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

This report treats the eject of wind-tunnel walls on the
oscillating two-dimensional air forces in a compressible medium.
The walls are simulated by the usual method of placing images
at appropriate distances above and below the wing. An im—
portant 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 Illach number ranges, in tunnels of nonuniform cross
section or even in open tunnels or jets.

The understanding of flutter and other nonsteady phe-
nomena requires a knowledge of the associated unsteady flow.-
In the underlying theories of unsteady flow, such assumptions
as small displacements, linearizations, 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 conform 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 cor-
respond to free-air conditions. The extension of the results
to compressible flow presents no difficulties 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 indications are
given that, for some ranges of a reduced-frequency param-
eter, the effect may be quite large.