Free-Vortex Filament Methods for the Analysis of Helicopter Rotor Wakes

Leishman, J. Gordon; Bhagwat, Mahendra J.; Bagai, Ashish

doi:10.2514/2.3022

Cited by 179 publications

(107 citation statements)

References 35 publications

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“…There are two commonly used methods to remove the singularity, one is to use a cut-off, the other is to apply a viscous vortex model with a finite core size. 19 The scheme of merging vortex elements when they are getting close to each other may offer a third option to avoid the singularity. A small cut-off ı is used in this paper, its effect is discussed in the Appendix A.…”

Section: Near Wake Modelmentioning

confidence: 99%

Verifying the Blade Element Momentum Method in unsteady, radially varied, axisymmetric loading using a vortex ring model

Ferreira

Kuik

et al. 2016

Wind Energy

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Although the Blade Element Momentum method has been derived for the steady conditions, it is used for unsteady conditions by using corrections of engineering dynamic inflow models. Its applicability in these cases is not yet fully verified. In this paper, the validity of the assumptions of quasi-steady state and annuli independence of the blade element momentum theory for unsteady, radially varied, axi-symmetric load cases is investigated. Firstly, a free wake model that combines a vortex ring model with a semi-infinite cylindrical vortex tube was developed and applied to an actuator disc in three load cases: (i) steady uniform and radially varied, (ii) two types of unsteady uniform load and (iii) unsteady radially varied load. Results from the three cases were compared with Momentum Theory and also with two widely used engineering dynamic inflow models-the Pitt-Peters and the Øye for the unsteady load cases. For unsteady load, the free wake vortex ring model predicts different hysteresis loops of the velocity at the disc or local annuli, and different aerodynamic work from the engineering dynamic inflow models. Given that the free wake vortex ring model is more physically representative, the results indicate that the engineering dynamic inflow models should be improved for unsteady loaded rotor, especially for radially varied unsteady loads. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

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Section: Near Wake Modelmentioning

confidence: 99%

Verifying the Blade Element Momentum Method in unsteady, radially varied, axisymmetric loading using a vortex ring model

Ferreira

Kuik

et al. 2016

Wind Energy

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“…A vortex model is implemented in WInDS, the Lamb-Oseen vortex model [23,24], and is used to cater for the viscous effects in the evolution of the near wake. This model is a solution to the one-dimensional laminar Navier-Stokes equations in which an axisymmetric solution for the swirl velocity was used, assuming that the axial and radial velocities are zero.…”

Section: Free-wake Vortex Modelmentioning

confidence: 99%

Combining Unsteady Blade Pressure Measurements and a Free-Wake Vortex Model to Investigate the Cycle-to-Cycle Variations in Wind Turbine Aerodynamic Blade Loads in Yaw

Elgammi

Sant

2016

Energies

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Prediction of the unsteady aerodynamic flow phenomenon on wind turbines is challenging and still subject to considerable uncertainty. Under yawed rotor conditions, the wind turbine blades are subjected to unsteady flow conditions as a result of the blade advancing and retreating effect and the development of a skewed vortical wake created downstream of the rotor plane. Blade surface pressure measurements conducted on the NREL Phase VI rotor in yawed conditions have shown that dynamic stall causes the wind turbine blades to experience significant cycle-to-cycle variations in aerodynamic loading. These effects were observed even though the rotor was subjected to a fixed speed and a uniform and steady wind flow. This phenomenon is not normally predicted by existing dynamic stall models integrated in wind turbine design codes. This paper couples blade pressure measurements from the NREL Phase VI rotor to a free-wake vortex model to derive the angle of attack time series at the different blade sections over multiple rotor rotations and three different yaw angles. Through the adopted approach it was possible to investigate how the rotor self-induced aerodynamic load fluctuations influence the unsteady variations in the blade angles of attack and induced velocities. The hysteresis loops for the normal and tangential load coefficients plotted against the angle of attack were plotted over multiple rotor revolutions. Although cycle-to-cycle variations in the angles of attack at the different blade radial locations and azimuth positions are found to be relatively small, the corresponding variations in the normal and tangential load coefficients may be significant. Following a statistical analysis, it was concluded that the load coefficients follow a normal distribution at the majority of blade azimuth angles and radial locations. The results of this study provide further insight on how existing engineering models for dynamic stall may be improved through the integration of stochastic models to be able to account for the cycle-to-cycle variability in the unsteady wind turbine blade loads under yawed conditions.

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“…Representative values of for helicopter rotor vortices range from 10 (at model scale) up to more than 1000 (at full scale). 28) As another illustration of the wake instability problem, Fig. 3 shows that a larger inflow is calculated at the border region of the rotors without any treatment, and results in overestimation of the overlap induced interference power factor ( ov ) for a tandem rotor configuration, with the distance between the rotors, d=D, of 1.25 for the same rotor height.…”

Section: Wake Instabilitymentioning

confidence: 99%

“…This work achieves a stable and accurate solution by applying slow start up for the first two revolutions to reduce the effects of the starting vortex and the viscous effects that Leishman et al 28) suggested. The vortex core diffusion effects are modeled using the following empirical relation:…”

Section: Wake Instabilitymentioning

confidence: 99%

“…However, it is known that the induced velocity generated from one rotor wake causes an upward velocity on the other rotor near the border, and hence reduces the average wake speed, followed by a lesser induced velocity at each rotor. 28) Figure 20(b) shows the inflow speed-decrease mechanism caused by wake interaction. It also shows that the region with ov below 1.0 exists because of the decrease in induced power due to the interactions.…”

Section: Hovering Case Of Tandem Rotor Systemmentioning

confidence: 99%

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Aerodynamic Characteristic Analysis of Multi-Rotors Using a Modified Free-Wake Method

Lee

Yee

2009

Trans. Japan Soc. Aero. S Sci.

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Much research is in progress to develop a next-generation rotor system for various aircrafts, including unmanned aerial vehicles (UAV) with multi-rotor systems, such as coaxial and tandem rotors. Development and design of such systems requires accurate estimation of rotor performance. The most serious problem encountered during analysis is wake prediction, because wake-wake and wake-rotor interactions make the problem very complex. This study analyzes the aerodynamic characteristics based on the free-wake method, which is both efficient and effective for predicting wake. This code is modified to include the effect of complex planforms as well as thickness by using an unsteady 3D panel method. A time-marching free-wake model is implemented based on the source-doublet panel method that assigns panels to the surface and analyzes them. The numerical wake instability, the most critical problem for analysis, is resolved by adopting slow start-up and by including viscous effects. Also, the instability due to wake interference in tandem rotor analysis is resolved by configuring the initial shapes of the multi-rotor wake as that of a single rotor wake trajectory. The developed code is verified by comparing with previous experimental data for coaxial and tandem rotors.

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Free-Vortex Filament Methods for the Analysis of Helicopter Rotor Wakes

Cited by 179 publications

References 35 publications

Verifying the Blade Element Momentum Method in unsteady, radially varied, axisymmetric loading using a vortex ring model

Verifying the Blade Element Momentum Method in unsteady, radially varied, axisymmetric loading using a vortex ring model

Combining Unsteady Blade Pressure Measurements and a Free-Wake Vortex Model to Investigate the Cycle-to-Cycle Variations in Wind Turbine Aerodynamic Blade Loads in Yaw

Aerodynamic Characteristic Analysis of Multi-Rotors Using a Modified Free-Wake Method

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