Table 2: External functions used in §3.0i and §4.0ii,iii.
Function Type Description
adj_vofandv Adjust Updates velocity profile for the gas-liquid flow with Reynolds stresses turbulence model
velo_calc1 On Demand Updates velocity profile for the thermal convection problem after each time-step
velo_calc2 On Demand Updates velocity and temperatures profiles for thermal convection problem after each time-step velo_calc3 Adjust Updates velocity profile for the thermal convection
problem before each iteration
velo_calc4 Adjust Updates velocity and temperatures profiles for the thermal convection problem before each iteration velo_calc5 Init Initialises velocity profile for the thermal convection
problem
velo_calc6 Init Initialises velocity and temperatures profiles for thermal convection problem
gl2d_mu1 Property Gas-liquid mixture viscosity gl2d_rho Property Gas-liquid mixture density
gl2d_xmom Source Gas-liquid x-momentum source gl2d_ymom Source Gas-liquid y-momentum source
gl2d_vof Source Source term for the volume fraction of gas phase with two-phase flow
gl2da_calc On Demand Updates velocity profile for the scalar mixture model for gas-liquid flow
gl2db_calc Init Initialises the domain for the scalar gas-liquid flow gl2dc_calc Init Initialises velocity profile and the domain for the gas-
liquid flow model
gl2dd_calc Adjust Calculates drift, mixture, phase and slip velocity for the gas-liquid scalar mixture model before each iteration with velocity updating for gl2db_calc gl2de_calc Adjust Calculates drift, mixture, phase and slip velocity for
the gas-liquid scalar mixture model before each iteration
gl2df_calc On Demand Updates velocity profile for the standard mixture model9 for gas-liquid flow
i See §3.0 for discussion of the velocity updating, for the standard mixture model9
ii See §4.0, §10.5 and §11.1 for equations and examples of the lateral convection subroutines, velo_calc1 to velo_calc6
iii See §4.0 for discussion of the gas-liquid flow mixture model equations and coding in §10.1, §10.4 and §10.7 where the discrete phase is a bubbly gas phase
Table 3: External functions used in §5.0 for solid-liquid flowi and gas-liquid-solid flowii.
Function Type Description
sl2d_mu Property Solid-liquid mixture viscosity sl2d_rho Property Solid-liquid mixture density sl2d_xmom Source Solid -liquid x-momentum source sl2d_ymom Source Solid -liquid y-momentum source
sl2d_vof Source Solid-liquid volume fraction equation source
sl2da_calc Adjust Calculates drift, slip velocities for the discrete phase, each phase velocity plus the mixture velocity
sl2db_calc Init Initialises the domain for the solid-liquid flow model gls2d_mu Property Gas-liquid-solid mixture viscosity
gls2d_rho Property Gas-liquid-solid mixture density gls2d_xmom Source Gas-liquid-solid x-momentum source gls2d_ymom Source Gas-liquid-solid y-momentum source
gls2d_vof Source Source term for the volume fraction of gas phase with three-phase flow models
slg2d_vof Source Source term for the volume fraction of solid phase with three-phase flow models
gls2da_calc Adjust Calculates drift, slip velocities for each discrete phase, each phase velocity plus the mixture velocity gls2db_calc Init Initialises the domain
i See §5.0 for discussion of the solid-liquid flow mixture model equations and coding in §10.1, §10.4 and §10.7 where the discrete phase is a bubbly gas phase.
ii See §5.0 for a description of the gas-liquid-solid flow models, also find for an example of the coding for three- phase flow in §11.3.
Table 4: External functions used in §6.0 for three-phase flow and reactioni.
Function Type Description
gls_s1_mu Property Gas-liquid-solid mixture viscosity gls_s1_rho Property Gas-liquid-solid mixture density gls_s1_xmom Source Gas-liquid-solid x-momentum source gls_s1_ymom Source Gas-liquid-solid y-momentum source
gas_s1_vof Source Source term for the volume fraction of gas phase with three-phase flow models
sol_s1_vof Source Source term for the volume fraction of solid phase with three-phase flow models, modelling the
transport of the cell culture where the specific growth rate is 6.500*10-5 s-1
sub_s1_conc Source Source term for the concentration of the substrate, where the yield coefficients are 0.118 and 0.442 kg kg-1 s-1
prod_s1_conc Source Source term for the concentration of the product, where the yield coefficient is 3.752 kg kg-1 s-1 a_gls_s1_calc Adjust Calculates drift, slip velocities for each discrete
phase, each phase velocity plus the mixture velocity b_gls_s1_calc Init Initialises the domain and the volume fraction of the
solid phase
gls_s2_mu Property Gas-liquid-solid mixture viscosity gls_s2_rho Property Gas-liquid-solid mixture density gls_s2_xmom Source Gas-liquid-solid x-momentum source gls_s2_ymom Source Gas-liquid-solid y-momentum source
gas_s2_vof Source Source term for the volume fraction of gas phase with three-phase flow models
sol_s2_vof Source Source term for the volume fraction of solid phase with three-phase flow models, modelling the
transport of the cell culture where the specific growth rate is1.522*10-4 s-1
sub_s2_conc Source Source term for the concentration of the substrate, where the yield coefficients are 0.148 and 1.087 kg kg-1 s-1
prod_s2_conc Source Source term for the concentration of the product, where the yield coefficient is 7.360 kg kg-1 s-1 a_gls_s2_calc Adjust Calculates drift, slip velocities for each discrete
phase, each phase velocity plus the mixture velocity b_gls_s2_calc Init Initialises the domain and the volume fraction of the
solid phase
i See §6.0 for discussion of the solid-liquid flow mixture model equations §10.1 and §10.4, also see §10.7 for the species transport and reaction models. The coding in for the implementation of these models is found in §11.3.