### 5.10.1. Phase-Dependent Turbulence Models

Phase dependent turbulence models can be used in conjunction with the inhomogeneous model (particle and mixture models) only.

#### 5.10.1.1. The Eddy Viscosity Hypothesis

The eddy viscosity hypothesis is assumed to hold for each turbulent phase. Diffusion of momentum in phase is governed by an effective viscosity:

| (5–194)

#### 5.10.1.2. Algebraic Models

##### 5.10.1.2.1. Zero Equation Model

The default zero-equation model uses a formula based on geometric length scale and the mean solution velocity. It is correlated for single-phase turbulent pipe flow. The turbulence viscosity is modeled as the product of a turbulent velocity scale, , and a turbulence length scale, , as proposed by Prandtl and Kolmogorov:

| (5–195)

where is a proportionality constant. The velocity scale is calculated to be the maximum velocity in phase . If you specify a value for the velocity scale, it will be used for all phases. The length scale is derived using the formula:

| (5–196)

where is the fluid domain volume.

##### 5.10.1.2.2. Dispersed Phase Zero Equation Model

| (5–197)

The parameter is a turbulent Prandtl number relating the dispersed phase kinematic eddy viscosity to the continuous phase kinematic eddy viscosity .

In situations where the particle relaxation time is short compared to turbulence dissipation time scales, you may safely use the default value . If the particle relaxation time is long compared to turbulence dissipation time scales, it may be better to use a value of . This is highly model dependent. Several models are available in the literature.

#### 5.10.1.3. Two-Equation Models

For the - model, the turbulent viscosity is modeled as:

| (5–198)

The transport equations for and in a turbulent phase are assumed to take a similar form to the single-phase transport equations:

| (5–199)

| (5–200)

Definitions of the terms are available. For details, see The k-epsilon Model in ANSYS CFX.

The additional terms and represent interphase transfer for and respectively. These are omitted in CFX, though they may be added as user sources.

Other two equation turbulence models are treated in a similar way.

#### 5.10.1.4. Reynolds Stress Models

The multiphase versions of Reynolds stress models are equivalent to the single phase version, with all flux and volumetric source terms multiplied by volume fractions. Single phase version information is available. For details, see Reynolds Stress Turbulence Models.

By default, no additional exchange terms are added, though they may be added as user sources.

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