An application of relaxation methods to transonic nozzle flow
An application of relaxation techniques to the solution of transonic flow in a converging - diverging nozzle is presented. The assumptions of steady, isentropic flow of a perfect gas were made. Successive line relaxation, similar to that of Garabedian and Korn, was employed in a transformed computat...
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Virginia Tech
2014
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| Online Access: | http://hdl.handle.net/10919/43932 http://scholar.lib.vt.edu/theses/available/etd-07282010-020109/ |
| Summary: | An application of relaxation techniques to the solution of transonic flow in a converging - diverging nozzle is presented. The assumptions of steady, isentropic flow of a perfect gas were made. Successive line relaxation, similar to that of Garabedian and Korn, was employed in a transformed computational plane. The potential function at interior points was obtained column by column through repeated application of the Thomas algorithm. Once the interior-point calculations were complete the values of the potential function on the boundaries were obtained by extrapolation using the wall-tangency and centerline-symmetry conditions where appropriate. A final solution was considered obtained when negligible changes were observed in the Mach number at all flow-field points from one iteration to the next.
To determine the accuracy of the method, the flow through a hyperbolic converging - diverging nozzle was calculated and the results were compared with an existing solution obtained by a series expansion method. The calculated lines of constant Mach number were in excellent agreement with the series expansion solution. The time required for this solution was faster than time-dependent and error-minimization-type solutions by more than a factor of four even though no attempt was made to optimize the computational efficiency of the program logic. === Master of Science |
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