Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T12:31:35.110Z Has data issue: false hasContentIssue false
  • English
  • Français

The influence of fluid–structure interaction on cloud cavitation about a stiff hydrofoil. Part 1.

Published online by Cambridge University Press:  26 May 2020

Samuel M. Smith Open the ORCID record for Samuel M. Smith [Opens in a new window] ,
James A. Venning Open the ORCID record for James A. Venning [Opens in a new window] ,
Bryce W. Pearce Open the ORCID record for Bryce W. Pearce [Opens in a new window] ,
Yin Lu Young Open the ORCID record for Yin Lu Young [Opens in a new window]  and
Paul A. Brandner Open the ORCID record for Paul A. Brandner [Opens in a new window]
Samuel M. Smith*
Affiliation:
Australian Maritime College, University of Tasmania, Launceston, TAS 7250, Australia
James A. Venning
Affiliation:
Australian Maritime College, University of Tasmania, Launceston, TAS 7250, Australia
Bryce W. Pearce
Affiliation:
Australian Maritime College, University of Tasmania, Launceston, TAS 7250, Australia
Yin Lu Young
Affiliation:
Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbour, MI 48109, USA
Paul A. Brandner
Affiliation:
Australian Maritime College, University of Tasmania, Launceston, TAS 7250, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The physics associated with various cavitation regimes about a hydrofoil is investigated in a variable-pressure water tunnel using high-speed photography and synchronised force measurements. Experiments were conducted on a relatively stiff stainless steel hydrofoil at a chord-based Reynolds number, $Re=0.8\times 10^{6}$ for cavitation numbers, $\unicode[STIX]{x1D70E}$, ranging from 0.2 to 1.2, with the hydrofoil experiencing sheet, cloud and supercavitation regimes. The NACA0009 model of tapered planform was vertically mounted in a cantilevered configuration to a six-component force balance at an incidence, $\unicode[STIX]{x1D6FC}$, of $6^{\circ }$ to the oncoming flow. Tip deformations and cavitation behaviour were recorded with synchronised force measurements utilising two high-speed cameras mounted underneath and to the side of the test section. Break-up and shedding of an attached cavity was found to be due to either interfacial instabilities, re-entrant jet formation, shockwave propagation or a complex coupled mechanism, depending on $\unicode[STIX]{x1D70E}$. Three primary shedding modes are identified. The Type IIa and IIb re-entrant jet-driven oscillations exhibit a non-linear dependence on $\unicode[STIX]{x1D70E}$, decreasing in frequency with decreasing $\unicode[STIX]{x1D70E}$ due to growth in the cavity length, and occur at higher $\unicode[STIX]{x1D70E}$ values (Type IIa: 0.4–1.0; Type IIb: 0.7–0.9). Shockwave-driven Type I shedding occurs for lower $\unicode[STIX]{x1D70E}$ values (0.3–0.6) with the oscillation frequency being practically independent of $\unicode[STIX]{x1D70E}$. The Type IIa oscillations locked in to the first sub-harmonic of the hydrofoil’s first bending mode in water which has been modulated due to the reduced added mass of the vapour cavity. Supplementary movies are available with the online version of the paper.

