Incompressible flow in contracting ducts

Abstract

This paper describes the incompressible flow through contracting ducts as used in windtunnel circuits. The value of the velocity gradients that are critically adverse to the boundary layer development are specified and the contraction profile is derived for two-dimensional flow. Solutions to the flow through three-dimensional contractions of circular, square, and square to rectangle shape are obtained. These lead to simple rules for scaling the profile of two-dimensional flow to provide three-dimensional shapes having short lengths with the required velocity distributions. The development of both laminar and turbulent boundary layers is calculated to provide criteria for the avoidance of separation.