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Minimum Drag Profiles in Infinite Cavity Flow


Whitney, Arthur Karl (1969) Minimum Drag Profiles in Infinite Cavity Flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/QM8Z-5141.


The problem considered is that of minimizing the drag of a symmetric plate in infinite cavity flow under the constraints of fixed arclength and fixed chord. The flow is assumed to be steady, irrotational, and incompressible. The effects of gravity and viscosity are ignored.

Using complex variables, expressions for the drag, arclength, and chord, are derived in terms of two hodograph variables, Γ (the logarithm of the speed) and β (the flow angle), and two real parameters, a magnification factor and a parameter which determines how much of the plate is a free-streamline.

Two methods are employed for optimization:

(1) The parameter method. Γ and β are expanded in finite orthogonal series of N terms. Optimization is performed with respect to the N coefficients in these series and the magnification and free-streamline parameters. This method is carried out for the case N = 1 and minimum drag profiles and drag coefficients are found for all values of the ratio of arclength to chord.

(2) The variational method. A variational calculus method for minimizing integral functionals of a function and its finite Hilbert transform is introduced, This method is applied to functionals of quadratic form and a necessary condition for the existence of a minimum solution is derived. The variational method is applied to the minimum drag problem and a nonlinear integral equation is derived but not solved.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Engineering Science)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Wu, Theodore Yao-tsu
Thesis Committee:
  • Unknown, Unknown
Defense Date:27 September 1968
Funding AgencyGrant Number
Naval Ship Research and Development CenterNonr 220(51)
Record Number:CaltechTHESIS:02192016-150014870
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9568
Deposited On:22 Feb 2016 21:11
Last Modified:06 May 2024 22:53

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