Optimizing Time-Step Size for Multiphase Simulations with Phase Change
Summary
Accelerate simulations and improve stability when simulating phase change using the Volumetric Source adaptive time-step provider. Simulations that include phase change mechanisms such as boiling, evaporation/condensation, impingement/stripping, cavitation, or user defined sources can be highly non-linear causing sudden jumps in mass transfer between phases requiring a small timestep. If the time-step is too large, then these sudden jumps can cause instability and divergence. To ensure simulation stability, a very small time-step must be chosen to avoid small cells being completely engulfed by mass transferred within a single time-step.
The Volumetric Source
adaptive time-step provider optimizes the time-step size by automatically adjusting
the time-step based
on ratio of the net volumetric continuity source from all the
participating phase interaction models to the (cell) volume. This avoids the
need for a very small constant time-step without de-stabilizing the simulation.
However, this adaptive time-step method needs additional treatment where
there is no phase change present, else the timestep will approach infinity. The
overall goal of implementing an adaptive time-step is to minimize total
calculation time – by maximizing the time-step – while limiting the maximum
time-step within a narrow band.
The described approach is natively implemented
as an adaptive time-step provided in Simcenter STAR-CCM+
version 2302 and higher via option.
Background
The density ratio between liquid and gas in a typical multiphase problem can be 1000 to 1 (1000/1) or more. This means a cell experiencing a phase change can lead to a large volume creation (e.g., when evaporation occurs) or volume destruction (e.g., when condensation occurs). This volume creation or destruction leads to a sharp pressure increase or decrease which can destabilize a simulation. The time-step in a simulation experiences a phase mass transfer (i.e., evaporation) must be limited so that the volume created in a given cell is never larger than a fraction of the cell volume.
Theory
The initial volume occupied by both gas and liquid phases in a cell at the time t can be calculated as follows:
Where, g and l subscripts represent gas and liquid phases, respectively. When a phase change (evaporation, condensation, etc.) occurs at time t + Δt then the volume occupied by the same mass is defined as follows:
Define the change in volume over the timestep Δt
by subtract the volumes as follows:
Redefine the net volumetric continuity source into a single variable called Q. This refers to the overall rate at which mass is being exchanged between the different phases within a computational cell. It is the net result of the contributions from various phase interaction models incorporated in the simulation. To calculate the value of Q, you would need to consider the individual contributions from the different phase interaction models relevant to your simulation. These models are typically based on physical phenomena and governing equations specific to the system being studied. It's important to note that the specific form of the equation may vary depending on the numerical method and the governing equations used in the simulation. The equation provided here is a general representation of the time-step constraint equation commonly used in multiphase flow simulations.
To avoid excessive pressure fluctuations during the simulation the volume change must be limited to a fraction of the cell volume V_c.
where:
Δt is the time-step size
C is a dimensionless factor (often referred to as the Courant number or scaling factor) that depends on the numerical scheme and stability criteria of the simulation. In this application it is a scaling factor with an allowable range of 0.001 to 10, the default is 1 (phase mass transfer fills the cell volume per time-step). Modify this value to limit the size of the time-step such that the phase mass transfer in a given cell is never larger than a fraction of the cell volume.
V_c is the volume of the computational cell
Q is the net volumetric continuity source from all participating phase interaction models.
In this equation, the term V_c / Q represents the characteristic time required to transfer the fluid volume within the cell based on the net transfer rate.
Implementation
Follow these step-by-step instructions to setup Volumetric Source adaptive time-step:
- Open or create a new Simcenter STAR-CCM+ simulation file with VOF or MMP multiphase models selected. Note, the selected physics models depend on the specific problem you are simulating.
- Enable Adaptive Time-Step Model.
- Right click Time-Step Providers located under Continua > Physics > Model Adaptive Time-Step in the Simulation tree. Select Volumetric Source.
- The Scaling Factor has an allowable range of 0.001 to 10, the default is 1 (phase mass transfer fills the cell volume per time-step). This example uses a value of 0.5, where phase mass transfer fills half (0.5) of the cell volume per time-step.
- Set the maximum allowable timestep under Solvers > Implicit Unsteady, Time-step in the simulation tree. It is important to clip the maximum allowable time-step when there is no phase change present, else the timestep will be too large. This example uses a value of 1E-5 s.
- Set the minimum allowable time-step under Solvers > Adaptive Time-Ste, Minimum Time-Step in the simulation tree. This example uses a value of 1E-8 s. Setting the minimum time-step is important to limit the computation resources required. This can be set a sufficiently small value to limit the computation resources required to solve the calculation.
- You may elect to activate the expert options. Verbosity sends additional time-step progress to the Output window. Time-Step Change Factor Bounds are useful when you have large variations in successive step size proposals, you can specify a lower and upper bound for the change factor (ratio) of successive time-steps. A proposed time-step size is then restricted to the specified range.
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