The development of Gortler vortices in a curved duct

Bohyun Shin, Purdue University

Abstract

This work focuses on the numerical study of the nonlinear development of Gortler vortices in a curved duct. For the numerical simulation, a three-dimensional incompressible Navier-Stokes code has been developed using a pseudo-compressibility technique. The conservative form of the governing pseudo-compressibility Navier-Stokes equations, in local orthogonal coordinates was discretized on a Kuznetsov mesh. McCormack's explicit algorithm was used as finite difference scheme. In addition an Orr-Sommerfeld stability analysis of the pseudo-compressibility Navier-Stokes equations has been performed. The stability analysis results indicate that pseudo-compressibility stabilizes the flow, so that steady state incompressible flows can be obtained at Reynolds numbers above the actual critical value. The optimal choice of artificial wave speed was examined for the designed Navier-Stokes code. The maximum convergence rate was found to occur when the artificial wave speed was comparable to the flow speed. With the main assumptions that the undisturbed flow is two-dimensional and the disturbed flow is periodic in the spanwise direction, a spanwise periodic three-dimensional curved duct flow was modelled with symmetry boundary conditions at the sides. Computed flow field data for the modelled geometry has been compared with Rashed's measured data and analyzed to reveal the details of the vortex flow along the curved duct. The comparison of computed solutions with measured data shows the major features of the experimental flow field were reproduced by the numerical simulation. The results of a detailed analysis of the computed vortex flow data indicate that if the axial momentum is reduced sufficiently by the upstream perturbation, the adverse axial pressure gradient near the entrance of the curved bend may generate a spiral node on the concave wall. The results also indicate that as the strength of the vortices increases in the axial direction, the vortices tend to move inboard to the symmetry plane. At some point, a small reverse flow region appears near the plane of symmetry. Beyond this point the vortices tend to weaken and move away from the symmetry plane. This process may occur more than once within the duct. Moreover, the results show that the downstream development of the vortices, i.e., vortex concentration, formation of a high shear layer, and generation of downstream separations, is not caused by the generation of upstream spiral node.

Degree

Ph.D.

Advisors

Williams, Purdue University.

Subject Area

Ecology

COinS