Regarding the Radiation Model in TFM

MFiX
#1

Hello everyone!

I am currently using the TFM model and I would like to know how it handles radiation?

I noticed that users could only specify the initial conditions of gamma Rg and TRg. So, how is the radiation term γRg (TRg4-Tg4) calculated in the subsequent calculation process?

Thank you very much!

#2

As you indicate, the radiation term is a difference of 4th powers of the radiation temperature and the gas temperature. The calculation can be seen in the file energy_mod.f in the MFiX source at around line 30.

  !vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvC
  !  Source terms for the energy equations.  The source term is linearized as
  !  S = S_c - S_p * T,  where S_c and S_p must be positive.
  !
  !  By default the source terms have been coded for radiation sources.
  !
  !  S_p for gas phase at i, j, k
  DOUBLE PRECISION FUNCTION S_Rpg(IJK)
    USE fldvar, only: t_g
    IMPLICIT NONE
    INTEGER IJK
    S_Rpg = 4.d0 * GAMA_Rg(IJK) *  T_g(IJK)**3
  END FUNCTION S_Rpg
  !  S_c for gas phase at i, j, k
  DOUBLE PRECISION FUNCTION S_Rcg(IJK)
    USE fldvar, only: t_g
    IMPLICIT NONE
    INTEGER IJK
    S_Rcg = GAMA_Rg(IJK) * ( T_Rg(IJK)**4 + 3.d0 * T_g(IJK)**4 )
  END FUNCTION S_Rcg

Because of the way source terms are linearized, we have we have +3T_g^4 in S_Rcg and a -4Tg^4 in S_Rpg. When these are subtracted, we get γRg (TRg4-Tg4) as expected.

#3

Thank you for your answer! So Gama_Rg is always a constant which equals to its initial value ic_gama_rg right?

#4

Yes, that is correct.