MATERIALS AND METHODS

Two-dimensional unsteady analysis of a vertical axis wind turbine model of NACA2415 camber airfoil was analyzed using a Computational Fluid Dynamic, CFD tool solving the reynolds-averaged navier-stroke equations based on moving mesh technique. Simulations were conducted on July 10 and 11, 2010, using high processing capacity of 8 GB computer. The laboratory is located in the Zoo Campus of Harbin Institute of Technology, Department of Manufacturing and Automation. The overall procedures followed in the analysis are described as follows:

Computational domain: Cambered airfoil type NACA2415 (Fig. 2) was selected as blade section. The airfoil was set to 1 m chord length and the turbine radius was set to 4 m to minimize the interference between the blades. For creating 2D model and mesh of the model, Gambit 2.3.16 version modeling software was used.

The domain size was set as shown in Fig. 3 with a rotating sub-domain surrounding the blades and stationary sub domains in the remaining region. Mesh for the rotating sub-domain and central sub-domains were generated with triangular blocks where as the rest sub-domains were generated with O-H structured grid. The rotating sub-domain was set to a diameter of 10 m. The inlet width and out let width were set to 3D. The inlet was located 3D upstream and outlet 6D downstream.

Computational method: The model and mesh generated in gambit modeling soft ware were read into the commercial CFD code, fluent V.6.2.30 for numerical iterative solution. The RANS equations were solved using the green-gauss node based gradient option and the sliding mesh method was used to rotate the sub-domain for the turbine blades. For pressure-velocity coupling, the simple algorithm was used. Standard was set as pressure discretization and first order upwind was set for momentum. Time integration was done implicitly and the minimum convergence criteria were set to 1e-06. The RNG k-epsilon model was adapted for the turbulence closure.

Fig. 2:	NACA2415 blade section

Fig. 3:	Computational domain

Fig. 4:	Boundary conditions

The boundary conditions are shown in Fig. 4. The inlet was defined as a velocity inlet, which has constant inflow velocity while the outlet was set as a pressure out let, keeping the pressure constant. The velocity at the out let was determined by the extrapolation from inside. The no slip shear condition was applied on the turbine blades, which sets the relative velocity of blades to zero. There were four domains in the computational domain with 72,908 cells of the meshes with 180 cells around each blade. The cells were concentrated near the blades for better result. The Reynolds number based on rotor diameter was 2.2 million and the blade chord reynolds number was 270,000.

For the moving mesh simulations, the computational sub-domain is split into a moving part around the turbine and a fixed part for the fixed environment. The rotational motion is simulated by allowing the mesh block around the wind turbine to rotate at constant angular velocity.

Fig. 5:	Overall view of the mesh

Fig. 6:	Rotating sub-domain

Fig. 7:	Mesh near the airfoil

The mesh movement is defined explicitly by specifying time-varying positions for all of the moving mesh block cell vertices. An interface boundary surrounding the moving mesh part within the model slides at the specified velocity. This represents the relative motion between the rotating wind turbine and the fixed environment.

Figure 5 shows the overall view of the 3-bladed turbine model mesh and Fig. 6 shows the zoom-in view around the rotating sub-domains. As can be seen from Fig. 5 and 6, the cells were concentrated near the blades for better result. Figure 7 shows the cells around the blades.

The flow condition used for the analysis is shown in Table 1. Time step size was set corresponding to 2 degree for each rotational speed of the rotor (ω) given in Table 1 corresponding to each TSR. Eighty iterations were used per time step.

The operating speed of the turbine, expressed as Tip Speed Ration (TSR) was set between 0.5 and 4.

TSR is defined as:

(1)

where, R is the turbine radius, ω is angular velocity and V_∞ is the free stream velocity.

RESULTS

Figure 8 shows simulated average torque values at lower TSR which was the main focus area of the study. It shows the average torque in N-m for complete revolution of the modeled turbine for TSRs 0.5 and 1.5. The torque values were obtained from coefficient moment (Cm) of the modeled turbine, air density, area of turbine, free stream velocity chosen and the radius of the turbine modeled.

Figure 9 shows simulated average torque values at higher TSR. This shows the average torque in N-m for complete revolution of the modeled turbine for TSRs 2.5, 3, 3.5 and 4. The torque values were obtained using the same principle as mentioned above. This graph is used to determine the efficiency of the modeled turbine.

Figure 10 shows the coefficient of power (Cp) for the simulated model, which determines the performance of the turbines. It shows Cp at the given value of TSR selected for the simulation. The maximum efficiency of the modeled airfoil was appeared around TSR of 2.5. The coefficients of power were obtained from the ration of the modeled turbine power to the available wind power in the air.

