T
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A NEW HEAT TRANSFER CORRELATION FOR
CONDENSATION IN THE PRESENCE OF A IR A N D ITS
TÜ RKİYE A T O M ENERJİSİ K U R U M U
TEKNİK RAPOR
A N E W H E A T T R A N S F E R C O R R E L A T IO N FO R
C O N D E N S A T IO N IN T H E PRESENCE O F A IR A N D ITS
IM P L E M E N T A T IO N IN T O R E L A P 5/M O D 3.3
2009
T Ü R K İY E A TO M ENERJİSİ KURUM U
2690 sayılı kanun ile kurulmuş olan Türkiye Atom Enerjisi Kurumunun ana görevi; atom enerjisinin barışçıl amaçlarla ülke yararına kullanılmasında izlenecek ulusal politikanın esaslarını ve bu konudaki plan ve programları belirlemek; ülkenin bilimsel, teknik ve ekonomik kalkınmasında atom enerjisinden yararlanılmasını mümkün kılacak her türlü araştırma, geliştirme, inceleme ve çalışmayı yapmak ve yaptırmak, bu alanda yapılacak çalışmaları koordine ve teşvik etmektir.
Bu çalışma TAEK personeli tarafından gerçekleştirilmiş araştırma, geliştirme ve inceleme sonuçlarının paylaşımı amacıyla Teknik Rapor olarak hazırlanmış ve basılmıştır.
TAEK
Teknik Rapor 2009/6
Türkiye Atom Enerjisi Kurumu yayınıdır. İzin alınmaksızın çoğaltılabilir. Referans verilerek kullanılabilir.
TÜRKİYE AT O M ENERJİSİ KURUMU
Adres : Eskişehir Yolu 9. km 06530 Ankara/Türkıye Tel : +90 (312) 295 87 00
Fax :+ 9 0 (312) 287 87 61 Web : www.taek.gov.tr
TO^EWO^RV
c.The current nuc (ear p o w er techno fogies have proven to Se economic, safe, a n d refiabfe, a n d they have a mature technofogicaf infrastructure a n d regufatory base. SuSstantiaf designs anddevefopm entaf programs are underway f o r fu rth e r technofogicaf improvements a n d f o r devefopment o f new reactor designs. Current w a te r coofed reactors a n d some new designs (advanced reactors) refy on redundant a n d diverse active systems to transfer decay heat from the core a n d from the containment Suifding in the event o f an accident. On the other hand, advanced designs incorporate safety systems retying on passive means w ith gravity, naturaf circulation, compressed gas, a n d condensation providing the driving force. (Passive safety systems can simpfify system design, improve the refiaSifity, mitigate the effect o f human errors a n d equipment fadure, increase the avaifaSfe time to cope w ith accident conditions a n d reduce the refiance on off-site p ow er suppfy.
d typicaf eıçampfe to advanced nuc fear reactor designs equipped w ith many passive safety systems is the Simp f if e d (Boifing ‘W ater (Reactor (ScB(l\df). dhe isofation condenser (10, which is the main component o f the passive containment coofing system, utifizes steam condensation f o r the removalofcore decay heat to a reservoir o f w a ter w ithin the containment. In performing this function, the IC must have the capaSifity to remove sufficient energy from the reactor containment in order to prevent the containment from exceeding its design pressure shortfy after design basis accidents a n d to reduce containment pressure in tong term [1]. ^Moreover, passive containment coofing a n d passive residua f heat removaf systems o f some advanced pressurized w a ter reactors are afso counted on the compensation phenomenon therefore, such technofogicaf improvements are necessitated the investigation o f operating prim ipfes o f condensation-based passive safety systems by means o f theoreticaf a n d e^perimentaf programs, dhese are afso cruciaffor the assessment a n d vafidation o f advanced computer codes that are generaffy employed f o r predicting reactor performance under norma f, transient a n d accident conditions.
Table o f Contents
List of Tables... i
List of Figures... ii
Executive Summary... iii
Abbreviations , Nomenclature and Subscripts... v
1. IN TR O D U C TIO N ... I 2. PREVIOUS W O R K ... 2
3. DESCRIPTION of METU CONDENSATION TEST FACILITY and DATA BASE... 5
3 .1 Steam-gas Supply...6
3.2 Connecting Piping and Pipe Fittings...7
3.3 Test Section... 7
3.4 Condenser Tube...7
3.5 Jacket Pipe...8
3.6 Experimental Test Matrix... 8
4. DEVELOPMENT of the CORRELATION...I I 4.1 Final Form of the Correlation...14
4.2 RELAP5 Model of the METU-CTF... 16
5. RESULTS and DISCUSSION...17
5.1 Temperature Distribution... 17
5.2 Heat Flux Distribution...20
5.3 Heat Transfer Coefficient... 22
5.4 A ir Mass Fraction Distribution... 26
6. CONCLUSIONS... 29 REFERENCES... 3 I
List of Tables
Table I. Test Matrix fo r Pure Steam Experimental Runs... 9 Table 2. Test Matrix fo r Air-Steam Experimental Runs... 9 Table 3. Estimated Parameters of Equation (4)... 15
List of Figures
Figure I. Flow Diagram of the METU-CTF... 5
Figure 2. Model of Film Condensation in the Presence of NC Gas... 14
Figure 3. RELAP5 Model of the METU-CTF...16
Figure 4. Wall Sub-cooling Degree fo r Pn- 3 bar... 18
Figure 5. Comparison of RELAP5 Results with All Experimental Data for Wall Sub-cooling Degree...20
Figure 6. Heat Flux Distribution Along the Condenser Tube for Pn = 4 bar (Comparison with modified RELAP5)...22
Figure 7. Heat Flux Distribution Along the Condenser Tube for Pn = 4 bar (Comparison with original R ELAP5)...23
Figure 8. Local Heat Transfer Coefficient for Pn= 4 bar (Comparison with modified RELAP5)...24
Figure 9. Local Heat Transfer Coefficient for Pn= 4 bar (Comparison with original RELAP5)... 24
Figure 10. Comparison of RELAP5 Results with All Experimental Data for Local Heat Transfer Coefficient...25
Figure 11. Comparison of RELAP5 Results with All Experimental Data for Local Heat Transfer Coefficient...26
Figure 12. Comparison of RELAP5 results with all Experimental Data for Local A ir Mass Fraction... 27
Executive S um m ary
In the framework of safety analysis of Light W ater Reactors, film condensation problems may be encountered in several situations. The passive heat removal applications in the current and the advanced water cooled reactors rely on the condensation heat transfer mode. Following the Loss of Coolant Accident (LOCA), the generation of steam can lead to rise in temperature and pressure inside the containment. In order to condense this steam and thus to limit the containment temperature and pressure, containment cooling condensers are provided in some advanced boiling water reactors (ABWR). The emergency condensers, which are located in core flooding pool, are also used in ABWR. The circuit of each condenser contains an anti-circulation loop so that practically no circulation of condensate takes place through the open lines to the reactor during normal operation. Only when there has been a drop in reactor pressure vessel (RPV) does the steam enter the condenser, with the resulting condensate being returned to the RPV [2].
