Wall jet similarity of impinging planar underexpanded jets

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 15–30 and nozzle pressure ratio in the range of 1.2–3.0. 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 mapping wall shear stress as a function of nozzle parameters.