scholarly journals Joukowsky actuator disc momentum theory

2017 ◽  
Author(s):  
Gijs van Kuik
Keyword(s):  
Vortex Core ◽  
Momentum Balance ◽  
Speed Ratio ◽  
Meridian Plane ◽  
Tip Speed Ratio ◽  
Momentum Theory ◽  
Rotor Design ◽  
Velocity Gradients ◽  
Actuator Disc ◽  
Singular Flow

Abstract. Actuator disc theory is the basis for most rotor design methods, be it with many extensions and engineering rules added to make it a well-established method. However, the off-design condition of a very low rotational speed Ω of the disc is still a topic for scientific discussions. Several authors have presented solutions of the associated momentum theory for actuator discs with a constant circulation, the so-called Joukowsky discs, showing the efficiency Cp → ∞ for the tip speed ratio λ → 0. The momentum balance is very sensitive to the choice of the vortex core radius δ as the pressure and velocity gradients become infinite for δ → 0. Viscous vortex cores do not show this singular behaviour so an inviscid core model is sought which removes the momentum balance sensitivity to singular flow. A vortex core with a constant δ does so. Applying this in the momentum balance results in Cp → 0 for λ → 0, instead of Cp → ∞. At the disc the velocity in the meridian plane is shown to be constant. The Joukowsky actuator disc theory is confirmed by a very good match with the numerically obtained results. It gives higher Cp values than corresponding solutions for discs with a Goldstein-based wake circulation published in literature.

scholarly journals Joukowsky actuator disc momentum theory

2017 ◽  
Vol 2 (1) ◽  
pp. 307-316 ◽  
Author(s):  
Gijs A. M. van Kuik
Keyword(s):  
Vortex Core ◽  
Delta Function ◽  
Momentum Balance ◽  
Speed Ratio ◽  
Meridian Plane ◽  
Tip Speed Ratio ◽  
Momentum Theory ◽  
Rotor Design ◽  
Velocity Gradients ◽  
Actuator Disc

Abstract. Actuator disc theory is the basis for most rotor design methods, albeit with many extensions and engineering rules added to make it a well-established method. However, the off-design condition of a very low rotational speed Ω of the disc is still a topic for scientific discussions. Several authors have presented solutions of the associated momentum theory for actuator discs with a constant circulation, the so-called Joukowsky discs, showing the efficiency Cp → ∞ for the tip speed ratio λ → 0. The momentum theory is very sensitive to the choice of the radius δ of the core of the centreline vortex as the pressure and velocity gradients become infinite for δ → 0. Usually the vortex core area is not included in the momentum balance, as it vanishes for δ → 0. However, the pressure in the vortex core behaves as a Delta function and so contributes to the balance, thereby cancelling the singular behaviour. Applying this in the momentum balance results in Cp → 0 for λ → 0, instead of Cp → ∞. The Joukowsky actuator disc theory is confirmed by a very good match with numerically obtained results. At the disc the velocity in the meridian plane is shown to be constant. The Joukowsky calculations give higher Cp values than corresponding solutions for discs with a Goldstein-based wake circulation published in literature.

Experimental, Numerical and Analytical Evaluation of a Helical-Turbine Performance

2019 ◽  
Author(s):  
Donghyuk Kang ◽  
Hiromasa Tsutsumi ◽  
Hiroyuki Hirahara
Keyword(s):  
The Other ◽  
Speed Ratio ◽  
Analytical Evaluation ◽  
Tip Speed Ratio ◽  
Momentum Theory ◽  
Turbine Performance ◽  
The Subject ◽  
Design Protocol ◽  
Novel Design ◽  
Blade Element

Abstract A helical wind turbine has been analyzed experimentally and numerically and a novel design protocol has been proposed by means of blade element and momentum theory. The subject of the present analysis is to discuss the effect of low tip speed ratio and high one, respectively. In the low tip speed ratio, the turbine is driven by the torque generated from the flow turning radially after colliding with the runner. On the other hand, in the high tip speed ratio, the turbine is operated by the torque generated from the flow passing through axially the turbine.

scholarly journals An Actuator Disc Analysis of a Ducted High-Solidity Tidal Turbine in Yawed Flow

2019 ◽  
Author(s):  
Mitchell G. Borg ◽  
Qing Xiao ◽  
Atilla Incecik ◽  
Steven Allsop ◽  
Christophe Peyrard
Keyword(s):  
Fluid Dynamic ◽  
Computational Fluid Dynamic Model ◽  
Hydrodynamic Performance ◽  
Speed Ratio ◽  
Angular Range ◽  
Power Development ◽  
Tip Speed Ratio ◽  
Power Increase ◽  
Actuator Disc ◽  
Tidal Turbine

Abstract This work elaborates a computational fluid dynamic model utilised in the investigation of the hydrodynamic performance concerning a ducted high-solidity tidal turbine in yawed inlet flows. Analysing the performance at distinct bearing angles with the axis of the turbine, increases in torque and mechanical rotational power were acknowledged to be induced within a limited angular range at distinct tip-speed ratio values. Through multiple yaw iterations, the peak attainment was found to fall between bearing angles of 15° and 30°, resulting in a maximum power increase of 3.22%, together with an extension of power development to higher tip-speed ratios. In confirmation, these outcomes were subsequently analysed by means of actuator disc theory, attaining a distinguishable relationship with blade-integrated outcomes.

