A sensitivity study of physical models using in RELAP5 code based on FEBA experimental data

Nội dung text: A sensitivity study of physical models using in RELAP5 code based on FEBA experimental data

1. Nuclear Science and Technology, Vol.10, No. 4 (2020), pp. 24-40 A sensitivity study of physical models using in RELAP5 code based on FEBA experimental data Tran Thanh Tram1*, Hoang Tan Hung2, Doan Manh Long1, Vu Hoang Hai1 1Nuclear Training Center, 140 – Nguyen Tuan, Thanh Xuan, Ha Noi 2Institute for Nuclear Science and Technology, Vietnam Atomic Energy Institute, 179 Hoang Quoc Viet street, Cau Giay district, Hanoi 100000, Viet Nam Email*: tttram80@yahoo.com (Received 23 November 2020, accepted 28 December 2020) Abstract: In the thermal-hydraulic safety analysis, simulation results using thermal-hydraulic codes depend mainly on modeling the physical phenomena built-in the codes. These models are the equations, and empirical formulas developed based on matching them to experimental data or based on the assumptions, simplifications for solving theoretical equations. Therefore, it is recommended that these physical models need to take into account the uncertainty they cause. The sensitivity study is performed to investigate the influence of physical models on the calculation results during the reflood phase after the loss of coolant accident. It is allowable to choose the physical models that have the most significant influence on the calculation results. This study conducted a sensitivity analysis of physical models in RELAP5 code based on experimental data measured on the FEBA test facility. Sixteen physical models have been selected for sensitivity analysis to find the most important models that influence the calculation results. Based on two criteria, the maximum cladding temperature and the quench time, the sensitivity analysis results show that four physical models significantly impact the calculation result. Four chosen physical models are considered further in the next step of their uncertainty evaluation. Keywords: physical model, FEBA, sensitivity, uncertainty, quench time, PCT. I. INTRODUCTION and one for vertical stratification) [1] in which heat transfer coefficients are the built-in In the large break of loss of coolant correlations in the code. The flow regimes accident (LBLOCA), the cladding temperature change from one to the others. A film boiling change could be divided into four main phases: heat transfer is established when the cladding blowdown, refill, reflood, and long-term temperature is higher than the surface cooling shown in Figure 1a. Reflood phase of rewetting temperature. A two-phase flow LBLOCA occurred after the initiation of the regime, either a dispersed flow regime or an accident when the lower plenum of the reactor inverted-annular, may occur depending upon vessel has filled, and the core begins to refill. the liquid and vapor flow rate. The cladding The quenching of fuel rods follows the refilling temperature is then reduced by film boiling. of the lower plenum. Steam is formed in the The flow regime then becomes a transition core because of the entering of water, and it boiling, and finally, a nucleate boiling in carries with many drops. The vertical flow single-phase liquid. Fuel rods rapidly cooled to regime map is used in thermal-hydraulic codes saturated temperature, and their cladding for simulating the reflood phase. This map is surface becomes wetted from bottom to the top modeled as nine regimes (four for pre-CHF thank to the injection of the emergency core heat transfer, four for post-CHF heat transfer, cooling system (ECCS). Because of the change â2020 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute
2. TRAN THANH TRAM et al. in flow regimes, heat transfer correlations alter phenomena occurring during the reflood phase correspondingly based on built-in heat transfer to evaluate further and improve the code correlations such as Chen, Dittus-Boelter, prediction capability. Full-Length Emergency Bromley, Zuber CHF, or CHF Look-up table Cooling Heat Transfer (FLECHT [7]) [1], [2]. Typical physical phenomena during Separate Effects and Systems-Effects Test the reflood phase are the exiting of parameters (FLECHT-SEASET) programs was conducted such as droplets and quenching front. Although focusing on the heat transfer mechanism at these parameters have a strong influence on high flooding flow rate with variating of the heat transfer coefficients [3], knowledge of power [8]. However, these tests were their effects is insufficient. insufficient to quantify the phenomena The reflood phase is an important period relevant to a detailed reflood mechanism due in which the fuel rod could be ballooned, be to some uncertainties generated in the bust, be oxidized, or even be melt if the fuel experiment [9]. RBHT (The Rod Bundle Heat rods could not be cooled adequately, as shown Transfer) program [10] was proposed to in Figure 1b. This reflood phase is a complex improve previous experimental limitations. transient in both the heat transfer and flow This test was conducted to investigate the regimes due to a two-phase mixture [4], [5]. bottom heat transfer at changing the flooding flow rate with the upper plenum pressure Thermal hydraulic (T/H) codes, variant. Like the RBHT test, FEBA (Flooding RELAP5, MARS, TRACE, or CATHARE, Experiments with Blocked Arrays) [11] was have been widely used in the reactor safety carried out to study the heat transfer analysis. Among them, RELAP5 code is the mechanism. More effects of grid spacers and preferable tool for use in rulemaking, ballooning during the reflood phase were licensing audit calculations, evaluation of considered for FEBA tests to develop and operator guidelines, and as a basis for a assess improved T/H models [10]. nuclear plant analyzer [1], [5]. In this software, together with initial and boundary The simulation results based on conditions, PMs are often used in simulations. RELAP5 code are influenced by many input These PMs were generally built theoretically parameters, such as the initial and boundary or experimentally. The theoretical ones use conditions, initial conditions, boundary assumptions, simplifications, and ideal conditions, material properties, power, and the processes to solve, while the experimental PMs [12]. PMs are suggested as vital influent ones were developed based on specific parameters that need to have further experiments with defined boundary conditions evaluations [12]. and initial conditions. It means that some A sensitivity analysis (SA) shows how limitations existed in T/H codes because of different values of an independent input their built-in PMs. Prediction accuracy in variable affect a particular dependent output simulations is always a challenging problem variable using a set of assumptions. Among that software developers need to deal with and all input parameters for the SA, some find ways to improve. parameters have little effect on the Researchers have carried out calculation result, while others significantly considerable experimental works to impact. Through the SA process, the most understand the T/H mechanism and influential input parameters are selected. 25
3. A SENSITIVITY STUDY OF PHYSICAL MODELS USING IN RELAP5 CODE The SA method could be a useful tool to This paper focuses on the sensitivity reduce the numbers of calculations by reducing the analysis of PMs used in simulating the considered input parameters, while the calculated reflooding phase. Series I of the FEBA test accuracy remains unchanged. As a result of the SA was chosen for our simulation as the process, a significant reduction of input parameters representative reflooding experiment at from twenty to hundreds of original input relatively low inlet flow rate conditions [11]. parameters to less than ten parameters [12], [13], The sensitivity study of PMs is carried out to [14]. Only five influential input parameters related select the most influential parameters on the to PMs were selected through the SA process for output. The obtained results are used for the FEBA test using different codes [12] from further work on the uncertainty evaluation of seventy-two input parameters. chosen PMs. a) Main phases during LBLOCA [[4]]. (b) Typical cladding temperature profile [[6]]. Fig. 1. The main phases and the cladding temperature profile during LBLOCA II. TOOLS AND FEBA MODELING development and assessment of improved IN RELAP5 code accuracy. The FEBA facility description and its model in RELAP5 will be Karlsruhe designed the FEBA given in detail in this part. experiment to investigate the thermal- A. Description of FEBA facility hydraulic behavior, including the grid spacers and blocked ratio effect relating to a The FEBA main test section contains a LOCA in a PWR study, the heat transfer full-length 5x5 rod bundle of pressurized water mechanisms to broaden the database for reactor (PWR) fuel rod dimension (Fig. 2a), 26
