Induced Velocity Distribution Research Articles

Inviscid analysis of horizontal axis wind turbines using distributed vorticity elements

The primary tool currently used for a wind turbine preliminary design is the blade element momentum method, which lacks a detailed wake model and relies on an assumption of non-interacting streamtubes. These simplifications limit the designer's ability to tailor the blade shape to minimize the induced power loss of the rotor. Improved prediction of the induced velocity distribution on the blades can be achieved through the use of vortex-based models at a computational cost low enough for use in design processes requiring many iterations. This paper presents the implementation of a potential flow, lifting-surface methodology using elements of distributed vorticity. The use of such elements provides several advantages including higher resolution than filament-based methods, simulation of non-planar blade planforms, and avoids the need for empirical corrections. Because the wake has a strong influence on the flow at the rotor, the accurate prediction of its geometry is highly important for wind turbine analysis. To this end, a force-free relaxed-wake model is presented as well as less numerically intensive fixed-wake and hybrid-wake models. Comparison is made to the blade element momentum method and Goldstein's theoretical solution for the ideal lightly loaded rotor.

PIV Analysis Of Skin Friction And Coherent Structures In Turbulent Drag Reduction Regimes

In the present work, planar and tomographic PIV are used to investigate how the organisation of wall turbulence is altered when actuators are operated with the objective of reducing the skin friction drag. When the wall is mechanically oscillated in the spanwise direction, high-resolution planar PIV enable the direct measurement of wall shear and a 15% reduction of skin friction is observed. The use of tomographic PIV enables access to the threedimensional organisation of low- and high-speed streaks, along with ejection events and associated hairpin vortices. These observations help forming a conceptual model of the salient drag reduction mechanism, whereby hairpin autogeneration is inhibited through a tilting action at the tail of low-speed streaks. The second part of the study documents an effort to surrogate the mechanical oscillation by means of a densely distributed array of AC-DBD plasma actuators. The latter are first characterised in quiescent flow, where the induced velocity distribution is obtained and compared to the solution of the classical second Stokes problem that models the mechanical oscillation. The induced peak of spanwise velocity is found to surpass the velocity of the oscillating wall. However, the wall jet height develops further away from the wall. More importantly, the spatially inhomogeneous distribution of the unsteady body force produces an unwanted lattice of starting streamwise vortices. The latter are deemed to be detrimental for the purpose of drag reduction, compared to the orderly and homogeneous sideways motion induced by mechanical wall motion. The application of the AC-DBD actuator currently leads to a pronounced momentum deficit in the logarithmic region and increases skin friction. Finally, further research directions are anticipated, that potentially circumvent the formation of streamwise vortices by means of AC-DBD actuators operating in steady regime.

Inverse aerodynamic design for DEP propeller based on desired propeller slipstream

Considering the multi-propeller characteristics of DEP (distributed electric propulsion) configuration, the lift-to-drag ratio of the wing is improved by optimizing the slipstream of the propeller, rather than changing the chord length and twist distribution along the span of the wing. In this paper, a propeller inverse design method based on slipstream characteristics is developed. In the case of propeller design, only a few general parameters and induction factor distribution form have to be prescribed and the design procedure returns the propeller geometry in terms of chord-length and blade-angle distributions along the radius. Propellers with different induced velocity distributions are designed based on this method. It is found that the propellers with larger induced velocity near the hub can improve the lift-to-drag ratio of the wing without changing the parameters of the wing, drag decreases by 12.32% and the lift-to-drag ratio of the wing with single propeller increase by 16.10%, respectively. A 27.12% drag reduction and 43.21% lift-to-drag ratio improvement can be obtained when three propellers are used.

Propeller-wing coupled aerodynamic design based on desired propeller slipstream

Considering the multi-propeller characteristics of DEP configuration, the lift-to-drag ratio of the wing is improved by optimizing the slipstream of the propeller, rather than changing the chord length and twist distribution along the span of the wing. First, a propeller design method is proposed to obtain the target induced velocity distribution, and then, a calculation model Prop−wing of propeller-wing integration is established based on the designed induced velocity distribution and panel method. Finally, an efficient optimization algorithm based on genetic algorithm (GA) and Kriging surrogate modeling is used to optimize the induced velocity distribution of the slipstream for higher lift-to-drag ratios. The optimization results show that when the thrust is constant, the larger the axial induced velocity close to the hub, the better the drag characteristics of the wing. When the chord length of propeller is not limited, the drag decreases by 30.48% and the lift-to-drag ratio increases by 51.93%. A 13.68% drag reduction and 18.80% lift-to-drag ratio improvement can be obtained.

