Volume of Fluid (Multiphase Flow)#

In this subsection, the parameters for multiphase flow simulation using the volume of fluid method (VOF) are specified.

In this method, the two fluids considered are given index of \(0\) and \(1\) respectively. The amount of fluid at any given quadrature point is represented by a phase fraction between \(0\) and \(1\). The interface is therefore considered located where the phase fraction \(= 0.5\). The interface between the two fluids is moved by a transport equation on the phase fraction.

Note

At the moment, a maximum of two fluids is supported. By convention, air is usually the fluid 0 and the other fluid of interest is the fluid 1. See Initial Conditions for the definition of the VOF initial conditions and Physical properties - Two Phase Simulations for the definition of the physical properties of both fluids. Do not forget to set VOF = true in the Multiphysics subsection of the .prm.

The default values of the VOF parameters are given in the text box below.

subsection VOF

  set viscous dissipative fluid = fluid 1
  set diffusivity               = 0
  set compressible              = false

  subsection interface sharpening
    set enable                  = false
    set verbosity               = quiet
    set frequency               = 10
    set interface sharpness     = 2
    set type                    = constant

    # parameter for constant sharpening
    set threshold               = 0.5

    # parameters for adaptive sharpening
    set threshold max deviation = 0.20
    set max iterations          = 20
    set tolerance               = 1e-6
    set monitored fluid         = fluid 1
  end

  subsection algebraic interface reinitialization
    set enable                        = false
    set output reinitialization steps = false
    set frequency                     = 1
    set steady-state criterion        = 1e-2
    set max steps number              = 5
    set diffusivity multiplier        = 1.0
    set diffusivity power             = 1.0
    set reinitialization CFL          = 1.0
    set verbosity                     = quiet
  end

  subsection phase filtration
    set type      = none
    set verbosity = quiet

    # parameter for the tanh filter
    set beta      = 20
  end

  subsection surface tension force
    set enable                                = false
    set verbosity                             = quiet
    set output auxiliary fields               = false
    set phase fraction gradient filter factor = 4
    set curvature filter factor               = 1
    set enable marangoni effect               = false
  end

end

  • viscous dissipative fluid: defines fluid(s) to which viscous dissipation is applied.

    Choices are: fluid 0, fluid 1 (default) or both, with the fluid IDs defined in Physical properties - Two Phase Simulations.

    Tip

    Applying viscous dissipation in one of the fluids instead of both is particularly useful when one of the fluids is air. For numerical stability, the kinematic viscosity of the air is usually increased. However, we do not want to have viscous dissipation in the air, because it would result in an unrealistic increase in its temperature. This parameter is used only if set heat transfer = true and set viscous dissipation = true in Multiphysics.

  • diffusivity: value of the diffusivity (diffusion coefficient) in the transport equation of the phase fraction. Default value is 0 to have pure advection.

  • compressible: enables interface compression (\(\phi \nabla \cdot \mathbf{u}\)) in the VOF equation. This term should be kept to its default value of false except when compressible equations of state are used.

Interface Sharpening#

  • subsection interface sharpening: defines parameters to counter numerical diffusion of the VOF method and to avoid the interface between the two fluids becoming more and more blurry after each time step. The reader is referred to the Interface sharpening section of The Volume of Fluid (VOF) Method theory guide for additional details on this sharpening method.

    • enable: controls if interface sharpening is enabled.

    • verbosity: enables the display of the residual at each non-linear iteration, to monitor the progress of the linear iterations, similarly to the verbosity option in Linear Solver. Choices are: quiet (default, no output), verbose (indicates sharpening steps) and extra verbose (details of the linear iterations).

    • frequency: sets the frequency (in number of iterations) for the interface sharpening computation.

    • interface sharpness: sharpness of the moving interface (parameter \(a\) in the interface sharpening model). This parameter must be larger than 1 for interface sharpening. Choosing values less than 1 leads to interface smoothing instead of sharpening. A good value would be around 1.5.

    • type: defines the interface sharpening type, either constant or adaptive

      • set type = constant: the sharpening threshold is the same throughout the simulation. This threshold, between 0 and 1 (0.5 by default), corresponds to the phase fraction at which the interface is located.

      • set type = adaptive: the sharpening threshold is searched in the range \(\left[0.5-c_\text{dev} \; ; 0.5+c_\text{dev}\right]\), with \(c_\text{dev}\) the threshold max deviation (0.2 by default), to ensure mass conservation. The search algorithm will stop either if the mass conservation tolerance is reached, or if the number of search steps reaches the number of max iterations. If the tolerance is not reached, a warning message will be printed.

