Albert D. Harvey

Two-Equation Turbulence Modeling for Impeller Stirred Tanks

In this study, the predictive performance of six different two-equation turbulence models on the flow in an unbaffled stirred tank has been investigated. These models include the low Reynolds number k-e model of Rodi, W., and Mansour, N.N., Low Reynolds Number k-e Modeling With the Aid of Direct Simulation Data, J. Fluid Mech., Vol. 250, pp. 509-529, the high and low Reynolds number k-ω models of Wilson, D.C., 1993, Turbulence Modeling for CFD, DCW Industries, La Canada, CA., the RNG k-e model, and modified k-ω and k-e models which incorporate a correction for streamline curvature and swirl. Model results are compared with experimental laser Doppler velocimetry (LDV) data for the turbulent velocity field in an unbaffled tank with a single paddle impeller. An overall qualitative agreement has been found between the experimental and numerical results with poor predictions observed in some parts of the tank. Discrepancies in model predictions are observed in the anisotropic regions of the flow such as near the impeller shaft and in the impeller discharge region where the model overpredicts the radial velocity component. These results are discussed and a strategy for improving two-equation models for application to impeller stirred tanks is proposed.

Solution-adaptive grid procedure for high-speed parabolic flow solvers

A solution-adaptive grid procedure based bn an error equidistribution scheme is developed and applied to a parabolized Navier-Stokes solver. An improved method of selecting weighting functions is introduced that involves normalizing a combination of flowfield gradients and curvature of a number of dependent variables and then selecting the largest at each point. The scheme redistributes grid points line by line with grid point motion controlled by forces analogous to tensional and torsional spring forces with the spring constants set equal to the weighting functions. Torsional terms are functions of the grid point positions along neighboring grid lines and provide grid smoothness and stability. A grid-fitting scheme is introduced for external flows in which the number of grid points in the freestream are reduced to a minimum. Results for several problems are presented to demonstrate the improvements obtainable with the solution-adaptive grid procedure.

Solution-adaptive grid procedure for the parabolized Navier-Stokes equations

A solution-adapt ive grid procedure based on an error equidistribution principle is developed and applied to a three-dimensional parabolized Navier-Stokes solver. The scheme redistributes grid points line by line in both crossflow directions, with grid point motion controlled by forces analogous to tensional and torsional spring forces. The tensional force is proportional to the error measure or a weighting function related to the error measure. The torsional force is used to control grid skewness relative to the upstream and cross-stream coordinate lines. Weighting functions are selected by first normalizing flowfield gradients and/or curvature of a number of dependent variables and then selecting the largest at each point. The hypersonic flow over a right-circular cone at three different yaw angles is studied to demonstrate the performance of the solution-adaptive grid procedure. Pitot pressure profiles and surface pressure computed using the solution-adaptive algorithm are compared with experimental results as well as with numerical results obtained using a fixed grid. Pitot pressure predictions using the adaptive grid algorithm show better agreement with experiment than those obtained using a fixed grid.

A solution adaptive grid procedure for an upwind parabolized flow solver

A solution adaptive grid procedure based on an error equi-distribution scheme is developed and applied to a Parabolized Navier-Stokes solver. An improved method for selecting weighting functions is introduced which involves normalizing a combination of flowfield gradients and curvature of a number of dependent variables and then selecting the largest at each point. The scheme re-distributes grid points line-by-line, with grid point motion controlled by forces analogous to tensional and torsional spring forces with the spring constants set equal to the weighting functions. Torsional terms are functions of the grid point positions along neighboring grid lines and provide grid smoothness and stability. A grid-fitting scheme is introduced for external flows in which the number of grid points in the freestream are reduced to a minimum. Results for several problems are presented to demonstrate the improvements obtainable with the solution adaptive grid procedure.

Space marching calculations about hypersonic configurations using a solution-adaptive mesh algorithm

A solution-adaptive marching algorithm is developed and applied to a three-dimensional parabolized NavierStokes equation solver. The resulting algorithm obtains accurate solutions by using a spatial-marching/adaptivegrid procedure. The adaptation step redistributes grid points line by line in both crossflow directions, with grid point motion controlled by forces analogous to tensional and torsional spring forces with the tensional force proportional to the error measure or weighting functions. The solution-adaptive marching procedure is applied to the hypersonic flow about two generic aircraft configurations. The first of these is an all-body-type geometry with elliptical cross sections and is studied at angles of attack of 0, 5, and 15 deg. The second geometry is a generic blended-vv ing-body design. Results are presented that demonstrate the improvements in flow field resolution obtainable with the solution-adaptive marching procedure over conventional fixed grid techniques. Computed pitot pressure profiles obtained using the solution-adaptive algorithm show improved agreement with experimental data compared to predictions obtained using a fixed grid.

A solution-adaptive grid procedure for the three-dimensional parabolized Navier-Stokes equations

A solution-adaptive grid procedure for the three-dimensional parabolized Navier-Stokes equations is developed on the basis of the two-dimensional line-by-line solution-adaptive technique of Harvey et al. (1990). It is shown that the new adaptive grid algorithm provides improved shock resolving characteristics over the conventional flow algorithm. The adaptation process has the ability of aligning grid lines with the existing flow-field structure, yielding increasing resolution of high gradient regions.