NUMERICAL DESIGN OF TRANSONIC AIRFOILS**The work presented in this paper is supported by the AEC Computing and Applied Mathematics Center, Courant Institute of Mathematical Sciences, New York University, under Contract AT(30-1)-1480 with the U. S. Atomic Energy Commission.
1971; Elsevier BV; Linguagem: Inglês
10.1016/b978-0-12-358502-8.50012-8
AutoresP. R. Garabedian, David G. Korn,
Tópico(s)Fluid Dynamics and Turbulent Flows
ResumoThis chapter discusses numerical design of transonic airfoils. It describes an inverse method of computing plane transonic flows past air foils that are not only free of shocks but also have adverse pressure gradients so moderate that no separation of the turbulent boundary layer should take place. Up-to-date existence and uniqueness theorems combine with the experimental evidence to assure that these flows are physically realistic and will occur in practice. The chapter presents the partial differential equations governing steady two-dimensional flow of an inviscid compressible fluid by numerical analysis of characteristic initial value problems for the analytic continuation of the solution into the complex domain. The finite difference scheme presented in the chapter was originally introduced to describe the detached shock wave in front of a blunt body but is actually better suited to the inverse problem of shaping air foils so as to achieve shock-free transonic flow. It is related to Bergman's integral operator method and does exploit simplifications associated with the linearity of the equations of motion in the hodograph plane.
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