### 7.15.4. Cavitation Model

Cavitation refers to the process by which vapor forms in a low pressure regions of a liquid flow. It occurs in a variety of applications such as throttles, pumps and injectors. In ANSYS CFX, cavitation is implemented as a multiphase model. Most simulations can use the homogeneous multiphase model because the vapor velocity field is often assumed to be the same as that of the liquid. However, the inhomogeneous model can be used if desired.

When solving a cavitating flow problem, you should first obtain a converged solution with the cavitation model turned off at the conditions where you would expect to see cavitation. The cavitation model can be turned on and off by selecting Cavitation or None in the Mass Transfer section of the Fluid Pairs tab, found on the Domains tab. The initial guess should use a liquid volume fraction of 1 and a gas vapor volume fraction of 0.

It should be emphasized that if a poor initial guess is supplied with the cavitation model active (that is, a non-zero initial vapor volume fraction), then it is possible to arrive at a physically impossible situation where most of the flow domain is cavitating.

For cavitation problems, the pressure level should be set at one of the boundaries, or by setting pressure level information on the Advanced tab of the Solver Control settings in CFX-Pre. For details, see Pressure Level Information. This is because the cavitation rate is driven by the difference between the local pressure and vapor pressure, so the pressure level is important. Inflow boundaries would normally use a vapor volume fraction of 0 because the vapor is generated within the domain.

When solving cavitation problems, several variables in the results file are new or are modified from their standard behavior:

- Interphase Mass Transfer Rate: The cavitation rate is calculated by the solver.

- Pressure: The cavitation model is a model for the interphase mass transfer rate, and does not guarantee that all absolute pressures calculated by the solver will be positive. They will, however, be less negative than if cavitation is not modeled.

  In order to make postprocessing more convenient, the variable called `Pressure` that is written to the results file is clipped in such a way that negative values for absolute pressure are clipped to zero. For example, if the reference pressure is 1e5 Pa, the `Pressure` variable is clipped to be not smaller than -1e5 Pa. The actual (non-clipped) pressure field computed by the solver can be visualized using the variable called `Solver Pressure`.

  Note, however, that the solver will output `Pressure` with non-clipped values (as for `Solver Pressure`) if you refer to `Pressure`:

  - in an expression

  - for output to a selected variables transient file

  - in the definition of a monitor point

  the solver will interpret this as `Solver Pressure` (non-clipped values). To use the clipped pressure in these contexts, use the variable name `Clipped Pressure` instead.

- Absolute Pressure: To avoid robustness issues associated with negative absolute pressure (for example if the simulation includes an ideal gas equation state), the variable called `Absolute Pressure` is clipped to be no smaller than the saturation pressure. However, the true absolute pressure must be used to calculate the cavitation rate. This variable is not available in the results file, but may be accessed in CEL (for example, for user defined cavitation models) with the name `Nonclipped Absolute Pressure`.

- Density: To enhance numerical stability, the vapor density field is clipped in a user-controlled fashion through the `Maximum Density Ratio` parameter, described below. The vapor density field in the results file shows the clipped values. The unclipped density (which is used to calculate the cavitation rate itself) is available in the variable field called `Nonclipped Density`.

The cavitation model appears as an interphase mass transfer option. If you choose cavitation as a mass transfer model, you have the choice between the Rayleigh Plesset model and a user-defined model:

#### 7.15.4.1. Rayleigh Plesset Model

The Rayleigh Plesset cavitation model requires the following parameters:

- Saturation Pressure: The saturation pressure must be specified as a value or expression. Note that this is an absolute, not relative, pressure. In ANSYS CFX, saturation data is not read from material property files (such as .rgp files used for defining real fluids). There are two possible ways of defining the saturation pressure:

  - Using the optional parameter Saturation Pressure under Rayleigh Plesset Model on the Fluid Pairs tab. It may be set as a constant, or an expression. If the latter, it should be defined as a function of temperature.

  - Alternatively, you may define a Homogeneous Binary Material (HBM) under the Material details view. The HBM should consist of the two materials undergoing phase change, and the saturation conditions should be defined as material properties of the HBM.

    You must use one of these methods to define the Saturation Pressure; otherwise, an error will be generated. If you use both methods, then the Saturation Pressure parameter of the Rayleigh Plesset Model takes precedence.

- Mean Diameter: The mean nucleation site diameter must be specified. The default value of 2e-06 m is a reasonable value.

The following optional parameters can also be set. If not specified, the default values shown are used. These defaults are appropriate for most cavitation simulations.

- Cavitation Condensation Coefficient: This is an empirical factor to account for the fact that condensation usually occurs slowly. The default value is 0.01.

- Cavitation Vaporization Coefficient: This is an empirical factor to account for the fact that vaporization usually occurs quickly. The default value is 50.

- Maximum Density Ratio: This is used to clip the vapor density for all terms except the cavitation source term itself, which must use the true density specified as the material property. The default value is 1000.

- Nuclei Volume Fraction: This is the volume fraction of the nucleation sites. The default value is 5e-4.

- Cavitation Rate Under-Relaxation Factor: The default value is 0.25.

Additional theoretical information on this model is available. For details, see The Rayleigh Plesset Model in the CFX-Solver Theory Guide.

#### 7.15.4.2. User Defined Cavitation Models

A user-defined cavitation model can be implemented for advanced users. It requires the following parameters:

- Cavitation Rate: This should be set through CEL or User Fortran. The cavitation rate is simply , the interphase mass transfer rate per unit volume from the liquid to the vapor phase, assuming the first fluid in the fluid pair is the liquid and the second is the vapor. If the order in the pair is reversed, the sign must be reversed. As an example, the interphase mass transfer rate for the Rayleigh Plesset model in ANSYS CFX is given by The Rayleigh Plesset Model in the CFX-Solver Theory Guide.

- Saturation Pressure: The saturation pressure must be specified as a value or expression. This may be set in the same way as explained above for the Rayleigh-Plesset Model.

The following optional parameters can also be set. If not specified, the default values shown are used. These defaults are appropriate for most cavitation simulations.

- Maximum Density Ratio: This is used to clip the vapor density for all terms except the cavitation source term itself, which must use the true density specified as the material property. The default value is 1000.

- Cavitation Rate Under-Relaxation Factor: The default value is 0.25.

When developing an expression for a user-defined cavitation rate:

- It was noted above that the cavitation model does not guarantee that all absolute pressures will be positive. If you calculate the vapor density as a CEL function of pressure, make sure you use the variable `pabs` in your expression. This variable is clipped to the saturation pressure, which is numerically well-behaved even when the absolute pressure becomes negative.

- The cavitation rate is driven by . The pressure used in this expression should be the nonclipped absolute pressure (variable name is `pabsnc`).

- The cavitation rate is typically proportional to the vapor density. The vapor density, however, may have been clipped by the Maximum Density Ratio parameter, which is inappropriate in this context. Instead, the true vapor density should be used, which is available as the variable `densitync`.

Solver information about user-defined models is available. For details, see User Defined Cavitation Models in the CFX-Solver Theory Guide.

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