Analysis of reynolds number effects in fluid flow through two-dimensional cascades

Abstract

This report describes an investigation into the effects of Reynolds number on the flow through two dimensional cascades of the diffusing type. Particular emphasis has been. placed on the causes of high loss especially at very low Reynolds numbers. Separation of both the laminar and turbulent boundary layers are verified as sources of low efficiency in this particular type of flow and these phenomena have, consequently, been studied in considerable detail. The main work consists of approximate mathematical analysis of representative flows but this theoretical work has been carried out in conjunction with, and is supported by, results drawn from an extensive programme of tests made in the low-speed wind tunnel at the Cambridge University Engineering Laboratory. These tests are fully described in Ref. 1. Mach number effects were specifically avoided in the experimental work although a wide range of Reynolds number was covered; the effects of compressibility have not, therefore, been considered in the main analysis. The transition to turbulent flow in the boundary layer is shown to be of vital importance in determining the pattern of flow, especially at low Reynolds numbers where laminar breakaway is likely to occur, and the need for a theoretical or semi-empirical method of predicting transition is stressed. In the theoretical work tile generally accepted approach has been followed in ttlat the potential flow pattern has been used as a basis for further calculation. The close agreement of the analysis with the experimental results has justified the use of the approximate methods of boundaw-layer calculation which were selected, i.e., Thwaites' method for the laminar layer and Hewson's method for the turbulent layer. In conclusion it is shown that design methods can be modified to ensure improved performance at a specified Reynolds number or over a range of Reynolds number. In the course of the report the importance of assessing wind-tunnel results in relation to secondary effects such as the contraction of the air stream in the plane perpendicular to that considered is well illustrated, and methods of correction to enable more universal application of particular results are outlined.