Double Multiple Streamtube Model and Numerical

Double Multiple Stream Tube Model and Matlab Analysis of Vertical Axis Wind Turbine Ege Konuk

Abstract This assignment paper contains analysis of a one of the two most common and comparable airfoils choices in Vertical wind turbine design. The first airfoil that is chosen is the DU 06-W-200. This airfoil is belong to a family that design by Delft University in Netherlands for purpose of implementing to small VAWT wind turbines for best efficiently and high power generation. Second airfoil is the NRE’s S835, which is, belong to another type of airfoil family that is named NREL (National Renewable Energy Laboratory) in US. In this paper Double Multiple Stream Tube analysis is conducted to those airfoils to generate side by side comparison in same input from the user by using Matlab programming. Keywords: Wind Turbine, Momentum Model, Stream Tube, VAWT

1. Introduction 1.1. Double Multiple Stream Tube Theory The Double Multiple Stream tube (DMST) version developed by Paraschivoiu models allowed for the difference between the upwind and downwind passes of each blade by dividing each stream tube into an upwind half and a downwind half as shown in Figure 1. The turbine’s interaction with the wind in the upwind and downwind passes of the blades separately. The assumption is made that the wake from the upwind pass is fully expanded and the ultimate wake velocity has been reached before the interaction with the blades in the downwind pass. The downwind blades therefore see a reduced ‘freestream’ velocity. This approach more accurately represents the variation in flow through the turbine. Each stream tube in the DMST model intersects the airfoil path twice; once on the upwind pass, and again on the downwind pass. The DMST model simultaneously solves two equations for the stream-wise force at the actuator disk; one obtained by conservation of momentum and other based on the aerodynamic coefficients of the airfoil (lift and drag) and the local wind velocity. These equations are solved twice; for the up- wind and for the downwind part of the rotor.

Figure 1

1.1. DMST Mathematical Derivation

Figure 2

where Va is the axial flow velocity (i.e. induced velocity) through the rotor, ω is the rotational velocity, R is the radius of the turbine, and θ is the azimuth angle. Normalizing the relative velocity using free stream wind velocity one can obtain:

In addition, angle of attack can be found as;

The normal and tangential coefficients can be ex-pressed as:

Where “h” is blade height and “c” blade chord length. The instantaneous torque (Qi) on one single airfoil at certain θ is;

Finally the total torque produced can be found by basic mean operation through the upstream and downstream of the turbine and though 0 to 360 deg. azitmual angles;

Torque and power coefficient found as follows;

Where D is the diameter of the turbine.

2.

RESULTS AND CONCLUSION

The results for VAWT obtain from Matlab implementation of the DMST method from 0 to 360 azitmual angles and 12 Stream tubes were utilized for this analysis. The two airfoil Cl and Cd values obtain from JAVAFOIL for optimal conditions in 2-d. The Cp,Total torque and Total Power has obtain from momentum equations .

First Case;

V∞=4m/s , D = 4m, C (chord) =0.2m

Left ones: DU 06-W-200 Right ones: NRE’s S835

Second Case;

V∞=4m/s , D = 4m, C (chord) =0.4m

Third Case; V∞=4m/s , D = 8m, C (chord) =0.2m

4rd Case;

V∞=8m/s , D = 4m, C (chord) =0.2m

Conclusion

It does apparent that the NRE’s S835 is the superior in most of the performance parameters. However, in some Maximum torque and power values DU 06-W-200has some advantages over NRE’s S835. When the chord length increases the power coefficient decreases gradually. It has seen that the most effective way to increase the power coefficient is to increase diameter of the turbine. However in real life application there numerous limitations for that parameter. Lastly, increase in wind speed seem to drop the power and torque values dramatically. This means that the fix pitch VAWT is produce more power in lower wind speed in these conditions.