A theoretical derivation of the Cordier diagram for turbomachines

Abstract

The design of high-efficiency fans is often based on the experience of the designer. In order to determine its main dimensions, fan designers use the Cordier diagram. For a given operating point (i.e. flowrate and pressure, and a rotating speed), the optimum diameter of high-efficiency fans can be found in the Cordier diagram. The Cordier diagram is an empirical diagram based on measurements. It delivers a relation between flowrate, pressure, rotating speed, and diameter. However, the Cordier diagram does not provide any information on the blade shape (i.e. the angles and the blade width). In order to fill this gap, there are design rules based on the experience of the designer and some analytical performance parameters in the literature. One very common performance parameter is the reaction, which is the ratio between the static and the total pressure rising from the impeller inlet to its outlet. These design rules and performance parameters are, however, of limited use. Therefore, the total-to-static ideal efficiency is introduced to yield, together with the speed and diameter numbers σ and δ, the essential parameters that distinguish the different turbomachines in the Cordier diagram. Based on the integral parameters of the flow and the geometry of turbomachines, a performance analysis of turbomachines is performed and the Cordier diagram is theoretically derived.