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. The transition Reynolds Number range appears to increase with increasing Mach Number in both firing-range tests, where relatively low surface temperatures occur, and in wind-tunnel tests, where relatively high surface temperatures occur.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. Perhaps the most significant deviation from the trend expected from the stability theory is the relative insensitivity of supersonic transition to surface-temperature variation. In general, the experimental data for transition confirm the trends indicated by the stability theory. The effects of the several variables on transition are compared with the theoretically predicted effects on boundary-layer stability. New supersonic data are included from rocket flights, firing-range tests, and wind-tunnel tests. This paper presents the available data in subsonic and supersonic flow for the effects of free-stream turbulence, surface curvature, pressure gradient, surface roughness, surface temperature, and Mach Number on the transition position. It has recently been extended to compressible flows with heat transfer and with pressure gradient. This theory is, however, useful in indicating possible effects of the several variables on transition. ![]() While the theory of laminar boundary-layer stability yields the conditions necessary for instability, it does not permit prediction of the transition point. Even in subsonic flow, the effects of such variables as free-stream turbulence, surface curvature, pressure gradient, surface roughness, and surface temperature are known only qualitatively. Although the effects of compressibility on the characteristics of both laminar and turbulent boundary layers are known rather well, little information has been available as to how the transition between the two types of flow is affected by compressibility and other factors. SUMMARY: Accurate prediction of the aerodynamic characteristics of a body at high flight speeds requires knowledge of the characteristics of the existing boundary layer.
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