ON THE DESIGN OF 3-DIMENSIONAL WIND-TUNNEL CONTRACTIONS

A method is given for the calculation of incompressible inviscid flow through nonaxisymmetric contracting ducts with rectangular cross sections. The method is based on a finite difference approximation to Laplace's equation which is solved by the method of successive overrelaxation. In attempt to provide practical criteria for the design of such contractions, the flows through a series of contraction shapes were calculated, each shape being based on a pair of matched elliptic arcs. This permitted choice of such parameters as length, local (i. e. , two-dimensional) contraction ratio, position and magnitude of the maximum slope. It was found that reducing the length of the contraction also reduced its effective length, although increasing the effects of overshoot and undershoot. This could be compensated for by designing a contraction with a steep, maximum slope which, with associated low curvatures at entrance and exit, reduced the values of overshoot and undershoot.