Skip to main content
SpringerLink
Log in

Calculation of coupled added mass of multibody system immersed in fluids

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The natural frequencies of structures submerged in a fluid are significantly influenced by fluid properties and adjacent structures, which can be expressed by added mass. Some finite element software can effectively determine the added mass matrix of arbitrary structures immersed in viscous fluids, provided the structure lengths are relatively long; however, the added mass specified in a second-order tensor cannot be used as is. Herein, we propose methods to calculate the coupled added mass as a single value for each structure using the MassInFlu code. When the x- and y-directional components of the coupled added mass are unequal, an effective added mass can be determined by rotating the structures or coordinate axes. Various examples considering different scenarios show that the coupled natural frequencies obtained using the coupled or effective added mass coincide with those obtained from fluid-structure interaction analyses.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

E :

Elastic modulus

C m :

Added mass coefficient

f :

Frequency

G :

Gap between structures

k :

Stiffness of structure

L :

Length of structure

m :

Mass of structure

M a :

Added mass

m c :

Coupled added mass

m eff :

Effective added mass

R:

Radius of structure

R, r :

Rotation matrix

S :

Stokes number

x :

Eigenvector

ε :

Eccentricity

μ :

Dynamic viscosity

θ :

Rotation angle

ρ :

Density

ω :

Angular velocity

References

  1. R. J. Fritz, The effect of liquids on the dynamic motions of immersed solids, J. Eng. Ind.-Trans. ASME, 94(1) (1972) 167–173.

    Article  Google Scholar 

  2. R. D. Blevins, Flow-induced Vibration, 2nd Ed., Krieger Publishing Company, Malabar, Florida, USA (2001).

    MATH  Google Scholar 

  3. J.-B. Park, Y. Choi, S.-J. Lee, N.-C. Park, K.-S. Park, Y.-P. Park and C.-I. Park, Modal characteristic analysis of the APR1400 nuclear reactor internals for seismic analysis, Nucl. Eng. Technol., 46(5) (2014) 689–698.

    Article  Google Scholar 

  4. J.-O. Sun, G. Kim, Y.-S. Choo and Y.-S. Yoo, Calculation of added mass for submerged reactor with complex shape, Trans. Korean Nucl. Soc. Autumn Meeting, Gyeongju, Korea (2016).

  5. S. Y. Je, Y.-S. Chang and S.-S. Kang, Dynamic characteristics assessment of reactor vessel internals with fluid-structure interaction, Nucl. Eng. Technol., 49 (2017) 1513–1523.

    Article  Google Scholar 

  6. Y. Zhong, X. Yang, D. Ding, Y. Zou and D. K. L. Tsang, Dynamic characteristics identification of two graphite bricks in molten salt reactor considering fluid-structure interaction, Nucl. Eng. Des., 335 (2018) 409–416.

    Article  Google Scholar 

  7. W. Li, D. Lu and Y. Liu, Numerical investigation on the fluid added mass of spent fuel storage rack, Nucl. Eng. Des., 339 (2018) 83–91.

    Article  Google Scholar 

  8. T. Yin, D. Lu, Y. Huang and Y. Liu, Study on added mass model for fluid-structure interaction of spent fuel storage rack, Nucl. Eng. Des., 353 (2019) 110224.

    Article  Google Scholar 

  9. S. S. Chen, M. W. Wambsganss and J. A. Jendrzejczyk, Added mass and damping of a vibrating rod in confined viscous fluids, J. Appl. Mech., 43 (1976) 325–329.

    Article  Google Scholar 

  10. H. Chung and S. S. Chen, Vibration of a group of circular cylinders in a confined fluid, ANL-CT-76-25, Argonne National Laboratory, USA (1976).

    Book  Google Scholar 

  11. S. S. Chen, J. A. Jendrzejczyk and M. W. Wambsganss, Experiments on fluidelastic vibrations of tube arrays, ANL-CT-77-16, Argonne National Laboratory, USA (1977).

    Google Scholar 

  12. S. Levy and J. P. D. Wilkinson, Calculation of added water mass effects for reactor system components, Trans. 3rd Int. Conf. on SMiRT, London, UK (1975).

  13. R. W. Wu, L. K. Liu and S. Levy, Dynamic analysis of multi-body system immersed in a fluid medium, Trans. 4th Int. Conf. on SMiRT, San Francisco, USA (1977).

  14. C. I. Yang and T. J. Moran, Finite-element solution of added mass and damping of oscillation rods in viscous fluids, J. Appl. Mech., 46 (1979) 519–523.

    Article  Google Scholar 

  15. C. I. Yang and T. J. Moran, Calculations of added mass and damping coefficients for hexagonal cylinders in a confined viscous fluid, J. Press. Vessel Technol.-Trans. ASME, 102 (1980) 152–157.

    Article  Google Scholar 

  16. G. H. Koo and J. H. Lee, Development of FAMD code to calculate the fluid added mass and damping of arbitrary structures submerged in confined viscous fluid, KSME Int. J., 17(3) (2003) 457–466.

    Article  Google Scholar 

  17. K. H. Jeong and M. J. Jhung, Added mass estimation of square sections coupled with a liquid using finite element method, Nucl. Eng. Technol., 49 (2017) 234–244.

    Article  Google Scholar 

  18. ANSYS, ANSYS Mechanical APDL Release 15.0, ANSYS, Inc. (2013).

Download references

Acknowledgments

This work was supported by the Nuclear Research & Development Program of the National Research Foundation with a grant funded by the Korea Ministry of Science and ICT.

Author information

Authors and Affiliations

  1. Korea Atomic Energy Research Institute, Daedeok-daero 989-111, Yuseong-gu, Daejeon, 34057, Korea

    Jin Haeng Lee, Jae-Hun Cho & Sung-Kyun Kim

Authors
  1. Jin Haeng Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jae-Hun Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sung-Kyun Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jin Haeng Lee.

Additional information

Jin Haeng Lee received his Ph.D. in Mechanical Engineering, Sogang University, Seoul, Korea. He is currently a Principal Researcher at Korea Atomic Energy Research Institute, Daejeon, Korea. His research interests include mechanical design of reactor and computational solid mechanics.

Jae-Hun Cho received his Master’s degrees in Mechanical Engineering from the Chungnam National University. He is participating in Versatile System Technology Development Div. at Korea Atomic Energy Research Institute. His research interests are mechanical structure design and finite element method.

Sung-Kyun Kim received his Ph.D. in Mechanical Engineering, Chungnam National University, Daejeon, Korea. He is currently in charge of a mechanical design of sodium fast reactor at Korea Atomic Energy Research Institute, Daejeon, Korea. His research interests include dynamics and structural vibrations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, J.H., Cho, JH. & Kim, SK. Calculation of coupled added mass of multibody system immersed in fluids. J Mech Sci Technol 35, 3781–3792 (2021). https://doi.org/10.1007/s12206-021-2101-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-021-2101-z

Keywords

Search

Navigation