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# f17_sp - Fluids – Lecture 17 Notes 1 Oblique Waves...

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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 ﬂow will propagate diagonally away as Mach waves . These consist of small isentropic variations in ρ , 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 normal-direction 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 μ of a Mach wave relative to the ﬂow 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 2-D) or sphere (in 3-D) 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 μ = arcsin = arcsin V t M which can be defined at any point in the ﬂow. In the subsonic ﬂow 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 µ 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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f17_sp - Fluids – Lecture 17 Notes 1 Oblique Waves...

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