Boundary condition procedures for unsteady three-dimensional Euler solvers with application to propulsive nozzles
Abstract
A numerical procedure has been developed for implementing boundary conditions for three-dimensional Euler solvers for predicting the flowfields inside propulsive nozzles. The conservation form of the governing equations is solved using the MacCormack explicit finite difference method. Compatibility equations in conservative variables are developed using a simple physical approach. These equations are applied at the boundaries of the flowfield using Kentzer's method, which is based on characteristic theory, but uses a finite difference method to solve the compatibility equations. The Euler equations in both chain rule conservation law form and strong conservation law form are applied at the interior points to compare their shock capturing capabilities. Steady state solutions are obtained from the converged asymptotic solution in time. The time step increment is calculated from an approximation to the Courant-Lewy-Friedrichs stability criterion. Verification studies are conducted for a number of two-dimensional and three-dimensional flowfields for which analytical solutions or experimentally measured data are available. Several other flowfields are analyzed to demonstrate some distinctive features of the algorithm. The numerical solutions predicted by the methodology are in excellent agreement with analytical solutions and experimental data. The chain rule conservation law form of the equations appears to capture shock waves as effectively as the strong conservation law form.
Degree
Ph.D.
Advisors
Hoffman, Purdue University.
Subject Area
Mechanical engineering
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