NUREG/IA-0181

International

Agreement Report

Assessment of

RELAP5/MOD3.2 for

Reflux Condensation Experiment

Prepared by

Y.M. Moon, H. C. No, KAIST

H.S. Park, KAERI

Y.S. Bang, KINS

Korea Advanced Institute of Science and Technology Korea Atomic Energy Research Institute

373-1, Gusung-Dong PO. Box 105

Yusung, Taejon Yusung, Taejon

305-701 Korea 305-600 Korea

Korea Institute of Nuclear Safety

P.O. Box 114

Yusung, Taejon

305-600, Korea

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

April 2000

Prepared as part of

The Agreement on Research Participation and Technical Exchange

under the International Code Application and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission
AVAILABILITY NOTICE

Availability of Reference Materials Cited in NRC Publications

NRC publications in the NUREG series, NRC regulations, and Title 10, Energy, of the Code of Federal

Regulations, may be purchased from one of the following sources:

1. The Superintendent of Documents

U.S. Government Printing Office

RO. Box 37082

Washington, DC 20402-9328

<http://www.access.gpo.gov/su-docs>

202-512-1800

2. The National Technical Information Service

Springfield, VA 22161-0002

<http://www.ntis.gov>

1-800-553-6847 or locally 703-605-6000

The NUREG series comprises (1) brochures

(NUREG/BR-)000Q, (2) proceedings of conferences (NUREG/CP-XXXX), (3) reports resulting

from international agreements (NUREG/IA-XXXX),

(4) technical and administrative reports and books

[(NUREG-XXXX) or (NUREG/CR-XXXX)], and (5)

compilations of legal decisions and orders of the

Commission and Atomic and Safety Licensing

Boards and of Office Directors' decisions under

Section 2.206 of NRC's regulations (NUREGXXOXX.

A single copy of each NRC draft report for comment is available free, to the extent of supply, upon

written request as follows:

Address: Office of the Chief Information Officer

Reproduction and Distribution

Services Section

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

E-mail: <DISTRIBUTION@nrc.gov>

Facsimile: 301-415-2289

A portion of NRC regulatory and technical information is available at NRC's World Wide Web site:

<http://www.nrc.gov>

After January 1,2000, the public may electronically

access NUREG-series publications and other NRC

records in NRC's Agencywide Document Access

and Management System (ADAMS), through the

Public Electronic Reading Room (PERR), link

<http://www.nrc.gov/NRC/ADAMS/index.html>.

Publicly released documents include, to name a

few, NUREG-series reports; Federal Register notices; applicant, licensee, and vendor documents

and correspondence; NRC correspondence and

internal memoranda; bulletins and information notices; inspection and investigation reports; licensee event reports; and Commission papers and

their attachments.

Documents available from public and special technical libraries include all open literature items, such

as books, journal articles, and transactions, Federal Register notices, Federal and State legislation,

and congressional reports. Such documents as

theses, dissertations, foreign reports and translations, and non-NRC conference proceedings may

be purchased from their sponsoring organization.

Copies of industry codes and standards used in a

substantive manner in the NRC regulatory process

are maintained at the NRC Library, Two White Flint

North, 11545 Rockville Pike, Rockville, MD

20852-2738. These standards are available in the

library for reference use by the public. Codes and

standards are usually copyrighted and may be

purchased from the originating organization or, if

they are American National Standards, fromAmerican National Standards Institute

11 West 42nd Street

New York, NY 10036-8002

<http://www.ansi.org>

212-642-4900

DISCLAIMER

This report was prepared under an international cooperative

agreement for the exchange of technical information. Neither

the United States Government nor any agency thereof, nor any

of 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.
NUREG/IA-0181

International

Agreement Report

Assessment of

RELAP5/MOD3.2 for

Reflux Condensation Experiment

Prepared by

Y.M. Moon, H. C. No, KAIST

H.S. Park, KAERI

Y.S. Bang, KINS

Korea Advanced Institute of Science and Technology Korea Atomic Energy Research Institute

373-1, Gusung-Dong P.O. Box 105

Yusung, Taejon Yusung, Taejon

305-701 Korea 305-600 Korea

Korea Institute of Nuclear Safety

P.O. Box 114

Yusung, Taejon

305-600, Korea

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

April 2000

Prepared as part of

The Agreement on Research Participation and Technical Exchange

under the International Code Application and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission

Assessment of RELAP5/MOD3.2 for Reflux

Condensation Experiment

Abstract

This report describes the experimental works and the assessment of the predictability of

RELAP5/MOD3.2 for the reflux condensation experiment in the presence of noncondensible

gases in a vertical tube having the same outer diameter of the U-tube riser in Korean standard

nuclear power plant (KSNPP). The reflux condensation experiment is performed in conditions

of the low pressure, low flow and the high mass fraction of noncondensible gas representing the

situation of the loss-of-residual-heat-removal (LORHR) accident during mid-loop operation.

The test facility is composed of the mixture gas generation part and the reflux condensation

part. The test section in the latter part is a vertical tube with 19.05mm diameter and 2.4m length

surrounded by the coolant block. Reflux condensation occurs in the range of very small flow

rates because of the flooding limit. Therefore, the injected steam is completely condensed in the

vertical tube.

The flooding as the upper limit of reflux condensation occurs in lower mixture upward flow

rate than that of Wallis' correlation. The heat transfer coefficients near the tube inlet increase as

the inlet steam flow rate and the system pressure increase. In the presence of noncondensible

gas, the heat transfer capability is dramatically decreased. An empirical correlation is developed

using the local data of heat transfer coefficients. The degradation factor in the correlation is

expressed with four nondimensional parameters. It turns out that the Jacob number and the film

Reynolds number are dominant parameters.

A non-iterative condensation model is developed to predict the steam condensation heat

transfer in the presence of the noncondensible gases, which is different from the existing

iterative model in the RELAP5/MOD3.2 code. The existing models, default model

(Colburn-Hagen model) and alternative model (Chato-UCB model), in RELAP5/MOD3.2 are

assessed with the reflux condensation data. The heat transfer coefficients estimated by the

present non-iterative model and by the existing models of the standard RELAP5/MOD3.2 code

are compared with the present experimental data. The default model and the alternative model

under-predicts and over-predicts, respectively. The non-iterative model better predicts than the

default and alternative models.

-iii-

Table of Contents

A bstract ......................................... ........................

Table of Contents .....

List of Tables .........

List of Figures ........

Executive Summary ....

Acknowledgement .....

Nomenclature ........

..................................................... V

.. .. . . ...... .... . Vli

................. vii

................ xi

.. x)ii

.................................................... Xv

1. Introduction ..........................

1.1. Background .......................

1.2. Objectives and Report Organization .....

2. Reflux Condensation Experiment ........

2.1. Objective of the Present Works ........

2.2. Previous Works ....................

2.3. Facility and Instruments ..............

2.4. Data Reduction Methods .............

2.4.1. Local Heat Transfer Coefficients..

.1

.1

2

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

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

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

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

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

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

0

I

Q

°

J

0

2.4.2. Local Steam and Condensate Flow Rates ..........

2.5. Results and Discussion ..............................

2.5.1. Experimental Conditions .......................

2.5.2. Limitation of the Reflux Condensation .............

2.5.3. Parametric Effects on the Heat Transfer Coefficients ..

2.5.4. Development of the New Empirical Correlation ......

° .3

.o 3

o ° 3

.° 6

... 15

... 15

... 16

... 19

... 19

... 22

... 24

... 29
3. Assessment of Condensation Models in Standard RELAP5/MOD3.2 ........ 32

3.1. Condensation Models in the RELAP5/MOD3.2 Code ................................................. 32

3.2. New Condensation Model - Non-iterative Model ........................................................ 32

3.2.1. Reference Modeling of Vertical In-Tube Condensation ...................................... 33

3.2.2. Solution Scheme of Non-Iterative Model ............................................................ 36

3.3. Calculation Procedures of the Modified Model .......................................................... 40

3.4. Simulation of Reflux Condensation Experiments ........................................................ 44

3.4.1. RELAP5/MOD3.2 Nodalization ......................................................................... 44

3.4.2. Base Case Calculation ........................................................................................... 44

3.4.3. Run Statistics ......................................................................................................... 46

4. Conclusions and Recommendations .................................................................... 57

Bibliography .......................................................................................................................... 59

Appendices ............................................................................................................................ 62

Appendix A Uncertainty Analysis of Reflux Condensation Experiment ............................ 62

Appendix B Input Deck for Reflux Condensation Experiment: #RC 11 ............................ 64

Appendix C Local Data of Reflux Condensation Experiment ........................................... 72

-vi-
List of Tables

2.1 Previous works related to the reflux condensation ............................................................. 5

2.2 Instruments on the components of facility with measurement uncertainty ..................... 14

2.3 Experimental ranges ........................................................................................................ 20

2.4 Test matrix for reflux condensation ................................................................................ 21

2.5 Experimental data of flooding .......................................................................................... 23

3.1 Steady state test conditions of reflux condensation experiments .................................... 45

3.2 The CPU time and the grind time of experiment RC02 ................................................... 46

-vii-
List of Figures

2.1 Overall schematic of reflux condensation facility ............................................................. 9

2.2 Top view of vertical tube and coolant block .................................................................... 10

2.3 Location of temperature measurements in a vertical tube ................................................ 11

2.4 Vertical tube and coolant block ........................................................................................ 12

2.5 Test section of the reflux condensation experiment ........................................................ 13

2.6 Locations of temperature measurements to calculate the local condensing flow rate ........... 18

2.7 Experimental domain in terms of air mass fraction and inlet steam flow rate ................ 20

2.8 Oscillation of tube centerline temperature due to the flooding ....................................... 23

2.9 Experimental results of flooding limit and comparison with Wallis' correlation ............ 24

2.10 Temperature distribution in the absence of air ............................................................... 26

2.11 Temperature distribution in the presence of air ............................................................. 26

2.12 Effect of air mass fraction on heat transfer coefficient ................................................ 27

2.13 Effect of inlet steam flow rate on heat transfer coefficient ............................................ 28

2.14 Effect of system pressure on heat transfer coefficient ................................................... 28

2.15 Comparison of the local heat transfer coefficients between experiment and correlation

(linear-scale) ........................................................................................................................ 31

2.16 Comparison of the local heat transfer coefficients between experiment and correlation

(log-scale) ............................................................................................................................ 31

3.1 Calculation procedure of reference iterative model ........................................................ 42

3.2 Calculation procedure of the present non-iterative model: the modified model .............. 43

3.3 RELAP5/MOD3.2 nodalization for reflux condensation experiment ............................. 48

-viii-
3.4 Heat transfer coefficients of reflux condensation: #RC 16 ............................................ 49

3.5 Heat transfer coefficients of reflux condensation: #RC13 ............................................... 50

3.6 Heat transfer coefficients of reflux condensation: #RC02 ............................................. 51

3.7 Heat transfer coefficients of reflux condensation: #RA02 .............................................. 52

3.8 Comparison of required CPU times of three condensation models .............................. 53

3.9 Time step sizes of the default condensation model ......................................................... 54

3.10 Time step sizes of the alternative condensation model ................................................. 55

3.11 Time step sizes of the modified condensation model ................................................... 56

-ix-

Executive Summary

The reflux condensation in the presence of noncondensible gas in a vertical tube is

performed and the existing models in the standard RELAP5/MOD3.2 code are assessed with the

present experimental data and the newly developed model.

In case of the LORHR during mid-loop operation in nuclear power plants, the reflux

condensation heat transfer in the riser part of the U-tube is an effective heat removal mechanism

without the loss of coolant inventory. However, the previous studies of the reflux condensation

are mainly interested in the flow regimes and their transitions.

The heat transfer data of the reflux condensation are very important results, which require

the separate effect tests to obtain the comprehensive data for the heat transfer coefficients. The

probability of the LORHR is revealed not to be negligible and the RELAP5/MOD3.2 code does

not properly estimate in conditions of the mid-loop operation; the high mass fraction of

noncondensible gases, and the low pressure and low flow. Therefore, the experimental study

and the code analysis in this report play an important role to predict a natural heat removal

capability by the primary coolant system.

The test facility is installed to perform the reflux condensation experiment. It is composed of

the mixture generation part and the reflux condensation part. The latter part includes the test

section. Test section has a vertical tube having the same outer diameter as the KSNPP, which is

surrounded by the coolant block.

The experiments are performed with variations of three main parameters; the system

pressure, the inlet steam flow rate and the inlet air mass fraction. Their ranges are 1-2.5bar,

1.348-3.282kg/hr and 11.8-55%, respectively. The experiments are also performed in pure inlet

steam flow rate to compare the effects with and without the noncondensible gas.

The heat transfer data of the reflux condensation and the flooding data are obtained. The

flooding is observed to know the upper limit of the reflux condensation. As a result, the onset of

flooding occurs at lower upward flow rate compared to Wallis' correlation in geometric

conditions of the sharp edge and the inner diameter of 16.56mm. The heat transfer coefficients

near the tube inlet increase as the inlet steam flow rate and the system pressure increase. In the

presence of noncondensible gas, the heat transfer capability is dramatically decreased. The

-xi-
empirical correlation is developed using the local data of heat transfer coefficients. The

deg•adation factor is correlated with four nondimensional parameters. It turns out that the Jacob

number and the film Reynolds number are dominant parameters.

The non-iterative model is newly developed to predict the steam condensation heat transfer

in the presence of the noncondensible gases. It is applicable to engineering. The condensation

models, default model and alternative model, in RELAP5/MOD3.2 are assessed with the reflux

condensation data. The heat transfer coefficients estimated by the non-iterative model and with

the existing models of the standard RELAP5/MOD3.2 code are compared with the present

experimental data. The default model and the alternative model under-predicts and over-predicts,

respectively. The non-iterative model better predicts than the present models do.

-Xii-
Acknowledgement

This report was performed under the sponsorship of Korea Institute of Nuclear Safety

(KINS) as one of the Ministry of Science and Technology (MOST). Authors appreciate the

KINS for the financial support.

-XIii-

Nomenclature

AMF air mass fraction

FA inlet air flow rate

FM inlet steam-air mixture flow rate

FS inlet steam flow rate

IET Integral Effect Test

KSNPP Korea Standard Nuclear Power Plant

LOCA Loss Of Coolant Accident

LORHR Loss Of Residual Heat Removal

NPP Nuclear Power Plant

RCS Reactor Coolant System

SET Separate Effect Test

SG Steam Generator

TB mixture bulk temperature

TC coolant temerature

TWo outer wall temperature

b blowing parameter

B mass driving force

C total number of node volumes

Cf friction factor

C, specific heat at constant pressure

d, D diameter

Dh hydraulic diameter

F degradation factor(= h,,, / hf)

g mass transfer conductance

h heat transfer coefficient

i enthalpy

Ja Jacob number

k thermal conductivity

L axial length of interval

-Xv-
th mass flow rate

thci local condensing flow rate

thic accumulated condensing flow rate

NA, NB a defined arbitrary nondimensional parameter

Nu Nusselt number

P pressure

PA a defined nondimensional parameter

Pr Prandtl number

q' heat flux

Re Reynolds number

Sc Schmidt number

Sh Sherwood number

St Stanton number

T temperature

U velocity, internal energy

W mass fraction

X mole fraction

x local axial length

y a defined nondimensional parameter

Greek

S liquid film thickness

p density

E, sand roughness

ft viscosity

Subscripts

AB mass transfer

a, air air

b bulk

C coolant

-xvi-
cd, cond

cv, conv

e

f

g

h

i

in

m

0

S

t, tot

V

w

0

conductive

convective

entrance region

condensate, liquid phase, film side

vapor phase, mixture side

heat transfer

inner, interface

initial

mixture

outer

steam, saturated

total

vapor phase

wall

no transpiration

Superscripts

* dimensionless form

-xvii-

Chapter 1.

Introduction

1.1 Background

In case of the loss-of-residual-heat-removal (LORHR) during mid-loop operation in nuclear

power plants (NPP), it is estimated that the safety of the reactor may be severely threatened by

the boiling of a coolant inventory when the decay heat is not properly removed. Such a

probability of accident inducing the core damage during mid-loop operation is revealed not to

be negligible when compared to the accidents during normal operation. For this reason, the

integral experiments and the code analysis for the LORHR accident during mid-loop operation

have been performed in several countries. In Korea, a few research groups have evaluated and

analyzed the experimental results of the integral effect tests (IET) in the foreign countries using

the thermal-hydraulic codes. But the separate effect tests (SET) representing the conditions of a

mid-loop operation are little observed.

As the results of the thermal hydraulic code analysis for the accident of mid-loop operation,

it did not properly estimates the low pressure, low temperature and low flow conditions such as

mid-loop operation. This was because the models in codes were on the basis of the accidental

situation in the high pressure and high temperature such as small break loss-of-coolant-accident

(LOCA) or large break LOCA. Therefore, the comprehensive study of the SET is needed

because the predictability of the individual models can be evaluated by the relevant

experimental database and an improvement can be incorporated into the code, if needed.

A reflux condensation is the countercurrent flow between upward flow of the steam-air

mixture and downward flow of the condensate, which has the upper limit by the onset of

flooding. The reflux condensation heat transfer in the U-tube plays an important role of the

residual heat removal to the secondary side of steam generator (SG) and has an advantage in

cooling the reactor coolant system (RCS) without loss of a coolant inventory.

-1-
1.2 Objectives and Report Organization

The objective of the present study is to obtain the heat transfer data through the SET, to

assess capability of the condensation model in the RELAP5/MOD3.2 code, and to develop a

new non-iterative model for the reflux condensation with noncondensible gas in a vertical tube

simulating the U-tube riser.

In the reflux condensation, the present experimental works are performed with the emphases

on the following conditions:

• high mass fraction of noncondensible gas

* low pressure, low temperature and low flow conditions

• local measurement of heat transfer capability along a single tube.

From the above conditions, the data of the local heat transfer coefficient are obtained and the

empirical correlation is developed. Additionally, the onset of flooding data is obtained to

examine the upper limit of reflux condensation.

The condensation models of the RELAP5/MOD3.2 code are assessed using the present

experimental data and a new condensation model is developed to improve the prediction

capabilities of RELAP5/MOD3.2.

In Chapter 2, the experimental works are described; test facility, its instruments, test

conditions, test results and discussion. The test results include the flooding limit to the reflux

condensation, the parametric effects on the heat transfer capability, and the development of an

empirical correlation. In Chapter 3, the existing condensation models in the current

RELAP5/MOD3.2 code are firstly introduced briefly. The newly developed model is secondly

described about its derivation and the application to the reflux condensation. Finally, the

assessment results of RELAP5/MOD3.2 for reflux condensation are described. The nodalization

is represented and the prediction capabilities of the existing and newly developed models are

compared using the present experimental data of reflux condensation. The uncertainty analysis

method, the RELAP5/MOD3.2 input deck, and the test data are attached in the Appendices.

-2-
Chapter 2.

Reflux Condensation Experiment

2.1 Objectives of the Present Works.

The objectives of the reflux condensation experiment are as follows:

" Perform an experiment of the reflux condensation heat transfer using the single vertical

tube.

" Observe theý flooding phenomenon in a vertical tube, and obtain the database of an onset

of flooding as the upper limitations of reflux condensation.

" Obtain the database of the local heat transfer coefficients.

" Develop the empirical correlation for heat transfer coefficients using the database.

Local heat transfer coefficients are obtained through the local temperature measurements

along the axial direction, which gives the distributions of the heat transfer capability and thus,

the effective heat transfer regions by the reflux condensation. It can be the noticeable results that

the local quantities of heat transfer in the presence of a noncondensible gas of high mass

fraction. Using the data of heat transfer coefficients, an empirical correlation is developed as the

function of several nondimensional parameters to show the governing factors of the reflux

condensation.

2.2 Previous Works

J.W. Park (1984) carried out several experiments on reflux condensation and flooding limits

with the low concentrations of noncondensible gas in pyrex tubes. From his results, the flooding

flow rate and heat transfer rate per unit axial area decreased as the air flow rate increases. It was

observed that once a tube was flooded, its heat removal capability was much less than that of

the tube before flooding. Banerjee et. al. (1981) carried out the experiment of the transition from

-3-
the reflux condensation to natural circulation and the behavior of condensing region and liquid

column. Also, they performed the theoretical analysis of heat removal and the stability of flow

regime. They related the pressure differences between the inlet and the outlet of the tube with

the length of a single phase liquid column. According to the study, liquid column was above the

reflux condensing region and occurred after flooding. Nguyen and Banerjee (1982) used the

inverted U-tube test section that was directly attached to the boiler, and observed various flow

patterns and oscillatory behavior. They described the pressure drop of the test section as the

parameter representing the flow regimes. Hein et. al. (1982) carried out the experiments using

the inverted U-tube made of stainless steel and the saturated secondary coolant pool. They made

a few steady states varying the amount of injected nitrogen gas and the secondary saturated

temperature. The transition of the active to passive condensing region was observed by

measuring the temperature along the axial direction. The active length became short as the

amount of injected nitrogen gas increased.

Tien et.. al. (1982) performed the 2-D analysis of the condensation in a tube with the

Nusselt's film condensation theory and the condensation experiments using the copper tube

evaporator that leads to the thermosyphoning and the collapse of liquid column at the head of

tube. Wan et. al. (1983) studied the formation of liquid column after flooding using the single

long tubes which are different from each other. And the constants, C and m, in Wallis' flooding

formula were newly evaluated from the experimental results. The diameter of the tube was

considered as an important factor in their study.

Chang et. al. (1983) used four tubes for their experiments and predicted the multi-tube

effects according to the fluctuation of liquid column exist. The fluctuation was magnified in the

multi-tube to the single tube. The heat removal capability was increased as the inlet pressure

increases. Marcolongo (1987) measured the local temperatures and investigated for the reflux

condensation and the flooding limit using the inverted U-tube. The experimental flooding

results were compared to a few correlations and it was concluded that Wallis' correlation is most

similar to the prediction of the experiments. In the range of high pressure (55 - 105 bar) the

empirical correlation for the heat transfer coefficient was developed using the film Reynolds

number. However, the data representing the correlation was insufficient.

Table 2.1 shows the experimental conditions and the test section geometries of the

previous works. In summarizing the previous works, three kinds of flow regimes exist as an

increase of gas-phase upward flow in a vertical condensation.

(1) Reflux condensation

-4-
(2) Flooding and oscillation of liquid column

(3) Natural circulation of liquid

The previous works were mainly interested in the above flow regimes and their transition,

and tried to modeling theoretically. These focus also make an agreement with the integral effect

test (LET) considering the mid-loop operation. They distinguished the transition points using the

amount of pressure drop.

