Additional Variables are variables that are added to a case to provide utility not offered by solution variables.
There are three basic types of Additional Variable:
A non-reacting scalar component that can be transported through the flow
Such an Additional Variable can be solved either on a per-unit-mass basis or on a per-unit-volume basis.
A scalar or vector variable with its value (or each component) defined by an algebraic expression
A Dynamic Variable that serves as a dimensionless CEL parameter that changes value several times during solution convergence, used in steady-state cases and harmonic balance cases
Dynamic Variables are used to change expression-based settings gradually, so as to maintain solution stability during convergence.
The following topics are discussed:
Additional Variables can be 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.
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.
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).
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.
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].
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, using an expression based on the following equation:
 | (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.In order to restart a simulation involving a recursive algebraic Additional Variable, expert parameter
algebraic variable restart optionmust be set appropriately. For details, see the description for expert parameteralgebraic variable restart optionin I/O Control Parameters.
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
A Dynamic Additional Variable, or simply Dynamic Variable, serves as a dimensionless CEL parameter that changes value several times during solution convergence, and applies to steady-state cases and harmonic balance cases.
A Dynamic Variable is used to stabilize the solution process without changing the final converged solution. Dynamic Variables are used as scaling factors in the expressions of expression-based settings. During a simulation, a Dynamic Variable's value automatically changes in separate steps, called control steps, and finally reaches unity. At each control step, specified convergence conditions are met before proceeding to the next control step, lending stability to the solution process. Once the Dynamic Variable reaches a value of unity, it no longer affects any expressions (assuming it is used only as a scaling factor) so does not affect the final converged solution.
Each Dynamic Variable has its own planned sequence of values and control step convergence conditions, which are specified in the Solver Control details view. Several scaling options are available to conveniently form a sequence of values that lead from an initial value to unity. Manual specification of the sequence of values is also an option.
To define a Dynamic Variable:
Create an Additional Variable with Variable Type set to
Dynamic Variable. For details, see Additional Variables in the CFX-Pre User's Guide.Set the Dynamic Variable properties in the Dynamic Model Control tab of the Solver Control details view. For details, see Dynamic Model Control Tab in the CFX-Pre User's Guide.
You can define multiple Dynamic Variables for the same simulation. Keep in mind that each variable follows its own set of control steps, leading to the possibility of different physical specifications being changed at different points in the convergence process. When all Dynamic Variables have completed their control steps, they are all set to unity and will not, in principle, affect the final converged solution.
Note: If any Dynamic Variable has not yet reached unity, the solution can be considered to be unconverged and should not be relied upon for accurate analysis.
To use a Dynamic Variable:
Use the Dynamic Variable in one or more expression-based physical specifications, for example to help define a boundary condition or source.
Note:
The Edit Run in Progress command (see Edit Run In Progress Command in the CFX-Solver Manager User's Guide) is not available for simulations involving Dynamic Variables.
The CFX-Solver Output (.out) file includes banners that mention which control step is being calculated.