JFM classification

Drops and Bubbles: Cavitation Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , A1
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akcabay, D. T., Chae, E. J., Young, Y. L., Ducoin, A. & Astolfi, J. A. 2014 Cavity induced vibration of flexible hydrofoils. J. Fluids Struct. 49 (Suppl. C), 463–484.CrossRefGoogle Scholar
Akcabay, D. T. & Young, Y. L. 2014 Influence of cavitation on the hydroelastic stability of hydrofoils. J. Fluids Struct. 49, 170–185.CrossRefGoogle Scholar
Akcabay, D. T. & Young, Y. L. 2015 Parametric excitations and lock-in of flexible hydrofoils in two-phase flows. J. Fluids Struct. 57, 344–356.CrossRefGoogle Scholar
Arndt, R. E. A. & Keller, A. P. 2003 A case study of international cooperation: 30 years of collaboration in cavitation research. In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference, pp. 153–166. American Society of Mechanical Engineers.Google Scholar
Ausoni, P., Farhat, M., Avellan, F., Escaler, X. & Egusquiza, E. 2005 Cavitation effects on fluid structure interaction in the case of a 2D hydrofoil. In ASME 2005 Fluids Engineering Division Summer Meeting, pp. 617–622. American Society of Mechanical Engineers.Google Scholar
Ausoni, P., Farhat, M., Escaler, X., Egusquiza, E. & Avellan, F. 2007 Cavitation influence on von Karman vortex shedding and induced hydrofoil vibrations. Trans. ASME J. Fluids Engng 129 (8), 966–973.CrossRefGoogle Scholar
Avellan, F., Dupont, P. & Ryhming, I. L. 1988 Generation mechanism and dynamics of cavitation vortices downstream of a fixed leading edge cavity. In 17th Symposium on Naval Hydrodynamics, pp. 1–13. National Academy Press.Google Scholar
Bisplinghoff, R. L., Ashley, H. & Halfman, R. L. 1955 Aeroelasticity, Addison-Wesley Publishing Corporation.Google Scholar
Blevins, R. D. 1977 Flow-induced Vibration. Van Nostrand Reinhold Co.Google Scholar
Brandner, P. A. 2018 Microbubbles and cavitation: microscales to macroscales. In Keynote Lecture: Tenth International Symposium on Cavitation, pp. 710–715. AMSE Press.Google Scholar
Brandner, P. A., Lecoffre, Y. & Walker, G. J. 2007 Design considerations in the development of a modern cavitation tunnel. In 16th Australasian Fluid Mechanics Conference, pp. 630–637. School of Engineering, University of Queensland.Google Scholar
Brandner, P. A., Walker, G. J., Niekamp, P. N. & Anderson, B. 2010 An experimental investigation of cloud cavitation about a sphere. J. Fluid Mech. 656, 147–176.CrossRefGoogle Scholar
Brennen, C. E. 1969 The dynamic balances of dissolved air and heat in natural cavity flows. J. Fluid Mech. 37 (1), 115–127.CrossRefGoogle Scholar
Brennen, C. E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.Google Scholar
Brennen, C. E. 2005 Fundamentals of Multiphase Flow. Cambridge University Press.CrossRefGoogle Scholar
Brennen, C. E., Oey, K. T. & Babcock, C. D. 1980 Leading-edge flutter of supercavitating hydrofoils. J. Ship Res. 24 (3), 135–146.Google Scholar
Callenaere, M., Franc, J., Michel, J. & Riondet, M. 2001 The cavitation instability induced by the development of a re-entrant jet. J. Fluid Mech. 444, 223–256.CrossRefGoogle Scholar
Clarke, D. B., Butler, D., Crowley, B. & Brandner, P. A. 2014 High-speed full-field deflection measurements on a hydrofoil using digital image correlation. In 30th Symposium on Naval Hydrodynamics. Office of Naval Research.Google Scholar
Crespo, A. 1969 Sound and shockwaves in liquids containing bubbles. Phys. Fluids 12 (11), 2274–2282.CrossRefGoogle Scholar
De La Torre, O., Escaler, X., Egusquiza, E. & Farhat, M. 2013 Experimental investigation of added mass effects on a hydrofoil under cavitation conditions. J. Fluids Struct. 39, 173–187.CrossRefGoogle Scholar