Ideal wind turbine performance at very low tip speed ratio

At very low tip speed ratios, wind turbine rotors behave similarly to stationary wings for which the well-known lifting line analysis gives the optimal loading. Lifting line analysis is applied to a stationary rotor of N blades for N = 1, 2, and 4. Analytic (for N = 1 and 2) or semi-analytic solutions (for N = 4) agree with the classical results obtained by conformal mapping. The present solutions compare well with numerical solutions for the Goldstein function for optimally loaded propeller or wind turbine rotors at low tip speed ratio. In all cases, the induced velocity is linear with radius. Assuming this result applies for all N, lifting line analysis is recast as a singular integral equation whose solution agrees with Goldstein's obtained using the same conformal mappings as in his general analysis for any tip speed ratio. The implication is that the assumed induced velocity distribution is correct, and is, therefore, fundamentally different from that at high tip speed ratios when the induced velocity is inversely proportional to radius. For any N, the power and thrust coefficients become proportional to the square of the tip speed ratio and the tip loss factor alters significantly from the common form used at higher tip speed ratios. Extending the analysis to finite pitch was not achieved but several important results were obtained, including the behaviour of the tip loss as N varies at low tip speed ratio. The behaviour is complex and the resulting tip loss factor exceeds unity for a significant part of the blade.

Correction of the definition of mass flow parameter in dynamic inflow modelling

The dynamic inflow model, which has been extensively developed by Peters and his co-workers for the last two decades, is a powerful tool for predicting the induced velocity distribution over a rotor disc. Scant attention has, however, been paid so far in using the model to analyse an autorotative rotor. The authors identified a necessary change to the mass flow parameter of the original model of Peters for autorotating rotors. In response, questions were raised by readers about how the modified and original inflow parameters should consistently be explained, why the original model of Peters is insufficient for autorotation, and how the validity of the modified mass flow parameter can mathematically be enunciated. Indeed, the discussion in the article by Murakami and Houston (2008) was held in a manner that readers might have received an impression that the modified model was derived independently of the original model, and the connection to the original model was not clearly presented. This technical note is written with an aim to elucidate the mathematically consistent relationship between the original and modified mass flow parameters, and it is confirmed that the original definition of the mass flow parameter contains an error in its definition. It is concluded that the unified mass flow parameter, which is presented in this article, should always be used in the dynamic inflow model.

Estimating the angle of attack from blade pressure measurements on the National Renewable Energy Laboratory phase VI rotor using a free wake vortex model: yawed conditions

AbstractWind turbine design codes for calculating blade loads are usually based on a blade element momentum (BEM) approach. Since wind turbine rotors often operate in off‐design conditions, such as yawed flow, several engineering methods have been developed to take into account such conditions. An essential feature of a BEM code is the coupling of local blade element loads with an external (induced) velocity field determined with momentum theory through the angle of attack. Local blade loads follow directly from blade pressure measurements as performed in the National Renewable Energy Laboratory (NREL) phase IV campaign, but corresponding angles of attack cannot (on principle) be measured. By developing a free wake vortex method using measured local blade loads, time‐dependent angle of attack and induced velocity distributions are reconstructed. In a previous paper, a method was described for deriving such distributions in conjunction with blade pressure measurements for the NREL phase VI wind turbine in axial (non‐yawed) conditions. In this paper, the same method is applied to investigate yawed conditions on the same turbine. The study considered different operating conditions in yaw in both attached and separated flows over the blades. The derived free wake geometry solutions are used to determine induced velocity distributions at the rotor blade. These are then used to determine the local (azimuth time dependent) angle of attack, as well as the corresponding lift and drag for each blade section. The derived results are helpful to develop better engineering models for wind turbine design codes. Copyright © 2008 John Wiley & Sons, Ltd.

Dynamic inflow modelling for autorotating rotors

AbstractThe dynamic inflow model is a powerful tool for predicting the induced velocity distribution over a rotor disc. On account of its closed form and simplicity, the model is especially practical for studying flight mechanics or for designing control systems for helicopters. Scant attention has, however, been paid so far in utilising the dynamic inflow model to analyse an autorotating rotor, which is different from a powered rotor in the geometric relation between the direction of the inflow and the rotor disc. Autorotation is an abnormal condition for helicopters, but for gyroplanes it is the normal mode of operation. Therefore the theoretical discussion on an autorotating rotor is of importance not only to improve the understanding of present gyroplanes, but also in the development of new gyroplanes and to analyse the windmill-brake state of helicopters. Dynamic inflow modelling is reviewed from first principles, and this identifies a modification to the mass flow parameter. A qualitative assessment of this change indicates that it is likely to have a negligible impact on the trim state of rotorcraft in autorotation, but a significant effect on the dynamic inflow modes in certain flight conditions. This is confirmed by numerical simulation, although considerable differences only become apparent for steep descents with low forward speed. It is concluded that while modification of the mass flow parameter is perhaps mathematically accurate, for practical purposes it is required only in a limited area of the flight envelope of autorotating rotorcraft.

