Vortical Description of Dynamics Stall Effects in A VAWT

1. Vortical Description of Dynamics Stall Effects in A VAWT P M V Subbarao Professor Mechanical Engineering Department Generation of Clues for Formulation of Better Design Method........

2. The Vision of A Genious

3. Vortical Structure Of Flows : The Start of Good Fluid Mechanics Research • The flow visualisation carried out by Leonardo da Vinci (1452-1519) can be considered as the start of experimental work • Flows are better described by the sketches of observed vortex motions.

4. Fascinating Vortex Phenomena Static Airfoil: Kutta-Joukowski Theorem Dynamic Airfoil: New Theorem?

5. Dynamics of Pitching Airfoil • Twisty vortex strings that produce infinite V -type velocities as distance from the filament goes to zero. • These twisty vortices are similar to tornados. How to quantify?

6. The Vortical Description • Dynamic stall involves the growth and subsequent separation and shedding of a leading and trailing edge vortices . • These unsteady effects dominate the flow field on VAWT blades. • This new physics must be understood fully to develop robust and efficient VAWTs.

7. Clockwise Vortices shed by a Blade of VWAT  = 108  = 90  = 133  = 70

8. Generation of Clockwise Vortices The upstream half of a representative three-bladed VWAT at equator.

9. Instantaneous Vorticity Contours on VAWT Blade =0 =0 =60  =19  =90 =27 Clockwise Counter-clockwise

10. Instantaneous Vorticity Contours on VAWT Blade =150 =-24 =120 =30

11. Dynamic stall regimes in VAWT Dynamic stall development (green) Trailing edge vortex shedding (magenta), Leading edge vortex development (red), Separated flow(blue).

12. The influence of Separation Vortices Dynamic stall creates significant differences in the flow field and forces during pitch-up and pitch-down on an airfoil. • During pitch up, there is significant stall-delay resulting in attached flow, and high lift well beyond the static stall angle ss. • Additionally, during pitch up a leading edge, or dynamic stall vortex, is seen to develop, and subsequently shed from the airfoil, with an associated drop in lift. • On pitch down there is a similar delay in the flow reattachment. Primary separation mode

13. Opportunities for VAWT design • Previous designers have utilized active flow control or active pitch control to curtail dynamic stall. • 21st century designers found the most attractive opportunity. • This is to attempt to delay the lift drop after the LEV sheds from the airfoil to a higher. • A non-dimensional measure that defines a precise point of occurrence for the delay is defined as convection time scale.

14. The Convection time Scale • The airfoil convection time for a VAWT blade is defined as: This equation can be integrated analytically resulting in a complex expression involving the elliptic integral of the second kind

15. Measures for Occurrence of Dynamic Events • LEV separation will occur at maximum angle of attack, or four convective times after the LEV forms. • Therefore it is possible that higher overall turbine torque could be achieved if four convection times took place exactly when the airfoil reached maximum angle of attack. • The unsteady lift benefits of the LEV can be applied over the entire cycle, potentially resulting in higher torque. • Any changes in airfoil geometry or kinematics will have other effects on the flow.

16. Parameters to Control LEV Initiation The formation time between LEV initiation and max angle of attack can be decreased by; Increasing the chord length : Results in a corresponding increase in Reynolds number and reduced frequency. Or by increasing the tip speed ratio : This results in a lower maximum angle of attack that occurs at a lower turbine angle. Such an increase would additionally result in a higher Reynolds number, and a decreased reduced frequency .

17. Modification of Blade Design to Control the LEV Initiation • The blade design can be modified to generate leading edge vortex separation earlier in the rotation cycle. • If the vortex could be shed completely from the airfoil near  = 90, it would be less likely to interfere further along in the cycle. • To cause the LEV to convect away from the airfoil at  = 90 both the vortex formation and separation take place signicantly earlier. • One option to achieve this is, to change the mean angle of attack from 0 = 0 to some positive value. • This change would encourage earlier flow separation and may increase overall torque by negating the vortex capture effect. =150 =-24 =90 =27

18. Evolution of Local Vortex shed from a blade element of A Giromill

19. The bounded vortex for an ith blade element Each of the blade element is a bound vortex filament called a Lifting line. According to the airfoil theory , the lift can also be formulated in terms of the two-dimensional sectional lift coefficient (Cl), the chord length (c) and the relative velocity (Vrel) as The strength of the bound vortex can be expressed as

20. The Shed Vortex • The relationship between the strength of the bound vortex of blade element i at time step j and the strength of the shed vortex from this element is given by the Kelvin's law. • This Law requires that the circulation around any closed curve remains constant over time. It satisfies the following equation Where, si,j is the strength of the shed vortex at element i and time step j.

21. The journey of Shed Vortices • In reality, shed vortices are released continuously at the trailing edge. • The newest shed vortices are placed at x % from the current location of the trailing edge to the location of the trailing edge at the previous time step. • The other shed vortices are transported by the calculated velocity.

22. Occurrence of Trailing Vortices • In order to satisfy Helmholtz's theorems, a trailing vortex must emit from the blade at each blade element. • This emission occurs at a location, where the strength of each discrete bound vortex changes to generate the varying circulation a (lift) along the span.

23. Strength of Trailing Vortices • The strength of a trailing vortex is the difference between the strengths of the bound vortices from where it emits. • It can be seen in The Field Generated by A VAWT is A System of Vortex Filaments........ This system of vortices generate a complex velocity field. Velocity field generates Pressure Field…..

24. Biot–Savart Law The contribution from the infinitesimal length vortex The contribution from the finite length vortex The Gaussian kernel Here, r is the position  is the circulation of vortex r denotes the complex conjugate of r

25. Topics for Course Project • DSV based Design of Vertical Axis Wind Turbines. • Effect of DSV on performance and control of HAWT. • Vortex Lattice Method of Design for VAWT. • Collect atleast 5 international journal papers published after 2000. • No two groups can have more than two same papers. • A group which collect all the research papers different from other groups will get 10% bonus marks. • Use original statements and uniform symbols used in lectures. • Graphs can directly take from papers.