IMPROVEMENT OF RELAP5 MODELS FOR CONDENSATION OF STEAM AND STEAM-GAS MIXTURE IN HORIZONTAL AND INCLINED TUBES

Transcription

1 IMPROVEMENT OF RELAP5 MODELS FOR CONDENSATION OF STEAM AND STEAM-GAS MIXTURE IN HORIZONTAL AND INCLINED TUBES P. Kral UJV Rez, a. s. / Division o Nuclear Saety and Reliability Hlavni 130, Husinec-Rez, Czech Republic pavel.kral@ujv.cz ABSTRACT The presented work is ocused on condensation o steam and steam-gas mixture in horizontal and sloped tubes. Presence o noncondensable gas (NCG) in coolant system o pressurized water reactor (PWR and VVER) has number o potential eects on thermal hydraulics (TH) o the system. One o the major eects is deterioration o heat transer at steam generator, mainly in the condensation regime. Ater deep analysis o condensation models in RELAP5 computer code, a set o improvements is proposed. Major modiications are usage o Jaster-Kosky correlation or horizontal condensation and extension o application o horizontal condensation to wider range o tube slopes. Both the original and modiied versions o code are assessed against data rom separate and integral test acilities. Results show improved capability to predict condensation heat transer and removal o some unphysical behavior in condensation in volumes with small non-zero slope. KEYWORDS Non-condensable gas, thermal hydraulics, condensation, heat transer, computer code, RELAP5, VVER 1. INTRODUCTION Condensation on primary side o steam generators (SG) o pressurized water reactors both PWR and VVER - is a very important heat transer mode in transient and accident conditions. So ar, most eort in this ield has been ocused on condensation in vertical tubes. Condensation in horizontal and sloped tubes is however also important. The horizontal or slightly sloped tubes are used in horizontal steam generators, some passive saety systems, number o heat exchangers etc. Further important issue is deterioration o steam condensation in presence o noncondensable gas. The initially homogeneous mixture o steam and gas changes due to condensation o steam to nonhomogeneous mixture with substantially higher concentration o noncondensable gas by the condensatevapor interace creating an insulation layer. Prediction o condensation o steam-gas mixture is thereore a challenging task or all TH computer codes. The presented work is ocused on condensation o steam and steam-gas mixture in horizontal and sloped tubes, improvements and extended validation o condensation models o RELAP5 computer codes [1], and on improved computational capability or saety analyses o VVER with horizontal steam generators. However, substantial part o indings and results are general and applicable also to other systems

2 2. CONDENSATION OF STEAM AND STEAM-GAS MIXTURE IN VERTICAL AND HORIZONTAL TUBES AS MODELED IN RELAP5 The system TH computer code RELAP5 is a world-wide used computational tool or saety analyses o transients and accidents in light water reactors (LWR) developed under US NRC sponsorship. The deault RELAP5 [1] condensation model or vertical and inclined suraces uses the maximum o Nusselt laminar model [2] and Shah turbulent model [3]. For strictly horizontal walls, Chato modiication o Nusselt is used [4]. The Colburn-Hougen iterative diusion method [5] is used to solve condensation heat transer in presence o noncondensable gas. See the overall computational algorithm in Figure 1 below. A more detailed description o equations used ollows. The RELAP5 [1] calculates condensation heat transer coeicients (HTC) based on ilmwise condensation model. The method o calculating the heat transer coeicient h c is given below. Once the h c is known, it is used to calculate the total heat lux: q '' t h c T w where q t is total heat lux by condensation, h c is the heat transer coeicient, T w is wall temperature and T sppb is saturation temperature based on partial pressure in the bulk. T sppb (1) Figure 1. Algorithm o condensation calculation in RELAP

