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• W2022147517 abstract "A simple numerical method for generating wing shapes that will be shock free at a specified Mach number is described. The method involves using a fictitious gas law for the supersonic domain to make the governing equations elliptic. Requirements on this gas law are detailed and a method for computing the real flow in the supersonic domain, given initial data on the embedded sonic surface, is described. The failure of the method to yield a shock-free flow when a limit surface occurs in the supersonic flow, and the difficulties that arise because the initial-value problem for the supersonic domain is ill-posed, are delineated. Finally, a small perturbation algorithm is used to illustrate the procedure and results are given for a simple baseline wing. NCREASED fuel efficiency, and in the case of commercial aircraft, productivity, can be achieved by operating aircraft at Mach numbers, provided that shock waves can be avoided or made acceptably weak. Two-dimensional procedures for prescribing airfoil sections that are shock free have already provided improvements in aircraft efficiency by employing these airfoils on swept wings. Three-dimensional effects have compromised such designs to some extent, and extensive wind tunnel development tests have been required to recapture the benefits of these supercritical airfoils. Sobieczky et al. l demonstrated a method of modifying baseline configurations so that they would be shock free at a prescribed Mach number and lift coefficient. This procedure provides a special opportunity for improving aircraft per- formance through a careful selection of the baseline con- figuration in order to provide wings and wing-body com- binations that are shock free at Mach numbers, and that have acceptable off-design performance. Yu2 and Yu and Rubbert3 have also documented that this procedure is possible and demonstrated its application. As was first described by Sobieczky,4 a numerical algorithm is used to solve a fictitious set of equations for the flow past the baseline configuration. These equations are identical to the correct equations for subsonic portions of the flow, but they are modified when the flow becomes super- sonic, so that even though the flow speed is larger than the local speed of sound the equations themselves remain elliptic. This procedure generates a numerical solution that satisfies the appropriate equations where the flow is subsonic, and the appropriate boundary conditions on the configuration outside of the supersonic zone. The results of this calculation provide the flowfield at the sonic surface. This surface and flowfield define an ill-posed initial value problem for the supersonic domain that is to be solved using the correct equations. Because this problem is ill-posed in three dimensions any numerical method must, in principle, be unstable. This in- stability, however, is of no consequence for moderate to high aspect ratios. However, if the detailed definition of the spanwise modifications required to make the wing shock free" @default.
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• W2022147517 date "1980-10-01" @default.
• W2022147517 modified "2023-09-26" @default.
• W2022147517 title "Shock-Free Wing Design" @default.
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• W2022147517 doi "https://doi.org/10.2514/3.50865" @default.
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