Aiming at designing more efficient components for refrigeration systems, a first-principles axial fan model is put forward in this paper, consisting of a discretization of the blade along the radial direction. The model is based on the tripod formed by blade element theory, airfoil aerodynamics, and momentum conservation-a framework known to have been used so far only for wind turbines and propellers. The set of nonlinear algebraic equations resulting from the sum of forces at each blade element is solved iteratively through an under-relaxation procedure. Numerical results based on an 8-inch 5-bladed condensing unit fan at 1350 RPM showed that the model reproduces well the pressure head and shaft power trends observed experimentally, albeit overestimating these quantities within 10 and 20 bounds, respectively. To illustrate the model potential for design purposes, the pitch angle distribution of the baseline fan was optimized for 0 and 10 Pa. The numerical results showed the optimized fans to be about 3 more efficient than the baseline one. The optimization took about 1 h, constituting a several orders of magnitude time reduction in comparison to the CFD approach.
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