NUREG/IA-0003

Intemational

Agreement Report

Influence of the Wetting State

of a Heated Surface on Heat

Transfer and Pressure Loss in

an Evaporator Tube

Prepared by

W. Kdhler, D. Hein

Kraftmerk Union AG

Erlangen, Federal Republic of Germany

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555

September 1986

Prepared as part of

The Agreement on Research Participation and Technical Exchange

under the International Thermal-Hydraulic Code Assessment

and Application Program (ICAP)

Published by

U.S. Nuclear Regulatory Commission
NOTICE

This report was prepared under an international cooperative

agreement for the exchange of technical information. Neither

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their employees, makes any warranty; expressed or implied, or

assumes any legal liability or responsibility for any third party's

use, or the results of such use, of any information, apparatus product or process disclosed in this report, or represents that its use

by such third party would not infringe privately owned rights.

Available from

Superintendent of Documents

U.S. Government Printing Office

P.O. Box 37082

Washington, D.C. 20013-7082

and

National Technical Information Service

Springfield, VA 22161
NUREG/IA-0003

International

Agreement Report

Influence of the Wetting State

of a Heated Surface on Heat

Transfer and Pressure Loss in

an Evaporator Tube

Prepared by

W. KMhler, D. Hein

Kraftmerk Union AG

Erlangen, Federal Republic of Germany

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555

September 1986

Prepared as part of The Agreement on Research Participation and Technical Exchange under the International Thermal-Hydraulic Code Assessment

and Application Program OICAP)

Published by

U.S. Nuclear Regulatory Commission
NOTICE

This report documents work performed under the sponsorship of the Kraftwerk

Union in the Federal Republic of Germany. The information in this report has

been provided to the USNRC under the terms of an information exchange

agreement between the United States and the Federal Republic of Germany

(Technical Exchange and Cooperation Arrangement Between the United States

Nuclear Regulatory Commission and the Bundesminister Fuer Forschung und

Technologie of the Federal Republic of Germany in the field of reactor safety

research and development, April 30, 1981). The Kraftwerk Union has consented

to the publication of this report as a USNRC document in order that it may

receive the widest possible circulation among the reactor safety community.

Neither the United States Government nor the Kraftwerk Union or any agency

thereof, or any of their employees, makes any warranty, expressed or implied,

or assumes any legal liability of responsibility for any third party's use, or

the results of such use, of any information, apparatus, product or process

disclosed in this report, or represents that its use by such third party would

not infringe privately owned rights.
ABSTRACT

The influence of the wetting state of a heated surface on heat transfer and

pressure loss in an evaporator tube was investigated for a parameter range occurring in fossil-fired steam generators. Included in the analysis are

quantities which determine the wetting state in steady and transient flow.

The experimental work consists of the following:

- occurrence of critical heat flux (CHF) and post-CHF heat transfer in a

vertical upflow evaporator tube

- influence of pressure and enthalpy transients on heat transfer in the

unwetted region

- influence of pipe orientation on heat transfer

- . two phase flow pressure loss in wetted and unwetted region.

Based on these experiments a method of predicting CHF for a vertical upflow

evaporator tube was developed. The heat transfer in the unwetted region was

newly formulated taking into account thermal nonequilibrium between the water

and steam phases. Wall temperature excursions during pressure and enthalpy transients are interpreted with the help of the boiling curve and the Leidenfrost phenomenon. A method is developed by means of which it is possible to

determine the influence of the pipe orientation on the location of the boiling crisis as well as on the heat transfer in the unwetted region. The influence

of the wetting state of the heated surface on the two phase flow pressure loss

is interpreted as "Wall effect" and is calculated using a simplified computer

model.

iii

TABLE OF CONTENTS

Page

ABSTRACT ................................................................. iii

1. INTRODUCTION AND OBJECTIVE .......................................... 1

2. TEST EQUIPMENT AND PROGRAM .......................................... 2

2.1 Experimental Loop .............................................. 2

2.2 Instrumentation of the Objects of Measurements ................. 2

2.3 Processing of the Measured Data ................................ 7

2.4 Test Program ................................................... 7

3. STEADY FLOW IN A VERTICAL UPFLOW TUBE ................................ 8

3.1 Flow Patterns and Heat Transfer Regions ........................ 8

3.2 Critical Boiling States ........................................ 10

3.2.1 Forms of Boiling Crisis in an Evaporator Tube ........... 10

3.2.2 Process for the Determination of Critical Boiling

States in the Entire Steam Quality Range ................ 11

3.2.3 Model Verification ...................................... 13

3.3 Heat Transfer in the Post-Dryout Region ........................ 18

3.3.1 The Heat Transfer Mechanism ............................. 18

3.3.2 Method of Calculation from the Literature ............... 20

3.3.3 Development of a Calculation Model for the Heat .........

Transfer in the Post-Dryout Region ...................... 23

3.3.3.1 The Heat Transfer in a Developed Thermal

Non-Equilibrium ................................ 23

3.3.3.2 The Heat Transfer at the Region Boundaries ..... 27

3.3.3.3 Model Verification ............................. 31

4. PRESSURE AND ENTHALPY TRANSIENTS ................................. 42

4.1 Transient Behavior of an Evaporator Tube .................... 42

4.2 Interpretation of the Transient Processes with Help of

the Boiling Curve ........................................... 48

4.3 Influence of the Leidenfrost Temperature .................... 53

4.4 Mathematical Model for the Determination of the Influence

of Pressure and Enthalpy Transients on the Heat Transfer .... 57

5. INFLUENCE OF THE TUBE ORIENTATION ON THE HEAT TRANSFER ........... 63

5.1 Flow Patterns and Heat Transfer Regions ..................... 63

5.2 Heat Transfer in the Wetted Region .......................... 65

5.3 Critical Boiling States ..................................... 67

5.4 Heat Transfer in the Post-Dryout Region ..................... 78

V
TABLE OF CONTENTS (Continued)

Page

6. PRESSURE DROP .................................................... 88

6.1 Pressure Drop Components in an Evaporator Tube .............. 88

6.2 Friction Pressure Loss in the Wetted and Unwetted Regions... 89

6.2.1 Experimental Observations and Their Interpretation... 89

6.2.2 Comparison of Various Pressure Loss Correlations ..... 91

6.2.3 Influence of the Heating and Entrance Effects ........ 98

6.3 Recommendations for the Determination of the Friction

Pressure Loss of a Two-Phase Flow ........................... 106

7. SUMMARY .......................................................... 114

NOMENCLATURE .......................................................... 116

BIBLIOGRAPHY .......................................................... 119

vi
1 INTRODUCTION AND OBJECTIVE

In many technical apparatuses a fluid evaporates through the supply of heat.

If the evaporation takes place in a fluid carrying pipe and if the fluid is

completely converted into steam, the heated surface lies partially in the

wetted and partially in the unwetted regions. A typical example of this are

the evaporator tubes of a fossil-fired steam generator. The wetted region is

characterized by high heat transfer coefficients while in the unwetted region

(post-dryout region) the heat transfer is usually greatly reduced. The

boiling crisis constitutes the boundary between both regions.

In view of the design of the evaporator heating surfaces of fossil-fired steam

generators the heat transfer in the unwetted region is of prime interest,

since the herein occurring material temperatures influence the service life of

the evaporator tubes. The heat transfer in the unwetted region depends

greatly on the thermal non-equilibrium between the steam flow and the water

droplets. Therefore, this effect has to be included in these studies.

Also the location of the boiling crisis influences the maximum heating surface

temperatures in the unwetted region. Should the boiling crisis occur already

at low steam qualities, the steam velocity and, thus, the cooling through

steam convection is still low and as a result the heating surface temperatures

are higher than those that occur at high steam qualities. The pressure and

enthalpy transients that occur near the critical pressure can displace the

location of the boiling crisis to lower steam qualities, thus leading to a

considerable increase of the heating surface temperatures in the unwetted

region.

The orientation of the tube influences the distribution of the phases over the

flow cross-section and thus also the occurrence of critical boiling states as

well as the heat transfer in the unwetted region. Since the influence of the

orientation of the tube on the heat transfer depends on many parameters (e.g.,

pressure, mass flow density, tube diameter) extensive investigations have to

be conducted in this respect.

For the flow-related design of evaporator tubes it is of interest to which

extent the pressure loss of the two-phase flow is influenced by the occurrence

of the boiling crisis. Since heat transfer calculations are frequently based

on the pressure loss, by comparison between calculation and measurement it can

be determined if heat transfer models are based on the actually occurring

pressure losses. The formulation of the heat transfer in the unwetted region

can be verified in this manner.

It is the aim of this study to investigate the influence of the wetting state

of a heated surface on the heat transfer and the pressure loss in an

evaporator tube. An essential part of this task is the determination and

analysis of the relevant quantities which determine the wetting state of a

heated surface.

1
2 TEST EQUIPMENT AND PROGRAM

2.1 Experimental Loop

A high-pressure loop (Figures 2-1 and 2-2) was available for the tests. Due

to the wide operating range of the test rig it was possible to simulate the

conditions existing in fossil-fired evaporators under full and partial load.

Pressure up to 330 bar

Flow rate up to 15 m3 /h

Heating capacity up to 1000 kW

Tube Length up to 6.1 m

The installation was operated in once-through mode with low flow rates (up to

2 m3 /h. The demineralized and degassed water was therein carried with a piston

pump through the preheater and the test tube, and wholly or partially evaporated

in the process. It was condensed and subcooled in the spray condenser and

finally carried to the drain via a pressure-reducing valve. The piston pump

was equipped with six pistons and a surge tank on the outlet side. Thus, it

was possible to limit the flow rate oscillations to a value of less than 0.5%.

In the case of high flow rates, the tests were conducted in recirculation

operation by means of a centrifugal pump.

The test tubes were horizontally and vertically installed. The heating was

by direct current, both axially and circumferentially uniform, whereby the

tube wall served as dissipative resistance.

A detailed description of the experimental installation is contained in /I/.*

2.2 Instrumentation of the Objects of Measurements

The measurements of heat transfer and pressure loss were conducted on three

measuring sections with tube dimensions of 17.15 x 2.31 mm, 18 x 2 mm and

33.4 x 4.55 mm. The instrumentation of the measuring sections are shown in

Figures 2-3 and 2-4. The temperature measuring points were installed along an

upper, a lateral and a lower surface line on the outside of the tubes. Only

thermocouples of one surface line were connected to the data logger in the case

of experiments with a vertical measuring section. Thermocouples with insulated

measuring points had to be used because of the direct heating of the tubes.

For the analysis, the measured outside-wall temperatures were converted to the

tube inside-wall values.

A mixing chamber was installed at the outlet of the test section. It had the

task to evaporate water droplets which could still exist in the superheated

fluid. Thus, energy balances can be performed, containing the preheater and

test section. Fluid thermocouples were installed at the inlet, and outlet, of

the test section as well as downstream of the mixing chamber. The determination

of the static pressure was made after a steadying stage at the pipe inlet and

downstream of the mixing chamber.

*Editor's note: Reference citations in this report are designated by slashes

bounding the number listed in the Bibliography.

2
Power supply

Test section

Pressurizer

-Preheater

Circulation pump SPiston pump

*_ _Feed pump

Figure 2-1 The BENSON test rig

3
Cooling tower

Figure 2-2 The BENSON test rig (circuit diagram)
U1

U 2 U3

6100

31 Thermocouples top

A B __________14 Thermocouples lateral -400 Mixing chamber

F

U1Fluid TE inlet

1 10 =1 11111 1

37

40 (a p,5) 3570 f40 p4) " Fluid TC

31 Thermocouples bottom

Fluid TC exit

View"A" View:"B" Thermocouple

Thermocouple

Tube: 3a& 4..55

17.15 2.31

Material: 1.4876

0 1mm Pressure tap - Thermocouple

Figure 2-3 Instrumentation of the test tubes with inside

diameters of 12.5 and 24.3 mm
Voltage taps U1

U2 t U3

45 Thermocouples

63 36

199 •_ _ 7 Thermocouples

Fluid TC inlet Fluid TC exit

0r 

1 6096

Thermocouple 

Tube: 18x2

Material: 1.4981

0 1mm Pressure tap

Thermocouple

View:"X"

Figure 2-4 Instrumentation of the test tube with an inside diameter of 14 mm
Furthermore, the pressure loss was measured over 3 tube sections.

The supplied power - and therefrom the heat flux - was determined by a voltage

and current measurement. For this purpose, total voltage and partial voltage

taps were installed within the test tube.

2.3 Processing of the Measured Data

A digital data logger with 64, and 96, channels was used for the recording of

the measured data. Software was available which scanned all measuring stations

once a second and recorded them on a magnetic tape. In order to eliminate temporary oscillations, the measured valued of one test point were recorded for

approximately 150 seconds.

The stored data were further processed using both the data logger as well as

the KWU main frame computer.

2.4 Test Program

The test program comprises the determination of the critical boiling conditions,

of the heat transfer in the post-dryout region and of the pressure loss in the

two-phase region. Furthermore, the influence of the pipe orientation on heat

transrer and pressure loss was also studies. Finally, the influence of pressureand enthalpy drops on the heat transfer in the post-dryout region was determined.

The parameter range of the experimental investigations overlaps the operating

range of fossil-fired steam generators under partial- and full load operations.

The main influence parameters were varied as follows:

System pressure 50 to 250 bar

Mass velocity 300 to 2500 kg/m 2s

Heat flux up to 600 kW/m 2

Mass velocities of 1000 and 2000 kg/m2 s were used for the investigations on the

influence of pressure- and enthalpy drops on the heat transfer in the postdryout region.

7
3 STEADY FLOW IN A VERTICAL UPFLOW TUBE

3.1 Flow Patterns and Heat Transfer Regions

The distribution of the steam and water phase over the flow cross-section is

symmetrical in a vertical upflow evaporator tube. Figure 3-1 shows the possible

flow patterns in a vertical evaporator tube, whereby with increasing steam

quality all shown flow configurations are not always transversed. With the

help of flow pattern charts /2,3,4/ it is possible to determine the flow pattern which occurs at a given parameter combination. However, not too high expectations should be placed in the accuracy of these charts.

C0.

C >

0

Bubbly Slug Churn Annular Drop

• V tL

Flow

Void fraction

Figure 3-1 Flow patterns in a vertical upflow tube

Figure 3-2 shows the typical flow patterns and heat transfer regions in a

vertical upflow evaporator tube:

The fluid is subcooled at the tube inlet. Single-phase flow with convective

heat transfer takes place. If the wall temperature slightly exceeds the

saturation temperature of the fluid subcooled boiling sets in at the wall.

Most of the steam bubbles condense within the fluid. The wall temperature

remains almost constant with increasing enthalpy.

Once the mean fluid temperature reaches the saturation temperature, the steam

quality increases corresponding to the further enthalpy increase. The very

good heat transfer remains almost constant.

8
Steam Flow pattern Heat transfer regime:

Single-phase

steam flow

Drop flow

Convective heat

transfer to steam

Post-Oryout region

Wall

temperature

Annular flow

with water

entrainment

Annular flow

Convective boiling

Slug flow

Bubbly flow

Single-phase

water flow

Saturated boiling

Subcooled boiling

Convective heat

Temperature '4 transfer to water

Water

Figure 3-2 Flow patterns and heat transfer regions in a vertical

evaporator tube
Annular flow sets in once a certain steam quality, which depends on the chosen

parameters, is reached. Therein, the fluid flows partially as film along the

wall and partially in the form of droplets in the flow core.

With high flow velocities the heat transfer improves somewhat compared with

the conditions under nucleate boiling.

With a further enthalpy increase a state is reached (critical boiling state)

at which the wetting of the heating surface can no longer be maintained. A

boiling crisis sets in because the fluid loses its contact with the wall. The

boiling crisis in a steam generator is usually caused by dryout of the heating

surface. Therein, the heat transfer is reduced most of the times and the wall

temperature increases correspondingly in the next region (post-dryout region).

If all fluid droplets are evaporated, the region with a single-phase convective

steam flow follows.

From Figure 3-2 it can be gathered that, at the beginning and at the end of the

evaporation zone, the water and steam phases are not in thermal equilibrium.

While voids at saturation temperature exist in subcooled fluid during subcooled

boiling, in the post-dryout region there are water droplets at saturation temperature present in a superheated steam flow.

3.2 Critical Boiling States

3.2.1 Forms of Boiling Crisis in an Evaporator Tube

The location at which the boiling crisis occurs separates the wetted and the

unwetted regions in an evaporator tube.

The occurrence of the boiling crisis is essentially determined by the parameters

for heat flux density, mass flow density, steam mass quality, pressure, and

hydraulic diameter. In connection with the occurrence of the boiling crisis

there is of interest either the steam quality (critical steam quality) or the

heat flux (critical heat flux), at which critical boiling states occur. IN the

case of upward flow in vertical tubes, according to /5/, the critical heat flux

can be represented as function of the critical steam quality by three characteristic curve segments (Figure 3-3):

Zone 1:

The void fraction in the flow is low, i.e., water is the continuous phase. At

the location of the boiling crisis is formed a steam film on the tube wall,

which separates the water from the heating surface (film boiling). In the literature this process is also called boiling crisis of the first kind, respectively

"Departure from Nucleate Boiling (DNB)." The extent of the critical heat flux

depends on the steam quality of the flow. An increase of the heat flux of the

flow displaces the onset of the film boiling to lower steam qualities.

Zone 2:

Steam becomes the continuous phase with increasing steam quality in the flow.

At the location of the boiling crisis the still existing water film breaks off

from the tube wall, or it dries out. In the literature this process is also

called boiling crisis of the second kind, or "dryout." Here the critical heat

flux decreases considerably with increasing steam quality.

10
Zone 3:

With a further decrease of the heat flux a movement of the location of the

boiling crisis moves towards higher steam qualities is observed. Obviously,

water droplets can thereby increasingly deposit on the tube wall, a reason why

this process is called "Deposition Controlled Burnout." As well as in Zone 2,

the occurrence of the boiling crisis is herein connected with a dryout of the

heating surface.

The processes which lead to critical boiling states in the individual steam

quality zones are, to a great extent, still beyond the possibility of an analytical calculation, so that practical equations for a rather extensive range of

parameters are of empirical nature.