To make a qualified design decision for such passive safety systems utilizing condensation, a fundamental question that arises is the behavior of the steam condensation when the noncondensable (NC) gas is present. It has been well established that the presence of NC gases in the vapor can greatly inhibit the condensation process due to buildup of NC at the condensate-mixture interphase leading to a decrease in vapor partial pressure and in the interphase temperature at which condensation occurs.
The theoretical analysis of the in-tube condensation in the presence of NC gas has been studied by many researchers by using different methods involving either the heat and mass transfer analogy o r the boundary layer analysis methods. The form er approach is generally based on the two-fluid model in which each phase is separately considered in terms of tw o sets of conservation equations governing the balance of mass, heat and energy. The interfacial friction factor is estimated by the single phase correlations and tw o phase empirical o r semi empirical correlations. O ther possible effects such as entrainment, deposition, suction effect, and interfacial roughness could also be taken into consideration by using suitable relations. Since the transport of mass, heat and momentum in the annular film-wise condensation with NC gas is strongly coupled with each others at the liquid-gas interface, for the systematic understanding of these transport phenomena, the boundary layer analysis, which is solving the governing equations in the gas-mixture and liquid film regions, is more helpful [3]. However, it should be noted that the boundary layer solutions are not readily usable form neither for design purposes nor system analysis codes.
In this study, a new correlation for vertical flow is introduced for the condensation in the presence of NC gas problem. The model of correlation is based on the Chen [4] type forced convective flow boiling correlations. Examination of Eq. (2) clearly reveals that while the first term on the right hand side is analogous to the enhancement factor, the second term could be treated as the suppression factor. The data extracted from the Middle East Technical University-Condensation Test Facility (METU-CTF) [5] were engaged to estimate the unknown parameters of Eq. (2) and the details of the data are given in Section (3.6) and Section (4). The implementation of the correlation into the RELAP5 code was also in the frame of the present study and this new version of the RELAP5 code is called as modified throughout the report. The comparison of wall sub-cooling of the modified RELAP5 results with experimental data is performed in Section (5.1). A t the mid-elevation of the condenser tube, the deviation was found in the range of ± I % and -5% for modified RELAP5. However, the maximum deviation of the original RELAP5 is —47%. This finding implicitly reveals that the axial variation of air mass fraction at both interface and bulk is well predicted by modified RELAP5.
The heatflux predictions and comparisons are reported in Section (5.2). Because of the air accumulation at condensate-mixture interface, the decreasing heat flux variation along the condenser tube was achieved as expected. The original RELAP5 code gives higher deviation, which is around 40%, than the modified version in which the deviations are hovered around 10%.
The local heat transfer coefficient (HTC) variations (given in Section 5.3) corresponding to 4 bar system pressure are provided in Fig. 8 and Fig. 9 for both modified and original RELAP5 codes, respectively. The achieved propensity is appropriated fo r the theoretical background and decreasing HTC, which is mainly caused by the accumulation of air at interface, were obtained in axial direction. The maximum mean deviations acquired from the modified RELAP5 are much lower than the original code and are 20% and 130%, respectively. The overall comparison given in Fig. 10 also shows that the HTC prediction of the modified RELAP5 is more accurate than that of original code and most of the data points are predicted within the range of the uncertainty band (24%) of the experimentally evaluated HTC.
The air mass fraction possesses vital importance for the accurate prediction of local heat flux and hence local HTCs. As discussed in Section (5.4), the deviations fo r the majority of data are below 5% for modified version. On the other hand, the original RELAP5 gives relatively higher deviations (> 25%) especially at the bottom of the condenser tube. The general conclusion drawn from this study is that the prediction of the modified RELAP5 is much better that that of original RELAP5.
Abbreviations , N o m en clatu re and Subscripts
Abbreviations
ABWR HTC 1C ID LOCA METU METU-CTF MITRPV
O D SBWR UCB: Advanced Boiling W ater Reactor : Heat Transfer Coefficient : Isolation Condenser : Inside Diameter
: Loss of Coolant Accident
: The Middle East Technical University
: The Middle East Technical University Condensation Test Facility
: The Massachusetts Institute of Technology : Reactor Pressure Vessel
: Outside Diameter
: Simplified Boiling W ater Reactor : The University of California at Berkeley
Nomenclature
cp : Specific heat at constant pressure (J/kg °C) d : Diameter of condenser tube (m)
F : Enhancement factor, dimensionless dT : Temperature difference (°C)
h : Convective heat transfer coefficient (W /m 2 K) : Specific heat of vaporization (J/kg)
HTC : Heat transfer coefficient (W /m 2 K) ID : Inside diameter (m)
Km : Convective mass transfer coefficient (kg/m2 s) m : Mass flow rate (kg/s)
O D : Outside diameter (m) P : Pressure (bar)
S : Suppression factor dimensionless q" : Heat flux (W /m 2)
Re : Reynolds number, dimensionless T : Temperature (°C)
dT : Temperature difference (°C) x : Axial distance (m)
X : Mass fraction, dimensionless
§ : Boundary layer thickness, condensate layer thickness (m)
Subscripts a b c cal cond cw exp f g i L mix n s v w A ir
Bulk (steam air mixture at the center of condenser tube) Centerline fo r T
Calculated Condensation
Cooling water in jacket pipe Experimental
Film
Gas phase, mixture Interface, inner Liquid Mixture Nominal Concentration Vapor
I. IN T R O D U C T IO N
It is well known that the passive cooling systems are one of the main features of the innovative and advanced nuclear designs, which incorporate simplification of system design that assures minimized demand on operator and improvement of plant safety. However, passive cooling capabilities could affect the behaviour of nuclear power plants under certain accident conditions. One aspect of passive cooling features comprises condensation of steam in the presence of NC gase(s).
Moreover, the phenomenon under consideration is important for advanced and innovative reactors designs. The isolation condenser of passive containment cooling system of the simplified boiling water reactors is atypical application area of in-tube condensation in the presence of NC. It is known that the presence of NC gases can greatly inhibit the condensation process due to build-up of NC gas concentration at the condensate-mixture interface, which affect the cooling performance of heat exchangers.
The experimental w ork conducted at the Middle East Technical University (METU) was undertaken to investigate the inhibiting effect of NC gas on the condensation phenomenon. The constituted data base covers the wide range of systems parameters such as mixture Reynolds number and air mass fraction. In this study, a new correlation is proposed defining condensation phenomenon in the presence of air and is modeled by using METU data base. N ot only the mixture Reynolds number but also condensate Reynolds number is taken into consideration to simulate the possible effect of interfacial waviness. The suppression effect of air, which is accumulated at condensate-mixture interphase, on heat flux is considered by supplementation of air mass fraction. The mean deviation with respect to the experimental data is determined as 19.4%. Furthermore, the correlation was tested on the RELAP5 code and the accuracy is determined as 20%. The overall performance of the correlation, as coded in the RELAP5 code, is satisfactorily good with respect to experimental data for local heat flux, HTC, air mass fraction and wall sub-cooling degree. The successful completion of this w ork leads us to capture the phenomenon of steam condensation and the effect of air on condensation process both in experimental and theoretical means.
