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National Advisory Committee for Aeronautics, Technical Notes - Considerations on the Effect of Wind Tunnel Walls on Oscillating Air Forces for Two Dimensional Subsonic Compressible Flow

This paper treats the effect of windetunnel walls on the oscillating
two-dimensional air forces in a compressible medium. The walls are simur
lated by the usual method of placing images at appropriate distances
above. and below the wing. An important result shown is that, for certain
conditions of wing frequency, tunnel height, and Mach number, the tunnel
and wing may form a resonant system so that the forces on the wing are
greatly changed from the condition of no tunnel walls. It is pointed
out that similar conditions exist for three—dimenSional flow in circular
and rectangular tunnels and apparently, within certain Mach number ranges,
in tunnels of nonuniform cross section or even in open tunnels or jets.

The understanding of flutter and other nonsteady phenomena requires
a knowledge of the associated unsteady flow. In the underlying theories
of unsteady flow, such assumptions as small displacements,'1inearizations,
and an inviscid fluid are made in order to obtain workable and usable
results. When it is necessary to investigate the effect of these assump—
tions on analytical results by measurements of the forces and moments on '
an oscillating wing in a wind tunnel or to treat cases that do not con—
form to theory, the question of the effect of the tunnel walls naturally
arises. In the case of steady flow the problem of the effect of tunnel .
walls is more or less classic and has been treated' by many investigators.
In general, these investigators have been able to obtain relatively simple
factors which can be used to modify measurements of the air forces on a
wing in a tunnel to correspond to free-air conditions.- The extension
of the results to compressible flow presents no‘difficfilties since the
results for incompressible flow can be corrected according to Prandtl-.
Glauert correction factors.

In the case of unsteady flow, Reissner, reference 1, and W. P. Jones,
reference 2, have published papers showing the effect of wind—tunnel walls
for the incompressible case. In both papers, the influence of the tunnel
walls is.found to be comparatively small for most cases, although indica—
tions are given that, for some ranges of a reduced—frequency parameter,
the effect may be quite large. .In the unsteady case, unlike the steady
case, the transition from results for incompressible flow to those for
compressible flow cannot be accomplished by simple transformations.