Energetics of a turbulent impinging jet with passive scalar transport

The heat transfer problem of a turbulent cold jet impinging orthogonally on a warm, constant-temperature, plate is investigated using direct numerical simulation. The jet is generated with a fully developed turbulent pipe flow at italic Re equals upper U Subscript b Baseline upper D divided by nu equals 5300 Re = U b D / ν = 5300 Re=Ub D / ν=5300 ( upper U Subscript b U b Ub is the mean bulk velocity, upper D D D is the pipe diameter, and nu ν ν is the kinematic viscosity of the fluid) and impinges on a solid surface located at a distance of two pipe diameters from the nozzle exit section. A confinement plate, at thermal equilibrium with the issuing jet, is located at the same height as the nozzle. The fluid is assumed to have a unit Prandtl number and the temperature is considered to be a passive scalar field. Dissimilar boundary values for the velocity and the scalar field on the impingement plate lead to large differences in the mean velocity and scalar temperature distributions. These reflect into dissimilar velocity and temperature boundary-layer growth along the impingement plate, and into dissimilar distributions of the mean friction coefficient and Stanton number in the wall jet region of the flow. An analysis of the integral balances of the total mechanical energy, viz. the sum of kinetic energy and pressure work, and the squared-scalar temperature field, upper Gamma equals theta squared divided by 2 Γ = θ 2 / 2 =θ ²/2 (here, theta θ θ represents the non-dimensional passive scalar temperature), is used to investigate the radial distribution of the thermal efficiency of the heat exchange at the impingement plate. It is shown that, at small radial distances, where the highest heat transfer rates are achieved, the mechanical power expenditure significantly exceeds the exchanged thermal power.