Similarity Solutions for Plane and Radial Jets Using a k-ε Turbulence Model

Abstract

When the eddy viscosity is defined by the standard k-ε turbulence model, the equations governing self-similar incompressible plane and radial jets have a solution that is not analytic at the jet edge. A transformation that stretches the similarity variable simplifies the defining set of ordinary differential equations and makes them amenable to efficient numerical integration. Highly resolved solutions for the velocity, turbulent kinetic energy and dissipation rate profiles are tabulated and entrainment, velocity decay rate and growth rate are determined. The growth rate differs by 6 percent from a parabolic marching asymptotic solution to the full partial differential equations.