A Computational Study of the Aerodynamics of a Spinning Cylinder in a Crossflow of High Reynolds Number

28TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES A COMPUTATIONAL STUDY OF THE AERODYNAMICS OF A SPINNING CYLINDER IN A CROSSFLOW OF HIGH REYNOLDS NUMBER E. R. Gowree and S. A. Prince Centre of Aeronautics, City University London [email protected]; [email protected] Abstract ambient wind speed the cylinder’s performance was vulnerable, and due to the large availability A Computational Fluid Dynamics (CFD) and low cost of fuel in that era the idea was analysis of the high Reynolds number (Re § 94k) rendered redundant. flow around a quasi-2D spinning cylinder in a The UAV (unmanned aerial vehicle) or crossflow, using a high resolution 3D time MAV (micro air vehicle) industry is currently marching unsteady Navier-Stokes solver was expanding due to these crafts ability to operate conducted. The lift coefficients predicted were in hostile and inhospitable environments. An in fair agreement with experimental results elaborate feasibility study conducted by C. except in the Inverse Magnus Effect region (0.4 Badalamenti [2] during his Doctoral research < ȍ < 0.7). The fact that these simulations were has demonstrated that spinning cylinders can be computed as purely laminar boundary layer an alternative for conventional fixed wings flows, and failed to resolve any evidence of the when high lift to drag ratio is required. In Inverse Magnus Effect, would tend to support addition, unlike conventional wings spinning the proposition that the Inverse Magnus Effect cylinders are not constrained by stall and is associated with boundary layer transition. therefore could therefore offer increased The trends in the experimentally measured payload capability. Further benefits in mission shedding frequency with cylinder spinning performance might be achieved during speed were captured reasonably well by the operations in high density ambient conditions numerical model which resolved the initial rise such as in Polar latitudes. One interesting in vortex shedding frequency with increased ȍ, application where high lifting capability would followed by a rapid fall. At ȍ§ 2, suppression be essential, and which needs some in the vortex shedding was observed and this investigation, would be for flight vehicles for finding demonstrates that vortex shedding the unmanned exploration of extra-terrestrial degradation and suppression with increase in environments such as the surfaces of Mars or velocity ratio is still present even for high Re Titan. flow in the subcritical regime. The lack of application for rotating cylinder wings due to practicality issues at high subcritical Reynolds number (Re) has hampered 1 Introduction the research directed towards understanding the An attempt to harness the energy generated highly complex flow physics, especially within from the ‘Magnus Effect’ from spinning the viscous layer and the behaviour of the cylinders was made by Anton Flettner [1] in the vortical wake. Experimental investigations at mid 1920’s. Later he demonstrated the concept high Re are usually hindered by structural by replacing the conventional sails by spinning dynamics issues related to the model and there circular cylinders for the propulsion of large are still arguments on the vortex shedding ships, through the modification of the ‘Buckau’ mechanism at high velocity ratios. Therefore, a and ‘Barbara’. However, being a function of the numerical study has been launched to investigate whether the vortex shedding and the 1 E. R. Gowree & S. A. Prince aerodynamics forces can be captured qualitatively at high Re and spinning speed using CFD, bearing in mind that the ‘Inverse Magnus Effect’ might present a challenge due to the transitional nature of the boundary layer. 1.1 The Magnus Effect The result of the survey on Magnus Effect conducted by Swanson [3] in the early 1960’s has demonstrated that in the grand scheme of things the magnitude of the lift coefficient (CL) Fig 1: Schematic reprensentation of the viscous flow generated by a spinning cylinder increases with engulfing a spinning cylinder. [3] increase in the ratio of peripheral to freestream velocity ratio (ȍ). The prime observation suggested that CL was a function of the aspect ratio (AR), end effects and Reynolds number and the maximum lift coefficient (CLmax) of 4ʌ, which Ludwig Prandtl initially suggested can be exceeded by use of cylinders with large AR. According to Swanson [4] and Krahn [5] the initial increase in CL with increase in ȍ was due to the asymmetrical laminar boundary layer separation between the upper and the lower surface. A larger extent of attached boundary layer and the associated region of suction, on the upper surface, compared with the lower Fig 