4. TRAN THANH TRAM et al. surrounded by a square housing made of noted in Fig. 2a that the chosen origin is on stainless steel. The cosine power of the fuel the top of the heated rod in a downward rods is approximated by seven steps of direction. The test was first heated at low different power density in the axial direction. nominal power (200 kW) to achieve a Seven grid spacers are located in the bundle, required initial cladding temperature before the same as those used in the PWR core. The simulating the transition. According to the heater rod nodalization in RELAP5, its grid 120% American National Standard (ANS) spacer positions, and its power profile are decay heat power curve, the test runs start shown in Figure 2c. The FEBA test section is using the power bundle about the 40s after modeling in three different parts, inlet the reactor shut down. The subcooled liquid volume (150), main test section including was injected from the bottom of the test heater rod (4500, 4501), and outlet volume section to simulate the reflood phase. During (650) are the lower plenum, heater rod, and the test, the cladding and housing the upper plenum in corresponding. The temperatures were measured at different heated rod length is 3900 mm. It should be axial locations along their axial surfaces. Fig. 2. (a) Cross-section of fuel rod simulators used in the FEBA test. (b) Cross-section of FEBA test bundle in a square housing. (c) Nodalized heater rod in RELAP5 and its axial power profile [[11]] B. Model of FEBA in RELAP5 The seven grids spacers are set at corresponding nodes as designed in the experiment. The nodalizated diagram of the FEBA facility in RELAP5 is illustrated in Figure 2c. Test number 216 of the FEBA test was The time-dependent volume (TDV) represents chosen for analysis. Its initial and boundary the inlet volume, and the TDV 650 defines the conditions are shown in Table I. As the outlet plenum. The flow channel was modeled by experimental process, after reaching the pipe 450, divided into 39 equalized lengths of 0.1 required steady-state, the power was changed m. It connects to the heat structure 14500 and to simulate the decay heat power according to 14501, which simulate rod bundle and housing. 120% ANS - Standard about 40 s after reactor 27
5. A SENSITIVITY STUDY OF PHYSICAL MODELS USING IN RELAP5 CODE shutdown. Together with that, the feedwater then performed for selected PMs to find the was injected into the inlet plenum at the bottom most influential parameters on the output of the test. results. Based on this study, the selected parameters could be used for further work on III. RESULTS AND DISCUSSIONS uncertainty evaluation. The reference case needs to be defined A. Reference case to perform a sensitivity analysis for test 216 The reference case is the case that all conducted on the FEBA experiment. The first considered PMs are set in default values of 1.0. part of this section presents the reference case The reference case was prepared using the result in comparing it with FEBA initial and boundary conditions of test 216, as experimental data. The sensitivity study is given in Table I. Table I. Initial and boundary conditions of FEBA test 216 [[11]] Feedwater Inlet Bundle power (kW) Pressure velocity temperature (C) (bar) (cm/s) 0-30 (s) end 0 s end 4.1 3.8 48 37 200 120% ANS Following the FEBA experimental temperature, the initial temperatures of cladding procedure, the calculation is first for a steady-state and housing are compared with corresponding for about 1000s. When reaching the designed experimental data, as shown in Figure 3. Fig. 3. Comparing the initial temperature for the reference case We could conclude that the calculated The next step for sensitivity analysis results are similar to experimental data. It activates all PMs in the input with a default value means that the heating process using of 1.0. The results need to be the same during this prepared input data for test 216 is identical to activation step. Figure 4 shows that the same the testing procedure and gives a good result. cladding temperature at nine different elevations, The input data, therefore, can be used for 02, 07, 12, 18, 20, 23, 26, 29, and 34 nodes further work. correspondingly, has been obtained before (no) 28
6. TRAN THANH TRAM et al. and after (with) the activation. In our reference obtained from the reference case. After reaching case calculated results, the PCT occurred at node the steady-state, the power curve was changed 26 chosen for reference elevation. So the PCT using the decay heat power according to 120% and quenching time at reference elevation (node ANS-Standard. The feed water was then injected 26) are computed for thirty-two calculations for into the test section from the bottom to simulate sensitivity study and compared to their values the reflood phase. Fig. 4. Cladding temperature at various elevations For the transitional period, the compared with experimental data and other cladding temperatures at three different calculations using MARS-3D (KAERI [12]), heights (at the bottom, in the middle, and at RELAP5 (UNIPI [12]) as shown in Figure 5 the top of the test section) are calculated and and Figure 6. Fig. 5. Comparison between calculated cladding temperature and experimental data at three elevations [12] 29
