A Semi-Analytical Approach to the Integral Equation (in Terms of the Acceleration Potential) for the Linearized Subsonic, Oscillatory Flow Over an Airfoil.
Abstract
The kernel of the integral equation which describes the oscillatory flow over an airfoil has severe singularities. The mathematical questions that arise here are usually circumvented by the use of physical concepts; one concentrates, for instance, the pressures into lines, or even points and evaluates the upwash field by means of the Biot Savart law. The upwash so expressed in terms of the parameters that describe the pressure field is then matched at selected 'control' points with the upwash prescribed by the boundary conditions. One thus obtains a finite linear system of equations for the parameters describing the pressure distribution. The selection of control points contains an element of uncertainty, because the upwash field generated by a pressure distribution of the assumed character is highly singular. In the present approach the pressure distribution is again represented by a finite number of parameters and one ultimately solves a linear system of equations. But for the pressure a much smoother representation is chosen (piece-wise linear continuous functions). The upwash is then computed directly from the integral equation. Matching between the upwash distribution due to the unknown pressure distribution and that given by the boundary conditions is carried out in the average over 'upwash areas.' Such a procedure requires repeated integrations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1986
- Accession Number
- ADA167313
Entities
People
- Karl G. Guderley
Organizations
- University of Dayton