Numerical Methods for the Unsteady Incompressible Navier-Stokes Equations and Their Application to the Direct Numerical Simulation of Turbulent Flows

by Muldoon, Frank Herbert

Two new methods for the efficient parallel computation of the unsteady incompressible Navier-Stokes equations are presented. Such efficient methods are desired for large scale parallel computations of unsteady turbulent flows such as Direct Numerical Simulations (DNS). The performance of the new methods has a distinct advantage over the artificial compressibility method, in that the methods exhibit robust convergence for a variety of flow problems without extensive need for tuning computational parameters. These methods and others have been implemented in a computer program designed for massively parallel computer architectures, written by the author and used to obtain all results in this work. A DNS of a film-cooling jet is performed in order to evaluate the accuracy of the modeled expressions in the k-e turbulence model. Using the results of the DNS, the terms in the exact and modeled k-e equations are computed. These terms are examined to see where the models fail for these flows. DNS budgets for k and dissipation in a film cooling jet flow are presented to provide turbulence modelers with information as to where the models used to replace the exact k-e equations need improvement for this particular type of flow. A DNS of a pulsed jet is performed to analyze the effect of external pulsing on the flow structures and the resulting mixing of the jet with the crossflow. As the problem is inherently unsteady, the key to the successful prediction of such flows is the ability to resolve the dynamics of all important flow structures resulting from the interaction of the unsteady pulsed jet with the crossflow. In the present work massless particles are released into the flow at various locations. These particles are colored by their seed locations and residence time, greatly aiding the understanding of the dynamics of the flow. A new origin for the formation of the wake vortices has been discovered for both pulsed and unpulsed jets. Pulsing is shown to drastically change the jet spreading and penetration and to increase the mixing of the jet with the crossflow. A significant asymmetry affecting primarily the wake vortices has been found for certain cases.