Theoretical Study of the Transonic Lift of a Double-Wedge Profile with Detached Bow Wave
Abstract
A theoretical study is described of the aerodynamic characteristics at small angle of attack of a thin, double-wedge profile in the range of supersonic flight speed in which the bow wave is detached. The analysis is carried out within the framework of the transonic (nonlinear) small-disturbance theory, and the effects of angle of attack are regarded as a small perturbation on the flow previously calculated at zero angle. The mixed flow about the front half of the profile is calculated by relaxation solution of a suitably defined boundary-value problem for the transonic small-disturbance equation in the hodograph plane (i.e., the Tricomi equation). The purely supersonic flow about the rear half is found by an extension of the usual numerical method of characteristics. Analytical results are also obtained, within the framework of the same theory, for the range of speed in which the bow wave is attached and the flow is completely supersonic. The calculations provide, for vanishingly small angle of attack, the following information as a function of the transonic similarity parameter: (1) chordwise lift distribution, (2) lift-curve slope, and (3) position of center of lift. As in previous studies, the aerodynamic characteristics of a profile of given thickness ratio show little variation with free-stream Mach number as the Mach number passes through 1. As the Mach number is increased to higher values, however, the lift-curve slope rises to a pronounced maximum in the vicinity of shock attachment and then declines. Correspondingly, the center of lift moves forward toward the leading edge and then returns aft. These findings are in marked contrast to the behavior of the drag coefficient at zero angle of attack, which was found in earlier work to decrease monotonically as the Mach number increased above 1. At Mach numbers above that for shock attachment, the results of the present calculations tend toward those given by classical linear theory.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1952
- Accession Number
- ADA377049
Entities
People
- Cleo B. Wagoner
- Walter G. Vincenti
Organizations
- National Aeronautics and Space Administration