Table 2.1 Previous works related to the reflux condensation

Test section geometry Inlet Fraction Temperature

Authors e D team sb NCG or amount1 measuning Atos Tube Tube Dia. Height iflowofNG pit

material shape [mm] [kg/hr] of NCG points

Park Pyrex U-tube 15.5 1.90- 1.63 0.75- 3.0 Air &M 0 0.-0.03 03 (in/mid.) 2

Banerjee & pyrex Vertical 17.6 4.0 -4.8 Air 0-_0.05 2

cinang (in/out)

Nguyen Pyrex U-tube 16.0 2.16 -6.1 Air - 2

& Banerjee ex(in/out)

Hein Stainless U-tube 20.5 1.05 -3.6 Injected 0.97- Local

Steel N2 3.4g points

Tien Copper Vertical 20.9/9.5 0.9 1.7-2.3 None - 3

Wan Girard & Pyrex Vertical 12-7-25 .4 4.0 7.0 None - 8.

Chang & 2

Girard & Pyrex U-tube 12.7 1.5 18 None - (in/out) Wan

W his Exp. )Staness VertiMca '.J9.05: 2.4• K1.4-3.3 Air 0-0.55I 11 N :fl nnnpnn1"S - teel. •.

The reflux condensation was not independently described but considered as one of the flow

regimes in countercurrent flow in the previous works. It was due to the SB-LOCA specific

phenomena was main interest in the transition of the flow regime. Flow regimes were visually

observed using the transparent tubes, e.g. pyrex tube, which makes impossible to measure the

local parameter in tube because of the manufacturing problems. Also, small concentrations of

noncondensible gas were treated in the previous works. The nitrogen or air was used as a

-5-
noncondensible gas, which made a vapor mixture in the ways of the pre-injected condition or

the steady flow condition. The concentrations of noncondensible gases in the previous works

had small fraction, which were within 10% as a vapor mass fraction unit. In some cases of the

previous works, the. local temperature measurements along the axial length are found, but this is

not to obtain the local heat transfer coefficients but to know the in-tube condition and flow

regime.

The present work treats the mixture flow with the large concentrations of the air as the

noncondensible gas. Also the major characteristics in this study are to measure the temperatures

at eleven local points along the stainless-steel tube such that the local heat transfer coefficient

distribution can be obtained.

2.3 Facility and Instruments

A test facility is installed for the reflux condensation experiments. The test facility is

composed of two parts. One is the steam-air mixture generation part and the other is the reflux

condensation part. The latter includes the main test section. Test section is composed of the

vertical tube, the coolant block, lower plenum and upper plenum, which has a geometry of the

total length of 3.56m, and the length of effective temperature measurement of 2.4m. Figure 2.1

shows an overall schematic of the test facility.

The steam-air mixture generation part is composed of steam tank, heater, power

controller, air line, air pre-heaters and flow mixer. The heater controller having the maximum

power of 150kW controls a steam generator. The steam generated from the steam tank and the

air from the air line individually flow into the flow mixer and mixed together. Before the air

arrives at the flow mixer from the air injection line, two air preheaters heats up the cold air to

have a temperature balance with saturated steam. Air preheaters have each power of 3kW and

are controlled by the preheater controller. An air flow is measured by the two rotameters having

different ranges: 2-201pm, 9.4-941pm. The air rotameters have a measuring errors of ±-2.5%.

The steam-air mixture from the mixer flows into the lower plenum in the reflux condensation

part. All pipings are 1-inch diameter size in this part. Thermal insulating material is used to

cover around the pipes and tanks to lose as low as possible. The droplet separator and the

turbinemeter are located on the steam-air mixture line. A droplet generated from the mixture

line by the heat loss is removed on the droplet separator and then the mixture flow rate is

-6-
measured by the turbinemeter that has a maximum range of 8.lm3/hr.

The reflux condensation part is composed of vertical tube, coolant block, lower and upper

plenum, drain tank, venting line and air-steam separator. K-type 0.5mm-dia. thermocouples are

attached on a vertical tube and used to measure the tube centerline temperatures and the outer

wall temperatures along the same axial locations. Figure 2.2 shows the position of

thermocouples' installation in a vertical tube. The coolant temperatures are also measured at the

same positions. The measuring points are located closer to the tube inlet because the capability

of heat transfer in this region becomes large. A vertical tube has the geometry of the outer

diameter of 0.75" (equal to the U-tube diameter of KSNPP), inner diameter of 16.56 mm and

effective length of 2.4m (temperature measuring region). The tube inlet has a shape of sharp

edge. The coolant block is installed around the vertical tube and establishes the annular shaped

flow of the coolant between the block and the tube. The outer diameter of coolant annulus is

57.15mm. The K-type 0.125" diameter thermocouples to measure the coolant temperature are

installed on a coolant region penetrating into the coolant block. Figure 2.3 shows the schematic

of the thermocouple attachments on the test section as a top view. Figure 2.4 shows the vertical

tube and the coolant block as a side view. For the stable inlet and outlet conditions, the upper

and lower plenums are installed at both ends of a vertical tube. They have a shape of 20 X 20 X

20cm cubic. The lower plenum has visual windows to observe the falling condensate in tube

inlet. The air-steam separator is installed on the venting line for extracting the remaining steam

in a vented flow. However, the most amount of inlet steam is condensed on the inner surface of

the vertical tube and no noticeable collection of the vented steam observed. Figure 2.5 shows

the view from the bottom to the top. In this photograph, the lower plenum is partially shown and

the coolant inlet is connected with four coolant injection hose. The thermocouples to measure

the coolant temperature are shown on the right side of the vertical test section.

Total 6 pressures, 4 flow rates and 53 temperatures are measured in the reflux condensation

experiment. There are two ways in the measurements of data. One is to observe or measure

visually, and the other is to measure the electric signals by the measuring instruments. The air

flow and coolant flow are measured by reading of the scale marks of rotameters. The steam flow

is measured by the turbinemeter. The pressures are measured by the pressure transducers, and

all the temperatures are measured by the K-type thermocouples. All data except the air flow rate

and the coolant flow rate are collected by the data acquisition system (DAS). The DAS is made

by Hewlett-Packard Co. and includes the main-frame (E1421B), MUX module (E1413C),

terminal block (64 channels) and so on, and uses the GP-IB interface for communicating with

-7-
the IBM 486 PC. The HP-VEE v.3.2 is used as software. The DAS collects 61 data per time

interval of 0.4 - 1.0 second, and displays data on monitor. The tube centerline temperatures are

graphically monitored to discriminate the temperature fluctuations by the onset of flooding.

Table 2.2 summarizes the instruments on the components of facility and their uncertainties. The

sample error analysis for the heat transfer coefficient is represented in Appendix A.

-8-
TO P0 Venting Line

Upper

Plenumil

Vertical

Condensing

Coolant Block Z J

Steam Tank 4I

Air

Injection

Line

E

'U

Air-Steam Mixture Generation Part

P: pressure

F: flow rate

T : temperature

Reflux Condensation Part

Figure 2.1 Overall schematic of reflux condensation facility
Primary Side

(steam-air

mixture)

Outer Wall

"Tempferatu&e

Figure 2.2 FTemperature Top view of vertical tube and coolant block

-10-
--

a,

I--

C

C.2

F)

FI-:

-TB11 , 2300mm

TB10, 1865mm

TB9, 1450mm

-TB8, 1200mm

-TB7, 950mm

E

E

C)%

0

4

TB6, 730mm

TWo1-11

TB5, 535mm

TB4, 365mm

TB3, 220mm

Condensat T82, 100mm

downf low - TB1 , 0mm

Steam-Air

upflow

Figure 2.3 Location of temperature measurements in vertical tube

-11-
Acryl Block

Test Tube

Figure 2.4 Vertical tube and coolant block

-12-
Figure 2.5 Test section of the reflux condensation experiment

-13-
Table 2.2 Instruments on the components of facility with measurement uncertainty

Component Identifier Parameter Instrument Uncertainty

Air-Steam Mixture Generation Part (full scale)

Steam PT steam tank pressure ABB PT-62;4 transducer 0.1%

Generation o- R koflrm -

Tank TT steam tank temperature K-type T/C 0.125" 0.5%

PA air line pressure PX425-100GV(Omega 0.2% AirirInnectioneCo.), 0-100 psig Air Injection -- yp T C_015

Line TA air line temperature K-type M~uc 1 000 0 C 1 0.5%

FA inlet air flow rate Dywer rotameters 2% FAinletairfowrate 2-201pm, 20-200SCFHI 2

Flow Mixer TM2 air-water mixture K-type T/C 0.125" 0.5% temperature on flow mixer Max. 1000 *C

air-water mixture f turbinementer(Sponsler FM rate on turbinemeter Co.) SP712-2 rev.B 1/2" 1%

(on loop) max. 8.1ml/hr

TM air-water mixture RTD4-20mA(SenTech Co.) 0.5% temperature on loop Max. 650 'C

Reflux Condensation Part

TO upper plenum temperature K-type Max. 1000 T/C °C0.062" 0.5%

Upper Plenurr transducer: PX425-IOOGV

PO upper plenum pressure (0-6.8)(Omega Co.) 0.2%

gauge: 0~5kgf/c__

TI lower plenum temperature K-type T/C 0.062" 0.5%

Lower transducer: FP3300/B

Plenum PI lower plenum pressure (0-50-5kgf/cd)(Konics 0.3%

C..V crange" 0-5kgf/r.Td

TB I air-water mixture bulk K-type T/C 0.02"(U) K-tye_ IC .02(U) 0.5% - temperature in tube Max. 760 0C

Vertical Tube TB11 center

TWol outer wall temperature K-type T/C 0.02"(U) 0.5%

T-ol 1 on vertical tube Max. 760 °C

FC coolant flow rate Dwyer, rotameter 2% F_ colatorte 0.5-2.51pm, 0.8-2.2gpm

Coolant Loop TC1

cooan tmpeatre K-type T/C 0.125"(U) 0.5%

TC11 Max. 760_C

TD _____Max. drain tank temperature K-type 1000 T/C 00.062" C 0.5%

Drain Tank

PD drain tank pressure pressure gauge 2% PD drain tank pressur 0 -5 kgf/cm_

FV vented air flow rate Dwyer, rotameter 2% FV___ vented air flow rate 10- 1001nmr

Vented K-type T/C 0.062"

Air-Water TV separator temperature Max. 1000 2 0.5%

Separator pressure gauge 2% PV separator pressure 0-1.5kgf/cm?

-14-
2.4 Data Reduction Methods

2.4.1 Local heat transfer coefficients

The calculation of the local heat transfer coefficients requires the measurement of the

temperatures at the tube centerline (Tb ), the tube outer wall (T, 0, ), and the coolant (T7). These

three temperatures are all measured along the 11 axial points. Therefore, total 33 measurements

of temperature are performed to obtain local heat transfer coefficients. In data reduction process,

the inner wall temperature and the heat flux can be also calculated.

Data reduction for heat transfer coefficients is first developed from the basic heat balance

concept. The heat loss by the reflux condensation from the inside of a vertical tube is transferred

to the secondary side of coolant annulus through the unit tube wall area, which is the same as

the heat gain by the increase of coolant temperature. This heat balance is expressed

mathematically asfollows:. ....... .

q'(x)dA = ihizCpdT7 (2-1)

where the q'(x) is the heat flux flowing out through a unit wall area by the condensation of

steam in the mixture and th, is the coolant flow rate. If the coolant flow rate and the coolant

temperature are known the local heat flux can be calculated using the following relationship:

q"(x) = ihCP daT (x) = hYhCp dT, (x) (2-2)

dA ;rd dL

where the L is the axial length of interval where the adjacent two coolant temperatures are

measured. The tube inner wall temperature can be calculated by the calculated heat flux and the

measured outer wall temperature:

TWf (x) = Tw0 (x) + q"(x) . R (2-3)

R = ln(D, I D,)Dh (2-4)

where Dh is the hydraulic diameter and k.. is the thermal conductivity of stainless-steel 304

as a material of vertical tube. Finally, the local heat transfer coefficient can be obtained through

the heat flux divided by the difference between the tube centerline temperature and the inner

wall temperature.

-15-
h(x) = q"(x) (2-5)

(Tb (x) -T, (x))

2.4.2 Local steam and condensate flow rates

The turbinemeter is used for measuring the steam-air mixture flow rate. However, the flow

data from the turbinemeter installed on the inlet piping has some different value from the actual

flow rate at tube inlet because of the heat loss in the region from the steam piping to the inlet

plenum and of the falling liquid condensate. The actual flow rate can be also obtained using the

local temperature data. Actual flow rate by data reduction is calculated, as results, it has a little

lower value than the measured flow rate by turbinemeter.

As a results of experiment, it was found that most of the steam is condensed through the

inside of vertical tube. Therefore, the amount of inlet steam flow should be the same as the

amount of falling condensate at tube inlet. The inlet steam flow rate is obtained as follows:

ths-. n, (2-6)

ifg

where L is the temperature measuring point of tube exit, and the ifs denotes the latent heat of

the steam. To obtain the local data for the steam flow rate (thj (x)) and the condensate flow rate

(rhf (x)), the following parameters are defined in the reduction process:

" local condensing flow rate (th, 1 ) : the amount of condensation in a specified local interval

" local condensate flow rate (ihf) : the amount of condensate flow at a local position

" accumulated condensing flow rate (mic,) : the amount of condensation in the interval

from inlet to the specified position

Local condensing flow rate in specified interval (i) is known as follows:

SrhC [T, (i + 1)- T, (i)] (2-7)

ife

The local steam flow rate (thi) is the value of the inlet steam flow rate subtracted from the

accumulated condensing flow rate (?hca) at the local point of x. Figure 2.6 shows the concept of

nodes for calculating the local condensing or condensate amounts, where x and i represent the

temperature measuring point and the number of interval between x and x+ 1, respectively.

The accumulated condensing flow rate at a position x is estimated as follows:

-16-
Iflca(x) = fihC,(T7(x)-T7(O)) = (28)

Then the local steam flow rate can be obtained as follows:

1h, W = fkci, (x). (2-9)

The local condensate flow rate (hfif) represents the actual amount of condensate at x. In

reflux condensation, the steam upward flow makes the countercurrent flow with the condensate

downward flow. Therefore, the condensing flow rate (filca) is different from the condensate

flow rate (thfi). Here, if (x) is the sum of the local condensing flow rate from x to L and is

also the accumulated condensing flow rate from 0 to L subtracted from that from 0 to x:

L-1

hfi (X) = E fia (i) = fh,,, (L) - fih,, (x). (2-10)

i=x

By Equation (2-9), the accumulated flow rate is obtained as follows:

fia (x) = fil.•, - 7i, (x), (2-11)

fic(L) = -is.,-is(L) = is.-(2-12)

Substituting the above equation into Equation (2-10), the condensate flow rate at x is

obtained as follows:

fif(x) =fWh.(L) -fhi(x)

= ,- [fi.. - fi, () (2-13)

The inlet flow rate of air is constant along the channel when it is flowing through the tube

because of its noncondensability.

h W(x) =fin. = 1a (2-14)

Moreover, the local air mass fraction can be obtained as follows:

i,(x) W W fiW fi°-- h (2-15)

-17-
TB11 , 2300mm

Number of Measuring

Points =x

i=6

TB6 730mm

i~=5

ii

Ti• 535mm

i=4

TB4, ,365mm

Number of "

Nme f TB3, 220mm

Interval =i'

A -A TB2, 100mm

i=1 '

TB1, 0mm

Figure 2.6 Locations of temperature measurements to calculate the local condensing flow

-18-
2.5 Results and discussion

2.5.1 Experimental Conditions

In the present experiment, 29 sets of data with variations of three main parameters are

obtained and each sets have 11 data at local points. Table 2.3 represents the experimental ranges.

Table 2.4 represents 29 data set of a reflux condensation experiment performed under various

main parameters as a test matrix form. Total 165 of local data are available for deriving the

correlation of the heat transfer coefficients, which are selected from 6 sets at 2.5 bar, 7 sets at

1.5 bar and 16 sets at 1.0-bar. Two sets at 1 bar are the cases of the inlet pure steam in the

absence of the air injection.

The experimental ranges of the system pressure, the inlet steam flow rate, and the inlet air

mass fraction are 1-2.5 bar, 1.348-3.282 kg/hr and 11.8-55.0 %, respectively. The inlet

steam is all condensed in a vertical tube. Therefore, the amount of vented air is the same as that

of injection.

Figure 2.7 shows the domain of the test conditions with respect to the inlet steam flow rate

and the inlet air mass fraction. In the figure, upper and lower limit are also plotted, which

represent the flooding limit proposed by Wallis (1969) and the measured range of turbinemeter,

respectively. The data has a somewhat dispersed distribution because the desired data on flow

rates and air mass fractions cannot be obtained as expected due to the difficulty in the control of

the low flow condition.

Inlet steam is completely condensed on the inner surface of a vertical tube. The length of the

active condensing region is approximately estimated to be within 1.865 m considering the local

heat transfer coefficients and the temperature profiles. After the active region, it is called as the

passive region, where the temperature gradients almost become zero. In reflux condensation,

most of condensates smoothly flow down along the tube wall and the very small portion of the

condensates falls directly. The local data used to the correlation development are attached in

Appendix C.

-19-
Table 2.3 Experimental ranges

Parameter Units Conditions Remarks

FS kg/hr 1.348-3.282 inlet steam flow rate

FA kg/hr 0, 0.551 -2.443 inlet air flow rate

FM kg/hr 1.875-4.443 inlet mixture flow rate

P bar 1, 1.5, 2.5 (approx.) system pressure

AMF % 0, 11.8-55.0 inlet air mass fraction

FC kg/s 0.0250-0.0630 coolant flow rate

0 10 20 30 40 50 60

Air Mass Fraction [%]

Figure 2.7 Experimental domain in terms of air mass fraction and inlet steam flow rate

-20-
Table 2.4 Test matrix for reflux condensation

FS FA FM Press FC Max. I.D. [kghrr] [kg [kg/br]h [kPa] [KgIs] TC1 Max. HF HTC

RA0I 3.282 18.4 0.742 4.023 265.3 0.0333 11.1 115032 2382

RA02 2.591 23.7 0.804 3.395 266.0 0.0504 21.5 81136 1738

RA03 2.525 37.9 1.538 4.062 258.2 0.0333 9.9 51074 1044

RA04 2.384 25.2 0.804 3.187 254.5 0.0504 23.7 38719 763

RA05 2.357 44.0 1.850 4.207 260.0 0.0333 10.0 35701 709

RA06 2.000 55.0 2.443 4.443 263.3 0.0333 10.0 25908 526

RBO1 2.448 24.5 0.796 3.244 157.2 0.0333 8.8 45126 1104

RB02 2.436 37.0 1.430 3.866 155.5 0.0333 8.7 40224 1024

RB03 1.985 41.4 1.403 3.388 152.0 0.0630 22.9 23195 736

RB04 1.967 21.9 0.551 2.518 156.5 0.0250 7.0 44897 1137

RB05 1.694 48.2 1.577 3.270 156.1 0.0250 6.5 25911 624

RB06 1.561 26.1 0.551 2.112 156.3 0.0250 6.7 25956 545

RB07 1.560 47.8 1.426 2.986 155A 0.0333 8.8 21752 473

RCO1 2.703 11.8 0.361 3.064 107.6 0.0333 12.0 56820 2231

RC02 2.287 29.1 0.938 3.225 107.4 0.0333 11.5 39285 1243

RC03 2.232 18.5 0.506 2.738 108.4 0.0333 11.6 39448 1243

RC04 2.119 16.9 0.432 2.550 106.9 0.0333 11.6 39316 1185

RC05 2.077 12.1 0.285 2.362 104.0 0.0504 20.1 37194 2091

RC06 2.046 12.2 0.285 2.331 104.0 0.0630 19.1 23800 805

RC07 1.916 26.0 0.672 2.588 107.0 0.0630 18.0 34596 1115

RC08 1.887 42.5 1.394 3.280 116.2 0.0333 11.2 22714 784

RC09 1.875 0.0 0.000 1.875 108.6 0.0263 13.8 121382 5645

RC1O 1.618 46.3 1.392 3.010 116.1 0.0333 10.5 21666 597

RC1 1 1.584 18.9 0.369 1.953 107.0 0.0630 18.1 40089 1149

RC12 1.535 47.3 1.380 2.915 109.4 0.0333 10.8 27529 837

RC13 1.504 41.8 1.081 2.585 105.4 0.0250 6.5 22245 632

RCI4 1.379 34.3 0.720 2.099 105.4 0.0250 6.9 23560 582

RC15 1.367 29.7 0.576 1.943 107.0 0.0333 15.6 40872 1272

RC16 1.348 0.0 0.000 1.348 107.3 0.0250 14.2 92803 3971

FS : inlet steam flow rate

FA: inlet air flow rate

HF: heat flux

TC1 : inlet coolant temperature

FM : steam-air mixture flow rate

FC : coolant flow rate

HTC : heat transfer coefficient

-21-
2.5.2. Limitation of the reflux condensation

The reflux condensation has an upper limit. When the upward flow rises over the upper limit,

the condensate becomes unstable and falls with perturbation. This phenomenon is no more

'reflux' flow regime. This upper limit is called 'flooding' and the flow regime changes beyond

the flooding. The flooding itself is an important phenomenon in countercurrent flow and gives a

limitation of the reflux condensation. Therefore, the experimental study of the onset of flooding

is investigated. As a result, it was found that the onset of flooding occurs at lower upward flow

rate when compared to the Wallis' correlation in geometric conditions of the sharp edge and the

inner diameter of 16.56mm.

The flooding discrimination in the previous works depends on the visual observation of the

transparent pyrex tube. In the present work, it is impossible to observe visually due to the use of

a stainless steel tube for temperature sensor installation. Instead, the severe oscillation of the

tube centerline temperature is regarded as a discrimination criterion of the .onset of flooding. It

is based on that the slugging or bridging of the cold condensate by the flooding cause a sudden

and intermittent drop of the tube centerline temperature, and that the oscillation of the

temperature can be discernable.

Figure 2.8 shows the oscillations of the temperature due to flooding as the stepwise increase

of upward flow. Table 2.5 shows the flooding results. J• and Ji represent the nondimensional superficial velocities of the steam-air mixture and the condensate, respectively. The

condensate flow rate is dependent on the inlet steam flow rate because the injected steam is

condensed and becomes condensate. Therefore, the distributions of data points are in the limited

range of J*. The values of constant C in the Wallis' correlation are 0.6383-0.7034 in the

experiments, which is lower than 0.725 suggested by Wallis (See Figure 2.9). The experimental

flooding data also covers a wide range of the air mass fraction. The subsequent study of the

effects of the air mass fraction may be useful.

