The Y+ Grid Spacing Calculator allows to estimate the required size of the first mesh cell near the wall in order to reach the correct y+ value.
Input Values
Ref. Length L
Ref. velocity U∞
Kinematic viscosity ν
Desired Y+
Output Values
Reynolds number Re
First Mesh cell size Δs
How to Use
Fill in the required parameters in the orange area. The parameters are unit-agnostic, check that all the values are using the same system of units. The required input parameters are reference length (e.g. a pipe’s diameter or a vehicle’s length), a reference free-stream velocity, kinematic viscosity of the fluid and desired y+ value. Output values are shown in the green area.
Background
In order to calculate the required first mesh cell’s size, the following parameters are required:
- L: reference length (e.g. a pipe’s diameter or a vehicle’s length);
- U∞: free-stream velocity;
- ν: fluid’s kinematic viscosity;
- y+: desired y+ value.
Kinematic viscosity can also be found from the following formula: ν = μ / ρ where ρ is the density, while μ is the dynamic viscosity of the fluid.
A useful list of kinematic viscosity values for common fluids can be found here.
The desired values of y+ are generally in the range of 1 to 300, according to the type of turbulence model used. As a rule of thumb, y+ values in the order of 1 should be chosen to resolve the sub-layer (e.g. required for high accuracy in force prediction), while values above 10 should be used for log-law treatment.
The calculation of the first mesh cell size near the wall is based on flat-plate boundary layer theory as described in Frank M. White’s Fluid Mechanics 5th edition.
(Eq. 2)
By using the definition of the kinematic viscosity in Eq.2:
(Eq. 3)
(Eq. 4)
(Eq. 5)
(Eq. 6)
Finally, the first mesh cell size near wall Δs is then calculated:
(Eq. 7)
Introducing Eq.4, Eq.5 and Eq.6 into Eq.7, it is possible to calculate the first mesh cell size near wall as function of the dynamic viscosity with the following equation:
(Eq. 8)
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