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)

**Cf**, function of Re:

(Eq. 4)

_{w}is then estimated according to the following equation:

(Eq. 5)

**U**:

_{f}(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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