Rachel Leuthold: Shape Optimization for Rigid Airfoils in Multiple-Kite AWE Systems

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Roland Schmehl

Presented during the AWESCO Midterm Review Meeting, 8 February 2017, KU Leuven, Belgium (H2020-ITN-642682).

Technology

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

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

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

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

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

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

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

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

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

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

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

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

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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

Rachel Leuthold: Shape Optimization for Rigid Airfoils in Multiple-Kite AWE Systems

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