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National Advisory Committee for Aeronautics, Technical Notes - Wall Pressure Fluctuations in a Turbulent Boundary Layer

When a turbulent boundary layer is produced by air flow past a
solid surface, the turbulence in the boundary layer can generate a
sound field. in the free stream and will also induce fluctuating loads
on the solid surface. If the surface is flexible, this motion will
generate an additional sound field on both sides of the surface.

In an initial investigation of the latter form of sound generation,
suitable equipment has been developed to measure the fluctuating wall
pressure in the turbulent boundary layer. The equipment includes a
specially designed low—noise— and low-turbulence-level wind tunnel and
a. small barium titanate transducer and preamplifier combination for fre-
quencies up to 50 kilocycles. The transducer and preamplifier' may be
useful for other applications.

Using this equipment, some of the properties of the wall pressure
fluctuations in a turbulent boundary layer have been measured. It was
found that the spectrum of the wall pressure fluctuations extended to
50 Idlocycles and that the root-mean—square wall pressure was a constant
part (0.0055) of the free-stream dynamic pressure for 0.2 < M < 0.8
and 1.5 < Re < 20 x 106. A few typical spectra are given for differ-
ent values of Reynolds number and Mach number.

A problem that has received little attention is that of noise pro—
duction by a turbulent boundary layer. A description of this problem
shows that there are really two sources or mechanisms of noise genera-
tion. Consider an external flow field which causes a turbulent boundary
layer to develop along one side of an impervious wall. 0n the other side
of the wall, which may be flexible or rigid, is a stationary fluid.

The first mechanism of sound generation will be singled out when
the wall is absolutely rigid, since the turbulent flow will then be the
onLy source of sound. This mechanism of sound generation has already
been discussed from a theoretical point of_view (refs. 1, 2, and 5).
However,'pertinent experiments to determine the characteristics of the
turbulent boundary-layer flow that are of importance in the generation
of this type of sound and the properties of the generated sound field
have not yet been made. In fact, the flow speed at which the intensity
of this type of sound field becomes appreciable is not yet known.