

packing void fraction 

steam specific volume 

water specific volume 

output variable array 

water effectiveness 

water flow rate 

water temperature 

procedure for water transport properties 

enthalpy of incoming water 

distance along main steam flow direction 

countercurrent convergence variables 

countercurrent convergence variables 

bulk steam mass fraction 

countercurrent convergence variables 

end distance at each integration step 

condenser length for eqilibrium 

distance at which calculations are 

terminated 

inlet inert gas mass fraction 

inlet inert gas mass fraction percent 

outlet inert gas mass fraction 

dissolved inert gas mass fraction 

dissolved inert gas mass fraction at inlet 

dissolved inert gas mass fraction at outlet 

inert gas mass fraction 

inert gas mass fraction 

Units 

mls 

mls 

mls 

mls 

mls 

mls 

mls 

mls 

mls 

m3/kg 

m3/kg 

(varied) 

kW 

m 

(varied) 

(varied) 

(varied) 

m 

m 

% 

revised countercurrent convergence variables (varied) 

steam outlet mass fraction 

inert gas mass fraction at equilibrium 

revised condenser length m 

outlet inert gas mass fra~tion at equilibrium 

conditions at any point in the condenser (varied) 

condenser Jakob number 

conditions at countercurrent condenser 

bottom (varied) 

244 
Table F-l. 

Variable 

Ybulk 

Yeqlbm 

Yin 

Yio 

Yiw 

Yiwi 

Yiwo 

Yml 

Ymole 

Yprime 

Yso 

Ysoeq 

Ytop 

Y-Est 

Zero in 

Zero-Flag 

TR-3108 

Cross Reference of Computer Program Variables (Concluded) 

Description 

bulk steam mole fraction 

conditions at equilibrium at the condenser 

outlet 

conditions at the condenser inlet 

outlet inert gas mole fraction 

dissolved inert gas mole fraction 

dissolved inert gas mole fraction at inlet 

dissolved inert gas mole fraction at outlet 

inert gas mole fraction 

inert gas mole fraction 

derivative of the state vector Y 

steam outlet mole fraction 

steam outlet mole fraction at equilibrium 

conditions at the top of countercurrent 

condenser 

estimated conditions at any point in the 

condenser 

procedure for finding zero of a function 

(labelled as CocurrentZeroin and 

CountercurrentZeroin ) 

flag to select zeroin options 

245 

Units 

(varied) 

(varied) 

(varied) 

(varied) 

(varied) 
TR-3108 

APPENDIX G EQUILIBRIUM CALCULATIONS 

G.l Cocurrent Condenser 

To evaluate a maximum possible performance of a co current condenser, we performed equilibrium calculations that assume 

• Steam and water exiting from the condenser are 1n equilibrium 

• Dissolved inert gas level in the exiting coolant is in equilibrium at the 

partial pressure of the inert gases in the exiting steam-gas mixture 

• Vapor pressure loss through the condenser is nonexistent; vapor kinetic 

energy is fully recovered. 

With these assumptions, the calculation procedure is as follows. 

The total flow rate of the water and steam, component 1, is denoted by 

(G-l) 

and that of inert gas, component 2, is denoted by 

(G-2) 

The total energy of the incoming vapor and inert gas mixture 1S 

(G-3) 

where Kin is the contribution caused by the kinetic energy of the mixture as 

(G-4) 

The incoming vapor momentum is calculated as 

Assuming that the water and steam exist at the equilibrium temperature Te ' 

three unknowns, namely Te ' the equilibrium temperature, mso ' the outlet ste~m flow rate, and mi so' theqinert gas flow in the exiting vapor mixture, need to 

be defined to fuliy quantify the exit conditions. 

These unknowns can be evaluated (in an iterative fashion) using the following 

equations. 

Energy balance: 

Energy 1n = Energy out (G-6) 

246 
=~ 

I 

Momentum balance: 

Pin + Min = Pout + Mout ' 

and Dalton's law of partial pressure of component yields 

We denote the outlet steam flow rate as 

and 

where 

= 

PPso 

Pout 

o < f1 < 1 and 0 < f2 < 1 • 

TR-3108 

(G-7) 

(G-8) 

(G-9) 

(G-10) 

Under equilibrium, we note that for condensation and desorption, f1 and 

f2 approach zero. 

