0
Research Papers: Fundamental Issues and Canonical Flows

Dynamic Stability Analysis of a Flexible Rotor Filled With Liquid Based on Three-Dimensional Flow

[+] Author and Article Information
Guangding Wang

School of Mechanical
Engineering and Automation,
Northeastern University,
Shenyang 110819, China

Huiqun Yuan

Institute of Applied Mechanics,
College of Science,
Northeastern University,
Shenyang 110004, China

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 4, 2018; final manuscript received August 29, 2018; published online November 8, 2018. Assoc. Editor: Kwang-Yong Kim.

J. Fluids Eng 141(5), 051202 (Nov 08, 2018) (9 pages) Paper No: FE-18-1323; doi: 10.1115/1.4041392 History: Received May 04, 2018; Revised August 29, 2018

This paper deals with the dynamic stability of a flexible liquid-filled rotor. On the basis of three-dimensional flow, the fluid perturbation motion is analyzed and the fluid–structure interaction equation is established, combining with continuity equation, the expression of fluid force exerted on rotor is derived in terms of Fourier series expansion. Considering the complex nonlinear relationship between fluid dynamic pressure and the rotor deformation function, they are expanded in terms of the eigenfunction of a dry rotor. The whirling frequency equation of a flexible rotor partially filled with liquid is obtained based on the rotor static equilibrium equation. Finally, the numerical technique is used to analyze the dynamic stability of the rotor system, and the influences of system parameters on unstable region are discussed.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Kollmann, F. G. , 1962, “ Experimentelle Und Theoretische Untersuchungen Über Die Kritischen Drehzahlen Flüssigkeitsgefüllter Hohlkörper,” Forsch. Geb. Ingenieurwes., 28(4), pp. 115–123. [CrossRef]
Kuipers, M. , 1964, “ On the Stability of a Flexibly Mounted Rotating Cylinder Partially Filled With Liquid,” Appl. Sci. Res., 13(1), pp. 121–137. [CrossRef]
Wolf, J. A., Jr. , 1968, “ Whirl Dynamics of a Rotor Partially Filled With Liquid,” ASME J. Appl. Mech., 35(4), pp. 676–682. [CrossRef]
Hendricks, S. L. , and Morton, J. B. , 1979, “ Stability of a Rotor Partially Filled With a Viscous Incompressible Fluid,” ASME J. Appl. Mech., 46(4), pp. 913–918. [CrossRef]
Saito, S. , and Someya, T. , 1980, “ Self-Excited Vibration of a Rotating Hollow Shaft Partially Filled With Liquid,” ASME J. Mech. Des., 102(1), pp. 185–192. [CrossRef]
Holm-Christensen, O. , and Träger, K. , 1991, “ A Note of Instability Caused by Liquid Motions,” ASME J. Appl. Mech., 58(3), pp. 804–811. [CrossRef]
Zhang, W. , Tang, J. , and Tao, M. , 1996, “ Dynamic Stability of a Rotor Filled or Partially Filled With Liquid,” ASME J. Appl. Mech., 63(1), pp. 101–105. [CrossRef]
Derendyeav, N. V. , and Sandalov, V. M. , 1982, “ On the Stability of Steady Rotation of a Cylinder Partly Filled With a Viscous Incompressible Liquid,” J. Appl. Math. Mech., 46(4), pp. 458–464.
Derendyaev, N. V. , and Senyatkin, V. A. , 1984, “ Stability Conditions for the Steady-State Rotation of a Cylinder Filled With a Stratified Nonuniform Viscous Incompressible Liquid,” J. Appl. Mech.Tech. Phys., 25(1), pp. 30–39.
Derendyaev, N. V. , Vostrukhov, A. V. , and Soldatov, I. N. , 2006, “ Stability and Andronov-Hopf Bifurcation of Steady-State Motion of Rotor System Partly Filled With Liquid: Continuous and Discrete Models,” ASME J. Appl. Mech., 73(4), pp. 580–589. [CrossRef]
Sato, Y. , 1990, “ Dynamic Absorber Using a Hollow Rotor Partially Filled With Liquid,” Trans. Jpn. Soc. Mech. Eng., 33(3), pp. 446–452.
Zhu, C. , 2002, “ Experimental Investigation Into the Instability of an Over-Hung Rigid Centrifuge Rotor Partially Filled With Fluid,” ASME J. Vib. Acoust., 124(4), pp. 483–491. [CrossRef]
Fang, Y. , and Farouk, B. , 2003, “ Numerical Simulations of Flows Inside a Partially Filled Centrifuge,” ASME J. Fluids Eng., 125(6), pp. 1033–1042. [CrossRef]
