# Dimensionless wall distance (y plus)

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A non-dimensional wall distance for a wall-bounded flow can be defined in the following way: | A non-dimensional wall distance for a wall-bounded flow can be defined in the following way: | ||

- | :<math>y^+ \equiv \frac{u_* | + | :<math>y^+ \equiv \frac{u_* \, y}{\nu}</math> |

Where <math>u_*</math> is the [[Friction velocity|friction velocity]] at the nearest wall, <math>y</math> is the distance to the nearest wall and <math>\nu</math> is the local [[Kinematic viscosity|kinematic viscosity]] of the fluid. | Where <math>u_*</math> is the [[Friction velocity|friction velocity]] at the nearest wall, <math>y</math> is the distance to the nearest wall and <math>\nu</math> is the local [[Kinematic viscosity|kinematic viscosity]] of the fluid. | ||

<math>y^+</math> is often refered to simply as ''y plus'' and is commonly used in boundary layer theory and in defining the [[Law of the wall|law of the wall]]. | <math>y^+</math> is often refered to simply as ''y plus'' and is commonly used in boundary layer theory and in defining the [[Law of the wall|law of the wall]]. | ||

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+ | == Estimation of y plus == | ||

+ | |||

+ | The following online tools can be used to estimate the necessary grid spacing in order to obtain a desired y plus: | ||

+ | |||

+ | *[http://www.cfd-online.com/Tools/yplus.php Y+ Wall Distance Estimation] | ||

+ | : A y+ wall distance estimation script provided by CFD Online. Uses the free-stream velocity and gas-data to estimate the wall distance needed to obtain a desired y+ value at a certain boundary layer length. This is one of those wonderful little tools that saves you from learning a formula! | ||

+ | |||

+ | *[http://geolab.larc.nasa.gov/APPS/YPlus/ Viscous Grid Spacing Calculator] | ||

+ | :A JavaScript that helps you to estimate at what normal distance from a wall you should place your first grid-line. Variants suitable for compressible flow using total conditions and Mach number also available. | ||

[[Category:Dimensionless parameters]] | [[Category:Dimensionless parameters]] |

## Revision as of 21:36, 12 June 2011

A non-dimensional wall distance for a wall-bounded flow can be defined in the following way:

Where is the friction velocity at the nearest wall, is the distance to the nearest wall and is the local kinematic viscosity of the fluid.

is often refered to simply as *y plus* and is commonly used in boundary layer theory and in defining the law of the wall.

## Estimation of y plus

The following online tools can be used to estimate the necessary grid spacing in order to obtain a desired y plus:

- A y+ wall distance estimation script provided by CFD Online. Uses the free-stream velocity and gas-data to estimate the wall distance needed to obtain a desired y+ value at a certain boundary layer length. This is one of those wonderful little tools that saves you from learning a formula!

- A JavaScript that helps you to estimate at what normal distance from a wall you should place your first grid-line. Variants suitable for compressible flow using total conditions and Mach number also available.