Simulation of Supersonic Flow about a Circular CylinderSimulation of Homogeneous, Compressible Turbulence

David H. Porter, Paul Woodward, and Sarah Anderson
University of Minnesota &
Army High Performance Computing Research Center, Minneapolis, MN
Annick Pouquet
Observatoire de la Cote D'Azur, Nice, France

Research Objective: To perform computational experiments which result in data sets describing the time development of homogeneous, compressible turbulence in detail, so that the predictions of various turbulence closure models can be compared with this data.

Methodology: The PPM gas dynamics code was used to simulate the development and self-similar decay of the compressible turbulence which results from the stirring of a gas with smooth velocity perturbations of fairly large amplitude (Mach 1 rms velocities). Periodic boundary conditions and cubic uniform grids of 512 and 1024 computational zones on a side were used. These very fine grids, in fact, the largest ever employed in any fluid dynamical simulation, were used in order to resolve features in the turbulent flow which are influenced neither by the periodic boundary conditions nor by viscosity. PPM approximates the inviscid Euler equations, and therefore viscous effects, which occur due to numerical viscosity, are minimal over a large range of length and time scales in these flows. In order to study the coherent structures of the turbulence in the "Kolmogorov inertial range," the simulation data was filtered in order to average over the small scale features. The billion-zone turbulence simulation, was performed through a collaboration with Silicon Graphics, who built a special hardware configuration for this project, the first "Challenge Array," in their manufacturing facility in Mountain View, California.

Accomplishments: A detailed data set was obtained from this computer simulation which describes a true Kolmogorov inertial range flow, uncontaminated by effects of boundary conditions or viscosity and uninfluenced by prior assumptions about the character of this turbulence. This data set was obtained in September, 1993, but analysis and visualization of this data has required over a year. The first glimpses at the vorticity structures in the Kolmogorov inertial range indicate that vortex tube structures are much shorter and much more strongly distorted than in the near dissipation range, the only range observed in previous computer experiments. With the wide range of scales in the Kolmogorov range which was produced in this work, strong quantitative evidence was found indicating that the well-known phenomenon of vortex stretching is indeed in operation, producing the turbulent cascade.

Significance: The phenomenon of compressible fluid turbulence is of fundamental importance in a wide variety of contexts. It plays a role in the wakes and boundary layers of aircraft, missiles, and projectiles in flight, in mixing regions of air and combustible material in reactive flows, in mixing layers near unstable material interfaces in laser fusion applications, and in environmental fluid dynamics of atmospheric storms and of fluid mixing in rivers and estuaries. Improving turbulence models is of fundamental importance to progress in all these areas of interest.

Future Plans: The dynamical evolution of our turbulent flow will be compared with the evolu-tion predicted by different turbulence closure models, in particular, the popular k-epsilon model. The billion-zone turbulence simulation will also be carried out further in time in the coming year. We are also beginning to experiment with continuously driven turbulent flows.

[icon]Vorticity of homogenous, compressible turbulence