Skip to main content
SpringerLink
Log in

Effect of obstacle position on attached cavitation control through response surface methodology

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

Abstract

The span-wise obstacle on the suction surface of a hydrofoil has been verified to be an effective passive control method for cloud cavitation. The position of obstacle significantly influences the performance of cavitation control. In this research, we investigated the effect of obstacle position on attached cavitation control on the suction surface of a NACA0015 hydrofoil through response surface methodology. The cavitation types covered from sheet cavitation to partial and transitional cavity oscillations. We derived regression equations and built response surfaces to illustrate the quantitative relationship between individual factors (obstacle position, cavitation number, and angle of attack) and cavitation dynamic response parameters (cavity length, acoustic intensity, and energy flux). Sheet cavitation was effectively suppressed because the obstacle increased the pressure at the near-wall region. However, the obstacle would induce a shear cavitation when its position was too close to the leading edge of the hydrofoil. Under partial cavity oscillation conditions, the obstacle was consistently performed well in cloud cavitation control. The cavitation dynamic response parameters significantly decreased. Under transitional cavity oscillation conditions, the obstacle cannot suppress the cavitation because the transitional cavity oscillation was likely a system-inherent instability. This research is beneficial for a comprehensive understanding of cavitation control mechanism using an obstacle and for further industrial application of obstacle in hydraulic machinery to control cavitation.

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

v R :

Velocity of re-entrant jet, m/s

δ R :

Thickness of re-entrant jet, m/s

Re:

Reynolds number

v ∞ :

Flow velocity in the working section, m/s

μ :

Dynamic viscosity of water, Pa · s

P ∞ :

Pressure at the inlet of the working chamber, Pa

P s :

Saturation pressure of water for the given temperature, Pa

\(c_{O_2}\) :

The amount of oxygen dissolved in water, mg/l

c :

Chord length of hydrofoil, mm

S :

Span length of hydrofoil, mm

±α :

Highest or lowest level of factor (see Tables 1 and 2)

k :

Number of factors (see Tables 1 and 2)

σ :

Cavitation number

α :

Angle of attack, °

l bar :

Obstacle position, mm

x 1 :

Coded value of cavitation number

x 2 :

Coded value of angle of attack

x 3 :

Coded value of obstacle position

l c :

Cavity length, mm

I :

Acoustic intensity, dB

E :

Energy flux, J/m2

PRESS:

Predicted residual sum of squares

ANOVA:

Analysis of variance

Δp i :

Amplitude of each time pressure fluctuation, Pa

Δt i :

Duration of each time pressure fluctuation, s

P m :

Peaks of surface pressure curve, m = 1, 2, 3,...

T n :

Troughs of surface pressure curve, n = 1, 2, 3,...

ρ :

Density of water, kg/m3

c s :

Sound velocity in the water, m/s

y 1 :

Response value of cavity length, mm

y 2 :

Response value of acoustic intensity, dB

y 3 :

Response value of energy flux, J/m2

LE:

Leading edge of hydrofoil

TE:

Trailing edge of hydrofoil

C p :

Pressure coefficient

f :

Frequency of surface pressure fluctuation, Hz

RSM:

Response surface methodology

DoE:

Design of experiment

Exp1:

Experiment one

Exp2:

Experiment two

References

  1. J.-P. Franc and J.-M. Michel, Attached cavitation and the boundary layer: Experimental investigation and numerical treatment, J. Fluid Meek., 154 (1985) 63–90.

    Article  Google Scholar 

  2. J.-P. Franc and J.-M. Michel, Fundamentals of Cavitation, Springer Netherlands, Netherlands (2006).

    MATH  Google Scholar 

  3. K. A. Mørch, Cavity cluster dynamics and cavitation erosion, Cavitation and Polyphase Flow Forum (1981) 1–10.

    Google Scholar 

  4. A. Kubota, H. Kato, H. Yamaguchi and M. Maeda, Unsteady structure measurement of cloud cavitation on a foil section using conditional sampling technique, ASME J. Fluids Eng., 111 (2) (1989) 204–210.

    Article  Google Scholar 

  5. Y. Kawanami, H. Kato and H. Yamaguchi, Three-dimensional characteristics of the cavities formed on a two-dimensional hydrofoil, Proc. of the Third International Symposium on Cavitation, Laboratoire des Ecoulements Géophysiques et Industriels (1998) 191–196.

