Similarity of the Wall Jet Resulting from Planar Underexpanded Impinging Jets*

Wall shear stress is mapped across nozzle parameters (stand off height, jet width and nozzle pressure ratio) for two dimensional planar underexpanded impinging jets using existing wall jet similarity theory. Computational fluid dynamics is used to calculate the flow field resulting from impinging jets with height to diameter ratios of 15-30 and nozzle pressure ratios of 1.2-3.0. A wall jet power law similarity solution with source coefficients is assumed for the inner and outer layers of the wall jet. Flow field data is used to fit wall jet characteristics and determine power law exponents. Source coefficient are determined as a function of nozzle parameters using the conjugate gradient method. It is found that normalizing by momentum, rather than characteristic length or source velocity, is optimal for achieving similarity.  Power laws for momentum normalized friction velocity and half velocity wall distance as a function of momentum normalized X location are successfully developed. These power laws allow for complete mapping of wall shear stress along the impingement surface for a wide range of nozzle parameters.