7. A SENSITIVITY STUDY OF PHYSICAL MODELS USING IN RELAP5 CODE Fig. 6. Comparison between cladding temperature and experimental data at three elevations [12] As shown in these figures, the bottom of sensitivity study for PMs was performed to the test was first quenched, then the middle, find the most influential parameters. and finally, the top of the heater parts. The B. Sensitivity Study reference case results give similar PCT at each elevation but underpredict the quenching time. Based on the available physical models The heater rods were quickly quenched for all built-in RELAP5 [2], sixteen PMs were chosen calculated results using codes compared to for SA. Main PMs are related to heat transfer experimental data for low flooding rate coefficients for interfacial and wall heat conditions. This phenomenon has been stated transfers for each flow regime during the by Choi and No [5] as the limitation of the reflood phase. They can be listed as Chen, RELAP5 code simulation. Similar predictions Dittus-Boelter, Bromley, Modified Bromley, are found in [12] calculated by UNIPI using Forslund-Rohsenow, Ishii-Mishima, Modified RELAP5. Our reference case gives better Bestion, Zuber CHF, and CHF Look-up table predictions for PCT and similar quenching correlations. Other PMs are droplets, and times with the results of UNIPI. Our reference quenching parameters, which are typical in case result shows that PCT along the heated reflood physical phenomena. Appendix A rod occurred at 1400 (mm), corresponding to shows those PMs in more detail. node 26 in our FEBA model. The reference Each PM varied in the range from elevation of 1400 mm (node 26) is selected for minimum to maximum values based on its given sensitivity calculations. Other researchers [15], probability distribution function (PDF) selected [16], [17], [18] experienced this early by the expert, as shown in Table II. Two cases of quenching situation. They pointed out that the minimum and maximum values for each reflood model, such as wall to fluid or wall to parameter are considered as two inputs for this vapor heat transfer correlations or the study. It means that thirty-two cases are interfacial friction models, needs improvement. calculated for the sensitivity work, the plot of Based on their researches, together with the cladding temperature at the elevation PCT opinion given in [12] by Kovtonyuk et al., the occurred (node 26), as shown in Figure 7. 30
8. TRAN THANH TRAM et al. Fig. 7. Sensitivity result for 16 physical models Because there is no measured data at the experimental data. However, the quench time point PCT occurred (1400 mm), the available has fluctuated significantly. Two phenomena data (at 1680 mm) closest to this point, PCT usually occur during the quenching process, the occurrence, was selected for comparison. The sudden quench and slow down the quenching obtained results show a reasonably good process. In our results of this sensitivity, temperature distribution compared with the prolonging the quenching process has happened reference case (the dashed line) and the in some calculations, as shown in Figure 7. Table II. Chosen PMs and their PDF for the sensitivity study Index Physical models (PM) PDF Range of Variation Chen correlation of nucleate boiling wall heat 1 L-N [0.4 – 2.8] transfer 2 AECL Look-up table CHF N [0.20 – 1.80] 3 Zuber CHF correlation L-N [0.50 – 2.00] 4 Transition boiling wall heat transfer N [0.50 – 1.50] 5 Film boiling heat transfer N [0.50 – 1.50] 6 Dispersed film boiling heat transfer N [0.50 – 1.50] Wall heat transfer transition criteria of steam flow 7 N [0.50 – 1.50] Reynold number 3000 8 Wall heat droplet enhancement factor of steam flow N [0.50 – 1.50] 9 Interfacial drag for bubbly flow L-N [0.50 – 2.00] 10 Liquid entrainment L-N [0.50 – 2.00] 11 Droplet We number for reflood L-N [0.50 – 2.00] 12 Interfacial heat transfer of IANN/ ISLG L-N [0.50 – 2.00] 13 The surface roughness of IANN/ISLG L-N [0.50 – 2.00] 14 Dry/wet wall criteria 30 deg-C L-N [0.50 – 2.00] 15 Liquid chunk flow regime N [0.50 – 1.50] 16 Droplet interfacial heat transfer N [0.80 – 1.20] 31
9. A SENSITIVITY STUDY OF PHYSICAL MODELS USING IN RELAP5 CODE The chosen criteria for our sensitivity Based on two chosen criteria, the PCT study are based on the given criteria [12]. For and quenching time are calculated for each the T/H evaluation and licensing process, the case at reference elevation and then compared PCT is the main criterion to be selected. With with reference results. this criterion, quenching time is a typical one, Figures 8 and 9 present the computed which is defined as the time required for heater results of the sensitivity study. It can be seen rod temperature to reach a temperature at 30oC that for both the sensitivity criteria, the PMs with corresponding index of 1 to 5 and 11 to 13 higher than the saturation temperature,Tq = do not affect the calculation results of the fuel 30 + Ts, is the reflood dominant characteristics. rod temperature or