2. P R E V IO U S W O R K
Condensation is a common phenomenon in nature and industry. Due to wide application and occurrence, condensation on cooled solids surfaces has been previously studied by numerous investigators. Most of the early investigations dealt with condensation of pure vapor, however, in recent years the comprehensive studies have been initiated on the effect of NC gases on condensation.
The first theoretical calculation procedure fo r predicting the heat transfer coefficient in laminar film condensation was developed by Nusselt [6] in 1916. In this model, laminar film flowing down on an isothermal vertical plate was considered without waves on the free surface. Also, it was assumed that temperature profile through the film is linear. This simple model yields good results fo r very thin films of non-metallic fluids such as water.
The earliest experimental w ork on steam-air mixture condensation was undertaken by O thm er [7] in 1929. He measured heat transfer rates fo r a 7.62 cm diameter by 1.22 m length copper tube placed in a stagnant air-steam mixture environment. An empirical correlation was derived relating the heat transfer coefficient to the steam-air volume ratio and the temperature difference between the cooled surface and stagnant steam-air mixture. O thm er found that the heat transfer coefficient would decrease by 50% when as little as 0.5% air by volume was added to the steam chamber.
The boundary layer solutions currently available deal primarily with the flat plate configuration and stagnant atmospheric conditions. Sparrow and Gregg [8], Sparrow and Lin [9], Koh etal. [10] and Minkowycz and Sparrow [ I I ] have carried out the boundary layer solutions. It should be noted that boundary layer solutions are not readily usable form fo r design purposes.
Vierow [12] conducted an experimental study using a 22.0 mm ID vertical tube for natural circulation steam-air system. The local heat transfer coefficients were correlated as a function of the local gas mass fraction and the local condensate Reynolds number. The authors found that at an air inlet mass fraction of 14% the heat transfer coefficients were reduced to one-seventh the values of pure steam.
Siddique et al. [13] used an experimental apparatus, which consists of an open cooling water circuit and an open steam-NC gas loop for forced convection condition, so called the Massachusetts Institute of Technology (MIT) Test Facility. The test section consists of a single vertical stainless steel tube inside of which condensation would occur. The condenser tube dimensions are 50.8 mm outside diameter, 46.0 mm inside diameter, and 2.54 m effective length. The test matrix of the MIT covers the range of 1.1—4.8 bar inlet pressure, 100—
I40°C inlet temperature, 2 .8 x l0 3- 9 .2 x l0 3 kg/s inlet steam flow and 0.09-0.35 air mass fraction. They found that hydrogen and helium have a more inhibiting effect on the heat transfer than that of air. The heat transfer characteristics of steam-hydrogen and steam-helium mixtures are nearly identical. The local heat transfer coefficient depends strongly on the mixture Reynolds number and it increases with increasing mixture Reynolds number.
Kuhn et al. [ 14] conducted an experimental study at the University of California, Berkeley, (UCB) Test Facility. The test section consists of a stainless steel condenser tube (2.42m long and 50.8mm/47.5mm O D/ID) surrounded by a jacket pipe (73.7mm ID). The active length of the test section is 2.42m. The steam-gas mixture flows downward in the condensing tube and cooling water flows upward in the annulus. The test matrix of the UCB covers a wide range of operating parameters, i.e., 1.09-5.18 bar inlet pressure, I0 0 -I5 4 °C inlet temperature, 8.3x10 3- l 7x103 kg/s inlet steam flow, and 0.0-0.4 air mass fraction. Simple correlations were developed for each mixture case (steam-air and steam-helium). These correlations do not distinguish between laminar and turbulent liquid film flow but the calculated Reynolds numbers indicate that the preponderance of data within the database lie in the laminar flow.
Ghiaasiaan et al. [15] analyzed the steady state condensation in the presence of NC in a cocurrent two-phase channel flow using two-fluid model. The effect of NCs on the combined heat and mass transfer at the liquid-vapor interface was accounted for by using the stagnant film theory. Model predictions were compared with published experimental data and reasonable results were obtained.
In-tube condensation of both pure steam and steam-air mixture was also conducted by Tanrikut [5]. Details of the METU-CTF are given in subsequent section.
Park and No [16] performed the condensation experiment in the presence of NC gas in a vertical tube of the passive containment cooling system of the CP- 1000, which is next generation passive nuclear reactor. The results are parallel to the aforementioned experimental studies, namely the heat transfer coefficient increases as the inlet mass fraction of the NC gas decreases. Another result is that the dependence of the heat transfer coefficient on the inlet mixture
Reynolds number is small for the operating range. Park and No also developed the empirical correlation with a standard deviation of 22.3%.
3. D E S C R IP T IO N of M E T U C O N D E N S A T IO N T E S T
F A C IL IT Y and D A T A BASE
The METU condensation test facility (METU-CTF) was installed atthe Mechanical Engineering Department of METU. The experimental apparatus, consisting of an open steam-gas system and open cooling water system, is depicted in the flow diagram of Fig. I. The details of the apparatus are described in the following sections:
3.1 Steam-gas Supply
Steam is generated in a boiler (1.6 m high, 0.45 m ID) by using four immersion type sheathed electrical heaters. Three of these heaters have a nominal power of 10 kW each and the fourth one has a power of 7.5 kW at 380 V. All the heaters can be individually controlled by switching on or off. One of these heaters, i.e. the one with 7.5 kW power, is connected to a variac for continuous control of power.
The boiler tank was designed to withstand an internal pressure of 15 atm (at T=20 °C) and was tested at this pressure. The maximum operating pressure of the tank is 10 atm. To ensure dry steam at the exit of the boiler, a mechanical separator directly connected to the exit nozzle was installed. However, electrical pre-heating with three heaters (0.5 kW per heater) is also available at the entrance of the test section to increase the temperature of steam, so that steam is guaranteed to be 100% dry. The boiler tank was thermally insulated to reduce environmental heat loss.
Compressed air can be supplied either to the boiler tank (directly to the water) o r to the steam line via a nozzle (after the orifice meter) on the horizontal part of the pipe which connects the boiler and the test section. Preference was given to the first method; i.e. injection to the boiler, during most of the experiments since system behavior is more stable compared to the second method, when air mass flow rate is increased. When air injection was performed by the second method (to the horizontal piping), air injected passes through the preheating section so that local steam condensation was avoided at the entrance of the test section due to thermal inequilibrium of steam and air. The air supply system consists of an air compressor and three compressed air tanks with a total capacity of 600 liters. The maximum pressure of the compressed air system is
10 bar.
The boiler tank is equipped with the measuring instruments given below; • level gauge with an operating pressure of 16 bar and a test pressure of 32
bar,
• safety vent valve of spring lift type with an operating pressure of 12 bar, • pressure controller for cutting the power off at a predetermined maximum
pressuresetting,
• pressure gauge (1-16 bar), • relief valve (19.05 mm ID).
