Harmonic Balance Guidelines

Wakes

The inlet boundary should be a stagnation inlet. Unsteady boundary conditions are prescribed by specifying an unsteady “Wake” at the inlet boundary.

This unsteady “Wake” can be specified either:

• By choosing a “standard” wake model, such as Sine, Gaussian and Hodson (as described in the journal paper: [reflink]), or
• By specifying a user table that contains the spatial variation of pressure, velocity, and temperature or their Fourier coefficients.

Without the wake, Simcenter STAR-CCM+ computes a steady flow.

Memory Requirements

The required memory scales approximately with the number of time levels that are used in the calculation. The number of time levels N is given by N = 2M + 1, where M is the number of user-specified modes. For most purposes, 1 to 3 modes are enough, with 3 a typical value. The larger the unsteadiness in the flow, the more harmonics you require.

Domain and Boundary Conditions

The physical domain depends on the physical geometry. Use the following guidelines for setting boundary conditions:

• You do not need to extend the domain to mitigate reflections. Instead, use non-reflecting boundary treatments on the inlet, outlet, and interfaces. Typically, five to ten non-reflecting modes are sufficient. It is often best to first converge a case with the non-reflecting treatment disabled.
• Specify boundary conditions as inlet total pressure and exit static pressure. Verify boundary conditions first with the steady solver. If a particular mass flow is desired, first use the steady solver in conjunction with a target mass-flow pressure outlet to determine the proper boundary pressure.
• Use mixing plane interfaces between blade regions. See Mixing Plane Interface.
• Only a single blade passage in each row is required, regardless of the relative blade count in each row.

Mesh

Use the following guidelines for setting up the mesh:

• The harmonic balance solver can solve on an arbitrary unstructured mesh. A structured mesh at the interface is not required.
• It is best to use either polyhedral grids or structured grids.
• Mesh resolution on inter-row interfaces must be uniform and relatively fine.
• The two sides of an inter-row interface must have equivalent cell sizing.
• Use a low y+ mesh whenever possible. Take special care to ensure a low y+ mesh on blades and vanes where separation occurs.

Physics

Use the following guidelines for setting up the physics:

• Use the following physics models:
  • Three Dimensional
  • Harmonic Balance
  • Ideal Gas
  • Turbulent
  • All y+ Wall Treatment
• The harmonic balance solver is currently compatible with most K-Epsilon, K-Omega, and Spalar-Allmaras turbulence models.
• Initiate the harmonic balance simulation from a converged steady simulation.
• Per-region partitioning is the most efficient partitioning method for most harmonic balance simulations.
• In the Blade Row Manager expert properties, set the Frequency Compute Option to Consider Only Neighbors for most cases. The Consider All Blade Rows option is best for cases where unsteady flow features persist more than one blade row upstream or downstream, but not for cases with more than four blade rows. See Blade Rows Manager Expert Properties.
• Set the Courant number to 5, to begin with. Cases with higher harmonic content may require a lower Courant number.
• To investigate high turbulence residuals, turn residual normalization off to determine if the absolute value of turbulence residuals is low. When starting from a converged steady solution, turbulence residual values may already be low.

Solution Procedure

It is usually best to begin a harmonic balance simulation from a converged steady solution. While it is sometimes possible to begin a harmonic balance simulation from a uniform initial condition, this often takes longer than first converging a steady solution, then reconverging the harmonic balance solver.

Use the following steps:

1. Generate a steady physics continuum.
   • Use the same models to be used with the harmonic balance model in the last step, such as these:
     • Three Dimensional
     • Steady
     • Ideal Gas
     • Turbulent
     • Spalart-Allmaras Turbulence
     • All y+ Wall Treatment
   • Use the same reference values as the harmonic balance physics continuum.
   • Set all regions to the steady physics continuum.
   • Set the initial conditions as follows:
     • Initial velocity: a non-zero value in the axial direction.
     • Initial temperature: an estimate of the inlet static temperature.
     • Initial pressure: the greater of inlet pressure and exit pressure
   • Set the Courant number to 20.
2. Disable non-reflecting treatment. Implicit (reflecting) interfaces can be more stable for initialization.
   • Set all indirect interfaces to implicit. See Mixing Plane Interface.
   • Turn off non-reflecting treatment on the inlet and outlet.
3. Initialize the grid to provide a good initial flow field for turbines and moderate pressure ratio compressors. Perform grid sequencing initialization with the following settings:
   • Maximum grid levels: 10
   • Maximum iterations per level: 200
   • Convergence tolerance per level: 0.005
   • CFL number: 20
4. Run the steady solver. At convergence, residuals should drop about four orders of magnitude and integrated quantities should approach a constant value.
5. Re-set values for the non-reflecting case:
   • Enable non-reflecting treatment on the inlet and outlet. Set the number of non-reflecting modes to between 5 and 10.
   • Change all indirect interfaces to explicit and enable the non-reflecting treatment. (See Mixing Plane Interface.) Set the number of modes on all interfaces to between 5 and 10.
     • Set the number of non-reflecting modes on both sides of every interface.
     • Do not set non-reflecting treatment on the boundary entity that makes up the interface. The boundary entity should be empty upon initialization.
6. Run the steady solver to convergence again.
7. Change all regions to the harmonic balance physics continuum and run the Harmonic Balance solver to convergence.