A numerically efficient mathematical model for the aerodynamics oflow speed axial fans of the arbitrary vortex flow type has been developed.The model is based on a blade-element principle, whereby therotor is divided into a number of annular streamtubes.For each of these streamtubes relations for velocity, pressure andradial position are derived from the conservationlaws for mass, tangential momentum and energy.The resulting system of equations is non-linear and, dueto mass conservation and pressure equilibrium far downstream of the rotor,strongly coupled.The equations are solved using the Newton-Raphson method, andsolutions converged to machine accuracy are found at small computing costs.The model has been validated against published measurementson various fan configurations,comprising two rotor-only fan stages, a counter-rotatingfan unit and a stator-rotor-stator stage.Comparisons of local and integrated propertiesshow that the computed results agree well with the measurements.Integrating a rotor-only version of the aerodynamic modelwith an algorithm for numerical designoptimization, enables the finding of an optimum fan rotor.The angular velocity of the rotor, the hub radius and the spanwise distributionsof pitch angle and chord length have been chosen as independent variablesin the optimizations.Besides restricting the geometry of the rotor,constraints have been added to ensure a required pressure rise as well asnon-stalled flow conditions.Optimizations have been performed tomaximize the mean value of fan efficiency in a design interval of flow rates,thus designinga fan which operates well over a range of different flow conditions.The optimization scheme was used to investigate the dependence ofmaximum efficiency on1: the number of blades,2: the width of the design interval and3: the hub radius.The degree of freedom in the choice of design variables andconstraints, combined with the design interval concept, providesa valuable design-tool for axial fans.To further investigate the use of design optimization, a modelfor the vortex shedding noise from the trailing edge of the bladeshas been incorporated into the optimization scheme. The noiseemission from the blades was minimized in a flow ratedesign point.Optimizations were performed to investigate the dependence ofthe noise on1: the number of blades,2: a constraint imposed on efficiency and3: the hub radius.The investigations showed, that a significant reduction ofnoise could be achieved, at the expense ofa small reduction in fan efficiency.
展开▼