quenching time. Among 16 Therefore, the two chosen criteria for our study PMs, we could see that PM with its index of 6, are PCT and quenching time: 14, and 15 is selected as the most influential ‐ The criterion for PCT is defined as the PMs using the PCT criterion (Fig. 8). By absolute value of variation in PCT: ∆Tref(= applying the quenching time criterion, two PMs with their index of 6 and 9 are chosen PCTi − PCTref) = 10 (°C) where i is the index of the calculation case. (Fig. 9). Based on the sensitivity study using ‐ The criterion for quenching time is the the PCT and quenching time criteria, four variation in rewet time: ∆t (= t − quench q,i influential PMs have been selected as tq,ref) = 50 (s). summarized in Table III. Fig. 8. Sensitivity study for calculation of rod surface temperature Fig. 9. Sensitivity study for calculation of rewet time 32
10. TRAN THANH TRAM et al. Table III. Four chosen PMs based on the SA IP Index Chosen PMs 6 Dispersed film boiling heat transfer 9 Interfacial drag for bubbly flow 14 Dry/wet wall criteria 30 deg-C 16 Droplet interfacial heat transfer It can be seen that all four chosen IV. CONCLUSIONS physical models influencing the PCT and quenching time results in our sensitivity Among the inlet conditions such as analysis are essential physical phenomena initial, boundary conditions, and PMs, the PMs are suggested to be the most influential during reflood. The film boiling coefficient parameters on the calculation results. (IP6) is a dominant phenomenon in the heat Therefore, PMs which have built-in BE codes transfer process during the reflood phase. are the main focus in uncertainty evaluation. Steam flow in the vapor phase with Sensitivity analysis for PMs is the main focus entrained droplets (IP9) of various sizes, of this study to better understand the T/H and velocities, strongly influences these mechanism during the reflood phase in which droplets to exert many essential flow and the most complex two-phase flow phenomena heat transfer processes [19] during reflood. happens. This analysis has performed for built- Experts recommend judging whether the in PMs in RELAP5 code using FEBA wall is dry or wet at a temperature 30oC experimental data to select the most influential above the saturated temperature (IP14). parameter for further work. However, two associated phenomena in this process, the sudden wetting and the delayed The reference case was selected and wetting process, exit during reflood. The evaluated, which proved the same heating phenomenon of slowing down the wetting process as the experiment has obtained. process appears quite a lot in our sensitivity Comparing the reference results with those calculation, as shown in Figure 7, which calculated by UNIPI (using RELAP5) and indicates that the wetting criterion also KAERI (using MARS-3D), similar quenching needs to be further considered. The last time predictions have been received. chosen physical model, the heat transfer at Sixteen PMs were chosen for the the droplet-steam interface (IP16), sensitivity study. Two criteria of PCT and contributes significantly to the heat transfer, quenching time have been used for finding the especially during the reflood phase. The influential PMs on the output result. The final number of water droplets carried by the results show that among sixteen considered steam and the size of droplets partly inlet parameters, four PMs with the determine the overall heat transfer capacity, corresponding index of 6, 9, 14, and 16 have leading to a decrease in the heater rod been selected, as listed in Table III. For our temperature. These factors cause quick or sensitivity study results, while the most slow rewetting. Therefore IP16 is also a influential parameter is the dispersed film parameter that needs to be considered as boiling heat transfer (IP6) using the PCT uncertainty generated parameter. criterion, the interfacial drag for bubbly flow 33
11. A SENSITIVITY STUDY OF PHYSICAL MODELS USING IN RELAP5 CODE (IP9) is the most significant parameter the such as initial condition, boundary condition, quenching time criterion. They are the most and physical models. Physical models have influential PMs, which will be used for further been recommended in the PREMIUM project work on uncertainty evaluation. as parameters that significantly impact the output calculation results. The considered NOMENCLATURE physical models are listed in Table II. They are often selected based on the conditions ECCS Emergency Core Cooling System related to flow regime, void fraction, or phase LBLOCA Large Break Loss Of Coolant Accident transition. The physical models are described IP(s) Input Parameter(s) in detail in this part. PMs Physical Models IP1: Chen's boiling correlation multiplier coefficient PDF Probabilistic Density Function In 1963, Chen [20] proposed the first CHF Critical Heat Flux flow boiling correlation for evaporation in PCT Peak Cladding Temperature vertical tubes. Chen's correlation included both BE Best Estimate the heat transfer coefficient due to nuclear boiling and the forced convection mechanism. A Area It should be noted that the heat transfer DH Hydraulic diameter coefficient varies significantly with the flow Ddrop Diameter of droplet rate in cases of slightly high vapor fractions. Under these conditions, the flow at the center hl Heat transfer coefficient for liquid of the flow will be very high, resulting in a hFZ Nucleate boiling heat transfer coefficient highly turbulent flow. This heat transfer h Forslund - Rohenow coefficient FR mechanism is called forced convection hFBGR Modified Bromley correlation coefficient evaporation. Chen proposed a correlation hDB Dittus-Boelter heat transfer coefficient where the heat transfer coefficient is the sum of a forced convection component and a nucleate agf Interfacial area per unit volume boiling component. The nucleate pool boiling c Specific heat capacity of liquid l correlation of Forster and Zuber [21] is used to Cl interfacial drag coefficient calculate the nucleate boiling heat transfer kl Thermal conductivity for liquid coefficient, hFZ. and the turbulent flow ρl Liquid density correlation of Dittus-Boelter [2], [22], [23], [24] is used to calculate the liquid-phase α Void fraction convective heat transfer coefficient, hl: Gr Grashof number Re Reynold number htp = hFZS + hlF ( . 1) We Weber number Where: 0.79 0.45 0.49 0.24 0.75 APPENDIX A. THE CONSIDERING kl cl ρl ∆Ts ∆p hFZ = 0.5 0.29 0.24 0.24 (A. 1a) PHYSICAL MODELS ς μl Hfg ρg Many parameters are used in the input kl 0.8 0.4 hl = 0.023 (Rel) (Prl) (A. 1b) to simulate the FEBA experimental facility, DH 34
12. TRAN THANH TRAM et al. Where: - Hfg is the vaporization enthalpy and - S is the nuclear boiling suppression DH is the equivalent diameter, factor, the ratio of the effective superheated to - Rel and Prl are Reynolds and Pranlt the wall superheated. It accounts for reduced numbers for the liquid phase. boiling heat transfer because the effective IP2: AECL CHF Look-up table overheating across the boundary layer is smaller than a superheater based on wall temperature. The CHF look-up table is widely used S=0.00122 for Forster and Zuber correlation, to predict CHF. The CHF look-up table is - F is the two-phase multiplier as a basically a normalized data bank for a function of the Martinelli flow parameter, vertical 8 mm water-cooled tube. The 2006 0.7 6 CHF look-up table is based on a database F = ( tt + 0.213) , containing more than 30,000 data points, in - kl, cl, ρl, μl is the coefficient of thermal the ranges of 0.1–21 Mpa pressure, 0–8000 conductivity, specific heat capacity, density, kg.m–2.s-1 (zero flow refers to pool-boiling and viscosity of the liquid, respectively, conditions) mass flux and –0.5 to 1 vapor - ∆p is the difference in saturation and quality (negative qualities refer to subcooled superheated wall pressures, conditions) [2], [25]. Table A.1. CHF Table Lookup Multipliers [[2]] CHF values are interpolated from pressure p, mass flow, G and quantity, X, for the experimental data based on the matrix of vertical pipe of 8 mm in diameter, then 35
13. A SENSITIVITY STUDY OF PHYSICAL MODELS USING IN RELAP5 CODE corrected for the other pipe diameters to be ∆Twchf = max ,3, min (40, Tw − Tspt)-, calculated through the correction factor [2]: and ∆Tchf = max (0, Tw − Tspt), with Tspt is CHF = CHFtablechfmul (A. 2) the saturated temperature calculated using total Where: pressure, and Tw is the wall temperature. chfmul = k . k2. k . k4. k5. k6. k8 PSI (Paul Scherrer Institute in These coefficients are listed in detail, as Switzerland) model developed to improve the in Table A.1 below. The coefficient k7 applied quench front behavior during the reactor core to low mass flowrate, G = -50 to 10 kg / s.m2 in reflood process concerning shear force to which the critical flux unsteady varies with the replace the Chen transition boiling correlation. change of mass flux [2]. The transition boiling heat transfer coefficient IP3: The CHF boiling pool boiling Zuber multiplier to liquid use of the Weismann correlation depends on the distance from the point in The reflood model in the RELAP5 code question to the quench front position, less than uses the modified Zuber CHF correlation 0.1 m and higher than 0.2 m. Its interpolated instead of using the Groeneveld Lookup Table values are for the other elevations [2]: for low mass flow. RELAP5 calculates the wall heat flux for both liquid and vapor phases and hfTB calculates the heat flux for both film boiling max(hmax, hw) zQF ≤ 0.1 m and transition boiling. The "Look-up table" = { hlow zQF ≥ 0.2 m value is used when the mass flux is over 200 interpolate 0.1m ≤ zQF ≤ 0.2 m kg/ m2s. Under a mass flux of 100 kg / m2s, a modified Zuber correlation was used [2]: Where, zQF is the distance from the considered point to the bottom quench front, 0.25 CHF = Kh [δg(ρ − ρ )] ρ0.5 ( . 