Theoretical aerodynamics of jets in ground effect. Phase 5: Asymptotic theory of turbulent wall jets

This report presents a systematic analysis of two dimensional and radial turbulent wall jets using the method of matched asymptotic expansions. The asymptotic solution is carried out in two stages. The first is based on a two parameter expansion of the full Reynolds averaged equations with a k-epsilon model of turbulence quantities. One of the small parameters, gamma, is related to the nondimensional friction velocity, U sub T, defined by the surface shear stress. It is basically a Reynolds number parameter, gamma = 0 (1n Re)-1, that primarily controls the shear stress effects induced by the wall. The other small parameter, alpha, is related to the modeling constants arising in the chosen turbulence closure. In the present k-epsilon model analysis alpha is identified with the constant, C sub u, appearing in the eddy viscosity formula for the Reynolds shear stress and is a measure of the turbulence levels in the outer free jet part of the flow. The alpha expansion reduces the problem to a classical boundary layer formulation to lowest order. The expansion for gamma approaching 0 leads to a four layer description of the wall jet. The outer layer is closely related to a free jet flow while the innermost layer is a classical law of the wall region. Two additional intermediate layers are needed to effect the matching of the outer and inner layers and to complete the solution. Leading order solutions for each layer are presented and the composite flow field result is compared with an existing numerical solution for the wall jet.