Critical heat flux Zone 1: Film boiling (DNB)

2: Heating surface dryout

(dryout) 3: Deposition controlled

burnout

3

Steam quality

Figure 3-3 Typical path of the critical heat flux

3.2.2 Process for the Determination of Critical Boiling States in the Entire

Steam Quality Range

The hitherto existing equations for the determination of the critical heat flux

always determine only portions of the critical boiling states. Of a process

for the determination of the critical heat flux in the entire steam quality

range it is required however, that the equations chosen for all allowable parameter combinations lead to a constant path along the limits of validity. This

aim was attained with the following method:

If one starts from Figure 3-3, which shows the critical heat flux as a function

of the local steam quality, one can see that with increasing steam quality the

11
critical heat flux in the film boiling region decreases less than in the dryout

region. If for each region there is chosen a suitable equation, the intersection of the two curves, determined with the two equations, represents the limit

between the two mechanisms of the boiling crisis. Mathematically, the choice

of region can be made by a comparison of the critical heat fluxes calculated

according to the two equations for a determined steam quality, in considering as

valid the lower value.

For the film boiling region (Zone 1 in Figure 3-3) there were chosen the tabular

values of V.E. DOROSHCHUK /6,7/. According to KEMNER /8/, these values proved

to be superior to other correlations in the case of high heat fluxes, as they

occur in nuclear fuel assembles. However, due to the easier use - even with a

slight loss of accuracy - there was used the empirical equation developed by

DOROSHCHUK from the tables:

qKr = 103 " [10.3 - 17.5(p/p ) + 8(p/pc) 2 ]-(8 • 10-3/d)0. 5 e- 1 5 (3-1)

W1000) (0.68(p/p c )-1.2 -0.3)

It has the following region of validity:

29 5 p 5 196 bar

500 5 m : 5000 kg/m 2s

0 5 AS 75 K

4-10-3 5 d 5 16-10-3 m

In equation (3-1) k is the steam quality. It is defined as the proportion of

steam mass flow in the total mass flow.

Based on a study by FECHNER /9/ which covers the parameters of the fossil-fired

steam generators, the KON'KOV /10/ equation was used for the region of the dryout of the heating surfaces (Zones 2 and 3 in Figure 3-3):

Pressure region p(bars)

qKr = 1.8447.108-8i-2" 6 6 4 (d'1000)-O' 5 6 eO'1 3 7 2 . p 4.9 - 29.4

qKr = 2.0048".10j°k'*-2.664 (d'100)-0.56 e-0.0204 " 29.4 - 98 (3-2)

qKr = 1.1853.1012kxm-2"664 (d'1000)- 0.56e' 00636 p 98 - 196

It has the following region of validity:

12
< 1200 kW/m2

200 5 A ; 5000 kglm2 s

4"10-3 5 d 5 32.10-3 m

The Figures 3-4 to 3-6 show typical courses of the critical heat flux as function of the steam quality, arrived at a combining of equations (3-1) and (3-2).

From these figures it can be gathered that the KON'KOV equation also covers the

"Deposition Controlled Burnout" region due to its form of construction.

Since the KON'KOV equation is used with the DOROSHCHUK equation up to the intersection, in respect to the heat flux there occurs in part an exceeding of the

validity region given by KON'KOV. This procedure is necessary, however, in

order to prevent "gaps" in the desired parameter region.

3.2.3 Model Verification

The determination of the critical heat flux according to the chosen procedure

was checked by means of 3044 test points (/5/ and /11 to 22/). Of these, 1663

test points were assigned to the film boiling, which was calculated by equation

(3-1) with a mean value of 0.99 and a standard deviation of 0.16. The mean

value was formed therein by the quotient of calculated and measured critical

heat flux:

M = n 7KrR (3-3) 4Kr M

The standard deviation refers also to the quotient of calculated and measured

critical heat flux.

For the remaining 1381 test points, in view of the choice of region described

in chapter 3.2.2, dryout of the heating surface was assumed, which was calculated by equation (3-2) with a mean deviation of -0.04 and a standard deviation

of 0.10. Due to the considerable decrease of the critical heat flux in this

region, the comparison was made by means of the measured and calculated critical

steam quality, whereby the mean deviation was defined as follows:

1x =- (£r - r) (3-4)

n KrR KrM

This error criterion ensures a constant weighted deviation in the entire steam

quality region. Herein, the standard deviation refers to the difference of

calculated and measured critical steam quality. Table 3.1 shows a list of

the test parameters of the various authors as well as of the accuracy of equations (3-1) and (3-2). From the test calculation it can also be gathered that

equation (3-1) can be applied beyond the given region of validity for the tube

bore of 16 mm. Up to a tube bore of 24 mm there was not observed a vitiated

result accuracy. The equation (3-2) can also be used beyond the given region

of validity for the heat flux.

13
Tube bore -10 mm

-- 20 mm

Mass velocity: 500 kglm2s

kW/m 2 30

100'

x

'4-

-I-

'U

ci

'U

LI

-aL.

U

N

N

N

N

I

I 1500

150

1000

500 -

0 -t-

-0.2 0 0.2 0A4 0.6 0.

Critical steam quality

1

Figure 3-4 Critical heat flux as a function of the critical steam quality

14
Tube bore -10 mm Mass velocity: 1000 kg/m2s

50

kW/m 2

30

X 2000-

76aJ

,--

u

100 Vy

150

NI

-'S

0,+

- 0,2 0 0,2 0.4 0.6 0,8

Critical steam quality

1

Figure 3-5 Critical heat flux as function of the critical steam quality

15
Tube bore Mass velocity: 2500 kg/m 2s

kW/m 2

30

SX \ 5

'100

1500 \- \

0 T

/

Pressure: \ \

200 bar \\\~

\\

l, \

-0,2 0 0,2 0A4 0.6 0.8

Critical steam quality

Figure 3-6 Critical heat flux as function of the critical steam quality

16
Table 3.1 Result accuracies of equations (3-1) and (3-2)

Calc. acc. to eq. (3-1) Calc. acc. to eq. (3-2) Test parameter

Standard Mean Standard Mass Tube Heat Au- Mean devia- devia- devia- Pressure velocity bore flux thor Number Value tion Number tion tion (bar) (kg/m 2s) (mm) (W/m210- 4 )

11 263 1.03 0.14 27 0.07 0.08 38 - 138 528 - 4855 4.6 - 23.6 59 - 621

12 75 1.03 0.11 13 0.01 0.07 30 - 90 501 - 4410 5.6 - 25.0 150 - 545

13 89 0.93 0.08 4 0.02 0.13 77 - 137 552 - 2805 10.0 30 - 548

14 965 0.99 0.16 354 0.05 0.14 29 - 138 500 - 4977 4.6 - 23.6 59 - 997

15 136 1.05 0.13 195 0.05 0.07 29 - 92 517 - 4795 10.0 93 - 344

5 - - - 162 0.07 0.05 67 - 73 506 - 2036 13.0 28 - 87

16 - 21 0.08 0.06 40 - 71 664 - 1383 15.0 71 - 113

17 - - - 83 0.09 0.07 160 - 180 650 - 2700 12.8 15 - 80

18 42 0.99 0.24 61 0.05 0.08 49 - 176 600 - 4800 10.4 70 - 186

19 4 1.11 0.14 55 0.03 0.05 50 - 150 501 - 2293 24.7 30 - 126

20 - - - 43 0.02 0.13 49 - 174 510 - 2539 14.0 9 - 61

21 - - - 61 0.06 0.05 68 - 70 994 - 2013 10.0 20 - 81

22 90 0.91 0.21 302 0.02 0.07 39 - 195 501 - 4828 5.1 - 24.7 23 - 250

H-
By way of example, in Figure 3-7 there are compared for each of the authors the

measured critical heat flux and the one calculated with the aid of equation (3-1)

as well as the measured critical steam quality and the one calculated with the

aid of equation (3-2).

Due to the high result accuracy it is possible to apply the chosen procedure

for the determination of the critical boiling states in a large pressure-, mass

velocity and diameter range. In the evaluation of the occurring errors it has

to be considered that even reproducibility tests 1211 may have an average deviation of approximately 6%.

3.3 Heat Transfer in the Post-Dryout Region

3.3.1 The Heat Transfer Mechanism

According to ILOEJE /23/, the following mechanisms are possible after reaching

the boiling crisis:

1. Convective heat transfer from the heating surface to the steam, which thus

becomes superheated.

2. Heat transfer from the heating surface to the water droplets, whereby a

difference is made between the direct form of heat transfer, by wetting

of the droplets on the wall, and the indirect form, by heat absorption in

the superheated boundary layer.

3. Heat transfer by radiation from the heating surface to steam and droplets.

It is only in the case of very high wall temperatures that the radiation contributes considerably to the heat transfer. According to ILOEJE /23/, also the

heat transfer between heating surface and fluid decreases very much with an

increasing difference between heat surface and saturation temperatures, so that,

according to MAYINGER /24/, this fraction has to be considered only during

transient boiling.

Thus, points 2 and 3 can be neglected for the parameter range of the fossil-fired

steam generators compared with point 1. Essentially, heat transfer takes place

in two stages:

First, the heat from the heating surface is transferred to the steam by convective heat transfer. Thereby, the steam is superheated and is no longer in thermal equilibrium with the entrained water droplets. In a second phase, the heat

is transported by the superheated steam to the water droplets. The higher the

temperature difference between steam and water droplets, the more heat is transferred from the steam to the droplets, which evaporate thereby.

This two-stages model, developed by BENNET and HEWITT /25/ in 1967, is the basis

of many heat transfer models in the post-dryout region.

For the heat transfer between steam and droplets there are two extreme cases:

1. No heat transfer between steam and water droplets, i.e., the water fraction

in the flow remains constant starting from the location of the boiling

crisis. The supplied heat is exclusively used for the superheating of the

18
Measured c t 7500

kW/m2

5000

2500'

0

0

Measured critic

titical heat flux

Accuracy of reproduction /

of equation 3-1 acc. to Ill/

a 0/

/

/

S 13,0 /

00

CIbi

/

/

/

/

/W

at

1

2500

steam quality

5000 kW/m 2

Calculated critical

7500

heat flux

1l A

0.75

0.5

0,250.2

Accuracy of reproduction /

of equation 3-2 acc. to /201 X /

/

/

/

XX /

X //

x XX/ /

x x• W / x 

/

/

A X

X/ XX

XXx

x/

/×

'/c

/xx

25 50.5 1

0.75

Calculated critical

1.00

steam quality

Figure 3-7 Comparison between calculated and measured critical

boiling states

19
steam, whereby the steam temperature and the temperature of the heating

surfaces increase continually (cf. Figure 3-8a).

2. An ideal heat transfer takes place between steam and water droplets, i.e.,

a superheating of the steam does not occur. The supplied heat is exclusively used for the evaporation of the water droplets. The steam quality

increases also after the location of the boiling crisis same as before

whereby, because of increasing steam velocity, the cooling increases and

the temperature of the heating surface drops again (cf. Figure 3-8b).

While case 1 occurs with low pressure and low mass velocity, case 2 is present

with high pressure and high mass velocity. From Figure 3-9 the manner can be

gathered in which the heat transfer mechanism changes with increasing pressure

from case 1 to case 2.

3.3.2 Method of Calculation from the Literature

The methods of calculation for the determination of the heat transfer after

the dryout of the heating surface, gathered from the literature, can be

grouped into two categories:

a,

CL

E

ccu

CU

E

iba

I--

Steam quality

b) Complete thermal

equilibrium

Xcr 'bat=1

Steam quality

a) Maximum degree of

non-equilibrium

Figure 3-8 Influence of the thermal non-equilibrium on the course of the

steam and heating surface temperatures

20
Wait temperature

Pressure: 50 bar 0

.0

0

0

Walt temperature

II Dr',e

r i sure: 200 bar 0

0.0

0

0

Massa*a* s 000 •• 0

IA

-0' Tube length - Tube length

Wall temperature I

Pressure: 100 bar

.060 * 0 0 00

.. m. a.

- Tube length

Figure 3-9 Typical wall temperature courses in dependence of pressure

1. Empirical equations

These are modifications of single-phase heat transfer equations, which take

into account the two-phase flow through special definitions of a "twophase" Reynolds number and steam-quality dependent factors.

2. Models, which consider the thermal non-equilibrium between steam and water

droplets.

Although empirical equations are easy to use, they have only a limited accuracy.

Figure 3-10 shows a typical comparison between measured values and known empirical equations from the literature. From the figure it can also be gathered

that the connection with the single-phase steam flow region (XBil -l) is not

uniform, since with neglect of the thermal non-equilibrium one would have to

reckon with wall temperatures that correspond approximately to the values of

the DOUGALL/ROHSENOW equation /26/.

21
Pressure: Mass velocity: Heat flux:

Wall temperature 101.9 bar 677 kg/m 2s 440 kW/m2

560-

oC•

480. •

400 * °'-----*• • o

400

320' • a

0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00

Calculated values taken -- Steam quality %bat

from literature

0 Dougall/Rohsenow 126/

A Bishop 127/

X Heinemann 128/

0 Miropolskiy 1291

+Groeneveld /30/ 0 Measured values

Figure 3-10 Comparison between calculated and measured wall

temperatures

Models which take into account the thermal non-equilibrium between the phases

allow a greater accuracy in the calculation of the heating surface temperatures.

They can also be divided into two main groups:

1. Models which have an empirical statement for the actual steam quality in

the flow. The actual steam quality is therein expressed as function of

the balance-determined steam quality and some other parameters. Hereto

belong the PLUMMER /31/ and GROENEVELD and DELORME /32/ models.

2. Models which determine the thermal non-equilibrium and therefrom the actual

steam quality, based on relationships between heating surface and steam

flow for the heat transfer as well as for the heat transfer between phases.

The empiricism shifts herein to the determination of the heat transfer

between steam and water droplets and of the representative droplet

diameter. The models SAHA /33/ and KOIZUMI /34/ belong to this category.

Due to their higher modelling degree, the models of the second category can

determine better than those of the first one the heat transfer in the postdryout region. However, the determination of the representative droplet diameter presents some difficulties, since this value does not only depend on the

system parameters but also that it changes, e.g., due to droplet disintegration

along the evaporation path. SCHNITTGER /35/ developed a model for this.

22
3.3.3 Development of a Calculation Model for the Heat Transfer in the PostDryout Region

3.3.3.1 The Heat Transfer in a Developed Thermal Non-Equilibrium

The water and steam fractions of the two-phase flow have still the same temperature at the location of the boiling crisis. Downstream, the steam can become

superheated while the water droplets remain at saturation temperature. A thermal non-equilibrium develops between the phases. The development of the thermal

non-equilibrium will be terminated after a certain tube length; i.e., there a

developed thermal non-equilibrium is present. Due to the higher velocity of

the two-phase flow and thus of the increased turbulence, with increasing steam

quality there can occur a reduction of the thermal non-equilibrium caused, ,e.g.,

by the droplet disintegration. At that time, the heat transfer increases to a

greater extent than corresponding to the increase of convection by the increasing mixture velocity. However, the highest heating surface temperatures occur

when the thermal non-equilibrium has just developed. If it is possible to calculate them with sufficient accuracy, the deviations before and after this zone

are of secondary importance for the design of the evaporator heating surfaces.

This type of consideration leads to a considerable simplification of the calculation of the heat transfer in an evaporator tube. Therein one starts from the

premise, that for each parameter combination there exists a value for the developed thermal non-equilibrium, through which the course of the heating surface

temperature is determined.

The extent of the developed thermal non-equilibrium can be determined from a heat

balance (Figure 3-11). The steam enthalpy would not change along the flow path,

so that it is possible to enter hDl = hD2. The supplied heat is exclusively used

for the evaporation and superheating of the newly originating steam.

Inlet enthalpy + Heat flux Outlet enthalpy

flux input - flux

r rh w-*h'

Water droplets

Figure 3-11 Determination of the thermal non-equilibrium with

help of a energy balance

23
Under this premise, the superheating of the steam is:

A~u =- 6 S 7-D Ah [- ~ + Ahv(D.F)Tr *1

-1 (3-5)

Herein, only the product (a • F)Tr from the heat transfer coefficient between

water droplets and steam and the surface of the evaporating water droplets is

unknown. Therein, the water droplets surface is in respect to a surface unit

of the heated tube wall.

In the literature there are frequently used the heat transfer equations for

spheres in flows for the heat transfer between droplets and steam for the

determination of the value of (a • F)Tr (SAHA /33/ and KOIZUMI /34/). The

Nusselt number relative to the droplet diameter is therein calculated by

Nr= 2 + a -R b 'Pc

NHr + Rer. Pr (3-6)

wherein different values are entered for the constants a, b and c.

This procedure requires knowledge about the representative droplet diameter and

the relative velocity between droplets and steam along the evaporation path of

the droplets. If, as already mentioned, one starts from the premise that for

each combination of system parameters there exists a value for the developed

thermal non-equilibrium, through which the course of the heating surface temperature along the flow path can be approximately determined, there can be omitted a detailed modelling of the heat transfer between droplets and steam. For

each parameter combination a value for (a • F)Tr, can then be assigned which is

assumed independently of the local steam quality and thus constant along the

flow path.

From the test values, whose parameter range was given in Chapter 2, an empirical

equation for the heat transfer coefficient and the heat-exchanging surface

between steam and water phase could be determined:

1.473 - 10-7 (;/A)1. 3 3 for ;/A 1767 - 10( F)Tr 3.078 - 10-24 . (;/A)4 for i/A > 1767 103(

Herein, m is the mass velocity and A the Laplace constant.

From a heat balance the actual steam quality can be determined:

kh h' (3-8)

Real Ahv + cD A&uu 

Here, h is the enthalpy of the flow, which depends on heating and mass flow and

is determined with the aid of a heat balance.

