Evaluation of Modified Two-Equation Turbulence Models for Jet Flow Predictions

Abstract

Three two-equation turbulence models developed specifically to improve prediction of jet flowfields are investigated. These models are the Tam-Ganesan k-" formulation, a standard k-" model with modification for heated jets referred to as the PAB temperature correction, and a standard k-" model employing variable diffusion for the k and " equations. Two standard two-equation models are also investigated for comparison with the modified formulations. The standard models are the Chien k-" and Menter shear stress transport formulations. All of the models were investigated for a reference nozzle producing heated and unheated jets at a low acoustic Mach number of 0.5 to avoid complications of large compressibility effects. The primary deficiency of the standard models was the delayed initial jet mixing rate. All of the modified turbulence model formulations provided improved mean flow predictions relative to the standard models. The improved mixing rate enabled by the Tam-Ganesan model and the variable diffusion correction resulted from increased turbulent diffusion enabled by both models. The TamGanesan model and PAB temperature correction improved predictions of mean axial velocities for the heated jet, but did not improve prediction of the calculated turbulent kinetic energy fields.Nomenclature a = speed of sound D = jet exit diameter k = turbulent kinetic energy L t = turbulent length scale M a = acoustic Mach number M t = turbulent Mach number Pr t = turbulent Prandtl number r = distance to centerline S ij = normalized rate-of-strain tensor T g = normalized stagnation temperature gradient T t = stagnation temperature t = time U jet = jet exit velocity u j = velocity tensor X = vortex stretching invariant x j = position tensor " = turbulent dissipation rate " s = solenoidal turbulent dissipation rate = dynamic viscosity = density contribution to the eddy viscosity T = total eddy viscosity, Tam-Ganesan model t = eddy viscosity = density ij = turbulent shear stress tensor = vorticity magnitude ! = specific turbulent dissipation rate ! ij = normalized rotation tensor

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