-22-
Table 2.5 Experimental data of flooding

FS FM AMF Pressure .* ., .112 .*1/2 .*1/2 C by

[kPa] Jf igf Jg Jg.waltis experiment

2.474 2.854 0.133 107 0.00828 0.3586 0.0910 0.5988 0.6340 0.6898

2.452 3.476 0.295 151 0.00816 0.3758 0.0903 0.6130 0.6347 0.7034

3.047 3.886 0.216 261 0.01031 0.3405 0.1015 0.5836 0.6235 0.6851

1.259 3.400 0.630 111 0.00415 0.3759 0.0644 0.6131 0.6606 0.6775

2.111 2.481 0.370 109 0.00700 0.3076 0.0837 0.5546 0.6413 0.6383

FS : inlet steam flow rate [kg/hr]

FM: inlet mixture flow rate [kgfhr]

AMF: air mass fraction

_ (at constant steam flow rate)

200 400 600 800 1000 1200 1400 1600

200 400 600 800 1000 1200 1400 1600

Time [sec]

Figure 2.8 Oscillation of tube centerline temperature due to the flooding

-23-
0.8-

0.7 _ -_-

0.6 0.53

0g.14 -" (for Sharp 5'

0.3.

0.2+] ____ I

/ '. !Wallisi Crreiation

,. (for Sharp.,Edge' CO01725.

0.1~ . * - i-- - . . . .

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

j f*1/2.

Figure 2.9 Experimental results of flooding limit and comparison with Wallis'

correlation

2.5.3 Parametric Effects on the Heat Transfer Coefficients

The parametric effects in the reflux condensation are experimentally investigated that the

heat transfer coefficient increases with an increase in the system pressure and in the inlet steam

flow rate, and decreases with an increase in the inlet air mass fraction. The active condensing

lengths are roughly estimated by the curves of the heat transfer coefficient or the temperature

profiles along the axial direction. The active region is enlarged or contracted according to each

condition of the increase of the air mass fraction and of the system pressure.

Figures 2.10 and 2.11 show the effects of the presence and the absence of the air in the inlet

flow on the temperature distributions. In case of pure steam in-flow, the injected steam is all

condensed near the tube inlet and the tube centerline temperatures suddenly fall off. Instead of a

short active condensing region, the heat transfer occurs intensively in this region. In case of an

-24-
inlet steam-air mixture flow, the active condensing region is enlarged in the case of the air

presence, which means the decrease of heat transfer capability by the presence of

noncondensible gas in this region.

Figure 2.12 shows the effects of the air mass fraction. The heat transfer coefficients in the

absence of the air are larger values than those in the presence of the air, which means the air

plays a role of the heat transfer resistance. For the different air mass fractions (11.8-55%), the

experimental results also confirm the effect of noncondensible gases on the heat transfer

coefficients. As air mass fraction increases in a high concentration range, the heat transfer

coefficient decreases near the tube inlet.

Figure 2.13 shows the effect of the inlet steam flow rate. An increase of steam flow causes

the overall increase of the local temperatures. The local heat transfer coefficients increase over

the entire active region with an increase in steam flow rate.

Figure 2.14 shows the effect of the pressure. With an increase in pressure, the active

condensing region becomes shorter. and the heat transfer capability is increased within this

region. The distribution of heat transfer coefficients is shifted and concentrated toward the tube

inlet, but its capability over the entire active region is not changed.

Therefore, it can be found that the decay power affecting the steam generation and the

amount of generated noncondensible gases may be the important factors in determining the

capability of heat removal through the U-tubes.

-25-
E

Lengh from tube inlet [m]

Figure 2.10 Temperature distribution in the absence of air

so.

E 50-

9

Figure 2.11 Temperature distribution in the presence of air

-26-
I * I * I * I *

4= 4.

E

-3000-

O

200

*~1000-

0-"

"Ilee

. o.... I FS=1 .348kg/hr, AMF=0.0% ..-

0 FS=1 .584kg/hr, AMF=1 8.9%

o . -- A.. FS=1.504kg/hr, AMF=41.8%

.................. ................... . . . system pressure. 1 bar.

0

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

.....T ... • . .. .. ................. ..... .. . . ........ . . . . .... ....... . .. .... ... ...... ....

A.

...... ......... A' .............. A......-.A.. .....

4.*

n -I. -..

0.0 0.5 a a

1.0 1.5

Length from tube inlet [m]

a2-0

Figure 2.12 Effect of air mass fraction on heat transfer coefficient

-27-
1400. "

1200~ -0 -0- 0.1O8MPa, 2.232kg/hr. 18.5%

,A -A- 0.1 07MPa, 1.584kg/hr, 18.9%

1000 ..... ....... .......

~8W. 0

0

" 6 0 0 .... . . ... .. ............ . .........

~600

4 0 0• ...... .. O" .......... ... ....... .. ...... .. . ....... ....

0, 0

200 . .

0

0.0 0.5 1.0 1.5 2.0

Length from tube inlet [m]

Figure 2.13 Effect of inlet steam flow rate on heat transfer coefficient

2-1600-

E

~1400 -

• 1200 -

% 1000- 0o

40 -o

200-

0.

.... A...... -- 1- 0.107MPa, FS=2.287kg/h

-0-.0.1 57MPa, FS=2.448kghM

-- 0.266MPa, FS=2.591 kg! M

0

r, AMF=29.1 %

AMF=24.5%

AMF=23.7%....

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

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

Io * i * I I 0.0 0.5 1.0 1.5 2.0 Length from tube inlet [m]

Figure 2.14 Effect of system pressure on heat transfer coefficient

-28-
2.5.4. Development of a new empirical correlation

In a vertical flow with condensation, the total heat transfer coefficient (ho, ) can be separated

into the heat transfer coefficient of film side (hf) and the heat transfer coefficient of steam-air

mixture side (h. ) with respect to two phases, and is separated into the convective ( and

condensation (hCOfld) heat transfer coefficients with respect to the heat transfer mechanisms. The

nondimensional parameters related to ho,, are Re., Prg and h

11

COfd can be expressed in

terms of Re., Ref , Wai, and Ja.

The degradation factor (F) is suggested for the nondimensionalization of the local heat

transfer coefficients. The F represents the relative factor of the wall condensation heat transfer

coefficient with noncondensible gases to that without them. F is defined as the ratio of h,., /hf

where h,,, is q'/(Tb -Twj) and hf is q"/(Tf -Tw4 ). T$ is a temperature at the interface

between the film layer and the mixture layer. The value of hf may be expressed as kf 15

.-according to.Nusselt's classical-film condensation theory (1916). kf is thermal conductivity

and 5 is a film thickness as follows:

3,f'Ref 1 / (216 = 4pf (p -pg)g J(-6

The degradation factor is developed as a function of 4 nondimensional parameters; the

steam-air mixture Reynolds number and the film Reynolds number (Reg and Ref ), the Jacob

number (Ja), and the local air mass fraction (Wa,,). The Prandtl number is excluded because

its effects are negligible in the present experimental condition. The least square method for

multi-variables is numerically used for correlation development.

The local data in the active condensing region among the entire region are selected for

developing correlation. The empirical correlation using 165 data of the local heat transfer

coefficients is produced as follows:

F = = 2.58 x 10-4 Re°o"-0 Re05 • Ja-° ( 42 (2-2 

where, 6119 <Reg < 66586 (2-18)

0.140<WWj, < 0.972 (2-19)

0.03 < Ja < 0.125 (2-20)

-29-
1.2 < Ref < 166.6 (2-21)

From this correlation, the variation of F ranging from 0.0153 to 0.3301 demonstrates that the

heat transfer is severely degraded by the presence of the air. The degradation factor also

decreases along the axial length. This correlation represents the reflux condensation heat

transfer in the active condensing region in conditions of the low flow, low pressure and low

temperature. Jacob number is the most dominant parameter: the temperature difference between

the tube centerline and the inner wall is very important to heat transfer. Film Reynolds number

is secondly dominant. This means that the degradation of heat transfer is low in the region of the

large temperature difference and the thick condensate film. The film thickness ranges from

3.07x105 to 1.19x10 4 m. The root mean square error of the present correlation is 17.7 %

compared with the experimental results.

Figures 2.15 and 2.16 show the comparisons of the ht, results from the experiment and

that from the correlation in linear-scale and log-scale. The difference between data from the

correlation and the experiment is nearly same irrespective of the vertical location.

-30-
0+ %

.0150•

0%

=1000. (RS eror

Z

03

00)

5 0;0 1"000 1500 2 000 2M 0

heat transfer coefficient (experiment) [WIm2K]

Figure 2.15 Comparison of the local heat transfer

coefficients between experiment and correlation

(linear-scale)

heat transfer coefficient (experiment) [W/m2K]

Figure 2.16 Comparison of the local heat transfer

coefficients between experiment and correlation

(log-scale)

-31-
Chapter 3.

Assessment of Condensation Models in

RELAP5/MOD3.2

3.1. Condensation Models in the RELAPS/MOD3.2 Code

The RELAP5/MOD3.2 code is used to analyze nuclear power plant transients and

loss-of-coolant accidents. Many heat transfer correlations in RELAP5/MOD3.2 are known to

have many uncertainties. In particular, 'ai there .. is no ~ reliable model for .~' condensation '" phenomena .... ...

with noncondensible gases in a vertical tube. The RELAP5/MOD3.2 condensation models can

be categorized into two groups. One is wall heat transfer, which occurs when the wall comes in

contact with a two-phase mixture through condensation, and the other is interfacial heat transfer,

which occurs through an assumed interface as a result of differences in the bulk temperature of

the liquid and vapor phases [6].

Two wall film condensation models, the default and the alternative, are used in

RELAP5/MOD3.2. For an inclined surface, the Nusselt-Shah-Colburn-Hougen correlations are

used as the default model, and the Nusselt-University of California-Berkeley (UCB)

correlations are used as the alternative model for the wall film condensation. The default model

uses Nusselt's and Shah's maxima, with Colburn-Hougen's diffusion calculation when

noncondensible gases are present. The alternative model is the Nusselt model with UCB

multipliers, which is revised to include the effects of interfacial shear and the presence of

noncondensible gas in a vertical tube.

The detailed description of the condensation models in the standard RELAP5/MOD3.2 code

are discussed in the authors' previous report [29].

3.2. New Condensation Model - Non-Iterative Model

A reference mechanistic model of vertical in-tube condensation in the original

-32-
RELAP5/MOD3.2 code, which was an iterative method, was developed for steam condensation

in the presence of a noncondensible gas in a vertical tube. A non-iterative model is developed

based on the reference mechanistic model to enhance its applicability to the code, which does

not need iteration to find the temperature and pressure at the liquid-gas interface. The

condensation heat transfer coefficient can be expressed in terms of non-dimensional bulk

parameters without using any interfacial data.

In the presence of noncondensible gases the iterative model has been widely used, which

was related to the heat and mass transfer analogy. The iterative model is newly developed to

include the following effects:

° The high mass transfer effect by condensation;

° The entrance effect of test section;

• The interfacial waviness effect.

The non-iterative model is newly developed which includes the advantages of the above new

iterative model. The non-iterative model also includes the assumption that the steam mass

fraction and temperature of mixture gas have the same distribution in a gas mixture boundary

layer, and the Nusselt number for condensation is derived with several mathematical

derivations.

The Nusselt number for condensation is expressed as a function of air mass fraction, Jacob

number, Stanton number for mass transfer, gas mixture Reynolds number, gas mixture Prandtl

number and film Nusselt number on condensate surface. As a new condensation model the

non-iterative model is presented.

3.2.1. Reference Modeling of Vertical In-Tube Condensation

Total heat flux can be obtained as the following:

q, = h, .(Tb- T.) (3-1)

where the total heat transfer coefficient, It,, is divided into the condensate film side heat

transfer coefficient, hif, and the mixture side heat transfer coefficient, h9, which is composed

of convective and condensation terms, h, and hcd, respectively.

-33-
1 11 1 1 += + 1(3-2)

h, hf h, hf hCd + h,,

Equation (3-2) is based on the assumption that the mixture and the condensate film are at

saturated state, the radiation heat transfer can be negligible, and the condensation and the

sensible heat transfer rate can be calculated simultaneously using the heat and mass transfer

analogy. The condensate film thickness is calculated using Munoz-Cobo et. al.(1996)'s

approximate method with its accuracy and simplicity, and the condensate film heat transfer

coefficient, hf, is calculated with Blangetti et. al.(1982)'s film model. The steam -gas mixture

side heat transfer coefficients, hCd and h,, are calculated using the momentum, heat and

mass transfer analogy. The heat flux through the condensate is balanced with the mass transfer

coefficient can be expressed with the mass transfer rate as follows:

hod .(Tb -Ti) = m'.(igl, -ifJ ) (3-3)

where i,,b is the bulk enthalpy and 'fj is the liquid enthalpy at the interface. The mass

transfer rate m" is expressed as follows:

w-W

n=-g . W.i ".b = g-B(3-4)

where g is the mass transfer conductance, B is mass transfer driving force, and Wv.b are the

steam mass fraction of the steam at the interface and at the tube centerline, respectively.

From Equations (3-3) and (3-4), the condensation heat transfer coefficient, hod, can be

derived.

I I-f. W .,-W•

hed = g .gJ f .8 (3-5)

1 -."i 7 -Tb

The convective heat transfer, h,, in Equation (3-2) and mass transfer conductance, g, in

Equation (3-5) can be calculated together using the heat and mass transfer analogy.

St h= , = Nu (3-6)

PgUg Reg Prg

Stab g = Sh

P9gU Re8 Scg (37)

where St and StAB are Stanton numbers for heat transfer and mass transfer, respectively, and.

SA and Sc are Sherwood number and Schmidt number, respectively. There are several

methods to calculate the Stanton number, St. Gnielinski(1976)'s calculation method can be used

-34-
for smooth tubes and Dipprey and Sabersky(1963)'s calculation method can be used for rough

tubes, which is applied to the present model.

For Stanton number for heat transfer,

Cf/ 2 (3-8)

1.0+Cf/2 -(5.19[ReJ-,'Cf/2- ID]°'2-pro'44-8.48)

where 6, is defined as follows:

C6, / D = e 3 O O4IIf', (3-9)

As the heat transfer coefficient strongly depends on the interfacial shear stress, it is very much

important to adopt the appropriate interfacial friction factor. The friction factor, Cf, is

calculated using Wallis(1969)'s correlation for the interfacial friction factor in the vertical

annular flow as follows:

Cf /2=Cf,/2.1 (1+300. (3-10)

where Cf., is the friction factor for the smooth tube and 8 is the film thickness.

Using the heat and mass transfer analogy, the Stanton number for mass transfer, StAB, is

calculated similarly.

StaB=1.0 + C-1/2.(5.19[Re,.17Cfc/2. ' ID]°' .Sc44 -8.48) (3-11)

where Sc is Schmidt number. The high mass transfer effect is also considered. The Stanton

number with blowing, Stab-, can be expressed with the Stanton number for no transpiration,

StAB.o, and the blowing parameter, bh:

StA= StABO bh (3-12)

where bh is the alternative heat transfer blowing parameter, which has explicit relation for

StAB.0 rather than the implicit equation. bh is theoretically derived and it can be expressed

with several nondimensional parameters as follows:

bh=m

StAB.0

Ja Nuf (3-13)

StAB.0 "Prg'Reg [Nuf+(Nucd+Nu,C).kslk/]

-35-
where m" is the mass transfer rate of the vapor, G_* is the mass flux of the free stream and

Ja is Jacob number.

The entrance effect on heat transfer should also be considered. For short tubes, where the

region of fully developed flow is a small percentage of the total length, the local value of the

Nusselt number of uniform velocity and temperature profile in the entrance region is given

based on the experimental data for gas (Bonilla, 1964).

Nu, = 1.5. 1 . Nuo, for 1< D<12

and x

Nu, = Nuo, for ->12 (3-15) D

where Nuo is the Nusselt number which the entrance effect is not considered.

3.2.2. Solution Scheme of Non-Iterative Model

Based on the description above, the condensation heat transfer coefficient can be determined

without any liquid-gas interface information such as the interface temperature. The condensate

film heat transfer coefficient, hj , can be calculated by the empirical correlation, and both

convective and condensation heat transfer coefficients, h, and hd, can be calculated by the

analogy between heat and mass transfer without using the interface temperature, T>

From the energy balance, the amount of heat transferred by the condensing vapor to the

liquid-vapor interface through the steam-noncondensible gas mixture boundary layer is equal to

that transferred through the condensate film. The heat flux through the condensate film layer is

calculated by qf = hj .(Tj - T,,. (3-16)

The heat flux through the mixture boundary layer is

q` = (hd + h,,,) -(Tb - Tj). (3-17)

The heat fluxes are balanced at the interface.

h1 -(T, -T,) = (hCd +h). (Tb -Ti), (3-18)

and

-36-
(h + hCd+ h,).(Tb - T) = hf. .(Tb - Tw). (3-19)

Using the Equations (3-18) and (3-19), the temperature difference between the bulk and the

interface is expressed with the temperature difference between the bulk and the condensing

wall.

Tb -T h= f .(T7 -T.)= h * (Tb -T,) (3-20) hd +h if+ h +h +,

The mass fraction of steam at the interface, W,.i, can be expressed in terms of the bulk mass

fraction of steam, Wb, by Taylor expansion.

W,,j = W., + aW,, aI• - 7(TI -Tb)+ aT._b -(Ti -Tb)]+..- (3-21)

Equation (3-21) can be approximated by taking the first order differential term only. The

properties of temperature and concentration are assumed to be changed proportionally in the gas

mixture bounda' layer. This is another expression of heat and mass transfer analogy. The terms

of W,.i - W.b and 1-W,.i can be calculated as follows:

W•,- vt,-•v ] •Ti-Tb) (3-22)

l aT b

1-Wv = I-Wv,b aW• '(i]b

+ _wb] (3-23)

Wv h+ 1 h +hv ~ TbT) aw b "- 1-W~bhj +h,, +h,, aT L'

and using these two equations, the Equation (3-5) can be expressed as follows:

aW, /aT],, h,ýd = g' (3-24) i* 1 - W +hf (hj +hcd+hc).(Tb-T,,,).(aW,,/aT]b)"

When Equation (3-24) is rearranged, a simple quadratic equation for the condensation heat

transfer coefficient, hCd , is derived as follows:

A.h%2d+B.h,,d +C =0, (3-25)

where

A= 1 - W,.b (3-26)

-37-
B=(hf +h,).(1-Wb) .W1 )+ [hf(Tb- T)-g.i) 8 T ]bj' (3-27)

and

C =-g.f .(hf +h•). T lb (3-28)

If the unknown variable, W, / aT], . is constant, calculated solutions should be exact. The

term aW• /lT can be determined as follows: The vapor mole fraction and the vapor mass

fraction is expressed in terms of the pressure ratio as follows:

X" = P / P,, (3-29)

where P, and P,,, are vapor partial and total pressures, respectively, and

W" = Mg M .P" /P. (3-30) .(1 -P,,/ P')+ M, .Pý' P,

The partial differentiation of vapor mass fraction with respect to temperature is derived and

approximated to be expressed with the bulk properties using the Clausius-Clapeyron equation as

follows:

LW. = LW.. ap.= 1.A OP i NA g(3-31) aT aI, aT P, aT P, T

where

NA M. " g, 2 (3-32)

Using the Equations (3-31) and (3-32), the coefficients, B and C, in Equations (3-27) and

(3-28) can be rewritten as follows:

B = HIA + H2 BT -B 3r (3-33)

and

C = -H 1•B3r (3-34)

where

H, = hj + h, (3-35)

H2 = hf, (3-36)

-38-
B2 = (ifg .p,) /(P, -T). (T, -T.).NA (3-37)

and

B3T = (g -ig- Pv)'(PI" T)- NA. (3-38)

As the coefficients A and C are always positive and negative, respectively, Equation (3.25)

has the following unique positive solution:

hCd = -B+IBI.41-4ACIB2 (3-39)

2A

Equation (3-39) can be nondimensionalized using Equations (3-26), (3-33) and (3-34) as

follows:

1 kf Nuf divl'div3l -[ddi v+Idivl. 1+4- 21(340 Nu 2 kg divl" div (340)

where

div = divl + div2 + div3, (3-41)

divl=N N PA, (3-42)

div2 = Ja, (3-43)

and

div3=1lNuf . 1kkf .Pr,- StAB -Reg. (3-44)

The nondimensional parameters in Equations (3-40) through (3-44) are defined as follows:

W9 b = 1 -9 Wa,; (3-45)

X .b = I1- X,.b; (3-46)

Nucd = hcdDhIks; (3-47)

Nuf =hf Dh/kf; (3-48)

StAB = g /lpju 8 ; (3-49)

Reg =pgugDh ItU; (3-50)

Prg = CP,/je / ks; (3-51)

-39-
PA =pt2 /(p2 -_ ).C I R; (3-52)

NB = Xg,- (1- Xg,) .[1 + Xb.(Mg IM, - 1)]. (3-53)

As the term div is always positive and the second term in the square root of Equation

(3-40) is a very small value compared with 1, the square root term of Equation (3-40) can be

expanded and approximated from the expansion of the Taylor series as follows:

1+ y, (3-54)

where

divl .div3

y = 4- (1 + h, I h1 ) div3 - (3-55)

Using the approximation of Equation (3-54), Equation (3-40) can be simplified as follows:

Nucd = (,+_h, Pr,- St}aB .Re, (3-56)

No" PA + Ja- Pr,-StAB -Reg Iuf kg

Nuf kf

StAB and h, in Equation (3-40) are corrected to consider the effects of high mass transfer

and entrance using Equation (3-12) and Equations (3-14) and (3-15), respectively. As the

convective heat transfer coefficient, h,, is negligibly small compared with the film side heat

transfer coefficient, hf , Equation (3-56) can be further simplified as follows:

NUcd = P-StAB -Reg (3-57)

NBS PA + Ja - PrS. StAB . ReS N---I kg

Nu f kf

Now, the Nusselt number for condensation can be calculated by those parameters of StAB,

Re., Pr,, Nuf, ks Ikf, Ja, NB, and PA. Several nondimensional parameters used in

Equation (3-57) are parameters used in empirical correlations proposed by several investigators,

e.g., Kuhn (1995), Araki et. al. (1995), Hasanein et. al. (1994), Vierow (1990), Vierow and

Schrock (1991), and Siddique et. al. (1993).

3.3. Calculation Procedures of the Modified Model

-40-
The calculation procedures are explained in Figures 3.1 and 3.2 for the reference model and

the present non-iterative model, respectively. The default model of the original

RELAP5/MOD3.2 code also has an iterative solution scheme similar to the reference model.

