NumericalSimulationofVerticalAxisWindTurbineatLowSpeedRatios

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3 Global Journal of Researches in Engineering ( I ) Volume XIV Issue I Version I Year a) b) Figure 1 : Basics of VAWT: a) sketch of a fixed-pitch straight-bladed VAWT; b) typical flow velocities in Darrieus motion From the vectorial description of velocities, Fig. 1b, we can obtain the following expression that establishes the relationship between angle of attack U sin sin 1 sin tan D or tan RU cos cos cos Another important parameter is the reduced frequency which governs the level of unsteadiness. The c reduced frequency k, defined as k where is the 2U eff angular frequency of the unsteadiness, c is the blade chord and Ueff is the effective velocity of the blade, can be expressed in terms of TSR as: c k (2) D 2 2 cos 1 D the tip speed ratio λ and azimuth angle of a blade in Darrieus motion (without the velocity induction). The variation of angle of attack, its D normalized values, and the reduced frequency Dmax are evaluated from eqs. (1) and (2) as function of the azimuth angle θ for various values of λ, as shown in Fig. 2. D (1) 2014 Global Journals Inc. (US)

4 Year Figure 2 : Flow conditions for Darrieus motion: a) variation of angle of attack; b) normalized angle of attack and sine-curve; c) reduced frequency as a function of λ and the azimuth angle θ This figure shows some specific features of the Darrieus motion which behaves differently in terms of TSR as: The variation of angle of attack for λ 1 presents a strong discontinuity-like type instability in the point of maximum incidence corresponding to the change of incidence direction at the downstream passage (θ = 180 ); for the values of λ > 1 the passage point is an inflectional instability of incidence variation when the angle of attack becomes zero, (Fig 2a). The unsteady flow phenomena caused by the instabilities of Darrieus motion is a complex mechanism which leads to formation of an intense leading-edge vortex, post-stall vortex shedding, reattachment of flow, and wake capture. The variations of normalized angles of attack α at the high values of (λ 2) are very similar to the sine-curve, i.e. sin with their peaks at about same azimuth angle of 90 0 ; unlike these variations, the variations at the low values of λ (λ < 2) contain elements of plunging motion and have their peaks at different azimuth angles (130 0 for λ = 1.5) (Fig. 2b). This difference is typically termed the phase shift which is an important parameter for generation of thrust. The variation of the reduced frequency k shows the existence of a band of tip speed ratios about λ= ( ) with the rough increase of frequency like a discontinuity. (Fig. 2c) ( ). According to the diagram from Fig.2c, the unsteadiness associated with the flow field and VAWT operating state can be classified into three levels: 2014 Global Journals Inc. (US) Global Journal of Researches in Engineering ( I ) Volume XIV Issue I Version I

6 data offer a good opportunity to examine the capacity of CFD at very high AOA s. The commercial CFD software Fluent was employed in flow computational. Fluent is based on the finite volume method which discretizes the computational domain into some small volumes and has been tested in many applications. The detailed computational treatments and algorithms are explained as follows: i. Mesh geometry and boundary conditions Figure 4a shows the geometric scheme and boundary conditions in the CFD model of single NACA 0018 airfoil. The far-field boundary was set as velocity inlet. It was located 30c away from the airfoil where c is the chord length of the airfoil, in order to avoid wave reflection. The oncoming flow velocity was 10 m/s, which, together with chord length, results in a Reynolds number of Year a b Figure 4 : Computational setup: for a single NACA0018 airfoil: a) model geometry and boundary conditions; b) mesh structure and y + value Both O and C-grid mesh topologies can minimize the skewness of a near-wall mesh and converge fast under a high-order discretization scheme. In this study, the O-grid topology was adopted because it can reduce grid number and avoid high aspect ratios of grids in the far wake. In order to resolve the laminar sub layer directly, the first grid spacing on the airfoil was determined to make y + less than 1. Grid-stretching was limited to less than 1.08 in both streamwise and cross flow directions to ensure numerical stability. Figure 4b shows the final mesh in 2D model. ii. Transition Model The incompressible Navier-Stokes equations are appropriate for solving the VAWT aerodynamics, transport equation for the intermittency, γ: U j t P 1 E1 P 2 E2 t x j t x j transport equation for the momentum thickness Reynolds number, ~ e : because the resultant flow velocity is generally smaller than 0.3 times the Mach number. Stall, either static or dynamic, may occur in a rotating VAWT and both are dominated by vortex separation and involve flow unsteadiness. Therefore, an unsteady fluid solver is necessary to investigate such kinds of flow. The choice of transitional models influences the computational results and the required computation resource. The transition model uses two transport equations, one for intermittency and one for a transition onset criterion in terms of momentum thickness Reynolds number [9]. R t Re U j Re t t Re t Pt t t t x j x j x j (3) (4) Global Journal of Researches in Engineering ( I ) Volume XIV Issue I Version I 2014 Global Journals Inc. (US)

