Title:
A Riemannian Geometric Mapping Technique for Identifying Incompressible Equivalents to Subsonic Potential Flows

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dc.contributor.advisor Mavris, Dimitri N.
dc.contributor.author German, Brian J. en_US
dc.contributor.committeeMember McMichael, Jim
dc.contributor.committeeMember Jagoda, Jechiel I.
dc.contributor.committeeMember Sankar, Lakshmi N.
dc.contributor.committeeMember Stephen, Ruffin
dc.contributor.department Aerospace Engineering en_US
dc.date.accessioned 2007-05-25T17:43:00Z
dc.date.available 2007-05-25T17:43:00Z
dc.date.issued 2007-04-05 en_US
dc.description.abstract This dissertation presents a technique for the solution of incompressible equivalents to planar steady subsonic potential flows. Riemannian geometric formalism is used to develop a gauge transformation of the length measure followed by a curvilinear coordinate transformation to map a subsonic flow into a canonical Laplacian flow with the same boundary conditions. The method represents the generalization of the methods of Prandtl-Glauert and Karman-Tsien and gives exact results in the sense that the inverse mapping produces the subsonic full potential solution over the original airfoil, up to numerical accuracy. The motivation for this research was provided by the analogy between linear potential flow and the special theory of relativity that emerges from the invariance of the wave equation under Lorentz transformations. Whereas elements of the special theory can be invoked for linear and global compressibility effects, the question posed in this work is whether other techniques from relativity theory could be used for effects that are nonlinear and local. This line of thought leads to a transformation leveraging Riemannian geometric methods common to the general theory of relativity. The dissertation presents the theory and a numerical method for practical solutions of equivalent incompressible flows over arbitrary profiles. The numerical method employs an iterative approach involving the solution of the incompressible flow with a panel method and the solution of the coordinate mapping to the canonical flow with a finite difference approach. This method is demonstrated for flow over a circular cylinder and over a NACA 0012 profile. Results are validated with subcritical full potential test cases available in the literature. Two areas of applicability of the method have been identified. The first is airfoil inverse design leveraging incompressible flow knowledge and empirical data for the potential field effects on boundary layer transition and separation. The second is aerodynamic testing using distorted models. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/14623
dc.publisher Georgia Institute of Technology en_US
dc.subject Grid generation en_US
dc.subject Coordinate transformations en_US
dc.subject Gauge transformations en_US
dc.subject Flow similarity en_US
dc.subject Relativistic fluid dynamics en_US
dc.title A Riemannian Geometric Mapping Technique for Identifying Incompressible Equivalents to Subsonic Potential Flows en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Mavris, Dimitri N.
local.contributor.author German, Brian J.
local.contributor.corporatename Daniel Guggenheim School of Aerospace Engineering
local.contributor.corporatename Aerospace Systems Design Laboratory (ASDL)
local.contributor.corporatename College of Engineering
local.relation.ispartofseries Doctor of Philosophy with a Major in Aerospace Engineering
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