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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. |
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