Simcenter STAR-CCM+ Modeling hypersonic cases in STAR-CCM+ (Mach >10)

Above around Mach 8.0, typical supersonic flight envelopes begin to change into hypersonic regimes. These cases differ significantly from typical external aerodynamics simulations and therefore require different best practices for setup and running.

The practices and suggestions provided below have been successful, however, it is important to note that these settings and processes may not be necessary or sufficient for all cases involving hypersonic flows.

Physics

It is advisable to try and converge using the MUSCL 3rd order scheme with the AUSM+ flux scheme. At times it may be needed to start with lower order and then change to the higher order after some level of convergence is achieved. These are selected in the properties of the Continua > Physics > Models > Coupled Flow node in the simulation tree. 

Starting with a turbulence model can cause divergence in some cases. In the event that this occurs, running the case inviscid for a good while until convergence is achieved has helped. The user can then restart with a full turbulent physics setup (if required, sometimes an inviscid solution is sufficient at these speeds). Running an inviscid model is straightforward, the user simply needs to select Inviscid for the viscous regime as shown below in Figure 1. 

 

Figure 1: Inviscid Model Selection

If turbulence is used, the suggested turbulence model is the K-Omega SST with the coefficient a1 = 0.355 [1] and QCR (quadratic) as the constitutive option. Further, k and omega should be explicitly set in the initial conditions and in regions as:

Where L is the mean aerodynamic chord or characteristic length.

In these regimes, ideal gas may not be the appropriate equation of state. Real gas equilibrium may be a better option. It does not model the individual dissociation of species that can occur at these flight envelopes, but it does model the material properties that are applicable due to dissociation. The associated gas material properties are the Sutherland model for the viscosity, equilibrium air properties for the specific heat and the speed of sound, and constant values for the other properties.

Reducing the AMG solver tolerance to 0.001 may be helpful for convergence of difficult problems. Further, use of the ILU underrelaxation method has been shown to help in hypersonic flight envelopes. These settings are selected/set under the Solvers > Coupled Implicit > AMG Linear Solver node as displayed in Figure 2. 
 

Figure 2: AMG Linear Solver Settings

Grid Sequencing Initialization (GSI) can be helpful as well. In these cases, use the Automatic CFL method for the coupled solver. For cases that are challenging to converge, using the Line Search underrelaxation may also be helpful rather than a constant value. It is recommended to use a CFL of between 1 and 3 for the grid sequencing. For the rest of the settings, leave as defaults. GSI selection is accomplished in the properties of the Coupled Implicit Solver as shown below in Figure 3.
 

Figure 3: Selecting Grid Sequencing Initialization 

The default limits for minimum pressure in the coupled solver and min/max temperature limits in the reference values are respectively: 1000 Pa, 100 K, and 5000K. For most cases these values are quite reasonable limits. However, for hypersonic simulations, they are often not. Absolute pressures of 10 Pa can be seen, as can temperatures rising to in excess of 10000K. Therefore, we often must change these limits to be sure we are dealing with physical reality of these extreme conditions.

The example sim file attached is a demonstration and not an endorsement of a best practice. It is provided to showcase the use of simulation features in a given application. The file was prepared in version 2021.1 and requires a version equivalent or newer to access. 

Figure 4: Inviscid Solution of Attached Sim File

STAR-CCM+ User Guide Sections:

• Home > Physics Simulation > Fluid Flow > Flow Reference > Flow Models Reference > Coupled Flow Solvers Reference 
• Home > Physics Simulation > Fluid Flow > Flow Solvers > Coupled Flow Solver > Convergence Accelerator 
• Home > Physics Simulation > Fluid Flow > Flow Solvers > Coupled Flow Solver > Evaluation of Inviscid Fluxes

References:

[1] N. Georgiadis and D. Yoder, “Recalibration of the shear stress transport model to improve calculation of shock separated flows,” in 51^st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, p. 685, 2013.