PhD Proposal by David J. Pate

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  • Date/Time:
    • Thursday December 17, 2015
      2:00 pm - 4:00 pm
  • Location: Weber Space Science and Technology Building (SST-II) Collaborative Visualization Environment (CoVE)
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Summary Sentence: A Surface Vorticity Method for Wake-Body Interactions

Full Summary: No summary paragraph submitted.

Ph.D. Thesis Proposal



 David J. Pate


(Advisor: Prof. Brian J. German)


10:00 AM, Thursday, December 17, 2015

Weber Space Science and Technology Building (SST-II) Collaborative Visualization Environment (CoVE)


A Surface Vorticity Method for Wake-Body Interactions



The objective of the proposed dissertation research is to develop a surface vorticity method for simulating high Reynolds number aerodynamic flows with strong unsteady interactions between wakes and lifting bodies. Examples of these types of flows include rotors in hover, propeller/wing installations, and impingement of vortex cores shed from wing strakes or flaps on downstream surfaces.  The proposed approach models both solid surfaces and wakes as thin shear layers represented by vortex sheets that are discretized into triangular panels with linearly varying strength. An analytical solution for the Biot-Savart integral for these panels has been developed as part of this work.

For bound vorticity on solid surfaces, the proposed approach is to solve for the surface vorticity at each panel vertex by requiring no normal flow and no divergence of vortex sheet strength.  This formulation results in an overdetermined system that is solved as a quadratic program to minimize the sum of the squared errors. The approach provides a fidelity analogous to second order source-doublet panel methods; however, a substantive advantage of the vorticity formulation is that velocity is immediately obtained from the solution and to the same order of accuracy, allowing for accurate predictions of on- and off-body streamlines. The accuracy and convergence behavior of the bound vorticity formulation have been explored by comparison to the analytical solution for potential flow around a tri-axial ellipsoid.

The evolution of wakes modeled as free vortex sheets is governed by the vorticity transport equation, which is satisfied by maintaining circulation along the edges of the triangulation as the vertices convect with the local flow velocity. This Lagrangian approach obviates the need for volume meshes, which is advantageous for modeling aerodynamics in design or flight simulation contexts. A regularization approach is implemented to limit the growth of vortex sheet surface area and to prevent curvature singularities. The regularization method is similar to that of the vortex blob method and related approaches in the field of vortex methods. At each time-step in the simulation: (1) surface vorticity is updated, (2) the velocity at each vertex is calculated, and (3) the vertices are displaced as prescribed by a Runga-Kutta integration method.  The approach has been tested with the well-known example of the evolution of a spherical vortex sheet in a uniform freestream.

Proposed work includes the development of an adaptive paneling scheme to manage refinement of the triangular mesh, implementation of a fast multipole algorithm to improve computational scalability, and formulation of an approach for shedding free vortex sheet wakes based on the unsteady Kutta condition.  The final method will be evaluated with representative engineering test cases such as a hovering rotor and wing-body-tail configurations.


Committee Members:

Prof. Brian German (advisor)

Prof. Graeme Kennedy

Prof. Lakshmi Sankar

Prof. Marilyn Smith

Additional Information

In Campus Calendar

Graduate Studies

Invited Audience
Phd proposal
  • Created By: Tatianna Richardson
  • Workflow Status: Published
  • Created On: Dec 16, 2015 - 4:23am
  • Last Updated: Oct 7, 2016 - 10:15pm