    Google Scholar 

  6. Y. Kawanami, H. Kato, H. Yamaguchi, M. Maeda and S. Nakasumi, Inner structure of cloud cavity on a foil section, JSME Int. J., Ser. B, 45 (3) (2002) 655–661.

    Article  Google Scholar 

  7. W. Haipeng, F. Song, W. Qin, H. Biao and W. Guoyu, Experimental and numerical research on cavitating flows around axisymmetric bodies, J. Mech. Sci. Technol., 28 (11) (2014) 4527–4537.

    Article  Google Scholar 

  8. G. Chen, G. Wang, B. Huang, C. Hu and T. Liu, Numerical study on the influence of interphase interaction in sheet/cloud cavitating flows around a 2D hydrofoil, J. Mech. Sci. Technol., 29 (3) (2015) 1075–1083.

    Article  Google Scholar 

  9. B. Ji, X. Luo, Y. Wu and K. Miyagawa, Numerical investigation of three-dimensional cavitation evolution and excited pressure fluctuations around a twisted hydrofoil, J. Mech. Sci. Technol., 28 (7) (2014) 2659–2668.

    Article  Google Scholar 

  10. R. Huang, X. Luo and B. Ji, Numerical simulation of the transient cavitating turbulent flowsaround the Clark-Y hydrofoil using modified partially averaged Navier-Stokesmethod, J. Mech. Sci. Technol., 31 (6) (2017) 2849–2859.

    Article  Google Scholar 

  11. Y. Kawanami, H. Kato, H. Yamaguchi, M. Tanimura and Y. Tagaya, Mechanism and control of cloud cavitation, ASME J. Fluids Eng., 119 (4) (1997) 788–794.

    Article  Google Scholar 

  12. N. Shimiya, A. Fujii, H. Horiguchi, M. Uchiumi, J. Kurokawa and Y. Tsujimoto, Suppression of cavitation instabilities in an inducer by j groove, ASME J. Fluids Eng, 130 (2) (2008) 021302.

    Article  Google Scholar 

  13. A. Danlos, J.-E. Méhal, F. Ravelet, O. Coutier-Delgosha and F. Bakir, Study of the cavitating instability on a grooved Venturi profile, ASME J. Fluids Eng, 136 (10) (2014) 101302.

    Article  Google Scholar 

  14. O. Coutier-Delgosha, J.-F. Devillers, M. Leriche and T. Pichon, Effect of wall roughness on the dynamics of unsteady cavitation, ASME J. Fluids Eng, 127 (4) (2005) 726–733.

    Article  Google Scholar 

  15. W. Shi, M. Atlar, R. Rosli, B. Aktas and R. Norman, Cavitation observations and noise measurements of horizontal axis tidal turbines with biomimetic blade leading-edge designs, Ocean Eng., 121 (2016) 143–155.

    Article  Google Scholar 

  16. R. E. Arndt, C. Ellis and S. Paul, Preliminary investigation of the use of air injection to mitigate cavitation erosion, ASME J. Fluids Eng, 117 (3) (1995) 498–504.

    Article  Google Scholar 

  17. H. Kato, H. Yamaguchi, S. Okada, K. Kikuchi and M. Miyanaga, Suppression of sheet cavitation inception by water discharge through slit, ASME J. Fluids Eng., 109 (1) (1987) 70–74.

    Article  Google Scholar 

  18. D. Chatterjee, Use of ultrasonics in shear layer cavitation control, Ultrasonics, 41 (6) (2003) 465–475.

    Article  Google Scholar 

  19. J. Huang, C. Yu, Y. Wang, C. Xu and C. Huang, Passive control of cavitating flow around an axisymmetric projectile by using a trip bar, Theor. App. Mech. Lett., 7 (4) (2017) 181–184.

    Article  Google Scholar 

  20. T. Capurso, G. Menchise, G. Caramia, S. Camporeale, B. Fortunate and M. Torresi, Investigation of a passive control system for limiting cavitation inside turbomachinery under different operating conditions, Energy Procedia, 148 (2018) 416–423.

    Article  Google Scholar 

  21. B. Che, N. Chu, S. Schmidt, L. Cao, D. Likhachev and D. Wu, Control effect of micro vortex generators on leading edge of attached cavitation, Phys. Fluids, 31 (4) (2019) 044102.