3 Because RELAP5 is a two-luid code, the liquid and the gas can both theoretically exchange energy with the wall. Although ilm condensation is the only condensation mode considered, currently RELAP5 allows both heat lux to liquid and to gas. The heat lux to liquid is deined as ollows: q '' h c T w where q t is condensation heat lux to liquid, h c is the condensation heat transer coeicient, T w is wall temperature and T is bulk liquid temperature. T The gas to wall heat lux is the dierence between the total heat lux q t and the liquid to wall heat lux q. The interacial mass transer term used in RELAP5 continuity equation comprises mass transer at the wall and transer in the bulk. The term or mass transer near the wall comprises only o the heat lux rom the gas to the wall. (2) Figure 2. Condensation at vertical wall with laminar and turbulent ilm region The basic approach o RELAP5 to determination o condensation heat transer coeicient is selecting o maximum rom Nusselt laminar model [2] and Shah turbulent model [3]: h max( h, h ) (3) c nusselt shah 2.1. Nusselt Model or Laminar Film Condensation at Vertical Wall The Nusselt expression or laminar ilm condensation [2] at vertical suraces uses the ilm thickness, δ, as the key parameter instead o the temperature dierence: k hc, nusselt (4)

4 where k is liquid conductivity and the ilm thickness δ is deined by this relation: 3 g 1 3 (5) where μ is liquid viscosity, Γ is liquid mass low rate per unit periphery, g is gravitational constant ρ is liquid density and Δρ is dierence between liquid and gas bulk density. Then the resulting Nusselt s expression or condensation heat transer coeicient is the ollowing: h c, nusselt g 3 k (6) 2.2. Shah Model or Turbulent Film Condensation The basic ormula in Shah model or turbulent ilm condensation at both vertical and horizontal suraces: 3,8 h c, shah hs 1 (7) 0, 95 Z where h s is supericial heat transer coeicient and parameter Z relects inluence o static vapor quality and reduced bulk pressure (or more details see [1] or [3]). As the Shah model or turbulent ilm condensation is not modiied, the paper will not describe it in detail Chato Modiication o Laminar Film Condensation Model or Horizontal Tubes Condensation in horizontal or sloped tubes is more complex thermal-hydraulic process than condensation in a vertical tube. Whereas in case o vertical tube, the condensate ilm lows predominantly in axial direction (1D problem), in case o horizontal tube the condensate ilm lows predominantly in circumerential direction (potentially inclined due to axial drag o steam) and the condensate in bottom pool lows in purely axial direction. Chato [4] developed a modiication to the standard Nusselt ormulation [2] which applies to laminar condensation inside horizontal tube. It is assumed that the liquid ilm collects on the upper suraces, drains to the tube bottom, and collects with negligible vapor shear. The condensate drains out one end because o a hydraulic gradient. The Chato ormula or condensation HTC looks as ollows: 3 g, h gbk h c chato F Dh Tsppb Tw 1 4 (8) where F is a correction term relecting liquid level in the tube bottom, g is gravitational constant, ρ is liquid density, Δρ is dierence between liquid and gas bulk density, k is liquid conductivity, D h is hydraulic diameter, μ is liquid viscosity, T sppb is saturation temperature based on steam partial pressure in the bulk, and T w is the wall temperature

5 (a) (b) Figure 3. Laminar ilm condensation in horizontal tube The F term in equation (8) corrects the condensation heat transer or the liquid level in the tube bottom (reducing the eective condensing wall surace) with the orm: F 1 F (9) The angle 2Φ corresponds to the angle subtended rom the tube center to the chord orming the liquid level (see Figure 3 b). The values or F range in magnitude upward rom 0.725, where 2Φ = zero. The angle 2Φ can be determined rom the ollowing expression: 0.5sin 2 (10) The analytical work indicates that the heat transer through the bottom layer was less than 2.5% o the total or angles o 2Φ between 90 and 170 degrees and was thereore neglected in the correlation. Chato suggests a mean value o F = which corresponds to Φ = 120 o. This constant value is used in RELAP5 [1]. The Chato correlation was tested rom horizontal to the inclined angles o about 37 degrees with reasonable results [4]. However, in RELAP5, the Chato model o horizontal condensation is applied only to strictly horizontal volumes (with elevation parameters delgrv < 0.001) Colburn-Hougen Diusion Method or Condensation with Noncondensable Prediction o condensation in presence o noncondensable gas is in RELAP5 done by help o the Colburn-Hougen diusion method [5]. The Colburn-Hougen diusion calculation involves an iterative method to solve or the temperature at the interace between the steam and water ilm. The method is based on the principle that the amount o heat transerred by condensing vapor to the liquid-vapor interace by diusing through the noncondensable gas ilm is equal to the heat transerred through the condensate ilm: Pvi 1 h P c Tvi Tw hmh gb vb ln (11) Pvb 1 P

