Effect of Blade Thickness on Darrieus Vertical-Axis Wind Turbine Performance

Marco Raciti Castelli1, Ernesto Benini2

1 Department of Mechanical Engineering University of Padua Via Venezia, 1 35131 Padova, Italy

marco.raciticastelli@unipd.it 2 Department of Mechanical Engineering University of Padua

Via Venezia, 1 35131 Padova, Italy ernesto.benini@unipd.it

Abstract. This paper presents a two-dimensional CFD analysis of the influence of blade thickness on the operation of a straight-bladed Darrieus-type vertical-axis wind turbine (VAWT). After describing the computational model and the relative validation procedure, a complete campaign of simulations based on full RANS unsteady calculations is proposed for a three-bladed rotor architecture. Two blade profiles are analyzed: a NACA 0012 and a NACA 0021 airfoil. For each proposed blade configuration, flow field characteristics in the neighborhood of the rotor are investigated at several values of tip speed ratio, allowing a quantification of the influence of blade thickness on flow geometric features, such as blade angles of attack, and dynamic quantities, such as rotor torque and blade tangential and normal forces. Finally, the rotor torque and power curves are compared for the two analyzed architectures, achieving a quantification of the effect of the blade thickness on overall rotor performance.

Keywords: CFD, vertical-axis wind turbine, NACA 0012, NACA 0021.

1 Introduction

The urgent need to reduce dependence on fossil fuels is being met, at least in part, by the development of wind turbines, both onshore and offshore: the awareness of the limited resources of fossil fuels and the rising concern for the effects of the increased amount of greenhouse gases in the atmosphere have given the wind turbine industry a considerable push forward. As pointed out by the First International Conference on Wind Turbine Noise [1], the development of onshore wind power results in wind turbines closer to habitations, leading to the possibility of noise problems, such that frequent objections raised in planning procedures concern noise and vibration.

In this scenario, the continuous quest for clean energy is now focusing on the local production of electric power, spread in a wide area, so as to cooperate with the big electric power plants located in just few specific strategic locations of the countries.

One of the most promising resources is wind power associated with local production of clean electric power inside the built environment such industrial and residential areas, which has lead to the development of the so called Computational

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Wind Engineering. This new discipline has also renewed the interest in vertical-axis wind turbines (VAWTs).

As observed by Raciti Castelli [2], the vertical axis wind turbine has an inherently non-stationary aerodynamic behavior, mainly due to the continuous variation of the blade angle of attack during the rotation of the machine: this peculiarity involves the continuous variation both of the relative velocity with respect to the blade profile and - although to a lesser extent - of the corresponding Reynolds number. This phenomenon, typical of slow rotating machines, has a significant effect both on the dynamic loads acting on the rotor and on the generated power and, therefore, on performance.

Until now wind tunnel tests, involving considerable time and financial resources, have been the only way to fully characterize the behavior of a rotor, in order to obtain the operating torque curves for the implementation of the control system. Nevertheless, Computational Fluid Dynamics (CFD) can nowadays be considered as a powerful design tool, whose integration into industrial development and production life-cycles is continuously rising. As observed by Caridi [3], this was made possible because of two main factors: the increase in computer performance and network facilities; the progress made in general purpose CFD software between modeling complexity

and practicability within the industrial environment. Performing CFD calculations provide knowledge about the flow in all its details,

such as velocities, pressure, temperature, etc. Further, all types of useful graphical presentations, such as flow lines, contour lines and iso-lines are readily available. This stage can be compared to having completed a wind-tunnel study or an elaborate full-scale measurement campaign [4].

Recently, Kumar et al. [5] proposed a low Reynolds number VAWT design and optimization procedure based on both CFD simulations and BE-M calculations, while Raciti Castelli and Benini [6] presented a model for the evaluation of energy performance and aerodynamic forces acting on a helical single-bladed VAWT depending on blade inclination angle. Also Raciti Castelli et al. [7] performed a numerical analysis validation campaign for a Darrieus micro-VAWT through a systematic comparison with wind tunnel experimental data. This work proved that it is possible to determine the best near-blade grid element dimension through statistical analysis of some indicators, such as the y+ parameter, in order to maximize the accuracy of the numerical prediction of rotor performance while maintaining a reasonable computational effort.

In the present work, two-dimensional, time-accurate, parallel CFD simulations of the flow field around a three-bladed Darrieus rotor, are performed with the aim of determining the influence of blade thickness on the operation of a straight-bladed Darrieus-type VAWT. The commercial finite volume flow solver ANSYS FLUENT is used for the simulations. The solutions are obtained using unstructured moving grids rotating with the turbine blades. Two different flow cases are investigated: a three-bladed configuration characterized by a NACA 0012 blade profile, named

Model_0012; a three-bladed configuration characterized by a NACA 0021 blade profile, named

Model_0021.