    Article  Google Scholar 

  22. R. E. Arndt, C. Song, M. Kjeldsen, J. He and A. Keller, Instability of partial cavitation: a numerical/experimental approach, Twenty-Third Symposium on Naval Hydrodynamics, National Academies Press (2000).

    Google Scholar 

  23. S. Watanabe, Y. Tsujimoto and A. Furukawa, Theoretical analysis of transitional and partial cavity instabilities, ASME J. Fluids Eng., 123 (3) (2001) 692–697.

    Article  Google Scholar 

  24. B. Che, L. Cao, N. Chu, D. Likhachev and D. Wu, Dynamic behaviors of re-entrant jet and cavity shedding during transitional cavity oscillation on NACA0015 hydrofoil, ASME J. Fluids Eng., 141 (6) (2019) 061101.

    Article  Google Scholar 

  25. Q. Le, J. P. Franc and J. M. Michel, Partial cavities: Global behavior and mean pressure distribution, ASME J. Fluids Eng., 115 (1993) 243–243.

    Article  Google Scholar 

  26. T. Pham, F. Larrarte and D. Fruman, Investigation of unsteady sheet cavitation and cloud cavitation mechanisms, ASME J. Fluids Eng., 121 (2) (1999) 289–296.

    Article  Google Scholar 

  27. M. Callenaere, J.-P. Franc, J.-M. Michel and M. Riondet, The cavitation instability induced by the development of a re-entrant jet, J. Fluid Mech., 444 (2001) 223–256.

    Article  MATH  Google Scholar 

  28. J.-B. Leroux, J. A. Astolfi and J. Y. Billard, An experimental study of unsteady partial cavitation, ASME J. Fluids Eng., 126 (1) (2004) 94–101.

    Article  Google Scholar 

  29. O. Coutier-Delgosha, B. Stutz, A. Vabre and S. Legoupil, Analysis of cavitating flow structure by experimental and numerical investigations, J. Fluid Mech., 578 (2007) 171–222.

    Article  MATH  Google Scholar 

  30. P. Pelz, T. Keil and T. Groß, The transition from sheet to cloud cavitation, J. Fluid Mech., 817 (2017) 439–454.

    Article  MathSciNet  MATH  Google Scholar 

  31. Y. Tsujimoto, S. Watanabe and H. Horiguchi, Cavitation instabilities of hydrofoils and cascades, Int. J. Fluid Mach. Syst., 1(1) (2008) 38–46.

    Article  Google Scholar 

  32. K. Sato, M. Tanada, S. Monden and Y. Tsujimoto, Observations of oscillating cavitation on a flat plate hydrofoil, JSME Int J., Ser. B, 45 (3) (2002) 646–654.

    Article  Google Scholar 

  33. W.-g. Zhao, L.-x. Zhang, X.-m. Shao and J. Deng, Numerical study on the control mechanism of cloud cavitation by obstacles, J. Hydrodyn., Ser. B, 22 (5) (2010) 792–797.

    Google Scholar 

  34. B. Stutz, Influence of roughness on the two-phase flow structure of sheet cavitation, ASME J. Fluids Eng., 125 (4) (2003) 652–659.

    Article  Google Scholar 

  35. L. Zhang, M. Chen and X. Shao, Inhibition of cloud cavitation on a flat hydrofoil through the placement of an obstacle, Ocean Eng., 155 (2018) 1–9.

    Article  Google Scholar 

  36. H. Ganesh, S. A. Mäkiharju and S. L. Ceccio, Interaction of a compressible bubbly flow with an obstacle placed within a shedding partial cavity, Journal of Physics: Conference Series, IOP Publishing (2015) 012151.

    Google Scholar 

  37. H. Ganesh, Bubbly shock propagation as a cause of sheet to cloud transition of partial cavitation and stationary cavitation bubbles forming on a delta wing vortex, Ph.D. Dissertation, Michigan University, Ann Arbor, Michigan (2015).

    Google Scholar 

  38. R. E. Arndt, Cavitation in fluid machinery and hydraulic structures, Annu. Rev. Fluid Mech., 13 (1) (1981) 273–326.

    Article  Google Scholar 

  39. P. Kumar and R. Saini, Study of cavitation in hydro turbines—A review, Renew. Sustain. Energy Rev., 14 (1) (2010) 374–383.

