A Survey of Unsteady Hypersonic Flow Problems

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mean incidence case; but, for t'he non-linear case, it represents not a speed
above which small disturbances will grow, but the size of the a, component of
s.n unstable limit cycle dscillstion for the corresponding speed. If the section
is flying at a speed corresponding to some horizontal line of the figure and
is subjected to a disturbance, the resultant motion of the wing will grow if the
amplitude of the initial disturbance is greater than the value of a, given by
the curve (and b), but it will decay if it is less.
There has been no direct experimental investigation of the results of
this non-linear analysis. In Ref. 61, where the values of Mach number would
make non-linear effects likely, some cases of limited-amplitude flutter after
a slow initial growth were experienced, and there were other oases where
finite-amplitude initial disturbances were necessary before flutter occurred, but
this behsviour could be the result of friction or structural non-linearities.
Ccmparxon of Theory and Experiment
The results available suggest that piston theoryffor sharp-nosed
sections may give predictions of flutter .ss adequate as other methods up to
M6 and Ma; this is suggested especially by the results
!?G:$gt ~$%6~fwhere ~6~ z 1.5 and ~a, et 1.7.
For blunt nose sections, it can be concluded from Goeta's results 60
that Newtonian theory may be adequate to predict flutter speed, but it can be
used only on an empirical basis; and that the Newtonian-piston theory,suggested
in Ref. 57, is likely to be no more adequate than Newtonian theory in the
simple form proposed - possibly this is because it does not take account of the
effects of the strong shock wave set up by the blunt nose, since attempts to
take account of such effects (Ref. 57 and. Fig. 49) suggest that they reduce the
flutter speed. Both theories e.re conservative in their predictions.
One point emerges from this review which is not strictly relevant to
its purpose, but which it may be useful to make. This is, that it is difficult
to assess the adequacy of aerodynamic theories for flutter analyses from
comparisons between experimental results and theoretical. predictions of flutter
speed and frequency, because of the structural uncertainties in the experimental
conditions. Greater attention needs to be paid to defining these conditions.
Such uncertainties are shown most clearly in Hanson's repor@, where the choice
of structural modes to be used in the analysis has e. considerable effect on the
agreement between theory and experiment, but it is no clear which choice is
more appropriate structurally; and in Young‘s report k, , where the level of
structural damping assumed in the analysis made a very large difference to the
agreement of theory and experiment on flutter frequency.
4.2.2 The flutter of slender configurations
It was pointed out earlier that flutter of the main structure of a
hypersonic vehicle was likely to involve chordwise bending modes of the dings,
and bending modes of the body. Information on flutter of these kinds is meagre.
The general forms of the equations involved are established in Ref. 62: for
slender bodies they are considered in Chapter 7 and for low aspect ratio lifting
surface flutter with chordwise bending modes in Chapter 8. But the aerodynamic
problems involved tare not examined. What can.be established. from the available
references is that chordwise bending modes can be important in the flutter of
low aspect ratio surfaces,
o theories must provide adequate
pictures of the pressure
and that the free-free flutter of a
slender/