Influence of Blade Loading Criteria and Design Limits on the Cordier-Line for Axial Flow Fans

Abstract

Volume flow rate, specific isentropic enthalpy difference, rotor outer diameter and rotational speed of a fan can be transformed to speed number and diameter number. These two non-dimensional numbers are related together in the so-called Cordier-diagram. For axial, radial and mixed flow fans, there is a single empirical relationship between both quantities and it is well accepted that this line represents “optimum” fan designs with high efficiency. Based on velocity triangles, a relationship between flow coefficient and pressure coefficient exists. This so-called performance curve captures off-design operating points as well as the design point of a fan. Therefore, the performance curve can be transformed to the Cordier-diagram to predict the relationship between speed number and diameter number. It is shown that the Cordier-line depends mainly on velocity triangles and the common argument of high efficiency, claimed in the majority of the literature, plays only a secondary role. Nevertheless, the requirement of high efficiency influences the fan design for a certain design point. This paper focuses mainly on axial flow fans. It gives a theoretical interpretation of the influence of blade loading criteria and design limits on the Cordier-line: (1) De Haller number, (2) cascade loading parameter, (3) Lieblein diffusion factor, (4) Strscheletzky swirl number. Criterion (1) reflects the minimum velocity ratio to avoid endwall separation in a linear compressor cascade. Criterion (2) is a combination of lift coefficient and cascade solidity. It reflects the aerodynamic loading of the suction side blade boundary layer. Criteria (1) and (2) are included in criterion (3). Finally, criterion (4) indicates the risk of hub separation due to strong swirl flow. The investigation shows that the transformation of these criteria to the Cordier-diagram gives very similar results. Furthermore, it is shown that the axial fan design limits in the Cordier-diagram are represented by certain hub-to-tip radius ratios.