Frank N. Coton

An experimental and numerical study of the vortex filaments in the wake of an operational, horizontal-axis, wind turbine

Abstract The paper describes a wind-tunnel study of the wake dynamics of an operational, horizontal-axis wind turbine. The behaviour of the vorticity trailing from the turbine blade tips and the effect of was interference on wake development were considered. Laser sheet visualisation (LSV) techniques were used to measure the trajectories of the trailing vorticity under various conditions of turbine yaw and blade azimuth. Selected results obtained in the experimental study were compared with the predictions of a prescribed wake model and are being used in the further development of the method.

A Modified Dynamic Stall Model for Low Mach Numbers

The Leishman–Beddoes dynamic stall model is a popular model that has been widely applied in both helicopter and wind turbine aerodynamics. This model has been specially refined and tuned for helicopter applications, where the Mach number is usually above 0.3. However, experimental results and analyses at the University of Glasgow have suggested that the original Leishman–Beddoes model reconstructs the unsteady airloads at low Mach numbers less well than at higher Mach numbers. This is particularly so for stall onset and the return from the fully stalled state. In this paper, a modified dynamic stall model that adapts the Leishman–Beddoes dynamic stall model for lower Mach numbers is proposed. The main modifications include a new stall-onset indication, a new return modeling from stalled state, a revised chordwise force, and dynamic vortex modeling. The comparisons to the Glasgow University dynamic stall database showed that the modified model is capable of giving improved reconstructions of unsteady aerofoil data in low Mach numbers.

A high resolution tower shadow model for downwind wind turbines

Abstract A high resolution model for tower shadow effects on horizontal axis wind turbines has been developed which involves the use of a prescribed wake vortex model and an efficient near wake dynamic model of the vorticity trailed from the blade. The prescribed wake model is applied at first stage of the modelling strategy to provide basic information on blade aerodynamics. The near wake model has been enhanced with appropriate modifications and integrated into an unsteady aerofoil scheme to produce a hybrid method capable of predicting the detailed high resolution unsteady response in the tower shadow region. The computational cost introduced by the high resolution near wake model is almost negligible. Comparisons of the results of the high resolution scheme with measurement show a reasonable level of agreement. The model shows a strong impulsive response of the blade loading when the blade is passing out of the tower shadow, which requires further investigation.

A New Stall-Onset Criterion for Low Speed Dynamic-Stall

The Beddoes/Leishman dynamic-stall model has become one of the most popular for the provision of unsteady aerofoil data embedded in much larger codes. The underlying modeling philosophy was that it should be based on the best understanding, or description, of the associated physical phenomena. Even though the model was guided by the flow physics, it requires significant empirical inputs in the form of measured coefficients and constants. Beddoes provided these for a Mach number range of 0.3–0.8. This paper considers one such input for a Mach number of 0.12, where, from the Glasgow data, it is shown that the current stall-onset criterion, and subsequent adjustments, yield problematic results. A new stall criterion is proposed and developed in the best traditions of the model. It is shown to be very capable of reconstructing the Glasgow’s data for stall onset both the ramp-up and oscillatory tests.

An experimental study of dynamic stall on a finite wing

This paper examines the dynamic stalling of a finite wing of aspect ratio 3·0 when subject to constant pitch motions up to and beyond stall. In particular, unsteady surface pressure data were obtained at 192 locations on the wing surface and these were then analysed to provide information on the nature and phasing of dynamic stall events in both the chordwise and spanwise directions. It was also possible to obtain sectional force and moment coefficients by integration of the pressures measured on specific chordal arrays. This provided valuable insight into the load distribution on the wing throughout the range of motion. On this basis, it was established that the wing loading distribution was consistent with conventional understanding of steady wing loading up to the incidence at which the dynamic stall vortex was initiated. Beyond this point, the formation and subsequent convection of the vortex structure was found to be strongly three-dimensional but, nevertheless, exhibited many of the features of two-dimensional dynamic stall.