For each proposed blade configuration, flow field characteristics in the neighborhood of the rotor are investigated at several values of tip speed ratio, allowing a quantification of the influence of blade thickness on flow geometric features, such as blade angles of attack, and dynamic quantities, such as rotor torque and blade tangential and normal forces. Finally, the rotor torque and power curves are compared for the two analyzed architectures, achieving a quantification of the effect of the blade thickness on overall rotor performance.

2 Model Geometry

The numerical analysis proposed in the present work is based upon the 2D vertical-axis Darrieus wind turbine geometry analyzed by Raciti Castelli et al. [7], [8]. Rotor's main geometrical features are summarized in Table 1. The solidity parameter is defined as Nc/Rrotor, as suggested by Strickland [9].

Table 1. Main geometrical features of the tested rotors.

Description Value Rotor diameter Drotor [mm] 1030 Rotor height Hrotor [mm] 1 (2D simulation) Blade number N [-] 3 Blade chord c [mm] 85.8 Rotor solidity [-] 0.5 Rotor swept area A [mm2] 1030 Rotor angular velocity [rad/s] from 25.1 to 57.6 Air density [kg/m3] 1.225 Wind velocity V [m/s] 9

Rotor azimuthal position was identified by the angular coordinate of the pressure

centre of blade No. 1 midsection (set at 0.25c for NACA 0012 and 0021 airfoils), starting between the 2nd and 3rd Cartesian plane octants, as can be seen in Fig. 1, while Fig. 2 shows a comparison between NACA 0012 and 0021 airfoil sections.

3 Spatial Domain Discretization

The use of moving sub-grids was necessary, due to the movement of the rotor elements. In particular, the discretization of the computational domain into macro-areas has led to two distinct sub-grids: a rectangular outer zone, determining the overall calculation domain, with a

circular opening centered on the turbine rotational axis, which was identified as Wind Tunnel sub-grid, fixed;

a circular inner zone, which was identified as Rotor sub-grid, rotating with rotor angular velocity .

Fig. 3 shows the main dimensions and the boundary conditions of the Wind Tunnel sub-grid area.

Fig. 1. Azimuthal coordinate of blade midsections centre of pressure (from: [8]).

Fig. 2. Comparison between Model_0012 and Model_0021 airfoil sections.

Two symmetry boundary conditions were used for the two side walls. The circumference around the circular opening centered on the turbine rotational axis was set as an Interface, thus ensuring the continuity in the flow field. An unstructured mesh was chosen for the Wind Tunnel sub-grid, in order to reduce engineering time to prepare the CFD simulations.

The Rotor sub-grid was the fluid area simulating the revolution of the wind turbine and was therefore characterized by a moving mesh, rotating at the same angular velocity of the turbine. Its location coincided exactly with the circular opening inside the Wind Tunnel sub-grid area and was centered on the turbine rotational axis. Fig. 4 shows the main dimensions and the boundary conditions of the Rotor sub-grid area.

An isotropic unstructured mesh was chosen for the Rotor sub-grid, in order to test the prediction capability of a very simple grid. All blade profiles inside the Rotor sub-grid area were enclosed in a control circle of 400 mm diameter. Unlike the Interface, it had no physical significance: its aim was to allow a precise dimensional control of the grid elements in the area close to rotor blades by adopting a first size function

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operating from the blade profile to the control circle itself and a second size function operating from the control circle to the whole Rotor sub-grid area, ending with grid elements of the same size of the corresponding Wind tunnel sub-grid elements. An Interior boundary condition was used for control circle borders, thus ensuring the continuity of the cells on both sides of the mesh. Some details of the grid are visible in Fig. 5: grid independent solutions were found using an unstructured mesh topology with approximately 106 cells. For more information about mesh generation and code validation, see also [7] and [8].

Fig. 3. Main dimensions [mm] of the Wind Tunnel sub-grid area (from: [8]).

Fig. 4. Main dimensions [mm] of the Rotor sub-grid area (from: [8]).

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4 Temporal Discretization and Convergence Criteria

The commercial CFD package used was ANSYS FLUENT 12.1 , that implements 2-D Reynolds-averaged Navier-Stokes equations using a finite volume-finite element based solver. The fluid has been assumed to be incompressible, being the maximum fluid velocity in the order of 60 m/s. The temporal discretization has been achieved by imposing a physical time step equal to the lapse of time the rotor takes to make a 1 rotation. An improved temporal-discretization simulation did not show any significant variation [7]. As a global convergence criterion, each simulation has been run until instantaneous torque coefficient values showed a deviation of less than 1% compared with the corresponding values of the previous period, corresponding to a rotation of 120 due to rotor three-bladed geometry. Residual convergence criterion for each physical time step has been set to 10-5.

The present simulations required about 16 CPU seconds per physical time step. An average of about 30 sub-iterations have been necessary to converge the solution at each physical time step. The simulations, performed on an 8 processor, 2.33 GHz clock frequency computer, have required a total CPU time of about 4 days for each simulation.

Fig. 5. Control circle for NACA 0012 blade section.

5 Results and Discussion

Fig. 6 represents the evolution of the rotor power coefficient, defined as:

Cp = P / [0.5 A V3] . (1)

for the two analyzed models as a function of the tip speed ratio, defined as:

T.S.R. = Rrotor / V . (2)

Fig. 6. Evolution of rotor power coefficient for the two analyzed models.

Fig. 7. Contours of absolute velocity [m/s] for Model_0012 (left) and Model_0021 (right) blades at 92 azimuthal position.

As can be clearly seen, Model_0021 maximum power coefficient (0.416) is 4.5% higher than Model_0012 corresponding value (0.398). The described phenomenon is probably to be connected with NACA 0021 higher stall characteristics with respect to NACA 0012 airfoil, due to its almost-doubled thickness. In fact, as observed by Raciti

Castelli et al. [10], during the operation of a VAWT, rotor blades experiment a wide range of angles of attack and, as reported in [8], the higher values of power generation correspond to those azimuthal blade coordinates (between the 4th and 5th Cartesian plane octants) were the angles of attack are quite higher with respect to the stall limit. Fig. 7 represents a comparison between Model_0012 and Model_0021 blades at 92 azimuthal coordinate (peak value of power generation) for T.S.R. = 2.33 (optimal angular velocity for Model_0021): a larger recirculation zone (evidenced by the red arrows) can be seen in correspondence of Model_0012, suggesting a more dramatic effect of blade separation. Further work should be done, in order to better correlate the physics of airfoil stall characteristics and rotor power output.

From Fig. 6 it can also be noticed that the optimal T.S.R. value for Model_0021 (2.33) is some 15% lower with respect to the corresponding value of Model_0012 (2.76), thus reducing the structural loads on the blades due to centrifugal forces. This phenomenon is connected with the higher blockage induced by the NACA 0021 blade profile on the incoming flow-field, due to its almost-doubled thickness with respect to the NACA 0012 airfoil: an increased blockage can be compared to an increased rotor solidity, thus determining a leftward shift of the optimal value of T.S.R.

References

1. Leventhall, G., Wind Turbine Noise: Perspective for Control, DEWI Magazin Nr. 27, August 2005, pp. 60-61

2. Raciti Castelli, M., Analisi numerica delle prestazioni di una micro-turbina eolica ad asse verticale modello Darrieus, PhD Thesis (in Italian), Universit di Padova, Italy, 2010, pp. 193-194

3. Caridi, D., Industrial CFD Simulation of Aerodynamic Noise, PhD Thesis, Universit degli Studi di Napoli Federico II, 2008

4. Jensen, A. G., Franke, J., Hirsch, C., Schatzmann, M., Stathopoulos, T., Wisse, J., Wright, N. G.: CFD Techniques Computational Wind Engineering, Proceedings of the International Conference on Urban Wind Engineering and Building Aerodynamics Impact of Wind and Storm on City Life and Built Environment Working Group 2, COST Action C14, Von Karman Institute, Rode-Saint-Gense (Belgium), 2004

5. Kumar, V., Paraschivoiu, M, Paraschivoiu, I., Low Reynolds Number Vertical Axis Wind Turbine for Mars, Wind Engineering, Vol. 34, No. 4, June 2010

6. Raciti Castelli, M., Benini, E., Effect of Blade Inclination Angle in a Darrieus Wind Turbine, Journal of Turbomachinery, October 2011, Vol. 133

7. Raciti Castelli, M., Pavesi, G., Benini, E., Battisti, L., Ardizzon, G., Modeling Strategy and Numerical Validation for a Darrieus Vertical Axis Micro-Wind Turbine, Proceedings of the ASME 2010 International Mechanical Engineering Congress & Exposition, November 12-18, 2010, Vancouver, British Columbia, IMECE2010-39548

8. Raciti Castelli, M., Englaro, A., Benini, E., The Darrieus Wind Turbine: Proposal for a New Performance Prediction Model Based on CFD, accepted for publication by: Energy

9. Strickland, J. H.: The Darrieus Turbine: A Performance Prediction Model Using Multiple Streamtube, SAND75-0431

10. Raciti Castelli, M., Garbo, F., Benini, E., Numerical Investigation of Laminar to Turbulent Boundary Layer Transition on a NACA 0012 Airfoil for Vertical-Axis Wind Turbine Applications, submitted for publication to: International Journal of Energy and Environmental Engineering