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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:

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.

Predicting separation in a diffuser-type geometry

 

 

 

 

 

 

 

 

 

 

 

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.

Contours of the eddy viscosity ratio on a low-Re grid illustrating high turbulent viscosity in the log-law region as opposed to the laminar sub-layer

 

 

 

 

 

 

 

 

 

 

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 function approach).

Bearing all of the above in mind, and keeping our eye on finding the right balance between accuracy, stability and speed, we can tackle a wide variety of CFD problems using the following guidelines:

What results am I interested in and am I using the right turbulence model?

If our aim is to accurately predict the boundary layer velocity or thermal profile, or if the developing boundary layer will tend to separate (due to a changing pressure gradient – and not because of sharp edges or discontinuities in the geometry), then we recommend the use of a low-Re model. Low-Re models are also required for accurate pressure-drop or drag calculations. We highly recommend the use of the Shear Stress Transport (SST) model, but all ω­-based models or ε-based models with enhanced wall treatment may be used. For high speed external aerodynamic flows, the one-equation Spalart-Allmaras model (with Y+ < 2) may also be considered to reduce the computational time. Alternatively, for flows where wall-bounded effects are not a priority, or if separation is expected to occur only due to sharp changes in the geometry, an ε-based wall function approach is more than sufficient. In ANSYS CFD, all ω-based models and the SST model are capable of resorting to a wall function formulation (automatic wall treatment) in the presence of coarse mesh resolutions near the wall without any further user input. Wall function models are also useful for calibrating our CFD models, due to the decreased simulation time.

Flow pattern with separation and reattachment on a rotor blade

 

 

 

 

 

 

 

 

 

 

What is my Y+ value and do I have a sufficient number of prism layers?

When using low-Re models or any models with enhanced wall treatment, the average Y+ value should be on the order of ~1 to ensure we are capturing the laminar sub-layer. When using wall function models, the Y+ value should ideally be above 15 to avoid erroneous modelling in the buffer layer and the laminar sub-layer. High quality numerical results for the boundary layer will only be obtained if the overall resolution of the boundary layer is sufficient. This requirement in some cases is more important than achieving certain Y+ values. The minimum number of cells to cover a boundary layer accurately is around 10, but values of 20 are desirable. The total thickness of the prisms should be implemented such that around 15 or more nodes are actually covering the boundary layer. Our next post in this series on the turbulent boundary layer will cover a very useful and practical technique to post-process the resolution of the boundary layer, and offer insight into modifications required to improve accuracy.

Boundary layer velocity profile modeled with standard k-e for three different mesh densities using Enhanced Wall Treatment

 

 

 

 

 

 

 

 

 

Am I using the right wall function?

In ANSYS CFD, all turbulence models are y-plus independent. However selecting the most appropriate wall function is dependent on level of refinement of our wall adjacent mesh, or the relative scales in our flow. Use of the standard wall function (ε-based models) implies that our boundary layer mesh lies entirely within the log-law region of the boundary layer. For industrial applications, this in fact might be difficult to achieve due to varying geometrical and velocity scales associated with our model – and therefore grids inherently designed with arbitrary refinement. We highly recommend the use of the scalable wall function, which offers an elegant solution to this ambiguity often encountered. This wall function virtually displaces the mesh to a Y+ ~ 11.225 (transition to the log-law composite layer) irrespective of the level of refinement, thereby avoiding the erroneous modelling of the laminar sub-layer and buffer region. It is also important to note that for grids designed with a Y+ > 11.225, the scalable wall function will provide identical results to the standard wall function. Enhanced wall treatment may further be selected for ε-based models on refined low-Re grids, and is also formulated such that it can perform well for meshes of intermediate resolution. However the use of enhanced (or non-equilibrium) wall treatment for low-Re modelling of the turbulent boundary layer is generally not recommended and more confidence in our solution can be obtained by selecting a suitable ω­-based formulation, such as the SST model.

Author: LEAP CFD Team

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12 Comments

  1. I have read your article and there is one think that I do not understand.

    “Scalable wall function – This wall function virtually displaces the mesh to a Y+ ~ 11.225 (transition to the log-law composite layer) irrespective of the level of refinement, thereby avoiding the erroneous modelling of the laminar sub-layer and buffer region.”

    Does this mean that using Scalable wall function the mesh will be rebuilt in the way to consist both phenomena: laminar and transition flow?