24
In case that no superheating of the steam exists, i.e., the water droplets and

the steam are in thermal equilibrium, equation (3-8) becomes the definition

equation for the steam quality according to the balance:

Bil - h' (3-9)

Ah v

For the definition of the thermal non-equilibrium there is frequently used the

non-equilibrium factor i which represents the ratio of the actual steam quality

to that of the balance:

XReal - (3-10)

k Bil

With equations (3-5), (3-8), (3-9), and (3-10) one obtains:

w= 2/+/1 + (4 .cq)/[Ahv(ct-F)Tr] + 1) (3-11)

In Figures 3-12 to 3-13 there are entered the thermal non-equilibrium factors,

calculated according to equation (3-11), for pressures between 50 and 210 bars,

mass velocities between 500 and 3500 kg/m 2 s and heat fluxes up to 1000 kW/m 2 .

The connection between the thermal non-equilibrium factor and steam superheating

can be gathered from Figure 3-14.

Figures 3-12 to 3-14 can serve for the rough determination of the steam superheating with developed thermal non-equilibrium.

For the determination of the wall temperature there is still need for the heat

transfer coefficient between the steam flow and the tube wall. For this the

GNIELINSKI /36/ equation proven for simple-phase flow is used:

(t/8) - (Re - 1000) • Pr

NU = (3-12)

1 + 12.7 4T (Pr2/ 3 - 1)

where

= (1.82 • loglo Re - 1.64)-2 (3-13)

The Reynolds number is formed herein with the mean velocity of the two-phase

flow. If one postulates that in the post-dryout region the phase slip can be

neglected, one obtains as Reynolds number of the two-phase flow:

Re = Wd [Real + (1 Real).(pD/Pw) (3-14)

25
3500

kg/m 2

s

3000

2500

2000

Z0

_i; 1500-

%A

I1000

500

3500"

kg/m 2s

3000-

2500-

2000

0

>. 1500-

1000

So00

0.7 0,75 0.8 0.85 0.9 0.95 1.0

Non-equilibrium factor 6

0.7 0.75 0.8 0,85 0.9 0.95 1.0

Non-equilibrium factor 6s

0,7 0,75 0.88 0.85 0.9 0.95

Non-equilibrium factor (c

1.0 0.7 0.75 0.8 0,85 0.9 0.95

Non-equilibrium factor 6

1.0

Figure 3-12 Determination of the thermal non-equilibrium factor

The Reynolds number determined with equation (3-14) is identical with the Reynolds number given in Chapter 6, equation (3-18), for the determination of the

pressure loss with unwetted wall. For the determination of the pressure loss

and also for the determination of the heat transfer in the post-dryout region

it is assumed, that the properties of the steam determine the momentum and heat

exchange with the heating surface.

As reference temperature for the characteristic values in equation (3-12)

there has to be used the mean boundary layer temperature, which is obtained

from the arithmetical mean of the steam and wall temperatures.

26
a

aJ

In

I,,

'UE

0

aJ

In

In

'U

0.7 0,75 0.8 0.85 0,9 0.95 1.0

Non-equilibrium factor 6

0.7 0.75 0.8 0,85 0.9 0.95 1.0

Non-equilibrium factor 6

0.7 0.75 0.8 0.85 0.9 0.95 1.0

Non-equilibrium factor 6

0.7 0.75 0.8 0.85 0.9 0.95 1.0

Non-equilibrium factor 6i

Figure 3-13 Determination of the thermal non-equilibrium factor

Finally, one obtains the wall temperature from the sum of the saturation

temperature Ss, the superheating temperature of the steam A&u and the wall

excess temperature q/aD of the steam flow:

"W= 8S +, 11u + /CD (3-15)

3.3.3.2 The Heat Transfer at the Region Boundaries

The post-dryout region in an evaporator tube is bounded on the side with low

enthalpy by the wetted part of the evaporator with nucleate boiling or

27
.3

4-

0 1.00-

%4--

E

:-

t.0E

0

0.90

0.80

Pressure: 210 bar 200 190 180 170 150 130 100

0.70 --

100 2 3 4 6 8101 2 3 4 6 8102

Stea

Figure 3-14 Determination of the steam superheating

2K3

superheat

28
convective boiling and on the side with higher enthalpy by the region of the

one-phase steam flow.

Up to the location of the boiling crisis (XKr), the flow is practically in

thermal equilibrium, i.e., water and steam have the same temperature. After

the location of the boiling crisis, the tube wall is unwetted and is essentially

cooled by the steam which thereby heats up. Since the entrained water droplets

remain at saturation temperature, the temperature difference between the water

and steam phase increases until at the location of the minimum heat transfer

(Xa min) the thermal non-equilibrium is fully developed (Figure 3-15). With a

further enthalpy increase the wall temperature decreases again because of the

better steam cooling due to an increasing steam velocity.

Temperature I

. . . . . -

Wait temperature

- Steam temperature

Saturation temperature

I .

Xcr X-M

---- Steam quality

Figure 3-15 Development of the thermal non-equilibrium

The following method is suggested for the calculation of the location of the

minimum heat transfer:

From the location of the boiling crisis to the location of the minimum heat

transfer it is assumed, that the entire supplied heat is used for the

heating-up of the steam originated until then.

Thus, from the energy balance the value min ), can be determined at which

the steam attains the superheating temperature which corresponds to the

developed thermal non-equilibrium:

29
XKr CDA& u

Xamin = XKr + Ahv

In Figure 3-16 the thus calculated difference of the steam mass quality between the location of the minimum heat transfer and that of the boiling crisis was compared. Calculation and measurement show, that with increasing

mass velocity this value decreases, while it is the opposite with the

influence of the heat flux.

By way of comparison, in Fig. 3-16 there was plotted a curve from HEIN et al.

/22/, which is based on a statistical evaluation of the measurement results.

The described calculation model for the determination of the wall temperatures has to be modified at the transition to the simple-phase steam flow. From the

tests it can be gathered, that starting from a determined, pressure-dependent

steam quality the wall temperatures do not continue to decrease with increasing

steam quality. This is caused by the decreasing surface of the entrained water

droplets, since the two-phase flow becomes increasingly "drier." This has the

result, that the steam temperature increases and thus compensates the effect of

the better heat transfer, which is brought about by the higher steam velocity.

afim min- c

I 0.25~

i( (kg/m2sI Measured Calculated

values values

600- 700 E 0

1350-1430 _ 0

2000-2500 A A•

0,20- Influence of P-'I

test parameters 4 - 03 430 - 42 L CM 430 /-

440 3 j 40290

0.15 430 L. 7] '280 0 -6 280

o~o "420L .i I

* Curve acc. 60 300•60

Hein et. at. £450 6400 00300 6458O 20000

5 80 o10 150 9 20 0

•"Pressure

Figure 3-16 Difference of the steam quality between the location of the

minimum heat transfer and that of the boiling crisis

30
This effect is simulated in the calculation model in such a manner, that starting from a determined steam quality (XLim), the wall temperatures are maintained

constant until all water droplets have evaporated, i.e., until'the single phase

steam flow state is attained. The boundary steam quality is a function of the

pressure:

XLim = 0.7 + 0.002-p (3-17)

If one assumes that steam and water droplets in the post~dryout region flow

approximately with the same velocity, the steam quality XLim corresponds to a

void fraction which lies always above 0.99.

The mathematical simulation of the transition to steam flow can be gathered

from the figures in Chapter 3.3.3.3.

3.3.3.3 Model Verification

The model was verified with the aid of 368 comparison calculations with heat

transfer tests of HERKENRATH /37/ and tests on the BENSON test rig. Figures

3-17 to 3-20 show typical comparisons between calculation and measurement with

vertical flow. In the upper halves of the figures are represented wall temperatures with low mass velocities in the bottom part of the wall temperature

with high mass velocities.

With horizontal flow, the heat transfer in the post-dryout region can be well

simulated if there is no influence of the tube orientation on the heat transfer

(e.g.; in Fig. 3-21). The conditions which lead to an influence by the tube

orientation on the heat transfer can be determined according to Chapter 5. The

location of the boiling crisis was determined with the procedure given in

Chapter 3.2.

Figures 3-17 and 3-21 show that also the development of the thermal non-equilibrium from the location of the boiling crisis to the location with the lowest

heat transfer coefficient is simulated with sufficient accuracy by the model.

The greatest deviations between calculation and measurement are caused by the

errors in the determination of the location of the boiling crisis and are therefore independent of the used calculation model for the heat transfer in the

post-dryout region. This type of comparison was chosen since it illustrates

that a calculation model for the heat transfer in the post-dryout region can be

only as good as the model with which the critical boiling state is determined.

In order to have an overview of the accuracy to be obtained with the calculation mode, Figure 3-22 shows the differences between the measured and calculated maximum wall temperatures in the post-dryout region. As abscissa the

quotient from mass velocity and the Laplace constant was chosen since this

magnitude is characteristic for the heat transfer between water and steam phase in the used calculation model (cf. equation 3-7). With this it is possible to

verify the empirical relationship for the heat transfer between steam and water

phase in a large pressure and mass velocity region.

From Figure 3-22 it can be gathered that the studied diameter range from 70 to

24 mm was well simulated by the model. Greater deviations between calculation

and measurement have to be almost exclusively attributed to tests which film

31
i,€

Li

a

oJ~

=1

mCw

E

aJ

m

Tube bore: 0.0125 m Test No.: 1029

Mass velocity: 1017.1 kg/mzs

o Pressure 51.0 bar

Heat flux: 488 kWlm2

a Measured values

- Calculated values

-- Fluid temperature

o0,

" U -U n 0 - -' ------ 1-0 - - -• - - -3 - 0-

Steam quality

0.6 0.*1 0.8 0.9 1.0

.1960.00 . I 2040.00 . . 2120.00 . . 2200.00 . . 2280.00 . . 2360.00 . ... 2440.00 2520.00 i 2600.00 2680.00 o. o . 2760.00 I I.. 2840.00.

Enthalpy (kJ/kg)

:3

0

E

Ci

T Tube bore: 0.0125 m Test No.: 1032

C Mass velocity: 2514.1 kglm2

s

- Pressure 53.4 bar

Heat flux: 594 kW/m 2

t Measured values

- Calculated values

-- Fluid temperature

0

o• "~C MO D 9 C313 O C3 0 

00

Cj

0

Steam quality

do.-C 0.5 o 6

0 ... .... v ..

I 78 0-00 1820.00 1860.00 1900.00 1940.00 1980.00 2020.00 2060.00 2100.00 2140-00 21B0-00 2220.00

Enthalpy (kJ/kg)

Figure 3-17 Calculated and measured wall temperature course with

vertical flow

32
M

0

30"0-

C- N,

E

A

C?

0-

W

0'.

Tube bore: 0.0125 m

Mass velocity: 997.0 kglm2s

Pressure : 99.2 bar

Heat flux: 4.95 kWIm2

c Measured values

Calculated values

-- Fluid temperature

Test No.: 1037

Mn Mn I Mn n ~ I n m

Mn

Dn

Steam quality

0.3 0.4 0.5 0.6 0:7 0.8 0.9

I t I I iI . 1 I | I I | I I |I I I I I T -720.00 1800.00 1880.00 1960.00 2040.00 2120.00 2200.00 2280.00 2360.00 2440.00 2S20.00 2600.00

Enthalpy (IkJ/kg)

0,

0

rL

E0

0

C,

C)

9U

C,

Tube bore: 0.0125 m Test No.: 1040

Mass velocity: 2543.2 kglm2s

Pressure : 102.0 bar

Heat flux: 589 kW/m 2

ci Measured values

Calculated values

-- Fluid temperature

- . I ------ -- - --- ----------------

Steam quality

0.3 0.4 0.5

-1160.0 180. .00 1880.004 1920.00 1960.00 2000.00 2040.00 2060.00 2120.00 2160.00 2200.00

Enthatpy (kJ/kg)

Figure 3-18 Calculated and measured wall temperature course with

vertical flow

33
0

0

0;

0

C?

0I

(V

E- 9

C?

Tube bore: 0.0125 m

Mass velocity: 1000.7 kglrm2

s

Pressure 149.9 bar

Heat flux: 496 kWlmr2

a Measured values - Calculated values

-- Fluid temperature

Test No.: 1045

0 C3 C

a1

- - -~ - U E 9 5 U

Steam quality

0.2 0.3 0.4 0.5s 0.56 a. a.s9 .e a I * *I I I I I•.

0o

1720.00 1800o.00 1880.00 1960.00 2040.00 2120.00 2200.00 2280.00 2360.00 2440.00 250o.00 2600.00

Enthalpy (kJ/kg)

0

C,=,

U

- -

Tube bore: 0.0125 m Test No.: 1048

Mass velocity: 2514.7 kglm2s

Pressure 149.4 bar

Heat flux: 601.0 kW/m2

a Measured values

Calculated values

-- Fluid temperature

Steam quality

0.2 0.3 0.4 0.5 0.6

1780.00 1820.00 1860.00 1900.00 1940.00 1980.00 2020.00 060.00 2100.00 2•40.00 218.000 2220.00

Enthalpy IkJ/kg)

Figure 3-19 Calculated and measured wall temperature course with

vertical flow

34
CL.J

E0

6-0

-4

I~0

a,-

0.0

Tube bore: 0.0125 m

Mass velocity:. 1002.3 kgrm2

s

Pressure 199.6 bar

Heat flux: 486 kWIm2

t) Measured values

Calculated values

-- Fluid temperature

Test No.: 1053

to ni

C3 -f-,,- - -- -- -- - - - - -- -- -- - In 0c 0 0

Steam quality

0.0 0.2 0.4 0.6 0.8 1.0

1840.00 1720.00 1800.00 1880.00 1960.00 2040.00 2120.00 2200.00 2280.00 2360.00 2440.00 2520.00

Enthalpy tkJlkgl

.7

CL

El

C,

-I

Tube bore: 0.0125 m Test No.: 1056

Mass velocity: 2472.4 kglm2

s

Pressure: 200.4 bar

Heat flux: 586 kWIm2

c1 Measured values

- Calculated values -- Fluid temperature

4.

CC?

LO

•- Stea nuait

o.2 4g- 0 -e o.4 0.- -V - rI - -

-_ .. " , , , , , ,

1900.00 1940.00 1980.00 2020.00 2060.00 2100.00 2140.00 2180.00 2220.00 2260.00" 2300.00 2340.00 Enthalpy (kJIkg)

Figure 3-20 Calculated and measured wall temperature course

with vertical flow

35
0

C?

(0

CL

EC

0U

0IC,

Tube bore: 0.0243 m Test No.: 3066

Mass velocity: 2393.8 kgmr2

s

Pressure : 52.1 bar

Heat flux: 594 kW/m 2

Measured values: & top

o lateral

o bottom

C (alculated values

-- Fluid temperature

3 S 

- - -- • - - - - - - - - - - - -•- 

0- 4Steam quality 0.O-

" .. .I .. . .T - O. 0 18co.o0 ;820.00 1840.00 1860.00 1880.00 1900.00 1920.00 1940.00 1960.00 1980.00 2000.00 2020.00

Enthalpy (kJIkg)

M

0

E

0-

3:

Tube bore: 0.0125 m Test No.: 2066

M Mass velocity: 2467.4 kglm2

s D Pressure : 50.3 bar - Heat flux: 605 kW/m 2

0

8- Measured values: &top

Olateral

obottom

oo

6 - Calculated values

- Fluid temperature

C,

:13

Steam quality 0.4 0.5 . 0 ... .. ..

|

1640.00 1688000 1720-00 1760-00 180000 1840.00 1880.00 1920.00 1960.00 2000.00 2040.00 2080.00

Enthalpy (kJ/kg)

Figure 3-21 Calculated and measured wall temperature course

horizontal flow

36
Wmax measured -

It

•rmax calculated

0 1.106 2-106 3-106 4.106 5.106

a-, Mass velocity /

6.106 ý 2 s 7.106

m Laplace constant

Figure 3-22 Comparison between calculated and measured maximum wall

temperature in the post-dryout region

boiling occurred. The location of the boiling crisis shifts thereby to very

low or even negative balance steam qualities, and parameter combinations are

obtained which lie beyond possible operating conditions of a fossil-fired steam

generator.

In view of the maximum wall temperature, 88% of all dryout tests of the

calculation program are verified with an accuracy of ±40 K. The mean value of

the deviations between the measured and calculated maximum wall temperature is

5.8 K. Standard deviation as well as the RMS error amount to 26K, and 27 K.

Figures 3-23 to 3-26 show examples for the course of the heat transfer

coefficient as function of the flow enthalpy, calculated with the described

model, respectively of the balance steam quality. In the region of the

saturated nucleate boiling the JENS and LOTTES /38/ equation was used and in

the single-phase region the GNIELINSKI equation /36/.

37
0

Li

L.

0J

U,

1V0

8 Tube bore: 15 mm

6 Pressure : 50 bar

5 Mass velocity: 500 kg/m 2s 4 Heat flux IkW/m 2

):

3 0 100

& 200

2 + 300

105

8

6

5

4 I

3 __ _ _ _ _ _ _ _

2 0

1() ff, I J I , I

8 /

6 1

5

4

3

2

Steam quality

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

ins- .. I . I'

15O0 2000 2500 kJ/kg

Enthalpy

3000

W/ G

W/m2

K 8

6

5-

4

3

2-

T r

Tube bore:

Pressure :

Mass velocity:

Heat flux (kWlrnm):

0 100

& 200

+ 300 >c 400

c4 500

15 mm

50 bar

2500 kg/m2s

as

04

r105-

8-

6-

5

4

3

2'

- ~ 600 4- 4

r'~~1~h

AUf III ///I/ III

8

6

5

4

3

2

Steam quality

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 103, ,t t ! I it I ' i I C

1000 1500 2000 2500 kl/kg

Enthalpy

3000

Figure 3-23 Calculated heat transfer coefficients

38
106

W/mK 8

6

5-

4

3

oJ

2-

0

r 1

Tube bore: 15 mm

Pressure : 100 bar

Mass velocity: 500 kglm's

Heat flux (kW/m 2):

+ 300

C-

'U

C4•

8 I

6

5

4

3 :

2

6

5

4 -

3

2-

Steam uality

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Id. 1 .. I . I

1000 1500 2000 2500 k/kg

Enthalpy

3000

W/m'K 8

6-

5-

2- 4 .=u 3-

z2-

Tube bore: 15 mm

Pressure : 100 bar

Mass velocity: 2500 kglm2s

Heat flux (kW/m2]:

0100 I

& 200 I

+300 I

x 400 I

0500

- 4 600 -4 CU

'A

10•-

6-

5.