3) 2 pb fg f g g hlow = 0.0001W/m K K, δ, and g are the number of IP5: Modified Bromley correlation multiplier hydrodynamic boiling stability, the surface The film boiling heat transfer coefficient tension of the liquid, and the gravitational to liquid, h , uses the maximum of a film constant. In the RELAP5 code, the value of K is: fTB coefficient, hFTB and Forslund - Rohenow K = 0.13 max ,0.04, 1 − α -. g coefficient, hFR , [2]: IP4: Modified Weismann multiplier hfTB This is the correlation used to replace = [1400 Chen's boiling-transition correlation for the fuel − 1800min(0.05, zQF.)] min(0.999 − αg, 0.5) bundle configuration in the reflood [2], [20]: 2 + hFBGR(1 − αg) 0.02∆T hw = hmaxe 0.2 G The first part of hfTB is an empirical +4500 ( ) e 0.0 2∆T ( . 4) GR length-dependent expression. The second 0.5CHF part includes a modified Bromley Where: hmax = for CHF is the ∆T correlation coefficient, hFBGR, which uses critical heat flux, zQF for the length in the denominator instead of the wavelength, as does the 36
14. TRAN THANH TRAM et al. normal RELAP5 Bromley correlation. The 0.8 kv GvDH 0.4 hDBv = 0.023 ( ) (Prv) (A. 7b) modified Bromley correlation coefficient DH μv used here is given by: 0.8 kl GvDH 0.4 hFBGR hDBl = 0.023 ( ) (Prl) (A. 7c) 0.25 DH μl gρgkg (ρf − ρg),hfg+0.5(Tw − Tspt)Cpf- = 0.62 [ ] (A. 5) max(0.05, zQF.) μg(Tw − Tspt) IP8: Wall heat droplet enhancement factor IP6: Forslund-Rohsenow coefficient multiplier A similar correlation is used in code TRACE as improved heat transfer coefficient: The film boiling heat transfer coefficient (1 − α)Gr to liquid, hfTB, uses the maximum of a film 2ɸ Ψ2ɸ = [1 + 25 2 ] ( . 8) coefficient, hFTB and Forslund-Rohenow Reg coefficient, h . Forslund-Rohsenow FR Where: correlation is determined as follows [2]: ρ gβ(T T ) D h Gr2ɸ = , Reg = αgρgvg are FR. μ μ 0.25 the Grashof number and Reynolds Number. gρgρfhfgk Here coefficients were obtained = h1 ( . 6) π experimentally by a factor of 25 for this entire μ d(T − T ) . / { g w spt 6 } correlation coefficient multiplication uncertainties considered. Where: 2 IP9: Modified Bestion drag model π 6(0.999 − αg) h1 = 0.4 . / [ ] multiplication factor 4 π The modified Bestion correlation is σ d = min*0.003, max,0.0004,3 max (0.01, (vf − ρ used for interfacial drag in vertical bubbly- 2 slug flow at pressures below 10 bars in place vg) )-+, of the EPRI correlation. Above 20 bars, the Where vf and vg are the liquid and EPRI correlation is used. Between 10 and 20 vapor velocities. bars, the interfacial drag is interpolated. The IP7: Single phase Vapor flow modified Bestion correlation for the code interfacial drag coefficient, C , is determined The empirical correlation of Dittus- i as [2]: Boelter [22] has gained widespread acceptance for prediction of the Nusselt number with 65αgρg(1 – αg) C = ( . 9) turbulent flow in the smooth surface tubes: i D 4 This correlation coefficient of u = 0.023Re5Prn (A. 7a) n = 0.4 for heating C0 =0.124 for the multiplication factor is Where { n = 0.3 for cooling considered as an uncertainty. The Dittus-Boelter correlation is only IP10: Ishii-Mishima correlation multiplier correct if: In the annular-mist flow regime, the 0.7 ≤ Pr ≤ 160, Re 10,000, ≥ 10 D calculation of wall-to-coolant heat transfer The Dittus-Boelter is used for both liquid requires the proper apportioning of the liquid and vapor phases in RELAP5/MOD3 [2]: 37
15. A SENSITIVITY STUDY OF PHYSICAL MODELS USING IN RELAP5 CODE in the wall region as an annular film and in the (a) the heat transfer between the large vapor region as droplets. The code uses the Taylor bubbles and the liquid surrounding them, Ishii and Mishima correlation for the and (b) the heat transfer between the small entrainment fraction as a basis for calculating bubbles in the liquid slug and their host liquid: the liquid volume fraction in the film region QB = H ∆T + H ∆T and the liquid volume fraction in the vapor ip ip,Tb ip,bub region. The correlation determines the fraction Thus, the coefficient of heat transfer in of liquid flux flowing as droplets by the this slug flow is calculated as the total following expression [2]: component heat transfer coefficient: 7 .25 0.25 H = H + H ( . 12) E = tanh(7.25 x 10 We Ref ) ( . 10) ip ip,Tb ip,bub Where effective Weber number for IP13: Slug flow interfacial heat transfer entrainment: area factor The Taylor bubble frontal area per unit ρ (α v ) D ρ ρ We = ( ) ; the total volume is αb/L, where L is the cell length. α ρ D Consequently, the interfacial area per unit liquid Reynold number: Ref = αfρfvf . μ volume, agf, là [2]: IP11: Weber number multiplier αb 3.6αgs agf = + (1 − αb) ( . 