Accession Number : AD0717339

Title :   Application of the Method of Integral Relations (MIR) to Transonic Airfoil Problems. Part I. Inviscid Supercritical Flow over Symmetric Airfoils at Zero Angle of Attack.

Descriptive Note : Research and development rept.,

Corporate Author : NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER WASHINGTON D C DEPT OF AERODYNAMICS

Personal Author(s) : Tai,Tsze C.

Report Date : SEP 1970

Pagination or Media Count : 42

Abstract : The feasibility of applying the method of integral relations (MIR) to transonic flows over symmetric airfoils was studied. In order to take account of the severe transversal flow variation and still retain simplicity in computation, the method is modified so that the number of strips used may be considerably higher than the order of the polynomial which approximates the integrand. An important feature of this modification, however, is its capability to extend the free-stream boundary to 'infinity'. Using one-strip and two-strip approximations, flow equations are reduced to a set of ordinary differential equations in a cartesian coordinate system. Numerical procedures, including the treatment of the sonic point and the determination of shock location, are also formulated. The fourth-order Runge-Kutta method was used in numerical computation. The advantage of small computer capacity and time required by the method is evidenced by exploratory calculations for a symmetric circular-arc airfoil and an NACA 0012 airfoil, traveling at supercritical speeds. It is also found that in transonic airfoil problems using a cartesian coordinate system, the order of polynomial approximating the integrand in the method of integral relations should be at least second-order or higher. (Author)

Descriptors :   (*TRANSONIC AIRFOILS, TRANSONIC CHARACTERISTICS), INTEGRAL EQUATIONS, FEASIBILITY STUDIES, APPROXIMATION(MATHEMATICS), ANGLE OF ATTACK

Subject Categories : Aerodynamics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE