A numerical procedure is presented for the solution of the transonic potential flow equation around an isolated airfoil, for the hydraulic analogy. The numerical method used was the finite difference method, appropriately modified for a mixed elliptichyperbolic system of equations. Potential flow analysis was used, since for all practical purposes, the flow is inviscid throughout the flow field, except for wake regions and boundaries. The mixed finite difference scheme has proven to be an effective technique in the solution of elliptic and hyperbolic flow problems. For conditions near the wave propagation velocity (sonic velocity), difficulties have arisen in proper solution convergence. Further research in this area is needed for successful results. The solution procedure developed has sufficient generality so that it may be applied to various airfoil profiles and flow conditions. Also, the analytical capability presented is the initial step for further computer-aided flow studies (via the hydraulic analogy) of two-dimensional gas-dynamics as applied to turbine stage development work.

Library of Congress Subject Headings

Fluid dynamics; Aerodynamics, Transonic; Nets (Mathematics); Numerical analysis

Publication Date


Document Type


Department, Program, or Center

Mechanical Engineering (KGCOE)


Karlekar, Bhalchandra


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