A Survey of Unsteady Hypersonic Flow Problems

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and values of M6 < 1) and shock expansion theory seem adequate for
two-dimensional sections and for wings with supersonic leading edges. Shock
expansion theory and the variational method should, in principle, deal
satisfactorily with slender bodies whose cross-sectlons are everywhere convex
though, in practice, there can be difficulties if the condltlons at the nose
are not given by a known solution, and if the cross-section is not circular
and the incidence is not small. At sufficiently high Mach numbers Newtonian
theory will give good results for surfaces that are convex, but it is liable
to be considerably in error on surfaces that ars concave, and on control
surfaces or flared sections lying within the shock layer of the body.
For steady conditions, experimental evidence supports these conclusions,
For unsteady conditions the evidence IS more limited. since very few direct
measurements of derivatives have been made, and the results which have been
obtained from flutter tests are inconclusive because of the experimental
uncertainties. It would seem likely from the nature of the theories that, whan
used within their limiting conditions, they would agree quite well with
experiments: but the size of the differences between measured aerodynamic
damping derivatives and calculated values suggest (as has been mentioned above)
that it may not be possible to assume a quasi-steady response of the boundary
layer to fluctuations of the external flow.
But these comparatively simple methods of analysis oannot be used,
at present, for many of the kinds of flows which are likely to ooour in
practice. In particular, they cannot be used for two-dimensional sections,
swept wings, or slender bodies, above the incidence for shook detachment; for
slender bodies where M6 < I, at large incidenoes; for blunted, thin,
two-dimensional sections and blunted slender bodies; for bluff bodies; and for
bodies on which it is neoessaly to consider interaction effects between surfaaes.
It is possible that a satisfactory semi-empirical method of analysis can be
developed for the blunted thin section and blunted slender bcdy by using a
suitable bluff body solution for the nose region combined with the shock
expansion method downstream but, in general, for most of these flows, it will
probably be necessary to use a small perturbation method for small amplitude
motions and a quasi-steady analysis for large amplitudes. Because of this,
there will necessarily be a very close relationship between the development of
unsteady analyses and the development of sultable steady analyses. It is likely
that, even when a satisfactory unsteady analysis has been developed, the need
to develop the results in a form suitable for use in flutter calculations will
remain a major problem, espeoially as flutter may involve longitudinal bend%
distortions of vehicles.
3.
The Dynamic Stability of &Personic Vehicles
The practical importanoe of unsteady flows is to be found in the
investigation of dynamic stability and flutter of vehicles and, in order to
assess the need for accuracy in the analysis of unsteady hypersonic flows, it
is necessary to have information on the stability and flutter characteristics
of the vehioles.
Dynamic stability has been investigated by extending the classical
analysis of aircraft stability to flight at very high speeds and constant
altitude, and by examining the oscillatory behaviour of vehicles in re-entry
flight. It appears that the form of the vehicle and its aerodynamic
charaotefistics at hypersonic speeds only effect the stability characteristios
in details, the qualitative behaviour being determined bY the high speed of