Continuous Phase Turbulence

For the continuous phase, Simcenter STAR-CCM+ solves two modified transport equations for the turbulence quantities. The modifications include the volume fractions of each phase and additional source terms that account for the effect of the dispersed phase on the continuous phase turbulence field.

Multiphase turbulence transport is presented in terms of a generic turbulence scalar equation for multiphase flows:

Figure 1. EQUATION_DISPLAY

\frac{\partial}{\partial t} \int_{V} α_{i} ρ_{i} ϕ_{i} d V + \oint_{A} α_{i} ρ_{i} ϕ_{i} {\bar{v}}_{i} \cdot d a = \oint_{A} α_{i} (μ_{i} + \frac{μ_{t, i}}{σ_{ϕ}}) \nabla ϕ_{i} \cdot d a + \int_{V} α_{i} P_{ϕ, i} d V - \int_{V} α_{i} D_{ϕ, i} d V + \int_{V} α_{i} S_{ϕ, i, u} d V + \int_{V} S_{ϕ, c, PIT} d V + \sum_{i \neq j} \int_{V} α_{i} S_{ϕ, ij} d V + \int_{V} \sum_{i \neq j} (m_{ij} ϕ_{j} - m_{ji} ϕ_{i}) d V

(2458)

where:

the subscript $i$ denotes the different phases.
$ϕ$ represents the transported scalar variable. Depending on the turbulence model, $ϕ$ is replaced by the turbulent kinetic energy $k$ , dissipation rate $ϵ$ , specific dissipation rate $ω$ , or the components of the specific Reynolds stress tensor $R$ .
$α_{i}$ is the volume fraction of phase $i$ .
${\bar{v}}_{i}$ is the mean velocity of phase $i$ .
$μ_{i}$ is the dynamic viscosity.
$μ_{t, i}$ is the turbulent viscosity.
$σ_{ϕ}$ is the turbulent Prandtl number.
$P_{ϕ, i}$ is the production term.
$D_{ϕ, i}$ is the dissipation term.
$S_{ϕ, i, u}$ is the user-defined source term.
$S_{ϕ, c, PIT}$ is the source term that is due to particle induced turbulence. This source term enters only the continuous phase transport equation.
$S_{ϕ, ij}$ is the source term due turbulence transfer between phases. This source term enters the transport equation only if the interphase turbulence model is enabled and only for the pair of phases for which the model is enabled.
$m_{ij}$ is the mass transfer rate from phase $j$ to phase $i$ .
$m_{ji}$ is the mass transfer rate from phase $i$ to phase $j$ .

The production and dissipation terms vary according to the selected turbulence model. For more information on RANS turbulence modeling, see also Reynolds-Averaged Navier-Stokes (RANS) Turbulence Models.

These transport equations are always solved for the continuous phase. They are also solved for the dispersed phase when you do not use a turbulent response model.