Maximal Achievable Efficiency of Fans
3.3 Cordier Guided Design Strategies
This paper discusses methods to estimate the upper limit of energy efficiency as a function of the fan type, the design point and the Reynolds number. Four fan types are investigated: axial rotor-only fans, axial fans with guide vanes, radial rotor-only fans and radial fans with volutes. The considered design points are consistent with the Cordier band, i.e. all typical design points of fans are taken into account.
It is distinguished between two efficiency limits: theoretical and practical. The theoretical limit is based on idealizing assumptions and only takes inevitable losses into account. This method to determine the efficiency limit does not yield the fan geometry required to achieve it. In fact, it might be impossible to achieve the limit with real fans. In order to determine the practical efficiency limit, real fan geometries must be considered. For that purpose, the shape of each fan type is parameterized by a set of geometrical parameters and the optimal parameters for given design point are indentified by CFD-based optimization. While the theoretical efficiency limit is supposed to be insuperable, the practical limit only holds true for the selected geometry parameterization and the CFD model. Exceeding the practical limit might be possible by allowing more complex geometries or by using a more accurate CFD model (this work is based on the comparatively cheap RANS method). The Reynolds number used in the simulations is approximately one million. Hence, scaling laws are required to estimate the efficiency limit at other Reynolds numbers.
It is found that the theoretical limit of the total efficiency is always very high except for high-pressure radial fans which feature increased losses due to the friction between the bottom disc and cover disc with the surrounding air. In contrast, the design point always has a strong impact on the achievable total-to-static efficiency which decreases with the specific diameter and specific speed. The theoretical efficiency limit is not consistent with the common assumption that axial and radial fans are more adequate for high and low specific speeds, respectively. The practical efficiency limit is closer to standard knowledge about fans, i.e. the highest efficiencies occur near the Cordier curve and the specific speed is decisive whether axial or centrifugal fans are more efficient. The highest practical efficiency values are found at a radial fan with volute and amount to 86 % (total-to-static) or 90 % (total) assuming a Reynolds number of one million.