The lag RST turbulence model applied to vortical flows

Matthew John Churchfield, Purdue University

Abstract

The subject of this work is the application of Olsen and Coakley’s Reynolds stress relaxation turbulence model, which they call the lag Reynold stress transport (RST) model, to wingtip vortex flows. The lag RST model is meant for general non-equilibrium turbulent flows, and has not been applied to vortical flows before this work. Such a model relaxes the Reynolds stresses toward their equilibrium value, determined by the Boussinesq approximation, at a rate depending on a model constant, α0, multiplied by the specific dissipation rate of the turbulence, ω. The α 0 constant can be adjusted to vary the rate at which the Reynolds stress tensor relaxes toward its equilibrium value. It performs this relaxation by solving for the equilibrium Reynolds stresses using Wilcox’s k-ω model, but then uses a relaxation equation to solve for the actual Reynolds stress tensor. The lag RST turbulence model allows the principal axes of the Reynolds stress tensor to be misaligned with those of the mean strain rate tensor, something linear eddy viscosity models cannot do, but something that occurs in actual vortical flows. The lag RST model is used with the Reynolds-averaged Navier-Stokes (RANS) equations to compute a one-dimensional, time-varying, line vortex with axial flow, called the q-vortex. Direct numerical simulation (DNS) data is available for comparison. Also, a modified version of the OVERFLOW code is used to solve the RANS and lag RST model equations in a three-dimensional wingtip vortex flow, for which there is experimental data. This work shows that computations performed with the lag RST model have a mean flow in much better agreement with the DNS or experimental data than those performed with the k-ω model, the lag RST model’s base. In fact, the lag RST model performs equally or better in this these flows than the well performing Spalart-Allmaras model with a correction for streamline curvature and rotation. As the lag parameter α0 is decreased, the amount of misalignment between the principal axes of the Reynolds stress and the mean strain rate tensors increases (which also results in an increased misalignment between the contours of the Reynolds shear stress components and those of their corresponding strain rate components), and the peak magnitude of the Reynolds stresses is decreased. In these vortex flows, values of α0 that provide the correct amount of misalignment between the principal axes of the Reynolds stress and the mean strain rate tensors predict too small of peak values of Reynolds stresses. There is currently no way to independently control the misalignment and the Reynolds stress magnitudes. The lag RST model also does not properly predict the growth and decay rates of turbulence in the q-vortex, no matter which value of α0 is chosen. Although it has some flaws, its performance in predicting vortical flows is very good and could be a useful tool in the study of wingtip vortices. However, improvement of the model should be pursued. An outline for modifications that should be explored to improve the model’s performance is included in this thesis. These modifications focus on replacing the model constant α 0 with a variable parameter and on the possibility of replacing the lag time scale, which is the specific dissipation rate of turbulent kinetic energy, ω, with a more relevant time scale that incorporates the mean flow.

Degree

Ph.D.

Advisors

Blaisdell, Purdue University.

Subject Area

Aerospace engineering

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