Calculation procedures are quite different between the reference model and the non-iterative

model. The reference model separately calculates the heat flux through the liquid film and

through the mixture boundary layer with an assumed interface temperature. It needs iteration to

get reasonable heat transfer coefficients by modifying the interface temperature until the heat

fluxes converge within a specified accuracy. The reference model separately calculates the heat

flux through the liquid film and through the air-vapor boundary layer.

-41-
Start

Input T, Tb, Wt,

.C.& B.C. WQ iTin

Initial properties WN, WW,

at each node mv.b, Xg.b

Initial guess eof interfacial Ti, xp 

propertiesI I

Physical properties p, p., D, ks,

(Liquid and Mixture) Co. Reg. Ref

Film thickness : Munoz-Cobo (1996)1 8I

Film side HTC :Blangetti (1982) hf

I St: Equation (3.8) Stanton numbers SB Equation (3.11)I

Entrance effect : Equations (3.14) and (3.15) High mass transfer effect :Equation (3.12)

I Ihcv :Equation (3.6)

Gas side HTCs g :Equation (3.7)

hcd: Equation (3.5)

SHeat transfer rates and Ofilm, Ogas.

interfacial properties Ti, xoi

No Convergen~ceet

\(Qilm - Qgas)/Qfilm < eJ

r, Yes No

Last node ?

j, Y ews

S End__)

Figure 3.1 Calculation procedure of reference iterative model

-42-
Start

[ Input data T., Tb, Wt,

I.C.& B.C. Wg, Pin, Tin

SInitial properties Wf, Wg,

at each node mv.b, Xg.b

= Physical properties [p, g., D, s,I

(L~iquiid and Mixture) QC .Reg. Ref

Film thickness Munoz-Cobo (1996) 8

Film side HTC : Blangetti (1982) hi

ISt Equation (3.8)

Stanton numbers StB: Equation (3.11)

Entrance effect : Equations (3.14) and (3.15)

hcv : Equation (3.6)

Gas side HTCs g : Equation (3.7)

NUcd: Equation (3.57)

High mass transfer effect: Equation (3.12)]

Correction to the hcv: Equation (3.6)1

gas side HTCs g: Equation (3.7) NUcd: Equation (3.57)

Last node ? •N

•,Yes

S End

Figure 3.2 Calculation procedure of the present non-iterative

model: the modified model

-43-
3.4. Simulation of Reflux Condensation Experiments

The RELAPS calculation is performed for the experiments discussed in Chapter 2. The

simulation results by two wall-film condensation models of the RELAP5JMOD3.2 code and the

modified condensation model are compared with the experimental data.

3.4.1. RELAPS/MOD3.2 Nodalization

Figure 3.3 shows the nodalization scheme of RELAP5/MOD3.2 for the reflux condensation

experiments. The present RELAP5/MOD3.2 nodalization used for this simulation contains 43

control volumes, 10 junctions, a valve and a heat structure.

The steam-air mixture is injected upward into the riser part of the U-tube of steam generator

as boundary conditions at various air mass fractions and steam flow rates. Both the steam-air

mixture and the coolant are injected at constant flow rates upward into the condensing tube and

into the annulus of the coolant jacket, respectively. In the RELAPS/MOD3.2 calculation, this

behavior is simulated using a time-dependent volume and a time-dependent junction to specify

flow and pressure boundary conditions. Time-dependent volumes acting as infinite sources or

sinks are used to represent boundary conditions both for the steam-noncondensible gas mixture

flow in a condensing tube and for the coolant flow in a coolant jacket.

For the simulation of the coolant jacket, two time-dependent volumes 200 and 280 are

connected to the annulus 240 via a time-dependent junction 210 and a single junction 270.

Similarly, for the simulation of the test section, two time-dependent volumes 100 and 180, a

time-dependent junction 105 and a single junction 165 are also used. A pipe volume 130 is used

to simulate an upper plenum and three pipe volumes 150, 160 and 157 are used to simulate a

lower plenum, a drain tank and a connecting pipe between the lower plenum and the drain tank,

respectively. The above three pipes are connected using single junctions 155, 156 and 158. A

valve 175 is used to regulate the venting of the mixture of the residual steam and the

noncondensible gas. A heat structure 140 with 11 sub-volumes is used to represent the heat

transferred from the steam-noncondensible gas mixture to the coolant through the condensing

tube.

3.4.2. Base Case Calculation

~44-
Four reflux condensation experiments are simulated using the RELAP5/MOD3.2 code.

Before 200 sec, the steady state conditions are achieved. Their steady state test conditions are

listed in Table 3.1.

Table 3.1 Steady state test conditions of reflux condensation experiments

I.D. T I Po I FS FA .D._ ___ AMF [kPa] [kg/h] [kg/h]

RC16 101.6 0 107.3 1.35 0

RC13 91.0 0.418 105.4 1.50 1.08

RC02 95.3 0.291 107.4 2.29 0.94

RA02 123.7 0.237 266.0 2.59 0.80

Two tests of RC16 and RC13 have different inlet air mass fractions under the similar inlet

saturated steam temperatures and inlet steam flow rates. Two tests of RC02 and RA02 have

different inlet saturated steam temperatures under the similar air mass fractions and inlet steam

flow rates. The calculated local heat transfer coefficients are compared for the tests with

different air mass fractions and different system pressures or inlet saturated steam temperatures.

Therefore, the effects of inlet air mass fraction and of inlet saturated steam temperature on the

local heat transfer coefficient can be investigated through the comparison of those tests.

Figures 3.4 through 3.7 show the local heat transfer coefficients along the tube length for the

reflux condensation experiments RC16, RC13, RC02, and RA02, respectively.

Figure 3.4 shows that the modified model gives accurate prediction over the experimental

data along the test section. However, both the default model and the alternative model of the

RELAP5/MOD3.2 code give much higher predictions than the experimental heat transfer

coefficient in the entrance region of the test section.

Figure 3.5 shows the simulation results of experiment RC13 with high inlet air mass fraction.

The calculated heat transfer coefficient from the default model is always lower than the

experimental data, while the calculated one from the alternative model is always higher than the

experimental data. The heat transfer coefficient calculated from the modified model shows

reasonable agreement with the experimental data in the entrance region.

Figures 3.6 and 3.7 shows the simulation results with different inlet steam temperatures. The

-45-
calculated heat transfer coefficients from the modified model are always between two

predictions from the alternative and the default models in RELAP5/MOD3.2, and they show

good agreement with the experimental data throughout the condensing tube.

In the atmospheric conditions (RC16, RC13, RC02), the under-predictions of the default

model become larger as the air mass fraction increases. With the increased system pressure

(RA02), the non-iterative model better predicts the experimental data, while the default model

under-predicts the experimental data.

From the aforementioned simulation results, we conclude that the local heat transfer

coefficients are well predicted with the modified RELAP5/MOD3.2 code but they are

under-predicted by the default model and over-predicted by the alternative model. Also the

modified RELAP5/MOD3.2 code better predicts the experimentally obtained active condensing

region and its length than the original codes.

3.4.3. Run Statistics

The computer used in the calculation is a Pentium III personal computer with Window 98

operating system. The random access memory is 128Mbyte and the clock speed of CPU is

500Mhz. The CPU time, the time step size, and the grind time are compared between three

calculation results. Table 3.2 shows the required CPU time and the grind time for the base case

calculation of RC02.

Table 3.2 The CPU time and the grind time of experiment RC02

Condensation model Node Problem CPU time Number of

used number timeond) ond) time stepme used number~~ (second) (eod iese

Default model 41 200 5485.3 25519 5.00

Alternative model 41 200 2235.4 14526 3.58

Modified model 41 200 2753.7 12866 4.98

Figure 3.8 shows the required CPU times with respect to the real problem time for the base

calculation of RC02. The required CPU times increase linearly for three calculation results,

-46-
except for the initial transient situation. The default model needs the highest CPU time and the

alternative model needs the lowest. The modified model needs lower CPU time than the default

model and slightly higher CPU time than the alternative model except for the initial transient

situation.

Figures 3.9 through 3.11 show the time step sizes with respect to the real problem time for

the default model, the alternative model and the modified model, respectively. The time step

sizes of the default model are 0.00781 sec except for the initial 0.0156 sec. The time step sizes

of the alternative model fluctuate between 0.00781 sec and 0.0156 sec during the initial

transient situation and they become 0.0156 sec after the problem time becomes approximately

40sec. The time step sizes of the modified model are 0.0156 sec except for the initial 0.00781

sec.

The grind time is expressed as follows:

CPU xl03

Grind time - (3-58) CxAT

where CPU is the CPU time, C is the total number of model volumes, and AT is the number

of time steps. The grind times are 5.00, 3.58 and 4.98 for the default model, the alternative

model and the modified model, respectively. The grind time of the modified model is slightly

lower than that of the default model but it is 28.1% higher than that of the alternative model.

-47-
pipel30

pipel4O

hxl4O

an240

pipel!

Figure 3.3 RELAP5/MOD3.2 nodalization for reflux condensation

experiment

-48-
I

a

6~E

U,

a)

0)

0

C.,

a)

U,

C

(U

H

CUa)

=

0.0 0.5 1.0 1.5 2.0

Length from the tube inlet (m)

Figure 3.4 Heat transfer coefficients of reflux condensation: #RC 16

2.5

-49-
o-0- Default model

E -0- Alternative model

8.. 800- 00 Non-iterative model

Co

0)

SU2600- 0-'

C)

""400,

0.0 0.5 1.0 1.5 2.0

Length from the tube inlet (m)

Figure 3.5 Heat transfer coefficients of reflux condensation: #RC13

2.5

-50-
I Experimental data I" -- Default model

E'O -0- Alternative model

"--S 1500 [-A-Non-iterative model

-.ao, 2

0

o1000-

0\ M

0

Fa~500-

I0

0.0 0.5 1.0 1.5 2.0 2.5

Length from the tube inlet (m)

Figure 3.6 Heat transfer coefficients of reflux condensation: #RC02

-51-
a-16 0 0 - I :I• IM II II'dI• It d l 4ii 

O -r-Default model

E -0-Alternative model

1400 -- A- Non-iterative model

*- 1200-

.2

1000-

0

800 -

~600- 1

-400

200 -

00. * II *I I

0.0 0.5 1.0 1.5 2.0

Length from the tube inlet (m)

Figure 3.7 Heat transfer coefficients of reflux condensation: #RA02

2.5

-52-
0 50 100 150 200

Problem time (second)

Figure 3.8 Comparison of required CPU times of three condensation models

-53-
uELIZu - i

I -- &- Default condensation moxlel

K

0

0.015-

0

CO

N

*F 0.010-

a)

E

0.005-

I I I MI

0

0

50 0 100 1

150 0 200

Problem time (second)

Figure 3.9 Time step sizes of the default condensation model

-54-
tjU~iU.

I)

I I

1--- Alternative condensation model I

-- 0.015 - -

0.05

"oI

ca)

N

0.00.

a)

E

F0.005.

0.000- , * * *

0 50 100 150 200

Problem time (second)

Figure 3.10 Time step sizes of the alternative condensation model

-55-
U.LI.Iu. I i i i !

I- M¶chfiecj conensation modelI

0.015-

0

0

CD

N

In5 0.010-

E

I- 0.005-

A

-k" - -- I - |||nil|

0 50 100 150

Problem tirre (second)

200

Figure 3.11 Time step sizes of the modified condensation model

-56-
Chapter 4.

Conclusions and Recommendations

The reflux condensation experiment in the presence of noncondensible gas is performed.

The flooding limit to the reflux condensation is firstly obtained in several air mass fractions. 29

data sets of the heat transfer coefficients are obtained, which represent the characteristics of

several parametric effects. The empirical correlation is developed using total 165 local data of

the heat transfer coefficients, where the degradation factor, F is described as a function of four

nondimensional parameters.

The standard frozen RELAP5/MOD3.2 code is assessed for the existing two condensation

heat transfer models. Also a new non-iterative condensation model is developed and

implemented into the RELAP5/MOD3.2 code, and the result of the new model is compared to

the experimental data and the code results for the two existing condensation models of the

standard RELAP5/MOD3.2 code.

From the above studies of the experiments and the code analysis, the conclusions are listed

as follows:

* The onset of flooding in conditions of the reflux condensation is lower than that of Wallis'

correlation. It may be resulted from the condensation effect on the film interface and the

presence of noncondensible gas.

* The heat transfer coefficients are affected by several parameters. The heat transfer

capability in the presence of noncondensible gas is dramatically decreased. For the range of

air mass fraction of 10-55 %, the heat transfer coefficient is decreased with an increase of

the air mass fraction. As the pressure increases, the heat transfer capability is enhanced

near the tube inlet. As the steam flow rate increases, the local heat transfer coefficients are

all increased in the active condensing region.

The empirical correlation is developed using four nondimensional parameters. The Jacob

number and the film Reynolds number are dominant parameters. However, the effect of the

-57-
mixture gas Reynolds number is relatively low. The correlation covers the local heat

transfer coefficients for the active condensing region up to about 1.5m from the tube inlet.

" The existing condensation models in the standard RELAP5/MOD3.2 code are assessed for

the reflux condensation. It shows that the default model under-predicts and the alternative

model over-predicts the experimental data, respectively. The under-prediction of the

default model becomes larger as the air mass fraction increases in the atmospheric

conditions.

" A non-iterative model is newly developed to be implemented into RELAP5/MOD3.2. The

non-iterative model predicts better the experimental data than the existing default model

and alternative model. It has good predictability especially in high pressure conditions.

" The flooding data are obtained in the condition of the reflux condensation with

noncondensible gas, but is not enough to represent the effect of the air mass fraction on

flooding. The effects of detailed noncondensible gas on the flooding limit may be useful as

part of the CCFL study. In this report, the experiment is performed about reflux

condensation before the onset of flooding. After flooding, the liquid column is formed and

the reflux condensation also occurs below the liquid column. The characteristics of the

reflux condensation may be different according to the conditions with or without the liquid

column.

* The local heat transfer data, especially with high air mass fraction, are comprehensively

obtained for reflux condensation and an empirical correlation is developed. With its

simplicity and mechanistic modeling, the non-iterative model can be used to improve the

condensation models in the presence of noncondensible gases in various thermal hydraulic

codes.

-58-
Bibliography

[1] Araki, H., Kataoka, Y. and Murase, M, "Measurement of Condensation Heat Transfer

Coefficient inside a Vertical Tube in the Presence of Noncondensible Gas," J. of Nuclear

Science and Technology, Vol. 32, No.6, pp.517-526, June 1995.

[2] Banerjee, S, Chang, J.S., Girard, R. and Krishnan, V.S., "Reflux Condensation and

Transition to Natural Circulation in a Vertical U-tube", ASME Winter Annual Meeting,

Washington D.C., Nov. 15-20 1981.

[3] Blangetti, F., Kerbs, R. and Schlunder, E.U., "Condensation in Vertical Tubes -

Experimental Results and Modeling," Chemical Engineering Fundamentals, Vol. 1, No. 2,

pp.20-63, 1982.

[4] Bonilla, C.F., "Heat Transfer," New York: Interscience, 1964.

[5] Chang, J.S., Girard, R., Revankar, S. and Wan, P.T., "Heat Removal Capability of Steam

Generators under Reflux Cooling Modes in a CANDU-PHT System," 4th Canadian Nuclear

Soc. Conf., 1983.

[6] Choi, K.Y., Park, H.S., Kim, S.J., NO, H.C., and Bang, Y.S., "Assessment and Improvement

of Condensation Models in RELAPS/MOD3.2," Nuclear Technology, Vol.124, No.2,

p.103-117, 1998.

[7] Colburn, A.P. and Hougen, O.A., "Design of Cooler Condensers for Mixtures of Vapors

with Non-condensing Gases," Industrial and Engineering Chemistry, Vol.26, No. 11, p.1178,

1934.

[8] Collier, J.G. and Thome, J.R., "Convective Boiling and Condensation", 3rd Edition, Oxford

university press, 1994.

[9] Dipprey, D.F. and Sabersky, R.H., "Heat and Momentum Transfer in Smooth and Rough

Tubes at Various Prandtl Numbers," Int. J. Heat Mass Transfer, vol.6, pp.329-353, 1963.

[10] Dittus, F.W. and Boelter, L.M, "Heat Transfer in Automobile Radiators of the Tubular

Type," Publications in Engineering, U.C.B., Vol.2, p.443, 1930.

[11] Dumont, D., Lavialle, G., Noel, B. and Deruaz, R., "Loss of Residual Heat Removal during

Mid-loop Operation : BETHSY Experiments," Nuclear Eng. and Design, Vol.149,

pp.365-3374, 1994.

[12] El-Wakil, "Nuclear Heat Transport", McGraw-Hill, 1978

[13] Girard, R., and Chang, J.S., "Reflux Condensation Phenomena in Single Vertical Tubes,"

Int. J. of Heat Mass Transfer, Vol.35, No.9, pp.2203-2218, 1992.

[14] Gnielinski, V., "New Equations for Heat and Mass Transfer in Turbulent Pipe and

Channel Flow," Int. Chem. Eng., Vol.16, No.2, pp.359-368, 1976.

[15] Hassanein, H.A., Golay, M.W. and Kazimi, M.S., "Steam Condensation in the Presence of

Noncondensable Gases under Forced Convection Conditions," MIT-ANP-TR-024: M.I.T.,

1994.

[16] Hassan, Y.A. and Raja, L.L., "Analysis of Experiments for Steam Condensation in the

-59-
Presence of Noncondensable Gases using the RELAP5/MOD3 Code," Nuclear Technology,

Vol.104, p.76, 1993.

117] Hein, D., Rippel, R., Weiss, P., "The Distribution of Gas in a U-tube Heat Exchanger and

its Influence on the Condensation Process", Proc. 7th Int. Heat Transfer Conf., 1982.

[18] Kageyama, T., Peterson, P.F. and Schrock, V.E., "Diffusion Layer Modeling for

Condensation in Vertical Tubes with Noncondensable Gases," Nuclear Engineering and

Design, Vol.141, pp.289-302, 1993.

[19] Kays, W.H. and Leung, E.Y., "Heat transfer in annular passages-hydrodynamically

developed turbulent flow with arbitrarily prescribed heat flux," Int. J. Heat Mass Transfer,

Vol.6, p.537, 1963.

[20] Kuhn, S.Z., "Investigation of Heat Transfer from Condensing Steam-Gas Mixtures and

Turbulent Films Flowing Downward Inside a Vertical Tube," Ph.D. thesis, M.I.T., 1995.

[21] Lee, C.H., Liu, T.J., Way, Y.S. and Hsia, D.Y., "Investigation of Mid-loop Operation with

Lass of RHR at INER Integral System Test (lIST) Facility," Nuclear Eng. and Design,

Vol.163, pp.349-358, 1996.

[22] Mills, A.F., "Heat and Mass Transfer," Richard D. IRWIN Inc., UCLA, 1995.

[23] Munoz-Cobo, J.L., Herranz, L., Sancho, J., Tkachenko, I. and Verdu, G., "Turbulent Vapor

Condensation with Noncondensable Gases in Vertical Tubes," Int. J. Heat Mass Transfer,

Vol.39, No.15, pp.3249-3260, 1996.

[24] Nakamura, H., Anoda, Y. and Kukita, Y., "Loss of Residual Heat Removal(RHR) during

PWR Mid-loop Operation : Experiments in ROSA-IV/LSTF," Int. Topical Meeting "Safety

of Thermal Reactors" of ANS Nuclear Reactor Safety Division, USA, July 21-25, 1991.

[25] Nguyen, Q. and Banerjee, S., "Flow Regimes and Removal Mechanisms in a Single

Inverted U-tube Steam Condenser", ANS Trans. Vol.43, 1982.

[26] NO, H.C., "Iterative and Non-Iterative Condensation Models for Steam Condensation with

Noncondensable Gas in a Vertical Tube," Proc. of NTHAS: First Korea-Japan Symposium

..on Nuclear Thermal Hydraulics and Safety, p.313, 1998.

[27] Noel, -B3. and Deruaz, R., "Reflux Condensation with Nitrogen in Steam Generator U-tubes

Analysis of BETHSY Test 7.2c Using CATHARE Code," 3rd Int. Symposium on Multiphase

Flow and Heat Trasfer, XIAN, China, Sept. 19-21, 1994.

[28] Nusselt, W.A., "The Surface Condensation of Water Vapor," Z. Ver. Deutsch. Ing., Vol.60,

pp.5 4 1-

54 6, 1916.

[29] Park, H.S., NO, H.C. and Bang, Y.S., "Assessment of RELAPS/MOD3.2for Steam

Condensation Experiments in the Presence of Noncondensables in a Vertical Tube of

PCCS", USNRC, NUREG/IA-0147, 1998.

[30] Park, H.S. and NO, H.C., "A Condensation Experiment in the Presence of

Noncondensables in a Vertical Tube of PCCS and Its Assessment with RELAPS/MOD3.2,"

Nuclear Technology, Vol.127, pp.160-169, 1999.

[31] Park, J.W., "An Experimental Investigation of Condensation Phenomena In A Vertical

U-tube With and Without Noncondensible Gas," M.S. Thesis, Dept. of Nuclear

Engineering, Korea Advanced Institute of Science and Technology, 1984.

[32] Peterson, P.F., Schrock, V.E. and Kageyama, T., "Diffusion Layer Theory for Turbulent

-60-
Vapor Condensation with Noncondensable Gases," J. Heat Transfer, Trans. of ASME,

Vol.115, pp.998-1003, 1993.

[33] Ransom, V.H., Trapp, J.A., ahd Wagner, R.J., "RELAPS/MOD3 Code Manual, Volume IV.

Models and Correlations," USNRC NUREG/CR-5535, INEL-95/0174, INEL, June 1995.

[34] Shah, M.M., "A General Correlation for Heat Transfer during Film Condensation Inside

Pipes," Int. J. Heat Mass Transfer, Vol.22, pp.547-556, 1979.

[35] Siddique, M., Golay, M.W. and Kazimi, M.S., "Local Heat Transfer Coefficients for

Force-Convection Condensation of Steam in a Vertical Tube in the Presence of a

Noncondensible Gas," Nuclear Technology, Vol.102, pp.386-402, June 1993.

[36] Siddique, M., Golay, M.W. and Kazimi, M.S., "Theoretical Modeling of Forced

Convection Condensation of Steam in a Vertical Tube in the Presence of a

Noncondensable Gas," Nuclear technology, Vol.106, pp.202-214, 1994.

[37] Tien, C.L., Fukano, T., Hijikata, K., and Chen, S.J., "Reflux Condensation and Operation

Limits of Countercurrent Vapor-Liquid Flows in a Closed Tube," EPRI/NP2648, Nov.

1982.

[38] Venugopalan, D., Girard, R. and Kirkaldy, J.S., "Optimal Staionary States in

Thermalhydraulics : Total Reflux Condensation," Canadian J. of Chemical Eng., Vol. 70,

Aug, 1992.