6 where T vi is vapor temperature at the liquid-gas-vapor interace, T w is the wall temperature, h m is mass transer coeicient, h gb is dierence o steam and liquid enthalpy in the bulk, P vi is partial pressure o steam at liquid-gas-vapor interace, P vb is steam partial pressure in the bulk, ρ vb is saturation vapor density at P vb, and P is the total pressure. From this energy conservation principle, the interace pressure and temperature (see Figure 4) is determined by iterations. The heat transer rate then is then determined. Figure 4. Film condensation in presence o noncondensable gas 3. PROPOSED SET OF MODIFICATIONS IN RELAP5 CONDENSATION MODEL FOR HORIZONTAL AND SLOPED TUBES Based on the deep analysis o RELAP5 condensation model (description in manual plus source code) and results o calculations o separate eect tests the ollowing modiications were proposed: A. Replacement o Chato correlation or horizontal condensation [4] by Jaster and Kosky modiication [6], which instead o constant F (see above) uses a unction o local void raction. B. Extension usage o horizontal condensation model rom strictly horizontal volumes also to inclined volumes. C. Change in parameter or decision between horizontal and vertical condensation models rom elevation parameter delgrv to slope parameters sing. D. Optional relaxation or inlet volume o condensation tube (weighting between condensation models with/without Colburn-Hougen to relect not yet ully developed NCG concentration proile at the tube inlet)

7 The Chato correlation or horizontal condensation [4] as programmed in RELAP5 [1] is using constant parameter F (value used) or degradation o eective condensation wall surace by pool o condensate in bottom part o tube. Jaster and Kosky [6] proposed modiication o this correlation which instead o constant F uses a unction o local void raction. This approach is more lexible and suitable or an advanced 6-equation TH code, which or each control volume evaluates the void raction α as one o the main 6 variables. Jaster and Kosky correlation has the ollowing orm: 3 3 g 4 h gbk h, 0, 725 c jasterkosky (12) Dh Tsppb Tw where α is a void raction, g is gravitational constant, ρ is liquid density, Δρ is dierence between liquid and gas bulk density, k is liquid conductivity, D h is hydraulic diameter, μ is liquid viscosity, T sppb is saturation temperature based on steam partial pressure in the bulk, and T w is the wall temperature. The horizontal condensation model as programmed in RELAP5 is used only in strictly horizontal volumes, or which the elevation parameter delgrv < (corresponds to slope or 1 m long volume). As soon as the slope is higher (e.g ) the vertical condensation model is used which is not the best approach and leads to unphysical results or small slopes as will be demonstrated in chapter 4. Such arguable usage o vertical condensation model or small slope tubes is potentially problematic or any horizontal heat exchangers (including horizontal steam generators o VVER). As nearly all horizontal SG s and heat exchangers use a small drainage slope. As soon as the analyst models the exact slope o the horizontal tubes, the code could produce wrong results in condensation mode. Several options are possible when extending the slope range, or which the horizontal condensation model should be applied, rom strictly horizontal volumes (original RELAP5 approach): a) Usage o horizontal condensation model in volumes with slope θ < 5 (the smallest change rom original RELAP5 approach, but covering small drainage slopes o all horizontal heat exchangers, including VVER steam generators); b) Usage o horizontal condensation model in volumes with slope θ < 37 (slope range or which the original horizontal condensation model [4] was validated); c) Usage o horizontal condensation model in volumes with slope θ < 45 (this slope would be most consistent with RELAP5 volume low regime map, as 45 is boundary between vertical and horizontal volume low regime maps; the horizontal volume low regime map contains among others the horizontal stratiied low regime); d) Usage o horizontal condensation model in volumes with slope θ < 30, vertical condensation model in volumes with slope θ > 60, and interpolation or volumes with slope in range In the modiied RELAP5 version used or validation calculation presented here the variant c was chosen (with boundary slope 45 ). However, rom the point o view o application to horizontal SG o VVER (with tubes slope approximately 0.5 ), all our variants are equal. 4. ASSESSMENT OF ORIGINAL AND MODIFIED RELAP5 ON COTINCO DATA Caruso et al perormed series o tests at the COTINCO separate eect test acility in [7][8][9] and then at the ITACSO acility in 2003 [10], both installed in the University o Roma "La Sapienza". The tests were ocused at the steam and air-steam condensation inside horizontal and inclined tubes

