Multi-point Optimization of Wind Turbine Blades Using Helicoidal Vortex Model

The availability of thorough wind assessment data has raised the question whether it would be possible to improve wind turbine power outputs with respect to existing data. At the University of California Davis wind turbine analysis codes have been developed as well as a wind turbine optimization code. This optimization is performed with respect to a specified wind speed. This chapter describes an attempt to expand the single-point optimization, that is performed with respect to one wind speed, to a multi-point optimization in which the probability distribution of wind speeds is taken into account. This multi-point optimization is expected to show the ability to trade-off between performances at different wind speeds. The trade-off is based on power output and the chance of occurrence. An objective function that describes the power production with respect to the discretized distribution function is defined. The optimization of the objective function is performed with respect to a limited drag force on the supporting tower.

[1]  Dimitri J. Mavriplis,et al.  Efficient Hessian Calculations Using Automatic Differentiation and the Adjoint Method with Applications , 2010 .

[2]  Jean-Jacques Chattot DESIGN AND ANALYSIS OF WIND TURBINES USING HELICOIDAL VORTEX MODEL , 2002 .

[3]  M. Rumpfkeil,et al.  Design Optimization Utilizing Gradient/Hessian Enhanced Surrogate Model , 2010 .

[4]  Matthew F. Barone,et al.  Measures of agreement between computation and experiment: Validation metrics , 2004, J. Comput. Phys..

[5]  Jean-Jacques Chattot,et al.  A Parallelized Coupled Navier-Stokes/Vortex-Panel Solver , 2005 .

[6]  Jean-Jacques Chattot,et al.  OPTIMIZATION OF PROPELLERS USING HELICOIDAL VORTEX MODEL , 2000 .

[7]  Scott Schreck,et al.  Wind Tunnel Testing of NREL's Unsteady Aerodynamics Experiment , 2001 .

[8]  Laurent El Ghaoui,et al.  Foreword: special issue on robust optimization , 2006, Math. Program..

[9]  S. Goldstein On the Vortex Theory of Screw Propellers , 1929 .

[10]  P. A. Newman,et al.  An Approximately Factored Incremental Strategy for Calculating Consistent Discrete Aerodynamic Sensitivity Derivatives , 1992 .

[11]  Earl P. N. Duque,et al.  Navier-Stokes and Comprehensive Analysis Performance Predictions of the NREL Phase VI Experiment , 2003 .

[12]  Gary B. Lamont,et al.  Considerations in engineering parallel multiobjective evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

[13]  Niels N. Sørensen,et al.  Navier-Stokes predictions of the NREL phase VI rotor in the NASA Ames 80-by-120 wind tunnel , 2002 .

[14]  Quang Dinh,et al.  Estimation of the impact of geometrical uncertainties on aerodynamic coefficients using CFD , 2008 .

[15]  Gene Hou,et al.  First- and Second-Order Aerodynamic Sensitivity Derivatives via Automatic Differentiation with Incremental Iterative Methods , 1996 .

[16]  V. Venkatakrishnan Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations , 1990 .

[17]  Jean-Jacques Chattot Optimization of Wind Turbines Using Helicoidal Vortex Model , 2003 .

[18]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[19]  Alper Ezertas,et al.  Performances of Numerical and Analytical Jacobians in Flow and Sensitivity Analysis , 2009 .

[20]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[21]  Sinan Eyi,et al.  Effects of the Jacobian evaluation on Newton's solution of the Euler equations , 2005 .

[22]  N. Qin,et al.  Numerical study of active shock control for transonic aerodynamics , 2004 .

[23]  Philip E. Gill,et al.  Practical optimization , 1981 .

[24]  D. Kraaijpoel Seismic ray fields and ray field maps : theory and algorithms , 2003 .

[25]  G. D. van Albada,et al.  A comparative study of computational methods in cosmic gas dynamics , 1982 .

[26]  H. Reissner,et al.  On the Vortex Theory of the Screw Propeller , 1937 .

[27]  Shigeru Obayashi,et al.  Robust Multidisciplinary Design Optimisation Using CFD and Advanced Evolutionary Algorithms , 2010 .

[28]  D. Ghate,et al.  Inexpensive Monte Carlo Uncertainty Analysis , 2005 .

[29]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[30]  J. O. Hager,et al.  Airfoil design optimization using the Navier-Stokes equations , 1994 .

[31]  P. Sagaut,et al.  Building Efficient Response Surfaces of Aerodynamic Functions with Kriging and Cokriging , 2008 .