Algebraic Reynolds stress modeling of planar mixing layer flows

This work investigates the ability of algebraic Reynolds stress models to predict planar mixing layer flows, including effects caused by increasing compressibility such as the reduction in mixing layer growth rate and disproportionate reduction in individual turbulent stresses which causes an increase in turbulence anisotropy. To achieve these results a new algebraic Reynolds stress model is developed from first principles with careful consideration for incorporating additional correlation terms which arise in compressible flows. A new explicit solution procedure for the Reynolds stresses is also developed using an appropriate three-term tensor basis representation for compressible flows. This new solution procedure is moderately more complicated than existing explicit solution procedures for incompressible algebraic stress models since it requires the solution of a quartic, rather than cubic, equation for one of the tensor basis coefficients. Special consideration must also be given to the treatment of specific degenerate cases which are self-correcting in the incompressible formulation. For two-dimensional incompressible flow; the new solution procedure properly reduces to that used in existing explicit algebraic stress models.; The new algebraic stress model has been calibrated against detailed experimental data for a benchmark incompressible mixing layer. To aid in this calibration an automated numerical optimization procedure was developed. This calibration yielded a new set of coefficients for the pressure-strain correlation tensor that improves the predicted incompressible mixing layer growth rate and turbulent stresses.; Recent experimental data and direct numerical simulations of compressible mixing layers indicate that the observed changes in mixing layer growth rate and turbulence anisotropy are caused by reduced pressure fluctuations. This reduced communication results in changes to the turbulent length scale and pressure-strain correlation tensor. Compressibility corrections based upon these physical mechanisms as well as explicit dilatational corrections have been examined. None of these corrections adequately predicts all of the observed changes in compressible mixing layers. However, this work shows that by combining the turbulent length scale correction with a reformulated correction factor to the pressure-strain correlation tensor better agreement with the mixing layer growth rate is achieved and simultaneous changes in the Reynolds stresses are demonstrated.