Conclusion

The panel method enables faster exploration of the design space. On a standard PC (3.40 GHz, 8 M Cache, 15 GB RAM) it takes about 90 minutes to run three seconds of FSI simulation (transient approach). Transient results converge to the results obtained from the steady approach for the cases where a steady state solution exists. Even though using panel method for flow modeling facilitates faster design evaluations and a comprehensive study of the design envelope at a lower cost during early design stages, limitations of the method should also be considered. Since no boundary layer model is coupled with the cur-rent panel method implementation, viscous drag is not included in the model.

In determining the final shape of the membrane, pressure force plays a much more important role than the viscous drag. However, the final design should inevitably be studied using a high-fidelity FSI analysis which is done in the upcoming chapter.

122 Chapter 6 FSI Analysis Using Panel Method Comparing the performance of the membrane wing with the baseline rigid wing, the following main observations have been made:

1. Increase in the camber for the membrane wing as well as shifting of the point of maximum camber towards the leading edge.

2. Higher lift curve slope for the membrane wing. A lower lift coefficient for zero angle of attack is observed for the membrane wing, but due to the higher lift curve slope, the membrane wing has higher lift coefficient than the baseline wing for higher angles of attack.

3. Vortex-induced oscillations have been observed for the membrane wing at higher angles of attack. Depending on the pre-stress level, they have been present either fromα= 6.0^◦or fromα= 7.5^◦. For both cases, the stall point is not reached yet, but as a consequence of membrane vibra-tion, oscillations in lift coefficient are observed for the membrane wing even before the stall angle of attack. The lift coefficient in these cases oscillates around a constant mean which is higher than that of the base-line rigid wing. The actual stress state in the membrane is dominated by induced stresses due to the elastic deformation. Even though differ-ent pre-stresses are set for the initial configuration, resulting in differdiffer-ent natural frequencies for the membrane wing configuration, actual stress distribution is quite the same regardless of the pre-stress value. Conse-quently, membrane oscillations in the three different pre-stress configu-ration share approximately the same frequency.

4. Elastic deformation of the trailing edge cable improves the lift coefficient of the membrane wing and postpones membrane vibration to higher an-gles of attack. The flexibility of the trailing edge reduces the amplitude of the membrane vibration as well.

7

The Membrane Blade

This chapter utilizes the methods discussed so far in the thesis for the analysis of the membrane blade concept. The analysis is done in three levels. Every level of the analysis compares the performance of the membrane blade with the baseline rigid blade which is the NASA-Ames Phase VI blade (Appendix B).

First, steady-state and transient FSI analysis of the blade in non-rotating con-figuration is performed. The steady-state analysis follows the idea of multi-fidelity analysis by using both panel method and CFD for solving the fluid problem.

Next, a workflow for using the blade element momentum (BEM) method, as the most common tool for aerodynamic analysis of wind turbines, for the anal-ysis of the membrane blade is proposed and tested in both steady-state and transient condition, considering the rotation of the rotor. In classical BEM, look-up tables for the lift and drag coefficients at different angles of attack and for a range of Reynolds number are used. For BEM analysis of the membrane blade, these tables are substituted with the two-dimensional panel code solver discussed in Section3.1.

Finally, high-fidelity FSI analysis of the membrane blade in steady-state con-dition is presented in Section7.4. The rotation of the blade is modeled using the Multi Reference Frame (MRF) approach in OpenFOAM. At all of the three levels of the analysis, the membrane blade promises certain advantages over the rigid baseline blade in terms of the lift force or the generated power which are discussed in the upcoming sections.

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124 Chapter 7 The Membrane Blade Parts of the results presented in this chapter have been published in Wind En-ergy Science Journal [68] and Journal of Physics [69]. They are presented here with written consent from the publisher.

7.1 The Membrane Blade Concept

TheSailwing concept was proposed by Ormiston during the70⁰s[15]. The basic schematic of the sailwing can be seen in Fig.7.1. The main frame of the sailwing consists of a leading edge mast which is assumed to be rigid and a number of ribs which are connected to the leading edge mast along the span of the wing. Upper and lower surfaces of the wing are elastic, pre-stressed mem-branes connected to the mast and to the ribs. The memmem-branes are supported at the trailing edge by pretensioned edge cables. The form of the wing in the operating condition depends on the interaction between the internal forces of the wing configuration and the aerodynamic loading.

Figure 7.1: Sailwing construction concept, from [15]

In the absence of aerodynamic loads, the shape of the sailwing is determined by the equilibrium of membrane and edge cable forces. In the unloaded state, membranes form a concave, double-curved surface. In the operating condition, the applied aerodynamic load deforms the membranes and edge cables. The interaction between external aerodynamic force and the internal pretensions governs the form of wing’s surface and its aerodynamic characteristics. As a result, fully-coupled fluid-structure interaction analysis is needed to evaluate the actual performance of the sailwing. Having the upper and lower surface of the wing made out of membranes with a weight of about1−1.5kg/m² facilitates light-weight construction of the wing. The flexibility of the sailwing enables it to adapt itself to the flow condition to some extent which promises a favorable loading on the wing in terms of fatigue life.

The studied membrane blade is inspired by the sailwing concept. It can be

7.2 Membrane blade in non-rotating configuration 125