Skip to main content
SpringerLink
Log in

Steady and unsteady motion of one-component two-phase bubbly flow in 1-D Geometry

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

The aim of this work is to present a mathematical model of the motion of a one-component two-phase bubbly flow in one-dimensional geometry. Bubbles are assumed to be spherical and far enough from each other in order to exclude reciprocal interactions. The mathematical model is derived by means of a phase average operation and assuming a suitable description of the velocity field in the liquid phase, in the neighbourhood of the bubbles. Two different sets of experimental conditions are then simulated: a steady motion in a convergent–divergent nozzle and two different unsteady flows: i.e. two water hammer transients. Both the experimental conditions considered are well reproduced, indicating the validity of the proposed model.

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

References

  1. Mariano PM (2004). Some thermodynamical aspects of the solidification of two-phase flows. Meccanica 39: 369–382

    Article  MATH  MathSciNet  Google Scholar 

  2. Huo Y and Mueller I (2003). ‘Nucleation of droplets in a binary mixture. Meccanica 38: 493–504

    Article  MATH  MathSciNet  Google Scholar 

  3. Saurel R and Le Metayer O (2001). A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation. J Fluid Mech 431: 239–273

    Article  MATH  ADS  Google Scholar 

  4. Kiselev SP, Vorozhtsov EV and Fomin VM (1999). Foundation of fluid mechanics with applications. Birkhäuser, Boston

    Google Scholar 

  5. Lee WH and Lyczkowski RW (2000). The basic character of five two-phase flow model equation sets. Int J Numer Methods in Fluids 33: 1075–1098

    Article  MATH  ADS  Google Scholar 

  6. Lyczkowski RW, Gidaspow D, Solbrig CW and Hughes ED (1978). Characteristics and stability analysis of transients one-dimensional two-phase flow equations and their finite differences appoximations. Nucl Sci Eng 66: 378–396

    Google Scholar 

  7. Drew DA (1983). Mathematical modeling of two-phase flow. Ann Rev Fluid Mech 15: 261–291

    Article  MATH  ADS  Google Scholar 

  8. Yoshizawa A (2003). Statistical theory of compressible turbulence based-weighted averaging, with an emphasis on a cause of countergradient diffusion. Phys Fluids 15(3): 585–596

    Article  ADS  Google Scholar 

  9. Saltz D, Lee W and Hsiang TR (2000). Two-phase flow analysis of unstable fluid mixing in one dimensional geometry. Phys Fluids 12(10): 2461–2478

    Article  ADS  Google Scholar 

  10. Biesheuvel A and Wijngaarden L (1984). Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. J Fluid Mech 148: 301–318

    Article  MATH  ADS  Google Scholar 

  11. Preston A, Colonius T and Brennen CE (2002). A numerical investigation of unsteady bubbly cavitating nozzle flows. Phys fluids 14(1): 300–311

    Article  ADS  Google Scholar 

  12. Wang YC and Chen E (2002). ‘Effects of phase relative motion on critical bubbly flows through a converging-diverging nozzle. Phys fluids 14(9): 3215–3223

    Article  ADS  Google Scholar 

  13. Espinosa-Paredes G, Cazarez-Candia O and Vazquez A (2004). Theoretical derivation of the interaction effects with expansion effects to bubbly two-phase flows. Ann Nucl Energy 31: 117–133

    Article  Google Scholar 

  14. Espinosa-Paredes G, Nunez-Carrera A and Martinez-Mendez EJ (2005). Interaction forces model on a bubble growing for nuclear best estimate computer codes. Ann Nucl Energy 32: 1546–1566

    Google Scholar 

  15. Alimonti C, Boccardi G, Celata GP (2003) Water two-phase flow through a convergent-divergent nozzle with variable backpressure: check of calculation cethod to estimate mass flow rate and critical flow conditions. Proceeding of seventh international conference of multiphase flow in industrial plants, pp 1–10

  16. Fletcher B (1984). Flashing flow through orifices and pipes. CEP 3: 76–81

    Google Scholar 

  17. Henry RE and Fauske HK (1971). ‘The two phase critical flow of one component mixtures in nozzles, orifices and short tubes’. J Heat Trans 5: 179–187

    Google Scholar 

  18. Muir JF, Eichhorn R (1963) Compressible flow of an air–water mixture through a vertical two-dimensional converging-diverging nozzle. In: Proceedings of the 1963 Heat Transfer and Fluid Mechanics Institute, Stanford University Press, Stanford, CA, pp 183–204

  19. Pezzinga G (1999) ‘Dissipazioni nei transitori di colpo d’ariete in presenza e in assenza di cavitazione’. Atti del XIV Congresso Nazionale AIMETA, Como

  20. Cannizzaro D, Pezzinga G (2001) Dissipazioni termodinamiche nei transitori con cavitazione. Atti del XV Congresso Nazionale AIMETA, Taormina

  21. Wylie EB, Streeter VL (1993) Hydraulic Transients. Prentice Hall, Englewood Cliffs, NJ

  22. Marchi E, Rubatta A (1980) Idraulica-Meccanica dei fluidi: principile applicazioni idrauliche. UTET, Bologna

  23. Fujii T and Akagawa K (2000). ‘A study of water-hammer phenomena in one component, two-phase, bubbly flow. JSME Internat J B-43(3): 386–392

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering Sciences, University RomaTRE, Via Vito Volterra 62, 00146, Rome, Italy

    Michele La Rocca & Paolo Mele

  2. Institute of Thermal-Fluid Dynamics, ENEA, “Casaccia” Research Center, Via Anguillarese 301, Rome, Italy

    Gino Boccardi

Authors
  1. Michele La Rocca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paolo Mele
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gino Boccardi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michele La Rocca.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rocca, M.L., Mele, P. & Boccardi, G. Steady and unsteady motion of one-component two-phase bubbly flow in 1-D Geometry. Meccanica 41, 483–499 (2006). https://doi.org/10.1007/s11012-006-0005-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-006-0005-8

Keywords

Search

Navigation