    Post a Reply
    • If your model has varying geometrical or velocity scales, then consequently your grid and near-wall refinement will have varying levels of resolution. To maintain consistency in our modelling approach the scalable wall function will virtually displace the near-wall mesh to a y+ value of 11.225, which is the transition to the log-law region. This is necessary since epsilon-based models are not ideal for modelling the laminar sub-layer and the scalable approach internally adjusts the mesh to ensure this region is not resolved. The scalable approach is the default option in ANSYS CFX and is an available option in ANSYS Fluent. The scalable wall function will not capture laminar or transitioning flow, as it is purely a turbulent wall function approach. To model aerodynamic flows with laminar-to-turbulent transition, we encourage the use of the SST transition model. This low-Re model requires fine resolution in the near-wall region due to the complexity of transitioning flow.

  2. Hi experts,
    You stated that with Scalable Wall Function method, it virtually displaces the mesh to a Y+ ~ 11.225. And on top up the page there is figure showing buffer layer yplus between 5 to 30.
    So it seems somehow wrong to place first layer in buffer layer!
    Can you explain more?
    Thank you in advance.

    Post a Reply
    • The scalable wall function will displace the mesh to a Y+ ~ 11.225 since this is noted as the numerical transition point from when a boundary layer operates in the laminar sub-layer to the turbulent log-law. It is simply a virtual scale of first cell height so that the solver internally operates as if we are in the log-law region and not within the laminar sub-layer.

  3. how does ansys calculte in the near wall region ?is it like this :at the first cell,use emprical correlation,and from the second cell solving k-e equation ?If it is like this ,why we need sufficient boundary layer?
    thank you for your reply..

    Post a Reply
  4. hiiii…
    My geometry is wing of airfoil cross section inside a rectangular box domain. I am using Standard k-e model. what should be my y+? Does k-e model is good or i should move to another model.

    Post a Reply
  5. Hi,
    I am modeling a shell and tube heat exchanger and i am having problem with pressure drop on shell side. My analytical calculations give pressure drop of 470 Pa while fluent gives 2300 Pa. Average Y+ value on tube walls is 20. Turbulence model is K-e with standard wall functions. Kindly help me in this issue.
    Thanks.

    Post a Reply
    • It is difficult for us to comment on this, since we do not have an understanding of the geometry or your choice of boundary conditions. Nor can we assume that your analytic calculations are in fact valid for the problem setup. The discrepancy in the result is likely not to be solely due to mesh resolution, rather it is likely to do primarily with the choice of boundary conditions. Our advice would be to attempt one of the tutorials from the help guide which address heat transfer to gain an understanding of a representative problem setup.

  6. Dear Leap Group:

    I saw we explained “Low-Re models are also required for accurate pressure-drop or drag calculations. We highly recommend the use of the Shear Stress Transport (SST) model, but all ω­-based models or ε-based models with enhanced wall treatment may be used.” in part “What results am I interested in and am I using the right turbulence model?”,

    But we said “However the use of enhanced (or non-equilibrium) wall treatment for low-Re modelling of the turbulent boundary layer is generally not recommended and more confidence in our solution can be obtained by selecting a suitable ω­-based formulation, such as the SST model.”

    I wonder if these two speaking are contradictory for Enhanced Wall Treatment used in Low-Re? So how we to understand Enhanced Wall Treatment for solving boundary layer?

    Post a Reply
    • It is necessary to understand the limitations and range of applicability of the eddy-viscosity turbulence models. No single model can be applied to all problems of interest – however the omega-based models and in particular the SST model are often preferred, particularly because of their favourable wall treatment. They are relatively more robust near the wall, and the y-plus insensitive treatment is facilitated through the automatic wall treatment. They are also relatively easier to combine with additional physics, such as transition. There is still ongoing development for epsilon-based models, in particular the y-plus insensitive treatment through the enhanced wall treatment and for many problems the use of realizable k-epsilon with enhanced wall treatment, for instance, will provide a valid result. In this post we aimed to provide our recommendation for a baseline model to capture boundary layer flows for a wide range of applications, and due to its robustness, we have opted for the SST model.

  7. hi,
    we use a wall function for boundary layer so why do we need to have some nodes in this region?
    my English is not good enough.
    thanks

    Post a Reply
    • We respectfully suggest that you re-read this post and other related posts on wall functions/full resolving the boundary layer on our Blog.

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