      Example of a warning message if sharpening is adaptive but the mass conservation tolerance is not reached:

      WARNING: Maximum number of iterations (5) reached in the
adaptive sharpening threshold algorithm, remaining error
on mass conservation is: 0.02
Consider increasing the sharpening threshold range or the
number of iterations to reach the mass conservation tolerance.

      Tip

      Usually the first iterations with sharpening are the most at risk to reach the max iterations without the tolerance being met, particularly if the mesh is quite coarse.

      As most of the other iterations converge in only one step (corresponding to a final threshold of \(0.5\)), increasing the sharpening search range through a higher threshold max deviation will relax the condition on the first iterations with a limited impact on the computational cost.

    • monitored fluid: Fluid in which the mass conservation is monitored to find the adaptive sharpening threshold. The choices are fluid 1 (default) or fluid 0.

    • tolerance: Value of the tolerance on the mass conservation of the monitored fluid.

      For instance, with set tolerance = 0.02 the sharpening threshold will be adapted so that the mass of the monitored fluid varies less than \(\pm 2\%\) from the initial mass (at \(t = 0.0\) sec).

    See also

    The Dam-Break example discussed the interface sharperning mechanism.

Algebraic Interface Reinitialization#

  • subsection algebraic interface reinitialization: defines parameters used to reinitialize the interface in VOF simulations. Alike the interface sharpening, this aims to reduce numerical diffusion of the phase fraction and redefine the interface sharply.

    Note

    A subsection on algebraic interface reinitialization will be added shortly to the Volume of Fluid (VOF) Method theory guide for additional details on this method.

    • enable: enable the algebraic interface reinitialization.

    • output reinitialization steps: when set to true, it enables outputs in parallel vtu format of the algebraic reinitialization steps. The files are stored in a folder named algebraic-reinitialization-steps-output located inside the output path directory specified in the simulation control subsection.

      Outputted quantities of interest are:

      • Reinitialized phase fraction scalar-field (reinit_phase_fraction);

      • VOF phase fraction scalar-field (vof_phase_fraction);

      • VOF projected phase gradient vector-field (vof_phase_gradient) and;

      • VOF projected curvature scalar-field (vof_curvature).

      Tip

      This feature can be used for debugging purposes by observing how the reinitialization steps affect the phase fraction field.

    • frequency: indicates the frequency at which the algebraic interface reinitialization process is applied to the VOF phase fraction field. For instance, if the user specifies frequency = 2, the interface will be reinitialization once every \(2\) time-steps.

    The interface reinitialization process ends either when steady-state (steady-state criterion) is reached or when an imposed maximum number of steps (max steps number) is reached.

    • steady-state criterion: one of the two stop criteria of the interface reinitialization process. This parameter \((\alpha_\text{ss})\) acts as a tolerance to the reaching of steady-state when solving the algebraic interface reinitialization partial differential equation (PDE).

      \[\alpha_\text{ss} \geq \frac{ \lVert \phi_\text{reinit}^{\tau + 1} - \phi_\text{reinit}^{\tau} \rVert_2}{\Delta \tau}\]

      where \(\tau\) is the pseudo-time used to solve the reinitialization PDE and \(\Delta \tau\) is the associated pseudo-time-step.

    • max steps number: indicates the maximum number of interface reinitialization steps that can be applied before the process ends.

    The algebraic interface reinitialization PDE contains a diffusion term. This term contains a diffusion coefficient \((\varepsilon)\) given by:

    \[\varepsilon = C h_\text{min}^d\]

    • diffusivity multiplier: factor \((C)\) multiplying the smallest cell-size value \((h_\text{min})\) in the evaluation of the diffusion coefficient of the PDE.

    • diffusivity power: power \((d)\) to which the smallest cell-size value \((h_\text{min})\) is elevated in the evaluation of the diffusion coefficient of the PDE.

    • reinitialization CFL: CFL condition of the interface reinitialization process. This is used to evaluate the pseudo-time-step \((\Delta\tau)\).

      \[\Delta \tau = C_\text{CFL} \, h_\text{min}\]

      where \(C_\text{CFL}\) is the imposed CFL condition and \(h_\text{min}\) is the size of the smallest cell.

