Contracting Cones Giving Uniform Throat Speeds

Abstract

A difficult problem in fluid mechanics which comes up frequently, especially in the design of venturi meters and wind tunnels, is to find the geometric form of contracting cones having uniform flow speeds a t the throat. The solution given in this report** makes use of the exact analogy between the magnetic field tha t is created by two coaxial and parallel coils carrying electrical current and the velocity field tha t is created by two corresponding ring vortices. The high uniformity of the magnetic field over a core area when the coils are suitably arranged is well known. A corresponding uniformity of the velocity field over the same core area is here obtained by simply translating the electromagnetic solution into an aerodynamic one and by choosing one of the stream surfaces as a flow boundary. The geometric form of the stream surfaces is found without difficulty. A family of these contracting cones is developed, the inner eight of which give throat speed distributions tha t are uniform theoretically within a fifth of 1 per cent. The distributions become less uniform for the outer cones, but variations from uniformity are still less than 1 per cent even for the outermost one. Essentially, the same throat uniformities will occur in the case of real airflows, provided the upstream flow is uniform and the downstream, or diffuser, flow does not separate.