( GENERAL DYNAMICS CORP. )

Interest has grown considerably in aircraft designed to operate efficiently in the high subsonic regime. This interest has increased the need for better unsteady transonic aerodynamic analysis techniques so that flutter and dynamic response characteristics can be accurately predicted in this flow regime. The characteristic of transonic flow which causes the greatest difficulty when attempting to apply uniform flow theory to such problems is the presence of shocks imbedded in the flow. Linear theory cannot account for this phenomenon and finite difference approaches often require extremely costly amounts of computer time. This computer program was developed to provide an analysis method based on a kernel function technique which uses assumed pressure functions with unknown coefficients. With this technique, generalized forces can be calculated in unsteady flow and pressure distributions can be obtained in both steady and unsteady flow. Once the aerodynamic matrices are computed and inverted, they may be saved and used on subsequent problems at very little cost as long as Mach number, reduced frequencies, and aerodynamic geometry remain unchanged. This method should be very useful for design applications where the structural mode shapes change continually due to structural changes and payload variations but the aerodynamic parameters remain constant.

In this program, a wing over which the flow has mixed subsonic and supersonic components with imbedded shocks is treated as an array of general aerodynamic lifting surface elements. Each element is allowed to have mutual interference with the other elements. Each element is assigned the appropriate Mach number and its downwash modified accordingly. The Mach number distribution and shock geometry may be obtained either experimentally or by a finite difference technique. The solution proceeds in a manner identical to ordinary aerodynamic interference methods based on a collocation technique. The unknown pressure function is assumed to be composed of a series of polynomials weighted by a user selected weighting function that is characteristic of each lifting surface. The non-planar kernel function is computed using a Mach number and a reduced frequency determined from values at a downwash control point. To link subsonic and supersonic linear theory solutions, it is assumed that the appropriate Mach number for computing downwash at a point is the Mach number at that point and that the reduced frequency is modified according to the local velocity such that the physical frequency is held constant. Thus, the computation procedure becomes a problem of testing the Mach number of the downwash point. If the downwash point is supersonic, the self-induced downwash and all interference effects at that point are computed with the supersonic kernel function. Likewise, if the downwash point is subsonic, the subsonic kernel function is used. The presence of a normal shock is simulated by a line doublet which represents the load induced by shock movement. The appropriate steady or unsteady normal shock boundary conditions are satisfied across the shock along the surface of the wing. The computed aerodynamic matrices may be saved on magnetic tape for use in subsequent analyses.

This program was released by NASA through COSMIC as LAR-12524. The italicized text above is from the official NASA release.

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