Title page for ETD etd-03022004-015240

Type of Document Dissertation
Author Muldoon, Frank Herbert
Author's Email Address fmuldoo@me.lsu.edu
URN etd-03022004-015240
Title Numerical Methods for the Unsteady Incompressible Navier-Stokes Equations and Their Application to the Direct Numerical Simulation of Turbulent Flows
Degree Doctor of Philosophy (Ph.D.)
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Sumanta Acharya Committee Chair
Dimitris Nikitopoulos Committee Member
John Tyler Committee Member
Robert Dorroh Committee Member
Arlo U. Landolt Dean's Representative
  • monotonic schemes
  • pulsed jets
  • pressure velocity coupling
  • turbulence budgets
  • wake vortices
Date of Defense 2004-01-21
Availability unrestricted
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


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