Turbulence modelling of a thermal stratification CFD model

In . J. Complex Sys ems in Science ol. 2(1) (2012), pp. 43–48 Tu bulence modelling o a he mal s a i ica ion CFD model M´onica Ma ´ınez1,†, Ra ael Mi ´o1, Te esa Ba achina1, Se gio Chi a2and Gume sindo Ve d´u1 1Ins i u e o Indus ial, Radiophysical and En i onmen al Sa e y (Isi ym), Uni e si a Poli `ecnica de Val`encia 2Mechanical Enginee ing and Cons uc ion Depa men , Uni e si a Jaume I Abs ac . The OECD/NEA ROSA p ojec es 1-1 was conduc ed in 2006 wi h he objec i e o ob ain he mul idimensional empe a u e dis ibu ions in cold legs and downcome du ing he Eme gency Co e Cooling Sys em (ECCS) wa e injec- ion in a P essu ized Wa e Reac o (PWR) o e ifica ion o compu e codes and models. In his pape , 3D Compu a ional Fluid Dynamics (CFD) s udy o OECD ROSA (Rig-o - Sa e y Assessmen ) p ojec es 1-1, using he comme cial CFD code Ansys-CFX 13 is p esen ed. The analysis was ocused on he u bulence models which a e he mos ele an physical models esponsible o models e - o s. S eady-s a e calcula ions we e pe o med wi h diffe en u bulence models: S anda d k−ε, RNG k−ε, Shea S ess T anspo and Reynolds S ess Model. Nume ical esul s o all he u bulence models selec ed could be conside ed sa - is ac o y o he p edic ion o he mal s a ified flow. Howe e , i is necessa y o es ablish a p ocedu e o e alua e he e o and unce ain y due o aspec s as mesh efinemen , ime s ep and u bulence models. Keywo ds: u bulence modelling, CFD codes, he malhyd aulics, nuclea enginee - ing MSC 2000: 76TXX, 76FXX, 65KXX, 76RXX, 80A20 †Co esponding au ho : moma[email p o ec ed] Recei ed: No embe 26 h, 2012 Published: Decembe 17 h, 2012 44 Tu bulence modelling o a he mal s a i ica ion CFD model 1. In oduc ion Comme cial CFD codes a e employed in enginee ing and scien ific applica- ions as ae ospace, au omo i e, chemical and nuclea indus ies o esea ch, simula e and op imize hei p ocesses. The ocus is on he fluid a iables (den- si y, p essu e, eloci y, empe a u e o ene gy) bu g id gene a ion, u bulence modelling and sol e pa ame e s play an impo an ole on he accu acy and s abili y o he solu ion. One o he CFD applica ion a eas o nuclea enginee ing pu poses is he s udy o he P essu ized The mal Shock (PTS) in a P essu ized Wa e Reac o (PWR). A PTS can occu du ing Loss o Coolan Acciden (LOCA), when cold wa e injec ion om he Eme gency Co e Cooling Sys em (ECCS) is needed. The he mal s a ifica ion o he cold leg flow could p o oke he g ow h o a cold plume in he PWR downcome . The p essu e essel in con ac wi h he cold plume suffe s a as cooling a high p essu e, affec ing he s uc u al in eg i y o he PWR essel. OECD ROSA (Rig-o Sa e y Assesmen ) p ojec was ca ied ou in he Japanese ROSA/LSTF (La ge-Scale Tes Facili y) o ob ain an expe imen al da abase o alida e code p edic i e capabili y and accu acy o he simula ion o empe a u e s a ifica ion du ing ECCS wa e injec ion [1]. In his pape , he influence o u bulence models on he esul s o he OECD ROSA es 1-1 p ojec using he comme cial CFD code Ansys-CFX 13 a e p esen ed. The s udy p oposes he e alua ion o se e al Reynolds A e age Na ie S okes (RANS) u bulence models: S anda d k−ε, RNG k−ε, Shea S ess T anspo Model (SST) and wo Reynolds S ess Models (RSM). 2. Tu bulence modelling An impo an aspec o sol e CFD equa ions is he phenomenon o he u bu- lence in a fluid flow. Tu bulence appea s in mos o he na u al fluid flows and consis s o andom fluc ua ions o he flow p ope ies. Also, i is inhe en ly h ee dimensional and ime dependen . The e a e se e al app oaches o he u bulence based on he de ail o cap u e he phenomenon [2]; howe e he compu a ional esou ces inc ease wi h he complexi y o he me hod. Com- me cial CFD codes use RANS simula ions based on he solu ion o he a e age Na ie -S okes equa ions in a easonable compu a ional ime. The momen um flow configu a ion can be ep esen ed by he Reynolds a e age Na ie S okes equa ions o u bulen flow, in Ca esian coo dina es as ollow: ρ∂Ui ∂ +ρUj ∂Ui ∂xj =−∂P ∂xi +∂ ∂xj(2µSji −ρu′ ju′ i)(1) M. Ma ´ınez e al 45 whe e ρis he densi y, Uis he a e age pa o he eloci y, iand ja e he indexes o he Ca esian di ec ions, Pis he a e age pa o he p essu e, he 2µSji ep esen s he iscosi y e m and he las e m is known as he Reynolds- S ess enso . In o de o sol e all mean-flow p ope ies o he u bulen flow unde con- side a ion, i is equi ed a p esc ip ion o compu ing he Reynolds-S ess en- so . The e a e diffe en models o compu e i . RANS Eddy- iscosi y models and RANS Reynolds-S ess models (RSM) a e he mos commonly used. The RANS Eddy- iscosi y models (S anda d k−ε, RNG k−εand SST) a e wo-equa ion models based on he Boussinesq eddy- iscosi y app oxima ion whils RANS Reynods-S ess Models a e based on he anspo equa ions o he indi idual componen s o he Reynolds s ess enso . These models a e he s anda d models o p ac ically all CFD codes. Howe e , a comple e s udy o he influence o hese models is equi ed in fluid p oblems wi h s ong buoyancy effec s, whe e he densi y o he fluid diffe s om he main s eam densi y [3]. 