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 Modified Dynamic Stall Model for Low Mach Numbers

Unsteady aerodynamics imposes additional demands on the modeling of vertical axis wind turbines. Large variations in the angles of attack of the blades cause force oscillations, which can lead to the fatigue-associated problems. Therefore, an accurate estimation of the dynamic loads is essential for the vertical axis wind turbines design. Dynamic stall modeling is in focus because it represents complex phenomena associated with the unsteady flow conditions. The purpose of the study is to find a suitable dynamic stall model for the vertical axis wind turbine conditions. Three versions of the Leishman–Beddoes model are explicitly presented. Additional modifications are implemented for the model to work when the angles of attack change sign and have high amplitudes. All the model parameters are presented. The model is assessed against measured data. The conditions for the simulation tests are close to the vertical axis wind turbine operational conditions. A version of the model, originally designed for low M...

Dynamic Stall Modeling for the Conditions of Vertical Axis Wind Turbines

or above the blade stall angle only The results show significant potential for flow control by jet blowing using all methods and approaches Single-sided blowing resulted in a 59% increase net energy yield, while double-sided blowing produced improvements in excess of 150%, even when secondary system losses were factored into the estimates

Effect of Leading-Edge Slot Blowing on a Vertical Axis Wind Turbine

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.

Prediction of Dynamic Stall Onset for Oscillatory Low-Speed Airfoils

The leading-edge flow structure of the NACA 0012 airfoil is experimentally investigated under dynamic-stall conditions (M=0.1; α=16.7, 22.4 deg; Rec=1×106) using planar particle image velocimetry. The airfoil was dynamically pitched about the one-fourth chord at a reduced frequency, k=0.1. As expected, on the upstroke, the flow remains attached in the leading-edge region above the static stall angle, whereas during downstroke, the flow remains separated below the static stall angle. A phase-averaging procedure involving triple velocity decomposition in combination with the Hilbert transform enables the entire dynamic-stall process to be visualized in phase space, with the added benefit of the complete phase space composed of numerous wing oscillations. The formation and complex evolution of the leading-edge vortex are observed. This vortex is seen to grow, interact with the surrounding vorticity, detach from the surface, and convect downstream. A statistical analysis coupled with instantaneous realization...

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Leading-Edge Flow Structure of a Dynamically Pitching NACA 0012 Airfoil

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

Improved Dynamic-Stall-Onset Criterion at Low Mach Numbers

National Renewable Energy Laboratory, USA (NREL) airfoils have been specially developed for wind turbine applications, and projected to yield more annual energy without increasing the maximum power level. These airfoils are designed to have a limited maximum lift and relatively low sensitivity to leading-edge roughness. As a result, these airfoils have quite different leading-edge profiles from airfoils applied to helicopter blades, and thus, quite different dynamic-stall characteristics. Unfortunately for wind turbine aerodynamics, the dynamic-stall models in use are still those specially developed and refined for helicopter applications. A good example is the Leishman―Beddoes dynamic-stall model, which is one of the most popular models in wind turbine applications. The consequence is that the application of such dynamic-stall model to low-speed cases can be problematic. Recently, some specific dynamic-stall models have been proposed or tuned for the cases of low Mach numbers, but their universality needs further validation. This paper considers the application of the modified dynamic low-speed stall model of Sheng et al. ( "A Modified Dynamic Stall Model for Low Mach Numbers, " 2008, ASME J. Sol. Energy Eng., 130(3), pp. 031013) to the NREL airfoils. The predictions are compared with the data of the NREL airfoils tested at the Ohio State University. The current research has two objectives: to justify the suitability of the low-speed dynamic-stall model, and to provide the relevant parameters for the NREL airfoils.

Roderick A. McD. Galbraith

Papers

Improved Dynamic-Stall-Onset Criterion at Low Mach Numbers

Applications of Low-Speed Dynamic-Stall Model to the NREL Airfoils

Applications of Low Speed Dynamic Stall Model to the NREL Airfoils