    • verbosity: displays the solution process of the algebraic interface reinitialization. The different level of verbosity are:

      • quiet: default verbosity level; no information on the algebraic interface reinitialization process is displayed.

        Warning

        As the verbosity of the algebraic interface reinitialization depends on the verbosity of the non-linear and linear solvers, some console outputs may remain if they are set to verbose.

      • verbose: displays reinitialization steps progression. Only indicates the details of the non-linear and linear iterations if the corresponding solvers are also set to verbose.

      • extra verbose: in addition to what is displayed at the verbose level, it displays the steady-state criterion progression through reinitialization steps. This may be used for debugging purposes.

Phase Filtration#

  • subsection phase filtration: defines the filter applied to the phase fraction. This affects the definition of the interface.

  • type: defines the filter type, either none or tanh

    • set type = none: the phase fraction is not filtered

    • set type = tanh: the filter function described in the Interface filtration section of The Volume of Fluid (VOF) Method theory guide is applied.

  • beta: value of the \(\beta\) parameter of the tanh filter

  • verbosity: enables the display of filtered phase fraction values. Choices are quiet (no output) and verbose (displays values)

Surface Tension Force#

  • subsection surface tension force: Surface tension is the tendency of a liquid to maintain the minimum possible surface area. This subsection defines parameters to ensure an accurate interface between the two phases, used when at least one phase is liquid.

    • enable: controls if surface tension force is considered.

      Attention

      When the surface tension force is enabled, a fluid-fluid material interaction and a surface tension model with its parameters must be specified in the Physical Properties subsection.

    • verbosity: enables the display of the output from the surface tension force calculations. Choices are: quiet (default, no output) and verbose.

    • output auxiliary fields: enables the display of the filtered phase fraction gradient and filtered curvature. Used for debugging purposes.

    • phase fraction gradient filter factor: value of the factor \(\alpha\) applied in the filter \(\eta_n = \alpha h^2\), where \(h\) is the cell size. This filter is used to apply a projection step to damp high frequency errors, that are magnified by differentiation, in the phase fraction gradient (\(\bf{\psi}\)), following the equation:

      \[\int_\Omega \left( {\bf{v}} \cdot {\bf{\psi}} + \eta_n \nabla {\bf{v}} \cdot \nabla {\bf{\psi}} \right) d\Omega = \int_\Omega \left( {\bf{v}} \cdot \nabla {\phi} \right) d\Omega\]

      where \(\bf{v}\) is a piecewise continuous vector-valued test function, \(\bf{\psi}\) is the filtered phase fraction gradient, and \(\phi\) is the phase fraction.

    • curvature filter factor: value of the factor \(\beta\) applied in the filter \(\eta_\kappa = \beta h^2\), where \(h\) is the cell size. This filter is used to apply a projection step to damp high frequency errors, that are magnified by differentiation, in the curvature \(\kappa\), following the equation:

      \[\int_\Omega \left( v \kappa + \eta_\kappa \nabla v \cdot \nabla \kappa \right) d\Omega = \int_\Omega \left( \nabla v \cdot \frac{\bf{\psi}}{|\bf{\psi}|} \right) d\Omega\]

      where \(v\) is a test function, \(\kappa\) is the filtered curvature, and \(\bf{\psi}\) is the filtered phase fraction gradient.

    Tip

    Use the procedure suggested in: Choosing Values for the Surface Tension Force Filters.

    • enable marangoni effect: Marangoni effect is a thermocapillary effect. It is considered in simulations if this parameter is set to true. Additionally, the heat transfer auxiliary physics must be enabled (see: Multiphysics) and a non constant surface tension model with its parameters must be specified in the physical properties subsection (see: Physical Properties).

See also

The surface tension force is used in the Rising Bubble example.

Choosing Values for the Surface Tension Force Filters#

The following procedure is recommended to choose proper values for the phase fraction gradient filter factor and curvature filter factor:

  1. Use set output auxiliary fields = true to write filtered phase fraction gradient and filtered curvature fields.

  2. Choose a value close to 1, for example, \(\alpha = 4\) and \(\beta = 1\).

  3. Run the simulation and check whether the filtered phase fraction gradient field is smooth and without oscillation.

  4. If the filtered phase fraction gradient and filtered curvature fields show oscillations, increase the value \(\alpha\) and \(\beta\) to larger values, and repeat this process until reaching smooth filtered phase fraction gradient and filtered curvature fields without oscillations.