Doctoral Dissertations

Date of Award

8-1995

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mechanical Engineering

Major Professor

Roy J Schulz

Committee Members

Roy Schulz, Ron Litchford, Dwayne McCoy

Abstract

Concentrated vortices are characterized by steep gradients in the velocity field and in the vorticity field. They are difficult to compute because they are strongly affected by the numerical diffusion associated with any numerical solu- tion procedure of the Navier-Stokes equations. Therefore, some special treatment for the vortical regions is needed to accurately and efficiently predict the flow in those regions.

In the present study, a numerical flow solver for the three-dimensional in- compressible Navier-Stokes equations is developed that involves a new method called "Vorticity Confinement." The method consists of adding a term to the discretized momentum conservation equations of fluid dynamics. The corrective term serves to convect vorticity back toward the center of the vortical region af- ter as it diffuses due to numerical dissipation. The confinement method allows a vortex to be numerically convected without spreading, and to maintain a fixed in- ternal structure of the vortical region. The additional term depends only on local flow variables and is zero outside the vortical regions. The discretized Navier- Stokes equation with the extra term included can be solved on a fairly coarse computational grid in connection with a standard low-order accurate numerical method, but will still lead to concentrated vortices.

In the present study, the confinement technique is embedded into a stan- dard fractional step method as the basic numerical scheme for the incompressible Navier-Stokes equations. The fractional step method with the confinement term consists of four separate steps which are executed at each time step: the computation of the convective flux term, the diffusive flux term, the confinement correction, and a solution of a Poisson equation to satisfy mass conservation. The last step provides the pressure field to enforce incompressibility. Here, an approximate factorization (AF) technique is applied for the numerical solution of the pressure Poisson equation.

The features of the Vorticity Confinement technique are first discussed for the case of a stationary, two-dimensional, axisymmetric vortex. Computations on a fixed Eulerian grid show that the solutions of the discretized Euler equations settle quickly to a fixed vorticity distribution in spite of the numerical diffusion associated with the basic flow solver.

The application of the Vorticity Confinement method to compute the flow over an aerospace plane configuration with a delta wing plan-form (ELAC-1) is then described. It is shown that the technique leads to a significant improvement of the numerical results over the unconfined solutions and to accurate solutions on a grid that would be too coarse for conventional methods. Good agreement between numerical results and experimental data is obtained over a range of values of the confinement parameter.

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