Modeling S-Gamma Particle Size Distribution

To correctly simulate the flow behavior in dispersed multiphase flows, you must account for the particle size distribution.

The steps in this procedure are intended to follow on from one of the following:

To use the S-Gamma particle size distribution:

  1. For the dispersed phase (under Multiphase > Eulerian Phases), in the phase model selection dialog, deactivate Auto-select recommended models, then select the following models in addition to the models that you previously selected:
    Group Box Model
    Optional Models Particle Size Distribution
    Particle Size Distribution S-Gamma
    S-Gamma Closure

    Choose one of the following:

    • Discrete Quadrature S-Gamma

      This model evaluates the integrals associated with the breakup and coalescence using an adaptive discrete quadrature method.

    • Pre-Integrated S-Gamma

      This model evaluates the integrals using an analytical method.

    See S-Gamma Models Reference.

  2. Expand the [dispersed phase] node and set the Discrete Quadrature S-Gamma or Pre-Integrated S-Gamma properties.

    If you use the Discrete Quadrature S-Gamma option, you can specify any Number of Quadrature Points. The default value of 5 is suitable for most purposes. However, for a large simulation, you should first converge the simulation with a smaller number of points and then increase the number of quadratures.

    If you perform a series of runs with different parameters (for example, different inlet velocities) and fit the parameters of the model (such as breakup rate) to the experimental data, it is recommended that you perform the entire set with the same number of quadrature points. Keeping the number constant allows you to isolate the effects of the physical parameters of the model (such as the inlet velocity, breakup rate, and wall temperature) from any numerical artifacts.

    See S-Gamma Model Properties.

  3. Select the [dispersed phase] > Initial Conditions > Size Distribution Specification node, set the appropriate Method, and then set the corresponding initial condition nodes: Sauter Mean Diameter and Particle Size Variance.

    See Initial Conditions.

  4. To include the effects of breakup and coalescence on the predicted size distribution:
    1. Right-click the Multiphase Interaction > Phase Interactions > [phase interaction] > Models node.
    2. In the Phase Interaction Model Selection dialog, select one or both of the following models:
      Group Box Model
      Optional Models
      • S-Gamma Breakup
      • S-Gamma Coalescence
      • S-Gamma Entrainment (Available with Multiple Flow Regime Topology only)

      See Discrete Quadrature S-Gamma Phase Interaction Models Reference and Pre-Integrated S-Gamma Phase Interaction Models Reference.

  5. Expand the Multiphase Interaction > Phase Interactions > [phase interaction] > Models node, and set the properties for the selected Breakup, Coalescence and Entrainment models.

    For Pre-Integrated S-Gamma Breakup, see Viscous Breakup Properties and Inertial Breakup Properties.

    For Pre-Integrated S-Gamma Coalescence, see Viscous Coalescence Properties and Inertial Coalescence Properties.

    For Discrete Quadrature S-Gamma Breakup, see S-Gamma Breakup Rate Properties, S-Gamma Number of Fragments Properties, and S-Gamma Variance of Fragments Properties.

    For Discrete Quadrature S-Gamma Coalescence, see S-Gamma Collision Rate Properties and S-Gamma Coalescence Efficiency Properties.

    For Discrete Quadrature S-Gamma Entrainment, see S-Gamma 夹带属性, S-Gamma 相夹带直径属性, and S-Gamma 气体夹带方法参数属性.

Set the particle size distribution boundary condition for the inlets and pressure boundaries. As the S-Gamma model assumes a log-normal particle size distribution, set the mean particle size and its variance to define the size distribution.
  1. Expand the Regions > [region] > Boundaries > [inlet or pressure boundary] > [dispersed phase] > Physics Conditions node, set the Size Distribution Specification method, and then set the relevant Physics Values.

    The process is similar to setting the initial conditions of the dispersed phase.

    Setting the variance to zero results in a mono-dispersed phase (single particle size). If the one-equation option is selected, the variance at flow boundaries is ignored, and the initial value that is set for the continuum is used.

    See Boundary Settings.

  2. If you want to specify source values for the S-Gamma size distribution equations, select the Regions > [region] > Phase Conditions > [dispersed phase] > Physics Conditions > S-Gamma Source Option node and activate S-Gamma Source Term. In the Physics Values, set the appropriate S-Gamma Source values.

    See Region Settings.

  3. If necessary, change the interaction length scale.

    By default, the Interaction Length Scale for the S-Gamma model is Sauter Mean Diameter. If you need to modify this setting for diagnostics purposes, select the Multiphase Interaction > Phase Interactions > [phase interaction] > Models > Interaction Length Scale > Interaction Length Scale node, and change the setting.

Return to Modeling Eulerian Multiphase Flow and continue with Step 5.