Mesoscale calculations of the dynamic behavior of a granular ceramic

Mesoscale calculations have been conducted in order to gain further insight into the dynamic compaction characteristics of granular ceramics. The primary goals of this work are to numerically determine the shock response of granular tungsten carbide and to assess the feasibility of using these results to construct the bulk material Hugoniot. Secondary goals include describing the averaged compaction wave behavior as well as characterizing wave front behavior such as the strain rate versus stress relationship and statistically describing the laterally induced velocity distribution. The mesoscale calculations were able to accurately reproduce the experimentally determined Hugoniot slope but under predicted the zero pressure shock speed by 12%. The averaged compaction wave demonstrated an initial transient stress followed by asymptotic behavior as a function of grain bed distance. The wave front dynamics demonstrate non-Gaussian compaction dynamics in the lateral velocity distribution and a power-law strain rate–stress relationship.

A theoretical analysis of formation flight as a nonlinear self-organizing phenomenon

This study analyses the existence, stability and self‐organization of formation flight utilized by migrant birds. Air is approximated as an incompressible inviscid flow, while birds are modelled as elliptically loaded lifting‐lines. Application of conventional wing theory leads to newly derived, basic equations that describe the problem as a dynamical system of multiple wings interacting with each other through induced flow field. Formation flight is defined as the steady‐state solution of the basic equations, in particular the solution that all the birds fly at the same speed. In the case of a prescribed thrust, constant transverse interval between adjacent birds, and a flock of physically identical birds, analytical study of the basic equations reveals the facts that (1) formation flight is self‐organized and (2) this formation flight is stable. The new implication is that a configuration of formation emerges as a result of nonlinear dynamical interaction between many birds and that this nonlinear dynamical system does not exhibit chaotic behaviour. Numerical calculation has also been done for cormorant‐type birds with the same transverse interval between flock members. The proposed numerical scheme quickly converges to very accurate results owing to the recently derived, closed‐form expression of induced velocity distribution around an elliptically loaded lifting‐line. Transverse intervals between birds are found to be a more important factor than the number of birds. Configurations of formations are found to be inverted U rather than inverted V. In these formations every bird enjoys the same amount of drag reduction.

地面近傍で低速飛行するロータまわりの流れ場の数値計算

It is known that when a rotor is flying over the ground at low speed, a ground vortex may appear in front of the rotor. The ground vortex, which can be formed by the interaction between the rotor downwash and the incoming flow in close proximity to the ground, will change the performance of the rotor. The flow environment becomes much more complex compared with that of O.G.E. flight. It is clearly necessary to investigate the basic physical phenomenon of the ground vortex and its effect on the aerodynamic characteristics of the rotor. Therefore, numerical study of the flowfields around a rotor in forward flight near the ground at low speed are carried out by solving the CFD code based on unsteady 3D compressible Euler equations with a moving grid system. In this paper, we present typical numerical results with respect to the formation of ground vortex, the induced velocity distribution on the rotor disc, and describe the effect of the rotor height and advanced ratio on the rotor thrust.

Studies of helicopter dynamic stability and control laws

Studies of the hingeless rotor helicopter dynamic stability and control laws are conducted. A new method is given for the calculation of stability and controllability of a helicopter in flight condition with lateral velocity. First, the rotary wing dynamic model considered is the one of flap‐pitch (including the elastic deformation of control system) – torsion coupling. The induced velocity non‐uniform distribution derived from vortex theory is taken into account. Then, according to the established motion model of the helicopter, the effects of induced velocity distribution, flap‐pitch‐torsion coupling and lateral velocity on the stability and controllability of the helicopter are analyzed. Based on the analyses of dynamic stability of the helicopter, the unstable mode and the necessity of installation of stability augmentation system (SAS) are recognized. Finally, the control laws of SAS for helicopter pitching, rolling and yawing motions are presented. After establishing helicopter flight control state ...

ティルトロータのブレードフラッピング運動と誘導速度分布

As basic researches to clarify aero-mechanical behaviors of a tilt rotor, the blade flapping motions during low speed transition state are analyzed using the proposed inflow model for a rotor being subjected to uniform flow with arbitrary attitude angle from 0° (rotor mode) to 90° (propeller mode). The inflow model is formulated by extending acceleration potential theory for a circular wing so aerodynamic load and corresponding induced velocity distributions as to be consistent with the flapping motions obtained by dynamic running test with the model rotor. Comparisons between calculated and measured blade flapping motions for the rotor both at fixed attitude and tilting conditions are made, thus ascertained usefulness and reasonability of proposed inflow model.

