Hydraulic Turbine Diffuser Shape Optimization by Multiple Surrogate Model Approximations of Pareto Fronts

[+] Author and Article Information
B. Daniel Marjavaara

Division of Fluid Mechanics, Luleå University of Technology, SE-97187 Luleå, Swedendama@ltu.se

T. Staffan Lundström

Division of Fluid Mechanics, Luleå University of Technology, SE-97187 Luleå, Sweden

Tushar Goel, Yolanda Mack

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611

Wei Shyy

Department of Aerospace Engineering, University of Michigan, 3064 FXB, 1320 Beal Avenue, Ann Arbor, MI 48109

J. Fluids Eng 129(9), 1228-1240 (Apr 04, 2007) (13 pages) doi:10.1115/1.2754324 History: Received August 08, 2006; Revised April 04, 2007

A multiple surrogate-based optimization strategy in conjunction with an evolutionary algorithm has been employed to optimize the shape of a simplified hydraulic turbine diffuser utilizing three-dimensional Reynolds-averaged Navier–Stokes computational fluid dynamics solutions. Specifically, the diffuser performance is optimized by changing five geometric design variables to maximize the average pressure recovery factor for two inlet boundary conditions with different swirl, corresponding to different operating modes of the hydraulic turbine. Polynomial response surfaces and radial basis neural networks are used as surrogates, while a hybrid formulation of the NSGA-IIa evolutionary algorithm and a ϵ-constraint strategy is applied to construct the Pareto front from the two surrogates. The proposed optimization framework drastically reduces the computational load of the problem, compared to solely utilizing an evolutionary algorithm. For the present problem, the radial basis neural networks are more accurate near the Pareto front while the response surface performs better in regions away from it. By using a local resampling updating scheme the fidelity of both surrogates is improved, especially near the Pareto front. The optimal design yields larger wall angles, nonaxisymmetrical shapes, and delay in wall separation, resulting in 14.4% and 8.9% improvement, respectively, for the two inlet boundary conditions.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Three-dimensional models of the diffuser geometries in focus: (a) ERCOFTAC Turbine-99 Workshop draft tube; and (b) simplified diffuser geometry

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Figure 2

Two-dimensional sketch of the diffuser geometry and its design variables. The dimensions are in millimeters.

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Figure 3

Sketch of the propeller curve and the operational modes

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Figure 4

Solution space (green dots), Pareto front (red dots), CFD calculated designs (blue and red stars), and the hybrid NSGA-IIa evaluated designs (black dots) for the constructed surrogate models: (a) full quadratic RS model based on the 34-case design plan; (b) full quadratic RS model based on the 49-case design plan; (c) RBNN model based on the 34-case design plan; and (d) RBNN model based on the 49-case design plan

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Figure 5

Solution space (green dots) for the RBNN model based on the enhanced 49-case design plan, and all calculated CFD data points (blue and red stars): (a) whole solution space; (b) zoomed solution space

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Figure 6

CFD calculated axial velocity fields at the A plane for two diffuser geometries: (a) Geo 1, T mode; (b) Geo 1, R mode; (c) Geo 60, T mode; (d) Geo 60, R mode; (e) Geo 6, T mode; and (f) Geo 6, R mode

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Figure 7

Flow characteristics in the solution space (green dots). The solution space is from the full quadratic RS model based on the enhanced 49-case design plan.



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