![]() When the gas passes through the shock wave, the velocity, pressure, density, and entropy of the gas abruptly change. In many theoretical studies the wave is replaced by a surface of discontinuity. ![]() Very small-of the order of the molecular mean free path. Supersonic flow: (a) along a wall with a sharp corner, (b) along a convex curved wall The thickness of such a wave can beįigure 2. A wave producing a pressure increase travels at a speed greater than the speed of sound. Waves in a gas that produce an increase in pressure propagate differently from waves that produce a decrease in pressure. In these two types of flows, which are known as Prandtl-Meyer flows, the gas parameters are constant along the straight characteristics. If, instead of forming a sharp corner, the two straight sections of the wall meet in a smooth curve (Figure 2,b), then the flow turns gradually and passes through a series of straight characteristics that start at each point of the curved section of the wall. The flow stops turning when it becomes parallel to the direction of the wall after the corner. After passing through this plane, the flow turns and expands in the angular region formed by the set of plane disturbance fronts, or characteristics, which start at the corner. The influence of the disturbances is limited by the envelope of the Mach cones, which is a plane inclined to the direction of the flow at an angle μ such that sin μ = α/v 1. In the case of a steady supersonic flow along a wall with a sharp convex corner (Figure 2,a), disturbances occur at the points on the line marking the corner. In the case of a nonuniform steady flow, the regions in which a disturbance can have an effect are bounded not by right circular cones but by conoids, or cone-shaped curved surfaces, with vertices at the given point. The two cones extend in opposite directions and have the same vertex angle. In addition, a small disturbance can have an influence at the given point O only when the source of the disturbance is located within the cone A OB, which is called the upstream Mach cone and has its vertex at O. The influence is carried downstream at a speed v > a and stays within what is known as the downstream Mach cone in Figure 1, the downstream Mach cone is indicated by COD. When a small change in pressure is produced by placing, for example, a body in a uniform supersonic flow, the influence of the disturbance cannot travel upstream. One important difference is a result of the principle that a small disturbance in a gas is propagated at the speed of sound. Supersonic gas flows have a number of qualitative differences from subsonic flows. Mach cones: (COD) downstream Mach cone, ( AOB) upstream Mach cone See Compressible flow, Fluid flowįigure 1. At a sufficient distance away, the flow field is unaffected by the presence of the body, and no discontinuity in velocity occurs. In a two-dimensional supersonic flow around a blunt body (see illustration), a normal shock is formed directly in front of the body, and extends around the body as a curved oblique shock. There is no change in the tangential velocity component across the shock. The downstream velocity component normal to any shock wave is always subsonic. Downstream of an oblique shock, the velocity may be subsonic resulting in a strong shock, or supersonic resulting in a weak shock. ![]() The velocity upstream of a shock wave is always supersonic. ![]() A normal shock is a plane shock normal to the direction of flow, and an oblique shock is inclined at an angle to the direction of flow. A Mach wave is a shock wave of minimum strength. Similarly, other properties change discontinuously across the wave. Shock waves propagate faster than Mach waves, and the flow speed changes abruptly from supersonic to less supersonic or subsonic across the wave. When a fluid at a supersonic speed approaches an airfoil (or a high-pressure region), no information is communicated ahead of the airfoil, and the flow adjusts to the downstream conditions through a shock wave.
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