The Secondary Flow About Struts and Airfoils

Abstract

The flow about a strut when the approaching velocity varies in the spanwise direction has been examined theoretically and experimentally. The theory supposes that the fluid is inviscid and incompressible and that the flow is a small disturbance of the two-dimensional potential pattern appropriate to the profile. I t is found that the shape of the profile at the nose influences the size of the disturbances appreciably. A rounded nose causes such large disturbances that the original assumptions of the theory are invalidated. The disturbances are much less with a wedge-shaped nose and least with a cusped nose. A method of designing profiles to minimize the disturbances is described and an example—a bicusped strut—is given. The flow about the bicusped strut is examined in detail and the energy in the secondary flow normal to the direction of the approaching flow is determined for one type of initial velocity distribution. This energy is found to vary as the fourth power of the thickness of the strut and to be a maximum at a certain value of the displacement thickness of the original nonuniform stream. The secondary flows produced by a biconvex profile are shown to be small. Calculations for a thin circular arc airfoil are presented to show the effect of lift and the existence of vortex sheet trailing off such an airfoil is indicated. Ling's experiments with a bicusped and conventional profile placed in a nonuniform stream are summarized to show their confirmation of the major effects predicted by the theory. The drag due to secondary effects is appreciably less with the bicusped strut and so is the general disturbance of the flow as shown by wake traverses. The energy in the secondary flow is of the order of that predicted by the theory (for the bicusped strut) but the drag is much greater than would be deduced from measured or calculated energy. Some experiments with struts placed in an hydraulic channel with a sandy bottom show that the scouring of the beds of rivers may be attributed to secondary flows. The use of a bicusped profile reduces the scouring considerably compared to an elliptic profile of the same thickness and chord.