8 4.1. Description o COTINCO Separate Eect Test The COTINCO experimental acility [7] has been designed to investigate the heat transer perormance o horizontal and inclined tubes with steam and air-steam mixture lowing inside with condensation. The main components o the experimental acility are the ollowing: Atmospheric steam generator, electrically heated, with a gross power ranging rom 375 W to a maximum o 6 kw; Auxiliary air system eeding the test section with a ixed air low rate, to perorm tests in steady or quasi-steady conditions; Mixing tank, where the air-steam mixture is generated, with a volume o about 1 m 3 ; Condensation test section, manuactured with a 22/25 mm internal/external diameter stainless steel tube, 1.5 m long. The air-steam mixture lows inside the tube. The cooling water lows through an annular zone realized with an external tube o 32 mm internal diameter; Cooling system, with water tank, pumps, heaters and a water sotener; Instrumentation and data acquisition system. Figure 5. COTINCO experimental loop The available power is 6 kw, but the test section has been designed to operate in the range 3 4 kw. This condition allows to have enough power to carry out tests with higher power level. The heat losses in the steam loop are very low (less than 0.2 kw) and they have been characterized through an integral mass measurement o the condensate at the inlet o the instrumented tube beore the assembling. Heat losses in the cooling side o the test section are negligible, due to the low coolant temperatures. The test section (condensation tube) used or measurement o the heat transer coeicients related to steam-air mixture had been designed according to the ollowing speciications: Max available power: 6 kw Operating power: 3-4 kw

9 Design pressure: 1 ate Operating pressure: 0 ate Air concentration: % Steam-air mixture inside tube (0.85 to 5.55 kg/m 2 s) External coolant in the annulus: water (with temperature increase 5-10 C) Average heat lux: rom 7500 to 136,000 W/m 2. Table I. Matrix o COTINCO Condensation Tests In the Table I above, a matrix o COTINCO tests is shown [7]. Figures 6 and 7 below show measured dependence o heat transer coeicient on air concentration and on slope o the tube and typical temperature proiles alongside test section o the condensation tube, respectively. Figure 6. Measured condensation HTC eect o air mass raction

10 Figure 7. Temperature proiles alongside condensation tube 4.2. RELAP5 Model o COTINCO and Results o Calculations During development o COTINCO input model or RELAP5, the nodalization (discretization) shown in Figure 8 below was selected. The condensing tube (test section) was modeled by 15 control volumes, each 0.1m long. The cooling annulus was discretized in the same way. Figure 8. Nodalization o COTINCO input model or RELAP5 The irst set o RELAP5 assessment calculations was ocused on condensation o pure steam and eect o slope o the condensing tube [8]. The velocity o steam at the tube inlet was 4.2 m/s. Measured data are available or slopes 0, -15, -30, and -45. The calculations were done or slopes 1, 0, -1, -5, -15, - 30, and -45 to test more in detail code perormance