[39] Vierow, K.M. and Schrock, V.E., "Condensation in a Natural Circulation Loop with

Noncondensable Gases: Part I - Heat Transfer," Proc. of the Int. Conf. on Multiphase

Flows '91, pp.183-186, 1991.

[40] Vierow, K.M., "Behavior of Steam-Air Systems Condensing in Concurrent Vertical

downflow," M.S. Thesis, U.C.B., 1990.

[41] Wallis, G.B., "One-dimensional Two-phase Flow", McGraw-Hill Book Co., 1969

[42] Wan, P.T., Girard, R., and Chang, J.S., "The Role of Flooding Phenomena in Reflux

Condensation in a Vertical Inverted U-tube," 3rd Multiphase Flow and Heat Transfer

Symposium Workshop, April 1983.

-61-
Appendices

Appendix A.

Uncertainty Analysis of the Reflux Condensation Experiment

Sample error analysis for the heat transfer coefficient are performed as follows:

The local heat transfer coefficient is defined as

h(x)= q"(x) (A-i)

(Tb -Tv.)

By the above equation, the total error of heat transfer coefficient is expressed as the

composite error in partially differentiated terms.

C.7.)2 + Th (A-2)

ah aq' ~a(T6 -T'1j) _Tj)

where Tb is directly measured and h and qi are calculated from the measured parameters.

The measured parameter has a measurement error and the calculated parameter has a composite

error. Differentiating Equation (A-i) partially with respect to q' and (Tb -Tw4), and

substituting into the Equation (A-2), we obtain

__= h:t q'J2+ ]2T,~W (A-3)

The heat flux is given as the following:

rh•C dT•

q"(x) = 7cd dLT- (x) (A-4)

Ycd dL

In the similar derivation with the above Equation (A-3), the relative error for heat flux is

obtained as the following:

T b e l e( iT fl d thueo rwlep(A-5)

The tube inner wall temperature is given as the heat flux and the tube outer wall temperature.

-62-
T= q'(x) R + TA,.o (A-6)

The error for (Tb -Tw, 1 ) is obtained as follows:

F, ) 2 /2 2 1 2

To,, +I U.... 

U,+T j ,oaq ' (A-7)

((Raq) 2 + (ao,, )2 )2

O(T _- T. = (O'T-2 + (ROa'.) 2 + Tr., 2)+ (A-8)

The error of measuring parameter is given by the instrument error. The flowmeter accuracy

is within ± 2.5% of the full scale reading.

a,;,, = 0.025 hiz, (full scale) (A-9)

All temperatures ifi: test section are measured by the K-type thermocouples whose error

limits are 1 *C. The minimum temperature difference between the surface inner wall and mixture

bulk is 7.2"C. The coolant temperature gradient, (dT7 IdL), is within 10% maximum.

Oab = Or., = Or., = CT, = 1.0 (A-10)

(Tb -T.•) =7.2 (A- 11)

o'(d7;,ML) = 0. 1 (dT, / dL) (A-12)

The maximum heat flux from experiment is 115,023W/m' and the relative error from

Equation (A-5) is 0.103. Therefore the heat flux error of a is 11,848.

The temperature difference error of o- -Tb .J) is 1.7619. Finally, the relative maximum error

for heat transfer coefficient is as the following:

(-h) = 0.266 (A-13)

-63-
Appendix B.

Input Deck for Reflux Condensation Experiment: #RC11

=RELAP5/MOD3.2 Simulation

* Reflux Condensation in the presence

* _ of noncondensible gas in a Vertical Tube

* Test #RC1 1: Reflux condensation experiment

* steam-air mixture, countercurrent

* Ptot--0.106Mpa, Tsat--96.5C,

* Wgin-=0.00044kg/s, air mass fraction=18.9%

* D-0.01656m, L=2.4m ,

* experimented by Young Min Moon

* coded by HSPARK

* Nov. 9. 1998

* miscellaneous control cards ***** *****•***•* **** * ******,•

100 new transnt

101 run

105 10. 20.

110 air

* time step cards

* original time step

* end min.st max ctrl minor major rstplt

203 200. 1.Oe-8 0.5 3 2500 10000 10000

*201 50.0 1.0e-7 0.05 3 100 1000 1000

*minor editor cards

* alp num main max

301 voidg 140020000 0.99 1.0

302 voidg 140030000 0.99 1.0

306 p 140020000 0. 10.e5

301 velgj 140020000 0. •5.0

302 velgJ 140030000 0. 5.0

310 quala 140020000 0. 1.0

311 quala 140030000 0. 1.0

312 quala 140050000 0. 1.0

313 quala 140070000 0. 1.0

314 quala 140090000 0. 1.0

315 quala 140110000 0. 1.0

341 hthtc 140000100 0.0 1.e4

342 hthte 140000200 0.0 1.e4

343 hthtc 140000300 0.0 1e4

344 hthtc 140000400 0.0 1.e4

345 hthtc 140000500 0.0 L.e4

346 hthtc 140000600 0.0 1.e4

347 hthtc 140000700 0.0 l.e4

348 hthtc 140000800 0.0 l.e4

349 hthtc 140000900 0.0 1.e4

-64-
350 hthtc 140001000 0.0 1.e4

351 hthtc 140001100 0.0 l.e4

365 htrnr 140000100 -1.e6 0.0

502 time 0 It null 0. 0. n 0.0

506 time 0 t null 0. 0. n -1.0

508 quala 130010000 gt null 0. 0.8 n 0

*hydrodynamic data: steam-air mixture tube

* component 100: S/G using time dependent volume

* name type

1000000 tdvlO0 tmdpvol * area length vol x angle elev rough dhydr vflag

10001012.0 2.0 0.0 0.0 0.0 0.0 1.e-4 0.0 00000 * noncondensible gas(air)

* cntrl

1000200 004 * var pressure temp. eq.quality

1000201 0.0 0.106e6 0.37065e3 1.0

* component 1

65: Steam flow initiation in kg/s * name type

1050000 tdj105 tmdpjun * from to area * cccOOOO00 cccvvOOOn

1050101 100000000 110010001 0.00051 * cntrl tr

1050200 1 52 * var waterflow steamflow interface vel.

1050201 -1.0 0.0 0.00044 0.0

1050202 0 0.0 0.00044 0.0

* component 110 : single volume near mixture inlet

name type

1100000 sv110 snglvol * area length vol x angle

1100101 0.000510.2 0.0 0.0 0. * elev rough dh vflag

1100102 0.00 1.e-4 0.0 00000 * cntrl pressure temp.

1100200 003 0.106e6- 0.37065e3

* component 115 : single volume to lower plenum

* name type

1150000 sJlI5 sngljun * from to areav kforw kbackw .flag

1150101 110010002 1500100010.00051 11.783 7.6080001000 * cntrl waterflow steamflow x

1150201 1 0.0 0.00044 0.0

component 130: upper plenum

name type

1300000 pipe130 pipe

* nv

1300001 3

* area nv 1300101 0.04 3

* length vn 1300301 0.06 1

1300302 0.08 2

-65-
1300303 0.06 3 * volume nv

1300401 0.0 3 * angle nv

1300601 -90.0 3

* rough dhydr nv

1300801 l.e-4 0.0 3 * vflag nv

1301001 00000 3

13011bi0100&0 2

* cntrl pressure temp. eq.quality vn

1301201 004 0.10606 0.37065e3 1.0 0.0 0.0 1

1301202 004 0.106e6 0.37065e3 1.0 0.0 0.0 2

1301203 004 0.106e6 0.37065e3 1.0 0.0 0.0 3 * cntrl

1301300 1

* waterflow steamflow int.vel ni

1301301 0.0 0.00044 0.0 1

* component 135 : upper plenum to condensing tube

* name type

1580000 sj135 sngljun * from to areav kforw kbackw 'flag

1580101 140130002 130030001 0.0002154 I17.83e-3 76.08e-3 0001000 * cntrl waterflow steaxnflow x

1580201 1 0.0 0.00044 0.0

* component 140: condensing tube

0ppe40 pipe

* nv: no. vol

1400001 13 * area nv

1400101 0.0002154 13 * length vn

cccO3Or- ccc0399

1400301 0.370 1

1400302 0.200 2

1400303 0.040 3

1400304 0.250 4

1400305 0.090 5

1400306 0.300 6

1400307 0.140 7

1400308 0.360 8

1400309 0.140 9

1400310 0.690 10

1400311 0.180 11

1400312 0.010 12

1400313 0.370 13 * volume nv * angle vn

1400601 90.0 13

* rough dhydr no, vol

1400801 1.e-4 0.0 13 * vflag no. vol

1401001 00000 13

I fl• ) a 0 0 0 u n

14 0 1 1 Ig 000000 12

* cntrl pressure temp. nv

1401201 004 0.106e6 0.37065e3

1401202 004 0.106e6 0.37065e3

1401203 004 0.106e6 0.37065e3

1401204 004 0.106e6 0.37065e3

1401205 004 0.106e6 0.37065e3

1401206 004 0.106e6 0.37065e3

1401207 004 0.106e6 0.37065e3

1401208 004 0.106e6 0.37065e3

1401209 004 0.106e6 0.37065e3

1401210 004 0.106e6 0.37065e3

1401211 004 0.106e6 0.37065e3

1401212 004 0.106e6 0.37065e3

1401213 004 0.106e6 0.37065e3

1.0 0.0 0.0

1.0 0.0 0.0

1.0 0.0 0.0

1.0 0.0 0.0

1.0 0.0 0.0

1.0 0.0 0.0

1.0 0.0 0.0

1.0 0.0 0.0

1.0 0.0 0.0

1.0 0.0 0.0

1.0 0.0 0.0

1.0 0.0 0.0

1.0 0.0 0.0

1

2

3

4

5

6

7

8

9

10

11

12

13

-66-
* cntrl

1401300 1 * water flow steam flow int.vel jn

1401301 0.0 0.0 0.0 12

* component 145 : condensing tube to lower plenum

* name type

1450000 sjl45 sngljun * from to area kforw kbackw iflag

1450101 150010002 140010001 0.0002154117.83e-5 76.08e-5 0001000 * cntrl waterflow steamflow x

1450201 1 0.0 0.0 0.0

* component 150: lower plenum

name type

1500000 pipe150 pipe

* nv 1500001 3

* area nv 1500101 0.04 3

* length vn 1500301 0.06 1

1500302 0.08 2

1500303 0.06 3

* volume nv 1500401 0.0 3

* angle nv 1500601 -90.0 3

* rough dhydr nv 1500801 1.e-4 0.0 3

* vflag nv

1501001 00000 3

* cntrl pressure temp. eq.q uality vn

1501201 004 0.1066 0.37065e3 1.0

1501202 004 0.106e6 0.37065e3 1.0

1501203 004 0.106e6 0.37065e3 1.0 * cntrl

1501300 1

* waterflow steamflow int.vel nj 1501301 0.0 0.0 0.0 2

******** ** ********* ************** * hyrodyamicdata : venting line

0.0 0.0 1

0.0 0.0 2

0.0 0.0 3

component 155 : lower plenum to drain tank name type

1550000 sj155 sngljun * from to areav kforw kbackw iflag

1550101 150030002 160050002 0.00001 92337&.24923317.240001000 * cntrl waterflow steamflow x

1550201 1 0.0 0.0 0.0

* component 156 : lower plenum to drain pipe

* name type

1560000 sj156 sngljun * from to areav kforw kbackw jflag

1560101 150030002 157050002 0.00012 21-09.13 4153.80 0001000 * cntrl waterflow steamflow x

1560201 1 0.0 0.0 0.0

component 157 : drain pipe name type

1570000 pipe157 pipe

* nv 1570001 5 * area nv

-67-
1570101 0.00012 5 * length vn

1570301 0.20 5

* volume nv

1570401 0.0 5

* angle nv

1570601 90.0 5 * rough dhydr nv

1570801 1.e-4 0.0 5

* vflag nv

1571001 00000 5 * jflag n

1571101 0000 4

* cntrl pressure temp. ec.quality vn

1571201 004 0.106e6 9.37065e3 1.0 0.0 0.0 1

1571202 004 0.106e6 0.37065e3 0.5 0.0 0.0 2

1571203 004 0.106e6 0.37065e3 0.0 0.0 0.0 3

1571204 004 0.106e6 0.37065e3 0.0 0.0 0.0 4

1571205 004 0.106e6 0.37065e3 0.0 0.0 0.0 5

* cntrl

1571300 1

* waterflow stearnflow int.vel nj

1571301 0.0 0.0 0.0 4

* component 160: drain tank n ame ipe pipe

1600000 pipeI pe

* nv

1600001 5

* area nv 1600101 0.7854 5

* length vn 1600301 0.20 5

* volume nv 1600401 0.0 5

* angle nv 1600601 90.0 5

* rough dhydr nv 1600801 1.e-4 0.0 5

* vflag nv 1601001 00000 5

1 601 lý Iag 000&• 4

* cntrl pressure temp. eq.quality vn

1601201 004 0.106e6 0.37065-e3 1.0 0.0 0.0 1

1601202 004 0.106e6 0.37065e3 0.5 0.0 0.0 2

1601203 004 0.106e6 0.37065e3 0.0 0.0 0.0 3

1601204 004 0.106e6 0.37065e3 0.0 0.0 0.0 4

1601205 004 0.106e6 0.37065e3 0.0 0.0 0.0 5

* cntrl

1601300 1

* waterflow steamflow int.vel nj

1601301 0.0 0.0 0.0 4

* component 165: upper plenum to single volume

* name type

1650000 sj165 sngljun * from to areav kforw kbackw jfla

1650101 130010002 170010001 0.0001267 2109.13e-8 4153.80e5 0001000 * cntrl waterflow steamflow x

16502011 0.0 0.0 0.0

* component 170: single volume near mixture outlet

* name type

1700000 svl70 snglvol * area length vol x angle

1700101 0.0001267 0.2 0.0 0.0 0. * elev rough dh vflag

1700102 0. 1.e-4 0.0 00000 * cntrl pressure temp.

1700200 003 0.106e6 0.29965e3

-68-
* componet 175 : valve for venting

name type 1750000 vv175 valve

* from to areav kforw kbackjflag

1750101 170010002 180000000 0.0001267 2109.13e-5 4153.80e-5 000100

* cntrl waterflow steamflow interface velocity

1750201 1 0.0 0.0 0.0 * valve type

1750300 trpvlv

* trip number(open when true)

1750301 506

* component 180: venting simulation using tdv

* name type

1800000 tdvl8O tmdpvol * area length vol x angle elev rough dhydr vflag

18001012.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 00000 * cntrl

1800200 004 * var pressure temp. e .quali

1800201 0.0 0.106e6 0.29965e3 1.0

*hydrodynamic data: coolant water annulus

* component 200: coolant source simulation using tdv

* name type

2000000 tdv200 tndpvol area length vol x angle elev rough dhydr vflag

2000101 2.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 00000 * cntrl

2000200003

* var p(latm) temp.

2000201 0.0 0.1013e6 0.29125e3

* component 210: coolant water flow initiation-> 0.13kg/s

* component 210 * * name type

2100000 tdj210 tmdpjun * from to area

2100101 200000000 240010001 0.00049 * cntrl tri

21002001 502

* var waterflow steamflow x

2100201 -1.0 0.063 0.0 0.0

2100202 0. 0.063 0.0 0.0

component 240 : outer tube for coolant water name type 2400000 out_tule annulus

* nv 2400001 11

* area nv 2400101 0.00228 11

* length vn 2400301 0.200 1

2400302 0.040 2

2400303 0.250 3

2400304 0.090 4

2400305 0.300 5

2400306 0.140 6

2400307 0.360 7

2400308 0.140 8

2400309 0.690 9

2400310 0.180 10

2400311 0.010 11

* volume nv 2400401 0.0 11

-69-
* angle nv 2400601 90.0 11

* rough hd nv 2400801 l.e-4 0.0 11

* vflag nv 2401001 00010 11 * jflag n".

2401101 OO0d20 10

* cntrl pressure temp. vn

2401201 C63 0.1013e6 0.29125e3

2401202 003 0.1013e6 0.29125e3

2401203 003 0.1013e6 0.29125e3

2401204 003 0.1013e6 0.29125e3

2401205 003 0.1013e6 0.29125e3

2401206 003 0.1013e6 0.29125e3

2401207 003 0.1013e6 0.29125e3

2401208 003 0.1013e6 0.29125e3

2401209 003 0.1013e6 0.29125e3

2401210 003 0.1013e6 0.29125e3

2401211 003 0.1013e6 0.29125e3

* cntrl

2401300 1

* waterflow steamnflow inLvel nj

2401301 0.063 0.0 0.0 10

0.0 0.0 0.0 1

0.0 0.0 0.0 2

0.0 0.0 0.0 3

0.0 0.0 0.0 4

0.0 0.0 0.0 5

0.0 0.0 0.0 6

0.0 0.0 0.0 7

0.0 0.0 0.0 8

0.0 0.0 0.0 9

0.0 0.0 0.0 10

0.0 0.0 0.0 11

* component 270: outer tube to coolant outlet name type 2700000 sj270 sngljun * from to area kforw kbackw iflag

2700101 240110002 280000000 0.00049 50.0 90.48 0001000

* cntrl waterflow steamflow x 27002011 0.063 0.0 0.0

* component 280: coolant water dumping

* name type

2800000 tdv280 tmdpvol * area length vol x angle elev rough dhydr vflag

2800101 2.0 2.0 0.0 0.0 0.b 0.0 0.0 0.0 00000

* cntrl

2800200003 * var p(latm) temp.

2800201 0.0 0.1013e6 0.29125e3

* heat structure input : pipe140 <-> annulus240

" (condensing tube simulation)

* heat structure 140 : heat transfer simulation through pipe

11400000 11 4 2 1 0.00828

11400100 0 1

11400101 3 0.009525

11400201 5 3

11400301 0 3

11400401 373.0 4

1

11400501 140020000 0 101 1 0.200 1

11400502 140030000 0 101 1 0.040 2

11400503 140040000 0 101 1 0.250 3

11400504 140050000 0 101 1 0.090 4

11400505 140060000 0 101 1 0.300 5

11400506 140070000 0 101 1 0.140 6

11400507 140080000 0 101 1 0.360 7

11400508 140090000 0 101 1 0.140 8

11400509 140100000 0 101 1 0.690 9

11400510 140110000 0 101 1 0.180 10

11400511 140120000 0 101 1 0.010 11

11400602 240020000 0 101 1 0.200 2

11400601 240010000 0 101 1 0.200 1

11400603 240030000 0 101 1 0.250 3

-70-
11400604 240040000 0 101 1 0.090 4

11400605 240050000 0 101 1 0.300 5

11400606 240060000 0 101 1 0.140 6

11400607 240070000 0 101 1 0.360 7

11400608 240080000 0 101 1 0.140 8

11400609 240090000 0 101 1 0.690 9

11400610 240100000 0 101 1 0.18010

11400611 240110000 0 101 1 0.010 11

11400701 0 0.0 0.0 0.0

11400801 0 10.0 10.0 10.0

11400901 0 10.0 10.0 10.0

11

10.0 0 0 1.0 11

10.0 0 0 1.0 11

heat structure thermnaproperty data : SUS (005) 18cr-8ni

20100500

20100501

20100502

20100503

20100504

20100505

20100506

20100507

20100508

20100509

20100510

20100511

20100512

20100551

20100552

20100553

20100554

20100555

20100556

20100557

20100558

20100559

20100560

20100561

end of file

tb~lfctn I I

teMp(k)

0.2732611e+03

0.2942611 e+03

0.3109278e+03

0.3664834e+03

0.4220389e+03

0.4775945e+03

0.5331500e+03

0.5887056e+03

0.6442611e+03

0.8109278e+03

0.9220389e+03

1.9220389e+03

temp(k)

0.274261 le+03

0.3109278e+03

0.3664834e+03

0A220389e+03

0.4775945e+03

0.5331500e+03

0.5887056e+03

0.6442611e+03

0.8109278e+03

0.9220389e+03

1.9220389e+03

thermal conductivity(w/m.k)

0.1489124e+02

0.1489124e+02

0.1505739e+02

0.1609584e+02

0.1696813e+02

0.1800657e+02

0.1885809e+02

0.1956423e+02

0.2041575e+02

0.2297030e+02

0.2423029e+02

0.2423029e+02

volumetric heat capacity(G/m3.k)

0.3831330e+07

0.3831330e+07

0.3985580e+07

0.4105300e+07

0.4224090e+07

0.4308800e+07

0.4359790e+07

0.4410320e+07

0.4561910e+07

0.4625250e+07

0.4625250e+07

-71-
Appendix C.

