LES Guidelines

This section provides guidelines for analysis of a combustor with spray, using Large Eddy Simulation and the Non-Adiabatic PPDF (Equilibrium or Flamelet) models.

Guidelines for LES differ from RANS guidelines in:

See LES Analysis Workflow.

Meshing

The fidelity of a scale resolving simulation is strongly related to the mesh: usually, the finer the mesh, the better the results. However, the available computational resources limit the number of cells.

To create a mesh that gives reasonably good results for an LES analysis, you can use one of the following approaches:

  • Choose a mesh size that gives a cutoff wavenumber within the inertial subrange in the region of interest. Keep the ratio of turbulent kinetic energy to subgrid kinetic energy (k/ksgs) above 5 and, if possible, above 20. When possible, avoid stretching the mesh. To estimate k/ksgs, use the following steps:
    1. Estimate the turbulence kinetic energy from the field variance values of the three velocity components and define a field function using this estimate.
    2. Use the field function for the turbulent kinetic energy and SGS Turbulent Kinetic Energy (the field function for subgrid scale turbulent kinetic energy) to determine the ratio of the two kinetic energies.

    Carry out 3-D simulations if the scales in the Z direction are large and must be captured accurately for a reliable LES study.

  • Run a preliminary RANS (K-Epsilon, K-Omega, or RST) simulation on an exploratory mesh [[356]. Using the RANS field functions Kolmogorov Length Scale and the Taylor Micro Scale, determine a reasonable cells size for the LES study.

    The Kolmogorov Length Scale denotes the smallest scales in the turbulent spectrum. At these smallest scales, LES results tend towards the results of a DNS. For this reason, the Kolmogorov Length Scale can be used to limit the local minimum cell size.

    The Taylor Micro Scale is an intermediate length scale, which lies at the dissipation region end of the inertial sub-range within the turbulence spectrum. Scales that are smaller than the Taylor Micro Scale are mainly viscous-driven. Addad and others [350] demonstrated that limiting the maximum cell size based on the Taylor Micro Scale can be used to construct a mesh that provides good results for scale resolving simulations.

    Therefore, using the Kolmogorov Length Scale η and the Taylor Micro Scale λ, you can determine a reasonable local cell size from η<Δ<λ, where Δ=(ΔxΔyΔz)1/3.

See How Do I Conduct an Aeroacoustics Analysis? and Turbulent Time and Length Scales.

Discretization

To ensure temporal and spatial fidelity for good LES results, it is important to achieve a Convective Courant number (available as a field function) with a value close to 1 in the domain of interest. This number depends on the mesh size; if you have a large mesh size, reduce time-step size to improve the Convective Courant number value. Use a second-order temporal discretization and a time-step of 1E-5 s or less. For faster convergence per time-step, increase the under-relaxation factors. As a result, you can then reduce the number of inner iterations to 15 or less, for a faster turnaround time.

Use Bounded Central Differencing (BCD) with LES—with appropriate blending factor. A value of 0 for Upwind Blending Factor implies pure central differencing. A value of 1 implies pure upwinding. See Bounded Central-Differencing.

Subgrid Scale Model

Depending on the application, you can choose from:

  • The Smagorinsky Subgrid Scale model. The default value for the Smagorinsky model constant is 0.1. For boundary layer flows and jets, consider using lower values. Higher values occur for homogeneous isotropic decaying turbulence. Take care to evaluate the value of the Smagorinsky model constant for each cases.
  • The Dynamic Smagorinsky Subgrid Scale model
  • The WALE Subgrid Scale model. The WALE model is computationally less expensive, more thoroughly validated, and more suitable for use near walls. Use the WALE model unless you require the Smagorinsky model for reasons of compatibility, standards, or legacy.

Initialization

A large proportion of computational time is spent in reaching a stage when it is possible to start collecting flow statistics for post-processing. The effects of initial conditions have to be eliminated before any time-averaging can begin. This process usually takes 2–5 flow-through cycles. To minimize the number of cycles needed:

  • Use results from a RANS calculation to give the right mean fields.
  • Get convergence on a coarse mesh and interpolate the results onto a fine mesh. This way, you can retain the larger turbulent scales, and the smaller scales can develop quickly.

Monitoring Solution

Always have several monitor points for quantities like velocity, to help you determine when to start averaging. Use time-steps as the triggers for these monitors, since the LES simulation is a transient simulation.

Monitor residuals to determine if the solution converges well within each time-step. Monitor other scalars of interest, (for example, Temperature or Velocity) versus inner iterations at different locations to determine if you have proper convergence within the specified inner iterations.

Sampling

Set Start Time:

Choose a time to start sampling. Typical start times are 2–5 flow-through times. Use one of the following methods to compute residence time:

  • Track the residence time for a massless particle, starting with the converged RANS solution. See Modeling Residence Time.
  • Divide combustor length by average axial velocity.

Define Field Monitors:

Define the following field monitors:

  • Field Mean Velocity Magnitude
  • Field Mean Temperature
  • Field Mean Mixture Fraction
  • Field Variance Velocity [i]
  • Field Variance Velocity [j]
  • Field Variance Velocity [k]

To define a field monitor:

  1. Right-click the Monitors node, select New Monitor, then select Field Mean or Field Variance.
  2. Select the monitor node. In the Properties window, select the Field Function and the Parts for the monitor.
  3. Expand the monitor node and select the Time-Step Frequency node. In the Properties window, enter the Start time.
  4. Rename the monitor node to indicate the selected function.

