# Wall Jet Similarity of Impinging Planar Underexpanded Jets

## TL;DR

This study uses CFD to analyze wall jet profiles and shear stresses in impinging planar underexpanded jets, establishing power-law relationships that depend on nozzle parameters for better wall shear stress prediction.

## Contribution

It introduces parameterized wall jet profiles and power-law relationships based on CFD data for impinging jets with varying nozzle parameters.

## Key findings

- Wall jet profiles are incomplete self-similar with a triple-layer structure.
- Compressibility effects are negligible for Ma<0.8.
- Power-law relationships describe maximum velocity and shear stress as functions of nozzle parameters.

## Abstract

Velocity profiles and wall shear stress values in the wall jet region of planar underexpanded impinging jets are parameterized based on nozzle parameters (stand-off height, jet hydraulic diameter, and nozzle pressure ratio). Computational fluid dynamics is used to calculate the velocity fields of impinging jets with height-to-diameter ratios in the range of 15 to 30 and nozzle pressure ratio in the range of 1.2 to 3.0. The wall jet has an incomplete self-similar profile with a typical triple-layer structure as in traditional wall jets. The effects of compressibility are found to be insignificant for wall jets with Ma<0.8. Wall jet analysis yielded power-law relationships with source dependent coefficients describing maximum velocity, friction velocity, and wall distances for maximum and half-maximum velocities. Source dependency is determined using the conjugate gradient method. These power-law relationships can be used for the mapping of wall shear stress as a function of nozzle parameters.

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Source: https://tomesphere.com/paper/1812.11220