Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Aerospace Engineering


The use of the full unsteady Navier-Stokes equations to solve the flow around complex three-dimensional bodies, such as the Space Shuttle Orbiter, requires a substantial amount of computer time and storage. However, if the inviscid portion of the flow is supersonic and if there is no streamwise separation, then the three-dimensional flow field can be solved using a simplified set of equations called the parabolized Navier-Stokes equations. These simplified equations are parabolic in the streamwise direction and as a result, the solution can be marched downstream from a given initial station, thereby significantly reducing the computer time;In this study, a general parabolized Navier-Stokes equation solver is developed and the supersonic viscous flow around a flat slab delta wing and the flow around the Space Shuttle Orbiter are solved. The generalized marching scheme requires initial data which are obtained by computing the flow in the blunt nose region. This region is computed for the two problems using an axisymmetric or three-dimensional unsteady Navier-Stokes solver. The use of a generalized transformation reduces the computational region required for the three-dimensional blunt nose region and this effectively reduces the computational time required to solve the flow around the blunt nose region. An algebraic grid clustering scheme, which has a potential to be developed into a grid generation scheme, clusters the grid points around the wing-tip and wing body juncture regions and describes the Space Shuttle Orbiter body shape accurately. A simple solution surface generation scheme, outlined here, allows the user to march the solution along the most appropriate direction;The numerical solutions obtained for the two problems are compared with the available experimental data. The shock shapes, pressure coefficients and heat-transfer coefficients compare well with the experimental data at various Mach numbers and angles of incidence. Also, the parabolized Navier-Stokes solver predicts the lee-side flow field very well including the location of cross flow separation and reattachment.



Digital Repository @ Iowa State University,

Copyright Owner

Ethiraj Venkatapathy



Proquest ID


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File Size

102 pages