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.