13) Before calculating the diameter of the L do droplets, Wecrit value for droplets, as well as Where αgs, αb be the average void for the biggest bubbles, must be determined. In fraction in the liquid film and slug region and RELAP5/MOD3 [2], the critical droplet value, the void fraction of a single Taylor bubble: Wecrit, at pre CHF, post CHF, and the αg − αgs maximum bubble are 3, 12, and 10, αb = 1 − αgs correspondingly. In the code RELAP5 / MOD3, the PSI reflood model uses numbers To provide a smooth transition into with a value of 12.0. However, the new reflood and out of slug flow, αgs, in the above model in TRACE5.0 uses a Weber value of 4.0. equation is considered as the free Therefore, the Weber number needs to take into parameter which varies from αBS at the account the uncertainty of the multiplier due to bubbly-to-slug flow regime transition to the variation of droplet diameter, d = d . nearly zero at the slug-to-annular-mist flow o 2 max Weber number is defined by: regime transition. The variation is represented by the exponential expression: ρc(vf − vg)dmax Wecrit = (A. 11) αg − αBS. ς αgs = αBS. exp [−8 ( )] αSA. − αBS Where ρc is the density of the continuous phase. IP14: Dry/wet criteria for Liquid chunk IP12: Slug flow interfacial heat transfer flow regime coefficient factor A wall is considered dry when its In slug flow, interfacial heat transfer can temperature is at least above saturation be divided into two distinct parts [2]: temperature 30 oC, Tw > Ts + 30 = Tq [2]. If 38
16. TRAN THANH TRAM et al. its temperature is at or below this temperature, ACKNOWLEDGEMENT Tq, the wall is considered to be wet. The uncertainty of 30°C related to the flow regime The authors would like to thank Vietnam should be considered. While heat transfer on Atomic Energy Institute (VINATOM) under the drywall is dominated by film boiling, it is grant CS/20/10-01 for funding this study. affected by transitional boiling, nuclear boiling, REFERENCES and forced convection on wet walls. This conversion standard is used to help code select [1]. USNRC, RELAP5/Mod3.3 code manual wet wall surface values close to the quench Volume I: Code Structure, System Models, and front. The 30°C reduction value is constructed Solution Methods., vol. 1, 2001. by comparing calculation results with the [2]. ISL, RELAP5/MOD3.3 code manual volume experiment [2]. IV: models and correlations, NUREG/CR- 5535/Rev P3-Vol IV, 2006. IP15: Transition criteria for liquid chunk flow regime [3]. E Elias, Rewetting and liquid entrainment during reflooding - state of the art, EPRI NP- The transition from bubbly flow to slug 435, (Research Project 248-1), Topical Report, flow is based on Taitel, Bornea, and Dukler May 1977. (TBD) [2]. The bubbly-to-slug transition void [4]. NEA, Nuclear fuel behaviour in loss-of-coolant fraction used in the code varies from 0.25 to accident (LOCA) conditions: State-of-the-art 0.5, depending on the mass flux. The lower Report, Nuclear Energy Agency, 2009. limit of 0.25 is based on a postulate of TBD [5]. Choi T. S., No H. C., Improvement of the that coalescence increases sharply when bubble reflood model of RELAP5/MOD3.3 based on the assessments against FLECHT-SEASET spacing decreases to about half the bubble tests, Nuclear Engineering and Design, Vol. radius, corresponding to about 25% void. TBD 240, pp.832–841, 2010. then cites three references as supporting this [6]. approximate level. However, the indication of college/research-centres-and-groups/nuclear- this limit is uncertain because TBD quotes are engineering/12-The-reflood-process.pdf. based on some other authors whose lower and [7]. Cadek F.F., Dominics D. P., Layse R. H., PWR upper bound values are not the same. FLECHT Final Report, WCAP-7665, 1971. Therefore, it is necessary to evaluate the [8]. Lee N. et al., PWR FLECHT-SEASET uncertainty of this coefficient. unblocked bundle, forced and gravity relood task data evaluation and analysis report, IP16: Droplet Interfacial Heat Transfer Coefficient NUREG/CR-2256, 1982. The heat transfer coefficient for interface [9]. G.H. Seo et al. Numerical analysis of RBHT to droplets based on the works of Andersen [2], reflood experiments using MARS 1D and 3D [27] in the form: Hid = hidAi6 modules, Journal of Nuclear Science and Technology, Vol. 52, pp.70-84, 2015. α 2 k Where, Ai6 = 6 ; hid = 1.8π D D [10]. Hochreiter L.E et al., RBHT relood heat transfer experiments data and analysis, 2.7σ Where, Ddrop = , NUREG/CR-6980, 2012. ρ max.v j / 0.25 [11]. P. Ihle, K. Rust, FEBA Flooding gσ∆ρ vdrop = 1.14 [ ] , jmt is the total mass flux. Experiments with Blocked Arrays ρ Evaluation Report, Mọrz 1984. 39
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