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Unformatted text preview: Fluids Lecture 17 Notes 1. Oblique Waves Reading: Anderson 9.1, 9.2 Oblique Waves Mach waves Small disturbances created by a slender body in a supersonic ow will propagate diagonally away as Mach waves . These consist of small isentropic variations in , V , p , and h , and are loosely analogous to the water waves sent out by a speedboat. Mach waves appear stationary with respect to the object generating them, but when viewed relative to the still air, they are in fact indistinguishable from sound waves, and their normaldirection speed of propagation is equal to a , the speed of sound. V > a a V supersonic flow still air body moving at supersonic speed fixed body fixed observer m o v i n g M a c h w a v e ( s o u n d ) equivalent s t a t i o n a r y M a c h w a v e The angle of a Mach wave relative to the ow direction is called the Mach angle . It can be determined by considering the wave to be the superposition of many pulses emitted by the body, each one producing a disturbance circle (in 2D) or sphere (in 3D) which expands at the speed of sound a . At some time interval t after the pulse is emitted, the radius of the circle will be at , while the body will travel a distance V t . The Mach angle is then seen to be at 1 = arcsin = arcsin V t M which can be defined at any point in the ow. In the subsonic ow case where M = V/a < 1 the expanding circles do not coalesce into a wave front, and the Mach angle is not defined. at Vt V/a > 1 1 V/a < at Vt 1 Oblique shock and expansion waves Mach waves can be either compression waves ( p 2 > p 1 ) or expansion waves ( p 2 < p 1 ), but in either case their strength is by definition very small (  p 2 p 1  p 1 ). A body of finite thickness, however, will generate oblique waves of finite strength, and now we must distin guish between compression and expansion types. The simplest body shape for generating such waves is a concave corner, which generates an oblique shock (compression), or a convex corner, which generates an...
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 Fall '05
 MarkDrela

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