4.

3-

2..

" III

'i

10'-

6-

5-

4

3

2

Steam quality

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 itns . I . 'II I

1000 1500 2000 2500 k],g

Enthalpy

3000

Figure 3-24 Calculated heat transfer coefficients

39
W/m'K

cJ

oJ

0

aJ

In

C

ci

=

106

8 Tube bore: 15 mm

6 Pressure : 150 bar

5 Mass velocity: 500 kglm 2

s 4- Heat flux (kW/m 2

):

3 . 0100

& 200

2- +300

105

8 r

6

5

4 -

3

2

8

6-

5

4

3

2

Steam quality

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

low0 1500 2000 2500 kl/kg 300

Enthalpy

1fl. 1

W m'K 8

6

5-

4-

"- 32

A:! 2

Tube bore:

Pressure :

Mass velocity:

Heat flui (kW/m 2J:

0 100

,& 200

-+-300

x 400

0 500

4 600

r":--

15 mm 150 bar

2500 kglm2s

C,

0

h

5 -

4 -

3-

2

/

!!

V! 5--ý

6-

5-

4-

3-

2-

Steam quality

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

l .. t ' i 'I 'II 'I '| 

1000 1500 2000 2500

E O/kg

nthalpy

3000

Figure 3-25 Calculated heat transfer coefficients

40
=.o

W/mV'K

14

aJ

0

1DL

8 Tube bore: 15 mm

6 Pressure : 200 bar

5 Mass velocity: 500kglm2

s 4 Heat flux (kW/m 2 ):

3 0100

&. 200

2 - + 300

6

5

4

3

2

101-

8

6

5

4

3

2

Steam quality

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

IDOO 1500 2000 2500 k3/kg 30C

Enthalpy

W/m2K 8 -

6-

5-

4-

.~3.

;= 2-

Tube bore:

Pressure :

Mass velocity:

Heat flux (kWlm2 j:

0 100

,& 200

+ 300

X400

0 500

4 600

15 mm

200 bar

2500 kglm2

s

ci F- 0

IA)

105-

8-

6 -

5 -

4-

3-

2J

J#l -It-ti- +

JA

8-

6

5

4

3-

2

Steam quality

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Vol _ I I I I I I I I I __I

1000 I I #l a

1500 2000 a 25;0 6g

Enthalpy

3000

Figure 3-26 Calculated heat transfer coefficients

41
4 PRESSURE AND ENTHALPY TRANSIENTS

4.1 Transient Behavior of an Evaporator Tube

If a fluid in an evaporator tube is fully converted into steam by supplied

heat, flow patterns and heat transfer regions are transversed from the

simple-phase fluid flow via the various regions of the two-phase flow up to

the simple-phase steam flow. Chapter 3.1 describes the flow patterns and heat

transfer regions occurring in a vertical upflow evaporator tube uniformly

heated along its length. Of special interest in connection with transient

process is the location of the boiling crisis and the heat transfer in the

post-dryout region.

During tests on the heat transfer in the post-dryout region it was observed,

that during the transfer from one steady state to another one there could

temporarily occur wall temperatures that are higher than expected according to

the knowledge on the steady state heat transfer conditions. The expected

steady state occurred only after a rather long period of time. This phenomenon

was always observed when, due to the parameter for the newly developing state,

the location of he boiling crisis had to be shifted toward the tube outlet,

i.e., in a tube section which previously was unwetted. Tests were conducted

for the analysis of this phenomenon, in which by a decrease of the pressure

from the supercritical pressure region there had to be initiated a wetting process; of which, by decreasing the enthalpy of the flow at the test tube inlet,

shifted the location of the boiling crisis farther to the tube outlet.

The transient-processes were investigated with the BENSON test layout, described

in Chapter 2. The test installation was somewhat modified for this purpose

(Figure 4-1). The transients were simulated by the following measures:

1. Decrease of system pressure

The pressure in the system was decreased in gradients of 5 to 20 bars per

minute through the injection of cold water into the pressurizer.

The other system parameters, such as the discharge flow of the pump and

the heating of the measuring section were not modified.

2. Enthalpy decrease at the test tube inlet

The enthalpy at the test tube inlet was reduced by 200 to 400 kJ/kg by

reducing the preheating capacity. The discharge flow of the pump, the

system pressure and the heating of the test tube were maintained

constant.

In both transient processes could be observed a partially considerable

worsening of the heat transfer in the post-dryout region. It was especially

significant and present over an extended period of time when the pressure,

respectively enthalpy, decrease occurred in the proximity of the critical

pressure.

42
t

Pressurizer

Spray

condenser

Reducing valve I Heating

capacity

1000 kW

45 Thermocouples

Test tube

6 m long

18 x 2 mm

Preheater

t

Piston pump

Figure 4-1 Test layout for the simulation of transient processes

43
Figure 4-2 presents a typical process of measured tube wall temperatures after

a pressure decrease from the super critical pressure region. In its initial

state at 247 bars, i.e., in the supercritical state, the tube has wall

temperatures ranging from 380 to 400*C over its entire length. After 165 s, a

temperature profile developed which, with an enthalpy of 1750 kJ/kg, presented

a steep temperature increase as indication of the location of the boiling

crisis. During the further course, the location of the boiling crisis shifted

in flow direction, whereby the maximum temperature decreases again and after

more than 600 s attains a steady state with a maximum temperature of about

4300C.

Figure 4-3 shows a detailed analysis of the test. In the diagrams, the

measured values are compared with the calculated values which were obtained

with the aid of a computer program /39/ for the simulation of dynamic processes

in a steam generator. In the verification of the calculation it was assumed,

however, that the transient process in respect to the heat transfer can be

represented as a series of quasi-steady states. This means that although the

conservation equations for mass, momentum and energy as well as the storage

and release processes of the tube wall were taken into account, for the determination of the boiling crisis it was assumed that it can follow unimpeded the

changing conditions in the tube.

In the initial state with supercritical pressure there is good agreement

within the expected accuracy between the measured and calculated maximum wall

temperature. Also the time slope of this maximum temperature is of similar

course during the first 100 s. If the system pressure falls below the

critical pressure the calculated maximum wall temperature increases to 440%C

and maintains this value up to the end of the experiment. On the other hand,

the maximum wall temperature rises to approximately 550'C in the experiment

and attains the calculated value after about 600 s, when the new equilibrium

condition sets in. The time slope of the enthalpy at the location of the

boiling crisis, also shown in Figure 4-3, contributes to the understanding of

this process. From the heat balance the enthalpy at the location of the

boiling crisis which existed in the experiment was determined. While

throughout the entire test time the calculation shows a constant value, which

lies above the saturation enthalpy of the water, the enthalpy at the location

of the boiling crisis increases constantly in the experiment and, in the time

frame between 100 and 300 s, lies below the saturation enthalpy. Thus, in the

case of a pressure reduction from the supercritical pressure region, tube

sections with very low and even negative balance steam quality attain the

unwetted state. This means that film boiling can occur and that the velocity

of the two-phase flow at the location of the boiling crisis is considerably

reduced in respect to the steady state, whereby the cooling effect is reduced

and the wall temperature increases correspondingly.

Through the enthalpy decrease at the inlet of the test tube there is caused a

temperature excursion of similiar effects. Figure 4-4 shows a typical course

of the tube wall temperature after a sloping decrease of the inlet enthalpy.

While in this case there could be expected a shifting of the temperature profile

at the time 0 in the flow direction, the maximum temperature increases from

about 4000C to about 480*C and it is only after 800 s that it approaches again

the value of the initial state. During this period, the location of the boiling

crisis shifts in the flow direction toward the tube outlet.

44
Temperature

550-

oC

Mass velocity: Heat flux:

Tube bore:

1*

1

I

I

I

A

500-

450-

Time (s)

0 0

o 65

A 165

+ 265

× 365

<> 465

*565

* 665

2000 kg/m 2s

619 kW/m 2

14 mm

Pressure (bar)

247

223

196

191

191

191

191

192

-ttl

I x

I +

I I

I 4-

130

tIII

I I I

000

A IA

+ ++++XX XO0O>O

/ k + X

+ 4AAA•o

0 8I888@0 6 ~0000

0 S+ 0000 0 400- 06

0o0

+

U1 i" / , i I

35:n I

'1600 1 1800 2000 kJ/k 9g 2200

P--+ Enthalpy

Figure 4-2 Course of the tube wall temperatures with pressure decrease
t 540 Maximum watt temperature 0C0

500

460 Calculation

420 Measurement

380

2200- Enthalpy at location of boiling crisis

~ kJ/kg2000. Calculation

~h'

1800-

-\-Measurement 1600 , , , , ,

t 250

bar System pressure

230 Mass velocity: 2000 kglm2s

PC. Heat flux: 619 kW/m 2

Tube bore: 14 mm

210. Rate of change

of pressure' 0.34 barls

190

o 160 200 360 400 560 660 700 s 80c

0- Time after initiation of pressure

reduction

Figure 4-3 Course of thermal and fluid dynamic magnitudes with a pressure

reduction in. the proximity of the critical pressure

)

46
Temperature

500t

OUj

450-

400-

Mass velocity:

Pressure:

Heat flux:

Tube bore:

Time (s)

o 0

& 100

+ 200

x 300

* 400

+ 500

600

z 700

Y 800

2007 kg/m2s

200 bar

595 kW/m 2

14 mm

x

+

-4 6

0

00 0o o

350

SX •-Saturation temperature

I p 300

0 0,25 0,50 0,75

- Steam quality at test begin

Figure 4-4 Course of the tube wall temperature with enthalpy decrease
Through a calculation with the described computer program in this case it is

possible to separate the expected effects from the processes to be studied.

Thus, it can be gathered from Figure 4-5 that, due to the enthalpy decrease

during the time period of 0 to 200 s, there occurs a reduction of the mass

flow in the test tube although the discharge flow of the pump remains constant.

This temporary mass flow decrease can be attributed to a "filling process" because due to the throttling of the supplied heat in the preheating region the

steam quality in the piping is reduced and thus the volume flow in the test

tube decreases although the enthalpy at the inlet of.the test tube has not yet

decreased. This mass flow reduction causes in the calculation a corresponding

increase of the maximum wall temperature during this period of time. In the

experiment, however, the wall temperature reaches the maximum value only then,

when the mass flow has again reached its initial value. Also in this case it

can be deduced from the comparison of the enthalpies at the location of the

boiling crisis, that the considerable increase of the wall temperature has to

be attributed to the non-wetting of the heating surface, since the wetting process is delayed in respect to the steady state. The location of the boiling

crisis does not shift in the tube outlet direction with the velocity which

would correspond to the changed flow enthalpy. Therefore, the enthalpy at the

location of the boiling crisis drops for a time range of 180 to 650 s below the

saturation enthalpy of the water. It can be seen from Figure 4-4 that in this

range the highest wall temperatures occur.

With the help of the course of the boiling curves of the heating element - fluid system there shall be interpreted the temperature excursions observed

during the described transient processes.

4.2 Interpretation of the Transient Processes with Help of the Boiling Curve

For pool boiling NUKIYAMA /40/ presented for the first time the connection

between heat flux and wall temperature for the various heat transfer regions

in a curve. In contrast to the conditions in an evaporator tube, where the

boiling crisis is brought about by dryout, with pool boiling film boiling

occurs after the exceeding of the critical heat flux. However, the connection

found by NUKIYAMA between heat flux and wall temperature can be qualitatively

applied also to the forced convection conditions. Figure 4-6 shows the

schematic course of the Nukiyama curve or boiling curve of the heating element

- fluid system.

In the case of a wall temperature controlled system, the boiling curve can be

traversed with increasing and decreasing wall temperatures in the same manner

without hysteresis. If the wall temperature increases, boiling occurs on the

heating surface after the convection region. Boiling crisis occurs it the

critical heat flux is reached. The transferred heat flux decreases now with

increasing wall temperature.

The heating surface is intermittently wetted and thus this heat transfer

mechanism is characterized by unstable film boiling. Stable film boiling occurs

if the Leidenfrost temperature is exceeded and a wetting is no longer possible.

On the other hand, a decrease of the wall temperature below the Leidenfrost

temperature leads to intermittent wetting processes until the heating surface

is fully wetted.

48
I 2000'

kg/m 2 s

1750-

.............. ..............

...............

.................... ....................

...................

................. ..........

...............

.............. ..............

............. ............

. WMass ve:to:city in

test tube

Pressure:

Tube bore:

Heat flux:

200 bar

14 mm

595 kW/m 2

Enthalpy reduction: 390 kJ/kg

1500 I

0 100 I 1 6

200 360 460 500 600 760 s 800 - Time after preheater power reduction

Figure 4-5 Course of thermal and fluid dynamic magnitudes with an enthalpy

decrease in the proximity of the critical pressure

49
In contrast, the attaining of the critical heat flux in a heat flux controlled

leads to a sudden temperature rise in the region of the stable film boiling and

a fall below the Leidenfrost temperature leads to a sudden temperature drop

with complete wetting of the heating surface. A cycle with heat flux increase

and subsequent reduction leads thus to a marked hysteresis in the heat flux

wall temperature course. However, also in a heat flux controlled system the

only possible conditions are those that lie on the boiling curve. It has to be

considered however that, when reaching the critical heat flux, the sudden rise

of the heating surface temperature is connected with an energy storage in the

heating element and that, when falling below the Leidenfrost temperature, the

sudden decrease of the heating surface temperature is connected with an energy discharge from the heating element. The course for a heat flux controlled

system, shown in Figure 4-6 by a broken line, can thus be characterized only as

an apparent boiling curve.

Heat flux

-- Wall temperature - Saturation

temperature - Watt temperature controlled

---- Heat flux controlled

Figure 4-6 Connection between heat flux and wall temperature with pool

boiling (boiling curve)

Additional influences occur for the determination of the boiling curve under

forced convection conditions. Figure 4-7, which was taken from /41/, shows

that in a uniformly heated evaporator tube there cannot be observed a

50
hysteresis in the heat flux-wall temperature course with an increase and a

subsequent decrease of the heat flux. Quasi-steady state changes of operating

parameters cause hereby a shifting of the location of the boiling crisis

according to the thermal and fluid dynamic state of the heating surface-fluid

system in the evaporator tube. The shifting of the location of the boiling

crisis is made possible by axial heat conduction from the unwetted to the

wetted tube wall, whereby an apparent boiling curve without hysteresis is

simulated.

Watt temperature

TI

z

B -A

I

I

I

_ -T-T-aturation temperature 1--

0:1 *0 0 M=4 **.

Heat

I

flux

I

B jI

Increasing heat flux .

Decreasing heat ftux

I mJ

Apparent boiling curve

at position Z

I

-- Wall temperature

Figure 4-7 Boiling crisis in a uniformly heated evaporator tube

51
If the influence of the axial heat conduction is excluded, there can be

observed a hysteresis in the heat flux wall temperature course also under

forced convection conditions. Figure 4-8 (taken from /41/) shows the result

of an experiment with a nonuniformly heated evaporator tube. At first, both

tube sections are heated with the same heat flux (q1 = q2 ) in such a manner,

that the boiling crisis occurs at the end of the first tube section and that

the second tube section lies in the unwetted region. Through a reduction of

Wall T.temperature z

A

-- 7-7s-tSaturation temperature

"0 0 ID 0.

A it it it it it it it it ~

Heat flux

I A

B7

Apparent boiling curves at

position Z:

m

- Increasing heat flux

Decreasing heat flux

Decreasing wall temperafure

-* Wall temperature

Figure 4-8 Boiling crisis in a nonuniformly heated evaporator tube

52
the heat flux of the second tube section (q 2 < qj) there can be obtained the

broken curve in the heat flux-wall temperature course, which is distinctly

different from the solid line for increasing heat flux.

One obtains a similar result, if the second tube section is provided with a

good heat-conducting storage mass and if after the superheating the second

tube section is no longer heated. The released heat flux can be then

determined from the rate of temperature drop of the storage mass and it shows

a course (dot-dash line) which approaches very closely that of the boiling

curve for pool boiling.

If one applies the findings from the course of the boiling curve under forced

convection to transient processes, it is possible to present the pressure

reduction from the super-critical pressure region according to Figure 4-9. In

the initial state with supercritical pressure there will set-in the operating

point A corresponding to the chosen heat flux. After the pressure reduction,

the local boiling curve allows a stable operating point (B) for the position Z

in the unwetted region and a stable operating point (C) in the wetted region.

It depends on the temperature in the initial state which operating point

occurs. If this temperature should be higher than the Leidenfrost temperature,

at first there will not occur any wetting of the heating surface and in the

opposite case wetting will occur. For the position Z shown in Figure 4-9, at

first will occur film boiling after the pressure reduction. The steady state

operating point C is finally attained by a wetting process, in which through

axial heat conduction from the unwetted to the wetted heating surface there

occurs a passing of the boiling curve from B to C.

Figure 4-10 shows the influence of an enthalpy reduction on the local boiling

curve and the course of the wall temperature. To the axial position Z, which

prior to the enthalpy decrease lies-in the unwetted part of the evaporator and

after the enthalpy decrease in the wetted part, can be assigned two boiling

curves which indicate the possible operating points prior to and after the

enthalpy decrease. In the initial state, at position Z the critical heat flux

is exceeded and the operating point A lies in the unwetted region. If the

local enthalpy is reduced, the boiling curve allows for position Z a stable

operating point (B) in the unwetted region and a stable operating point (C) in

the wetted region. Since, because of the reduced steam velocity, the cooling

is worse after the enthalpy decrease than in the initial state, the heating

surface temperature increases at first form A to B. The steady state operating

point C is attained, same as after the pressure drop, through a wetting process

whereby is made possible a passing of the boiling curve from B to C.

4.3 Influence of the Leidenfrost Temperature

Since the rise of the heating surface temperature has to be attributed to a

delayed wetting of the heating surface in respect to steady state, an advancing

of the wetting front, which separates the wetted from the unwetted tube section, has a strong influence on this process. The advancing of the wetting

front, which is based on the axial heat conduction in the tube wall, can be

calculated according to a model by YAMANOUCHI /42/.

