Model for Wall Shear Stress from Obliquely Impinging Planar Underexpanded Jets

Though inclined under-expanded planar jets are used in many practical applications, the wall stress resulting from their impingement has not been adequately characterized. Reduced-order models for wall shear as a function of jet parameters have not been reported. This work uses computational fluid dynamics to determine wall shear stress as a function of the nozzle parameters and jet angle. The simulations of the impinging jet are validated against the experimental data and direct numerical simulation; then, the jet parameters are varied to formulate an empirical relationship for maximum wall shear stress as a function of a nozzle pressure ratio, standoff distance, jet Reynolds number, and impingement angle. The global expression for shear stress agrees with the numerical results within a mean deviation of 3%. The relationship can be used for applications where shear stress information is required to design or assess the performance of practical systems, such as surface cleaning, particle resuspension from the surface, and surface cooling.