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An expansion fan is the resulting sound within a fluid that is flowing past the side of some solid object at supersonic relative-speed that passes a convex corner such that the stream of fluid adjacent to the side of the object is abruptly away from that side. The fluid passing the corner suddenly has the room to expand, which constitutes a disturbance at the corner. The relative motion between corner and fluid triggers the fan when the speed difference is sufficiently high that all the resulting sound-propagation is within fluid already passed by the disturbance. A particular pattern is produced in the sound propagation, a cone-shape of various air pressures, the cone expanding outward from the disturbing corner.
It is analogous to a shock wave. It propagates away from the corner, carried away by the fluid (if the fluid is moving past the object) or left behind by the object (if the object is moving through the fluid). Ludwig Prandtl and Theodor Meyer modeled it as infinitely many "low pressure" waves fanning propagating from the corner, their directions fanned out, the initial wave propagation-direction angled (Mach angle) which is determined by the fluid's relative speed as it reaches the corner along with its relative speed once it has reached the corner.