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National Advisory Committee for Aeronautics, Report - Theoretical and Experimental Investigation of the Effect of Tunnel Walls on the Forces on an Oscillating Airfoil in Two Dimensional Subsonic Compressible Flow

This report presents a theoretical and ecperimental investi-
gation of the efi'ect of wind-tunnel walls on the air forces on an
oscillating wing in two—dimensional subsonic compressible
flow. A method of solving an integral equation which relates
the downwash on a wing to the unknown loading is given, and
some comparisons are made between the theoretical results and
the experimental results. A resonance condition, which was
predicted by theory in a previous report (NAOA Rep. 1150),
is shown experimentally to exist. In addition, application of
the analysis is made to a nitmber of examples in order to illus—
trate the influence of walls due to variations in frequency of
oscillation, Mach number, and ratio of tunnel height to wing

semichord.
INTR ODUC’I‘ION

In the evaluation of results obtained by measurement of
the forces on a wing in a wind tunnel, the question of the
effect of the tunnel walls arises. In the case of steady flow
the problem has been extensively investigated and, in gen-
eral, relatively simple factors have been determined which
can be used to modify measurements of the forces on a wing
in a tunnel to correspond to free-air conditions. However,
the corresponding problem of the effect of walls on an os~
cillating airfoil has received relatively little attention, par-
ticularly in the case of compressible flow. The present
report concerns the wall effects in the oscillating case and
treats the problem in two-dimensional subsonic compressible
flow.

In incompressible flow, theoretical treatments of wall
effects on oscillating wings have been made by several in-
vestigators and reported in references 1, 2, and 3. These
investigators have shown generally that the tunnel-wall
effects are a maximum for some small values of the reduced
frequency and that the wall effects become negligible as the
reduced frequency is increased. Extension of the theoretical
treatment of the problem to include the effects of compressi-
bility of the fluid has been reported in reference 4. In this