( 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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