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.
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 modelling philosophy was that it should be based on the best understanding, or description, of the associated physical phenomena. Even although the model was guided by the flow physics, it requires significant empirical inputs in the formThese conditions are normally associated with pitching and plunging motions and were initially of much interest to helicopter rotor-aerodynamicists, who required an assessment of rotor loads during forward and manoeuvring flight. Today, dynamic stall is also relevant to the performance and durability of wind turbines.Carr [4] gives an illustration for the events of a dynamic stall process, for an aerofoil undergoing a sinusoidal pitch profile, shown in Figure 1. Chronologically, the dynamic stall events start at point (a), where the pitching aerofoil passes the staticstall angle of attack, but without any discernible change in the flow around the airfoil, and the flow remains fully attached.Then the flow reverses near the surface at the trailing edge region starting at point (b), but still with no large separation due to the dynamic effects. This reversal moves up the chord until it covers most of the aerofoil, at which stages ((c) and (d)) the leading edge flow no longer remains attached and a strong vortical flow develops (point (e)). As the vortex enlarges and remains close to the leading edge, there is an obvious increase in the lift-curve slope at (f) and associated vortically induced normal force coefficient, N C , ((g) and (h)). The vortex subsequently convects downstream and finally detaches from the trailing edge, inducing a strong nose-down pitching moment at (i). After that, when the flow over the aerofoil upper surface is fully separated, the lift break (lift stall) occurs (j). As the angle of attack decreases continuously, the reattachment process takes place. According to Niven et al [5], at some angle of attack (close to the static fully-stalled state), the leading edge reattachment occurs. This is characterised by two distinct but related events. First, all the large eddies, due to the stall, are convected over the chord and into the free stream at constant speed and, second, following closely behind is the reestablishment of a fully attached boundary layer. The convective component, i.e. the first, normally takes a few chord lengths of free-stream travel, at which point the lift reaches its lowest value. Then the flow transits to a fully attached state at the end of stage (k). Obviously, the whole process forms a large hysteresis loop, shown in figure 1, which is taken from Carr et al.[6].Leishman [7] explores the flow topology of dynamic stall and summarises that the aerofoil dynamic behaviour is significantly different from the steady case in following three aspects:-Under dynamic conditions, since the circulation is shed into the wake at the trailing edge of the aerofoil, the induced un...
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