Therein it is assumed, that for the determination of the velocity of the

wetting front the heat transfer in the unwetted region can be neglected in

53
Wall temperature

I /

/

/

/ Transient f

/

/

B 6-

Steady

A state

C /

z -* Tube length

Wall temperature distribution - before

---- after pressure reduction

Heat flux 1T

-- + Wall temperature-Saturation temperature

Local boiling curve at position Z -- before eafter pressure reduction

Figure 4-9 Influence of the pressure reduction on the course of the wall

temperature and the local boiling curve

respect to that in the wetted region (Figure 4-11). By solving the

one-dimensional, non-steady heat conduction equation, YAMANOUCHI obtains for

the velocity of the wetting front

54
1 a X

(&C L 

-S) (4-1)

p, c and X are the values of the wall material, 6 is the wall thickness of the

tube and u is the heat transfer coefficient in the wetted region. a., is the

temperature of the wall material in the unwetted region.

Wall

temperature I

• I

/

I

pTransient

B/

C 1 Steady state

S..a.....tuaiontem ert

Saturation temperature e

.1.

Wall temperature distribution

- before _ L_, ..... -

z --- Tube length

_J..*__

---- after eontalpy reduction

Heat flux

I~

Local boiling curve at position Z - before

---- after enthalpy reduction

- Wall temperature -

Saturation temperature

Figure 4-10 Influence of an enthalpy decrease on the course of the wall

temperature and the local boiling curve

55
Wetted

zone

ai

.4-

CEI

CU

CU

Ma

L Unwetted

zone

Wall temperature in

unwetted zone (.o,, I /

atuting temperature ( 9L)

.aturation S'. temperature ( ýas.)

x >> 0

o= 0

4

c~ Q

Figure 4-11 Wetting process according to the YAMANOUCHI model

56
*Equation (4-1) shows that the velocity of the wetting front depends greatly on

the difference between the Leidenfrost and the saturation temperatures.

If the Leidenfrost temperature is considerably higher than the saturation

temperature of the fluid, the wetting front can follow the fluid-dynamic changes

of the system and the transient process behaves quasi-steady in respect to the

heat transfer. Otherwise, the wetting front velocity drops considerably.

The dependence of the Leidenfrost temperature on the pressure was experimentally

determined by HEIN /43/ for water and the model medium R 12 based on the cooling

curves of a submersible probe. While for R 12 it was possible to investigate

the pressure dependence up to the critical pressure, due to the design limits

it was possible to conduct the experiments with water only up to a reduced pressure of 0.32. From Figure 4-12 it can be gathered that in R 12 the Leidenfrost

temperature in the lower pressure region lies approximately 30 to 50 K above

the saturation temperature and in the high pressure region only approximately 4

K. Also, from the results presented in the same figure it can be seen, that

with increasing pressure there occurs an approximation of the Leidenfrost temperature to the saturation temperature, and that in the high pressure region

also for water there can be qualitatively started from a similar course of the

Leidenfrost temperature as in the case of R 12.

Also measurements of the wetting temperature with forced convection, which were

conducted by KEFER /44/ up to a pressure of 220 bars, show the approximation of

the Leidenfrost temperature to the saturation temperature in the proximity of

the critical pressure (Figure 4-13). Due to the higher turbulences, however.

the measured wetting temperatures are herein higher than the values determined

with a submersible probe.

The approximation of the Leidenfrost temperature to the saturation temperature

in the proximity of the critical pressure is thus responsible for the observed

wall temperature excursions. On the other hand, during transient processes in

the low pressure region there were measured only rises of wall temperatures

which, taking into account the mass dynamics or changes of the material

values, can be attained by calculations.

4.4 Mathematical Model for the Determination of the Influence of Pressure

and Enthalpy Transients on the Heat Transfer

As shown in the foregoing chapters, a decrease of the heat transfer takes

place if the wetting front cannot follow the thermal and fluid-dynamic changes

of the system during the transient.

While the system magnitudes, such as pressure-, enthalpy-and mass flow course

can be determined with the aid of computer programs taking into consideration

the storage processes, the location of the boiling crisis for the steady state

can be calculated according to Chapter 3.2.

Equation (4-1) can be used in principle for the determination of the wetting

front velocity. Therein there has to be known for each moment the temperature

of the wall material in the unwetted region, the Leidenfrost temperature as

well as the heat transfer coefficient in the wetted region. For the availability of these magnitudes there is required a numerical calculation method with

accurate time and local discretization.

57
Wetting

temperature

Wetting

temperature 1T

120

oc

100 K IPc

o0

<3c

•A

9-0 Saturation temneratur'E

60 x __ - --. . - .

40_

2 0-Z 1 __Medium: R12

0 5 10 15 20 25 30 35 bar 40

- Pressure p

400

+c +

+

300 8+ + + + + 3• IF + + +

+

250 1- -

0

U

- - .•Saturation

i I

temperature

200

150

+ 4 4 4 -4

/ 4 -4- 4 4 4

/ Medium: H2 0

I I 100

T1

0

t 1 4 -. 4

10 20 30 40 50 60 bar 70

Pressure p

Figure 4-12 Dependence of Leidenfrost temperature on pressure

58
dO0

700

600

C_ Wetting temperature

c- 500

i .Critical point

400

300

Saturation temperature

200 -

100

0

0 20 40 60 80 100 120 140 160 180 200 220 bar

Pressure

Figure 4-13 Course of the Leidenfrost temperature with forced convection

From the experimental values there was determined an empirical relationship

for the progress of the wetting front. With the aid of the known magnitudes

from equation (4-1) it is possible to apply the result to a tube geometry with

different material values and different wall thickness.

From the measured wetting front velocities there can be derived the following

statements:

1. The wetting front velocity is independent of the extent of the enthalpy

or pressure decrease and it is also independent of how quickly this

change takes place. However, the transient has to occur at least so

quickly, that the wetting front cannot quasi-steady follow the process.

Otherwise, the wetting front velocity can be determined from the

locations of the boiling crisis for the intermediate states that are to

be considered steady.

2. If the ratio of supplied heat flux to the mass flow remains constant, the

wetting front velocity remains also constant. This can be attributed to

the fact that the wall temperature in the unwetted region remains constant

at the first approximation if the ratio of the heat flux to the mass flow

is not changed. If one assumed that the Leidenfrost temperature and the

heat transfer coefficient is the wetted region remain unchanged for the

considered parameter change, from equation (4-1) it can be gathered that

59
the wetting front velocity cannot change if the wall temperature in the

unwetted region is of a constant value.

3. In a semilogarithmical plot it is possible to represent the influence of

the pressure on the wetting front velocity as a straight line. The

wetting front velocity drops considerably with increasing pressure, which

is caused by the approximation of the Leidenfrost temperature to the

saturation temperature.

Taking into account these statement and the material value and geometry

influence of equation (4-1) there was formulated the semi-empirical equation

(4-2) for the determination of the wetting front velocity:

u = 27.35 • --I- . ( e- 0

O 0 1 9 "p (4-2) p'c

Herein p, c and X are the values of the wall material and 6 the wall thickness

of the evaporator tube. m, q and p are the operating parameters mass

velocity, heat flux and pressure.

The influence of the values of the wall material (p, c and X) as well as the

wall thickness 6 of the evaporator tube were taken from the YAMANOUCHI model

(equation 4-1).

The factor (;/ý)2 in equation (4-2) was empirically determined. If one

assumes, that the wall temperature in the unwetted region is considerably

higher than the saturation temperature and the Leidenfrost temperature,

according to equation (4-1) the wetting front velocity becomes approximately

inversely proportional to the difference between wall and saturation

temperature in the unwetted region.

u ~ VOCW - as) .(4-3)

If, as with single-phase flow, the heat transfer coefficient in the unwettd

region were approximately proportional to the mass flow and independent of the

heat flux, according to equation (4-3) it follows

u ~ (4-4)

However, in the post-dryout region the heat transfer coefficient increases

more than proportionally with increasing mass flow and decreases with

increasing heat flux. This can be attributed to the thermal non-equilibrium

between steam and water droplets (cf. Chapter 3) and explains the dependence of

the wetting front velocity on the mass and heat flux, as determined by

equation (4-2).

Also the influence of the pressure was empirically determined by equation

(4-2) with

u ~ 0."019"p (4-5)

60
According to YAMANOUCHI (equation (4-1)) the wetting front velocity is approximately proportional to the difference between Leidenfrost and saturation

temperature

u &L - " &S (4-6)

This difference decreases with increasing pressure. This is taken into account

in equation (4-2) by the described pressure dependence.

As shown by Figures 4-14 and 4-15 it is possible to verify the measured wetting

front velocities with sufficient accuracy by equation (4-2). The comparison

was based on experiments with a stainless steel tube with a wall thickness of

6 = 2 1 O-3m.

0.1 _0.1

Heat flux Heat flux

rn/s kWmd IkW/mW I

o I d 200 0 . 1 600

- Calculation -- Calculation

Heat flux: Heat flux:

aj>

• o.oi P C o

>: 22 kW:60 k/m

Mass velocity: 1000 kglm2

s Mass velocity: 2000 kglm2

s

0 001 20 001

ISO 160 170 180 190 200 bar 210

Pressure

150 160 170 180 190 200 bar 210

Pressure

Figure 4-14 Wetting front velocity with a pressure drop

61
Enthalpy reduction Heat flux

200 kJikg 

kW/m "

o 1 1 I00

0 1 300

Enthalpy reduction Heat flux

kJ/kg kW/mz

S 11 300

0o 600 I

0.1

Cn0.0

1.0

rn/S

_o 0.1

a.,,

3 0.01

0.001

50 100 150 bar 200

Pressure

so 100 ISO bar 200

Pressure

Figure 4-15 Wetting front velocity with an

enthalpy reduction

62
5 INFLUENCE OF THE TUBE ORIENTATION ON THE HEAT TRANSFER

5.1 Flow Patterns and Heat Transfer Regions

While in a vertical tube flow there is present a symmetrical distribution of

the steam and water phase over the cross-section, in the case of a tube with

horizontal flow there occurs a more or less distinct phase separation due to

the gravity effect. The heavier medium (water) flows preferably in the lower

tube region while the lighter steam flows above it. The greater the ratio of

the buoyant forces to the turbulent mixed forces of the flow, the greater the

difference to the vertical tube flow. This is the case with decreasing

specific mass flow or increasing tube diameter.

Figure 5-1 shows typical flow configurations in a horizontal tube. With

increasing steam quality the shown flow configurations traverse not always an

evaporator tube. With the help of flow pattern charts /45/ to /47/ it is

possible to determine which flow patterns are possible in a horizontal tube

with a d4termined parameter combination.

Bubbly flow

Plug flow

Stratified flow

Slug flow

Annular flow

ELZJ

Drop fltow

Wavy flow

Figure 5-1 Flow patterns in horizontal tube

Since the flow pattern also influences the heat transfer it has to be expected

that, if the flow patterns differ greatly with vertical and horizontal tube

orientations, there will also occur different heat transfer regions. Figure 5-2

shows a typical wall temperature course for a horizontal tube with strong influence of the tube orientation on the heat transfer. Therein can be observed the

following developments with increasing flow enthalpy:

63
Caused by a thermal convection flow occurring in a heated, horizontally

flow-traversed tube, which is superposed over the forced convection flow, the

fluid temperature, and thus also the wall temperature, rises higher on the

upper.side than on the bottom side of the tube. Boiling occurs correspondingly

earlier on the upper side. Due to the force of gravity, the originating steam

collects in the upper tube part. Stratified flow occurs and dryout of the

heating surface takes place on the upper side of the tube. Boiling was not

even attained at the tube bottom at the same axial tube position.

With increasing enthalpy the void fraction in the flow and thus the mixture

velocity increases. Slug or annual flow occurs and the upper side of the tube

is rewetted. Finally, with a further heat supply the water film breaks off,

and dries out, at first at the upper side and with a much higher enthalpy also

at the bottom side.

From the shown example it can be seen, that in a horizontal evaporator tube a

dryout of the heating surface on the upper side can occur already in the

subcooled region, while the bottom side remains wetted up to the complete

evaporation of the fluid.

If the mass velocity is greatly increased, the turbulent mixture forces of the

flow prevail and cause a symmetrical distribution of the steam and water

Mass velocity: 500 kglm2s

Pressure: 100 bar

Tube bore: 24.3 mm

Heat flux: 300 kWIm2

Wall inside temperature

t

600

oc

500

400

300

0 0.1 0,2 0.3 04

200 -

800 1000 1200 1400 1600 1800 2000 2200 .2400 2600 kI/kg 3000

- Enthalpy

- - - - - - - - - - - - - - - - - - -------

06

Figure 5-2 Influence of gravity on the heat transfer in horizontal tubes

64
phase. Thus, the wall temperature on the upper and the bottom sides of the

tube have the same course. Figure 3-21 is an example of this. The heat

transfer regions are therein identical with those in the vertical tube.

5.2 Heat Transfer in the Wetted Region

In the horizontal tube, with certain parameter combinations, there were measured

great temperature differences between the upper and the bottom sides of the

tube in the region of the water flow. From Figure 5-3 it can be gathered that,

with a mass velocity of 500 kg/m 2 s and a heat flux of 300 kW/m 2 , these temperature differences amount to approximately 40 K. The measured wall temperatures

with vertical flow, which were also entered in the Figure, lie between the temperatures of the upper and bottom sides. They are however shifted toward the

temperatures on the bottom side of the horizontal tube. Also the temperatures

which were measured along a lateral surface line on the horizontal tube do not

Wall inside temperature

400- Mass vet

'C IHeat flux

Wall inside temperature

ocity: 500 kg/m 2

s

300 kW/m 2

350-

300-

250-

200-6( I g 1 1200 k]/kg 1600

s-Enthalpy

1200 1300 1400 1500 k./kg 1700

- Enthalpy

Tube bore: 12.5 mm

Pressure: 150 bar

Measured values

Vertical tube --- *--- Horizontal tube -

Figure 5-3 Influence of the tube orientation on the heat transfer with onephase water flow and with subcooled boiling

65
lie in the middle between the values on the upper side, and bottom side. They

are also shifted toward the temperatures on the bottom side. From Figure 5-3

can also be gathered, that the temperature differences disappear when the mass

flow is increased.

The temperature differences between the upper and the bottom side of the horizontal tube are caused by a thermal convection flow, which is superposed over

the forced convection flow. Thereby, the heated fluid rises upward in the

proximity of the wall. Figure 5-4 presents typical wall temperatures, measured

on the outside of the heated tube. If one conceives the gravity-dependent

thermal convection flow in the shown manner, on-the upper side of the tube there

is created a stagnation zone which the thermal convection flow takes in only to

a limited extent. The fluid is there considerably quicker heated-up than in

the rest of the tube, whereby the wall temperature rises correspondingly. It

is of interest that the turbulent fluctuations, which should be already very

distinct with a Reynolds number of 96000, does not lead to a greater reduction

of the temperature differences.

For the verification of the temperature differences there was used the

PETUYKHOV /48/ model, which covers the thermal convection flow and allows thus

to calculate the wall temperatures as a function of the peripheral angle.

According to this model, the local Nusselt number has the following form:

Nu 340-Gr-cos'P 1 (5-1)

Nu Re2 .75-PrO'5 1 + 2.4 Re--1/8.pr2/3 _ 1)

is the mean Nusselt number and, according to PETUKHOV, is calculated as

N-u- (/8) - Re - Pr (5-2)

1.07 + 12.7 • V/8 - (Pr 2 / 3 - 1)

where = (1.82.lOgloRe - 1.64)-2 Tube friction coefficient

Gr = Grashof number

Re = mnd Reynolds number fl

Pr = ~c Prandtl number

= peripheral angle (upper side T = 0, bottom side ' = n)

As it can be gathered from Figure 5-3, the model renders sufficiently well the

test values with a mass velocity of 500 kg/m 2 s. If the mass velocity is increased to 2500 kg/m2 s, with the chosen parameters for the model, as well as

in the experiment, there cannot be observed an influence of the thermal

convection.

66
Parameters:

Water temperature:

Pressure:

Mass velocity:

Heat flux:

Tube bore:

216 0C

100 bar

500 kglm2s

300 kW/m 2

24.3 mm

Measured watt temperatures

,345"E

Stagnation zone

296"C

Reynolds number: 96000

Figure 5-4 Influence of the thermal convection on

course with horizontal flow

the wall temperature

In the case of the extreme conditions, which is the case with a high ratio from

the Grashof to the Reynolds number, the PETUKHOV model can fail and even calculate-negative Nusselt numbers on the upper side of the tube. Thus, the model

furnishes, e.g., for the parameters in Figure 5-2, excessively high temperatures

on the upper side of the tube.

The temperature differences between the upper and the bottom sides of the horizontal tube disappear, or they cannot be detected with the measuring technique

used if boiling sets in over the entire tube circumference (cf. Figure 5-3).

5.3 Critical Boiling States

As already shown by Figure 5-2, in the horizontal tube transfer from the wetted

to the unwetted heating surface state does not take place in an axial position.

The course of the critical heat flux as function of the steam quality can be of

entirely different shape on the upper side of the tube than on the bottom side

(cf. Figure 5-5). In a limited region of the heat flux it is also possible to

record several times the boiling crisis on the upper side of the tube. However,

for the evaluation of the heat transfer in the region of the boiling crisis it

suffices to know the locations of the first occurrence of the boiling crisis

(on the upper side of the tube) and of the last one (one the bottom side of the

tube).

67
Figures 5-6 to 5-11 show measured critical heat flux as function of the steam

quality. The values for the first occurrence of the boiling crisis (A) are

connected with the values for the last occurrence (3) by horizontal lines.

Therefrom can be seen the steam quality region, in which has to be expected

the boiling crisis in the tube. If the boiling crisis on the upper side was

recorded several times (as, e.g., in the example shown in Figure 5-2), several

triangles are entered on one line. If the boiling crisis could not be measured

on the bottom side up to the outlet of the tube, there is no square entered

and the horizontal line is drawn up to the steam quality at the outlet of the

tube.