3.2 Connecting Piping and Pipe Fittings
The pipe connecting the boiler tank and the test section has a length of approximately 2 m and an ID of 38.1 mm. The pipe was connected to the boiler tank via an isolation valve. This isolation valve (38.1 mm ID) is used to isolate the boiler until inside pressure of the tank is increased to a pre-determined level. The measurements performed on this part of the experimental facility are mass flow rate via a differential pressure transmitter and temperature. There are three electric heaters (0.5 kW each at 220 V) installed to the horizontal part of the piping between the orifice meter and the test section. The pipe connecting the boiler and the test section was thermally insulated.
3.3 Test Section
The test section is a heat exchanger of countercurrent type, that is, steam or steam-gas mixture flows downward inside the condenser tube (inner tube) and cooling water flows upward inside the jacket pipe (outer pipe).
3.4 Condenser Tube
The condenser tube consists of a 2.15 m long seamless stainless steel tube with 33/39 mm ID/OD and is flanged at both ends with sealing materials. The condenser tube was flanged to the inlet (33.5/42.6 mm ID/O D) and exit (33.5/42.6 mm ID/OD) pipes of the test section. The total length of the inlet pipe from the horizontal part of the pipe section down to the condenser tube is approximately 33 cm (10 x d , where d. is the inner diameter of the tube) and this length is long enough fo r the mixture flow to become fully developed before entering the condenser. It should also be noted that some uncertainties (such as irregular film development or dropwise condensation) associated with the liquid film development at the entrance of the condenser tube are expected to occur in this development region since the entrance region was not thermally insulated. A pressure measurement port was located at the vertical part of the inlet pipe flanged to the condenser tube.
A total of 13 holes (1.5 mm diameter) were drilled with an angle of 30° at different elevations along the condenser tube length to fix the thermocouples for inner wall temperature measurements. The condenser tube was tested at 10 atm pressure to check that inner wall of the tube was not pierced during the drilling process.
The outlet of the condenser tube is connected to a tank via exit part of the test section. This tank is used to keep the system pressure at a constant level
by controlling the flow rate of steam or air-steam mixture through a valve connected to the tank. The measured parameters at the exit of the test section are pressure and temperature.
3.5 Jacket Pipe
The jacket pipe surrounding the condenser tube is made of sheet iron and has a length of 2 .1 33 m and 8 1.2/89 mm ID/OD. The cooling water is supplied via a nozzle which has been welded on the jacket pipe. Similarly, cooling water outlet consists of a nozzle which is connected to the building water discharge system. Inner diameter of all these nozzles is 12.7 mm. A total of 15 holes ( 1.5 mm diameter) were drilled radially at different elevations for installation of the thermocouples to be used for cooling water temperature measurements. The measured cooling water temperature is used to determine heat flux profile along the annulus region. The jacket pipe was thermally insulated to reduce environmental heat losses.
3.6 Experimental Test M atrix
The experimental test matrix (Table I and Table 2) for the steady-state conditions consists of tw o parts: pure steam and air-steam mixture runs. It is to be noted that the mass flow rate measurement was performed using a differential pressure transmitter, so in some experimental runs the differential pressure rather than the mass flow rate, was set to an almost constant predetermined value while changing the system pressure. This means that the vapor mass flow rate increases as the system pressure increases. For comparison with corresponding pure vapor runs, the system pressure and vapor mass flow rate in the air-vapor mixture runs were kept close to those of the pure steam runs. The reason for selecting the vapor mass flow rate as a fixed parameter, rather than the total mixture mass flow rate, in the air-steam mixture runs is to fix the amount of vapor at the entrance of the test section to make the data more comparable with those of the pure steam runs and to understand the inhibiting effect of air. Some additional experiments, however, were performed using the same vapor flow rate and a different system pressure to observe the effect of system pressure on the condensation process. Besides these, in some experiments the total mixture mass flow rate was kept the same as that of the corresponding pure steam run while varying the air quality only. Repeating certain experiments by turning off the pre-heaters checked the effect of inlet superheating. In all experiments, including the transient case, the cooling water mass flow rate was kept nearly the same, i.e., 0.2 kg/s.
Monitoring the system parameters, i.e., the temperature, pressure, and flow rate, on a computer via a data acquisition system, allowed control of the steady- state conditions. Data were recorded with I second intervals approximately for a 2 minutes period.
The experimental test matrices are given in Table I and Table 2. The coding of these experimental runs is based on the following logic:
R U N - X Y Z
r
^
Air mass fraction
, , * x System Pressure
1—>(pure steam) J
> 1 —>(steam-air mixture)
Vapor mass flow rate
Table I. T est m atrix fo r pure steam experimental runs
Code P (bar) m„(kg/s) ReV mcwo<g/s) x dr
RUN-1.1.1 1.376 1.409x 102 43814 0.177 0.0 RUN-1.2.1 1.829 1.808x 102 54770 0.221 0.0 RUN-1.2.1R 1.799 1.812x 102 54991 0.242 0.0 RUN-1.3.1 3.029 2.314x102 66875 0.223 0.0 RUN-1.4.1 3.959 2.72 lx I0 2 76645 0.226 0.0 RUN-1.5.1 4.837 3.101x102 85675 0.225 0.0 RUN-1.6.1 5.452 3.419x1 O'2 93365 0.226 0.0 RUN-1.2.1NH 1.919 1.831 x 102 55236 0.233 0.0 RUN-1.3.1NH 2.970 2.297x10 2 66502 0.237 0.0 RUN-1.4.1 NH 3.91 2.701x10 2 76187 0.239 0.0 RUN-1.2.2 1.919 2.740x10 2 77183 0.240 0.0 RUN-1.3.2 3.1 2.800x10 2 80742 0.240 0.0
Table 2. T est m atrix fo r air-steam experim ental runs
Code P (bar) m m i * ( k S ^ S ) Rem ix mcwo<g/s) Xair
RUN-2.1.1 1.544 1.465x1 O'2 45091 0.199 0.106 RUN-3.1.IR 1.454 I.530x l0 2 47957 0.229 0.194 RUN-4.1.IR 1.469 1.776x102 55694 0.232 0.211 RUN-2.2.1 1.919 1.771X102 53748 0.198 0.099 RUN-2.2. IR2 1.919 1.853X102 56228 0.232 0.095 RUN-3.2.1 1.956 1.865X102 56879 0.236 0.191 9
Table 2. (Continued) RUN-4.2.1 2.01 2.055X 102 62949 0.232 0.275 RUN-2.3.1 2.969 2.306X 102 66771 0.23 0.099 RUN-2.3. IRI 2.93 2.428X 102 70801 0.232 0.092 RUN-3.3.1 2.901 2.366X 102 69543 0.231 0.189 R U N -4.3.1 3.16 2.664X 102 78258 0.238 0.279 RUN-5.3. IR 3.13 1.804X102 53938 0.237 0.421 R U N -2.4.1 3.982 2.833X 102 80253 0.234 0.097 R U N -3.4.1 3.90 2.77X10 2 79188 0.223 0.193 RUN-3.4. IRI 3.79 2.644x102 75884 0.237 0.208 R U N -4.4.1 3.94 2.987X 102 85898 0.231 0.274 R U N -5.4.1 3.94 2.193X 102 63663 0.253 0.369 R U N -6.4.1 3.906 1.526X102 45195 0.253 0.519 RUN-2.5.1 4.312 2.918X 102 82043 0.237 0.097 RUN-6.5.1 4.36 1.881X 102 54476 0.253 0.43 R U N -2.6.1 5.257 3.386X 102 93388 0.234 0.098 RUN-2.2. IN H 1.88 1.748x102 53269 0.237 0.130 RUN-2.3. IN H 2.93 2.416 x l 0 2 70480 0.237 0.098 RUN-2.4. IN H 4.06 2.864x102 81074 0.237 0.1 13 RUN-3.4. IN H 3.79 2.630x 102 75697 0.237 0.242 RUN-4.4. IN H 3.87 2.982x102 85980 0.237 0.284 RUN-5.4. IN H 4.09 2.109x 102 61278 0.240 0.408 RUN-3.3.2 2.97 2.749x102 80492 0.240 0.168 RUN-5.3.2 2.97 2.380x 102 70533 0.241 0.310 RUN-3.4.3 3.98 2.1 18x 102 60615 0.241 0.230 RUN-5.4.3 3.94 1.647x 102 47968 0.241 0.398 RUN-3.2.3 1.90 1.276x102 39293 0.250 0.276 RUN-3.3.3 3.27 1.900x 102 55369 0.250 0.223
4. D E V E L O P M E N T o f the C O R R E L A T IO N
In many applications, convective heat transfer is accompanied by change in phase. Such processes occur in condensation, evaporation, and boiling [17]. The condensation can occur whenever a saturated or superheated vapor comes into contact with a surface, which is at a temperature lower than the saturation temperature of the vapor. The latent heat thereby liberated represents the major portion of the heat transferred from vapor to liquid. The amount of condensate formed represents the mass that is transformed from vapor to liquid phase [18].
