The effect of the induced potential flow on plane turbulent wall jets

Abstract

Abstract Considered is the plane turbulent jet issuing from an orifice in a lateral wall and propagating along a base wall. Both walls are assumed to be plane and very large. The inclination angle of the lateral wall with respect to the base wall is a parameter, with the particular value $$\pi /2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> representing a lateral wall normal to the base wall and the value $$\pi$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> characterizing the absence of a lateral wall. The Reynolds number of the jet is assumed to be very large, and distances from the orifice are considered that are sufficiently large to neglect the influence of the details of the flow at the orifice. The entrainment of fluid into the jet gives rise to an outer potential flow, which is determined by representing the slender jet as a plane sink sheet. The coupling between the jet flow and the potential flow is taken into account by applying local scaling laws in terms of the slowly varying momentum flow of the jet. Accounting for the contributions of both the entrainment of momentum and the wall shear stress to the decay of jet momentum flow leads to an ordinary differential equation that can be solved in closed form. Main flow quantities such as the spreading rate of the jet and the maximum flow velocity in a cross section are then determined as functions of the jet momentum flow. Favorable comparisons with available experimental data confirm the analysis.