Prediction of Lobed Mixer Vortical Structures with a k - e Turbulence Model

Abstract

Numerical simulations of an incompressible planar shear layer and a lobed mixer e owe eld are presented and validated against the detailed experimental measurements of McCormick and Bennett (McCormick, D. C., and Bennett, J. C., Jr., “ Vortical and Turbulent Structure of a Lobed Mixer Free Shear Layer,” AIAA Journal, Vol. 32, No. 9, 1994, pp. 1852 ‐1859). The study focused on quantifying the predictability of these e ows using the standard k‐≤ turbulence model. Simulations for the planar shear layer showed that, whereas the self-similar behavior can be captured by the model, the measured near-e eld development of the shear layer could not be reproduced in the simulations. Inconsistencies between simulations and experiments arise as a result of the Kelvin ‐Helmholtz instability that is not captured in the simulations. Predictions for the lobed mixer shear layer revealed a lag of 1 :75 lobe heights in the shear-layer development with respect to the measured data. Global parameters such as momentum thickness and streamwise circulation generally showed an underprediction of 20% and an overprediction of 65% with respect to measured values, respectively. Good prediction of the primary Reynolds shear stresses that control the variation of the momentum thickness was obtained. An analysis for the equation of the streamwise component ofvorticity revealedthattheimportantcontribution tothestreamwisecirculation decay rateisthesecondary shear stress and the normal stress anisotropy. Neither is well predicted by the k‐≤ model, leading to poorer predictions of the streamwise circulation decay rate.