Turbulent Plane Wall Jet Flows: A Numerical Benchmark

Abstract

Abstract The paper investigates the turbulent flow generated by a wall jet. A numerical benchmark of six turbulence closures including two-equation and seven-equation models in their high- or low-Reynolds number formulations, is performed. The Standard <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k hyphen epsilon" display="inline" overflow="scroll"> <mml:mi>k</mml:mi> <mml:mtext>-</mml:mtext> <mml:mi>ε</mml:mi> </mml:math> , Realizable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k hyphen epsilon" display="inline" overflow="scroll"> <mml:mi>k</mml:mi> <mml:mtext>-</mml:mtext> <mml:mi>ε</mml:mi> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k hyphen omega" display="inline" overflow="scroll"> <mml:mi>k</mml:mi> <mml:mtext>-</mml:mtext> <mml:mi>ω</mml:mi> </mml:math> SST, the linear and quadratic pressure-strain Reynolds Stress Models (RSM) and RSM based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega" display="inline" overflow="scroll"> <mml:mi>ω</mml:mi> </mml:math> available within Ansys Fluent 2023R2 and OpenFOAM v11 are systematically compared with reference experimental data available from the literature for the jet Reynolds number of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R e Subscript j Baseline equals 9,600" display="inline" overflow="scroll"> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>e</mml:mi> <mml:mi>j</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>9,600</mml:mn> </mml:math> . Generally, the specific dissipation rate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega" display="inline" overflow="scroll"> <mml:mi>ω</mml:mi> </mml:math> appears to be a better candidate than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="epsilon" display="inline" overflow="scroll"> <mml:mi>ε</mml:mi> </mml:math> to determine the length scale of the turbulence for this particular configuration. Thus, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k hyphen omega" display="inline" overflow="scroll"> <mml:mi>k</mml:mi> <mml:mtext>-</mml:mtext> <mml:mi>ω</mml:mi> </mml:math> SST and RSM- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega" display="inline" overflow="scroll"> <mml:mi>ω</mml:mi> </mml:math> models perform better than the others to predict the wall jet spreading rate, maximum Reynolds number or friction coefficient. The linear pressure-strain RSM fails to predict the mean streamwise velocity profile, exhibiting a large deficit in the log region. A budget analysis of the turbulence kinetic energy transport equation is also performed for the low-Reynolds number models. The intriguing behavior of the linear pressure-strain RSM is confirmed by the production term’s profile, which peaks earlier than the other models at about <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="y Superscript plus Baseline asymptotically equals 5" display="inline" overflow="scroll"> <mml:msup> <mml:mi>y</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>≃</mml:mo> <mml:mn>5</mml:mn> </mml:math> . Overall, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k hyphen omega" display="inline" overflow="scroll"> <mml:mi>k</mml:mi> <mml:mtext>-</mml:mtext> <mml:mi>ω</mml:mi> </mml:math> SST model can be recommended because it offers a good trade-off between accuracy and computational efforts.