Magnus type wind turbines: Prospectus and challenges in design and modelling

Abstract

a b s t r a c tOne of attracting concepts has been the use of Magnus effect to produce lift from rotating cylinders in various engineering applications. With emerging innovative Magnus type wind turbine technology, it is important to determine power performance and characteristics of such generators as correctly as possible. As stressed by Seifert, there is lack of theories in design and modelling of using Magnus force in engineering which is particularly noticed for the horizontal axis Magnus type wind turbines. In this study, the importance of research carried out for determining lift and drag forces of rotating circular cylinders is highlighted and reviewed. Then, the theoretical methods used in designing commercial aerofoil type wind turbines are extended to apply on the Magnus types. New formulation is presented for potential flow around the Magnus blades. The blade element momentum (BEM) theory is formulated for the Magnus wind turbines. A cubic function for angular induction factor is found from the BEM analysis which is strongly dependant on the drag to lift ratio. It is also observed that the relative wind incidence angle and the local power coefficient of the Magnus cylinder are independent functions of spin ratio.

Net Power Coefficient of Vertical and Horizontal Wind Turbines with Crossflow Runners

“…The 2D CFD model is also applied in this configuration, which means working in the 0 < α regime (Section 6). In this case, lift (Cl) and drag (Cd) coefficients of the spinning cylinders are calculated and used in a 3D analytical approximation (based on [15]) for estimating the Cp value as a function of TSR and α. In addition, we develop a formulation for estimating the net power coefficient that takes into account the power needed for spinning the runners in HAWT.…”

“…At spinning ratios α higher than 0.3, the flow at the wake of a crossflow runner clearly resembles that of a spinning cylinder at similar Re (see Figure 26; [39]). Therefore, the Cp equation is based on the analytical formulation developed by Sedaghat [15], who studied the performance of Magnus wind turbines (HAWT with spinning cylinders). The analytical approximation applies the blade element-momentum theory in which the blade is divided into elements of infinitesimal thickness dr along the radial direction.…”

“…The Magnus effect arises when a spinning cylinder is immersed in a flow and it provides a lift force that is the responsible for producing the required torque (see, e.g., [18]). Several versions of Magnus type turbines have been investigated, varying the number of spinning cylinders and their rotational speeds ω [15,[18][19][20]. The performance of Magnus type turbines depends on the cylinder spin ratio α, defined as…”

“…Sedaghat [15] has recently developed a theory for designing Magnus wind turbines with rotating cylinders working as blades in HAWT, estimating an optimum of C p = 0.35 at TSR = 1 in the range of 1.5 < α < 2.5 (see Table 1). In comparison with plain rotating cylinders, higher values of the lift coefficient have been obtained by using spiral fins [21,22], although the lift coefficient substantially decreases as the TSR tends to zero [22].…”

“…On the other hand, external energy (not related with the incoming air flow) is required for spinning the runner at fixed angular velocities in other regimes (e.g., 0 < α). This is a proper functioning for crossflow runners that work as blades in HAWT (as in Magnus HAWT [15]; see Table 2 and Figure 1). Table 2 also indicates the sign convention of α and the sense of rotation of the crossflow runner in all the figures of the present paper.…”