A Theory for Power Extraction from Passive Accelerators and Confined Flows

Abstract

No valid fluid theory exists for power extraction from unpressurized confined flow. The absence of a valid model to determine baseline uniform power extraction in confined flows creates difficulties in characterizing the coefficient of power. Currently, the primary body of research has been limited to Diffuser Augmented Wind Turbines (DAWTs) and passive fluid accelerators. Fluid power is proportional to the cube of velocity; therefore, passive acceleration is a promising path to effective renewable energy. Hypothetical models and experiments for passive accelerators yield low ideal power limits and poor performance, respectively. We show that these results derive from the misapplication of Betz’s Law and lack of a general theory for confined flow extraction. Experimental performance is due to the low efficiency of DAWTs and prior hypotheses exhibit high predictive error and continuity violations. A fluid model that accurately predicts available data and new experimental data, showing disk specific maximum CP for the confined channel at 38% of power available to disk, is presented. This is significantly lower than the 59% Betz freestream limit yielded by hypothetical models when the area ratio equals one. Experiments and their results are presented with non-DAWT accelerators, where new experimental results exceed CP limits predicted previously and correlate with the proposed predictive model.

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