7 Global Journal of Researches in Engineering ( I ) Volume XIV Issue I Version I Year iii. Simulation setup The 2D Unsteady Reynolds-Averaged Navier- Stokes (URANS) approach was selected to solve the discretized continuity and momentum equation, and a second order implicit formula was used for the temporal discretization. The SIMPLEC scheme was used to solve the pressure-velocity coupling. SIMPLEC converges faster than SIMPLE. Time step size is a crucial parameter in unsteady flow simulations. To get accurate results of an airfoil beyond stall, Sorensen et al. [10] and Travin et al. [11], suggested the non-dimensional time tu steps to be 0.01 and respectively. c 0.01 (according to the real time step Δt = ) was applied in the simulations of the single airfoil. b) CFD simulation of three straight-bladed VAWT Figure 5a shows the geometry and the flow conditions of the VAWT model in the CFD simulation. a) The radius of the VAWT was R= m. A velocity inlet with a constant wind speed U = 10 m/s was located at 4.5 m (i.e. 14R) in front of the turbine. The applied outflow condition combined a zero diffusion flux of all flow variables in the normal direction to the exit plan and an overall mass balance correction. The side boundaries were 4.5 m (14R) from the turbine center to minimize the blocking effect. A free-slip all boundary conditions was applied where the normal velocity components and the normal gradients of all velocity components were assumed to be zero. The mesh configurations used in the CFD model of the single static airfoil were transferred into the VAWT model with new boundary adaptation as is shown in Fig. 5b. b) Figure 5 : Computational setup for 3 straight-bladed VAWT: a) model geometry and boundary conditions; b) mesh structure for whole domain 2014 Global Journals Inc. (US)

8 The dynamic effects of the blade influence the energy extraction process of VAWT, and thus, the determination of the time step should consider amplitude, frequency and far field velocity. In the present study, the reduced frequency was k = 0.24, the physical 0 1 time step was 0.5 and the corresponding nondimensional time step was 0.02 [12]. IV. Numerical Simulation of Vertical Axis Wind Turbine at Low Speed Ratios Results and Discussions The flow in the VAWT operating at wind speed of 10 m/s was simulated using 2D URANS. Results for a single airfoil blade in high angle of attack flow were compared with the results obtained by a three straightbladed rotor at low TSR. The CFD simulation of airfoil flow with an AOA higher than 45 o is rarely discussed in the literature where the flow is dominated by the dynamics of the interacting vortices generated by the separating boundary layer. Figure 6a, b shows the pressure field superimposed on the instantaneous streamlines computed for both single α = 30 0 blade and three-confined blades. The single airfoil blade in high angle of attack flow produces a different wake structures as the AOA increases, Fig.6 a. In the near wake there are two main vortices: leading edge vortex (LEV) and trailing edge vortex (TEV). The position of vortices change in terms of the AOA as : when the AOA is α = 30 o, the LEV is stronger than TEV and this is the last shed vortex (SV) so that the flow produces a classical von Karman vortex street; when the AOA is of order α 45 o, the both LEV and TEV have comparable strengths, SV becomes nearer the airfoil and the flow produce pairs of counter-rotating vortices of equal strengths, called viscous (weak) vortex doublet (VD); and when the AOA exceeds the value α 60 o, noticeably in the flow pattern near the airfoil there are a cluster of the two main vortices and the formation of a quasi-potential (strong) vortex doublet (QPD). Considering Reynolds number circumstances in this study, these vortex structures forming slowly rotating QPD street are perceived as large separation bubbles shedding from the blade. Year Global Journal of Researches in Engineering ( I ) Volume XIV Issue I Version I α = Global Journals Inc. (US)

