Note on the limits to the local Mach number on an aerofoil in subsonic flow

Abstract

It has been noted in some experiments that the local Mach number just ahead of a shock wave on an aerofoil in subsonic flow is limited, values of the limit of the order of 1.4 are usually quoted. This note presents two lines of thought indicating how such a limit may arise. The first starts with the observation that the pressure after the shock will not be higher than the rain stream pressure. Fig.1 shows the calculated relation between local Mach number ahead of the shock (M„ 1 ), shock inclination (S), mainstream Mach number (M1) and pressure coefficient just aft of the shock. • (Cp) It is noted that, for given M1 , Cp and .5 ,two shocks are possible in general, a strong one for which Ms , > 1.48, and a weak one for which MS1 < 1.48, and it is argued that the latter is the more likely. The second approach is based on the fact that a relation between stream deflection (8) and Mach number for the flow in the limited supersonics regions on a number of aerofoils has been derived from some. experimental data. Further analysis of experimental data is required before this relation can be accepted as general. If it is accepted, however, then it indicates that the Mach numbers increase above unity for a given deflection is about one-third of that given by simple wave theory (Fig.2). An analysis of the possible deflections on aerofoils of various thicknesses (Fig.3) then indicates that deflections corresponding to local Mach numbers of the order of 1,5 or higher are unlikely except at incidences of the order of5 ° or more, and may then be more likely for thick wings than for thin wings. Flow breakaway will make the attainment of such high local Mach numbers less likely.