11 Condensation heat transer coeicient - eect o tube slope EXP R5-orig R5-modi HTC [W/m2K] Tube slope [ ] Figure 9. Measured and calculated HTC eect o tube slope Results o measurements show increase o average heat transer coeicient with increasing slope (declination angle) o the tube rom 0 to -45 (Figure 9). Calculations with original version o RELAP5 lead to underprediction o the condensation HTC and show unphysical results (drop o HTC) or small nonzero slopes. It is consequence o usage o vertical condensation model or these angles (discussed above in chapters 2 and 3). Calculations with modiied version o RELAP5 gives better results and agreement with measured data, plus no local drop o HTC or small nonzero slopes. For the available data points i.e. without HTC or the small nonzero angles (where the experimental data are not available) - the RELAP5 modiication leads to reduction o standard deviation rom 3533 to 1492 W/m 2 K. The second set o RELAP5 recalculations o COTINCO data [9] was ocused on condensation length in tests with pure steam condensation (various steam low rates rom to kg/s and various tube slopes rom 0 to -45 ). Agreement between experimental and computation results was ater modiication o RELAP5 condensation model improved rom m to m (standard deviation). See the results o calculation with original and modiied RELAP5 shown in Figure 10 and 11, respectively. The given set o experimental data [8] doesn t show any strong eect o tube inclination on condensation length, so just the average values or each inlet steam low were used or comparison in Figure 10 and 11. The last set o RELAP5 assessment calculation used COTINCO measurement [7] o steam-air condensation with various air concentrations. The air mass raction (air quality, X air ) at tube entrance was 2%, 4%, 10%, 20% a 25% and the tube slope was -15. Comparison o experimental data and calculation results with original and modiied RELAP5 are shown in Figure 12. Measured and predicted average HTC are in perect agreement at air quality about 10 %. For lower qualities code underpredicts HTC, or higher qualities code overpredicts HTC. Modiication o RELAP5 condensation model improved agreement in region o lower gas qualities (X air 2 10%) where the standard deviation was reduced rom 550 to 229 W/m 2 K

12 Condensation length - COTINCO and original RELAP Length [m] Exp Calc Calc -1 Calc -5 Calc Calc -30 Calc Steam low rate at tube entrance [kg/s] Figure 10. Condensation length or various steam low test and original RELAP5 1.6 Condensation length - COTINCO and modiied RELAP Length [m] Exp Calc 0 Calc -1 Calc -5 Calc -15 Calc -30 Calc Steam low rate at tube entrance [kg/s] Figure 11. Condensation length or various steam low test and modiied RELAP

13 Heat transer coeicient in condensation o steam-air mixture - eect o air mass raction Exp R5orig R5modi438 HTC [W/m2K] Xn [%] Figure 12. Measured and calculated HTC eect o air mass raction 4.3. Further Assessment o Modiied RELAP5 Limited scope o this paper does not allow presenting o all results rom the assessment and validation o modiied RELAP5 condensation models. Besides the code validation against COTINCO tests (presented above), the ollowing validation exercises were done: a) Validation calculations against condensation tests perormed at ITASCO acility [10][13] Tests ocused on local heat transer coeicient during steam-air condensation. b) Validation calculations against data rom PMK integral test acility [11][12] Recalculation o test T3.1 medium break loss-o-coolant (LOCA) rom shutdown conditions with nitrogen in PRZ, comparison o results o calculation with original and modiied RELAP5. c) Test calculations with model o PMK acility Analysis o artiicial small-break LOCA scenario without HPIS and with secondary steam dump and condensation in SG, with original and modiied RELAP5. d) Comparison calculations with SG model. New test calculations with separate model o horizontal steam generator. Calculations with ixed and with lowing boundary conditions, with original and modiied RELAP5. Assessment against ITASCO tests proved improved capabilities o modiied RELAP5 to predict local heat transer coeicient during steam-air condensation. Validation analyses with model o PMK integral test acility [12] and with separate SG model showed stability o modiied version and improved prediction o condensation in horizontal SG (although the dierences between original and modiied RELAP5 were not so remarkable like in calculations o separate eect tests)