The outgoing energy of the water-stearn-gas mixture ~s expressed as 

Eout = ~wohf(Teq) + ~sohg(Teq) 

+ ~i,woCpiTeq + ~isoCpiTeq 

+ Kout , 

where 

K = kinetic energy of the exiting gas mixture out 

2 

= (' +' . )Ubu1k 

mso m~so 2 

Energy out can be rewritten as 

Eout = ~lhf(Teq) + ~lf1hfg(Teq) 

+ ~2CpiTeq + Kout • 

A momentum balance across the condenser yields 

Pout = Pin + Min - Mout , 

247 

(G-ll ) 

(G-12) 

(G-13) 

(G-l4) 
TR-3l08 

where 

(G-lS) 

Equations G-8, G-l3, and G-lS are solved simultaneously in an iterative manner 

to arrive at fl' f2' and Teq in the neighborhood of fl and f2 = O. 

At this point, we observe that an ideal cocurrent condenser may perform worse 

than an actual condenser because we assumed 100% of equilibrium gas liberation 

in the ideal case as opposed to less than 20% liberation in an actual case. 

G.2 Countercurrent Condenser 

To evaluate the maximum performance of an ideal countercurrent condenser, we 

calculated the equilibrium assuming 

• Water exiting the condenser 1S 1n equilibrium with the steam entering from 

the bottom 

• Dissolved inert gas in the exiting water 1S also in equilibrium with the 

partial pressure of inerts in the entering steam 

• The steam and inert gas mixture. exiting from the top of the condenser 1S 1n 

equilibrium with the incoming water 

• The incoming water is predeaerated to an extent corresponding to its equilibrium level with the steam and inert gas mixture at the top. 

Countercurrent equilibrium calculations differ from cocurrent calculations 

since steam and water enter the condenser at different ends. Based on a given 

set of steam and inert gas mixture inlet conditions and a specified inlet 

water temperature, we calculate a minimum waterflow to attain equilibrium at 

both ends of the condenser. The dissolved inert gas level in the water 1S 

adjusted to satisfy equilibrium concentrations. Steam pressure at the exit is 

adjusted to account for momentum recoveries. The calculations proceed as 

follows. 

Exit momentum of vapor 1S initially assumed to be zero 

Mout = 0 , (G-l6) 

then the outlet static pressure is evaluated using 

(G-17) 

Exit vapor is in equilibrium at a saturation temperature equal to the water 

inlet temperature Twi ' i.e., 

Tso = Twi • (G-l8) 

248 
TR-3108 

Assuming the desorbed gas from the coolant l.S initially zero, mid = 0, we 

evaluate the exit steam mole fraction 

Yso = (G-19) 

The inert gas mass flow rate is 

(G-20) 

The partial pressure of inert gases at the exit now defines an equilibrium for 

the dissolved gas level in the incoming water as 

PPio 

Yiwi = He(Twi) • 

The dissolved gas level l.n the exiting water for equilibrium l.S given by 

PPii 

Yiwo = ( ). He Tsi 

(G-2l) 

(G-22) 

Equations G-2l and G-22 allow us to evaluate the inert gas desorbed per unit 

of water mass flow rate. 

The energy balance on the inlet and outlet steam and inert gas mixture and the 

specified water temperature rise allows us to evaluate the equilibrium water 

flow rate. Pressures are reevaluated using the momentum balance. Calculations are repeated until we obtain the convergence on desorbed inert gas and 

condenser exit pressures. 

249 
TR-3108 

APPENDIX H WATER, STEAM, AND AIR PROPERTIES 

H.I Water (Coolant) 

The present version of the computer code uses freshwater properties with a 

molecular weight of 18.015. Other properties are fitted to curves as functions of temperature in degrees Celsius from data in Kellogg (1975) as 

follows: 

Density (kg/m3 ): 

p = 1000.0 - (-0.6922 - 0.001757T + 0.005571T2 ) (H-l) 

for T > 1l.85°C; otherwise p = 1000.0. 

Celsius. 