Depending on the wetting properties of the cooled wall, the condensate will either wet the surface to form a continuous film o r form discrete droplets. The form er case is named as film-wise condensation, while the latter is classified as drop-wise condensation that is not the topic of the present study.
Film-wise condensation has been extensively analyzed both theoretically and experimentally. The heat exchanged by this condensation mechanism can be predicted as a function of temperature difference between the bulk steam-gas mixture or centerline and the wall, the system pressure, the surface characteristics, the velocity field and the composition of the steam-gas mixture [19]. Existence of a NC gas in vapor is well known for degrading the condensation heat transfer in variety of condensing mixtures in different geometries. Predicting this degradation is crucial for designing new systems for power and process industries.
Near the tube inlet, the condensation HTC change sharply with distance. This change is due mainly to the fact that interfacial shear stress effect on the condensate film thickness is very important near the tube inlet, because the mixture Reynolds number is very high, as given by Munoz-Cobo et al. [20]. This result is also observed by Chen and Ke [21] who concluded that the interfacial shear stress due to the vapor flow had significant effects on condensation HTC and was more pronounced for high mixture flow rates.
The mixture Reynolds number also affects the air accumulation at the interface which influences the axial HTC variation. Theoretical investigations based on the two-fluid model undertaken by Ağlar [22] clearly reveals that at low mixture Reynolds numbers the intensive air accumulation is observed at
mixture interface. On the other hand, the interface air accumulation drastically reduces with increasing mixture Reynolds number. This phenomenon is caused by the sweeping of air from interface resulting in higher mass transfer rate and hence increasing HTCs. Wang and Tu [23] developed a model in order to determine the effect of mixture Reynolds number and pressure on laminar film-wise condensation of a vapor-gas mixture flowing turbulently in a vertical tube. They concluded that the reduction in heat transfer due to the NC gas was found to be more significant at low pressures and at low Reynolds numbers. The liquid condensate layer (film) flowing downward on a vertical plate o r inside a tube under influence of the gravity is essentially laminar over the upper part of the surface but may change to turbulent flow over the lower part if the rate of condensation is sufficiently high. The film roughness (waviness) markedly affects the gaseous laminar sub-layer and destabilizes it by breaking it up. Therefore, the effect of film roughness and the mass transfer should be more pronounced for high Schmidt number fluids because in these fluids the concentration boundary layer is thin compared with the hydrodynamic boundary layer. On the other hand, fo r low Schmidt number fluids like steam-air and steam-helium mixtures, the concentration boundary layer is thicker compared with the hydrodynamic boundary layer and therefore the roughness is not effective in breaking up the laminar sub-layer.
Kang and Kim [24] conducted an experimental study to investigate the effect of NC gas and wavy liquid film on condensation heat transfer. The experiments were performed in a nearly horizontal square duct of 0 .1 m height, 0 .15 m width and 1.52 m length at atmospheric pressure. A liquid film in a steady thermal condition was injected to simulate the effect of a wavy interface on the condensation. The experimental data for HTC and the interfacial structure of the wavy condensate were obtained along with the three parameters: air mass fraction, mixture velocity, and film flow rate. When the interface is smooth, the HTCs with o r w ithout NC gas agree reasonably with the previous theories. The waviness of condensate film increases the heat transfer up to several of a percent.
In condensation, the liquid is effectively impermeable to the NC species, so the NC gas accumulates next to the condensate-mixture interface (Fig. 2). A balance occurs between the bulk convection of NC gas toward the surface and diffusion of NC gas from the interface. The balance between convection and diffusion results in a logarithmic gas concentration distribution near the interface. Colburn and Hougen [25] first proposed a theory that the condensation mass transport is controlled by diffusion across a thin layer with the driving potential across the film given by the difference of the gas partial pressures in the bulk steam-gas mixture and interface, divided by the log mean partial pressure ratio.
As the ambient gas concentration approaches to zero, the resistance to the condensation becomes negligible.
The build up of NC gas at interface does not only cause a resistance to diffusion of vapor but it also reduces the effective thermal driving force for heat transfer. As a consequence, the partial pressure of condensing vapor at a region adhering to the interface is lowered, which in turn lowers the interface temperature. The net effect is, therefore, a reduction in condensation and heat transfer rates. The effects, already discussed in preceding paragraphs, necessitate that present correlation include mixture Reynolds number, condensate Reynolds number and air mass fraction. Therefore,
^ c o n d = ^ c o n d ( ^ e m i v 5 ^ e L 5 ^ a )
(0
and the present correlation is proposed as:
f = (l + c , ReL-H C
2
R e ^ - C3
X 2a) (2
)where
r = (h / h ^
cond Mnusselt / (3) C., C_, C^, m, n and z are the constants to be determined, h is the ratio of the thermal conductivity of the condensate to the condensate layer thickness. hcond is the condensation heat transfer coefficient in the presence of air. It should be noted that the first parenthesis on the right hand side of the Eq. (2) could be taken as the enhancement factor. Similarly, the second parenthesis is the suppression factor corresponding to the accumulation of the NC gas on the interface and is responsible for the reduction in condensation HTC.
Figure 2. M odel of film condensation in the presence of N C gas
4.1 Final Form o f the Correlation
The data used in the present correlation is extracted from METU-CTF [5] (Fig. I). The METU-CTF consists of tw o open systems; steam-air and cooling water systems. The test matrix of METU-CTF covers a wide range of operating parameters such as 1.8-5.5 bar inlet pressure, 45,000-94,000 inlet vapor Reynolds number and 0-52% inlet air mass fraction. It should be stated that METU-CTF also cover the pure steam condensation data but in the present study only steam-air mixture data is taken into consideration.
