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Rachel Leuthold: Shape Optimization for Rigid Airfoils in Multiple-Kite AWE Systems
- 1. Shape Optimization for Rigid Airfoils in Multiple-Kite AWE Systems Rachel Leuthold S´ebastien Gros, Moritz Diehl Albert-Ludwigs-University, Freiburg, Germany February 8, 2017 Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 1
- 2. Hello... Prof. Dr. Moritz Diehl me aerodynamics background in: & wind energy (potential flow methods) ALU-FR AWE group Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 2
- 3. Tether Drag and Multiple-Kite Systems Consider an AWE system with rigid kites, in pumping-cycle operation... Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 3
- 4. Tether Drag and Multiple-Kite Systems Tether drag proportional to tether’s apparent velocity squared and frontal area Significant loss in system efficiency. What to do? tether apparent velocity is significant over majority of tether for single-kite AWE systems Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 4
- 5. Tether Drag and Multiple-Kite Systems Tether drag proportional to tether’s apparent velocity squared and frontal area Significant loss in system efficiency. Multiple-Kite Systems balance multiple kites to keep main-tether stationary and tether drag small Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 5
- 6. Research Question What does this look like? For a multiple-kite pumping-cycle system, what kite shape, system geometry and flight path will maximize the mechanical power output? Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 6
- 7. Research Question What does this look like? For a multiple-kite pumping-cycle system, what kite shape, system geometry and flight path will maximize the mechanical power output? argmin parameters, states, controls, etc − w1 power + w2 regularization st. modelled physics ⇒ forces and moments forces and moments ⇒ dynamics physical limits ⇒ variable bounds Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 7
- 8. A Note on Methodology argmin parameters, states, controls, etc − w1 power + w2 regularization st. modelled physics ⇒ forces and moments forces and moments ⇒ dynamics physical limits ⇒ variable bounds Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 8
- 9. A Note on Methodology argmin parameters, states, controls, etc − w1 power + w2 regularization st. modelled physics ⇒ forces and moments forces and moments ⇒ dynamics physical limits ⇒ variable bounds very nonlinear problem Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 9
- 10. A Note on Methodology argmin parameters, states, controls, etc − w1 power + w2 regularization st. modelled physics ⇒ forces and moments forces and moments ⇒ dynamics physical limits ⇒ variable bounds very nonlinear problem - solution approach: homotopy e.g., F = (1 − ι)Ffictitious + ι (Lkite + Dkite + Dsec. tether) , 0 ≤ ι ≤ 1 Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 10
- 11. A Note on Methodology argmin parameters, states, controls, etc − w1 power + w2 regularization st. modelled physics ⇒ forces and moments forces and moments ⇒ dynamics physical limits ⇒ variable bounds very nonlinear problem - solution approach: homotopy e.g., F = (1 − ι)Ffictitious + ι (Lkite + Dkite + Dsec. tether) , 0 ≤ ι ≤ 1 - reduce constraint nonlinearity by lifting variables e.g., CL − 2πα 1 + 2c/b = 0 ⇔ CL(b + 2c)ζ − 2πbξ = 0, ξα − ζ = 0 Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 11
- 12. A Note on Methodology argmin parameters, states, controls, etc − w1 power + w2 regularization st. modelled physics ⇒ forces and moments forces and moments ⇒ dynamics physical limits ⇒ variable bounds very nonlinear problem - solution approach: homotopy e.g., F = (1 − ι)Ffictitious + ι (Lkite + Dkite + Dsec. tether) , 0 ≤ ι ≤ 1 - reduce constraint nonlinearity by lifting variables e.g., CL − 2πα 1 + 2c/b = 0 ⇔ CL(b + 2c)ζ − 2πbξ = 0, ξα − ζ = 0 - solve with open-source interior-point solver IPOPT via CasADi Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 12
- 13. What Needs to be Done? External geometry and trajectory optimization Internal structure optimization Validation Hopefully: prototype construction Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 13
- 14. What Needs to be Done? External geometry and trajectory optimization Model selection Internal structure optimization Validation Hopefully: prototype construction Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 14
- 15. What Needs to be Done? External geometry and trajectory optimization Model selection so far: aerodynamic model must include induction [L., Gros, Diehl. Induction in Optimal Control of Multiple-Kite Airborne Wind Energy Systems. submitted to IFAC 2017] currently: next: does aero. model need to consider skewed-wake effects? determine skewed-wake model for multi-kite systems Internal structure optimization Validation Hopefully: prototype construction Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 15
- 16. What Needs to be Done? External geometry and trajectory optimization Model selection Andrea Zanelli optimization algorithms Elena Malz effect of wind data Thomas Haas model validation Internal structure optimization Ashwin Candade structure optimization methods Validation Hopefully: prototype construction Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 16
- 17. What Needs to be Done? External geometry and trajectory optimization Model selection Chalmers Uni. optimization in AWE problems 3 months Uni. Victoria optimal design with potential flow methods 2 months Internal structure optimization TU. Delft structure optimization (and more potential flow methods) 2 months Validation Hopefully: prototype construction Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 17
- 18. Conclusion there is a lot to do, but moving steadily forwards... Thank you for your attention Shape Optimization in Multi-Kite AWE Systems Rachel Leuthold (ALU-FR) 18