The temperature T 1.S ln degrees 

Specific heat (kJ/kg °C): 

Cp = {4217044 - 3504.25T + 113.17T2 - 1.309T3 )/106 • 

Viscosity (kg/m s): 

where 

[ 0.38 281 ] 

a = (T + 273.15)/647.3 - 0.2163 • 

Thermal conductivity (W/m °C): 

k = 0.569 + 0.001575T • 

Schmidt number (air diffusing in water): 

372.7,,2 Sc = ----------~~~-----------

2.71 x 10-9 (T + 273.15) 

(Reid, Prausnitz, and Sherwood 1987). 

(H-2) 

(H-3) 

(H-4) 

(H-5) 

These fitted curves are applicable from 2° to 40°C and are coded ln the computer program (procedure Watertransprop). 

Equilibrium inert gas concentration is determined by Henry's Law. The Henry's 

Law constant He is a function of temperature and determined from a fitted 

curve of solubility (Sol) in moles air per mole water at atmospheric pressure 

as follows (Kellogg 1975): 

Sol = {2.333 - 0.054256T + 0.006236T2)/105 (H-6) 

250 
He = Patm/Sol , 

where Patm is atmospheric pressure (101,325 Pa). 

H.2 Saturated Steam Properties 

TR-3l08 

(H-7) 

Saturated steam properties, including temperature, pressure, specific volume 

of liquid and gas, and the enthalpy of liquid and vapor, are fitted with simple equations. The saturation temperature and pressure curves are fitted to a 

modified Antoine equation (Smith and Van Ness 1975) with data from properties 

of water and steam in S1 units (Schmidt 1969) between 0° and 40°C. The curves 

have the following form: 

(H-8) 

and 

Tsat = (H-9) 

where 

Psat = saturation pressure (Pa) 

Tsat = saturation temperature (OC) 

PI = constant = 161. 7574 

P2 = constant = 18.4779 

P3 = constant = 4026.9759 

P4 = constant = 234.7384 

P5 = constant = 3.7383. 

The specific volume of the saturated water is assumed to be constant at 

0.001 m3/kg. The specific volume of the saturated gas 1S found using the 

ideal gas law. 

The enthalpy of the saturated water 1S based on an average constant specific 

heat: 

where 

hL = enthalpy of water (kJ/kg) 

CpL = specific heat of water = 4.186 (kJ/kg DC). 

The enthalpy of the saturated steam is found similarly as 

where 

hG = enthalpy of steam (kJ/kg) 

hGo = enthalpy of steam at O°C = 2501.6 (kJ/kg) 

CpG = specific heat of steam = 1.860 (kJ/kg DC). 

251 

(H-lO) 

(H-ll ) 
TR-3108 

Approximate expressions for steam transport properties valued 1n the range of 

0° to 40°C were used as follows: 

Thermal conductivity (W/m K): 

k = (1.82 + 0.006T) x 10-2 

Viscosity (kg/m s): 

~ = (8.02 + 0.04T) x 10-6 

Specific heat(kJ/kg K): 

Cp = 1.854 + 0.00775T , 

where T is in degrees Celsius (Schmidt 1969). 

H.3 Air Properties 

Air thermal conductivity k (W/m K): 

with T in kelvins. 

Air viscosity ~ (kg/m s): 

(1.458 x 10-6 )T1.5 

~ = T + 110.4 

with T in kelvins and a constant air specific heat Cp (kJ/kg K) used as 

Cp = 1.005 • 

Air molecular weight used is 28.97 (Bolz and Tuve 1976). 

For air-water vapor mixtures, mutual diffusivity was calculated as 

Molecular diffusivity (m2/s): 

2.9l8(T/313)1.75 = --~~~--~----

p 

where T is in kelvins, and p 1S the mixture pressure 1n Pascals. 

H.4 Gas Mixture Properties 

(H-12) 

(H-13) 

(H-14) 

(H-15) 

(H-16) 

(H-17) 

(H-18) 

The gas mixture properties are calculated using the properties of the pure 

components, at the proper temperature and pressure, and the standard mixture 

rules. 

252 
TR-3l08 

If Xl and X2 stand for the mass fractions of steam and gas in the mixture, 

then the mixture properties are written as 

Specific heat: 

Mole fraction: 

Density (kg/m3): 

Factor: 

Viscosity: 

Thermal conductivity: 

Prandtl number: 

Schmidt number: 

where 

T = temperature 

1 

Y1 = """'1-+~("""'1~/X-1---'1)""'('-M-1"""/M-2"""<'"") 

II = 

k = 

(K) 

p = 

P(X1M1 + X2M2) 

8314.3T 

Y1 11 1 + Y2 11 2 

Y1 + Y2IP12 Y2 + YlIP21 

nk1 

+ Y2k2 

Yl + Y2IP12 Y2 + Y2IP21 

M = molecular weight 

Subscript 1 = water vapor 

Subscript 2 = alr. 