Local Data of Reflux Condensation Experiment

Nomenclature (for Appendix C)

Characters

Twi : inner wall temperature(°C)

TB : centerline temperature in tube(°C)

TC : coolant temperature(°C)

mu : viscosity(N-s/m2)

Rho : density(kg/m3)

F : flow rate(kg/hr)

FA : air flow rate(kg/hr)

FS : steam flow rate(kg/hr)

FM steam-air mixture flow rate(kg/hr)

Delta film thickness(m)

Re Reynolds number

Ja Jacob number

W_air :air mass fraction

HTC : heat transfer coefficient(W/m 2-°C)

F : degradation factor (= hto, / hf)

RMS : root mean square error (= J(h.p -hc.,,) IhexpI)

Subscripts

mix, g : steam-air mixture

in : inlet

f : film

exp : by experiment

corr : by correlation

cond : condensate

-72-
Table C.1. 165 local data for correlation development (inlet steam-air mixture flow)

N Length . . ,. Cp(x- .:,m F.db.nd.7. 'A FS; . . '

Exp. N I Tx) TCft.TCl - muNo. mu-mlx I [ J [Rh ::: -. [KIhr]

1 RA01 0.1 68.9 120.2 16.1 11.1 4186.2 4.045E-04 1.35348E-06 942.4 1.4058 1.141 0.742 0.0333 3.282

2 RAO1 0.22 59.5 118.3 18.4 11.1 4184.9 4.719E-04 1.35911E-06 944.0 1.3998 1.665 0.742 0.0333 3.282

3 RA01 0.365 50.8 114.8 20.5 11.1 4183.8 5.502E-04 1.36389E-06 946.9 1.3938 2.143 0.742 0.0333 3.282

4 RA01 0.535 43.6 109.0 22.2 11.1 4183.0 6.281E-04 1.36495E-06 951.6 1.3916 2.530 0.742 0.0333 3.282

5 RAO1 0.73 38.3 100.2 23.5 11.1 4182.5 6.938E-04 1.35897E-06 958.2 1.3995 2.826 0.742 0.0333 3.282

6 RAO1 0.95 33.4 89.0 24.4 11.1 4182.1 7.612E-04 1.34437E-06 966.1 1.4237 3.031 0.742 0.0333 3.282

7 RA01 1.2 30.3 76.2 24.9 11.1 4181.9 8.074E-04 1.31657E-06 974.2 1.4663 3.145 0.742 0.0333 3.282

8 RA02 0.1 76.1 121.7 23.9 21.5 4182.3 3.634E-04 1.37021E-06 941.2 1.3965 0.816 0.804 0.0504 2.591

9 RA02 0.22 62.3 119.6 25.0 21.5 4181.9 4.504E-04 1.37509E-06 942.9 1.3908 1.212 0.804 0.0504 2.591

10 RA02 0.365 54.0 115.9 26.0 21.5 4181.5 5.197E-04 1.37758E-06 946.0 1.3864 1.569 0.804 0.0504 2.591

11 RA02 0.535 46.1 110.2 26.9 21.5 4181.2 5.997E-04 1.37511E-06 950.6 1.3864 1.864 0.804 0.0504 2.591

12 RA02 0.73 40.1 100.7 27.6 21.5 4181.0 6.710E-04 1.36024E-06 957.9 1.3985 2.091 0.804 0.0504 2.591

13 RA03 0.1 64.5 111.0 11.4 9.2 4189.1 4.340E-04 1.35828E-06 950.0 1.3952 0.497 1.538 0.0333 2.525

14 RA03 0.22 52.5 108.1 13.5 9.2 4187.7 5.336E-04 1.36186E-06 952.3 1.3932 0.970 1.538 0.0333 2.525

15 RA03 0.365 44.4 104.2 15.4 9.2 4186.6 6.188E-04 1.3646E-06 955.3 1.3937 1.399 1.538 0.0333 2.525

16 RA03 0.535 39.2 98.9 17.1 9.2 4185.6 6.821E-04 1.3655E-06 959.2 1.3991 1.782 1.538 0.0333 2.525

17 RA03 0.73 34.3 91.4 18.5 9.2 4184.8 7.483E-04 1.36018E-06 964.5 1.4152 2.097 1.538 0.0333 2.525

18 RA03 0.95 30.2 82.9 19.5 9.2 4184.3 8.089E-04 1.34912E-06 970.1 1.4424 2.322 1.538 0.0333 2.525

19 RA03 1.2 27.9 73.6 20.2 9.2 4184.0 8.451E-04 1.33177E-06 975.7 1.4809 2.480 1.538 0.0333 2.525

20 RA04 0.1 74.0 121.7 27.1 24 4181.2 3.747E-04 1.38506E-06 941.1 1.3864 1.073 0.804 0.0504 2.384

21 RA04 0.22 57.5 119.5 27.8 24 4180.9 4.887E-04 1.38826E-06 943.0 1.3821 1.325 0.804 0.0504 2.384

22 RAO5 0.1 60.5 107.7 10.3 8.7 4189.9 4.639E-04 1.35701E-06 952.6 1.3955 0.360 1.85 0.0333 2.357

23 RA05 0.22 51.7 104.9 11.9 8.7 4188.8 5.413E-04 1.35739E-06 954.7 1.3962 0.719 1.85 0.0333 2.357

24 RA05 0.365 41.4 100.8 13.5 8.7 4187.7 6.545E-04 1.35532E-06 957.8 1.4001 1.079 1.85 0.0333 2.357

25 RA05 0.535 35.6 95.4 15.1 8.7 4186.7 7.301E-04 1.35158E-06 961.7 1.4086 1.438 1.85 0.0333 2.357

26 RA05 0.73 32.4 87.8 16.6 8.7 4185.9 7.758E-04 1.34261 E-06 966.9 1.4271 1.774 1.85 0.0333 2.357

27 RA05 0.95 28.4 79.3 17.9 8.7 4185.1 8.371E-04 1.33194E-06 972.3 1.4555 2.066 1.85 0.0333 2.357

28 RA05 1.2 26.1 70.4 19.0 8.7 4184.6 8.745E-04 1.32078E-06 977.6 1.4947 2.313 1.85 0.0333 2.357

29 RA06 0.1 52.1 98.9 9.9 8.8 4190.2 5.374E-04 1.34657E-06 959.2 1.4050 0.245 2.443 0.0333 2

30 RA06 0.22 48.1 95.5 11.1 8.8 4189.3 5.780E-04 1.34244E-06 961.6 1.4107 0.512 2.443 0.0333 2

31 RA06 0.365 39.9 91.5 12.4 8.8 4188.4 6.732E-04 1.338E-06 964.4 1.4188 0.801 2.443 0.0333 2

-73-
Exp. No. :FS(x) .. Fjf(x) FM(x) ýx~ Dla h s.g RJ J arx X):: HG..x> F-exPf .TCe For F~cr,: •. RMS M ::. (Kg/hrl [Kogir. [K- :/hrJ; Rr - - '.. ,. .' .

1 RA01 2.141 2.1413 2.8833 1.1689E-04 5628.7 45497.8 113.06 0.09762 0.2573 1570.4,1 ,.826.7i 0.27900! 0.14688: 0.4736

2 RA01 1.617 1.6171 2.3591 1.1193E-04 5802.0 37072.0 73.19 0.11186 0.3145 674.0,.573.8 0.11617:, 0.09889 0.1487

3 RA01 1.139 1.1387 1.8807 1.0459E-04 6123.6 29451.0 44.20 0.12172 0.3945 442.7i 'z:402.4i 0.07229! 0.06571! 0.0910

4 RA01 0.752 0.7516 1.4936 9.4864E-05 6665.7 23370.6 25.56 0.12436 0.4968 292.2 296.2; 0.04384- 0.04444: 0.0137

5 RAO1 0.456 0.4556 1.1976 8.2606E-05 7577.1 18821.9 14.03 0.11769 0.6196 196.6j:. 234.21 0.02595:- .0:03091 0.1913

6 RAOI 0.251 0.2508 0.9928 6.9442E-05 8923.2 15771.5 7.04 0.10571 0.7474 131.4". 192.7; 0.01473 0.02160: 0.4667

7 RAO1 0.137 0.1369 0.8789 5.7566E-05 10692.5 14258.2 3.62 0.08726 0.8442 90.3r 178.1i 0.00845 0.01665; 0.9720

8 RA02 1.775 1.7746 2.5786 1.0604E-04 6258.9 40192.0 104.28 0.08680 0.3118 1258.0! 886.0' 0.20099-- .0.14156 0.2957

RA02 1.379 1.3791 2.1831 1.0459E-04 6234.1 33907.9 65.39 0.10924 0.3683 510.2:559.1 0.08185;i0.08969' 0.0958

10 RA02 1.022 1.0223 1.8263 9.9064E-05 6499.2 28314.6 42.01 0.11804 0.4402 344.6 0.530241r 00..60150 0.1904

11 RA02 0.727 0.7267 1.5307 9.2427E-05 6872.8 23773.3 25.88 0.12207 0.5253 230.3 0 0.03351 N0.04. 9 0.3368 12 RA02 0.500 0.4998 1.3038 8.4270E-05 7453.5 20470.9 15.91 0.11550 0.6167 159.3 0•5i I__0.02138,,-'0.03393 0.5872

13 RA03 2.028 2.0284 3.5664 1.1689E-04 5595.6 56077.6 99.82 0.08756 0.4312 990.3•' '761.i 0.176981" :0.13601i- 0.2315

14 RA03 1.555 1.5547 3.0927 1.1442E-04 5613.5 48501.2 62.23 0.10466 0.4973 651.8. 503.9 0.11611-. 0,08977. 0.2269

15 RA03 1.126 1.1264 2.6644 1.0774E-04 5877.7 41700.0 38.87 0.11253 0.5772 455.8:: 372.1; 0.07755- 0.06330 0.1837

16 RA03 0.743 0.7433 2.2813 9.6630E-05 6489.0 35680.9 23.27 0.11232 0.6742 327.6! ,'.-296.7, 0.05049! i0 0: 04572j 0.0943

17 RA03 0.428 0.4279 1.9659 8.2604E-05 7515.7 30868.3 12.21 0.10740 0.7823 233.3:,. 239.7` 0.03104 .1'.0.03189 0.0274

18 RA03 0.203 0.2027 1.7407 6.5831E-05 9348.0 27556.3 5.35 0.09912 0.8836 164.0' : 196.9: 0.01754;. 0.02106 0.2006

19 RA03 0.045 0.0451 1.5831 4.0313E-05 15187.1 25387.6 1.14 0.08594 0.9715 116,8: 155.0 0.00769" .6.01021 0.3272

20 RA04 1.311 1.3114 2.1154 9.6851E-05 6835.6 32619.7 74.75 0.09097 0.3801 630.1 ý,: , :'7 26 .0; 0.09218nij; ,0.106211 0.1522

21 RA04 1.059 1.0589 1.8629 9.8402E-05 6579.2 28660.0 46.28 0.11815 0.4316 269.2 '.. 438.8 0.04092:; 0.066691 0.6300

22 RA05 1.997 1.9973 3.8473 1.1869E-04 5479.5 60550.4 91.95 0.08852 0.4809 708.9.'> 702.2] 0.12937': *>-0.1t2816j 0.0094

23 RA05 1.638 1.6377 3.4877 1.1678E-04 5492.8 54876.8 64.61 0.09975 0.5304 542.5;' 522.91 0.09877!•' . 0.09520' 0.0361

24 RA05 1.278 1.2784 3.1284 1.1430E-04 5509.3 49297.3 41.72 0.11134 0.5914 406.5,.• 374.0i 0.07378: - 0";'•l0i.067881 0.0800

25 RA05 0.919 0.9192 2.7692 1.0591E-04 5877.4 43758.0 26.89 0.11207 0.6681 328.01,' -302.1! 0.05581..: :0.05140( 0.0790

26 RA05 0.583 0.5826 2.4326 9.2503E-05 6684.4 38695.5 16.04 0.10380 0.7605 279.4 263.2' 0.04180.: ..0.03938 0.0579

27 RA05 0.291 0.2909 2.1409 7.4993E-05 8173.2 34329.1 7.42 0.09535 0.8641 231.7-:'218.5 0.02835': :'0.02673. 0.0570

28 RA05 0.044 0.0442 1.8942 4.0459E-05 15070.2 30629.7 1.08 0.08298 0.9767 198.3;'" 158.8. 0.013161: 0.01054: 0.1992

29 RA06 1.755 1.7552 4.1982 1.1885E-04 5400.7 66586.2 69.75 0.08687 0.5819 526.4'( 593.3: 0.09747,:' 0.109851 0.1270

30 RA06 1.488 1.4883 3.9313 1.1505E-04 5540.8 62544.6 55.00, 0.08797 0.6214 463.7: 520.8. 0.08369, 0.09400 0.1232

31 RA06 1.199 1.1992 3.6422 1.1243E-04 5584.7 58138.0 38,05 0.09574 0.6707 372.9,. 399.7 0.06677i.0.(7157i 0.0719

-74-
Length F 'F Lengtho. TwI(x) '[ T(x) .. .K TC "" fit;TCli "g"fs Cl):•,"," Cpw x mu ... film " mu.mix . .• Rhoj . .. .

Rho-m;ix . F.nd FA _ *, . .Sjn No. [ ],Exp. l T..- - ., [Jk J ..... "" _MIX :...[;.... [. .... - Kg~h

32 RA06 0.535 30.8 86.3 13.7 8.8 4187.6 7.998E-04 1.33073E-06 967.9 1.4322 1.090 2.443 0.0333 2

33 RA06 0.73 29.8 78.9 15.0 8.8 4186.8 8.151E-04 1.31729E-06 972.6 1.4558 1.379 2.443 0.0333 2

34 RA06 0.95 26.5 71.2 16.1 8.8 4186.2 8.679E-04 1.30239E-06 977.1 1.4858 1.623 2.443 0.0333 2

35 RA06 1.2 24.3 63.2 17.2 8.8 4185.5 9.049E-04 1.28843E-06 981.5 1.5238 1.867 2.443 0.0333 2

36 RBOI 0.1 62.6 100.7 10.2 8.2 4189.9 4.478E-04 1.29179E-06 957.9 0.9377 0.446 0.796 0.0333 2.448

37 RB01 0.22 54.4 99.2 12.2 8.2 4188.6 5.158E-04 1.29765E-06 959.0 0.9476 0.891 0.796 0.0333 2.448

38 RBO1 0.365 42.3 96.3 14.1 8.2 4187.4 6.435E-04 1.30268E-06 961.1 0.9630 1.314 0.796 0.0333 2.448

39 RB01 0.535 37.6 91.7 15.7 8.2 4186.4 7.030E-04 1.30537E-06 964.3 0.9858 1.670 0.796 0.0333 2.448

40 RBO1 0.73 31.6 85.2 17.1 8.2 4185.6 7.877E-04 1.30715E-06 968.6 1.0214 1.981 0.796 0.0333 2.448

41 RBOI 0.95 27.3 77.5 18.2 8.2 4185.0 8.548E-04 1.30913E-06 973.4 1.0715 2.226 0.796 0.0333 2.448

42 RBO0 1.2 24.5 69.8 19.0 8.2 4184.6 9.015E-04 1.31286E-06 977.9 1.1335 2.404 0.796 0.0333 2.448

43 RB02 0.1 59.9 96.2 9.6 7.9 4190.4 4.687E-04 1.3018E-06 961.1 0.9627 0.377 1.43 0.0333 2.436

44 RB02 0.22 52.6 94.4 11.4 7.9 4189.1 5.326E-04 1.30624E-06 962.4 0.9742 0.776 1.43 0.0333 2.436

45 RB02 0.365 42.6 91.5 13.2 7.9 4187.9 6.400E-04 1.30984E-06 964.4 0.9908 1.175 1.43 0.0333 2.436

46 RB02 0.535 38.7 86.9 14.8 7.9 4186.9 6.886E-04 1.30958E-06 967.5 1.014 1.529 1.43 0.0333 2.436

47 RB02 0.73 33.4 80.3 16.3 7.9 4186.0 7.612E-04 1.30587E-06 971.7 1.0494 1.861 1.43 0.0333 2.436

48 RB02 0.95 29.6 73.1 17.5 7.9 4185.4 8.182E-04 1.30086E-06 976.0 1.0927 2.127 1.43 0.0333 2.436

49 RB02 1.2 25.9 65.2 18.5 7.9 4184.8 8.778E-04 1.29469E-06 980.4 1.1470 2.348 1.43 0.0333 2.436

50 RB03 0.1 72.4 103.9 23.5 23 4182.5 3.836E-04 1.33506E-06 955.5 0.9578 0.197 1.403 0.063 1.985

51 RB03 0.22 68.0 102.1 24.1 23 4182.3 4.103E-04 1.33666E-06 956.8 0.9659 0.453 1.403 0.063 1.985

52 RB03 0.365 58.2 99.4 24.7 23 4182.0 4.829E-04 1.33626E-06 958.9 0.9770 0.710 1.403 0.063 1.985

53 RB03 0.535 44.9 95.0 25.3 23 4181.8 6.130E-04 1.33146E-06 962.0 0.9928 0.951 1.403 0.063 1.985

54 RB03 0.73 39.7 88.9 25.8 23 4181.6 6.758E-04 1.32085E-06 966.1 1.0142 1.166 1.403 0.063 1.985

55 RB04 0.1 62.2 99.7 8.1 5.5 4191.5 4.508E-04 1.27733E-06 958.6 0.9301 0.435 0.551 0.025 2.27

56 RB04 0.22 49.8 97.9 10.5 5.5 4189.7 5.603E-04 1.28068E-06 959.9 0.9389 0.835 0.551 0.025 2.27

57 RB04 0.365 37.0 94.7 12.8 5.5 4188.2 7.110E-04 1.28314E-06 962.2 0.9531 1.219 0.551 0.025 2.27

58 RB04 0.535 32.6 90.2 14.7 5.5 4187.0 7.729E-04 1.28455E-06 965.3 0.9738 1.536 0.551 0.025 2.27

59 RB04 0.73 27.3 83.1 16.2 5.5 4186.1 8.548E-04 1.28014E-06 970.0 1.0051 1.786 0.551 0.025 2.27

60 RB04 0.95 23.7 74.8 17.3 5.5 4185.5 9.152E-04 1.27294E-06 975.0 1.0466 1.970 0.551 0.025 2.27

61 RB04 1.2 22.1 66.5 18.1 5.5 4185.0 9.434E-04 1.26602E-06 979.7 1.0965 2.103 0.551 0.025 2.27

62 RB051 0.1 48.3 87.2 6.6 5.1 4192.6 5.758E-04 1.29256E-06 967.3 0.996 0.247 1.577 0.025 1.694

-75-
Exp. DFS(x) Fjf(x) .FM~x hJ Ro.. cet .... - . No.~ [Jo.J[Klr]I GKghr Walr(x) HTC..xp HTC.. -,o F .xpý -..Corr RM -- . - .De-lta________________F______________________________________

321 RA06 11 0.910 0.91031 3.3532 1.0836E-041 5686.51 53818.21 24.311 0.10296 0.7285 296.0 • "

33 RA06 0.621 0.6215 3.0645 9.5714E-05 6423.8 49684.5 16.28 0.09107 0.7972 278,31'

34 RA06 0.377 0.3771 2.8201 8.2490E-05 7398.4 46246.1 9.28 0.08289 0.8663 249.0,!*:'

35 RA06 0.133 0.1329 2.5759 5.8903E-05 10308.1 42698.2 3.14 0.07213 0.9484 228.4 t.

36 RBOI 2.002 2.0023 2.7983 1.1694E-04 5578.1 46264.5 95.49 0.07083 0.2845 1101.7',

37 RBOI 1.557 1.5569 2.3529 1.1264E-04 5719.9 38724.8 64.46 0.08325 0.3383 757.9!<

38 RBO1 1.134 1.1340 1.9300 1.0895E-04 5790.0 31642.1 37.63 0.10032 0.4124 488.1j

39 RBOi 0.778 0.7780 1.5740 9.8742E-05 6330.0 25753.0 23.64 0.10048 0.5057 361.6!.'ýý

40 RBOI 0.467 0.4667 1.2627 8.6234E-05 7158.0 20630.8 12.65 0.09954 0.6304 260.2,,:

41 RB01 0.222 0.2221 1.0181 6.8961E-05 8866.0 16609.7 5.55 0.09321 0.7818 188.6ý',

42 RBOI 0.044 0.0443 0.8403 4.0883E-05 14858.5 13669.6 1.05 0.08410 0.9473 136.5,

43 RB02 2.059 2.0589 3.4889 1.1957E-04 5434.2 57239.2 93.82 0.06717 0.4099 1024.3V

44 RB02 1.660 1.6599 3.0899 1.1603E-04 5536.4 50520.7 66.56 0.07732 0.4628 749.8•

45 RB02 1.261 1.2611 2.6911 1.1240E-04 5615.2 43878.8 42.09 0.09043 0.5314 520.1.;

46 RB02 0.907 0.9068 2.3368 1.0297E-04 6083.6 38109.0 28.12 0.08911 0.6120 413.5.,::i

47 RS02 0.575 0.5747 2.0047 9.1190E-05 6795.1 32786.9 16.12 0.08669 0.7133 321.2!

48 RB02 0.309 0.3091 1.7391 7.5747E-05 8113.5 28553.1 8.07 0.08039 0.8222 252.8!..

49 RB02 0.088 0.0879 1.5179 5.0839E-05 11987.9 25039.5 2.14 0.07262 0.9421 197.4 i". :'

50 RB03 1.788 1.7875 3.1905 1.0712E-04 6168.5 51040.2 99.52 0.05873 0.4397 735.8R,',-

51 RB03 1.532 1.5321 2.9351 1.0397E-04 6320.8 46897.7 79.75 0.06358 0.4780 623.3

52 RB03 1.275 1.2755 2.6785 1.0311E-04 6285.2 42810.4 56.42 0.07673 0.5238 422.8M-"

53 RB03 1.034 1.0339 2.4369 1.0388E-04 6102.0 39088.8 36.02 0.09337 " 0.5757 274.8;'

54 RB03 0.819 0.8189 2.2219 9.9000E-05 6339.8 35926.6 25.88 0.09174 0.6314 213.7,":

55 RB04 1.835 1.8354 2.3864 1.1380E-04 5729.2 39901.5 86.95 0.06965 0.2309 1074.4

56 RB04 1.435 1.4346 1.9856 1.1260E-04 5678.4 33112.9 54.68 0.08930 " 0.2775 654.3'-.•,I

57 RB04 1.051 1.0508 1.6018 1.0971E-04 5690.0 26660.7 31.56 0.10708 0.3440 405.2!.

58 RB04 0.734 0.7339 1.2849 9.9872E-05 6193.9 21362.5 20.28 0.10686 0.4288 286.7.

59 RB04 0.484 0.4838 1.0348 8.9601E-05 6823.7 17263.9 12.09 0.10350 0.5325 198.31

60 RB04 0.300 0.3004 0.8514 7.7936E-05 7779.7 14285.4 7.01 0.09477 0.6471 137.9 i

61 RB04 0.167 0.1671 0.7181 6.4542E-05 9358.3 12114.6 3.78 0.08233 0.7673 96.5 i

." 299.4A 0.05205ý7 --.0.05265 0.0115

* 288.1: 0.04332,. 0.04485; 0.0352

256.8F 0.03366' • . 0.03471, 0.0312

218.5; 0.0 22 161', 0:02119: 0.0435

905.61 0.19750Q:: 0.16234C 0.1780 .. 635.71 0.13250!:, 0.11114; 0.1612

398.81 0.08430 0.06887' 0.1830

3 14ý..8 005712' 0.04974: 0.1292

237.3ý 0.03635 -0.03315: 0.0880

184.2 0.02127!" 0.02077 0.0234

M13.2! 0.00919 0,00883 0.0390

863. 5 0.18849' 0.15891: 0.1569

640.61 0.13543 0.11570' 0.1457

438.8J 0.09262 W0.07815' 0.1563

368.21 0.06797; 0.06052: 0.1096

295.9: 0.04727 0.04355. 0.0786

246.21 0.03116M, 0.03035. 0.0261

"187.9: 0.01647,:,'. 0.01567i 0.0481 ..1057.2; 0.11929 ':0.17138 0.4367

887.5) 0.09861l,-- 0.140416 0.4238

* 631.3, 0.06727;... 0.10044 0.4931

4i40ý0 0.045031: 0.06784 0.5064

354.2i 0.033711.- 0.05588t 0.6576

916.3- 0.18753 0.15994: 0.1471

565.A1 0.11523 0.09952 0.1363

347.5 0.07121 0.06108 0.1422

275.0! 0.04629 0.04440 0.0408

216.8: 0.02906. 0.03177 0.0933

-182.7: 0.01773' 0.02348 0.3248

163.8t 0.01031: :.0.01750. 0.6976

62 RB05 11 1.447 1.4467 3.0237 1.1337E-041 5625.11 49961.61 53.661 0,071261" 0.5215 624.0,.. 596.5, 0.11093. 0.10604, 0.0441

