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Iterative solution of transonic flows over airfoils and wings, including flows at mach 1
Author(s) -
Jameson Antony
Publication year - 1974
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160270302
Subject(s) - transonic , airfoil , aerodynamics , mach number , subsonic and transonic wind tunnel , physics , aerospace engineering , mathematics , computer science , mechanics , engineering
at low supersonic speeds in the range from Mach 1 to 1.3 (a regime in which the sonic boom should pose no serious problem). The hodograph method of generating a o w together with the corresponding boundary shape has been perfected by Bauer, Garabedian and Korn (2). It now provides a exible tool for the design of supercritical wing sections which produce shockfree o w at a specied speed and angle of attack. Since, however, it yields no information about the o w at o design conditions, and is restricted to two dimensions, it needs to be complemented by a method for calculating the o w over specied shapes in two and three dimensions throughout the desired range of speed and angle of attack. An accurate and reliable method would eliminate the need to rely on massive wind tunnel testing, and should lead to more rational designs. Following the initial success of Murman and Cole (3), substantial progress has recently been made in the development of nite dierence methods for the calculation of transonic o ws (cf. (4), (5), (6), (7)). These methods have generally been restricted, however, either to o ws which are subsonic at innit y, or to small disturbance theories. The present paper describes a method using a new 'rotated' dierence scheme, which is suitable for the calculation of both two- and three-dimensional o ws without restriction on the speed at innit y, and which has been successfully applied to a variety of o ws over airplane wings, including the case of igh t at Mach 1. The mathematical diculties of the problem are associated primarily with the mixed hyperbolic and elliptic type of the equations and the presence of discontinuities. The computational method should be capable of predicting the location and strength of the shock waves, and if it is to be capable of distinguishing a good from a bad aerodynamic design, it should also provide an indication of the associated wave drag. In three-dimensional applications the rapid growth in the number of points in the computational lattice also excludes any method which is not rather economical in its use of the computer. In meeting these objectives the primary choices to be made concern rst the most suitable formulation of the equations, second the construction of a favorable coordinate system, and third the development of a nite dierence scheme which is stable, convergent, and also capable of accommodating the proper discontinuities.