Tip Loss Correction for Actuator/Navier–Stokes Computations

2005 ◽  
Vol 127 (2) ◽  
pp. 209-213 ◽  
Author(s):  
Wen Zhong Shen ◽  
Jens Nørkær Sørensen ◽  
Robert Mikkelsen
Keyword(s):  
Experimental Data ◽  
New York ◽  
Navier Stokes ◽  
Speed Ratio ◽  
Tip Speed Ratio ◽  
Actuator Disk ◽  
Axisymmetrical Flow ◽  
Actuator Disc ◽  
The Difference ◽  
Blade Element

A new tip loss correction, initially developed for 1D Blade Element/Momentum (BEM) computations (submitted to Wind Energy), is now extended to 2D Actuator Disc/Navier–Stokes (AD/NS) computations and 3D Actuator Line/Navier–Stokes (AL/NS) computations. In the paper, it is shown that the tip loss correction is an important and necessary step for actuator/Navier–Stokes models. Computed results are compared to experimental data and to results from BEM computations using the new tip correction as well as the original one of Glauert (Aerodynamic Theory, Dover, New York, Chap. VII, Div. L, pp. 251–268). From the results it is concluded that the tip loss correction has been correctly employed in the Navier–Stokes based actuator models. The results also demonstrate that the difference between actuator line and actuator disk-based models may increase, especially for flows at a low tip speed ratio. Since the flows at a low tip speed ratio are too far to be considered as axisymmetrical flows, the actuator disk models that are based on axisymmetrical flow behaviors may not be valid.

Lift Limit of Horizontal Axis Wind Turbine

2014 ◽  
Vol 1070-1072 ◽  
pp. 1869-1873
Author(s):  
Hai Bo Jiang ◽  
Yun Peng Zhao ◽  
Zhong Qing Cheng
Keyword(s):  
Wind Turbine ◽  
Lift Coefficient ◽  
Speed Ratio ◽  
Theoretical Limit ◽  
Horizontal Axis Wind Turbine ◽  
Tip Speed Ratio ◽  
Momentum Theory ◽  
Fluid Environment ◽  
Drag Ratio ◽  
Blade Element

The lift coefficient of any wind turbine must have highest limit. In this paper, an analytical expression of lift coefficient associated with tip-speed ratio and lift-drag ratio of airfoil of wind turbine with ideal chord has been deduced by integrating along the blade wingspan using the blade element - momentum theory, which can be used for pre-estimating lift coefficient of actual wind turbine in design. Further, considering ideal fluid environment ( the drag coefficient is close to 0 ), an expression of the highest performance of lift only associated with tip-speed ratio has been deduced too, which is the highest boundary of lift coefficient of any actual wind turbine with same tip-speed ratio. The results show that for the wind turbine in steady state, there is a theoretical limit of the lift coefficient, 0.57795, which is the highest boundary that any actual wind turbine can not be crossed; if the tip-speed ratio is greater than 6 and lift-drag ratio less than 200, the lift coefficient is unlikely to exceed 0.2.

scholarly journals On the velocity at wind turbine and propeller actuator discs

2020 ◽  
Vol 5 (3) ◽  
pp. 855-865
Author(s):  
Gijs A. M. van Kuik
Keyword(s):  
Wind Turbine ◽  
Axial Velocity ◽  
Rotational Speed ◽  
Positive Energy ◽  
Speed Ratio ◽  
Meridian Plane ◽  
Turbine Disc ◽  
Actuator Disc ◽  
High Torque ◽  
Uniform Deviation

Abstract. The first version of the actuator disc momentum theory is more than 100 years old. The extension towards very low rotational speeds with high torque for discs with a constant circulation became available only recently. This theory gives the performance data like the power coefficient and average velocity at the disc. Potential flow calculations have added flow properties like the distribution of this velocity. The present paper addresses the comparison of actuator discs representing propellers and wind turbines, with emphasis on the velocity at the disc. At a low rotational speed, propeller discs have an expanding wake while still energy is put into the wake. The high angular momentum of the wake, due to the high torque, creates a pressure deficit which is supplemented by the pressure added by the disc thrust. This results in a positive energy balance while the wake axial velocity has lowered. In the propeller and wind turbine flow regime the velocity at the disc is 0 for a certain minimum but non-zero rotational speed. At the disc, the distribution of the axial velocity component is non-uniform in all actuator disc flows. However, the distribution of the velocity in the plane containing the axis, the meridian plane, is practically uniform (deviation <0.2 %) for wind turbine disc flows with tip speed ratio λ>5, almost uniform (deviation ≈2 %) for wind turbine disc flows with λ=1 and propeller flows with advance ratio J=π, and non-uniform (deviation 5 %) for the propeller disc flow with wake expansion at J=2π. These differences in uniformity are caused by the different strengths of the singularity in the wake boundary vorticity strength at its leading edge.