H.5 References 

(H-19) 

(H-20) 

(H-21) 

(H-22) 

(H-23) 

(H-24) 

(H-25) 

(H-26) 

Bolz, R. E., and G. L. Tuve, eds., 1976, Handbook of Tables for Applied 

Engineering Science, 2nd ed., Cleveland, OH: CRC Press. 

M. W. Kellogg Company, 1975 (Oct.), Saline Water Conversion Engineering Data 

Book, NTIS No. PB 250 907, Washington, DC: Office of Water Research and 

Technology. 

Reid, R. C., J. M. Prausnitz, and T. K. Sherwood, 1987, The Properties of 

Gases and Liquids, 4th ed., New York: McGraw Hill. 

253 
TR-3l08 

Schmidt, E., 1969, Properties of Water and Steam 1.n SI-Units, New York: 

Springer-Verlag. 

Smith, J. M., and H. C. Van Ness, 1975, Introduction to Chemical Engineering 

Thermodynamics, 3rd ed., New York: McGraw-Hill. 

254 
TR-3108 

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TR-3108 

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Document Control 11. SERI Report No. 12. NTIS Accession No. 

Page SERI/TR-252-3108 

4. Title and Subtitle 

Direct-Contact Condensers for Open-Cycle OTEC 

Applications Model Validation with Fresh Water 

Experiments for Structured Packings. 

7. Author(s) D. Bharathan, B. K. Parsons, and J. A. Althof 

9. Performing Organization Name and Address 

Solar Energy Research Institute 

A Division of Midwest Research Institute 

1617 Cole Boulevard 

Golden, CO 80401-3393 

12. Sponsoring Organization Name and Address 

Solar Energy Research Institute 

A Division of Midwest Research Institute 

1617 Cole Boulevard 

Golden, CO 80401-3393 

15. Supplementary Notes 

16. Abstract (Limit: 200 words) 

3. Recipient's Accession No. 

5. Publication Date 

October 1988 

6. 

8. Performing Organization Rept. No. 

10. Project/Task/Work Unit No. 

OE 713101 

11. Contract (C) or Grant (G) No. 

(C) DE-AC02-83CHI0093 

(G) 

13. Type of Report & Period Covered 

Technical Report 

14. 

The objective of the reported work was to develop analytical methods for evaluating 

the design and performance of advanced, high-performance heat exchangers for use ~n 

open-cycle ocean thermal energy conversion (OC-OTEC) systems. This report describes 

the progress made on validating a one-dimensional, steady-state analytical computer 

model of direct-contact condenser using structured·packings based on extensive sets 

of fresh water experiments. The condenser model represents the state of the art ~n 

direct-contact heat exchange for condensation for OC-OTEC applications. This ~s 

expected to provide a basis for optimizing OC-OTEC plant configurations. Using the 

model, we examined two condenser geometries, a cocurrent and a countercurrent configuration. This report provides detailed validation results for important condenser parameters for co current and countercurrent flows. Based on the comparisons and 

uncertainty overlap between the experimental data and predictions, the model ~s 

shown to predict critical condenser performance parameters wi th an uncertainty 

acceptable for general engineering design and performance evaluations. 

17. Document Analysis 

a. Descriptors Condense.rs~ Ocean Tl1ermal. E~ergy~Conversion~ OTEC;Direct 

Contact Heat Exchangers; . Packings;', Fresh W?1:er; 'Seawater; 

Desalination; Numerical Solution 

b. Identifiers/Open-~ed Terms 

Direct Contact Condensers; Cocurrent Condensers; Countercurrent 

Condensers; Structured Packings 

c. UC Categories 

262 

18. Availability Statement 

National Technical Information Service 

u.S. Department of Commerce 

5285 Port Royal Road 

Springfield, Virginia 22161 

Form No. 0069 (3-25-82) 

19. No. of Pages 

272 

20. Price A12