3. CFD model The analysis was pe o med by he comme cial CFD code Ansys CFX 13 [4]. The Bes P ac ice Guidelines [5] o he use o CFD in Nuclea Reac o Sa e y applica ions we e ollowed du ing he de elopmen o he CFD model. The CFD simula ion analyzed was he cold leg A wi h coolan mixing con- side ing single-phase condi ions. Mass flow a es we e gi en as inle bounda y condi ions, while he alue o p essu e was imposed as an ou le bounda y condi ion a he lowe pa o he downcome . Fluid eci cula ion was in- cluded as inle bounda y condi ion on he op o he downcome . Adiaba ic wall bounda y condi ions we e selec ed o he walls while symme y condi- ions we e imposed in he igh and le sides o he downcome model. Figu e 1 shows he ANSYS-CFX model de ails. An uns uc u ed e ahed al mesh wi h p isma ic nea wall elemen s was gene a ed au oma ically. The mesh is composed o 1108933 elemen s. Wa e p ope ies we e ex ac ed om he ables o Ansys lib a y IAPWS- IF97 in he ange o 273 K and 823 K a a p essu e o 15.5 MPa. The buoyancy o ces we e conside ed and he buoyancy e e ence densi y was aken as 763.32 kg/m3, which is an app oxima e a e age alue o he expec ed domain densi y. The ini ial condi ions o he flow in he main pipe assigned we e a empe a u e o 553.5 K and a ela i e p essu e o 15.5 MPa, whils 296.5 K was assigned in he ECCS line. Tes condi ions and expe imen al da a we e ex ac ed om he Final Da a Repo o OECD/NEA ROSA Tes 1-1 (ECCS Wa e injec ion unde na u al ci cula ion condi ion). 46 Tu bulence modelling o a he mal s a i ica ion CFD model Figu e 1: Ansys-CFX model de ails 4. Discussion and Resul s A la ge numbe o s eady-s a e calcula ions we e execu ed. The simula ions we e pe o med using pa allel local p ocessing HP-MPICH. CFX Sol e was un on a PC wi h wo p ocesso s In el Co e i-5 2.3 GHz and a RAM memo y o 4Gb, unde Windows 7 Home P emium. Simula ions we e pe o med using he upwind nume ical scheme (fi s o de ). A oo mean squa e (RMS) esidual a ge alue o 10−6was defined as he con e gence c i e ia o he simula ion in double p ecision. Au oma ic ime s ep was selec ed. Typical compu a ion ime o de aul g id case was abou 3 hou s. Th ee wo-equa ion models (S anda d k−εmodel, RNG k−εand SST) and wo Reynolds S ess Model (SSG and BSL) we e selec ed o s udy i s influence on he empe a u e s a - ifica ion ange. Scalable wall unc ions we e selec ed o u bulence models. Mo eo e he ull buoyancy model and he o al ene gy hea ans e model we e sol ed. The mal s a ifica ion can be obse ed in all nume ical esul s. The cold wa e s ays a he bo om while he ho wa e occupies he uppe pa o he pipe. The cold bo om laye does no mix wi h he wa me uppe wa e laye . Mo eo e , compa ison be ween measu ed and calcula ed esul s along a line nea he ECCS injec ion pipe (middle TE-2 plane) indica es ha all u bulence models gi e a he simila esul s. Those eul s a e shown in figu es 2 and 3. M. Ma ´ınez e al 47 Figu e 2: Tempe a u e dis ibu ions. RANS Eddy- iscosi y models Figu e 3: Compa ison be ween diffe en u bulence models. Expe imen al da a and nume ical esul s 48 Tu bulence modelling o a he mal s a i ica ion CFD model 5. Conclusions This pape cons i u es a fi s app oach o he assesmen o he ANSYS-CFX code o simula e he mal s a ifica ion phenomena. The calcula ions pe - o med wi h upwind scheme, ull buoyancy model and o al ene gy wi h he fi e u bulence models cap u e he s a ifica ion p ocess in he cold leg. All he nume ical simula ions p oduced simila esul s and we e in good ag ee- men wi h he expe imen al da a compa ed. Howe e , i is necessa y o define a p ocedu e o e alua e e o and unce ain y due o aspec s such as mesh efinemen , ime s ep and u bulence models. Re e ences [1] JAEA,Final da a epo o OECD/NEA ROSA p ojec es 1-1 (2008). [2] D. Wilcox,Tu bulence Modeling o CFD, Ed. DCW Indus ies (1998). [3] T. Fa kas and I. To h,Fluen analysis o a ROSA cold leg s a i ica- ion es , Nuclea Enginee ign and Design 240, 2169-2175 (2010). [4] Ansys CFX Re e ence Guide. Release 13. ANSYS, Inc. (2010). [5] J. Maha y e al.,Bes P ac ice Guidelines o he Use o CFD in Nuclea Reac o Sa e y Applica ions. NEA Repo NEA/CSNI/R(2007)5.