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• W2137304753 abstract "The Blade Element Momentum theory is based on the work of Glauert who formulated the equations to derive thrust, torque and power as a function of the tip speed ratio λ and axial induction. The moment of momentum applied to the wake, is taken into account in his theory with one major simplification. The radial pressure distribution required to maintain the swirl in the wake is ignored, and not included in the momentum balance and the final results. For high λ the swirl is negligible so this simplification has no effect, but for low λ this is questionable. After Glauert, many authors have published solutions for the low λ regime of discs with constant circulation, all with different assumptions on the radial distribution of flow quantities, the momentum balance or the impact of the infinite pressure in case of a discrete vortex at the disc axis. A common property of the results is that the power coefficient Cp increases above the Lanchester-Betz-Joukowsky limit. As for most other authors, the present analysis proceeds from actuator discs with constant circulation, yielding a wake flow characterized by a singular vortex at the downstream disc axis. Without any further assumption, the impact of the radial pressure distribution on the momentum balance and the Bernoulli equation is taken into account, as is the effect of the infinite pressure at the disc axis due to the discrete vortex. The results are presented in analytical expressions for the axial and azimuthal velocities through the disc and in the far wake, and similarly for the thrust, power and torque. The inclusion of the pressure-due-toswirl gives Vaxial-disc > 0.5(Vwake+Vundisturbed) and the maximum power coefficient indeed tends to infinity for λ→0. Furthermore, the maximum Cp-value is always greater than the Lanchester-Betz-Joukowsky limit at 16/27. The explanation for this is that the axial velocity through the disc becomes larger than the undisturbed velocity: air at a radial distance that is larger than the disc radius is sucked through the disc due to the under-pressure induced by the swirl. This behavior has been the subject of many considerations and explanations. Glauert (1935) stated that the condition of constant circulation cannot be fully realized in practice since it implies that near the roots of the blades the angular velocity imparted to the air is greater than the angular velocity of the propeller itself. Other investigators, such as de Vries (1979) and Wilson and Lissaman (1978), dealt the view point of Glauert that the solution is unphysical as it results in infinite values of power and circulation when the tip speed ratio tends to zero. In a recent work, Sharpe (2004) argues that the theory in principle establishes that there is no loss of efficiency associated with the rotating wake and that it is possible, at least in theory, to exceed the Lanchester-Betz-Joukowsky limit. Thus, still today, there seems not be fully agreement in the validity of the model." @default.
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• W2137304753 date "2009-12-31" @default.
• W2137304753 modified "2023-09-29" @default.
• W2137304753 title "Actuator disc momentum theory for low lambda rotors" @default.
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