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National Advisory Committee for Aeronautics, Technical Notes - Study of the Momentum Distribution of Turbulent Boundary Layers in Adverse Pressure Gradients

Evaluation and analysis were made of the mean and turbulent terms
of the equations of motion and the stress tensor at four stations in a
turbulent boundary layer with a progressively increasing adverse pres—
sure gradient.

Good agreement between the values of skin friction obtained by heat
transfer a skin friction instrument measurements and by the evaluation
of the Ludwieg-Tillmann empirical equation was found to exist. The eval—
uation of skin friction from the integrated momentum equation failed to
agree with the results of other methods of obtaining skin friction.

Evaluation of the terms of the turbulent stress tensor indicates'
that the normal stresses pvz and pwZ and the shear stress -95; are
of congarable magnitude, while the normal stress pu2 was found to be
roughly four times as large near the wall. The angle between the prin—
cipal axis of the turbulent stress tensor and the boundary appeared to
be largely independent of x—dlstance or pressure gradient.

Evaluation of the x— and y-direction equations of motion shows that
the rate of change normal to the wall of the mean square of the y-
direction turbulent velocity in the y—direction equation when taken near
the wall is as large as or larger than any term in the x-direction equa-
tion. The x— and y-momentum equations are, however, still independent.

In recent years progress has been made in the measurement of the
statistical properties of specialized turbulent shear flows. For the
free turbulent shear flows in the wakes of circular cylinders and in
free air Jets, Townsend (ref. 1) and Corrsin (ref. 2), respectively,
have evaluated from experiments the important statistical terms. The
most accurate investigations have been made in free turbulent shear flows,
since the absence of solid boundaries greatly facilitates measurements.
In fully developed turbulent flow in pipes and. channels, which is the
other extreme, Laufer (refs. 5 and 4) has presented extensive measure-
ments. Laufer's results brought to light significant features of flows
with solid boundaries; it was found that flow conditions in the close
proximity of the wall were of major importance.