UA-33602782-1
May06

Turbulence Part 4 - Reviewing how well you have resolved the Boundary Layer

In recent posts we have comprehensively discussed inflation meshing requirements for resolving or modeling wall-bounded flow effects due to the turbulent boundary layer. We have identified the y-plus value as the critical parameter for inflation meshing requirements, since it allows us to determine whether our first cell resides within the laminar sub-layer, or the logarithmic region. We can then select the most suitable turbulence model based on this value. Whilst this theoretical knowledge is important regarding composite regions of the turbulent boundary layer and how it relates to y-plus values, it is also useful to conduct a final check during post-processing to ensure we have an adequate number of prism layers to fully capture the turbulent boundary layer profile, based on the turbulence model used (or more precisely, whether we aim to resolve the boundary layer profile, or utilize a wall function approach). In certain cases, slightly larger y-plus values can be tolerated if the boundary layer resolution is sufficient. How can I check in CFD-Post that I have adequately resolved the boundary layer? For the majority of industrial cases, it is recommended to use the two-equation turbulence models, or models which utilize the turbulent viscosity concept and the turbulent viscosity ratio (i.e. the turbulent viscosity over the molecular viscosity). We can make use of this concept to visualize the composite regions of the turbulent boundary layer, and ultimately visualize how well we are resolving the boundary layer profile. Consider the conceptual case-study of the turbulent flow over an arbitrarily curved wall. Prism layers are used for inflation, and tetra elements in the free-stream. Once we have calculated the solution, within CFD-Post we can create an additional variable for the eddy viscosity ratio. Then by plotting this variable on a suitable plane, and superimposing our mesh in the near-wall region, we can visualize the boundary layer resolution.                   Figure 1 provides an example of a reasonable wall function mesh. There is a good cell transition from the prisms to the free stream tetra elements. The y-plus we have prescribed at the first cell indicates we are in the logarithmic composite region of the turbulent boundary region, which is the region largely dominated by inertial forces and thus we have high levels of turbulence. The turbulence gradually dissipates as we approach free stream conditions (where the levels of turbulence are governed by inlet conditions), which is expected. At this stage, we could even reduce the number of cells in the inflation layer as we are clearly capturing the logarithmic region layer before approaching the free stream. Correspondingly, we could aim to reduce the...

Apr12

Turbulence Part 3 - Selection of wall functions and Y+ to best capture the Turbulent Boundary Layer

In recent posts in our series of Turbulence Modelling posts, we have covered boundary layer theory and touched on some useful meshing and post-processing guidelines to check you are appropriately resolving the boundary layer profile.  Today we will consider three critical questions that are often asked by CFD engineers when developing or refining a CFD simulation:   - Am I using the correct turbulence model for the type of results I am looking for? - Do I have an appropriate Y+ value and a sufficient number of inflation layers? - Am I using the right wall function for my problem? This topic is so important because we know that in turbulent flows the velocity fluctuations within the turbulent boundary layer can be a significant percentage of the mean flow velocity, so it is critical that we capture these effects with accuracy. A Reynolds averaging approach using turbulence models will provides us with an estimate of the increased levels of stress within the boundary layer, termed the Reynolds stresses. In order to appreciate the use of wall functions and the influence of walls on the turbulent flowfield, we should first gain familiarity with the composite regions of the turbulent boundary layer:                 In the laminar sub-layer region (Y+ < 5) inertial forces are less domineering and the flow exhibits laminar characteristics, which is why this is known as the low-Re region. Low-Re turbulent models (e.g. the SST model) aim to resolve this area and therefore require an appropriate mesh resolution to do this with accuracy. This is most critical for flows with a changing pressure gradient where we expect to see separation, as observed below.                       In the law of the wall region, inertial forces strongly dominate over viscous forces and we have a high presence of turbulent stresses (this is known as the high-Re composite region). If using a low-Re model, the whole turbulent boundary layer will be resolved including the log-law region. However, it possible to use semi-empirical expressions known as wall functions to bridge the viscosity-affected region between the wall and the fully-turbulent region.                     The main benefit of this wall function approach lies in the significant reduction in mesh resolution and thus reduction in simulation time. However, the shortcoming lies in numerical results deteriorating under subsequent refinement of the grid in wall normal direction (thus reducing the Y+ value into the buffer layer zone). Continued reduction of Y+ to below 15 can gradually result in unbounded errors in wall shear stress and wall heat transfer (due to the damping functions inherent within the wall...

Aug17