Computational Fluid Dynamics Study of Three-Dimensional Dynamic Stall of Various Planform Shapes

Numerical simulation of 3-D dynamic stall has been undertaken using computational fluid dynamics. As a first step, validation calculations have been performed for cases in which experimental data were available. Although the amount and quality of the experimental data available for 3-D dynamic stall does not match what is available for 2-D cases, the computational fluid dynamics was found capable of predicting this complex 3-D flow with good accuracy. Once confidence on the computational fluid dynamics method was established, further calculations were conducted for several wing planforms. The calculations revealed the detailed structure of the 3-D dynamic stall vortex and its interaction with the tip vortex. Remarkably, strong similarities in the flow topology were identified for wings of very different planforms.

Control of Rotorcraft Retreating Blade Stall Using Air-Jet Vortex Generators

A series of low-speed wind tunnel tests was carried out on an oscillating airfoil fitted with two rows of air-jet vortex generators (AJVGs). The airfoil used had an Royal Aircraft Establishment 9645 section, and the two spanwise arrays of AJVGs were located at x/c = 0.12 and 0.62. The devices and their distributions were chosen to assess their ability to modify/control dynamic stall, the goal being to enhance the aerodynamic performance of helicopter rotors on the retreating blade side of the disk. The model was pitched about the quarter chord with a reduced frequency k of 0.1 in a sinusoidal motion defined by a = 15 + 10sin ωt deg. The measured data indicate that, for continuous blowing from the front row of AJVGs with a momentum blowing coefficient C μ greater than 0.008, modifications to the stalling process are encouraging. In particular, the pitching moment behavior exhibits delayed stall and there is a marked reduction in the normal force hysteresis.

An Unsteady Prescribed Wake Model for Vertical Axis Wind Turbines

This paper describes the development of a fully unsteady three-dimensional aerodynamic performance prediction scheme for vertical axis wind turbines (VAWTs). The method is based on the prescribed wake approach of Basuno in which the turbine is represented by a series of bound vortex segments from which emanates a wake consisting of shed and trailing vorticity filaments. Unlike a free vortex method, these wake filaments are constrained to follow a predetermined path, the shape of which is dictated by momentum considerations. By coupling this technique with the unsteady aerofoil performance method of Leishman and Beddoes, a fully unsteady V AWT model is developed. The difficulties associated with coupling the two techniques are discussed and a new formulation for the tangential blade force is introduced. The resulting calculation scheme is shown to agree well with field data from a straight bladed vertical axis wind turbine, even at very low tip speed ratios.

Prediction of Dynamic Stall Onset for Oscillatory Low-Speed Airfoils

This research presents some common features of oscillatory airfoils, and the method for indicating dynamic stall onset for the unsteady process. Under deep stall conditions, the stall-onset angle in oscillation is independent of the mean angle of the oscillatory motion, and by combining the reduced frequency and the amplitude of the oscillatory motion, the equivalent reduced pitch rate is an analog of this motion to the constant reduced pitch rate of the ramp-up motion. By correlating with the measured data, and with the ramp-up results, the equivalent reduced pitch rate can be defined as a representation for the oscillatory motion. Accordingly, the triple-parameter problem of an oscillation (mean angle, reduced frequency, and amplitude) degrades into the single-parameter problem (equivalent reduced pitch rate). Based on these foundations, an extension of the stall-onset criterion is then made for oscillatory airfoils: a method of extracting the stall-onset parameters directly from oscillatory test data, and an indication of stall onset for the oscillatory airfoils. The results from the new proposed method have shown the consistency with the data of Glasgow University and the public data.

Improved dynamic-stall-onset criterion at low Mach numbers

cN = normal force coefficient, N=qc cp = pressure coefficient, p=q D = drag f = dimensionless separation point in terms of chord length, x=c L = lift of airfoil section M = Mach number m = pitching moment about the axis of the quarter-chord N = normal force q = dynamic pressure, 0:5 V r = reduced pitch rate, _ c=2V (for oscillatory motion of an airfoil, 0 cos!t) r0 = reduced pitch rate that delimits the dynamic stall and quasi-steady stall (normally, 0:01) s = nondimensional time, 2Vt=c T = time-delay constant for angle of attack t = time V = freestream velocity = angle of attack or incidence 0 = lagged angle of attack cr = critical onset angle (dependent on reduced pitch rate) ds = angle of dynamic-stall onset ds0 = constant critical onset angle ss = static stall angle = a step change in a sampled system 0 = amplitude of airfoil oscillation k = reduced frequency, !c=2V = linear fit coefficient for stall-onset incidences ! = frequency of oscillatory motion of airfoils Introduction