-76-
Exp. No. Length Twl(x) TCfit TCV - COTB(x)" , jiim nmx. Rho!c Rhomx o -n- *. FA 16: rm] iý [J/kgK]' -mi Rh ,[ghl'~lh]F~ [gh

63 RB05 0.22 43.9 84.3 8.2 5.1 4191.4 6.246E-04 1.29215E-06 969.2 1.0110 0.511 1.577 0.025 1.694

64 RB05 0.365 34.7 81.0 9.8 5.1 4190.2 7.427E-04 1.29227E-06 971.3 1.0301 0.774 1.577 0.025 1.694

65 RB05 0.535 27.7 76.5 11.4 5.1 4189.1 8.483E-04 1.29064E-06 974.0 1.0566 1.038 1.577 0.025 1.694

66 RB05 0.73 25.9 70.1 12.8 5.1 4188.2 8.778E-04 1.28308E-06 977.8 1.0922 1.268 1.577 0.025 1.694

67 RB05 0.95 22.8 63.1 14.1 5.1 4187.4 9.310E-04 1.27532E-06 981.5 1.1372 1.482 1.577 0.025 1.694

68 RB05 1.2 21.0 56.1 15.2 5.1 4186.7 9.633E-04 1.26796E-06 985.1 1.1889 1.663 1.577 0.025 1.694

69 RB06 0.1 49.6 96.0 7.0 5.5 4192.3 5.623E-04 1.27785E-06 961.3 0.9436 0.250 0.551 0.025 1.561

70 RB06 0.22 41.3 93.5 8.6 5.5 4191.1 6.557E-04 1.2792E-06 963.0 0.9546 0.516 0.551 0.025 1.561

71 RB06 0.365 30.7 89.3 10.1 5.5 4190.0 8.013E-04 1.27743E-06 965.9 0.9712 0.765 0.551 0.025 1.561

72 RB06 0.535 24.4 83.8 11.6 5.5 4189.0 9.032E-04 1.2766E-06 969.5 0.9976 1.015 0.551 0.025 1.561

73 RB06 0.73 21.3 76.4 12.9 5.5 4188.1 9.578E-04 1.27444E-06 974.1 1.0381 1.231 0.551 0.025 1.561

74 RB06 0.95 18.3 67.6 14.0 5.5 4187.4 1.014E-03 1.27418E-06 979.1 1.0993 1.413 0.551 0.025 1.561

75 RB07 0.1 46.4 90.0 9.0 8.5 4190.8 5.967E-04 1.29764E-06 965.4 0.9869 0.120 1.426 0.0333 1.56

76 RB07 0.22 43.5 86.9 10.1 8.5 4190.0 6.291E-04 1.29543E-06 967.5 1.0006 0.355 1.426 0.0333 1.56

77 RB07 0.365 37.9 83.3 11.1 8.5 4189.3 6.993E-04 1.29237E-06 969.8 1.0166 0.568 1.426 0.0333 1.56

78 RB07 0.535 27.7 78.5 12.0 8.5 4188.7 8.481E-04 1.28582E-06 972.8 1.0379 0.772 1.426 0.0333 1.56

79 RB07 0.73 24.2 71.7 13.0 8.5 4188.1 9.071E-04 1.27432E-06 976.8 1.0691 0.982 1.426 0.0333 1.56

80 RB07 0.95 22.5 64.3 14.0 8.5 4187.4 9.356E.04 1.2647E-06 980.9 1.1117 1.208 1.426 0.0333 1.56

81 R807 1.2 20.8 57.1 15.1 8.5 4186.7 9.672E-04 1.2632E-06 984.6 1.1715 1.460 1.426 0.0333 1.56

82 RCO1 0.1 71.4 97.6 13.1 10.5 4188.0 3.893E-04 1.25257E-06 960.1 0.6758 0.577 0.361 0.0333 2.703

83 RC01 0.22 60.5 96.8 15.6 10.5 4186.4 4.639E-04 1.25835E-06 960.7 0.6897 1.131 0.361 0.0333 2.703

84 RCO0 0.365 46.9 94.7 17.9 10.5 4185.1 5.909E-04 1.26477E-06 962.2 0.7130 1.641 0.361 0.0333 2.703

85 RCO0 0.535 39.5 91.2 19.8 10.5 4184.2 6.783E-04 1.2742E-06 964.6 0.7519 2.062 0.361 0.0333 2.703

86 RCO1 0.73 33.3 85.1 21.4 10.5 4183.4 7.627E-04 1.29217E-06 968.7 0.8288 2.416 0.361 0.0333 2.703

87 RCOI 0.95 28.9 75.8 22.6 10.5 4182.9 8.292E-04 1.33463E-06 974.5 0.9934 2.682 0.361 0.0333 2.703

88 RC02 0.1 61.4 90.7 11.9 10.2 4188.8 4.569E-04 1.26618E-06 965.0 0.7417 0.374 0.938 0.0333 2.287

89 RC02 0.22 53.7 89.2 13.6 10.2 4187.7 5.223E-04 1.27096E-06 966.0 0.7603 0.749 0.938 0.0333 2.287

90 RC02 0.365 42.9 86.4 15.4 10.2 4186.6 6.364E-04 1.27558E-06 967.8 0.7890 1.145 0.938 0.0333 2.287

91 RC02 0.535 38.3 82.9 17.0 10.2 4185.6 6.938E-04 1.28145E-06 970.1 0.8270 1.497 0.938 0.0333 2.287

92 RC02 0.73 33.7 77.1 18.5 10.2 4184.8 7.569E-04 1.28585E-06 973.7 0.8852 1.826 0.938 0.0333 2.287

93 RC02 0.95 28.7 70.7 19.7 10.2 4184.2 8.323E-04 1.29284E-06 977.4 0.9606 2.090 0.938 0.0333 2.287

-77-
Exp. FS(x) FJf(x) FMX)hf R.. HT.co Fep F..or RS

-I [KgfhrJ IKglhr] [Kgthrl ,____________No. ______,O? aa), - r,,

631 RB05 1.183 1.1830 2.7600 1.0879E-041 5815.81 45619.4 40.45 0.07399 1 0.5714 521.1 '.:?

64 RB05 0.920 0.9195 2.4965 1.0582E-04 5871.9 41260.6 26344 0.084773 0.6317 38.9"'l65 RB05 0.656 0.6562 2.2332 9.8658E-05 6202.9 36954.4 16.52 0.08932 0.7062 297.5U,: .

66 RBOS 0.426 0.4258 2.0028 8.6177E-05 7072.0 33338.1 10.38 0.08088 0.7874 260.6k.,':

67 RB05 0.212 0.2120 1.7890 6.9477E-05 8708.1 29960.4 4.86 0.07373 0.8815 220.1 V'.l.,

68 RB05 0.031 0.0312 1.6082 3.6998E-05 16281.5 27087.8 0.69 0.06421 0.9806 189.5L':i:i*?

69 RB06 1.311 1.3113 1.8623 1.0930E-04 5847.5 31124.9 49.80 0.08583 0.2959 520.5•

70 RB06 1.045 1.0450 1.5960 1.0654E-04 5909.6 26647.2 34.04 0.09654 0.3452 391.8ý:.!

71 RB06 0.796 0.7956 1.3466 1.0380E-04 5935.3 22513.5 21.21 0.10834 0.4092 285.8'j..,

72 RB06 0.546 0.5462 1.0972 9.5060E-05 6388.8 18356.6 12.92 0.10979 0.5022 223.5s-:

73 RB06 0.330 0.3302 0.8812 8.1712E-05 7377.5 14767.9 7.36 0.10183 0.6253 184.81,

74 RB06 0.148 0.1475 0.6985 6.3436E-05 9432.4 11708.2 3.11 0.09109 0.7888 152.8.

75 RB07 1.440 1.4402 2.8662 1.1470E-04 5541.0 47173.0 51.55 0.08007 0.4975 473.2:,ý'-

76 RB07 1.205 1.2053 2.6313 1.0985E-04 5755.2 43382.2 40.92 0.07955 0.5419 416.19 ,

77 RB07 0.992 0.9924 2.4184 1.0649E-04 5872.8 39965.4 30.31 0.08342 0.58971 309.9!.

78 RB07 0.788 0.7881 2.2141 1.0495E-04 5831.2 36775.8 19.85 0.093241 0.6441 236.:;:

79 RB07 0,578 0.5781 2.0041 9.6531 E-05 6288.1 33588.5 13.61 0.08723 0.7115 233.6

80 RB07 0.352 0.3522 1.7782 8.2458E-05 7332.6 30029.6 8.04 0.07666 0.8019 257.2 !

81 RB07 0.100 0.1000 1.5260 5.4657E-05 11015.4 25800.1 2.21 0.06668 0.9345 293.2ý'i:,-

82 RCOl 2.126 2.1261 2.4871 1.1368E-04 5805.9 42407.0 116.64 0.04849 0.1451 2049.2"::

83 RCO1 1.572 1.5718 1.9328 1.0893E-04 5970.3 32804.1 72.36 0.06716 i 0.1868 1165.0;,

84 RCO1 1.062 1.0621 1.4231 1.0351E-04 6145.8 24031.4 38.39 0.08842 0.2537 666.6

85 RCol 0.641 0.6413 1.0023 9.1453E-05 6860.4 16799.8 20.19 0.09561 0.3602 441.31!:•t

86 RCO1 0.287 0.2870 0.6480 7.2543E-05 8540.0 10710.9 8.04 0.09577 0.5571 300.0:,

87 RC01 0.021 0.0214 0.3824 3.1272E-05 19622.2 6119.3 0.55 0.08670 0.9440 214.7':

88 RC02 1.913 1.9126 2.8506 1.1537E-04 5644.6 48082.5 89.40 0.05383 0.3291 1243.0•:i

89 RC02 1.538 1.5384 2.4764 1.1210E-04 5740.7 41613.4 62.91 0.06520 0.3788 865.21.

90 RC02 1.142 1.1424 2.0804 1.0829E-04 5831.6 34831.9 38.34 0.07988 0.4509 576.41:.

91 RC02 0.790 0.7905 1.7285 9.8429E-05 6359.0 28807.9 24.33 0.08188 0.5427 443.31.

92 R,02 0.461 0.4607 1.3987 8.4434E-05 7343.5 23232.1 13.00 0.07966 0.6706 346.3;

:501I7j 0.08960,, 0.08627 0.0371

.3568.7!0. 0.06109i 0.0656

.276.4i 0.047968 0..04 I 0.0741

252.6i o.o3685. 0.03572 0.0306

215.11 0.02528:.. 0.02470; 0.0228

:157.61 0.01164 C," 0.009681 0.1683

553,81 0.08901 ~' 0.09470, 0.0639

-400.3 0.066301/:,'0.06773 0.0216

273,1I', 0.048155 0.04601 0.0446

207.5, 0.0o3498, ' 0io0 0.0715 0248 

172.1 0.02505 0.02333; 0.0685

138.32 0.01620T 0.01468: 0.0948

534.4 0.08540 0.09644; 0.1293

'478,1 0.07244',:.,," 0.08307! 0.1467

392.2: 0.05278: 0.066781 0.2654

282.2: 0.04058, 0.048391 0.1925

,251.91 0.03714W.: 0.04006' 0.0786

232..7 0.03508"( 0.03174' 0.0952

d186.81 0.02662. ,,'0.016961 0.3628

1539.0- 0.35295: 0.26508 0.2490

902.60 0.19513:::: 0.15118i 0.2253

S494• 0.10847 0.08039 0.2588

324.7 0.06433. 0.047331 0.2643

208.9, 0.03513 0.024467 0.3037

104.8- 0.01094C 0.00534. 0.5119

1028.21 0.22021 0.18216' 0.1728

:727.6' 0.150711 0.12675, 0.1590

468.0 0.09884!/ 0.08026 0.1880

367.9; 0.06971. 1,.:0.05786; 0.1700

287.21 0.04716!' 0.03911ý 0.1707

931 RC02 0.197 0.1970 1.1350 6.5489E-05 9365.5 18749.7 5.051 0.077081 0.8264 262.7•:',: 212.0; 0.02805 0.022631 0.1931 U ___________ .1. .1.

-78-
Length • :. Cp(x)' ,.ond F; FA F... I, Exp. No. m Tw(x) ft TC1 mujfilm mu-mix Rho. ho-mix F r ,

94 RC03 0.1 66.0 95.1 12.0 10.3 4188.7 4.235E-04 1.25812E-06 961.9 0.6997 0.376 0.506 0.0333 2.232

95 RC03 0.22 55.0 93.8 13.7 10.3 4187.6 5.103E-04 1.2619E-06 962.8 0.7140 0.752 0.506 0.0333 2.232

96 RC03 0.365 42.2 91.1 15.4 10.3 4186.6 6.448E-04 1.26459E-06 964.7 0.7363 1.128 0.506 0.0333 2.232

97 RC03 0.535 34.5 87.4 17.0 10.3 4185.6 7.455E-04 1.26947E-06 967.2 0.7707 1.482 0.506 0.0333 2.232

98 RC03 0.73 30.1 81.7 18.4 10.3 4184.9 8.105E-04 1.27551E-06 970.8 0.8258 1.791 0.506 0.0333 2.232

99 RC03 0.95 25.8 74.8 19.6 10.3 4184.3 8.795E-04 1.29146E-06 975.0 0.9175 2.056 0.506 0.0333 2.232

100 RC04 0.1 63.5 94.0 12.1 10.4 4188.6 4.412E-04 1.25117E-06 962.7 0.6951 0.376 0.432 0.0333 2.119

101 RC04 0.22 53.1 92.9 13.8 10.4 4187.5 5.279E-04 1.2558E-06 963.4 0.7096 0.751 0.432 0.0333 2.119

102 RC04 0.365 39.7 89.9 15.4 10.4 4186.6 6.757E-04 1.25727E-06 965.5 0.7319 1.104 0.432 0.0333 2.119

103 RC04 0.535 33.0 86.0 17.0 10.4 4185.6 7.670E-04 1.26302E-06 968.1 0.7696 1.458 0.432 0.0333 2.119

104 RC04 0.73 28.8 79.4 18.3 10.4 4184.9 8.307E-04 1.26757E-06 972.3 0.8299 1.744 0.432 0.0333 2.119

105 RC04 0.95 25.1 69.5 19.4 10.4 4184.4 8.912E-04 1.27675E-06 978.1 0.9392 1.987 0.432 0.0333 2.119

106 RCO5 0.1 80.4 96.8 20.4 19.3 4183.9 3.426E-04 1.24931E-06 960.7 0.67531 0.365 0.285 0.0504 2.077

107 RC05 0.22 67.1 96.0 21.5 19.3 4183.4 4.160E-04 1.25305E-06 961.3 0.6858 0.723 0.285 0.0504 2.077

108 RC05 0.365 49.3 93.9 22.5 19.3 4182.9 5.650E-04 1.25523E-06 962.8 0.7027 1.073 0.285 0.0504 2.077

109 RC05 0.535 36.6 90.0 23.5 19.3 4182.5 7.166E-04 1.25668E-06 965.4 0.7303 1.393 0.285 0.0504 2.077

110 RC05 0.73 32.7 83.1 24.3 19.3 4182.2 7.708E-04 1.25601E-06 970.0 0.7786 1.668 0.285 0.0504 2.077

111 RC05 0.95 28.8 71.3 24.9 19.3 4181.9 8.304E-04 1.25239E-06 977.1 0.8709 1.892 0.285 0.0504 2.077

112 RC06 0.1 66.5 94.2 19.2 18.5 4184.5 4.204E-04 1.23992E-06 962.5 0.6754 0.295 0.285 0.063 2.046

113 RC06 0.22 57.5 92.7 19.9 18.5 4184.1 4.888E-04 1.23961E-06 963.6 0.6841 0.592 0.285 0.063 2.046

114 RC06 0.365 43.8 89.4 20.6 18.5 4183.8 6.259E-04 1.2356E-06 965.8 0.6977 0.898 0.285 0.063 2.046

115 RC06 0.535 30.4 84.4 21.4 18.5 4183.4 8.064E-04 1.22849E-06 969.2 0.7192 1.194 0.285 0.063 2.046

116 RC06 0.73 28.0 74.7 22.0 18.5 4183.1 8.428E-04 1.21063E-06 975.1 0.7571 1.466 0.285 0.063 2.046

117 RC06 0.95 25.3 60.9 22.6 18.5 4182.9 8.879E-04 1.18637E-06 982.7 0.8255 1.705 0.285 0.063 2.046

118 RC07 0.1 64.6 91.9 18.8 17.9 4184.7 4.333E-04 1.26497E-06 964.1 0.7316 0.367 0.672 0.063 1.916

119 RC07 0.22 60.8 90.8 19.5 17.9 4184.3 4.614E-04 1.27075E-06 964.9 0.7489 0.670 0.672 0.063 1.916

120 RC07 0.365 50.1 88.2 20.2 17.9 4184.0 5.577E-04 1.27414E-06 966.6 0.7729 0.956 0.672 0.063 1.916

121 RC07 0.535 37.3 84.6 20.8 17.9 4183.7 7.073E-04 1.27618E-06 969.0 0.8038 1.204 0.672 0.063 1.916

122 RC07 0.73 31.3 79.3 21.3 17.9 4183.5 7.915E-04 1.27377E-06 972.3 0.8426 1.407 0.672 0.063 1.916

123 RCO8 0.1 54.5 88.3 11.6 10.4 4189.0 5.149E-04 1.28451E-06 966.6 0.7904 0.264 1.394 0.0333 1.887

124 RC08 0.22 50.0 86.0 12.9 10.4 4188.1 5.583E-04 1.28603E-06 968.1 0.8107 0.549 1.394 0.0333 1.887

-79-
Exp. F: ) Jx FM(X) j HTCcr J ' W corr

LNo., [Kg/hr -[Kg/hi] [Kg/hr% .De. t . ,... . .rx a H .: ... ,, - F .x,. F... , , ,

94I RC03 1.856 1.85581 2.36181 1.1160E-04 5873.01 40092.31 93.581 0.053721 0.214g 1243.0;,z

95 RC03 1.480 1.4797 1.9857 1.1005E-04 5860.0 33608.0 61.92 0.07161 0.2548 773.5,i'r:

96 RC03 1.104 1.1039 1.6099 1.0776E-04 5852.6 27188.6 36.57 0.09023 0.3143 501.2!:.

97 RC03 0.750 0.7503 1.2563 9.9274E-05 6256.2 21135.3 21.49 0.09759 0.4028 363.91:.i

98 RC03 0.441 0.4410 0.9470 8.5292E-05 7213.5 15856.3 11.62 0.09517 0.5343 284.1

99 RC03 0.176 0.1759 0.6819 6.4341E-05 9470.0 11277.6 4.27 0.09037 0.7420 214.5•::

100 RC04 1.743 1.7433 2.1753 1.1073E-04 5898.5 37132.0 84.39 0.05623 0.1986 1185.31.

101 RC04 1.368 1.3678 1.7998 1.0837E-04 5932.7 30608.7 55.34 0.07336 0.2400 755.2 .i

102 RC04 1.015 1.0145 1.4465 1.0636E-04 5901.1 24571.9 32.07 0.09250 0.2987 477.4 V':'.:'

103 RC04 0.661 0.6614 1.0934 9.6034E.05 6446.9 18488.9 18.42 0.09764 0.3951 348.2K:.

104 RC04 0.375 0.3746 0.8066 8.1364E-05 7539.9 13590.1 9.63 0.09320 0.5356 269.41

105 RC04 0.132 0.1319 0.5639 5.8595E-05 10381.7 9433.7 3.16 0.08177 0.7660 217.9:-'ý

106 RC05 1.712 1.7121 1.9971 1.0131E-04 6581.6 34141.0 106.73 0.03023 0.1427 2091.4

107 RC05 1.354 1.3544 1.6394 9.9922E-05 6569.0 27941.9 69.53 0.05340 0.1738 978.8"

108 RC05 1.004 1.0040 1.2890 1.0004E-04 6386.4 21931.2 37.95 0.08222 0.2211 506.4 .

109 RCOS 0.684 0.6838 0.9688 9.5106E-05 6558.5 16465.6 20.38 0.09864 0.2942 323.31'.'-

110 RC05 0.409 0.4088 0.6938 8.1834E-05 7561.4 11797.9 11.33 0.09302 0.4108 252.6

111 RCOS 0.185 0.1854 0.4704 6.4148E-05 9564.0 8022.4 4.77 0.07850 0.6058 211.71.1:

112 RC06 1.751 1.7513 2.0363 1.0914E-04 6009.0 35074.4 88.97 0.05109 0.1400 804.8

113 RC06 1.454 1.4540 1.7390 1.0778E-04 6006.4 29961.2 63.53 0.06488 0.1639 547.6

114 RC06 1.148 1.1481 1.4331 1.0802E-04 5856.0 24771.6 39.18 0.08410 0.1989 354.811,:

115 RC06 0.852 0.8519 1.1369 1.0617E-04 5798.4 19765.3 22.56 0.09945 0.2507 244.5i.

116 RC06 0.580 0.5796 0.8646 9.4379E-05 6489.1 15253.1 14.69 0.08596 0.3296 223.71

117 RC06 0.341 0.3408 0.6258 8.0035E-05 7604.1 11265.0 8.20 0.06554 0.4555 224.9'1.

118 RC07 1.549 1.5495 2.2215 1.0573E-04 6187.1 37507.1 76.37 0.05017 0.3025 1115.2'1-

119 RC07 1.246 1.2461 1.9181 1.0034E-04 6484.3 32236.9 57.68 0.055041 0.3504 781.1

120 RC07 0.960 0.9605 1.6325 9.7892E-05 6534.3 27363.7 36.78 0.07013 0.4116 468.0:

121 RC07 0.712 0.7116 1.3836 9.5725E-05 6525.2 23155.0 21.49 0.08694 0.4857 275.1!.'

122 RCO07 0.509 0.5092 1.1812 8.8684E-05 6956.5 19804.9 13.74 0.08808 0.5689 225.37

123 RC08 1.623 1.6234 3.0174 1.1355E-04 5675.1 50169.3 67.34 0.06194 0.4620 784.9,.

1173.61 0-2116-5-1 0.199831 0.0558

732.4! 0.13200i... 0)12498' 0.0532

440.81 0.08564 i0 07532A 0.1204

307..2 0.05811i(i-•6 049101 0.1559

.232.9: 0.03938.';:. 0.03229! 0.1801

165.0; 0.02265 0.017420.2309

109031 0.20095 0.18485 0.0801

687.21 0.12729, 0.11583. 0.0900

.406.41 0.08090 :0.06887! 0.1488

088.4 .0501 0.04443: 0.1774

.2 17.'6" 0.03573 0 0.02886i 0.1923

1.58.7 0.02099'.:: 0.01529' 0.2715

2172.9: 0.317771'. : 0.33014: 0.0389

1111.41 0.14900i" 0."16920; 0.1355

8 •13 0.07930; ';" 008504i 0.0724

-3191 0.04930. 0:04877; 0.0108

245.01 0.033407,-'-, 0.03252: 0.0265

189. 0.02213: 0.01978i 0.1065

i306.2i 0.13393ý1.. 0.21737: 0.6230

881.8i 0.09117j. 0;.14682: 0.6104

5 524. 4! 0.06059 . 008955! 0.4780

319.3! 0.04217. 0.05506! 0.3058

'2806. 0.03448 0.04329- 0.2556

254.3 0.02958:, 0.03344: 0.1306

1058.21 0.18025;' 0.17103 0.0512

849.6; 0.12047T 0.13102 0.0876

544.0 0.07162 .0.083251 0.1624

335A 0.04215 '0.051441 0.2202 2 6 4 4 0.03 2 3T ".."0.03801! 0.1735

.760.8) 0.13831, 0.13405! 0.0308

1241 RC08 1.3381 1.33791 2.7319 1.0925E-04 5854.4 45369.2 51.181 0.065961 0.510T 634.711 628.3d 0.10841, 0.10733: 0.0101 L U II. I _____________ L .J .L.....~