In data reduction process, experimentally measured quantities are converted into suitable quantities that are engaged in the correlation. Data reduction is performed by using a computer code, which is extracted from Kuhn [14]. Data fitting subroutine of this code is renovated with Marquardt-Levenberg non-linear parameter estimation method and hence not only the high accuracy was obtained but also more functions were tested. Input file of the data reduction code contains some geometric data and experimentally measured
parameters such as inner and outer diameters of condenser tube and jacket, thermocouple locations, axial temperature variation of coolant, wall and centerline temperatures, flow rates of air, steam and coolant, and inlet pressure of condenser tube. O utput file consists of heat flux, condensate and steam-air mixture flow rates with corresponding Reynolds numbers and HTCs.
The unknown parameters of the Eq. (2) were estimated using all of the condensation data obtained from the METU-CTF. In connection with this assignment the Marquardt-Levenberg non-linear regression method was used. The resulting heat transfer correlation in its final form is:
hcond = h nusselt(l + C 1R e : ı + C î Re"Xî —C 3X : ) (4) where the unknown parameters are provided in Table 3.
The mean deviation of the heat transfer correlation with respect to the experimental data, as given by the Eq. (5), is determined as 19.4%.
1 N
MeanDeviation = — X
N !
(hcal- O 00
hexp (5)
In this equation, h , and h stand fo r calculated and experimental local HTCs.
' cal exp r
The summation was made over the number of data (N). Table 3. Estimated parameters of equation (4)
P a r a m e te r s X <0.15a X >0.15a C, 22.9793 1.4949 -5.82217 -3.22768 C 3 4.1 14635 0.91809 m -0.16399 0.008503 n -0.20919 -0.23775 z 0.95367 0.4210 15
4.2 RELAP5 M odel o f the M E T U -C T F
The RELAP5 model of the METU-CTF (Fig. 3) consists of 24 volumes, 23 junctions and 17 heat structures. The heat structures are modeled fo r the condenser tube only and the total number of mesh points of the respective heat structures is 221. Environmental heat losses are not considered in the model due to satisfactorily good insulation of the piping of the METU-CTF [5]. The RELAP5 simulations were performed by using the measured inner wall temperatures as the boundary conditions since all potential uncertainties are preferred to be restricted to the primary side (inside of the condenser tube) only.
Time dependent volumes in RELAP5 model are used for simulating the boundary conditions associated with the inlet conditions of air (TDV-001), steam (TDV-003) and steam-air mixture outlet (TDV-405). Mass flow rates of air and steam are controlled through time dependent junctions, i.e. TJ-002 and TJ-004, respectively. Steam is mixed with air at the single volume (SV-222), which represents the horizontal pipe of the facility. The two-component model was selected for TDV-001 that needs pressure, temperature and static quality as input, and static quality was set to 0.0 to initialize the volume to dry air.
TDV 003 SV 222 \-TJ 004 (steam inlet) T C -1 T C -2 T C -3 P 402 T C - 4 Condenser tube Di/D0=33/39 mm T C -5 T C -6 L=2.158 m T C -7 T C -8 XXX c o m p o n e n t n u m b e r T C -9 yyyy h e a t s t r u c tu r e n u m b e r T C - 1 0 H S h e a t s t r u c tu r e T C -1 1 P p ip e T C - 1 2 SJ s i n g le j u n c t i o n T C - 1 3 S V s in g le v o lu m e T C th e r m o - c o u p le T D V ti m e d e p e n d e n t v o lu m e T J tim e d e p e n d e n t j u n c t i o n SV 224 — j— SV 226 1 t SV 404 t [ TDV 405 |
Pipe between boiler
SJ 223 A A
and condenser SJ 225
SJ 227
HS 4021
Measured inner wall temperature given as boundary condition for HS 4021
SJ 403 SJ 412
5. RESULTS and D IS C U S S IO N
The results fo r RELAP5 runs as compared with the corresponding experimental data of the METU-CTF are presented and discussed in this section. The main parameters considered in discussion are temperature distribution, heat flux, HTC and air mass fraction. The experimental data base used for the assessment of the RELAP5 code cover the range of 2-5.3 bar inlet pressure, 45,000-94,000 inlet vapor Reynolds number and IO%-52% inlet air mass fraction.
It is to be noted that the results given in this section are based on the RELAP5/ mod3.3 code [26] with modification made to the subroutine of condensation by replacing Colburn-Hougen model [25] with the METU-CTF correlation derived from the experimental data of the METU-CTF, as discussed in Section 4.
5 . / Tem perature Distribution
The background information, which is needed to understand the condensation heat transfer when a mixture of air and vapor exists, can be briefly described as follows: Condensation is defined as the removal of heat from a system in such a manner that vapor is converted into liquid. This may happen when vapor is cooled sufficiently below the saturation temperature to induce the nucleation of droplets. Such nucleation may occur heterogeneously on the walls of the system, which can occur in tw o forms: drop-wise and film-wise. The heat power exchanged by film-wise condensation mechanism, which is the topic of investigation under consideration can be characterized as a function of temperature difference of bulk steam-air mixture and wall (wall sub-cooling degree), total vapor pressure, surface characteristics, velocity field and NC gas mass fraction. The presence of even a small quantity of NC gas in the condensing vapor has a profound influence on the resistance to heat transfer in the region of the condensate-mixture interface. The sub-cooling of the tube inner wall provides a driving force for steam condensation. However, gas mixed with vapor can directly affect the wall sub-cooling degree and hence the condensation rate. Since the NC gas can not pass into the liquid film formed next to inner wall, it accumulates at the condensate-mixture interface. By this mechanism a vapor- gas diffusion layer is formed through which steam is to be passed by diffusion and convection to be condensed. The accumulation of gas near the
mixture interface leads reduction of interface saturation temperature below that of bulk steam-air mixture, which then leads to reduction of wall temperature. Measurements show that the suppression of inner wall temperature is more than that of vapor temperature at the centerline, as air mass fraction increases, which causes wall sub-cooling degree to increase [27].
Fig. 4 shows the wall sub-cooling degree (dTw) as predicted by the modified RELAP5 code for the system pressure of 3 bar. There is an agreement with the data fo r cases with different inlet air mass fraction, which simply reveals the fact that the thermodynamics state of the steam-air mixture at the core of the condenser tube is calculated well by the Gibbs-Dalton law used by the RELAP5 code [26]. This law simply states that the steam-air mixture temperature corresponds to the partial pressure of steam, which is calculated as total pressure minus partial pressure of air. Since the steam-air mixture is treated as an ideal gas mixture, partial pressure of air is calculated from the total pressure and the local air mass fraction that are estimated by RELAP5 at
every time step by using continuity equation fo r each control volume. The boundary condition for time zero is imposed by user input values for mass flow rate of steam and air hence air mass fraction is determined by user at
the initialization of the problem. The predicted results have the deviation of ~ l %-5% compared with the data at the middle of the channel, which is quite acceptable. The overall evaluation of the predicted results also leads us to conclude that the code calculates well the dependency of dTw on air mass fraction, which is characterized as an increase of dT with air mass fraction.w Inspection of Fig. 4 shows that increasing inlet air mass fractions gives rise to increasing dT values. However, in flow direction dT variation is nearly constant. The reason of this becomes apparent when sweeping of air from interface caused by high mixture Reynolds number flow, which impedes the accumulation of air at interface, is taken into account. It is also fact that irrespective of the mixture Reynolds number, the local air mass fraction does not exhibit a drastic change in axial direction until at the end of test section. Therefore, (Xb-X ) and accordingly dTw remain almost unchanged in flow direction.
