A STEADY AND OSCILLATORY KERNEL FUNCTION METHOD FOR INTERFERING SURFACES IN SUBSONIC, TRANSONIC AND SUPERSONIC FLOW ( GENERAL DYNAMICS CORP. ) Interest has grown considerably in aircraft designed to operate ef- ficiently 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 the- ory cannot account for this phenomenon and finite difference approaches of- ten require extremely costly amounts of computer time. This computer pro- gram was developed to provide an analysis method based on a kernel func- tion technique which uses assumed pressure functions with unknown coeffi- cients. With this technique, generalized forces can be calculated in un- steady 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 un- changed. 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 su- personic components with imbedded shocks is treated as an array of general aerodynamic lifting surface elements. Each element is allowed to have mu- tual 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 experimen- tally or by a finite difference technique. The solution proceeds in a man- ner identical to ordinary aerodynamic interference methods based on a col- location technique. The unknown pressure function is assumed to be com- posed of a series of polynomials weighted by a user selected weighting func- tion that is characteristic of each lifting surface. The non-planar ker- nel function is computed using a Mach number and a reduced frequency deter- mined from values at a downwash control point. To link subsonic and super- sonic linear theory solutions, it is assumed that the appropriate Mach num- ber 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 pro- cedure becomes a problem of testing the Mach number of the downwash point. If the downwash point is supersonic, the self-induced downwash and all in- terference 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 dou- blet 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. 1 This program is written in FORTRAN IV and has been implemented on the CDC CYBER 175 computer with a central memory requirement of approximately 111K (octal) of 60 bit words. The program is overlayed to reduced core re- quirements. The program was developed in 1976. COSMIC, and the COSMIC logo are registered trademarks of the National Aeronautics and Space Administration. All other brands and product names are the trademarks of their respective holders. LANGUAGE: FORTRAN IV MACHINE REQUIREMENTS: CDC CYBER 70 SERIES PROGRAM SIZE: APPROXIMATELY 5,948 SOURCE STATEMENTS DISTRIBUTION MEDIA: 9 Track 1600 BPI EBCDIC Card Image Format Magnetic Tape PROGRAM NUMBER: LAR-12524 DOMESTIC - DOCUMENTATION PRICE: $33.00 PROGRAM PRICE: $500.00 INTERNATIONAL - DOCUMENTATION PRICE: $66.00 PROGRAM PRICE: $1000.00 2