Theoretical Interpretation of the CORDIER-Lines for Squirrel-Cage and Cross-Flow Fans

Squirrel-cage fans are centrifugal fans with forward-curved blades. A large number of short blades of thin circular arc sheet metal provide a low diameter drum-type rotor of high axial length. Cross-flow fans have a similar rotor design. However, the flow passes the rotor in radial direction two times. One consequence of the forward-curved blades is that there is more or less no pressure rise in the rotor and the casing has to convert the high absolute rotor exit velocity into a global pressure rise. Both types are used in applications requiring low size, relative high volume flow rates, low costs and low noise at the drawback of relative low efficiency. Volume flow rate, specific isentropic enthalpy difference, rotor outer diameter and rotational speed of a single stage fan can be transformed to speed number and diameter number. For axial, radial and mixed flow fans, a single relationship (CORDIER-diagram) exists and it is well accepted that this line represents “optimum” fan designs with high efficiency. The paper provides a theoretical interpretation of the CORDIER-lines for squirrel-cage and cross-flow fans, since they differ considerably from the classical relationship. Based on velocity triangles and energy transfer, CORDIER-line of squirrel-cage fans depends on absolute inlet flow angle, relative exit flow angle, rotor inlet to exit diameter ratio, relative axial rotor width and circumferential efficiency. Additionally, the CORDIER-line of cross-flow fans depends on the degree of admission. At a distinguished pressure coefficient, a maximum speed number is found, corresponding to maximum volume flow rate.