The aerodynamic problems, involving the solution of the Euler equations of motion, are presently almost exclusively solved using an Euler formulation. This requires the generation of a spatial grid over which the problem is discretized. The grid generation process adds to the complexity to the problem being solved, especially in the case of complex body-shapes with flow discontinuities, such as shock waves and sliplines. ALso, the Euler formulation is difficult to use for the aerodynamic problems of unspecified geometry. / A Lagrangian formulation permits to avoid the complexity of a grid generation while making it possible to obtain very accurate results. This Lagrangian formulation use the stream function and Lagrangian distance to represent the flow instead of the Cartesian coordinates. Thus, the streamlines become coordinate lines in the Lagrangian formulation, which can easily represent complex body-shapes and sliplines, and is also more suitable to solve complex problems involving bodies of unspecified geometry. / This method was tested and validated against several test problems of specified geometry, including the supersonic flows with shock waves in a duct with a circular arc bump and past airfoils, as well as the flow in a nozzle. The solutions obtained with this Lagrangian method were found to be very accurate, displaying a high at a computational efficiency (actually providing second-order accuracy at a computational load of a first order solution). Then, this Lagrangian method has been used to solve several aerodynamic problems with geometrically-unspecified body-shape, such as (i) the determination of the geometry of a bump corresponding to a specified pressure distribution in supersonic flow, and (ii) the design of the geometry of a supersonic nozzle, based on the reflection-suppression condition, for a specified uniform flow at exit.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.22668 |
| Date | January 1994 |
| Creators | Nasrallah, Pierre |
| Contributors | Mateescu, D. (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Engineering (Department of Mechanical Engineering.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001445173, proquestno: MM05467, Theses scanned by UMI/ProQuest. |
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