The steam qualities, calculated according to KON'KOV (cf. equation (3-2)) and

measured on a vertical upflow tube, lie frequently between the values of the

upper and bottom sides of the horizontal tube. With increasing tube diameter

(Figures 5-9 to 5-11), increases the difference of the critical steam quality

between the upper side and the bottom one.

Heating surface: B = wetted

U = unwetted

Heat flux

I

Figure 5-5 Course of the critical heat flux density with horizontal flow

68
600

kW/m 2

400

200-o 03

a-c

ra-

'-' 600

kW/m 2

4.00 -

200 •

A

Mass velocil

600

kW/m2

400

200

0 1

bar 600

kW/m'

400

200

0

Iy:

Pressure: 100 bar

I I Ii

0 0,2 0,4 0,6 0,8

Pressure: 200 bar

500 kg/m2s

150

v I . .... 0 0.2 0,'. 0.6 0.8 1 -1 -0,6 -0,2 0 0,2 0,6

Critical steam quality Critical steam quality

Measurement: X vertical tube Calculation: o acc. to Kon'kov

A top of horizontal tube

o bottom of horizontal tube

Figure 5-6 Critical heat flux as function of the steam quality (tube bore 12.5mm)
Mass velocity:, 1000 kg/m 2s

600

kW/m

2

400,

_ 200

aJ

--• 0 ra 0

L-J 600-

oJ kW/Mr

400-

200

0

Pressure: 50 bar

I II I

0,2 0,4 0.6 0,8 1

Pressure: 150 bar

600"

kW/m 2

400-

200-

0

0

600

kw/m 2

400

200

0-

Pressure: 100 bar

I I

0.2 0,4 0,6 0,8 1

Pressure: 200 bar

.I

0 0.2 0,4 0,6 0.8

Critical steam quality

I 0 0,2 0,. 0,6 o,8

Critical steam quality

1

Measurement: X vertical tube Calculation: o acc. to Kon'kov

A top of horizontal tube

0 bottom of horizontal tube

Figure 5-7 Critical heat flux as function of the steam quality (tube bore 12.5 mm)
Mass velocity: 2500 kg/m 2s

600

kW/m 2

X 400

rM 200.

tM 0

600-

kW/m.

400-

200

0

0.4 0.6 0,8

600

kW/m 2

400

200

0

600

kW/m 2

400

200

Pressure: 100 bar

0 0,2 0,4 0,6 0,8 1

SPressure: 200 bar

0 0 I I

0 0.2 0,.4 0.6 0.8 1

Pressure: 150 bar

0 I I 1 10.2 0.,4 0.6 08 Critical steam quality

leasurement: X vertical tube

A top of horizontal tube

0 bottom of horizontal tube

V

Critical steam quality

Calculation: o acc. to Kon'kov

Figure 5-8 Critical heat flux as function of the steam quality (tube bore 12.5 mm)
Mass velocity: 500 kg/m 2s

600 -

kW/m 2

400 - X

200-

ai

"_ 0

LJ

w -

U

600-

kW/m 2

400-

200-

0

0

600

cW/m 2

400

200

0-

-1

600"

kW/rn 2

400-

200-

A

Pressure: 100 bar

I I I I I I I I

Pressure: .150 bar Pressure: 200 bar

10 1 10 Critical steam quality Critical steam quality

Measurement: A top of horizontal tube Calculation: o acc. to Kon'kov

0 bottom of horizontal tube

Figure 5-9 Critical heat flux as function of the steam quality (tube bore 24.3 mm)
Mass velocity: 1500 kg/m 2s

600-

kW/m 2

400-

i'4

4'-- 200

ra 0-

600

kW/m 2

60

kW/m2

40

20

60

40

20

0- Pressure: 100 bar

0-

0-

0 0 . . I I 0 0,5

(Ai

0- Pressure: 200 bar

2 r

0"

'0

0 0.5

Critical steam quality Critical steam quality

Measurement: A top of horizontal tube Calculation: o acc. to Kon'kov

0 bottom of horizontal tube

Figure 5-10 Critical heat flux as function of the steam quality (tube bore 24.3 mm)
Mass velocity: 2500 kglm2s

600

kW/m 2

400

X

%1. 200

4--

0 r--

W. 600-

kW/m 2

400-

200-

0

Pressure: 50 bar

0 O's I I I

600

kW/m2

400

200

0

600

kW/m

2

400

200

0

Pressure: 100 bar

I0I O

0 0,5

Pressure: 150 bar Pressure: 200 bar

-.---1----------------1- I I

#

0 I I c I I q ai ty 0,5

Critical steam quality 0 0.5

Critical steam quality

Measurement: A top of horizontal tube Calculation: o acc. to Kon'kov

0 bottom of horizontal tube

Figure 5-11 Critical heat flux as function of the steam quality (tube bore 24.3 mm)
Figure 5-12 shows, by way of example, the course of the critical heat flux for

various mass velocities with a pressure of 100 bars. In contrast to the

vertical tube, where a monotonic decrease of the critical heat flux can be

expected with increasing steam quality, the relationships in Figure 5-12 are

considerably more complicated.

The difference of the critical steam quality between the upper and the bottom

sides of a tube with horizontal flow is shown in Figure 5-13. Within the

measured heat flux region there was determined an average critical steam

quality region for each of the parameters mass velocity, pressure and tube

diameter. The difference of the critical steam quality decreases with

increasing mass flow and increases with rising pressure.

An increasing mass flow leads to increased turbulent fluctuations in the flow

and thus to a decrease of the influence of gravity. On the other hand, if one

compares experiments with the same mass velocity, the velocity of the two-phase

mixture decreases with rising pressure as a consequence of the increasing steam

density. With higher pressure the velocity effect prevails evidently over the

influence of the decreased buoyance of the steam phase. A larger tube diameter

causes an increase of the gravitational influence.

Critical heat flux

Tube bore: 24.3 mm

Pressure: 100 bar

Mass velocity (kg/m 2

s) Top Bottom

300 , 500 , 0

750 A n

1000 A 01

1500 A

2500 A

-0.5 0 0,5

Critical

1

steam quality

Figure 5-12 Course of the critical heat flux with horizontal flow

75
Dlifference of critical steam qualities *cru- icro cr. Xcru

1,1 150\200 bar . i\-N

200 \Tube bore (mm): 1,0 150 12,5 \--24,3

0,8 Pressure (bar): e 50

0100

o 150

0,6 5011001 m 200

I-'

0.2 1 "

0-

0 500 1000 1500 kg/m 2s 2500

10 Mass velocity

Figure 5-13 Critical steam quality region with horizontal flow

Frequently it is of interest if for the chosen parameters the tube orientation

has any influence at all on the location of the boiling crisis and, thus, on

the heat transfer in the post-dryout region. The Froude number seems to be an

adequate quantity for such an evaluation. It represents the relation of the

inertia to the buoyant force of a flow.

CUrio /49/ formed a Froude number with the kinetic energy of the water flow in

saturation state and could thus furnish a criterium about the parameter

combination with which one has to reckon with an influence of the tube

orientation on the location of the boiling crisis. For

Fr = (m/p').cosO _ 6 to 7 (5-3) V/g.d.(p' - p)p

according to CUMO, the location of the boiling crisis is no longer influenced

by the tube orientation.

76
Equation (5-3) was verified through heat transfer experiments in the pressure

range of 50 - 200 bars. In Figure 5-14 there is entered as abscissa the

Froude number determined by equation (5-3) and as ordinate the difference of

the critical steam quality between the upper and the bottom sides of the

horizontal tube. It can be seen that the thus formed Froude number does not

render an accurate statement about the anticipated influence of the tube

orientation on the location of the boiling crisis. Apparently, this relation,

which is based on experiments with a pressure of 180 bars, cannot be applied

to other pressures.

The following method was studied by a second step:

According to a modelling by WALLIS /50/, it is possible to evaluate

stratification effects of a two-phase flow in the horizontal tube through a

dimensionless group, which has the inertia force of the steam in the numerator

and the buoyant force in the denominator. This is again a Froude number

Difference of critical steam qualities XCr, - XCro

I

0.7'*1

0

0.6-

Mass velocity:

Tube bore:

Pressure:

300 - 2500 kg/m 2s

12.5 mm

50 - 200 bar

0,5-

0.4-

0.3"

0,2"

0.1-

I

6

S

0

0

S

S

0

0

S

S

0

S

S. 0

0 Os

S

S

114 ZZU ~ -

S

0 5 10 15 20 2s 30

Froude Number

Figure 5-14 Difference of the critical

Froude number according to

steam quality as

euation (5-3)

function of the

77
which, however, is in respect to the steam quality of the flow. The inertia

force is therein formed with the superficial velocity of the steam. Since the

steam velocity depends greatly on the steam quality, the latter has to be

known at the location of the boiling crisis. The critical steam quality with

vertical flow was taken as reference magnitude for this. It is known with

sufficient accuracy and it can be determined, e.g., according to the method

described in Chapter 3.

The stratification effects were thus evaluated by a Froude number as follows:

Fr = 0 r P1(5-4) VFg-d.(p, - p,)/p

From Figure 5-15 it can be gathered that, according to equation (5-4), for

Froude numbers higher than 7 the tube orientation has practically no influence

on the location of the boiling crisis. The difference of the critical steam

quality between the upper and the bottom sides of the tube is below 0.1. On

the other hand, with Froude numbers below 3 one has to reckon with strong

stratification effects. In the case of horizontal tubes, the boiling crisis

occurs already at very low steam qualities on the upper side while the bottom

sider remains wetted almost up to the point of complete evaporation.

5.4 Heat Transfer in the Post-Dryout Region

The heat transfer in the post-dryout region of vertical tubes can be calculated

with the method described in Chapter 3, which considers the thermal nonequilibrium between the steam and the water droplets. In order to investigate

the applicability of such a model to tubes with horizontal flow, information is

required on the influence of the tube orientation on the heat transfer in the

post-dryout region.

Figure 5-16 shows a typical wall temperature-enthalpy course. The boiling

crisis in the case of a tube with horizontal flow sets-in on the upper side

with considerably lower enthalpy than in a vertical tube, while on the bottom

side it sets-in at a higher enthalpy. The rise of the wall temperature after

the occurring of the boiling crisis on the upper side is however lower in the

horizontal than in the vertical tube. This has to be attributed to the heat

flux in peripheral direction from the unwetted upper side to the wetted bottom

side of the tube. Figure 5-17 shows this influence on the wall temperature

distribution. If the heat conduction in peripheral direction were neglected,

there could be expected a wall temperature course (8'o) on the upper side,

which lies considerably above the measured wall temperature course (8o). In

the case of the horizontal tube there could thus occur, that the wall

temperatures in the post-dryout region are lower than in a vertical tube

although the location of the first boiling crisis is present at considerably

lower steam quality and thus in the region with reduced steam cooling.

The influence of the heat conduction in peripheral direction depends on the

ratio of the heat flows in radial direction and in peripheral direction and,

thus, on the heat conductivity of the wall material as well as on the wall

thickness. Thus, boundaries are set for an accurate but not too cumbersome

calculation of the post-dryout heat transfer with horizontal flow. No models

can be developed which, as in the case of the vertical tube, calculate the

78
Difference of critical steam qualities

1 • 0 Tube bore (mm)

Xcru - XCro

1,0

0,9

0,8

0,7

0,6

0,5

0A4

0,3

0,2

0.I

0

0 5 10 15 20 25 30

-• Froude Number

Figure 5-15 Difference of the critical steam quality as function of the

Froude number according to equation (5-4)

79
Walt inside

600

oC

500

400

temperature

A A

I

**

I\

I

I •\

JAAA

A A

A

A 0

A I

I

*_=.E *• i n*.MO _ _

Mass velocity:

Pressure:

Heat flux:

Tube bore:

1000 kg/m 2s

150 bar

500 kW/m 2

12.5 mm

Measured values:

Vertical tube

Horizontal tube

A

*0

N

A N

d

.- __ _ _ - •. • •.

temperature -.1111 4 "UVV

1400 I I I 1 I

1600 1800 2000 2200 k)/kg 2600

Enthalpy

Figure 5-16 Influence of the tube orientation

in the post-dryout region

on the heat transfer

temperature unaffected by the dimensions and properties of the tube. In the

transfer of the test results it has to be further considered that most of the

ferritic steels used in steam generators have a heat conductivity which is

approximately double than that of the test tubes out of austenitic steel.

Thus, the influence of the heat conductivity from the unwetted upper side to

the wetted bottom side increases even more.

From the experiments it can be gathered that at the moment when in the

horizontal tube the boiling crisis on the upper and on the bottom sides occurs

at the same axial position, the heat transfer in the post-dryout region is

equal to that in the vertical tube (Figures 5-18 and 5-19). In Figure 5-19,

the wall temperature course of the vertical tube is shifted on the enthalpy

axis by about 150 kJ/kg in respect to the horizontal one. This value lies

still within a deviation of 6% with which, according to CUMO /21/, one has to

reckon in reproducibility tests.

With a larger tube diameter there is an increase of the temperature difference

between the upper and bottom sides of the tube in the post-dryout region

80
Influence of thermal conduction Wall temperature

I

1,v

Horizontal tube

e d

Unwetted

wall

7777t/7/_Z77Y 1111177771

"- A VerTical Tube Wall temperature

Section A - A

Figure 5-17 Heat conductivity from the unwetted upper side to the wetted

bottom side of the tube

(Figure 5-20). From the figure it can be gathered that this temperature

difference is still present, if the critical heat flux is exceeded over the

entire tube circumference. Since in the post-dryout region is present steam

flow with water droplets and thus the steam is the continuous phase, it was

studied if also in this case - analogous to the water region - the temperature

differences are caused by a thermal convection flow of the steam, which have

calculated according to the PETUKHOV model. It was evidenced, however, that

the thermal convection flow in this region has practically no influence on the

wall temperatures. The statement by SCHNITTGER and MAYINGER /51/ is more plausible, that the water droplets concentrate in the lower tube region. Thus, the

thermal non-equilibrium in it is reduced while it increases in the upper tube

region.

An indicative value for the expected temperature differences between the upper

and the bottom sides of the tube in the post-dryout region is the temperature

81
740oC

660

*1

Tube bore: 0.0125 m

wC4--

(M

C- a)

CL

E

,4--

ro

0o

5B0

500

420 -

Vertical tube:

Pressure:

100.4 bar

Heat flux:

148 kW/m 2

Mass velocity:

529.8 kg/m 2s

Horizontal tube:

99.6 bar

145 kW/m 2

521.1 kg/m 2s

0

Fluid temperature

340

260

A A rl A. f , " W t:W1

180 -p I I I I I I I I I I I I I I I I I

2160 2210 2320 2400 2480 2560

Enthalpy

2640 2720 2800 2860 kJ/kg 2960

Figure 5-18 Influence of the tube orientation on the heat transfer in the post-dryout region
740

°C Tube bore: 0.0125 m

660 - Vertical tube: Horizontal tube:

**

*

OJ 580

CC- G,

C- 500 -

E

.4-

'ý: 420

Pressure:

50.0 bar

*F

*l

*

*

*

*

*

*"

50.5 bar

A

A8

AO *

AO * 0*

*

*.

*

(O

Heat flux:

300 kW/m 2 291 kW/mr2

Mass velocity: 2

508.7 kg/m 2s 524.3 kg/mr2s

*

0

0 340

260

180 -

1500

A

3

A

0 *

*

*

**

Fluid temperature

I I # I

1700 1900 2100 2300 2500 2700 2900 3100 3300 kJ/kg 3500

Enthalpy

Figure 5-19 Influence of the tube orientation on the heat transfer in the post-dryout region
740-

oc

660

580 -

Tube bore:

0.0243 m 0.0125 m

aJ

C4 -

CaJ

E

aJ

4-I

-D

-3D

500

420

Pressure:

100.8 bar

Heat flux:

401 kW/m 2

Mass velocity:

755.8 kglm2s

100.1 bar

391 kW/m 2

755.3 kg/m 2s

AA

AA

0

AA

A 0

Co.

AAA

A A A A

A~~ 000U

ONWoso

A

co A 0

A 0

340

260

180

A 0 0 U

U

Fluid temperature

1750 1850 1950 2050 2150 2250 2350 2450 2550 2650 kJ/kg 2750

Enthalpy

Figure 5-20 Influence of the tube diameter on the heat transfer in the post-dryout region
difference between steam and water droplets (thermal non-equilibrium) in a vertical tube. It can be determined according to the model of Chapter 3. A prerequisite for this procedure is that, based on the parameters, there has to be

reckoned with an influence of the tube orientation on the heat transfer (cf.

Chapter 5.3). Otherwise, there cannot be expected any temperature differences

around the tube circumference.

Figure 5-21 shows that an increased tube diameter leads to a considerable rise

of the wall temperatures if the boiling crisis on the upper side of the tube

occurs at very low steam quality - apparently in the region of the stratified

flow. If, on the other hand, the tube orientation.does not have any influence

on the heat transfer, a diameter change influences only very slightly the wall

temperatures in the post-dryout region (Figure 5-22).

85
820

4C

740

Tube bore:

0.0243 m

C-

(U

CE

aJ

.4-

-a

:3:

660

580

500

Pressure:

201.2 bar

Heat flux:

406 kW/m 2

0.0125 m

200.7 bar

405 kW/m 2

1054.1 kg/m 2s

AAA

A AA A

coCn

Mass velocity:

1008.1 kg/m 2 A s

A AAA

420

340

260

A

A A

r& Qri ri r- rl rn -

0 13

A 11A11 f• r'-' - r-1 -A 61 AA

rgl -- mm mm m mm-- m

Fluid temperature•

I I I I I I I I A

1640 1720 1800 1880 1960 2040 2120 2200 2280 2360 kJ/kg 2440

Enthalpy

Figure 5-21 Influence of the tube diameter on the heat transfer in the post-dryout region
740°C Tube bore:

0.0243 m 0.0125 m

660

.4-

CaJ

580

500

420-

Pressure:

52.1 bar

Heat flux:

594 kW/m 2

Mass velocifty:

2393.8 kglm s

50.3 bar

605 kWIm2

Co 2467.4 kglm2s

A

0 UI

340-

260 -

0

0A 3 A Q -A O

Fluid temperature

IRA I.4

1480

I I I I

1560 1640 i i i I I I I I I I I I I I

1720 1800 1880 1960 2040 2120 2200 kJ/kg 2280

Enthalpy

Figure 5-22 Influence of the tube diameter on the heat transfer in the post-dryout region
6 PRESSURE DROP

6.1 Pressure Drop Components in an Evaporator Tube

The total pressure drop in an evaporator tube is composed of the terms for friction, acceleration and gravity.

