Aerodynamics and Design for Ultra-Low Reynolds Number Flight

V total / ωr
1.0
0.9
0.8
Classical Angular Momentum
Average Wake Deficit
Gaussian Wake
0.7
0.2 0.3 0.4 0.5 0.6
r/R
0.7 0.8 0.9 1.0
FIGURE 6.37 Local relative flow velocities using three different viscous swirl models.
Of the three models considered, the classical angular momentum provides the best
Chapter 6
agreement with the OVERFLOW-D results presented earlier. The Gaussian wake model
as currently implemented has no effect and the average wake deficit model grossly
under-predicts the sectional thrust and torque. None of these models provides an ideal
solution. The angular momentum model is appropriate in the outer blade region where
the Reynolds numbers are higher and the local annular solidity much lower, but inboard,
the models based on actual viscous wake profiles and a direct accounting of local
solidity should more accurately represent the flowfield. In spite of these issues, the
classical angular momentum correction is satisfactory overall for analysis since higher
fidelity is not needed inboard due to the triangular loadings typical of rotors.
6.7.2 Effect of Wake Modeling on Performance Estimation
The impact on performance estimation of the two wake models, the classical Prandtl tip
loss correction and the contracted vortex ring model, has also been explored using the
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