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Research Papers: Flows in Complex Systems

Construction of Pump-Turbine Characteristics at Any Specific Speed by Domain-Partitioned Transformation

[+] Author and Article Information
Wei Zeng

State Key Laboratory of Water Resources and
Hydropower Engineering Science,
Wuhan University,
Wuhan 430072, China
e-mail: wzeng@whu.edu.cn

Jiandong Yang

State Key Laboratory of Water Resources and
Hydropower Engineering Science,
Wuhan University,
Wuhan 430072, China
e-mail: jdyang@whu.edu.cn

Yongguang Cheng

State Key Laboratory of Water Resources and
Hydropower Engineering Science,
Wuhan University,
Wuhan 430072, China
e-mail: ygcheng@whu.edu.cn

1Corresponding authors.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 6, 2014; final manuscript received September 17, 2014; published online October 21, 2014. Assoc. Editor: Satoshi Watanabe.

J. Fluids Eng 137(3), 031103 (Oct 21, 2014) (12 pages) Paper No: FE-14-1116; doi: 10.1115/1.4028607 History: Received March 06, 2014; Revised September 17, 2014

Pump-turbine characteristics are important for designing pumped-storage plants and indispensable for simulating hydraulic transients, but are often not available in the preliminary design stage. Therefore, constructing a set of pump-turbine characteristics is necessary, when no suitable characteristics at the same specific speed can be used for substitution. In this paper, we propose a new method for pump-turbine characterization at any specific speed using a database of 25 available sets of pump-turbine characteristics. The intersecting curves, defined by the intersections of the characteristic curves with a coordinate axis, are formularized to prepare for the characterization primarily. Next is an introduction of a transformation method for characteristic curves base on domain partition, through which the curves are transformed into eight characteristic surface meshes in eight separate domains. Then, we present the construction procedures in each domain, which include merging the transformed surface meshes for all the sets of collected characteristic curves into a cube mesh, constructing a super surface by interpolation to construct the regular characteristic surface meshes for an arbitrary specific speed, and transforming the constructed meshes reversely to get the conventional characteristic curves. This method is verified by comparing them to measured characteristic curves with reasonable accuracies.

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Figures

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Fig. 1

Characteristics curves and domains. (a) n'1-Q'1 plane and (b) n'1-M'1 plane.

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Fig. 2

Procedures and methods for constructing characteristic curves

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Fig. 3

Velocity triangles at the runner inlet and outlet of a pump-turbine. (a) Inlet, (b) axial streamline, and (c) outlet.

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Fig. 4

Fitting analysis of n'1 when Q'1T=0 at optimal openings

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Fig. 5

The curves for n'1=0. (a) α-Q'1 and (b) α-M'1.

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Fig. 6

The curves for M'1=0. (a) α-Q'1 and (b) α-n'1.

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Fig. 7

Numerical fits of the coefficients (α-Q'1 as n'1=0). (a) aα versus ns and (b) bα versus ns.

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Fig. 8

Numerical fits of the b coefficients (α-M'1 as n'1=0). (a) aβ versus ns and (b) bβ versus ns.

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Fig. 9

Validation of the general formulae. (a) α-Q'1 on the n'1=0 axis and (b) α-Q'1 relation on the M'1=0 axis.

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Fig. 10

Regular surfaces created by B-spline interpolation in Domains 1–8 ((a)–(j)). (a) Domain 1(a), (b) domain (b), (c) domain 2, (d) domain 3, (e) domain 4, (f) domain 5, (g) domain 6, (h) domain 7, (i) domain 8(a), and (j) domain 8(b).

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Fig. 11

Fitting results of characteristic surfaces in domain 3

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Fig. 12

Comparison of S-shaped regions of two pump-turbines with same specific speed

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Fig. 13

Building of characteristic super surface in domain 2. (a) Cube mesh and (b) super surface.

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Fig. 14

Transient pressures with different S-shaped curves. (a) S-shaped curves and (b) transient pressures.

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Fig. 15

Comparisons of constructed and measured characteristics of pump-turbine ((a)–(f)). (a) n'1-Q'1 plane (82.15), (b) n'1-M'1 plane (82.15), (c) n'1-Q'1 plane (142.6), (d) n'1-M'1 plane (124.6), (e) n'1-Q'1 plane (154.4), and (f) n'1-M'1 plane (154.4).

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Fig. 16

Comparisons of constructed and measured characteristics of a model pump-turbine. (a) n'1-Q'1 plane and (b) n'1-M'1 plane.

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Fig. 17

Constructions of typical, relatively severe, and gentle S-shaped curves. (a) n'1-Q'1 plane and (b) n'1-M'1 plane.

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