Exercise

Introduction

The simulation setup of the turbulent, incompressible flow through a diffuser did not yield good results compared with experimental measurements. There are two main issues, which might be responsible:

• Near-wall mesh resolution to coarse with a non-dimensionless wall distance of \(y^+ \approx 20\).
• Standard \(k-\epsilon\) simply not able to model flows under adverse pressure gradients and with separation.

In order to resolve these issues, additional simulations should be performed.

Tasks

1. Increase Near-wall Mesh Resolution

Increase the mesh resolution at the wall by using a total of 12 inflation layers.

Subtasks

1. Rename the original case folder from diffuser to something more descriptive, like kEpsilon_coarse.
2. Duplicate this folder and rename it to kEpsilon_fine. This way the results of the first simulation do not get overwritten by this second simulation.
3. Within the kEpsilon_fine case folder, remove all results folders (except 0) and the postProcessing folder for a clean setup.
4. Increase the number of inflation layers in meshDict in the system directory by changing the entry nLayers from 1 to 12.
5. Generate the mesh using cartesian2DMesh and check the quality of the mesh using checkMesh.
6. Rerun the simulation with the solver simpleFoam.
7. Analyse the simulation results with ParaView similar to the first simulation.

Questions

1. Did the convergence change compared to the first simulation?
2. Are there any improvements in the prediction of the flow separation at the lower diffuser wall?

2. Simulation with the SST \(k-\omega\) Turbulence Model

Repeat the simulations with the SST \(k-\omega\) turbulence model instead of the Standard \(k-\epsilon\) model. This involves changing the turbulence model, applying suitable boundary conditions for the new variable specific dissipation rate \(\omega\) and adjusting the solver and discretization schemes.

Subtasks

1. Duplicate the folder with the refined mesh from Task 1 and rename it to kOmegaSST_fine.
2. Within the kOmegaSSt_fine case folder, remove all results folders (except 0) and the postProcessing folder for a clean setup.
3. Change the turbulence model from kEpsilon to kOmegaSST in the turbulenceProperties file in the constant dictionary.
4. In the 0 folder, rename the epsilon file to omega for the new variable solved and apply the following changes to the file itself:
   • Set the name of the object in line 14 to omega.
   • Change the dimensions of the variable to \(\text{seconds}^{-1}\).
   • The inlet boundary condition must be of type turbulentMixingLengthFrequencyInlet.
   • Replace the epsilonWallFunction at the wall patches with omegaWallFunction.
5. In controlDict, fvSchemes, and fvSolution in the system directory, replace all instances of epsilon with omega to use the same discretization schemes, solver settings, residual criteria, and relaxation factors for the \(\omega\) transport equation as for the \(\epsilon\) transport equation in the previous simulations.
6. Add the following entry in the fvSchemes file, which specifies how the SST \(k-\omega\) turbulence model computes the distance from a cell to the next wall:

   wallDist
   {
    method              meshWave;
   }
   

7. Rerun the simulation with the solver simpleFoam.
8. Analyse the simulation results with ParaView similar to the first simulation.

Questions

1. Are there any improvements in the prediction of the flow separation at the lower diffuser wall?
2. Plot the velocity profile of of all three simulations and the experimental measurements in a single graph in ParaView. Which model is best suited for modelling this complex flow?