LES Analysis Workflow

Use the following steps:

  1. Run the case using RANS until you reach a reasonable level of convergence. See RANS Simulation Settings.
  2. Estimate the Lagrangian residence time.
  3. Estimate the flow-through time.
  4. Set up the LES models. See LES Simulation Settings.
  5. Run the Lagrangian solver with all other solvers frozen. Use a time period of about twice the residence time of the spray. This practice ensures that the spray catches up with the flow field. See Lagrangian Update.
  6. Unfreeze all the other solvers and run an LES analysis. See LES Analysis.

    If the time-step is small (about 1E-5 or lower), you can use a Lagrangian Update Frequency of once per time-step for a faster turnaround time.

RANS Simulation Settings

Select a RANS model. (See Reynolds-Averaged Navier-Stokes (RANS) Turbulence Models.)

For the Non-Adiabatic PPDF Flamelet combustion model:

  • Select the following physics models:
    Group Box Model
    Equation of state Ideal Gas
    Material Multi-Component Gas
    Time Steady
  • Under the Multi-Component Gas physics model node, set the following properties:
    Node Property Setting
    Mixture Properties
    Molecular Weight Method PPDF Table
    Specific Heat Method PPDF Table
  • Under the PPDF Flamelet (Adiabatic) physics model node, set the following properties:
    Node Property Setting
    PPDF Flamelet Table Identical Mixture Fraction Space Activated

For the Non-Adiabatic PPDF Equilibrium combustion model:

  • Select the following physics models:
    Group Box Model
    Equation of state Ideal Gas
    Material Multi-Component Gas
    Time Steady
  • Under the Multi-Component Gas physics model node, set the following properties:
    Node Property Setting
    Mixture Properties
    Molecular Weight Method PPDF Table
    Specific Heat Method PPDF Table
  • Under the PPDF Flamelet (Adiabatic) physics model node, set the following properties:
    Node Property Setting
    PPDF Equilibrium Table Identical Mixture Fraction Space Activated

For solvers, set the following properties:

Solver Property Setting
Lagrangian Multiphase Maximum Courant Number 0.5
Minimum Courant Number 0.3
Two-Way Coupling Under-Relaxation Factor 0.75
Steady > Update Frequency Time-Step Update Frequency 10
Partitioning > Load balancing options Rebalance Frequency 200
Velocity Under-Relaxation Factor 0.7
Under-Relaxation Ramp Ramp Method Linear Ramp
Linear Ramp Start Iteration 1
End Iteration 100
Initial Value 0.5
Pressure Under-Relaxation Factor 0.3
Under-Relaxation Ramp Ramp Method Linear Ramp
Linear Ramp Start Iteration 1
End Iteration 100
Initial Value 0.1
Energy Under-Relaxation Factor 0.9
Under-Relaxation Ramp Ramp Method Linear Ramp
Linear Ramp Start Iteration 1
End Iteration 100
Initial Value 0.7
PPDF Combustion Under-Relaxation Factor 0.9
Under-Relaxation Ramp Ramp Method Linear Ramp
Linear Ramp Start Iteration 1
End Iteration 100
Initial Value 0.7

LES Simulation Settings

Use the following steps:

  1. Set the following models, in order, with Auto-select recommended models activated:
    Group Box Model Action
    Enabled Models Steady Deselect
    Time Implicit Unsteady Select
    Enabled Models Two-Layer All y+ Wall Treatment Deselect
    Enabled Models Realizable Two-Layer K-Epsilon Deselect
    Enabled Models K-Epsilon Turbulence Deselect
    Enabled Models Reynolds-Averaged Navier-Stokes Deselect
    Turbulence Large Eddy Simulation Select
    Subgrid Scale Turbulence Wale Subgrid Scale Select
    Enabled Models All y+ Wall Treatment (Selected automatically)
  2. Set the following properties:
    Node Property Setting
    Segregated Flow model Convection Bounded Central Differencing
    Non-Adiabatic PPDF model > Mixture Fraction Variance Method Algebraic Relationship
  3. Set boundary conditions as required.
  4. For solvers, set the following properties:
    Solver Property Setting
    Lagrangian Multiphase Maximum Courant Number 0.5
    Minimum Courant Number 0.3
    Two-Way Coupling Under-Relaxation Factor 0.75
    Implicit Unsteady > Update Frequency Time-Step Update Frequency Once per time-step
    Partitioning > Load balancing options Rebalance Frequency 200
    Velocity Under-Relaxation Factor 0.7
    Pressure Under-Relaxation Factor 0.3
    Energy Under-Relaxation Factor 0.9
    PPDF Combustion Under-Relaxation Factor 0.9
  5. Set Stopping Criteria > Maximum Inner Iterations to 15. (You can reduce this number further if the residuals converge before 15 iterations and you set velocity URF to 0.8 and pressure URF to 0.4.)
  6. Set up all mean and variance monitors with appropriate collection start times (equal to the Lagrangian update time plus 4–5 flow-through times).
  7. Set up appropriate reports and plots for post-processing.
  8. Save the file.

Lagrangian Update

Next, run Lagrangian Update to synchronize the unsteady spray with the flow field:

  1. Freeze all solvers except Implicit Unsteady and Lagrangian Multiphase.
  2. Set Stopping Criteria > Maximum Inner Iterations to 1.
  3. Set Stopping Criteria > Maximum Physical Time to 2 × Lagrangian Residence Time.
  4. Run Lagrangian Update for 2 Lagrangian residence times, to let the spray catch up with the flow.
  5. Save the file.

LES Analysis

Finally, run LES with BCD:

  1. Unfreeze all the solvers.
  2. Set Stopping Criteria > Maximum Inner Iterations to 15.
  3. Set Stopping Criteria > Maximum Physical Time to 10 × flow-through time.
  4. Run for ~5 flow-through times, or as required. Then switch on data sampling and continue running for another 5 flow-through times (so that total run time is 10 flow-through times).
  5. Save the file.