TransitionModelSolver#
The laminar to turbulence transition model supported by Flow360 is the 2019b version of the Amplification Factor Transport (AFT) model created by James Coder, University of Tennessee.
This model adds two additional equations to the flow solver in order to solve for the amplification factor and intermittency flow quantities.
More details about the model can be found here.
Below are a list of configuration parameters for the transition model.
Either N_crit or turbulence_intensity_percent can be used to tune the location of transition from laminar to turbulent flow.
absolute_tolerance#
The absolute_tolerance is the primary convergence metric for steady cases. At least 5 orders of magnitude reduction is recommended for all residual values. The absolute_tolerance can also be used for unsteady cases, but is less meaningful than the relative_tolerance, as the initial residual values change between different physical steps.
relative_tolerance#
The relative residual is defined as the ratio of the current pseudoStep’s residual to the maximum residual present in the first 10 pseudoSteps within the current physicalStep. When running unsteady cases, the relative_tolerance is typically set to 1e-2 or 1e-3. Once the nonlinear residuals drop by 2 or 3 orders of magnitude, the solver will continue to the next physicalStep. The relative_tolerance is ignored for steady cases.
order_of_accuracy#
As recommended in the orderOfAccuracy of navierStokesSolver, when solving unsteady cases, it may be necessary to initialize the flow field with order_of_accuracy set to 1. Once the flow field has been initialized, the user can create a child case and switch the order_of_accuracy back to 2.
When adjusting the order_of_accuracy for the TransitionModelSolver, the navierStokesSolver and turbulenceModelSolver should be adjusted as well.
linear_solver#
The transition solver is typically easier to converge than the NS solver. Therefore, the value of max_iterations for the transition solver, typically set to ~20, is less than max_iterations for the NS solver. However, if the linear residual reduction ratio after linear solver is not enough, increasing max_iterations up to ~50 could be helpful. The default max_iterations for transition solver is 20.
update_jacobian_frequency#
Similar to the NS solver, the default value for update_jacobian_frequency is 4, indicating that the Jacobian for evaluating the transition equations is only updated every 4 pseudo-steps. For more challenging cases, update_jacobian_frequency may need to be reduced from 4 to 1. This will not significantly slow down the solver, since the transition equation is not as computationally expensive as the NS equation.
equation_evaluation_frequency#
As mentioned above, the transition equation is typically easier to converge than the NS equations.
Therefore, by default, equation_evaluation_frequency is set to 4, meaning that the transition equation is only evaluated every 4 pseudo-steps. For challenging cases, equation_evaluation_frequency may need to be reduced from 4 to 1 as well. This change will not significantly impact the solver’s performance.
N_crit#
N_crit is the critical amplification factor. Boundary layer transition is triggered when the amplified frequency of the Tollmien-Schlichting waves reaches this value. Higher values delay the onset of laminar-turbulent transition. Only N_crit or turbulence_intensity_percent, can be specified in the flow configuration file. The value has a range of 1 to 11 in Flow360.
turbulence_intensity_percent#
turbulence_intensity_percent is used to compute the N_crit parameter (see above) when N_crit is not set for the AFT transition model using: \(N_{crit} = -8.43 - 2.4*ln (0.025*tanh(\text{turbulenceIntensityPercent})/2.5)\). Higher values of turbulence_intensity_percent therefore lead to earlier transition. The value of turbulence_intensity_percent has a range of 0.03 to 2.5 (%) in Flow360.