Ducoin, A., Astolfi, J. A. & Sigrist, J. 2012 An experimental analysis of fluid structure interaction on a flexible hydrofoil in various flow regimes including cavitating flow. Eur. J. Mech. (B/Fluids) 36, 63–74.CrossRefGoogle Scholar
Foeth, E. J., Van Doorne, C. W. H., Van Terwisga, T. & Wieneke, B. 2006 Time resolved piv and flow visualization of 3D sheet cavitation. Exp. Fluids 40 (4), 503–513.CrossRefGoogle Scholar
Franc, J. 2001 Partial cavity instabilities and re-entrant jet. In Keynote Lecture: Fourth International Symposium on Cavitation. California Institute of Technology.Google Scholar
Franc, J. & Michel, J. 2004 Fundamentals of Cavitation. Kluwer Academic Publishers.Google Scholar
Furness, R. A. & Hutton, S. P. 1975 Experimental and theoretical studies of two-dimensional fixed-type cavities. Trans. ASME J. Fluids Engng 97 (4), 515–521.CrossRefGoogle Scholar
Ganesh, H., Mäkiharju, S. A. & Ceccio, S. L. 2016 Bubbly shock propagation as a mechanism for sheet-to-cloud transition of partial cavities. J. Fluid Mech. 802, 37–78.CrossRefGoogle Scholar
de Graaf, K. L., Brandner, P. A. & Pearce, B. W. 2017 Spectral content of cloud cavitation about a sphere. J. Fluid Mech. 812, R1.CrossRefGoogle Scholar
Harwood, C., Felli, M., Falchi, M., Garg, N., Ceccio, S. L. & Young, Y. L. 2019 The hydroelastic response of a surface-piercing hydrofoil in multi-phase flow. Part 1. Passive hydroelasticity. J. Fluid Mech. 881, 313–364.CrossRefGoogle Scholar
Harwood, C., Felli, M., Falchi, M., Garg, N., Ceccio, S. L. & Young, Y. L. 2020 The hydroelastic response of a surface-piercing hydrofoil in multiphase flows. Part 2. Modal parameters and generalized fluid forces. J. Fluid Mech. 884, A3.CrossRefGoogle Scholar
Ihara, A., Watanabe, H. & Shizukuishi, S. 1989 Experimental research of the effects of sweep on unsteady hydrofoil loadings in cavitation. Trans. ASME J. Fluids Engng 111 (3), 263–270.CrossRefGoogle Scholar
Jakobsen, J. K. 1964 On the mechanism of head breakdown in cavitating inducers. Trans. ASME J. Basic Engng 86 (2), 291–305.CrossRefGoogle Scholar
Kaplan, P. & Lehman, A. F. 1966 Experimental studies of hydroelastic instabilities of cavitating hydrofoils. J. Aircraft 3 (3), 262–269.CrossRefGoogle Scholar
Kato, K., Dan, H. & Matsudaira, Y. 2006 Lock-in phenomenon of pitching hydrofoil with cavitation breakdown. JSME Intl J. B 49 (3), 797–805.CrossRefGoogle Scholar
Kawakami, D. T., Fuji, A., Tsujimoto, Y. & Arndt, R. E. 2008 An assessment of the influence of environmental factors on cavitation instabilities. Trans. ASME J. Fluids Engng 130 (3), 031303.CrossRefGoogle Scholar
Kawanami, Y., Kato, H. & Yamaguchi, H. 1998 Three-dimensional characteristics of the cavities formed on a two-dimensional hydrofoil. In Third International Symposium on Cavitation, vol. 1, pp. 191–196. Laboratoire des Ecoulements Géophysiques et Industriels, Grenoble, France.Google Scholar
Kawanami, Y., Kato, H., Yamaguchi, H., Tanimura, M. & Tagaya, Y. 1997 Mechanism and control of cloud cavitation. Trans. ASME J. Fluids Engng 119 (4), 788–794.CrossRefGoogle Scholar
Kjeldsen, M. & Arndt, R. E. 2001 Joint time frequency analysis techniques: a study of transitional dynamics in sheet/cloud cavitation. In 4th International Symposium on Cavitation (CAV2001). California Institute of Technology.Google Scholar
Kjeldsen, M., Arndt, R. E. A. & Effertz, M. 2000 Spectral characteristics of sheet/cloud cavitation. Trans. ASME J. Fluids Engng 122 (3), 481–487.CrossRefGoogle Scholar