The general comparison for the wall sub-cooling degree against all experimental data comprising various P, Remjx and X. values is presented in Fig. 5. It is interesting that the original version of the code exhibits a strong underestimation for dTw, which is the interface temperature minus the wall temperature. However, if all the resistances inside the condenser tube are considered, dT should bew defined as the temperature difference between the bulk steam-air mixture and the wall. Hence, aforementioned underestimation for dT is unavoidable forw the original code, which is considered to be quite misleading. The deviation of the modified RELAP5 results, at the mid-elevation of the condenser tube, is in the range of ± I % - 5%. However, maximum deviation of the original RELAP5 is -47%.
Figure 5. Com parison of RELAP5 results w ith all experim ental data fo r wall sub-cooling degree
As stated earlier, the assessment of the RELAP5 code is based on the model without the jacket pipe so as to reduce o r better to say to restrict potential uncertainties to the inside of the condenser tube. The uncertainties associated with the existence of the jacket pipe could be due to the interfering factors like thermocouple wiring inside the jacket pipe and disturbance of velocity boundary layer. These kinds of uncertainties make simulations much difficult to assess since measurement e rro r normally do not include this type of sources of uncertainties. Besides, a strong angular dependency, if not weak, for measured inner wall temperatures is not expected since air-steam mixture velocity is high and the test section has been fixed at ideal vertical direction. W orking with higher mixture Re numbers in vertical direction fits well with the heat transfer solution technique in l-D (radial direction) codes such as REI_AP5, however some angular dependency could be expected at the bottom of the test section due to set-up configuration (bend, T-junction etc.).
5.2 H eat Flux Distribution
The heat flux distribution is important in characterizing the heat transfer from inside of the condenser tube to the secondary side since this parameter is the one used in deriving other related parameters fo r the experimental data.
As stated in related references [27, 28] fo r the experimental data of the METU-CTF, it is clear that the local axial temperature gradient (dTcw/dx) was computed from an exponential fit of the measured coolant temperature as a function of axial distance, and the local heat flux (based on inner diameter, d.) was determined from:
q "(x )= r i l c P dTcw(x )
Tidj dx (6)
However, the local heat flux is computed in RELAP5 based on the Colburn- Hougen diffusion method involving an iterative process to solve T. The formulation is based on the energy conservation principle, which reveals the fact that the heat transfer by condensing vapor at condensate-mixture interface is equal to the heat transferred through the condensate layer.
m X ^ c f r - T w ) (7)
For situation where the jacket is not modeled as performed in this study, Tw in Eq. (7) is treated as boundary condition and is equal to the experimentally measured value.
The heat flux distributions fo r experimental runs and modified RELAP5 calculations, corresponding to Pn—4 bar, are presented in Fig. 6. This figure includes the data of steam-air mixture case with different values of X and Re . There are tw o major conclusions that can be drawn from this figure: First, the local heat flux drastically decreases as inlet air mass fraction increases for the same pressure setting and second, the performance of the condenser considerably decreases towards the exit of the condenser due to increase of local air mass fraction. The aforementioned first concluding remark is the evidence for how some amount of air, mixed with vapor, degrades the overall performance of the condenser while the second shows the axial dependency of the condenser performance on local air mass fraction.
The modified RELAP5 results (with the METU-CTF correlation) are yielded satisfactorily good results for the local heat flux, as presented in Fig. 6. The maximum deviation from the data is about -13% at the middle of the axial position for the case with X. = 19% while the absolute deviation is less than 10% for other cases in central region (The deviation is calculated to be as low as ± I % for X. =37%). These results are acceptable in the sense of deviation from the data since the maximum uncertainty of the experimental data for heat flux was reported as ± I I % [5].
Figure 6. H eat flux distribution along the condenser tube fo r Pn = 4 bar (Com parison w ith modified REI.AP5)
The same simulation is repeated by using the original RELAP5 code and results are presented in Fig. 7. It is clear that the original RELAP5 code yields results with greater deviation than given fo r the modified version and the deviation is calculated as high as 40% at the central region of the channel.
5.3 H eat Transfer Coefficient
The local HTC inside the condenser tube is defined as following:
h = ___ _______
""" [Tc( x ) - T w(x)] (8) In this equation, h , is the local total HTC and T and T are the centerline and wall surface temperatures, respectively. By assuming that the total thermal resistance is estimated as a combination in series of steam-air mixture and liquid phases, neglecting radiative contribution to heat transmission, and summing up the effects of condensation and convection, h may be expressed as [29]:
190.0 CM E 5 X 3 nj 0) 165.0 140.0 115.0 90.0 65.0 40.0 O X= 19%, R e =79,000 □ X =37%, R e =64,000 A X =52%, R e =45,000 —‘♦ — R S -o rig in a l —■ — R5- o r ig in a l — R5- o r ig in a l O T < > □ □ r V 1 <0 ° N \ A A " □ □ □ [ a O : o * ' " ' S l D . A □ A O □ A o □ 1> A h( □ 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Axial Position (m)
Figure 7. H eat flux distribution along the condenser tube fo r Pn = 4
bar (Com parison w ith original R E IA P 5)
1 1 1
^ total h r ( h c „ „ d + h g )
(9)
The centerline temperature of vapor phase is calculated from the Gibbs-Dalton law in both the experimental data and the RELAP5 code. The uncertainty band of the experimental data for HTC is reported as ±24% [5].