-80-
Exp. No. Length Twl(x) T'(x) TCflt.TC! . mufilm - mix- Rho..fT Rh.o-mix . . ., FC [K .. . _________ -kg/hy] '..:[Kg/hr

125 RC08 0.365 41.7 83.0 14.2 10.4 4187.3 6.508E-04 1.28719E-06 970.0 0.8368 0.834 1.394 0.0333 1.887

126 RC08 0.535 32.4 78.8 15.4 10.4 4186.6 7.758E-04 1.28569E-06 972.6 0.8697 1.098 1.394 0.0333 1.887

127 RC08 0.73 29.9 73.0 16.6 10.4 4185.9 8.136E-04 1.28179E-06 976.1 0.9153 1.361 1.394 0.0333 1.887

128 RC08 0.95 26.7 66.7 17.6 10.4 4185.3 8.646E-04 1.2768E-06 979.6 0.9680 1.580 1.394 0.0333 1.887

129 RC08 1.2 24.9 60.1 18.5 10.4 4184.8 8.946E-04 1.27286E-06 983.1 1.0318 1.778 1.394 0.0333 1.887

130 RC1O 0.1 47.1 85.0 11.1 10 4189.3 5.887E-04 1.28096E-06 968.7 0.8094 0.241 1.392 0.0333 1.618

131 RC1O 0.22 45.2 82.5 12.2 10 4188.6 6.097E-04 1.28158E-06 970.3 0.8305 0.482 1.392 0.0333 1.618

132 RC10 0.365 40.6 79.1 13.3 10 4187.9 6.644E-04 1.28084E-06 972.5 0.8578 0.722 1.392 0.0333 1.618

133 RC10 0.535 30.5 75.1 14.3 10 4187.2 8.043E-04 1.27902E-06 974.9 0.8900 0.941 1.392 0.0333 1.618

134 RC10 0.73 25.2 69.2 15.3 10 4186.6 8.896E-04 1.27299E-06 978.3 0.9343 1.159 1.392 0.0333 1.618

135 RC1O 0.95 23.6 62.7 16.2 10 4186.1 9.170E-04 1.26626E-06 981.8 0.9876 1.356 1.392 0.0333 1.618

136 RC1O 1.2 22.3 56.2 16.9 10 4185.7 9.398E-04 1.25836E-06 985.0 1.0435 1.509 1.392 0.0333 1.618

137 RC11 0.1 62.0 92.7 19.0 18.1 4184.6 4.525E-04 1.25363E-06 963.6 0.7072 0.366 0.369 0.063 1.584

138 RC1l 0.22 55.9 91.4 19.5 18.1 4184.3 5.019E-04 1.25626E-06 964.5 0.7201 0.575 0.369 0.063 1.584

139 RC1_ 0.365 44.8 88.3 20.0 18.1 4184.1 6.140E-04 1.25504E-06 966.5 0.7387 0.779 0.369 0.063 1.584

140 RCI 1 0.535 32.9 83.8 20.4 18.1 4183.9 7.690E-04 1.25087E-06 969.5 0.7642 0.964 0.369 0.063 1.584

141 RC1l 0.73 27.1 76.7 20.8 18.1 4183.7 8.588E-04 1.24005E-06 973.9 0.7990 1.122 0.369 0.063 1.584

142 RCI1 0.95 25.1 66.6 21.1 18.1 4183.5 8.907E-04 1.21991E-06 979.7 0.8458 1.249 0.369 0.063 1.584

143 RC12 0.1 56.9 87.5 11.4 10.3 4189.1 4.936E-04 1.29255E-06 967.1 0.8106 0.242 1.38 0.0333 1.535

144 RC12 0.22 50.8 85.6 12.7 10.3 4188.2 5.502E-04 1.2981E-06 968.4 0.8354 0.527 1.38 0.0333 1.535

145 RC12 0.365 41.7 82.6 13.9 10.3 4187.5 6.508E-04 1.30156E-06 970.3 0.8666 0.790 1.38 0.0333 1.535

146 RC12 0.535 35.1 78.5 15.1 10.3 4186.7 7.371E-04 1.30481E-06 972.8 0.9091 1.053 1.38 0.0333 1.535

147 RC12 0.73 31.4 72.9 16.1 10.3 4186.2 7.907E-04 1.30361E-06 976.2 0.9605 1.272 1.38 0.0333 1.535

148 RC12 0.95 27.9 66.5 16.9 10.3 4185.7 8.451E-04 1.29925E-06 979.7 1.0186 1.448 1.38 0.0333 1.535

149 RC13 0.1 47.3 82.5 6.6 6.5 4192.6 5.865E-04 1.25586E-06 970.3 0.7830 0.016 1.081 0.025 1.504

150 RC13 0.22 43.6 80.4 8.0 6.5 4191.6 6.281E-04 1.25662E-06 971.7 0.8009 0.246 1.081 0.025 1.504

151 RC13 0.365 34.7 77.0 9.5 6.5 4190.5 7.427E-04 1.25524E-06 973.7 0.8263 0.491 1.081 0.025 1.504

152 RC13 0.535 26.0 72.9 10.9 6.5 4189.5 8.761E-04 1.253E-06 976.2 0.8577 0.721 1.081 0.025 1.504

153 RC13 0.73 23.7 67.3 12.2 6.5 4188.6 9.152E-04 1.24729E-06 979.3 0.8984 0.933 1.081 0.025 1.504

154 RC13 0.95 20.5 61.5 13.4 6.5 4187.8 9.724E-04 1.24308E-06 982.4 0.9483 1.130 1.081 0.025 1.504

155 RC13 1.2 18.8 55.5 14.4 6.5 4187.2 1.004E-03 1.23879E-06 985.3 1.0049 1.293 1.081 0.025 1.504

-81-
Exp. FS(x) F(x) F .::Delta hf Re.. .Re . da war(x) HTC..;.-,,. Fexp F©orr RMS Ka .. fKr] , HTC. .. R.r;

-No.jl ghr [Kg lhr] [Kgqr _____ _______ ___________________

1251 RCO8 1.0531 1.0525 2.446r 1.0601E-041 5943.71 40593.51 34.541 0.07565 0.5698 463.7[:

126 RC08 0.789 0.7892 2.1832 1.0193E-04 6066.1 36266.7 21.73 0.08498 0.6385 334.3t

127 RC08 0.526 0.5260 1.9200 9.0245E-05 6814.6 31990.7 13.81 0.07892 0.7261 24. 0

128 RC08 0.307 0.3067 1.7007 7.6751 E-05 7955.2 28447.2 7.58 0.07324 0.8197 232.71

129 RC08 0.109 0.1093 1.5033 5.4916E-05 11072.1 25224.1 2.61 0.06444 0.9273 195.7ti

130 RC10 1.377 1.3772 2.7692 1.1223E-04 5670.3 46170.7 49.97 0.06921 0.5027 597.6 I

131 RC10 1.136 1.1365 2.5285 1.0639E-04 5961.0 42137.2 39.81 0.06810 0.5505 522.7;1

132 RC10 0.896 0.8959 2.2879 1.0099E-04 6226.0 38149.1 28.80 0.07028 0.6084 423.31•

133 RCIO 0.677 0.6772 2.0692 9.7885E-05 6291.0 34551.7 17.98 0.08140 0.6727 295.5):

134 RC10 0.459 0.4586 1.8506 8.8687E-05 6860.7 31047.5 11.01 0.08029 0.7522 235.5t

135 RCIO 0.262 0.2618 1.6538 7.4150E-05 8174.9 27894.6 6.10 0.07134 0.8417 201.5ii'!

136 RC10 0.109 0.1089 1.5009 5.5679E-05 10853.1 25473.4 2.47 0.06185 0.9275 172.0•,

137 RC1l 1.218 1.2179 1.5869 9.9027E-05 6581.6 27034.9 57.48 0.05653 0.2325 951.0;•

138 RC1l 1.009 1.0086 1.3776 9.6204E-05 6713.5 23419.6 42.92 0.06521 0.2679 467.7:.-.

139 RC1l 0.805 0.8047 1.1737 9.5290E-05 6650.9 19972.8 27.99 0.08003 0.3144 301.8(.

140 Rl 1 0.620 0.6196 0.9886 9.3957E-05 6587.5 16880.0 17.21 0.09362 0.3732 196.2-i"

141 RC1l 0.462 0.4619 0.8309 8.8121E-05 6934.4 14310.3 11.49 0.09131 0.4441 147.0':.

142 RC1 1 0.335 0.3349 0.7039 7.9820E-05 7621.7 12322.9 8.03 0.07633 0.5242 123.3:'

143 RC12 1.293 1.2935 2.6735 1.0376E-04 6234.1 44175.5 55.97 0.05604 0.5162 836.61-,

144 RC12 1.008 1.0082 2.3882 9.8922E-05 6474.5 39292.6 39.14 0.06372 0.5778 621.3

145 RC12 0.745 0.7449 2.1249 9.4456E-05 6670.6 34868.4 24.45 0.07487 0.6494 433.7'i

146 RC12 0.482 0.4818 1.8618 8.4996E-05 7316.3 30473.9 13.96 0.07944 0.7412 322.5.

147 RC12 0.263 0.2625 1.6425 7.0908E-05 8701.4 26910.1 7.09 0.07595 0.8402 257.9!.

L148 RC12 0.087 0.0872 1.4672 5.0082E-05 12224.6 24117.8 2.20 0.07063 0.9406 204.4•::

149 RC13 1.488 1.4876 2.5686 1.1488E-04 5541.3 43682.3 54.17 0.06411 0.4209 631.6:'4

150 RC13 1.258 1.2582 2.3392 1.1106E-04 5693.9 39756.5 42.78 0.06701 0.4621 523.1;,..

151 RC13 1.013 1.0125 2.0935 1.0908E-04 5696.4 35620.1 29.12 0.07700 0.5164 381.3-

152 RC13 0.783 0.7833 1.8643 1.0563E-04 5771.0 31777.2 19.09 0.08535 0.5798 280.1:

153 RC13 0.571 0.5706 1.6516 9.6229E-05 6300.8 28280.1 13.31 0.07933 0.6545 238.81:

154 RC13 0.374 0.3743 1.4553 8.5141E-05 7066.5 25003.2 8.22 0.07459 0.7428 194.6,

456.65 0.07802. 0'.076801 0.0155

0.05511i, i0.05371 0.0254

0.04168] 0.04240: 0.0174

248.31 0.02925' 0.03121 0.0670

208.2 0.01768i.: 1* 0.01880: 0.0637

,. 587.21 0.10539i :"0,10355 0.0175 0.08769 " 0,08965! 0.0224

" 444.8) 0.06799': 6

:' 0:07.1,44L 0.0508

308.91 0.04697i-i 6 0.049106' 0.0453

'253,11 0.03433.' 003689 0.0746

230.3" 0.02465:,. 0.02817 0.1430

ý204.4 0.01585 •:.'. 0.01883i 0.1882

960.01 0.14449t-i"ii 0.13719' 0.0505

681.2, 0.06967 0.101471 0.4563

44:.! 0.04538 i0.06688, 0.4738

289.41 0.02979,'- 0.04393! 0.4745

234. 0.021201 . 0.03379i 0.5938

2. 0.0-1617ý 0.02952: 0.8256

* 770.61 0.13420"- .0.12361 789

585.3! 0.09596: 0.09039i 0.0580

4"07A 0.06502 • 0.06107 0.0606

3066.J 0.04408, 0.04183, 0.0509

25231 0.02964 6' 0.02900 0.0217

196.6' 0.01672.: 0.01608: 0.0382

648.2! 0.11398," . 0.11698 0.0263

5,51j 0.09187 . 0.09688' 0.0546

396•.2 0.06694, , ,,0.06955i 0.0391

288.9; 0.04854 . ':06050056 0.0313

F;l.21.61 0.03790W 0.04152! 0.0956

. 226.7i 0.02754 : 0'.03208. 0.1650

1551 RC13 0.2111 0.2107 1.291- 7.0921 E-05 8447.61 22270.4 4.481 0.066751 0.8369 162.1V: 203,.7 0.01919 ' 0.02412;, 0.2568 11 LI.

-82-
ExNo WI(x) 9M1-

- m ,*: [•hj ( ghl F ( EXp. No. L n.th .. - .wix :TB(x ) ;:TC t ft!;TC1 Cp' ".'-••''• •" nu.J fi n mr -m umix :,- Rho f -. ,,Rho-mu x ..cn A Ig/l , . .,+, 17-7,+ 

:,.(w r , +.• .. •; • l,:

156 RC13 1.45 18.6 48.8 15.1 6.5 4186.7 1.008E-03 1.22909E-06 988.4 1.0617 1.408 1.081 0.025 1.504

157 RC14 0.1 47.7 85.9 7.1 5.8 4192.3 5.822E-04 1.26005E-06 968.2 0.7650 0.214 0.72 0.025 1.379

158 RC14 0.22 42.1 84.1 8.5 5.8 4191.2 6.460E-04 1.26433E-06 969.3 0.7862 0.444 0.72 0.025 1.379

159 RC14 0.365 32.4 80.6 9.9 5.8 4190.2 7.758E-04 1.26589E-06 971.5 0.8168 0.675 0.72 0.025 1.379

160 RC14 0.535 24.3 76.2 11.3 5.8 4189.2 9.049E-04 1.26932E-06 974.2 0.8608 0.905 0.72 0.025 1.379

161 RC14 0.73 21.8 70.4 12.4 5.8 4188.4 9.488E-04 1.26928E-06 977.6 0.9146 1.085 0.72 0.025 1.379

162 RC14 0.95 18.9 63.1 13.4 5.8 4187.8 1.002E-03 1.26888E-06 981.5 0.9891 1.250 0.72 0.025 1.379

163 RC15 0.1 63.6 93.2 12.1 10.3 4188.6 4.404E-04 1.28373E-06 963.2 0.7541 0.397 0.576 0.0333 1.367

164 RC15 0.22 54.8 92.0 13.9 10.3 4187.5 5.122E-04 1.30561E-06 964.1 0.7992 0.795 0.576 0.0333 1.367

165 RC15 0.365 42.4 89.4 15.6 10.3 4186.4 6.423E-04 1.34533E-06 965.8 0.8872 1.170 0.576 0.0333 1.367

-83-
'Exp FS(X) Ff(:x) FM.;. xK) HT C- ,., .. 2 No."': [Kg/hr.-[K i] : K hr] . .-... "f.. ... J •'Wa"r" .'"e'"

156 RC13 0.096 0.0963 1.1773 5.4581E-05 10971.0 20457.4 2.04 0.05493 0.9182 139.6,'. 1i94.2! 0.01272, O.001770i 0.3909

157 RC14 1.165 1.1650 1.8850 1.0579E-04 6021.7 31950.4 42.74 0.06986 0.3820 574.21 569.2 0.09536,009,53' 0.0086

158 RC14 0.935 0.9347 1.6547 1.0169E-04 6201.0 27951.5 30.90 0.07679 0.4351 441.2[:',:442.2! 0.07115 ,0.07131i 0.0022

159 RC14 0.704 0.7045 1.4245 9.8218E-05 6295.5 24032.9 19.39 0.08811 0.5055 31471 -A, 4.31 0.04999 .0,04833: 0.0331

160 RC14 0.474 0.4744 1.1944 9.0453E-05 6712.6 20096.0 11.20 0.09485 0.6028 231.3U'.217ii 0.03446 ';',.0.32341 0.0615

161 RC14 0.294 0.2936 1.0136 7.8136E-05 7724.5 17055.6 6.61 0.08880 0.7103 189.0i•"86.01 0.02447 ,0.02408. 0.0161

162 RC14 0.129 0.1294 0,8494 6.0390E.05 9923.2 14296.1 2.76 0.08075 0.8477 153.31 -:.151.41 0.01545 i' 0.'015251 0.0126

163 RC15 0.970 0.9695 1.545 9.0979E-05 7180.3 25712.5 47.01 0.05453 0.3727 1272.5 804.118 0.17722 '.011199' 0.06•8

164 RC15 0.572 0.5722 1.1482 8.0206E-05 8038.0 18782.8 23.86 0.06851 0.5016 840,0 483.2 0.10450 .!' 0.060111 0.4248

1651 RC15 0.197 0.1972 0.7732 6.0570E-05 10416.2 12274.7 6.56 0.08653 0.745 5:33.3K .'•,23. 0.051201 0.•-'22561 0.5593

-84-
Table C.2 Local data without noncondensible gas ( inlet pure steam flow)

RC16 0 99.3 67.7 75.9 14.2 92,803.5 3,971.3

0.1 98.3 74.4 80 19.5 62,663.3 3,416.4

0.22 35.2 24.2 26.1 21.7 20,882.7 2,282.8

0.365 21.2 22.3 22.8 22.5 5,656.7 -

0.535 21.1 21.9 22 22.7

0.73 21.1 21.8 21.8 22.7

0.95 21 21.5 21.5 22.8

1.2 21.2 21.3 21.3 22.8

1.45 21.6 22.4 22.4 22.8

1.865 21.6 22.3 22.3 22.8

2.3 21.8 22 22 22.8

RC09 0 99.1 64.7 75.5 13.5 121,382.6 5,134.8

0.1 99 76.7 84.1 20.1 83,882.4 5,645.0

0.22 59.2 29.3 32 23.2 30,518.5 1,122.3

0.365 24.2 25.1 25.9 24.3 9,173.2 -

0.535 24.1 24.7 24.9 24.7 2,234.3 -

0.73 24.1 24.7 24.7 24.8 -

0.95 24 24.3 24.3 24.8 -

1.2 24 24.1 24.1 24.8 - -

1.45 24.6 25.2 25.2 24.8 -

1.865 24.4 25 25 24.8 -

2.3 24.6 24.7 24.7 24.8 -

The unreasonable calculations of heat flux and heat transfer coefficient are represented as blank cells.)

•'?

-85-

NRCr-ORM 338 U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT • NM3ER

r2-8) (Aesgnd by RC. AM VaL, Supp., Rv. NRCM 110Z, Ord Addeadum Numbers V W )y MM1. 3= BIBUOGRAPHIC DATA SHEET

2. T"TLE AND SUBTITLE NUREGIA-0181

Assessment of RELAP5IMOD3.2 for Reflux Condensation Experiment 3. DATE REPORT PUBLSHE

MOT YEAR

Apri 2000

4. FIN OR GRANT NUMBER

5. AUTHOR(S) 6. TYPE OF REPORT

Y.M. Moon, H.C. No, KAIST Technical

H.S. Park, KAERI

Y.S. Bang, KINS 7. PERMOW COVERED o=wDew,

8. PEaORIAN ORGANIZATIOce ofSRie - NAMn AMt ADDREtSS pcde Korea DT onteq. NuclearSfety U.S. Koram Atm Emnegy # edsearc Inosrtit

Korea Advanced Instiute of Science and Technoio, gy Korea Institute of Nuclear Safety Korea Atomic Energy Research Institute

373-1, Gusung-Dong

Yusung, Taejon

305-701 Korea

P.O. Box 114

Yusung, Taejon

305-600, Korea

P.O. Box 105

Yusung, Taejon

305-600 Korea

9. SPONSORING ORG. ~ATIOt4 - NAME AND ADDRESS gvM~C~ ~. 'Sw~. a2 abow~ Wconhcb~ p~v~e M~GDv~ OWceo-Re~b~ U.S M~RbyCoemr*~sa~ 9. SP0ONSORING ORGiNIZATION - NAME AND ADORESS tY,•Rc, bWe "Swase abovla', k provd AM Dvi Ofk orep U.& Akiwtuir Cowba

aidn mr-fJ

Division of System Analysis and Regulatory Effectiveness

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washinaton. DC 20555-0001

10. SUPPLEMENTARY NOTES

11. ABSTRACT (Jor so ah-)

This report describes the experimental works and the assessment of the predictabity of RELAP5/MOD3.2 for the reflux

condensation experiment in the presence of noncondensible gases in a vertical tube having the same outer diameter of the U-tube

riser in Korean standard nuclear power plant (KSNPP). The reflux condensation experiment is performed in conditions of the low

pressure, low flow and the high mass fracton of noncondensible gas representing the situation of the loss-of-residual-heat-removal

(LORHR) accident during mid-loop operation. The test facility is composed of the mixture gas generation part and the reflux

condensation part The test section in the latter part is a verticle tube with 19.05mm diameter and 2.4m length surrounded by the

coolant bloclk Reflux condensation occurs in the range of very small flow rates because of the flooding limit. Therefore, the

injected steam is completely condensed in the vertical tube. '

12. KEY WORDSIDESCRIPTORS gist words orphaswe b wa&w neseere, in boceg ta"rpaort) 13. AVA.LASOY STATEMENT

RELAP5 unlimited

Reflux Condensation 14. SECUFlY CLASSIRCAIMN

unclassified

unclassified

15. NUMBER OF PAGES

16. PRICE

NRC FORM 335 (24-1)
. .-.. 

..

.

.. .. 

.

. .. ! 

-

. 4 - , .. .. , 

.

Federal Recycling Program

UNITED STATES

NUCLEAR REGULATORY COMMISSION

WASHINGTON, D.C. 20555-0001

SPECIAL STANDARD MAIL

POSTAGE AND FEES PAID

USNRC

PERMIT NO. G-67