Tao, M. , and Zhang, W. , 2002, “ Dynamic Stability of a Flexible Spinning Cylinder Partially Filled With Liquid,” ASME J. Appl. Mech., 69(5), pp. 708–710. [CrossRef]
Ishida, Y. , and Liu, J. , 2010, “ Elimination of Unstable Ranges of Rotors Utilizing Discontinuous Spring Characteristics: An Asymmetrical Shaft System, an Asymmetrical Rotor System, and a Rotor System With Liquid,” ASME J. Vib. Acoust., 132(1), p. 011011.
Firouzabadi, R. D. , and Haddadpour, H. , 2010, “ The Flexural Instability of Spinning Flexible Cylinder Partially Filled With Viscous Liquid,” ASME J. Appl. Mech., 77(1), p. 011001. [CrossRef]
Yoshizumi, F. , 2011, “ Self-Excited Vibration Analysis of a Rotating Cylinder Partially Filled With Liquid, (Nonlinear Analysis by Shallow Water Theory),” J. Syst. Des. Dyn., 5(2), pp. 372–387.
Firouz-abadi, R. D. , Permoon, M. R. , and Haddadpour, H. , 2012, “ On the Instability of Spinning Cylindrical Shells Partially Filled With Liquid,” Int. J. Struct. Stab. Dyn., 12(3), p. 1250018. [CrossRef]
Firouz-Abadi, R. D. , Askarian, A. R. , and Kheiri, M. , 2013, “ Bending–Torsional Flutter of a Cantilevered Pipe Conveying Fluid With an Inclined Terminal Nozzle,” J. Sound Vib., 332(12), pp. 3002–3014. [CrossRef]
Kern, D. , and Jehle, G. , 2016, “ Dynamics of a Rotor Partially Filled With a Viscous Incompressible Fluid,” PAMM, 16(1), pp. 279–280. [CrossRef]
Chatterjee, D. , and Gupta, S. K. , 2015, “ Numerical Study of the Laminar Flow past a Rotating Square Cylinder at Low Spinning Rates,” ASME J. Fluids Eng., 137(2), p. 021204. [CrossRef]
Kozlov, N. V. , Kozlova, A. N. , and Shuvalova, D. A. , 2016, “ Dynamics of Immiscible Liquids in a Rotating Horizontal Cylinder,” Phys. Fluids, 28(11), p. 112102. [CrossRef]
Lopez, J. M. , 2016, “ Subcritical Instability of Finite Circular Couette Flow With Stationary Inner Cylinder,” J. Fluid Mech., 793, pp. 589–611. [CrossRef]
Rietz, M. , Scheid, B. , Gallaire, F. , Kofman, N. , Kneer, R. , and Rohlfs, W. , 2017, “ Dynamics of Falling Films on the Outside of a Vertical Rotating Cylinder: Waves, Rivulets and Dripping Transitions,” J. Fluid Mech., 832, pp. 189–211. [CrossRef]
Kumawat, T. C. , and Tiwari, N. , 2017, “ Stability Analysis of Rimming Flow Inside a Horizontally Rotating Cylinder in the Presence of an Insoluble Surfactant,” Phys. Fluids, 29(12), p. 122102. [CrossRef]
Dyakova, V. , Kozlov, V. , and Polezhaev, D. , 2016, “ Oscillation-Induced Sand Dunes in a Liquid-Filled Rotating Cylinder,” Phys. Rev. E, 94(6), p. 063109. [CrossRef] [PubMed]
Craig, A. E. , Dabiri, J. O. , and Koseff, J. R. , 2016, “ A Kinematic Description of the Key Flow Characteristics in an Array of Finite-Height Rotating Cylinders,” ASME J. Fluids Eng., 138(7), p. 070906. [CrossRef]
Craig, A. E. , Dabiri, J. O. , and Koseff, J. R. , 2016, “ Flow Kinematics in Variable-Height Rotating Cylinder Arrays,” ASME J. Fluids Eng., 138(11), p. 111203. [CrossRef]
Nikiforov, A. , 2016, “ Natural Surface Oscillations of Rotating Fluid along Radial Baffles of Rotor,” ASME J. Fluids Eng., 138(6), p. 061202. [CrossRef]
Wang, G. , and Yuan, H. , 2018, “ An Analysis of Dynamic Stability for a Flexible Rotor Filled With Liquid,” Phys. Fluids, 30(3), p. 037101. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Flexible rotor filled with liquid: (a) rotor structure and (b) rotor whirling

Grahic Jump Location
Fig. 2

F−S curves: (a) γ=0.2 and (b) γ=0.04

Grahic Jump Location
Fig. 3

The influence of fluid-fill ratio γ on unstable region: (a) γ>0.1 and (b) γ≤0.1

Grahic Jump Location
Fig. 4

Variation of unstable region with fluid-fill ratio γ

Grahic Jump Location
Fig. 5

The influences of mass ratio μ on unstable region for: (a) γ=0.2 and (b) γ=0.04

Grahic Jump Location
Fig. 6

Variation of unstable region with mass ratio μ

Grahic Jump Location
Fig. 7

Variation of unstable region with parameter

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In