The local HTCs corresponding to 4 bar system pressure are given in Figs. 8 and 9, for the modified and original RELAP5 codes, respectively. It is clearly seen from these figures that increase of inlet air mass fraction results in decrease of local HTCs, as expected, and this is mainly governed by the suppression of local heat flux and inner wall temperature. It is reported by the experimenters that since the suppression of inner wall temperature due to existence of air are more dominant than that of centerline vapor temperature, the increase of air mass fraction results in increase in dT that contributes to the decrease ofw HTC along with the decrease in local heat flux [28]. The dominancy of dTw for suppression of HTC is well simulated by the modified RELAP5 code as implied by Fig. 8. However, local heat flux prediction is dominating for deviation of HTC at the entrance of the test section when compared with experimental data. This can be best seen in Fig. 8, i.e. for case with inlet air mass fraction of 27% the modified RELAP5 yielded an overestimated HTC for the
HT C (k W /r rt 2 K ) HTC (k W /m 2 K ; \ O X = 1 9 % , R e = 7 9 , 0 0 0 Ö X = 2 7 % , R e = 8 6 , 0 0 0 □ X = 3 7 % , R e = 6 4 , 0 0 0 A X = 5 2 % , R e = 4 5 , 0 0 0 ♦ R 5 -c o r r e la t io n — R 5 -c o r r e la t io n m R 5 -c o r r e la t io n A R 5 -c o r r e la t io n -V_/ Jk, \ N ? 0 O ___ İ % □ A L O 0 . 2 5 0 . 5 0 . 7 5 1 1 .2 5 1 .5 1 .7 5 2 Axial Position (m)
Figure 8. Local heat transfer coefficient fo r Pn= 4 bar (Com parison w ith modified RELAP5)
Axial Position (m)
Figure 9. Local heat transfer coefficient fo r Pn= 4 bar (Com parison w ith original RELAP5)
first three axial locations purely due to overprediction of local heat flux in respective nodes. In fact this is valid fo r all cases at the entrance region of tube but it is more pronounced in this concerned case and this may be attributed to the deficiency of the correlation with respect of suppression factor as far as the explicit link between heat flux and HTC is concerned. The deviation of the modified RELAP5 results is about -20% (maximum) and 3% (minimum) at the center of the channel, which falls into the uncertainty band of the experiments (±24%). However, same agreement with the data does not hold true for the results of the original RELAP5 code, as shown in Fig. 9. The deviation from the data in this case is as high as ~ l 30%, which is not acceptable.
The overall comparison of both original and modified versions of the RELAP5 code against the experimental data covering all test matrix cases is presented in Fig. 10. For about 80% of the total simulation runs, the overall deviation of the modified version from the data lies below the limit of 24% (absolute value for the uncertainty band of the measurements for HTC), whereas the deviation is well above this limit fo r the original version of the code.
H TC (kW /m 2 K )-R E L A P 5
Figure 10. Com parison of RELAP5 results w ith all experimental data fo r local heat transfer coefficient
Since the condenser system under consideration was operated with steam-air mixtures, the condensation local HTC has a strong dependency on the local air mass fraction, especially for higher air mass fractions. This dependency has
been taken into account during development of the METU-CTF correlation, as discussed in Section (4). Fig. I I depicts the HTC trend as the function of X a. The modified version of the RELAP5 code captures the general trend of the data. The local HTCs decrease towards the exit of the condenser in all runs (as could be seen more clearly in Fig. 8 fo r four cases) due to dominating resistance of air on diffusion of vapor in the vapor-gas boundary layer, as the result of increase of local X a along the channel. The local HTC is almost the linear function of the local X a in experimental data and the RELAP5 results follow the trend but in a rather exponential manner due to the effect of air mass fraction distribution along the condenser tube. The deviation of the predicted results, for HTC versus X a, from the data is mainly governed by the HTC since prediction of X a is in much better agreement with the data as discussed in the following section.
Figure 11. Com parison of RELAP5 results w ith all experimental data fo r local heat transfer coefficient
5.4 Air M o s s Fraction Distribution
The realistic prediction of the local air mass fraction is important for correct prediction of the local HTC and in turn the local heat flux, as explained earlier. As could be seen in Fig. 12, both versions of the RELAP5 code yield acceptable
results as compared with the experimental data, which is important to reduce uncertainties in assessing the condensation models used in the code. In other words, the air mass fraction has a less significant role in characterizing the deviations of other computed parameters (like heat flux and HTC) from the data though those parameters are the function of the air mass fraction. The modified version that uses the METU-CTF correlation has a maximum deviation of about 3% at the middle of the condenser tube while the original version yields about 7%. The original version of RELAP5 yields more deviation compared to experimental data towards the bottom of the test section, i.e. maximum deviation at the bottom of the tube is about 25% and 12% fo r original and modified versions, respectively. It is w orth to note that majority of the runs with the modified version of RELAP5 has yielded deviations from the data less than 5%, which is quite acceptable.
Air Mass Fraction (--) - REI.AP5
Figure 12. Com parison of REI.AP5 results w ith all experimental data fo r local air mass fraction
A final point of interest is that on the contrary of heat flux, the local air mass fraction is predicted with reasonable accuracy by RELAP5 for a given run. It is well known that the heat flux strongly depends on the accurate prediction of mass flux of vapor to be condensed, which is determined by concentration profile between interface and center of the condenser tube and the mass transfer
coefficient as given in Eq. 10. From this definition, it is possible to conclude that original RELAP5 can not predict well the interface air mass fraction that causes the discrepancy between predicted and experimental heat fluxes for an identical local air mass fraction variation.
m'v = - K m In
6. C O N C L U S IO N S
In this report, a new heat transfer correlation has been developed for the film- wise condensation inside the vertical tube when the NC gas is present. The correlation was evolved by engaging the METU-CTF database, which covers high mixture Reynolds number and NC gas mass fraction. It accounts for interfacial shear stress, sweeping of NC gas from interface, liquid condensate layer waviness and accumulation of NC gases at interface by taking mixture Reynolds number, condensate Reynolds number and NC gas mass fraction into consideration. Furthermore, coupling of the present correlation with a RELAP5 code was also examined and plausible results were obtained. The following conclusions are found to be conspicuous.
I. The present correlation could be simplified as:
= h— FS ( I I )
where F and S are the enhancement and the suppression factors, respectively. Comparison of Eq. (4) and Eq. ( I I ) reveals that while F is expressed by means of mixture and liquid condensate Reynolds numbers, S is modeled as a function of mass fraction of air at condenser tube centerline. It is found that F values at most of the data points are greater than I as expected. On the other hand, all S values are less than I in the range of correlation. 2. The wall sub-cooling providing a driving force fo r condensation is one of the
most important parameters. Accumulation of NC gas at interface affects the wall sub-cooling and hence the condensation rate. In Fig. 5, comparison of wall sub-cooling values extracted from modified RELAP5 with their experimental counterparts is provided. It is fact that the agreement is excellent and the maximum deviation fo r mid-elevation is found as ~5%. The average deviation is about - 1 .6%. The same figure also depicts the wall sub-cooling distribution of original RELAP5 model and the experimental values. It is obvious that the deviation is much greater (average —40%) than that of obtained from the modified RELAP5 code.
3. Although the present correlation estimates the condensation HTC, the heat flux change along the condenser tube is also well predicted and the deviation
is less than 13% at the middle of the test section (Fig. 6). The reason for this becomes apparent when accurate prediction of the HTC and wall sub cooling estimated by the correlation are taken into account. However, original RELAP5 model prediction is rather poor with a mean deviation of nearly 40% at the middle location (Fig. 7).
4. Careful examination of Fig. 10 reveals that the HTC is overpredicted by
the original RELAP5 code with an average deviation of 104%. The modified code, however, deviates from the data by 2.6% (average), and about 80% of data points are estimated with a mean deviation less than 24%.
5. A final point of interest is that the comparison of air mass fraction extracted
from the modified and original RELAP5 codes with the experimental values shows relatively good agreement in regard to other parameters discussed earlier. Though the deviations are below the 20% for both codes, modified RELAP5 gives more accurate result than that of original RELAP5. It is found that majority of data simulated by modified RELAP5 is scattered within the range of 5%. Average deviations fo r original and modified versions are 3% and -0.2%, respectively.
