We at Volupe strive to be able to give you (all the simulation engineers out there) the best support possible. Therefore, we have created a y+ calculator at our webpage, linked here: Volupe’s y+ calculator.This y+ calculator is the first published content in our own handbook for engineers, to which we will add further functionality that is useful for engineers in their daily work. This week’s blog post will describe the purpose of using a y+ calculator, features in Volupe’s y+ calculator and how to use the y+ calculator (together with some tips) when deciding mesh settings. Summary of tips from the blog post: 
Boundary layer thickness – By specifying if you have boundary layer that is laminar or turbulent in your simulation, you get a value for the thickness of the boundary layer. The default values for the input parameters in this part (length downstream to evaluate and Reynolds number) are updated automatically from part 1 of the y+ calculator. The parameter length downstream to evaluate, uses characteristic length as default value. The equations that are used to determine the boundary layer thickness are based on flat plate theory. This means that the boundary layer thickness has a linear dependence of the length downstream to evaluate. If the region where you want to estimate the boundary layer thickness does not have flow similar to flow over a flat plate, this estimation will be less accurate (then it can be wise to run a test-simulation to get a better approximation of how thick the boundary layer is, and use the calculated value as input from parts 2 of the y+ calculator).The illustration to the right, in the picture below, a typical profile for laminar and turbulent boundary layer is visualized. 
Settings for the prism layer mesher – in Simcenter STAR-CCM+ there are three different distribution modes (ways of defining parameters) to specify your settings for the prism layer mesher. The same resulting mesh is possible to obtain regardless the choice of distribution mode. By defining first cell height (automatically updated to the value from part 1 in the calculator), prism layer stretching (also known as growth rate) and number of prism layers – the output is given so that you can copy the parameter values directly into your simulation software, regardless of which distribution mode you selected. You will also get the value of the height for the last prism cell, since this value can be good to know in the next step, part 4. The text in the picture below describes which parameters are required to specify, depending on which distribution mode that is selected. In the illustrations to the right the parameters are visualized. 
Transition from prism layer to bulk mesh – To get a good transition, from the prism layer mesh to the bulk mesh (mesh in the free stream), part 4 compares the last prism layer cell height (automatically updated from part 3 in the calculator) to the first cell in the bulk mesh. This train of thought can be used both for polyhedral and trimmed (hexahedral cells) meshers, but since trimmed cells are always growing by a ratio of 2 (becomes twice as large in a dimensions), there might be a “transition cell layer” of cells automatically added between the prism layer mesh and bulk mesh. This layer of cells, is difficult to predict (since it depends on where the bulk mesh cells are located relative the geometry), but will only help making the transition smoother.The illustration to the right in the picture below visualizes how the transition from a boundary prism layer mesh of polyhedral cells to a bulk mesh could look like, and how the ratio in the output is defined. 
- The y+ calculator is divided into four parts. If you determine the mesh settings in order part 1 to 4, you will automatically obtain the calculated outputs as inputs in the following steps.
- You can of course use each part of the y+ calculator independently as well.
- Use the calculated boundary layer thickness in part 2 to have a value to aim for in part 3 for the prism layer total thickness.
- How to define your prism layer mesh, dependent on your prism layer distribution mode in Simcenter STAR-CCM+.
- Make sure your transition between the prism layer mesh and the bulk mesh is smooth, by defining your base size close to the value of the last prism layer cell height.
- For the bulk mesh cells adjacent to the prism layer mesh, make sure you obtain cells with high aspect ratio by defining the surface mesh target size to the value of the last prism cell height.
What is a y+ calculator?
A y+ calculator is a way of determining the height of the first cell by the wall in a CFD simulation based on overall settings in the simulation and the desired y+ value. Since the velocity, when you use the no-slip condition to a stationary wall, is zero at the wall, but non-zero in the fluid domain, you get large gradients in the velocity field close to walls. These gradients need to be resolved, in order to get an accurate solution close to the walls. This y+ calculator will help you to determine both the first cell height at the wall, and setting all other properties for the mesh as well, to obtain a good mesh at the first try. The process of creating a mesh for CFD simulations is very delicate and several settings must harmonize. This can be an iterative and time-consuming process, but hopefully we can help you save both time and increase the overall quality of the final mesh with our y+ calculator.Description of all parts of Volupe’s y+ calculator
The calculator is divided into 4 parts (each part is described in a section below, with a picture of the default settings used on the webpage):- First cell height in prism layer
- Boundary layer thickness
- Settings for the prism layer mesher
- Transition from prism layer to bulk mesh
Boundary layer thickness – By specifying if you have boundary layer that is laminar or turbulent in your simulation, you get a value for the thickness of the boundary layer. The default values for the input parameters in this part (length downstream to evaluate and Reynolds number) are updated automatically from part 1 of the y+ calculator. The parameter length downstream to evaluate, uses characteristic length as default value. The equations that are used to determine the boundary layer thickness are based on flat plate theory. This means that the boundary layer thickness has a linear dependence of the length downstream to evaluate. If the region where you want to estimate the boundary layer thickness does not have flow similar to flow over a flat plate, this estimation will be less accurate (then it can be wise to run a test-simulation to get a better approximation of how thick the boundary layer is, and use the calculated value as input from parts 2 of the y+ calculator).The illustration to the right, in the picture below, a typical profile for laminar and turbulent boundary layer is visualized. 
Settings for the prism layer mesher – in Simcenter STAR-CCM+ there are three different distribution modes (ways of defining parameters) to specify your settings for the prism layer mesher. The same resulting mesh is possible to obtain regardless the choice of distribution mode. By defining first cell height (automatically updated to the value from part 1 in the calculator), prism layer stretching (also known as growth rate) and number of prism layers – the output is given so that you can copy the parameter values directly into your simulation software, regardless of which distribution mode you selected. You will also get the value of the height for the last prism cell, since this value can be good to know in the next step, part 4. The text in the picture below describes which parameters are required to specify, depending on which distribution mode that is selected. In the illustrations to the right the parameters are visualized. 
Transition from prism layer to bulk mesh – To get a good transition, from the prism layer mesh to the bulk mesh (mesh in the free stream), part 4 compares the last prism layer cell height (automatically updated from part 3 in the calculator) to the first cell in the bulk mesh. This train of thought can be used both for polyhedral and trimmed (hexahedral cells) meshers, but since trimmed cells are always growing by a ratio of 2 (becomes twice as large in a dimensions), there might be a “transition cell layer” of cells automatically added between the prism layer mesh and bulk mesh. This layer of cells, is difficult to predict (since it depends on where the bulk mesh cells are located relative the geometry), but will only help making the transition smoother.The illustration to the right in the picture below visualizes how the transition from a boundary prism layer mesh of polyhedral cells to a bulk mesh could look like, and how the ratio in the output is defined. 