A Numerical Study of Unsteady Two-Dimensional Subsonic Compressible Base Flow
Rudy, David Henry
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https://hdl.handle.net/2142/70144
Description
Title
A Numerical Study of Unsteady Two-Dimensional Subsonic Compressible Base Flow
Author(s)
Rudy, David Henry
Issue Date
1987
Department of Study
Mechanical Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Aerospace
Abstract
In subsonic flow, the wake behind a two-dimensional body with a blunt trailing edge is dominated by a regular array of alternately shed vortices. This separated flow produces a low pressure on the base of the body, resulting in a drag component known as the base drag, which can constitute a major portion of the total drag of the body in many cases. One of the devices that has been found to reduce the base drag in wind-tunnel experiments is a trailing-edge cavity. However, the flow mechanisms responsible for this drag reduction had not been determined from the limited experimental data available. Therefore, the unsteady flow past a slender two-dimensional body with and without a trailing-edge cavity has been studied using numerical solutions of the Navier-Stokes equations.
The solution procedure utilized an explicit finite-difference scheme with second- or fourth-order accuracy in a space and second-order accuracy in time. A major element in the solution procedure was the selection of an outflow boundary condition which minimized reflections from the boundary back into the solution domain. The effectiveness of this boundary condition was demonstrated in computations of a model problem. The boundary treatment allowed the shed vortices to pass smoothly out of the computational domain without significant reflections. This solution procedure was verified in computations of subsonic flow past square and circular cylinders, for which excellent agreement was obtained between computed shedding frequencies and experimental values.
Solutions for the slender body with an unmodified base were obtained for a range of Reynolds numbers from $2.1 \times 10\sp{3}$ to $1.96 \times 10\sp{4}$, based on model length, for Mach 0.4 and 0.6 laminar flow. The computed shedding frequency was found to increase with increasing Reynolds number, asymptotically approaching a limit approximately equal to the value found in wind-tunnel experiments with the same body at higher Reynolds numbers.
For two of the flow conditions, calculations were also made for the same body with two rectangular base cavities of different depths. Comparisons with the corresponding solutions for the unmodified base showed that the cavity produced a significant reduction in the base drag. The presence of the cavity was found to have an effect on the location at which the vortices formed, the frequency at which they were shed, and the structure of the vortices in the near-wake flow. The pressure on the rear surface of the body was found to increase as the distance from the appropriate rear surface to the location of the fully-formed vortex increased.
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