9 Global Journal of Researches in Engineering ( ) Volume XIV Issue I Version I Year I α = 60 0 α = 75 0 a α = 90 0 Figure 6 : Pressure field superimposed on the instantaneous streamlines computed using the transition SST model for NACA0018 airfoil at Re c = 10 5 : a) single static airfoil; b) 3-confined airfoils rotating at λ = 1.0 b 2014 Global Journals Inc. (US)

11 Global Journal of Researches in Engineering ( ) Volume XIV Issue I Version I Year I Figure 7 : Static and dynamic lift and drag coefficients of NACA0018 airfoil for Re c = Global Journals Inc. (US)

13 Global Journal of Researches in Engineering ( I ) Volume XIV Issue I Version I Year CEBECI T., PLATZER M., CHEN H., CHANG K.C., SHAO J.P., Analysis of low-speed unsteady airfoil flows, Springer, Germany, WANG S., INGHAM B.D., MA L., POURKASHANIAN M., TAO Z., Numerical investigations on dynamic stall of low Reynolds number flow around oscillating airfoils, Computers & Fluids, 39, pp , ALLET A., HALLE S., PARASCHIVOIU I., Numerical simulation of dynamic stall around an airfoil in Darrieus motion, Journal of Solar Energy, 121, pp , WERNER P., GEISSLER W., RAFFEL M., KOMPENHANS J., Experimental and numerical investigations of dynamic stall on a pitching airfoil, AIAA J., 34 (5), pp , EKATERINARIS J.A., PLATZER M.F., Computational prediction of airfoil dynamic stall, Progress in Aerospace Sciences, 33, pp , PARASCHIVOIU I., Wind turbine design with emphasis on Darrieus concept, Polytechnic International Press, Montreal, SCHELDAHL R. W., LIMAS P. C., Aerodynamic characteristics of seven symmetrical airfoil sections through 180-degree angle of attack for use in aerodynamic analysis of vertical axis wind turbines, Tech. Rep. SAND , Sandia National Laboratories, Albuquerque, NM, USA, LANGTRY R. B., MENTER F. R., Transition modeling for general CFD applications in aeronautics, AIAA Paper, , SØRENSEN N. N., MICHELSEN J. A., Drag prediction for blades at high angle of attack using CFD, Journal of Solar Energy Engineering, 126 (Nov), pp , TRAVIN A., SHUR M., STRELETS M., SPALART P. R., Physical and numerical upgrades in the detached-eddy simulation of complex turbulent flows, Advances in LES of complex flows, pp , GHARALI K., JOHNSON D.A., Numerical modeling of an S809 airfoil under dynamic stall, erosion and high reduced frequencies, Appl. Energy, (DOI: 1016/ ), SØRENSEN N.N., MICHELSEN J.A., Drag prediction for blades at high angle of attack using CFD, J. Solk. Energy Eng., 126 (Nov), pp , GAO H., HU H., WANG Z.J., Computational study of unsteady flows around dragonfly and smooth airfoils at low Reynolds number, in 46 th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Global Journals Inc. (US)

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