Research Papers: Multiphase Flows

Coupled Multipoint Shape Optimization of Runner and Draft Tube of Hydraulic Turbines

[+] Author and Article Information
A. E. Lyutov

Department of Mathematics and Mechanics,
Novosibirsk State University,
2 Pirogova Street,
Novosibirsk 630090, Russia
e-mail: lyutov.alexey@gmail.com

D. V. Chirkov

Institute of Computational Technologies SB RAS,
6 Academic Lavrentjev Avenue,
Novosibirsk 630090, Russia
e-mail: chirkov@ict.nsc.ru

V. A. Skorospelov

Sobolev Institute of Mathematics SB RAS,
4 Academic Koptyuga Avenue,
Novosibirsk 630090, Russia
e-mail: vskrsp@math.nsc.ru

P. A. Turuk

Sobolev Institute of Mathematics SB RAS,
4 Academic Koptyuga Avenue,
Novosibirsk 630090, Russia
e-mail: turuk@math.nsc.ru

S. G. Cherny

Institute of Computational Technologies SB RAS,
6 Academic Lavrentjev Avenue,
Novosibirsk 630090, Russia
e-mail: cher@ict.nsc.ru

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 19, 2014; final manuscript received May 15, 2015; published online June 25, 2015. Assoc. Editor: Kwang-Yong Kim.

J. Fluids Eng 137(11), 111302 (Nov 01, 2015) (11 pages) Paper No: FE-14-1769; doi: 10.1115/1.4030678 History: Received December 19, 2014; Revised May 15, 2015; Online June 25, 2015

This paper suggests a method of simultaneous multi-objective shape optimization of hydraulic turbine runner and draft tube (DT) with the objective to increase turbine efficiency in wide range of operating points (OPs). Runner and DT are the main sources of energy losses in hydraulic turbines. Coupling runner and DT in computational fluid dynamics (CFD) analysis enables correct statement of boundary conditions for efficiency evaluation, while simultaneous variation of these components allows more flexible adjustment of flow passage geometry. Detailed runner parameterization with 28 free geometrical parameters and DT parameterization with nine free parameters are given. Optimization problem is solved using multi-objective genetic algorithm (MOGA). For each variation of runner and DT shapes, flow field in wicket gate (WG), runner, and DT is simulated using steady-state Reynolds-Averaged Navier–Stokes (RANS) equations with k-e turbulence model. Energy-based boundary conditions are used for the calculations, allowing determination of efficiency of the whole turbine in correspondence with International Electrotechnical Commission (IEC) standard. Formulations of multiple OP efficiency objective functions and constraints are discussed in detail. To demonstrate the advantages of simultaneous runner and DT variation, two optimization problems are solved for a medium specific speed Francis turbine. Namely, single runner and coupled “runner–DT” optimizations are carried out. It is shown that optimized runner–DT geometry outperforms the result of single runner optimization by about 0.3% in terms of average efficiency, showing the potential of the developed approach to improve multiregime turbine characteristics in practical design optimization problems.

Copyright © 2015 by ASME
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Fig. 1

Head losses in Francis turbine components versus relative discharge

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Fig. 2

Peak efficiency versus specific speed for Francis turbines [20]

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Fig. 3

Turbine flow passage with cross sections 1–5

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Fig. 4

Angular deviation function Φ˜(u,v) for Francis runner

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Fig. 5

Variation of RZ-projection of Francis runner

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Fig. 6

DT parameterization

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Fig. 7

DT shape construction

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Fig. 8

Computational domain and mesh in WG, runner, and DT cone inlet

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Fig. 9

Computational domain: DT

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Fig. 10

Efficiency hill diagrams: experimental and computed on basic and fine meshes

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Fig. 11

Optimization procedure

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Fig. 12

Efficiency hill diagram of the initial turbine

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Fig. 13

Pareto fronts for optimization runs Opt01 and Opt02

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Fig. 14

Initial and optimized runners

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Fig. 15

Comparison of initial and optimized DTs

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Fig. 16

Efficiency hill diagrams of initial and optimized flow passages for n11 = 70

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Fig. 17

Component losses in OP2

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Fig. 18

Meridian (Vm) and circumferential (Vu) velocity profiles downstream the runner in OP1

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Fig. 19

Meridian (Vm) and circumferential (Vu) velocity profiles downstream the runner in OP2

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Fig. 20

DT skin friction lines in OP2

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Fig. 21

Axial velocity distribution at DT outlet in OP2



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