Abstract
The paper provides an evaluation of the errors embodied in the Axial Momentum Theory (AMT) as applied to a uniformly loaded actuator disk model without wake rotation. Although this model exhibits some unphysical features, such as the tip singularity and the violation of the angular momentum equation, it is still considered a touchstone in the theoretical aerodynamics of propellers. To simplify the model, a purely mathematical assumption is commonly used in the differential form of the axial momentum equation, i.e., the contribution of the pressure forces on the lateral surface of the infinitesimal streamtubes swallowed by the disk is neglected. In this paper, the errors introduced by this simplifying assumption are evaluated by comparing the results of the AMT with those of a nonlinear method modelling the free wake as the superposition of ring vortices distributed along the wake boundary. Firstly, the validity of this method is verified in terms of global performance coefficients. Then, using a CFD approach, it is also verified in terms of local flow quantities. The comparison between the ring-vortices method and the AMT shows that, for a highly loaded propeller, significant errors exist in the axial velocity at the disk, especially near the tip. Moreover, despite the uniform load, the axial velocity at the disk varies in the radial direction. Instead, the velocity magnitude remains almost uniform only for values of the thrust coefficient lower than 1.
Highlights
Not disregarding the classical CFD approaches [1,2,3,4,5,6], the design and/or analysis of aeronautical and marine propellers are generally carried out using many numerical methods such as lifting-line [7,8], lifting surface [9,10] and panel methods [11,12]
The errors embodied in the Axial Momentum Theory (AMT) as applied to a uniformly loaded propeller are evaluated comparing its results with those of a free-wake ring-vortex actuator disk (FWRV-AD) method which models the wake through the superposition of ring vortices placed in the control points of N straight panels [37,38]
The wake axial velocity at downstream infinity vz (z → +∞, r ) is termed vz,w. This quantity can be related to the pressure jump across the disk by applying the Bernoulli equation to the streamtubes swallowed by the rotor
Summary
Not disregarding the classical CFD approaches [1,2,3,4,5,6], the design and/or analysis of aeronautical and marine propellers are generally carried out using many numerical methods such as lifting-line [7,8], lifting surface [9,10] and panel methods [11,12]. The evaluation of these errors is carried out by comparing the MT results with those of more advanced actuator disk approaches which do not rely on the MT simplifying assumptions. Despite the large amount of works on this topic, a precise evaluation of the AMT errors as applied to the classical uniformly loaded propeller is still missing The relevance of this issue relies on the fact that the uniformly loaded disk still represents the benchmark model for two reasons. The errors embodied in the AMT as applied to a uniformly loaded propeller are evaluated comparing its results with those of a free-wake ring-vortex actuator disk (FWRV-AD) method which models the wake through the superposition of ring vortices placed in the control points of N straight panels [37,38].
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