加速度計を用いたティルトロータブレードのフラッピング運動の計測と誘導速度分布の同定

Induced velocity fields around a rotor which is subjected to uniform velocity with arbitrary attitude angles are estimated using measured blade flapping motion and system identification technique. The blade flapping motions are detected by blade mounted accelerometers and potentiometer so that blade flexibility effects on its aero-mechanical behavior could be captured. The measured data reconstructed by the sensor equation are fed into the kinematic observer for flapping rate estimation and then parameters which describe induced velocity distribution are identified by the recursive least-square method. Induced velocity distributions for a tilting rotor are modeled by interpolating these identified parameters. Comparisons between calculated and measured blade flapping responses for a tilting rotor are made. It is understood that identification processes are quite smooth and usefulness of the proposed identification procedure are ascertained.

Modeling the unsteady aerodynamic forces of a maneuvering rotor

The details of predicting the aerodynamic forces of maneuvering helicopter rotors are discussed in this paper. A new approach to modeling the unsteady rotor aerodynamic forces is presented based on the insight into nonuniform induced velocity distribution, inflow dynamics and unsteady airfoil behavior. For a specified maneuver, the rotor control inputs and helicopter flight attitudes during the maneuvering are first obtained using inverse solution technique, and then the unsteady rotor forces are numerically simulated by synthetically applying the vortex theory, dynamic inflow theory and unsteady airfoil aerodynamic models. Good results of the sample calculations of lateral jink and pop‐up maneuvers are obtained.

Application of Asymptotic Acceleration Potential Method for the Calculation of Yawed Inflow Effect on Horizontal Axis Wind Turbine Rotor.

We describe a method of calculating yawed inflow effects on horizontal axis wind turbine rotors. Yawed inflow brings about asymmetric induced velocity distributions on the rotor plane due to an inclined vortex wake construction. For the calculation of yawed inflow phenomena, an inviscid aerodynamic model based on pressure distributions is adopted. Under the assumptions of an incompressible inviscid irrotational flow, the pressure perturbation satisfies the Laplace equation and acts as an acceleration potential function. The rotor blades are represented by spanwise and chordwise pressure distributions composed of analytical first-order asymptotic solutions to the Laplace equation. Integration of the accelerations determines the velocities in the rotor plane. With these velocities the aerodynamic loads can be calculated. An advantage of this model is that evaluation of the relatively complicated unstationary effects from the vorticity in the wake is not necessary in the calculation procedure.

走行実験による低速飛行時のヘリコプタロータの縦横連成効果に関する実験的研究

The cross coupling effects of a helicopter rotor in low advance ratio are experimentally studied using the Dynamic Running Test Facility which was built at National Defense Academy recently. Design features and basic performances of the facility are briefly described. Flapping motions of the model rotor blade are precisely measured together with its thrust and torque characteristics at various combinations of test parameters. It is clarified that nonlinear behavior of the cross coupling effects on the advance ratio are attributed to the phase shift properties of blade flapping motions due to nonuniformity of induced velocity distributions on the rotor disc. Usefulness of a dynamic running test is also ascertained for accurate measurements of aerodynamic and dynamic phenomena of a rotorcraft in low speed flight.

Induced Airflow Created by Large Hovering Beetles

When hovering, the rhinoceros beetle, Strategus sp., produces a downstream wake pattern such that the induced velocity peak value occurs close to the body. Implicit are large radial inflows at the flapping plane. Such a pattern contrasts greatly with classic helicopter, propeller, and assumed insect induced velocity distributions.

Pitch damping of helicopter rotor with nonuniform inflow

Pitch or roll damping of helicopter rotor has been experimentally studied by using model rotors in rocking motion. The rotors have articulated blades with spring constrained hinges and different combinations of Lock number, flapping hinge offset, and hinge constrained stiffness. By considering nonuniform induced velocity distribution a theoretical estimation based on the momentum and blade element theory has shown good coincidence with the experimental results. In contrast with analyses based on the vortex theory the present theory is very simple and does not require complex calculations so that the analytic evaluation and the quick estimation of the dynamic stability derivatives of rotor will be possible. The blade flapping behavior during sinusoidal rocking motion has also been analytically and experimentally analyzed and the mechanism of generation of direct damping and cross coupling moments have been clearly explained.

ローターの逆対称荷重が,ローター・ディスク面内の誘導速度の分布に及ぼす影響について

The purpose of this investigation is to seek the distribution of the induced velocity of a rotor in forward flight. Several analytical reports have been published on the induced velocity field of rotors having non-uniform disc loading, but they have not suCCeeded to express the irresults by utilizable analytic functions. In this report, we substituted a circular wing for a rotor under suitable assumptions, and using the antisymmetric solutions of acceleration poten- tial of this circular wing, we could express the effect of antisymmetric disc loading to the distri-bution of induced velocity of the rotor by analytic functions. During this investigation, we could also clear out a correlative relation between the load and the induced velocity distribution along the lateral direction.