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

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.