2: The effect of AR on the amount of lift generated. [2] surface, results in increased lift. Swanson suggested that this shift in the separation point was a consequence of the 1.2 The Inverse Magnus Effect displacement of the boundary layer origin which progressed along the direction of rotation as Based on Swanson’s analysis, unlike the AR, shown in figure 1. increasing the Re of the flow has a more The most recent experimental study to complicated effect on the magnitude of the prove the dependency of CL on AR was aerodynamic forces, especially at ȍ < 1.0. From undertaken by Badalamenti and Prince [6] in Swanson’s experimental results shown in 2008 on a cylinder with AR = 5.1. A Figures 3(a) and 3(b) (where the Re of each comparison of the authors’ results with previous corresponding cases has been quoted in Table 1 experimental results for a range of AR is shown 1). For Re 61k a loss in CL similar to the post in Figure 2 (more information of the references stall characteristic on an aerofoil can be quoted in the legend can be obtained from observed, this effect has been referred as the reference 4). It was shown that an increase in ‘Inverse Magnus Effect’ which was initially AR would lead to a higher achievable maximum presented by Lafay [7] in 1910. The effect lift, and for low and medium AR (1.5 < AR < 6) became more pronounced for 225k Re 365k the point where CL starts to plateau (maximum as there was rather an initial decrease in CL. A point followed by a constant lift) could be similar trend was encountered by Badalamenti shifted upward through the introduction of et al. at Re > 43k, therefore it might be fair to endplates which were at least 1.5 times the hypothesise that this effect is dependent on the diameter of the cylinder. 1 ‘k’ represents 103 2 A COMPUTATIONAL STUDY OF THE AERODYNAMICS OF A SPINNING CYLINDER IN A CROSSFLOW OF HIGH REYNOLDS NUMBER interaction of the fluid and the amplification of wake due to the transitional nature of the the disturbances within the viscous layer. boundary layer which stays attached over a further extent once in their turbulent state. In this regime the viscous layer appears to be very vulnerable to small instabilities in the flow. Keeping this in mind, Swanson suggested that as ȍ is increased the ‘relative Reynolds number’, (1±ȍ), of the boundary layer on the lower surface would increase with respect to ܴ݁the௥௘௟ freestreamൌ ܴ݁ Re due to an increase in relative velocity, and vice versa, and thus it would transition to turbulent. In this state it would stay attached further downstream and the suction on the surface concerned would be extended, hence reducing the net lift generated. This effect would become more pronounced Fig 3(a): The effect of Re on the variation of CL with ȍ [3]. with an increase in ȍ until both of the boundary layers become fully turbulent, which will be marked by the minimum point in the trend. Fig 3(b): The effect of Re on the variation of C with ȍ L Fig. 4: The effect of Re on the magnitude of aerodynamic [3]. forces generated by a stationary circular cylinder in a Prior to the detailed analysis of the Inverse crossflow [8]. Magnus Effect, which was observed at ȍ > 0.35 in the case considered above, it might be helpful to investigate the nature of the viscous layer in Table 1: The Re for the corresponding cases represented that flow regime. Referring to figure 3, which in Figure 3(a) and 3(b). Case Re Case Re was produced by Zdravkovich [8] for the Re of the current investigation, on a stationary a 36k i 225k cylinder the flow is essentially subcritical and in b 49k j 260k the upper limit of transition in the shear layer c 61k k 295k regime. This fact can also be supported by the d 79k l 325k drag measurement performed by Swanson (see e 99k m 365k ‘Figure 6’ of reference 3) on the stationary f 128k n 420k cylinder where a sudden decrease in CD with g 152k o 450k further increase in Re was observed for Re > h 182k p 501k 99k (case ‘e’). This behaviour is common with low speed flows around bluff bodies, and is a direct effect of the reduction in the size of the 3 E. R. Gowree & S. A. Prince 1.3 Vortex Shedding strongly related to the AR, where low AR causes the trailing vortices to migrate inboard and the Stationary circular cylinders in crossflow are use of cylinders with larger AR, such as in the known to undergo periodic vortex shedding experiments mentioned above, might be another (Von Karman Vortex Street). The vortex reason why the secondary shedding mode did shedding can commence at Re as low as 65 not appear. However there was no mention of where the flow is purely laminar and is still the occurrence of the secondary mode at Re = present in fully developed turbulent flow of Re 98k.

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