APGes = APR + APB + APG (6-1)

Total Friction Acceleration Hydrostatic

pressure = pressure +- pressure + pressure

drop loss drop drop

Depending on the parameter combination and on the tube orientation one or more

of these fractions dominate in a particular case.

The greatest uncertainties exist always in the determination of the friction

pressure loss. Even the verification of a correlation for the friction pressure

loss with the help of measured values is not always possible to be accurate since

it is always the total pressure drop that is measured and the friction fraction

has to be determined according to equation (6-1). While in a single-phase flow

there can be determined the acceleration and the hydrostatic pressure drop merely

from the parameters and properties of the fluid, for a two-phase flow there is

still required data on the phase velocities and/or phase distribution, on the

flow cross-section, since this flow has additional degrees of freedom. Flow

models (homogeneous or heterogeneous) /50/, which agree sufficiently well with

reality in certain parameter regions, were developed for the mathematical handling of this. The most accurate statement about the friction pressure loss is

possible with an unheated and horizontal two-phase flow since in this case the

friction pressure loss corresponds approximately to the measured total pressure

drop. Since, however, the investigations below correspond mostly to heated and

not always horizontal flows, it is necessary to study closer all occurring

fractions.

The friction pressure loss of the two-phase flow is in respect to the friction

pressure loss which occurs, when the entire mass would flow as liquid in the

saturation state. This is the magnitude for the two-phase pressure loss most

frequently used in the literature and leads to the following definition of the

two-phase multiplier:

R = (APR)2ph (6-2)

(APR)lph,w

wherein

L j2

(APR)lphw = -d-- d " -p- (6-3)

with

= [O.86859.ln[Re'/(1.964.lnRe' - 3.8215)]] (6-4)

88
(according to Friedel /52/ for Re' > 1055)

and

m'd

Re' 

(-5

r7 (6-5)

The acceleration pressure drop is caused

e.g., through evaporation of the liquid.

constant, the acceleration pressure drop

by the change of the flow momentum,

If the flow cross-section remains

for a tube section in which the steam

quality changes from x1 to x2 and the void fraction from tj to &2 becomes:

APB n

x2

&2 P2p

( X2)2 k- k* 2

+

(1 - )2

( E)p1J

(6-6)

(12 - &2)P2 • I t

The hydrostatic pressure drop is caused by the

of the fluid.

change of the potential energy

AP G = H -g p (6-7)

AH is the difference in the height between the start and the end of the considered tube section and p is the mean density

is calculated by

AH

1 fpdH

0

of the fluid in this region and

(6-8)

The densities to be entered into equations (6-6) and (6-8) also depend on the

velocity ratio of both phases. If one assumes the same velocity for water and

steam, the mixture density can be calculated as follows:

-Ph p-r7 + 1

p

(6-9)

6.2 Friction Pressure Loss in the Wetted and Unwetted Regions

6.2.1 Experimental Observations and Their Interpretation

The heating surface of an evaporator tube in which the liquid is completely

evaporated lies partially in the wetted and partially in the unwetted region.

In order to investigate the influence of the wetting state of the heating surface on the pressure loss, in the experiments on the heat transfer in the postdryout region there was measured the pressure loss in three equally long tube

sections (instrumentation layout, cf. Chapter 2). The location of the boiling

crisis was therein shifted to the boundary between two tube sections, so that

one of them was completely in the wetted region and the other two in the unwetted region. Figure 6-1 shows a typical wall temperature course with one wetted

and two unwetted tube sections. The two-phase multiplier for the three tube

89
sections, calculated from the measurement, was also entered in the figure. It

can be seen, that the pressure loss in the wetted region lies distinctly higher

than in the unwetted one. This effect was observed in almost all experiments.

For the first time, TARASOVA and LEONTIEV /53/ and /54/ described the reduction

of the friction pressure loss in the unwetted region. They attribute the effect

to a "pressure loss crisis" and compare this process with the occurrence of the

boiling crisis during heat transfer. Quantitative values for the friction pressure loss in the unwetted region were published by BEATTIE /55/ and /56/ based

on boundary layer analysis which, however are not expounded in more details in

any of the two articles. WHITCUTT and CHOJNOWSKY /57/ conducted extensive measurements of the two-phase pressure loss at vertical upflow evaporator tubes.

Heating surface:

Two-phase

multiplier

Wetted Unwetted Unwetted

I

T!0 r15-

'/ail temperature

400

oC

300- 0C300300300oDDO0D30D 00 1

Fluid temperature

200 2 _ _ _ _

2500 26001 2700 kJ/ka 12E

Flow direction:

Pressure:

Mass velocity:

Heat flux:

Tube bore:

vertical

upwards

50 bar

1010 kg/m 2s

150 kW/m 2

12.5 mm

B00

I Enthalpy

* 0 S00 0

-U - A 

Ap2 Ap3

Figure 6-1 Two-phase multiplier in the wetted and the

unwetted region of a heated tube flow

The boiling crisis occurred therein mostly at the outlet of the tube, so that

the pressure loss was measured in the wetted region. The comparison of the

measured values with the homogeneous model in the OWENS /58/ formulation showed

only an average deviation of 9% between calculation and measurement. The mass

velocity was varied between 400 and 3500 kg/m2 s in these experiments, the pressure between 110 and 205 bars and the steam quality between 0 and 80%. According to OWENS expressions, the viscosity of the liquid phase was used - independently of the steam quality - for the determination of the friction coefficient

of the tube.

90
For the evaluation of the measurements of the two-phase pressure loss there

were used the OWENS model and the BEATTIE model for the friction pressure loss.

According to the homogeneous model, the pressure loss of a two-phase flow is

calculated according to equation (6-3) whereby instead of the fluid density p'

there has to be entered the mixture density, determined by equation (6-9):

L ý2

(APR)h = t - • (6-10)

d 2-Ph

The friction coefficient t is - same as in the single-phase region - dependent

on the Reynolds number (equations (6-4) and (6-5)), wherein exist many expressions

for the "representative" viscosity in the two-phase region (cf. /41/ and /59/).

Since according to the OWENS model the viscosity of the liquid phase is used

for the two-phase region, also the tube friction coefficient t becomes independent of the steam quality and the two-phase multiplier becomes very simple by

using the equations (6-2), (6-3), (6-9), and (6-10):

ROWENS =1+ k( -1) (6-11)

The two-phase multiplier for the unwetted region is calculated according to

BEATTIE by

R (•) ( 1 + - 1 1 .(6 -1 2 )

BEATTIE P' ..

The verifications of the experiments carried out with the equations (6-11) and

(6-12) are shown in Figure 6-2 to 6-4 for the horizontal tube and in 6-5 to 6-6

for the vertical upflow tube. In the Figures was identified the wetting state

of the heating surface, which was determined from the course of the wall temperatures. It can be noted, that the friction pressure loss in the wetted

region is covered sufficiently well, on the average, by the OWENS homogeneous

model and well in the unwetted region by the BEATTIE model. It is peculiar that

the scattering of. the two-phase multiplier in the wetted region is considerably

higher than in the unwetted one.

From the Figures 6-2 to 6-6 it can be deduced that in the investigated parameter range there is obtained a high accuracy in the calculation of the two-phase

pressure loss, if in the wetted region the calculation is made according to OWENS

and in the unwetted one according to BEATTIE. Figure 6-7 shows a comparison between the measured two-phase multiplier and the one calculated according to this

procedure. The pressure loss for the entire parameter range is sufficiently

well determined both for the horizontal as well as for the vertical upflow tube.

6.2.2 Comparison of Various Pressure Loss Correlations

For the design of evaporator tubes there are frequently proposed correlations

which were obtained from experiments on adiabatic two-phase flows. In order

to check their applicability for this purpose, measured two-phase multipliers

91
Two-phase multiplier

S3 -Flow direc

Tube bore

30- Pressure:

Measured values:

Heating surface Wetted Unwetted

500 0o

Mass velocity 1000 _

(kg/m 2s) 2500 x _

2500 , <

25

20

Calculated values:

to 15 Homogeneous model acc. to OWENS UMWNm BEATTIE Model

10

5

0

0 0,2 0,4

00,

0,6

Steam

0,8 quality

Figure 6-2 Influence of the wetting state of the heating surface on the two-phase multiplier
Two-phase 715- multiplier

T Flow directi

Tube bore:

Pressure:

Measured values:

Heating surface Wetted Unwetted

Mass velocity 500 _ o [ (kglm2s) 1000 _ _ _ 1

1

Calculated values:

Homogeneous model acc. to OWENS

BEATTIE Model Lb mmmMI

Steam quality

Figure 6-3 Influence of the wetting state of the heating surface on the two-phase multiplier
Two-phase multiplier I 8 S Flow directio

Tube bore:

6 -Pressure:

Measured v"lues:

n: horizontal

12.5 mm

Heating surface Wetted Unwetted

Mass velocity: 1000 13

(kg/m2s) 2500 0 >

15

4-

2-

0 bar

1-01

Measured values:

Homogeneous model acc. to OWENS

(0 U BEATTIE Model I I

0 0,2 0,4

I 1

0,6 0,8

Steam quality

- - -

5

4

3

2

1

0

0,4 0,6 0,8

P_- Steam quality

Figure 6-4 Influence of the wetting state of the heating surface on the two-phase multiplier
Two-phase multiplier

5- Flow directi,

I Tha hk r'"

Measured values:

Heating surface Wetted Unwetted

Mass velocity 1000 _ _ _ _

(kg/m2s) 2500 _ _

15U

25

20

15

Calculated values:

Homogeneous model acc. to OWENS

BEATTIE Model U, J

10

5

0

0,4 0,6 0,8

0, Steam quality

Figure 6-5 Influence of the wetting state of the heating surface on the two-phase multiplier
Two-phase multiplier

T8 Flow directic

6- Tube bore:

Measured values:

Heating surface Wetted Unwetted

Mass velocity 1000 0

(kg/m 2s) 2500 _ _ _

4

2

0

Calculated values:

Homogeneous model acc. to OWENS

BEATTIE Model

0,4 0,6 0,8

-I- Steam quality

5.

4-

3-

2-

1-

0

Pressure: 200 bar

WO

I I I I I

0 0,2 0,4 0,6 0,8

Steam quality

i

Figure 6-6 Influence of the wetting state of the heating surface on the two-phase multiplier
Flow direction: horizontal

Calculated

vertical upwards

Calculated

two-phase multiplier

A100- I •Mean error:

Standard de

Measured two-phase

multiplier

12.5 mm

50-200 bar

500-2500 kg/m 2s

Tube bore:

Pressure:

Mass velocity:

Measured two-phase multiplier

Calculation:

acc. to OWENS for wetted heating

surface

acc. to BEATTIE for unwetted

heating surface

Figure 6-7 Comparison between measured and calculated two-phase multipliers
and those calculated with various correlations were compared to each other.

Figure 6-8 shows this comparison for the suggested process and calculation

according to LOMBARDI /60/ and FRIEDEL /61/. Plotted was the number of the

measuring points which lies within a defined error range. The error was

defined therein as follows:

RR - RM

Y RM (6-13)

With the suggested process with, e.g., an admissible error of ± 20% for

horizontal and vertical flows, it is possible to verify approximately 80% of

all measuring points. The other equations used for the comparison lead to

considerably higher errors in the calculation since they do not consider the

wetting state of the heating surface.

In addition to the experiments with heated tube flow there were analyzed

pressure loss measurements on unheated tubes. Figure 6-9 shows a comparison

of several correlations with measured values which were taken from a data bank

/62/. The data bank contains essentially the values for the medium water of

the data collection compiled by FRIEDEL /52/. The corresponding parameter regions

are enumerated in Table 6-1. In this comparison were also included the newly

developed STOREK /63/ model and the homogeneous model in the OWENS formulation

/58/. It is of interest to observe that with horizontal flow the homogeneous model reproduces the test values better than the three relations used for the

comparison.

The FRIEDEL equation furnishes the best agreement in the case of vertical tube

flow. Also herein the homogeneous model presents advantages over the other two

methods, since it covers all measuring values already with an error range of

±70% and does thus not produce any large "spreads." However, the OWENS homogeneous model has lead to errors during the transition to the steam flow, since

herein the viscosity of the liquid phase is used for the determination of the

friction coefficient.

6.2.3 Influence of the Heating and Entrance Effects

The influence of the heating on the friction pressure loss in the two-phase

region was investigated on a horizontal tube. Figures 6-10 and 6-11 show the

measured two-phase multiplier as a function of the steam quality. For the case

of the heated flow, the friction pressure loss was obtained from the difference

between the measured total pressure drop and the acceleration pressure drop

(equation 6-6). The acceleration pressure drop, which due to the slight heating

is only of secondary importance, was determined according to the homogeneous

model. It can be seen that in the wetted region the pressure loss of the heated

flow is practically identical with the pressure loss of the unwetted flow of

the same steam quality. In the unwetted region the pressure loss of the heated

flow lies below that of the unheated one.

From Figures 6-10 and 6-11 it can also be gathered that the pressure loss with

partially wetted heating surface, in which in the horizontal tube the critical

heat flux on the upper side of the tube was exceeded, lies between the values

98
Proportion of measured points

1%

80,

Calculation models:

* Proposed method

o LOMBARDI

& FRIEDEL

Mass velocity:

Tube bore:

Pressure:

500-2500 kg/m 2s

12.5 mm

50-200 bar

Flow direction:

vertical upwards

0 ±20 ±-40 ±60 ±80 % ±100

Error bandwidth

Figure 6-8 Number of measuring points within a defined

error range (heated tube flow)

99
Proportion of measured points

I 100

80

Calculation models:

0 OWENS

0

+,

LOMBARDI

FRIEDEL

60 / STOREK

40

20

0

0 ±20

Proportion of measured t 100

%

80

60-

40

20'

±4(.0 ±6'0

points

±80 % ±100

Error bandwidth

±60 ±80 % ±100 - Error bandwidth

Figure 6-9 Number of the measuring points within a defined

error range (unheated tube flow)

for the wetted and the unwetted heating surface. This can be seen especially

in Figure 6-11 with a pressure of 100 bars. Herein the limiting curve for the

unwetted wall (BEATTIE model) is obtained when the heating surface is unwetted

around the entire circumference.

From Figure 6-10 it can be gathered that in the wetted region the pressure

loss can lie still considerably above the values calculated according to the

100
Table 6-1 Parameter range of the experiments on unheated tubes

Flow direction Number Mass velocity Steam quality Pressure

(-) (kg/m 2s) H-) (bar)

Horizontal 95 334 - 2739 0.05 - 0.98 .1 - 97

374 201 - 4458 0.01 - 0.99 1.7 - 97

377 17 - 1615 0.07 - 0,99 1,4 - 19

35 1004. - 4013 0.04 - 0.58 10 - 37

134 112 - 1232 0,0 - 0,33 11 - 177

Vertical 86 331 - 2751 0.04 - 0,98 41 - 97

upwards

252 398 - 1835 0.0 - 0.04 1,0 - 1,7

314 99 - 1532 0,01 - 0,36 11 - 197

323 392 - 3995 0.02 - 0.87 17 - 100

1877 497 - 4658 0.01 - 1.0 20 - 89

34.7 961 - 4577 0.02 - 0.84 1.9 - 70

101 500 - 3000 0,08 - 0.70 30 - 90

40 S00 - 1000 0.10 - 0.92 69

156 397 - 1579 0.03 - 0.51 2.1 - 19

17 990 - 4036 0.05 - 0.56 19 - 30

42 481 - 2120 0,01 - 0.38 20 - 31

101
Two-phase multiplier

35 -

30

Measured values:

Heating surface

Heated(100 kW/m 2)

Unheated I 0

I Unheated 0

25 - ,

20 - 50 ba.,/I Calculated values:

0 /./ . Homogeneous model acc. to OWENS

• 15 - / Homogeneous model with steam viscosity

BEATTIE Model

10 * Pressure:

[] 100 bar,'*"

5 / I Mass velocity: 750 kg/m2s

1-01 I Tube bore: 24.3 mm 20bar'

G2 cFlow direction: horizontal

0

0,4 0,6 0,8 1

Steam quality

Figure 6-10 Influence of the heating on the two-phase multiplier
Two-phase TA 30, multiplier Measured values:

Heating surface IWetted

Heated(200 kW/m 2)I 1

25

20

15

Unheated I O

Calculated values:

Homogeneous model acc. to OWENS

Homogeneous model with steam

viscosity

1-

BEATTIE Model 10

5

0

Mass velocity: 1500 kg/m 2s

Tube bore: 24.3 mm

Flow direction: horizontal

0 0,2 0,4 0,6 0,8 1

Steam quality

Figure 6-11 Influence of the heating on the two-phase multiplier
homogeneous model by OWENS. This has to be attributed to the influence of the

deformation turbulence (cf. /63/) which, with low mass velocity and - as in this

case - with large tube diameter cannot be neglected in respect to the influence

of the Reynolds turbulence.

In the case of the heated tube, the transfer from the course of the pressure

loss with wetted heating surface to that with unwetted heating surface is determined by the location of the boiling crisis which can be determined, e.g., according to Chapter 3.2 for conditions occurring in steam generator tubes. In

the case of the unheated tube, when approaching the single-phase steam flow

there can be sometimes observed a considerable drop of the friction pressure

loss (Figure 6-10 at 50 and 100 bars) and with other parameters an increase of

the friction pressure loss (Figure 6-11 at 100 bars). This has to be attributed

to the different entrainment behavior of the two-phase flow. While in the first

case, even with very high steam qualities, there is a water film on the wall

which thus increases considerably the pressure loss, the wall in the second

case would be essentially blown dry, whereby the considerably lower viscosity

of the steam is decisive for the pressure loss.