    Article  MathSciNet  Google Scholar 

  40. X.-w. Luo, J. Bin and Y. Tsujimoto, A review of cavitation in hydraulic machinery, J. Hydrodyn., Ser. B, 28 (3) (2016) 335–358.

    Article  Google Scholar 

  41. M. Kjeldsen, R. E. Arndt and M. Effertz, Spectral characteristics of sheet/cloud cavitation, ASME J. Fluids Eng., 122 (3) (2000) 481–487.

    Article  Google Scholar 

  42. D. T. Kawakami, A. Fuji, Y. Tsujimoto and R. Arndt, An assessment of the influence of environmental factors on cavitation instabilities, ASME J. Fluids Eng., 130 (3) (2008) 031303.

    Article  Google Scholar 

  43. G. E. Box and K. B. Wilson, On the Experimental Attainment of Optimum Conditions, Breakthroughs in Statistics, Springer, New York (1992) 270–310.

    Book  Google Scholar 

  44. R. H. Myers, D. C. Montgomery and C. M. Anderson-Cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 4th edition, John Wiley & Sons, USA (2016).

    MATH  Google Scholar 

  45. M. A. Bezerra, R. E. Santelli, E. P. Oliveira, L. S. Villar and L. A. Escaleira, Response surface methodology (RSM) as a tool for optimization in analytical chemistry, Talanta, 76 (5) (2008) 965–977.

    Article  Google Scholar 

  46. S. Yi, Y. Su, B. Qi, Z. Su and Y. Wan, Application of response surface methodology and central composite rotatable design in optimizing the preparation conditions of vinyltriethoxysilane modified silicalite/polydimethylsiloxane hybrid pervaporation membranes, Sep. Purif. Technol., 71 (2) (2010) 252–262.

    Article  Google Scholar 

  47. L. V. Candioti, M. M. De Zan, M. S. Cámara and H. C. Goicoechea, Experimental design and multiple response optimization. Using the desirability function in analytical methods development, Talanta, 124 (2014) 123–138.

    Article  Google Scholar 

  48. T. Okada, Y. Iwai, S. Hattori and N. Tanimura, Relation between impact load and the damage produced by cavitation bubble collapse, Wear, 184 (2) (1995) 231–239.

    Article  Google Scholar 

  49. S. Hattori, H. Mori and T. Okada, Quantitative evaluation of cavitation erosion, ASME J. Fluids Eng., 120 (1) (1998) 179–185.

    Article  Google Scholar 

  50. S. Hattori, T. Hirose and K. Sugiyama, Prediction method for cavitation erosion based on measurement of bubble collapse impact loads, Wear, 269 (7) (2010) 507–514.

    Article  Google Scholar 

Download references

Acknowledgments

This research is supported by the KSB Foundation Project No. 1326 and Fundamental Research Funds for the Central Universities (2017QN81001). The authors greatly appreciate the efforts of Dr. Ning Qiu for the experiments and the support of the School of Aeronautics and Astronautics, Zhejiang University.

Author information

Authors and Affiliations

  1. Institute of Process Equipment, Zhejiang University, Hangzhou, 310027, China

    Bangxiang Che, Ning Chu, Dmitriy Likhachev & Dazhuan Wu

  2. Institute of Advanced Technology, Zhejiang University, Hangzhou, 310027, China

    Linlin Cao

Authors
  1. Bangxiang Che
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Linlin Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ning Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dmitriy Likhachev
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Dazhuan Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Linlin Cao.

Additional information

Recommended by Associate Editor Sangyoup Lee

Bangxiang Che is currently a Ph.D. candidate in the Institute of Process Equipment, College of Energy Engineering, Zhejiang University (China). His research interests include mechanism and passive control of attached cavitation on hydrofoil.

Linlin Cao is currently a lecturer in the Institute of Advanced Technology, Zhejiang University (China). She received her Ph.D. in mechanical engineering from Kyushu University (Japan) in 2014. Her research interests include cavitation, vibration and noise in hydraulic machinery.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Che, B., Cao, L., Chu, N. et al. Effect of obstacle position on attached cavitation control through response surface methodology. J Mech Sci Technol 33, 4265–4279 (2019). https://doi.org/10.1007/s12206-019-0823-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-019-0823-y

Keywords

Search

Navigation