Maximum Wall Stress on a Smooth Flat Plate Under Planar Jet Impingement

Abstract

This paper investigates the maximum wall shear stress value τmax and its location xmax as measured on a smooth flat plate impinged upon by a normal planar jet. τmax and xmax are found to be closely related to the stagnation pressure Ps and the half-width of the mean wall pressure profile bpw. The measurements were made by two different techniques: a Stanton probe and oil film interferometry. The maximum wall shear stress location xmax is found to be independent of the jet Reynolds number. At a small nozzle-to-plate distance H≲6 Djet, xmax is related to the jet slot width as xmax≈1.1Djet. At a large nozzle-to-plate distance H≳6 Djet, the maximum wall shear stress location is related to the mean wall pressure half-width as xmax≈1.4 bpw. A new Reynolds number, referred to as the stagnation Reynolds number, is defined as Res=def2bpwPs/ρ/ν, where ρ is the fluid density and ν is the kinematic viscosity. The maximum wall shear stress is found to be strongly influenced by the stagnation Reynolds number, and the dependence as measured by Stanton probes is approximated by a power law of τmax/Ps≈0.38/Res0.38. The solution of the laminar flow equations in the Appendix gives an alternate relation for τmax, which is in better agreement with the oil film interferometry measurements. Dimensional analysis is performed to gain insight into the empirical findings.