Scaling of Convective Heat Transfer in Laminar and Turbulent Wall Jets With Effects of Freestream Flow and Forcing

Abstract

Despite its importance as a canonical two-dimensional flow, the laminar wall jet has not been extensively studied using modern computational fluid dynamic methods. The plane laminar wall jet with a specified velocity profile at the jet exit is numerically investigated. In these types of flows in which the flow field evolves to its self-similar behavior, the location of the dimensionless hydrodynamic virtual origin is carefully investigated and expressed as a function of Reynolds number for uniform and parabolic jet profiles. The local skin friction coefficient is observed to converge to the analytical self-similar solution at downstream locations. Since no analytical solution exists for the temperature field in either the developing or self-similar regions of this problem, the thermal solution is investigated for both isothermal and isoflux boundary conditions at the wall. The dimensionless thermal virtual origin is correlated as a function of Reynolds number. The Nusselt number dependence on Prandtl number, Reynolds number and the downstream location are obtained for both jet profiles and wall boundary conditions.The turbulent wall jet is experimentally investigated for jet Reynolds number varying between 6000 and 10000. The effect of the free stream on the wall jet film cooling effectiveness and on the local heat transfer are investigated for blowing ratio varying between 2.4 to infinity. The local Nusselt number dependence on Reynolds number and on the downstream location is identified and the obtained results are correlated for the various considered blowing ratios. The forcing effect reveals a dramatic reduction in the film cooling effectiveness which is more pronounced in the absence of a free stream flow. The Nusselt number decreases with increasing forcing amplitude and frequency in the vicinity of the jet exit, however, at further downstream locations an inflection point is observed in the Nusselt number decay with the streamwise direction which results in a larger Nusselt number value than the one observed in the unforced case. The inflection point is not seen in the presence of a free stream flow.