The influence of the entrainment on the pressure loss was investigated on measurements by GASPARI /64/ on a vertical upflow adiabatic tube flow. F'igure 6-12

shows the fraction of the liquid carried in the steam in the form of water drop

lets for the transfer to the single-phase steam flow k 1) according to a method

by HUHN /65/. In the case of high mass velocities, the entire liquid fraction

is in the steam flow; thus, there is no longer a film on the wall and the pressure

loss increases when approaching the single-phase flow as a result of the increasing flow velocity. On the other hand, with lower mass flow decreases the

entrainment and there continues a water film which disappears only when approach- ing the single-phase steam flow. When the water film is removed with increasing

steam quality, more steam comes comes into direct contact with the wall whereby

the pressure loss decreases again. While with a heated flow this transition

occurs in a very limited steam quality range, the change during the course of

the pressure loss with an unheated flow occurs over a wider region.

In Figure 6-13, for GASPARI /64/ measurements, the two-phase multiplier is entered

as function of the steam quality. It can be seen that with high mass velocities,

also with an unheated flow, the pressure loss can drop again already at medium

steam contents with increasing steam quality. In the Figure was also plotted

the fraction of the water mass flow, calculated according to HUHN, which flows

as film on the wall.

The steam quality range, in which can be observed a drop of the pressure loss

with high mass flow, can therefore be assigned to the disappearance of the water

film on the wall. From the comparison between the measured values and the calculation of the pressure loss according to the homogeneous model it can be gath- ered that, in the region with the low entrainment, the use of the fluid viscosity

furnishes more accurate values for the determination of the tube friction coefficient while with high entrainment it is the steam viscosity.

The influence of entrance effects can be gathered from Figures 6-14 and 6-15.

For a two-phase flow the literature /66/ mentions entrance effects up to a length

to diameter ratio of 50. From the figures, it can be seen that in the investigated parameter range with a length to diameter ratio of 90, there is no longer

present a noticeable influence of entrance effects in the two-phase region while

104
Pressure drop gradient

+400 T 400]Tube bore: 5

Pressure: 7

kN/m 3

300

200

100

0

Entrainment acc. to

HUHN for *--- 1 in %

100

99,5

98

94

87

78

0,4 0,6 0,8

-o Steam quality

Figure 6-12 Connection between entrainment and pressure loss in

an unheated flow

in the single-phase region they have disappeared almost completely with a relative length of 14. From the figures, it can also be gathered that the entrance

effects are strongest in the medium steam quality region.

105
Two-phase multiplier -1

t Tube bore: 15.2 mm 100- Pressure: 20 bar

ELJ _ ! o

I

50-

20-

101

5-

rmass veLocily:

kg/ms

2

0 500

o 750

0 999

A 1249

V 1496 0.

A 1757

0 1986 oa' o

I0

I

ni

Calculation

iccording to the

ogeneous model:

1 i ý

1

S0,01 0,02 I I I I

0,05 0,1 0,2 0,5 1

- 0 Steam quality

as film Entrainment Wate I.I I

ATr mass flow

IUU 80- V - "20

60- 40\

4n - . . . . . . .. n

47

20. Calculation acc.

to HUHN

.80

Ii. i i IIUU

0.01 0,02 0,05 0,1 - .

0,2 0,5 1

Steam quality

Figure 6-13 Connection between entrainment and pressure loss

in an unheated flow

6.3 Recommendations for the Determination of the Friction Pressure Loss of

a Two Phase-Flow

From the investigations described in the foregoing chapters it can be gathered

that the wetting state of the wall has a decisive influence on the pressure

loss. This applies both to heated as well as unheated-tube flows, wherein the

transition from the wetted to the unwetted wall state takes place in the first

case through the evaporation of the liquid film in connection with a droplets

entrainment into the core flow and in the second case only by entrainment.

However, during the transition to the single-phase flow even with a flow without

entrainment there has to disappear the water film on the wall.

106
, -, 1 m -1 . 2 _ 1 .

0,35 m-*1 4-1,87 m4-1,87 m--41,87 m!44-

Two-phase multiplier

Unheated

30

Mass velocity: Tube bore:

Tube orientation:

1, 2, 3

25 -

20-

1

12

H_

15-

1 rI

S2

50 bar

100 bar

200 barL

750 kg/m 2s

24.3 mm

horizontal

Number of

section

101

5

0

3

2

3

@2 3

02

9) 1 OD

183,

] 0:2 0,4 II

0,6 0,8 1,0

Steam quality

Figure 6-14 Influence of entrance effects on the pressure loss
.mI 11 2 3 L I I I I |

0,35 m-- 41,87 m--1,87 m--1,87 mTwo-phase mulfiplier

Mass velocity:

Tube bore:

Tube orientation:

1, 2, 3 Unheated,!, 7

1500 kg/ m2s

24.3 mm

horizontal

Number of tube

section

30-

25 -

20-

03

S1"

3

>1

2

350 bar

03

.00

15-

10-

5.

0ý

3

2

100 bar

200 bar,

fe 8) 8) E

9

IF 0,I 0A 0,2 0,4 0,6 008 1,o0

--- + Steam quality

Figure 6-15 Influence of:entrance effects on the pressure loss
The influence of the wetting state of ,the wall on the~pressure loss-can be easily

represented according to-formulae if'one starts from a.flo6w in.w hich the deformation turbulence can be neglected in respect to the effect of the viscosity and

the Reynolds turbulence. The process can be then described with the homogeneous,

respectively with a quasi-homogeneous, model.

For the determination of the tube friction coefficient in'the wetted region it

is suggested to use the viscosity of the liquid-phase, which leads to the twophase multiplier used by OWENS /58/ (equation 6-11). The'Reynolds number necessary for the determination of the tube friction coefficient is as follows:

Re - d(6-14)

For the determination of the tube friction coefficient in:the case of an unheated

flow with high entrainment it is suggested to use the steam viscosity. Thus

the Reynolds number becomes:

Re -,n, d (6-15)

and the two-phase multiplier becomes:

R +k i (6-16)

The exponent n depends on the'course of the tube friction coefficient • as function pf the:.Reynolds number'in accordance with-equation (6-17):

Re-n (6-17)

n decreases with increasing Reynolds number. For the investigated parameter

range, according to COLBURN /67/, n can be fixed at 0.2. The decision if the

two-phase multiplier shall be calculated according to equation (6-11) or (6-16)

can be taken after a determination of the'entrainment.'(e.g., accordihg',toýHUHN

/65/).

In the. unwetted region of a heated tube flow the water component does not

reach the:wall. -Therein, due~tothehigherwall temperature,- the Leidenfrost'-

temperature.is exceeded most~of'the times." Between the water droplets and the'

-tube wall, .when the.droplets approachithe wall,,steam is formed mainly on the.

side of.the droplets facing the wall, preventing thus a contact between the

droplets-and the wall' . .

GARNIC and ROHSENOW /68/ investigated in an analytical manner the influence of

the wall:' temperatureron.thedroplet~trajectories of-evaporatinginitrogen. 'As

shown .in,:.Figure6-16, the droplets cannot-advance to the wall if a-certain walltemperature is exceeded.- This temperature depends on'the depositionwvelocity;

of the .droplets;on the:droplets diameter, the mean flow..velocity,:'the thickness

of the laminar sub layer as well" as on the'prOperties ofthe.liquid and'gaseous

phase. From the considerable drop of the friction pressure loss in the post109
Distance from

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0

wall (non-dimensional)

0 2 4 6 8 10 12 14 16

--* Axial distance (non-dimensional)

Wall temperatures:

41< 0- 2 <0- 3

Figure 6-16 Influence of the wall temperature on the trajectories

of evaporating nitrogen droplets (according to

GARNIC and ROHSENOW)

dryout region, which can also be observed with lower heat fluxes and thus lower

wall temperatures, it can be deduced that the wall temperature in the post-dryout

region is most of the times so high, that droplets cannot reach the wall. Apparently, regardless if the wall temperature lies above or below the experimentally

determined Leidenfrost temperature with forced convection (cf. Figure 4-13),

the pressure loss is not influenced.

If one starts from the premise that in the unwetted region there a direct

momentum transfer between water droplets and heating surface is not possible,

the water droplets behave passively in respect to the pressure loss and increase

by their presence merely the mean flow velocity. The pressure loss is then

solely determined by the properties of the steam.

110
Thus, the Reynolds number necessary for the determination of the tube friction

coefficient becomes

w-d p" *m-d (6-18)

Re q-• = : ph 71-

and the pressure loss can be calculated as follows:

L ((

R d U (6-h9)

With equations (6-2), (6-3),. (6-9), (6-17), (6-18), and (6-19) the two-phase

multiplier becomes

R =(1)n .( 11)1n [i+ pi)2I - n (-20)

For n = 0.2, the equation (6-20) is converted into the equation given by BEATTIE

for the two-phase multiplier in the post-dryout region.

Figure 6-17 shows the transition from the wetted to the unwetted wall state for

an unheated and a heated tube flow. In the case of unheated tubes, the two-phase

multiplier can present in the transition region an increasing or decreasing

tendency. The course depends on the length of the transition region and on the

occurring changes of the pressure loss. In the case of horizontal tubes, the

transition region is frequently longer than in vertical tubes due to separation

phenomena. A transition region region occurs also in heated tubes if they are

horizontal. The boiling crisis occurs therein on the upper side of the tube

while the bottom side is still wetted. The length of the transition region in

a heated tube flow can be determined according to Chapter 5.

In Figure 6-18 are summarized the calculation possibilities for the two-phase

pressure loss with distinct Reynolds turbulence.

ill
multiplier

Homogeneous model acc. to OWENS

Homogeneous model with steam viscosity

BEATTIE Model

Pressure: 100 bar

Two-phase

¶12.

10.

I-1

8

6

4

Two-phase multiplier

¶12 -

10

8 Transition

boiling criý

6

4-

2-/.

0"*

2

0

0 0,2 0,4 0,6 0,8

-* Steam quality

1 0 0,2 0,4 0,6 0,8

-- Steam quality

1

Figure 6-17 Recommended calculation possibilities for the two-phase pressure loss with

distinct Reynolds turbulence
State of wall Parameters determini

Viscosity Density

t Transition through

entrainment

(almost)

Unwetted

Unheated

ng pressure drop

Two-phase multiplier

1+i('

Wetted 1+i(.%,,-1) H

H

CA~ Heated or

unheated

F

ITransition through boiling crisis

C)0

/c /,, /.,0" Unwetted Heated Q #1

n = ,2 for 104 < Re <5 .106

Figure 6-18 Recommended calculation possibilities for the two-phase pressure loss with distinct Reynolds turbulence
7 SUMMARY

The influence of the wetting state of the heating surface on the heat transfer

and pressure loss was investigated for the parameter range of fossil-fired

steam generators.

For the determination of the fundamental mechanisms one started at first from

a steady state vertical upward tube flow. For this case a method was developed

for the determination of critical boiling states in the entire steam quality

region, which was compared to test results with the help of comparative calculations. The heat transfer after the exceeding of the boiling crisis was experimentally investigated. Based on these investigations there was developed a

model for the heat transfer in the unwetted region, taking into consideration

the thermal non-equilibrium between the water and the steam phase. This model

is based on the simplified premise, that for each parameter combination there

exists a value for the thermal non-equilibrium, through which the course of the

heating surface temperature is determined. Thus, the heat transfer from the

location of the minimum heat transfer until the transition to the single-phase

steam flow can be described with sufficient accuracy.

The influence of pressure and enthalpy transients on the heat transfer in the

unwet7ted region was experimentally investigated. Therein was observed a considerable ride of the wall temperature for transients, which occurred in the

proximity of the critical pressure, which has to be attributed to a temporary

non-wetting of a wetted heating surface in steady state. A semi-empirical model

was developed for the advancing of the wetting front under pressure and enthalpy

transients, which was verified with the obtained test results.

The influence of the tube orientation on the heat transfer was investigated in

horizontal and vertical tubes. The tests showed that already in the region of

the single-phase heat transfer with turbulent fluid flow there can occur considerable temperature differences between the upper and the bottom sides of the

tube in the case of horizontal flow. The boiling crisis in the horizontal tube

occurs in most cases much earlier on the upper side than on the bottom one.

Due to the heat conduction in the wall material from the unwetted upper side

to the wetted bottom side it is possible that the wall temperatures, after

exceeding the boiling crisis, are distinctly lower in the horizontal tube than

in the vertical one. Based on a force balance there was developed a method

with which it can be determined at which parameter combination there can be

expected an influence of the tube orientation on the location of the boiling

crisis and on the heat transfer in the unwetted region.

Concomitantly with the heat transfer there was measured the pressure loss of

the flow at horizontal and vertical tube orientation. Therein was observed a

considerable influence of the wetting state of the heating surface on the

pressure loss of a two-phase flow. The pressure loss is considerably lower in

the unwetted region than in the wetted one. A method was developed with which

it is possible to determine accurately the friction pressure loss with wetted

and unwetted heating surfaces for the parameter range of fossil-fired steam

generators. As shown by the analysis of measured friction pressure losses, the

wall state has influence on the two-phase pressure loss also with an unheated

tube flow. The transition from wetted to the unwetted state is herein effected

by droplet entrainment into the core flow.

114
From the investigations on the pressure loss and heat transfer it can be

gathered that in the considered parameter range with unwetted heating surface,

the influence of the liquid droplets on the heat and momentum transfer with

the heating surface can be disregarded.

115
NOMENCLATURE

A m Laplace Constant

c kJ/kgK Specific thermal capacity

d m Tube bore

F - Surface of the water droplets per

unit area of heated tube wall

Fr - Froude number

g m/s 2 Acceleration due to gravity

GR Grashof number

h kJ/kg Enthalpy

Ahv kJ/kg Specific evaporation enthalpy

AH m Height difference

L m Length

kg/m 2 s Mass velocity

M - Mean value

n - Number of measurements; exponent

Nu - Nusselt number

Nu - Mean Nusselt number

p bar Pressure

PC bar Critical pressure

Ap N/m2 Pressure loss, pressure drop

Pr Prandtl number

kW/m 2 Heat flux

kW Heat flux rate

R Two-phase multiplier

RR Calculated two-phase multiplier

RM Measured two-phase multiplier

116
Re - Reynolds number

u m/s Wetting front velocity

w m/s Flow velocity

- Steam quality

XLim - Boundary steam quality

Ax - Mean deviation of the steam quality

Y - Error magnitude

kW/m 2K Heat transfer coefficient

1/K Coefficient of expansion

a m Tube wall thickness

C - Void fraction

S- Thermal non-equilibrium factor

1 kg/ms Dynamic viscosity

8 0C Temperature

AME K Inlet subcooling

A&u K Superheating of the steam in the

two-phase region

8' oC Fictitious wall temperature on the

upper side of the horizontal tube

o rad Angle of inclination

X kW/mK Heat conductivity

v m2 /s Kinematic viscosity

- Tube friction coefficient

p kg/m 3 Density

kg/m 3 Mean density

a N/m Surface stress

rad Peripheral angle

117
Subscripts (or superscripts)

B Acceleration

Bil According to balance

D Steam

G Hydrostatic

Ges Total

h Homogeneous

Kr Critical boiling state

KrR Calculated critical boiling state

KrM Measured critical boiling state

L Leidenfrost

o Upper side of the horizontal tube

R Friction

Real Real (actual)

S Saturation

Tr Droplets

u Bottom side of the horizontal tube

v Vertical tube

W Water, wall

a min Minimum heat transfer coefficient

Saturation state of water

Saturation state of steam

Iph, w Single-phase, water

2ph Two-phase

118
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123

NaC IORM 233 US NUCLEARP IGULATORYCOMuISSION ' RE'T NUMBERIA/eqwMv JDC.V.1 . bv.

0241,1 kCM 11102.

JIM.23202 BIBLIOGRAPHIC DATA SHEET NUREG/IA-0003

SIFIE INSTRuCTIONS ON THE REVERSE

2. TITLE AND SUITITLE 3 ILVE BLANK

Influence of the Wetting State of A Heated Surface

on-Heat Transfer and Pressure Loss In an Evaporator

Tube 4 DATE REPORT COMPLETED

MONTH V EAR

B AUTHORIS September 1986

Wolfgang Kohler, Dietmar Hein 5 DATE REPORT ISSUED

PONT H YE1AR

September 1 1986

7. PERFORMING ORGANIZATION NAME AND MAILING ADDRESS tl,.c.& ZP Code) U If:JECT•rASKfWORK UNIT NUMBER

Kraftmerk Union AG 9 fItOR GRANT NUMBER

Erlangen, FRG

10 SPONSORING ORGANIZATION NAME AND MAILING ADDRESS PJ,.cf,/vZw Codr; Ila YPE OF REPORT

Office of Nuclear Regulatory Research Technical

U. S. Nuclear Regulatory Commission b PSP:OO COVERED .,ndusm.,w an

Washington, D. C. 20555

12 SUPPLEMENTARY NOTES

13 ABSTRACT (20 w"O or m.l!

The influence of the wetting state of a heated surface on heat transfer and pressure

loss in an evaporator tube was investigated for a parameter range occurring in

fossil-fired steam generators. Included in the analysis are quantities which determine

the wetting state in steady and transient flow.

Based on the experiments performed a method of predicting CHF for a vertical upflow

evaporator tube was developed. The heat transfer in the unwetted region was newly

formulated taking into account thermal nonequilibrium between the water and steam

phases. Wall temperature excursions during pressure and enthalpy transients are

interpreted with the help of the boiling curve and the Leidenfrost phenomenon. A method

is developed by means of which it is possible to determine the influencer of the pipe

orientation on the location of the boiling crisis as well as on the heat transfer in

the unwetted region. The influence of the wetting state of the heated surface on

the two phase flow pressure loss is interpreted as "Wall effect" and is calculated

using a simplified computer model.

14 DOLUMENT ANALYSIS - a KEYWORDSODESCRIPTORS

Critical Heat Flux (CHF), Heat Transfer, Wetting State

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