### Y Plus / Y+ Calculator for First Cell Wall Distance for Turbulent Flows

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02 July

Mesh near wall is very critical to capture boundary layer physics in CFD. This Y Plus / Y+ calculator gives first mesh cell height required for desired Y+ value selected based on turbulence model wall treatment.

This Y plus calculator gives first cell / grid height based on input values of free stream velocity, density and viscosity of working fluid, and a reference length. The desired wall Y+ value in the solution. These calculations are based on flat-plate boundary layer theory.

#### Y Plus / Y+ Calculator for First Cell Wall Distance

 Input Parameters Free Stream Velocity [m/s] Density [kg/m3] Dynamic Viscosity [kg/ms] Reference Length [m] Desired Y+ Value  (Help ?) Estimated Reynolds Numbers Estimated First Cell Height [mm]

##### Background Information

In CFD, there are two ways to capture the boundary layer physics of turbulent flow. The first method is to resolve the physics all the way to wall by capturing complete boundary layer. The second way is to use wall function which involves resolving certain part of boundary layer and using imperials relations to model the remaining part. Capturing or resolving means creating the necessary grid and solving flow and turbulence equations in the region. By modelling means, not creating the gird or solving the required equations, but to use some formula /imperial relations to extrapolate the values.

Above two approaches of boundary layer treatment are available in most of the CFD software like ANSYS FLUENT, ANSYS CFX, STAR CCM+. To use appropriate wall treatment, it is necessary to create mesh with required resolution including first cell height, the growth ratio and number of elements in boundary layer. The process creating the grid which satisfies wall Y+ is an iterative process. In one attempt, it’s hard to create a mesh satisfying Y+ at all locations on the wall as it depends on the boundary layer physics near the wall. So typical procedure followed is :

1. Get approximate estimate of first cell height based on average / free stream velocity
2. Create the grid with estimated first cell height, growth ration and required number of layers
3. Solve for this initial grid.
4. Check the resultant Y plus after solution
5. Identify min, max value, region where Y+ criteria is not satisfied
6. Do coarsening / refinement in the identified regions
7. Re-run the simulation

This procedure is followed until Y plus criteria is satisfied for the selected turbulence model and wall treatment. The above procedure needs estimate of distance of first cell height from wall. Once this value is calculated first time, the later adjacent could be done based on CFD simulation results.

 Turbulence Modeling for CFD By David C. Wilcox A First Course in Turbulence By Henk Tennekes and John L. Lumley Turbulent Flows By Stephen B. Pope Computational Fluid Mechanics and Heat Transfer By Richard H. Pletcher, John C. Tannehill and Dale Anderson

##### Sanket Dange

Sanket is working as a CFD engineer in CCTech. He has worked on numerous CFD projects in the filed of automobile and HVAC. He has worked as a tutor at LearnCAx and taught to students through LeanrCAx online as well as offline course modules.

Currently he is working in the field of CFD software development which is mainly based on ANSYS FLUENT. Sanket has written blogs on various topics in CFD. He also has interest in open source CFD technologies.

Sanket holds a Bachelors degree in Mechanical engineering from University of Pune.

Y Plus / Y+ Calculator for First Cell Wall Distance for Turbulent Flows - 4.8 out of 5 based on 21 votes

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