### 1.2.12. Additional Variables

Additional Variables are non-reacting, scalar components that are transported through the flow, or through a solid (including the solid portion of a porous domain). They can be used to model, for example, the distribution of dye through a liquid, or smoke from a fire. ANSYS CFX typically interprets Additional Variables as concentrations within the fluid domain.

Additional Variables can be set up as either algebraic equations, Poisson equations, or transport equations. For algebraic Additional Variables, you must provide an expression for its value throughout the domain.

Mathematical information on the Additional Variable transport equation is available in Transport Equations for Additional Variables in the CFX-Solver Theory Guide and Additional Variable Transfer Through the Fluid and Solid in the CFX-Solver Theory Guide.

#### 1.2.12.1. Kinematic Diffusivity

For most applications, the transport of Additional Variables is both a convective and diffusive process (including both laminar and turbulent diffusion), and you will therefore need to specify the molecular kinematic diffusivity for each Additional Variable you use. This describes how rapidly the scalar quantity would move through the fluid in the absence of convection. It is generally a function of the properties of the fluid and the medium that the Additional Variable represents, and consequently has no default value. It is usually small (of the order 10-5 m2/s for smoke in air).

For convection-dominated flows, the kinematic diffusivity can have little effect because convection processes dominate over diffusion processes. You may want to specify an Additional Variable whose transport through the fluid is a purely convective process. You can neglect diffusion effects by not setting a kinematic diffusivity for an Additional Variable when you include it in your domain. For turbulent flows, the turbulent diffusion (which is a consequence of averaging the advection term) is still included even when you do not set the kinematic diffusivity.

Poisson equations are diffusive and therefore the kinematic diffusivity must be specified for a successful run.

Note: Diffusivity of an Additional Variable can depend on what fluid it is diffusing through. It is not possible to have density or specific heat dependent on Additional Variables. A more logical approach is to use a multicomponent fluid. For details, see Multicomponent Flow.

#### 1.2.12.2. Turbulent Flux Closure

The Turbulent Flux Closure may be optionally enabled for specification for Additional Variables that are set up as a transport equation. The default when not enabled for specification is the Eddy Diffusivity model with the turbulent Schmidt number set to a value of 0.9. The turbulent Schmidt number may be non-constant using expressions (CEL).

#### 1.2.12.3. Volumetric and Specific Additional Variable

Volumetric and specific Additional Variables are distinguished only by a factor of material density in that the volumetric form of an Additional Variable can be obtained from the specific form by multiplying the specific Additional Variable value by density. The CFX-Solver always directly solves for the variable using the specific form, and then calculates the volumetric values at the end of the run for postprocessing.

A volumetric Additional Variable is specified in terms of the amount of the Additional Variable per unit volume of fluid.

| (1–12)

The conserved quantity often has units of mass, in which case is called mass concentration and you should set units that have dimensions of Mass / Length3 (for example, kg quantity / m3 fluid).

A specific Additional Variable is specified in terms of the amount of the Additional Variable per unit mass of fluid.

| (1–13)

Like the volumetric form, in most cases the conserved quantity will have units of mass, in which case is called mass fraction and you should set units that have dimensions of Mass / Mass (for example, kg quantity / kg fluid).

In addition, the units for boundary condition and source specifications must be consistent with the Additional Variable units:

- Additional Variable value: Units of .

- Flux boundary condition: Units of conserved quantity per unit area per unit time.

- Source value: Units of conserved quantity per unit volume per unit time.

- Source coefficient: Units of Source value per unit .

CFX-Pre will automatically make the appropriate units available when you set one of these quantities. If you use an expression and provide incorrect units, CFX-Pre will not enable you to set the quantity.

At the end of the solver run, the Additional Variable will be made available in the results file in both volumetric and specific form for postprocessing purposes.

#### 1.2.12.4. Additional Variables In Units Other Than Mass

The units of Additional Variables are more flexible than the two examples given in the previous section. In general, any units are acceptable for an Additional Variable. In this case, you just enter whatever units you like for the variable, and, if desired, also enter the appropriate diffusivity with dimensions of Length2 / Time.

For example, to solve an Additional Variable equation for temperature (), with units of Kelvin [K], you could create a specific Additional Variable with units of [K], and the CFX-Solver will solve the following transport equation:

| (1–14)

where is the thermal diffusivity (that is, ), is the fluid density, is the turbulent eddy viscosity and is the turbulent Schmidt number. In this case, the solver writes two fields that can be viewed in CFD-Post: the specific form of the variable (temperature) with units of [K], and the volumetric form (which is simply the specific form multiplied by fluid density) with units of [K kg m-3].

#### 1.2.12.5. Unspecified Additional Variables

Unspecified Additional Variables can be used when you want to calculate the value of a quantity using an algebraic expression. This type of variable can have any units you like and, if an expression is assigned to this variable, then the expression result must have the same units as the variable.

For example, you could create an Additional Variable for a pressure coefficient by creating an unspecified Additional Variable with dimensionless units and assigning it to an expression:

| (1–15)

where is absolute pressure is the domain reference pressure or some other reference pressure state, is the fluid density and is the fluid velocity.

Note: For cases involving multicomponent fluids, if any component-specific variables are involved in the algebraic expression for an Additional Variable, be sure to qualify those variables with their respective component names (write "`<Component_Name>.<Variable_Name>`", replacing "`<Component_Name>`" and "`<Variable_Name>`" as appropriate). Any unqualified variables are assumed to be in the context of the mixture rather than any particular mixture component.

#### 1.2.12.6. Tensor Type

The Additional Variable's Tensor Type can be set to `Scalar` or `Vector`. If an Additional Variable is defined as type `Vector`, the components of a vector algebraic equation can be defined at the domain level.

Vector Additional Variables cannot be directly referenced in CEL expressions. The syntax for referencing a component of a vector Additional Variable is as follows:

    <Component Name>.<Additional Variable Name>_x

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