How to implement production term due to buoyancy for k-omega equations? Note that this is automatically taken into account for k-epsilon models and RSM.

These terms will be automatically taken into account in the future release.
For versions Fluent12.1 (and previous releases), use the following UDF:
It works for incompressible ideal gas option and can be easily adapted to boussinesq approximation.

/* A source term to the k equation could be invoked through a */
/* DEFINE_SOURCE UDF to include this effect in k-omega model */
#include "udf.h"
#include "sg.h"
#include "models.h"

/* UDF to compute buoyancy production in TKE equation */
DEFINE_ADJUST(store_tg,domain)
{
Alloc_Storage_Vars(domain, SV_T_RG, SV_T_G, SV_NULL);
T_derivatives(domain);
Free_Storage_Vars(domain, SV_T_RG, SV_NULL);
}

DEFINE_SOURCE(tke_gb, c0, t0, dS, eqn)
{
real beta, mu_t, temp;
real prod1=0.,source;
real pr_t = M_keprt;

/* Compute Buoyancy Production */
mu_t = C_MU_T(c0,t0);
temp = C_T(c0,t0);
/* This assumes ideal gas behavior. More general */
/* implementation would query beta from the solver */
beta = 1./temp;
if(NNULLP(T_STORAGE_R_NV(t0, SV_T_G)))
{
prod1 = beta*mu_t/pr_t*NV_DOT(M_gravity,C_T_G(c0,t0));
}
else
if (c0==0) Message0("Error, temperature gradient not storedn");
source = prod1;

return source;
}


/* option full buoyancy directional */
DEFINE_SOURCE(omega_gb_directional, c0, t0, dS, eqn)
{
real beta, mu_t, temp;
real prod1=0.,source;
real pr_t = M_keprt;
real C_epsilon3=1.;

/* Compute Buoyancy Production */
mu_t = C_MU_T(c0,t0);
temp = C_T(c0,t0);
/* This assumes ideal gas behavior. More general */
/* implementation would query beta from the solver */
beta = 1./temp;
if(NNULLP(T_STORAGE_R_NV(t0, SV_T_G)))
{
prod1 = beta*mu_t/pr_t*NV_DOT(M_gravity,C_T_G(c0,t0));
}
else if (c0==0) Message0("Error, temperature gradient not storedn");

C_epsilon3=compute_keC3(C_U(c0,t0),C_V(c0,t0),C_W(c0,t0));

source=C_epsilon3*M_keC1*MAX(0,prod1)*0.09*C_O(c0,t0);

return source;
}





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