Table 1:	Flow condition

Fig. 8:	Torque for TSR 0.5 and 1.5

Fig. 9:	Torque for higher TSR

Fig. 10:	Power coefficients vs. TSR

Fig. 11:	Coefficient of moment vs. TSR

Figure 11 shows the coefficient of moment (Cm) of the simulated model, which determines the average torque of wind turbines. It shows the value of the coefficient of moment of airfoils for the given TSR. The Cm values were obtained from the average moment of the three airfoils modeled through CFD computational analysis.

DISCUSSION

To verify the reliability of the computational method, hydrodynamic forces acting on the NACA2415 airfoil from different angles of attack were computed. The cord length was set to 1m and the corresponding cord-based Reynolds number Re, was 85,000. The converged solution was obtained after 4,000 iterations. Figure 12 shows the comparison of the computational solutions and experimental data (Kirke, 1998). The computed lift forces are in good agreement with the data for angles of attack between -10 and 10° which is considered to be the normal operating range of turbine blades.

Torque: The blade aerodynamic forces and torque are computed from the solution of RANS equations through the integration of the pressure and shear stress over the blade surface. The total wind turbine force components and torque are obtained by adding the 3 blade force components and torque. The driving torque is obtained by calculating the average of the instantaneous values corresponding to the last revolution of the rotor. These values were used to derive the expected wind turbine power coefficient (Cp). The turbine was allowed to turn until stable torque was created and the minimum no of turns used for this model was 6.

(2)

Fig. 12:	Lift coefficient of NACA2415

Fig. 13:	Blade position at time = 0.00e+00, ΔΦ = 0°

where, p is expected out put power of turbine, ω is angular velocity of turbine, T averaged torque

Cp is then calculated as:

(3)

where, ρ is the air density, V₈ free stream velocity, A frontal area of the turbine.

Traditionally airfoils that are used for VAWTs are symmetrical airfoils NACA0012, NACA0015 and NACA0018. The main drawbacks with these types of section are their minimum or negative torque generation for the lower TSR. As can be seen from the result, all the torque values are positive for lower TSR for the modeled NACA2415 which implies camber airfoils have great potential in self staring of VAWTs. However, the coefficient power (Cp) result shows a reduced efficiency as compared to the conventional symmetrical airfoils of NCACA 0012, NACA0015 and NACA0018 which are not self starting. This is in agreement with Lazauskas (1992), Barker (1983), Kirke and Lazauskas (1991), Healy (1978) and Kotb (1990) that a judicious choice of camber airfoil can increase starting torque but reductions in peak efficiency and narrower operating ranges are the drawbacks.

Fig. 14:	Pressure contours for TSR = 3 at time = 5.2776e-01, ΔΦ = 90°

Fig. 15:	Pressure contours for TSR = 3 at time = 1.005552e+00, ΔΦ = 180°

The pressure contours at four different positions change of azimuth angle (ΔΦ) for one complete turn of the turbine are shown with the help of figures. The snap shot pressure contour distributions were taken for TSR 3 and the turbine was modeled to turn anticlockwise.

Figure 13 shows blade position at stationary stage of the turbine. At this point time is zero and change of azimuth angle (ΔΦ = 0). Figure 14 shows a snap shot of pressure distribution after the turbine has rotated 90°. The time at this position is 0.52776 s and the change of azimuth angle is 90°. Figure 15 shows a snap shot of pressure distribution after the turbine has rotated 180°. At this position the time is 1.05552 s and the change of azimuth angle is 180°. Figure 16 shows a snap shot of pressure distribution at time 1.58328 s and change of azimuth angle of 270°. Figure 17 shows a snap shot of pressure distribution after the turbine has turned one complete revolution. The time at this position is 2.11104 s and the change of azimuth angle is 360°.

Fig. 16:	Pressure contours for TSR = 3 at time = 1.58328e+00, ΔΦ = 270°

Fig. 17:	Pressure contours for TSR = 3 at time = 2.11104e+00, ΔΦ = 360°

Firstly the hydrodynamic forces acting on NACA2415 cambered airfoil section were computed from different angles of attack to validate the computational method to experimental data. Then 2D unsteady flow analysis using the selected airfoil section with fixed pitch three blades based on RANS equation have been analyzed with a moving mesh technique. The simulated average torque result shows that camber airfoils have the potential to self start if used for vertical wind axis wind turbines. However, the power coefficient of the simulated model shows a reduction in peak efficiencies compared to the conventional non-self starting airfoils.