Several extensions of the KE-EP model for carrier-phase turbulence modulation have been proposed in the literature, with notable contributions from Pourahmadi and Humphrey [1983], Elghobashi et al [1984], Chen et al [1985, 1986, 1990] and Mostafa and Mongia [1988]. None of these models can truly be recommended as a standard model; so PHOENICS provides two representative extensions which allow for these effects.
These are the models of Chen & Wood [1985,1986] and Mostafa & Mongia [1988], which introduce additional source terms into the turbulence transport equations. These source terms, which are coded in subroutine GXDISP, are always negative and hence act to reduce KE and EP. However, depending on the relative extent of the reductions KE and EP, the turbulent viscosity may be either reduced or increased by the presence of particles.
The modifications proposed by Chen and Wood involve the introduction the following additional volumetric source terms in the KE and EP equations:
SKE,p = - (2*RHOd*Rc*Rd*KE/TP)*(1.-EXP(-BK*TP/TE)) .... (7.6.1)
SEP,p = - 2.*RHOd*Rc*Rd*EP/TP .... (7.6.2)
where: RHOd is the density of the dispersed phase; Rc and Rd are the volume fractions of the carrier and dispersed phases; and BK is empirical constant (=0.0825).
TP and TE are, respectively, timescales characterising the particle response and large-scale turbulent motion:
TP = RHOd * Vslip * Rd / F" .... (7.6.3)
TE = CT*KE/EP .... (7.6.4)
where CT is an empirical constant (=0.165) and F"' is the absolute magnitude of the interphase drag force per unit volume.
The foregoing source terms are activated by the following PIL command: PATCH(KEDISP,CELL,1,NX,1,NY,1,NZ,1,LSTEP) COVAL(KEDISP,KE,GRND2,0.0); COVAL(KEDISP,EP,GRND2,0.0)
In addition, when STORE(TE,TP) appears in the Q1 file, the timescales TE and TP may be printed in the RESULT file or viewed via PHOTON or AUTOPLOT.
For the Mostafa-Mongia model, the additional volumetric source terms in the KE and EP equations are:
SKE,p = - 2*RHOd*Rc*Rd*KE/(TE+TP) .... (7.6.5)
SEP,p = - 2*CPE*RHOd*Rc*Rd*EP/(TE+TP) .... (7.6.6)
where CPE is an empirical constant (=1.0), and TP and TE are given by equations (6.3) and (6.4) above with CT=0.35.
The foregoing source terms are activated by the following PIL command: PATCH(KEDISP,CELL,1,NX,1,NY,1,NZ,1,LSTEP) COVAL(KEDISP,KE,GRND1,0.0); COVAL(KEDISP,EP,GRND1,0.0)
As with the Chen-Wood model, TE and TP may be STOREd for printing in the RESULT file and viewing via PHOTON and AUTOPLOT.
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