Citation
O'Pray, John Edwin (1970) A semiinverse design technique for leading edge slats. Engineer's thesis, California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd03312009144546
Abstract
A design technique for analytically generating a leading edge slat which will induce the modulating field required to match a specified pressure distribution on the nose of an elliptical airfoil was developed. This planar potential flow solution can be readily generalized to the design of slats to prevent boundarylayer separation at the nose of an arbitrary airfoil. The technique is described as semiinverse because the singularity representation for the slat is constrained so that only realistic slat shapes will be generated.
The elliptical airfoil is mapped to a halfplane. In this domain, the slat is represented by a finite series of distributed singularities on an inclined chord line which is placed along a zero order nose flow streamline. These distributed singularities correspond to the singular and regular camber and thickness modes of thin airfoil theory. A suitable slat chord location in the halfplane is selected by examination of the distribution of the specified modulating velocity. For a fixed slat location, the slatinduced velocity field can be written explicitly in terms of the unknown series coefficients. A least squares matching to the specified modulating field is used to select the coefficients. The velocity distribution along the chord line is integrated to determine the slat surface streamlines which are then transformed back to the ellipse plane.
The digital computer program for the semiinverse solution can be executed rapidly. Once an appropriate slat chord location in the halfplane has been selected, an accurate matching of the specified pressure distribution on the airfoil can be achieved. The airfoil nose flow calculated by the semiinverse solution agrees very closely with the flow computed by the DouglasNeumann direct solution for the same slat geometry.
The airfoil nose flow is very sensitive to the distribution of camber and thickness along the chord line. In some test cases, a modified semiinverse solution was required in which the minimum acceptable slat thickness was prescribed and a restricted inversion solution was conducted to select the camber mode coefficients required to match the specified modulating field. For a thin airfoil with a severe nose suction peak, a small, thin, highlycambered slat which is located close to the airfoil nose is desirable.
Item Type:  Thesis (Engineer's thesis) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Aeronautics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  29 May 1970 
Record Number:  CaltechETD:etd03312009144546 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd03312009144546 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1233 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  01 Apr 2009 
Last Modified:  26 Dec 2012 02:36 
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