14 5. CONCLUSIONS The paper describes work on assessment and modiication o condensation model o RELAP5 computer code. The eort is ocused on condensation o steam and steam-gas mixture in horizontal and sloped tubes. Introductory deep analysis o RELAP5 condensation model resulted in proposal o set o modiications o this model the main modiications are the usage o Jaster-Kosky correlation or horizontal condensation (instead o Chato correlation) and extension o application o horizontal condensation models to wider range o slopes. Both original and modiied version o the code is assessed against experimental data rom separate eect test acilities COTINCO and ITASCO. The results show improved capability to predict condensation heat transer. Also the unphysical drop in predicted condensation heat transer coeicient or small non-zero slopes detected in original RELAP5 was removed in modiied version. Modiied RELAP5 is also tested in calculations o integral tests medium and small break LOCA tests with model o PMK acility and test calculations with separate SG model. Also the results rom integral tests prove improved perormance in prediction o condensation heat transer and good stability o the modiied RELAP5 code. REFERENCES 1. RELAP5/MOD3.3 Code Manual. Volume IV: Models and Correlations, NUREG/CR-5535/Rev P4- Vol IV, prepared by ISL or US NRC (2010). 2. W. Nusselt, Die Oberlachenkondensation des Wasserdampes, Ver. deutsch. Ing. 60, (1916). 3. M.M. Shah, A General Correlation or Heat Transer during Film Condensation inside Pipes, Int. Journal o Heat and Mass Transer Vol. 22, (1979). 4. J. C. Chato, Laminar Condensation Inside Horizontal and Inclined Tubes, American Society o Heating, Rerigeration, and Air Conditioning Eng. Journal 4, (1962). 5. A.P. Colburn, O.A. Hougen, Design o Cooler Condensers or Mixtures o Vapors with Noncondensing Gases, Industrial and Engineering Chemistry, 26 (1934). 6. H. Jaster, P.G. Kosky, Condensation Heat Transer in a Mixed Flow Regime, Int. Journal o Heat and Mass Transer Vol. 19, (1976). 7. G. Caruso, F. Cumo, A. Iorizzo, A. Naviglio, Experimental Study on In-Tube Steam Condensation in Presence o High Percentage o Non-Condensables, Aimed at the Design o an Inherently Sae Heat Transer Emergency System, 2nd Intn l Symposium on Two-Phase Flow, Pisa, Italy (1999). 8. G. Caruso, A. Naviglio, The Inluence o Noncondensable Gases on Condensation Inside Tubes: An Experimental Analysis, Universita di Roma La Sapienza (1999). 9. G. Caruso, F. Giannetti, A. Naviglio, Experimental Investigation on Pure Steam and Steam Air Mixture Condensation Inside Tubes, Intn l Journal o Heat and Technology 30, pp (2012). 10. G. Caruso, A. Naviglio, P. Spalvieri, Heat Transer Coeicient Evaluation o Condensing Steam-Air Mixtures in Tubes, Proceedings o XXII Congresso Nazionale sulla Trasmissione del Calore, Genova 2004, pp , (2004). 11. P. Král, RELAP5/MOD3.3 Assessment against PMK Test T3.1 - LBLOCA with Nitrogen in PRZ, USNRC NUREG/IA-0246 (2010). 12. L. Szabados, G. Ezsol, L. Perneczky, I. Toth, Results o the Experiments Perormed in the PMK-2 Facility or VVER Saety Studies, Akademiai Kiado, Budapest, Hungary (2007). 13. P. Král, Analysis o Wall Condensation Models - Part 2, US NRC CAMP Meeting Spring 2014, Zagreb (2014)