## Tips & Tricks: Estimating the First Cell Height for correct Y+

In previous posts we have stressed the importance of using an appropriate value in combination with a given turbulence modelling approach. Today we will help you calculate the correct first cell height () based on your desired value. This is an important first step as the global mesh resolution parameters will also be influenced by this near-wall mesh as well as the Reynolds number. Let's review the two main choices we have in choosing a near-wall modelling strategy: Resolving the Viscous Sublayer Involves the full resolution of the boundary layer and is required where wall-bounded effects are of high priority (adverse pressure gradients, aerodynamic drag, pressure drop, heat transfer, etc.) Wall adjacent grid height must be order Must use an appropriate low-Re number turbulence model (i.e. Shear Stress Transport) Adopting a Wall Function Grid Involves modelling the boundary layer using a log-law wall function. This approach is suitable for cases where wall-bounded effects are secondary, or the flow undergoes geometry-induced separation (such as many bluff bodies and in modern automotive vehicle design). Wall adjacent grid height should ideally reside in the log-law region where All turbulence models are applicable (e.g. Shear Stress Transport or k-epsilon with scalable wall functions) During the pre-processing stage, we need to estimate the first cell height ( ) so that our falls within the desired range. The computed flow-field will dictate the actual value which in reality will vary along the wall. In some cases, we may need to locally refine our mesh to achieve the desired value in all regions. So how to calculate the First Cell Height for a desired Y+ value? Firstly, we should calculate the Reynolds number for our model based on the characteristic scales of our geometry such that: , where and are the fluid density and viscosity respectively, is the freestream velocity, and is the characteristic length (e.g. pipe diameter, body length, etc.). The definition of the value is such that: The target value and fluid properties are known a priori, so we need to calculate the frictional velocity , which is defined as: The wall shear stress, can be calculated from skin friction coefficient, , such that: The ambiguity in calculating surrounds the value for . Empirical results have been used to provide an estimate to this value: Flow Type Empirical Estimate Internal Flows External Flows We can then input these known values into the above equations to estimate our value for . When considering simple flows and simple geometry, we might find this correlation is highly accurate. However, when considering complex geometry, refinement in the boundary layer may be required to ensure the desired value is achieved. In these cases, you can choose to re-mesh in ANSYS Meshing or use anisotropic mesh adaption (ie. adaption of local cells only in...

## 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...

## 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...

## How does the Reynolds Number affect my CFD model?

The Reynolds number (Re) is the single most important non-dimensional number in fluid dynamics and is recommended to be calculated before you begin any new CFD modelling project. The Reynolds Number is defined as the dimensionless ratio of the inertial forces to viscous forces and quantifies their relevance for the prescribed flow condition: Where U∞ and L are the characteristic velocity and length scale of the problem, ρ is the fluid density and μ is the dynamic viscosity. The use of the Reynolds number frequently arises when performing a dimensional analysis and is known as Reynolds principle of similarity. For example, air flow of U∞ = 1 [m/s] over a flat plate of L = 1 [m] will exhibit the same flow pattern as air flow of U∞ = 10 [m/s] over a flat plate of L = 0.1 [m]. This concept holds since the Re is equal and the flow is incompressible (i.e. the Mach number is low). The Re also allows us to characterize whether a flow is laminar or turbulent. Laminar flow is characterized by lower Re and high diffusion over convection. Turbulent flow on the other hand is characterized by higher Re where inertial forces dominate considerably, resulting in largely chaotic flow. The flow may also undergo a transitioning phase whereby the flow exhibits neither completely laminar nor completely turbulent characteristics. Note: Inertial forces are proportional to the square of velocity, while viscous forces vary linearly with velocity. Therefore as the Re → 0 it is reasonable to neglect convective terms (e.g. creeping flow). Similarly, as the Re → ∞ the viscous terms of the momentum equation can be neglected and the problem can be characterized purely by the generation of inertial forces (e.g. high supersonic and hypersonic flows). For flows in a pipe of diameter L or non-circular pipes with hydraulic diameter L, empirical studies have shown that laminar flow occurs for ReL < 2500 and fully developed turbulent flow occurs for ReD > 4000. In the interval between, transition occurs. For external flows (e.g. flow over a flat plate), laminar flow is observed up to approximately ReD ~ 1×105 to 5×105 (where D is the distance from the leading edge) before transition to turbulence takes place and turbulent flow is observed thereafter. Factors influencing transition include roughness and local acceleration. The Turbulence Modelling team at ANSYS Inc, led by Dr. Florian Menter, have developed world-leading capabilities to allow CFD users to accurately model these transition effects. Using the Reynolds number, we can determine whether or not it is necessary to include...

## Webinar: Recent Advancements in Turbulence Modelling with Dr. Florian Menter

As part of the visit to Australia by Dr Florian Menter, world-recognised expert in turbulence modelling, LEAP Australia is pleased to announce a webinar to be held on Thursday Aug 30th at 11am AEST. This webinar will provide an overview of recent advancements in turbulence modelling and is being held for those customers unable to attend the Advanced Turbulence training courses in Sydney, Melbourne and Perth. More information on the training courses can be found here in a separate post. Who should attend? This webinar is suitable for all engineers, researchers & managers involved in performing CFD modelling of turbulent flows. ABOUT THE PRESENTER Dr. Menter is a world-recognised expert in turbulence modelling. He developed the widely used Shear-Stress Transport (SST) turbulence model, which has set a milestone in the accurate prediction of aerodynamic flows. He has also contributed to the formulation of one-equation turbulence models, advanced near wall treatment of turbulence equations, transition modelling and unsteady flow models. He has been in charge of the turbulence modelling program at ANSYS for more than 15 years and has been involved in a wide range of industrial modelling challenges. He has published more than 50 papers and articles at international conferences and in international journals. Most recently, Dr. Menter has been involved in the implementation of new turbulence models for unsteady flow simulations, including Scale-Adaptive Simulation (SAS) and Embedded/Zonal LES models. These models are particularly relevant for the many industrial applications where time varying information is essential to the engineering outcomes (such as aerodynamics, acoustics, combustion, fluid-structure coupling, etc.). REGISTER HERE WEBINAR DETAILS Date: August 30, 2012 Time : 11am – 12:30 (MEL/SYD) Duration : 90 minutes For more information, please phone LEAP on 1300 88 22 40 or (02) 8966 7888 (from mobiles or outside Australia) or email us. Full login details for the webinar will be provided upon...