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Research Papers

Inverse Design of Single- and Multi-Rotor Horizontal Axis Wind Turbine Blades Using Computational Fluid Dynamics

[+] Author and Article Information
Behnam Moghadassian

Department of Aerospace Engineering,
Iowa State University,
Ames, IA 50010
e-mail: behmogh@iastate.edu

Anupam Sharma

Department of Aerospace Engineering,
Iowa State University,
Ames, IA 50010
e-mail: sharma@iastate.edu

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received March 16, 2017; final manuscript received October 27, 2017; published online January 22, 2018. Assoc. Editor: Yves Gagnon.

J. Sol. Energy Eng 140(2), 021003 (Jan 22, 2018) (11 pages) Paper No: SOL-17-1090; doi: 10.1115/1.4038811 History: Received March 16, 2017; Revised October 27, 2017

A method for inverse design of horizontal axis wind turbines (HAWTs) is presented in this paper. The direct solver for aerodynamic analysis solves the Reynolds-averaged Navier–Stokes (RANS) equations, where the effect of the turbine rotor is modeled as momentum sources using the actuator disk model (ADM); this approach is referred to as RANS/ADM. The inverse problem is posed as follows: for a given selection of airfoils, the objective is to find the blade geometry (described as blade twist and chord distributions) which realizes the desired turbine aerodynamic performance at the design point; the desired performance is prescribed as angle of attack (α) and axial induction factor (a) distributions along the blade. An iterative approach is used. An initial estimate of blade geometry is used with the direct solver (RANS/ADM) to obtain α and a. The differences between the calculated and desired values of α and a are computed and a new estimate for the blade geometry (chord and twist) is obtained via nonlinear least squares regression using the trust-region-reflective (TRF) method. This procedure is continued until the difference between the calculated and the desired values is within acceptable tolerance. The method is demonstrated for conventional, single-rotor HAWTs and then extended to multirotor, specifically dual-rotor wind turbines (DRWT). The TRF method is also compared with the multidimensional Newton iteration method and found to provide better convergence when constraints are imposed in blade design, although faster convergence is obtained with the Newton method for unconstrained optimization.

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References

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Figures

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Fig. 1

Isometric view of the computational mesh used for the proposed inverse design

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Fig. 2

Results of the mesh sensitivity study. RANS/ADM predicted distributions of angle of attack (α) and axial induction factor (a) are compared for four different mesh sizes. (a) Angle of attack and (b) axial induction factor.

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Fig. 3

Flowchart of the inverse design algorithm

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Fig. 4

Visualization of the Jacobian matrix: (a) a schematic showing the arrangement of the four different blocks in the Jacobian matrix and (b)–(e) contour plots for each of the four blocks of the matrix. The contour levels are different in each block. (a) Schematic, (b) ∂α/∂θ, (c) ∂α/∂c, (d) ∂a/∂θ, and (e) ∂a/∂θ.

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Fig. 5

Results for test case 1: input geometry (c and θ distributions) and output aerodynamic performance (α and a distributions) at the first iteration (top two plots) and final iteration (bottom two plots)

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Fig. 6

Results for test case 2: lines show converged geometry (c and θ) and converged α and a distributions at the final iteration; symbols show original geometry from Ref. [32] and its aerodynamic performance (α and a) obtained via direct analysis using RANS/ADM

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Fig. 7

Results for test case 3: converged c and θ distributions (left) and α and a distributions (right) at the final iteration. Predicted α and a distributions (lines) are compared with desired values (symbols) in the right plot to show convergence.

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Fig. 8

Comparison between multidimensional Newton iteration and TRF methods

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Fig. 9

Schematic of the Jacobian for DRWT cases

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Fig. 10

Results for test case 4: converged geometry (c and θ) and aerodynamics (α and a) for upstream (top two plots) and downstream (bottom two plots) rotors. Plots on the right show desired aerodynamic performance with symbols and predicted performance of the final geometry with lines.

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Fig. 11

Results for test case 5: converged geometry (c and θ) and corresponding α and a distributions for upstream (top two plots) and downstream (bottom two plots) rotors. Symbols show original c, θ and α, a, and lines show corresponding converged quantities.

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Fig. 12

Different blocks of the Jacobian matrix for test case 5 after convergence

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