An experimental determination of the intensity of friction on the surface of an aerofoil

Abstract

1. The principal part of the present investigation* is concerned with an experimental determination of the intensity of friction on the surface of an aerofoil from the well known relation f = (∂V/∂ z ) z - 0 , where f is the intensity of friction, μ. the coefficient of viscosity, and V the velocity parallel to the surface at a normal distance z from the surface. In general, the velocity changes rapidly near the surface, so that the velocity gradient (∂V/∂ z ) z = 0 can only be predicted reliably when the velocity observations are taken very close to the surface. A review of the instruments available for the measurement of the velocity very close to a surface led to the conclusion that the most suitable device would be a surface tube of the type designed by Sir Thomas Stanton, and used to examine the conditions at the boundary of a fluid in turbulent motion. The special feature of this tube is that the inner wall of the tube is formed by the surface itself. Three surface tubes were used in the present experiments, the widths of the openings being 0·0020, 0·0032 and 0·0044 inch respectively. These tubes were calibrated in the known laminar flow in a pipe with a rectangular cross-section, and with them it was possible to measure the velocity at points situated about 2 to 3 thousandths of an inch from the surface. The observations taken with the three tubes were found to be mutually compatible and allowed predictions to be made of the velocity gradients at the surface, and so of the frictional intensities. A check on the general accuracy of these values of frictional intensity was obtained from a comparison of the resultant frictional drag of the aerofoil predicted from them, with that obtained when the form drag due to the normal pressures on the surface was subtracted from the total drag deduced from the total head losses in the wake. In addition, explorations of total head in the boundary layer, that is, the thin layer adjacent to the surface throughout which the retarding influence extends, were made with small tubes. It was found that the velocities measured near the surface with these tubes were compatible with those measured still closer to the surface with the surface tubes. The frictional drag of the aerofoil was also determined from the changes of momentum along the boundary layer.* 2. The experiments were made on a large model aerofoil mounted horizontally with very small clearances, between the vertical walls of a 7-foot wind tunnel. The observations were taken midway between the walls, where the flow was closely two-dimensional. To obtain a smooth surface in this region, the middle part (6-inch span) of the model was formed from a hollow gunmetal casting accurately milled to shape and polished. The remainder of the model was a light but stiff wooden framework built up of two longitudinal spars, nose and tail pieces, and transverse ribs, with a hand-finished surface covering of three-ply wood.