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Numerical analysis of unstable turbulent flows in a centrifugal pump impeller considering the curvature and rotation effect

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Abstract

In this study, a modified partially averaged Navier-Stokes model (MSST PANS) is proposed by treating a modified shear stress transport (SST) k-ω model as the parent turbulence model. The unstable turbulent flow in a centrifugal pump that considers the curvature and rotation effect is investigated as the test case to evaluate the performance of the MSST PANS model and analyze the flow instability in a centrifugal pump. The SST k-ω and the standard k-ε PANS models are also evaluated for comparison. Results show that the MSST PANS model exhibits excellent performance and delivers the most satisfactory prediction results of the positive slope of the characteristic curve, time-averaged internal flows, and velocity profiles. The energy loss based on the energy balance equations is adopted to provide an explanation of the internal flow evolutions in pumps. The findings also indicate energy loss distribution is associated with the positive slope phenomenon. The high-velocity gradient flows at the entrance of the blade-to-blade passage and the reverse flows at the impeller exit are the main reasons for the high turbulent kinetic energy in the impeller. The MSST PANS model demonstrates promising applications in the field of hydraulic machinery, where unstable turbulent flows are prevalent.

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Abbreviations

P k :

Production term

γ1, γ2 :

Turbulent model constants, γ1 = 5/9, γ2 = 0.44

β1, β2 :

Turbulent model constants, β1 = 0.075, β2 = 0.0828

σk1, σk2 :

Turbulent model constants, σk1 = 1.1765, σk2 = 1.0

σω1, σω2 :

Turbulent model constants, σω1 = 2.0, σω2 = 1.168

β :

Turbulent model constant, β = 0.09

C 2 :

Turbulent model constant, C2 = 1.9

C 1 :

Turbulent model parameter

μt*:

Modified eddy viscosity

C μ :

Modified eddy viscosity coefficient

f k :

Unresolved-to-total ratio of kinetic energy

f ε :

Unresolved-to-total ratio of dissipation

f ω :

Unresolved-to-total ratio of turbulent frequency

k, k u :

Total and unresolved turbulent kinetic energy, respectively

ε, ε u :

Total and unresolved turbulent dissipation, respectively

ω, ω u :

Total and unresolved turbulent frequency, respectively

Λ:

Taylor turbulent length scale

Δ:

Local grid size

H :

Pump head (m)

H d :

Pump head under the design point condition (m)

bep:

Best efficiency point

T n :

Impeller rotation period

P :

Power

P in :

Input power

P e :

Effective power

P l :

Power loss

δx, δy, δz :

Length, width, and height of each mesh cell, respectively

ψ :

Head coefficient

ϕ :

Flow coefficient

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Acknowledgments

This work was financially supported by the National Key Research and Development Program of China (2018YFB0 606101), National Natural Science Foundation of China (No. 51536008), Beijing Natural Science Foundation (3182014), and Tsinghua National Laboratory for Information Science and Technology.

Author information

Authors and Affiliations

  1. State Key Laboratory of Hydroscience and Engineering, Department of Energy and Power Engineering, Tsinghua University, Beijing, 100084, China

    Weixiang Ye & Xianwu Luo

  2. Beijing Key Laboratory of CO2 Utilization and Reduction Technology, Tsinghua University, Beijing, 100084, China

    Weixiang Ye & Xianwu Luo

  3. Key Laboratory of Fluid Transmission Technology of Zhejiang Province, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Zuchao Zhu

  4. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, 430072, China

    Zhongdong Qian

Authors
  1. Weixiang Ye
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  2. Zuchao Zhu
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  3. Zhongdong Qian
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  4. Xianwu Luo
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Corresponding author

Correspondence to Xianwu Luo.

Additional information

Recommended by Editor Yang Na

Weixiang Ye obtained his B.S. from North China Electric Power University in 2017. He is currently a Ph.D. candidate at the Department of Energy and Power Engineering, Tsinghua University, Beijing, China. His main area of research is the flow instability in pumps and turbulence modelling.

Xianwu Luo obtained his B.S. and M.S. from Tsinghua University, Beijing, China in 1991 and 1997, respectively, and his Ph.D. in Mechanical Engineering from Kyushu Institute of Technology, Japan, in 2004. He is currently a Professor at the Department of Energy and Power Engineering, Tsinghua University, Beijing, China.

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Ye, W., Zhu, Z., Qian, Z. et al. Numerical analysis of unstable turbulent flows in a centrifugal pump impeller considering the curvature and rotation effect. J Mech Sci Technol 34, 2869–2881 (2020). https://doi.org/10.1007/s12206-020-0619-0

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  • DOI: https://doi.org/10.1007/s12206-020-0619-0

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