Knapp, R. T. 1955 Recent investigations of the mechanics of cavitation and cavitation damage. Trans. ASME 77, 1045–1054.Google Scholar
Kubota, A., Kato, H., Yamaguchi, H. & Maeda, M. 1989 Unsteady structure measurement of cloud cavitation on a foil section using conditional sampling technique. ASME J. Fluids Engng 111 (2), 204–210.CrossRefGoogle Scholar
Laberteaux, K. R. & Ceccio, S. L. 2001a Partial cavity flows. Part 1. Cavities forming on models without spanwise variation. J. Fluid Mech. 431, 1–41.CrossRefGoogle Scholar
Laberteaux, K. R. & Ceccio, S. L. 2001b Partial cavity flows. Part 2. Cavities forming on test objects with spanwise variation. J. Fluid Mech. 431, 43–63.CrossRefGoogle Scholar
de Lange, D. F. & de Bruin, G. J. 1998 Sheet cavitation and cloud cavitation, re-entrant jet and three-dimensionality. Appl. Sci. Res. 58 (1–4), 91–114.CrossRefGoogle Scholar
Le, Q., Franc, J. & Michel, J. 1993 Partial cavities: global behaviour and mean pressure distribution. Trans. ASME J. Fluids Engng 115, 243–243.CrossRefGoogle Scholar
Leroux, J., Astolfi, J. A. & Billard, J. Y. 2004 An experimental study of unsteady partial cavitation. ASME J. Fluids Engng 126 (1), 94–101.CrossRefGoogle Scholar
Noordzij, L. & Van Wijngaarden, L. 1974 Relaxation effects, caused by relative motion, on shockwaves in gas-bubble/liquid mixtures. J. Fluid Mech. 66 (1), 115–143.CrossRefGoogle Scholar
Pearce, B. W., Brandner, P. A., Garg, N., Young, Y. L., Phillips, A. W. & Clarke, D. B. 2017 The influence of bend-twist coupling on the dynamic response of cavitating composite hydrofoils. In 5th International Symposium on Marine Propulsors (SMP’17), pp. 803–813. VTT Technical Research Center of Finland Ltd.Google Scholar
Pelz, P. F., Keil, T. & Groß, T. F. 2017 The transition from sheet to cloud cavitation. J. Fluid Mech. 817, 439–454.CrossRefGoogle Scholar
Pham, T. M., Larrarte, F. & Fruman, D. H. 1999 Investigation of unsteady sheet cavitation and cloud cavitation mechanisms. ASME J. Fluids Engng 121 (2), 289–296.CrossRefGoogle Scholar
Prothin, S., Billard, J. & Djeridi, H. 2016 Image processing using proper orthogonal and dynamic mode decompositions for the study of cavitation developing on a NACA0015 foil. Exp. Fluids 57 (10), 157.CrossRefGoogle Scholar
Reisman, G. E., Wang, Y. C. & Brennen, C. E. 1998 Observations of shockwaves in cloud cavitation. J. Fluid Mech. 355, 255–283.CrossRefGoogle Scholar
Russell, P. S., Venning, J. A., Brandner, P. A., Pearce, B. W., Giosio, D. R. & Ceccio, S. L. 2018 Microbubble disperse flow about a lifting surface. In 32nd Symposium on Naval Hydrodynamics. US Office of Naval Research and Hamburg University of Technology.Google Scholar
Schmidt, O. T., Towne, A., Rigas, G., Colonius, T. & Bres, G. A. 2018 Spectral analysis of jet turbulence. J. Fluid Mech. 855, 953–982.CrossRefGoogle Scholar
Shamsborhan, H., Coutier-Delgosha, O., Caignaert, G. & Nour, F. A. 2010 Experimental determination of the speed of sound in cavitating flows. Exp. Fluids 49 (6), 1359–1373.CrossRefGoogle Scholar
Smith, S. M., Venning, J. A., Brandner, P. A., Pearce, B. W., Giosio, D. R. & Young, Y. L. 2018 The influence of fluid–structure interaction on cloud cavitation about a hydrofoil. In Proceedings of the 10th International Symposium on Cavitation (CAV2018). ASME Press.Google Scholar
Smith, S. M., Venning, J. A., Giosio, D. R., Brandner, P. A., Pearce, B. W. & Young, Y. L. 2017 Cloud cavitation behaviour on a hydrofoil due to fluid-structure interaction. In 17th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC 2017.Google Scholar
Smith, S. M., Venning, J. A., Giosio, D. R., Brandner, P. A., Pearce, B. W. & Young, