4.2 Moving and Oscillating Airfoi
4.2移动和振荡机翼
As explained previously, the profile in Darrieus motion is subjected to a stronglyvarying angle of attack and velocity magnitude (see Figure 1b). In order t investigate the aerodynamic forces at a single airfoil, this motion is decomposed in anapproximate way as a combination of rotational and linear oscillation. Neglecting the retardation of the flow due to momentum change at the airfoil, the variation of angle of attack is approximated as
where αmax is the maximal angle of attack (pitching amplitude), ω = λUw/R is the angular velocity of the rotor and t is time. Similarly, the effective wind velocity at the airfoil W may be approximated with as
Equations 3 and 4 may be described with the model depicted with Figure 5. In thestream field Ustream = λUw, the airfoil moves periodically with the period T = 2π/ω.The airfoil velocityxdirection and the angular velocity around the quarter cord point
are respectively:
The above described motion is modeled using the mesh deformation technique available in ANSYS-CFX. As shown in Figure 6, the solution domain is pided in
6 sub-domains. The mesh in sub-domain 4 rotates with the angular velocity ω0 and
moves (together with the mesh in sub-domain 3) with the velocity Ux. Sub-domains1 and 6 are defined as stationary and the displacement of sub-domain 4 is compensated with the mesh deformation in sub-domains 2 and 5. The velocity Ustream is prescribed at the inlet boundary and other boundaries are defined as in subsection 4.1. The aerodynamic coefficients are defined in term of the relative wind velocity at the airfoil U = Ustream − Ux. The angle of attack α defined at the rotor is the reversed angle of attack defined in Equation 3. The predicted aerodynamic coefficients are shown in Figure 7. For various λ and αmax, the lift coefficient is plotted together with the lift coefficient of a stationary profile in Figure 7a. The predicted lift coefficients are strongly dependent on the pitching amplitude. As expected, at large angle of attack beyond static stall angle stall delays. The dynamic stall with the hysteresis effect is obvious in all cases. The deviation of lift in the upstroke motion as compared to the static values is not clear and needs to be investigated. Figure 7 shows the predicted drag coefficient for λ = 3.5. It is observed,
that during the hysteresis loop negative drag - the thrust appears.