Channel flow utilizing parallel computation

A parallel approach to the solution of a turbulent flow problem was developed. Our approach was highly parallelized. Two-dimensional channel flow at known and unknown pressure gradient was studied. The study was divided into two phases. In phase one, fully developed channel flow at known pressure gradient was studied. The pressure gradient was considered constant and was obtained from Laufer's experimental data at Re=30,800. Reynolds stresses were modeled by using Jones and Launder's k-ε model at a low Reynolds number. The equations for turbulent mean velocity, turbulent kinetic energy and rate of dissipation were solved numerically. Data parallel computer codes were developed in the CMFortran by adapting Patankar's method SIMPLE. These codes were run on Connection Machine CM-200. The computed results for turbulent mean velocity, turbulent kinetic energy and rate of dissipation compared well with the experimental results of Laufer and the serially computed results of Kim. In phase two, developing/fully developed channel flow at unknown pressure gradient was studied. A Falkner-Skan transformation was used to get a transformed coordinate system in the developing/fully developed laminar flow zone and a physical coordinates system was used in the developing/fully developed turbulent zone. A transition point was predicted by using Michel's formula. Reynolds stresses were modeled by using Cebeci and Smith's eddy viscosity model. A computer code was developed for each zone in data parallel language CMFortran. These codes were developed and run on the Connection Machine CM-5 by adapting the Keller's Box method. Two different initial conditions were used to examine the results of these codes and to compare them to experimental results. The first initial condition was a known turbulent mean velocity profile at a specific location. Downstream development of the turbulent flow from that location was computed and found to compare well with the Comte-Ballot experimental results at Re=480,000. For the second initial condition, a uniform laminar velocity profile was used. The calculated fully developed turbulent zone at Re=30,800 compared well with the experimental results of Laufer at the same Reynolds number. The performance of both algorithms compared well to the results of the serial algorithms found in the literature. Overall, the objectives of developing an effective parallel algorithm to solve developing turbulent flow problems in a two dimensional channel on a multi-processing machine were achieved.