Citation
Ardalan, Kayvan (1996) Compressible vortex arrays. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd02062008091358
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
We construct steady, two dimensional, compressible vortex arrays with specified vorticity distributions. We begin by examining the effects of compressiblity on the structure of a single row of hollowcore, constant pressure vortices. The problem is formulated and solved in the hodograph plane. The transformation from the physical plane to the hodograph plane results in a linear problem that is solved numerically. The numerical solution is checked via a RayleighJanzen expansion. It is observed that for an appropriate choice of the parameters [...], the Mach number at infinity, and the speed ratio, a, transonic shockfree flow exists. Also, for a given fixed speed ratio, a, the vortices shrink in size and get closer as the Mach number at infinity, [...], is increased. In the limit of an evacuated vortex core, we find that all such solutions exhibit cuspidal behaviour corresponding to the onset of limit lines.
The hollow core vortex array corresponds to a vorticity distribution wherein the vorticity is concentrated on the vortex boundary. In the second part of this thesis, we examine vortex arrays with continuous vorticity distributions. In particular, we construct Stuarttype vortices in a channel by requiring the vorticity distribution to be an exponential function of the stream function of the flow. The problem is formulated and solved in the physical plane. The numerical solution is checked via a RayleighJanzen expansion of the unbounded Stuart vortex solution. It is shown that, in the limit of infinite speed of sound (incompressible flow), as the channel walls tend to infinity, [...] , the Stuart vortex solutions are recovered. Furthermore, it is shown that unbounded, compressible Stuart vortices exist and that a generalized Stuart vortex solution is the proper incompressible limit. For a given fixed circulation, [...], Mach number, [...], and [...], (a measure of the compactness of the vorticity distribution) it is shown that the limit of a very narrow channel, [...]0, is a parallel shear flow. Exact analytical solutions for the compressible parallel shear flow are also found in implicit form.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Applied And Computational Mathematics 
Thesis Availability:  Restricted to Caltech community only 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 September 1995 
Record Number:  CaltechETD:etd02062008091358 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd02062008091358 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  525 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  20 Feb 2008 
Last Modified:  26 Dec 2012 02:30 
Thesis Files
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