Lift Performance of Wind Turbine with Blade Tip Loss

2014 ◽  
Vol 971-973 ◽  
pp. 569-572
Author(s):  
Hai Bo Jiang
Keyword(s):  
Wind Turbine ◽  
Correction Factor ◽  
Lift Coefficient ◽  
Speed Ratio ◽  
Calculation Formula ◽  
Blade Element Momentum Theory ◽  
Tip Speed Ratio ◽  
Momentum Theory ◽  
Blade Tip ◽  
Blade Element

Blade tip losses would reduce lift and power of wind turbine. This paper analyzed the mechanism of tip losses, and according to Prandtl and Glauert tip loss correction factor and blade element - momentum theory derived the blade chord formula with tip losses. Further, lift coefficient calculation formula was obtained by integrating along the blade span. The lift coefficient formula considering tip loss expressed the highest value of lift coefficient of any practical wind turbine with tip losses. The research shows, the impacts of tip losses to chord concentrated in the tip area; tip losses will reduce the lift coefficient about 2 to 6 percent when tip speed ratio changes from 10 to 4.

A simplified vortex model of propeller and wind-turbine wakes

2013 ◽  
Vol 725 ◽  
pp. 91-116 ◽  
Author(s):  
Antonio Segalini ◽  
P. Henrik Alfredsson
Keyword(s):  
Wind Turbine ◽  
Vortex Core ◽  
Roller Bearing ◽  
Operating Conditions ◽  
Tip Vortex ◽  
Speed Ratio ◽  
Core Size ◽  
Vortex Model ◽  
Momentum Theory ◽  
Good Agreement

AbstractA new vortex model of inviscid propeller and wind-turbine wakes is proposed based on an asymptotic expansion of the Biot–Savart induction law to account for the finite vortex core size. The circulation along the blade is assumed to be constant from the blade root to the tip approximating a turbine with maximum power production for given operating conditions. The model iteratively calculates the tip-vortex path, allowing the wake to expand/contract freely, and is afterward able to evaluate the velocity field in the whole domain. The ‘roller-bearing analogy’, proposed by Okulov and Sørensen (J. Fluid Mech., vol. 649, 2010, pp. 497–508), is used to determine the vortex core size. A comparison of the main outcomes of the present model with the general momentum theory is performed in terms of the operating parameters (namely the number of blades, the tip-speed ratio, the blade circulation and the vortex core size), demonstrating good agreement between the two. Furthermore, experimental data have been compared with the model outputs to validate the model under real operating conditions.

scholarly journals Performance assessment and optimization of a helical Savonius wind turbine by modifying the Bach’s section

2021 ◽  
Vol 3 (8) ◽  
Author(s):  
M. Niyat Zadeh ◽  
M. Pourfallah ◽  
S. Safari Sabet ◽  
M. Gholinia ◽  
S. Mouloodi ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Performance Assessment ◽  
Turbulent Flows ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Tip Speed Ratio ◽  
Basic Model ◽  
Turbine Performance ◽  
Primary Model ◽  
Savonius Wind Turbine

AbstractIn this paper, we attempted to measure the effect of Bach’s section, which presents a high-power coefficient in the standard Savonius model, on the performance of the helical Savonius wind turbine, by observing the parameters affecting turbine performance. Assessment methods based on the tip speed ratio, torque variation, flow field characterizations, and the power coefficient are performed. The present issue was stimulated using the turbulence model SST (k- ω) at 6, 8, and 10 m/s wind flow velocities via COMSOL software. Numerical simulation was validated employing previous articles. Outputs demonstrate that Bach-primary and Bach-developed wind turbine models have less flow separation at the spoke-end than the simple helical Savonius model, ultimately improving wind turbines’ total performance and reducing spoke-dynamic loads. Compared with the basic model, the Bach-developed model shows an 18.3% performance improvement in the maximum power coefficient. Bach’s primary model also offers a 12.4% increase in power production than the initial model’s best performance. Furthermore, the results indicate that changing the geometric parameters of the Bach model at high velocities (in turbulent flows) does not significantly affect improving performance.

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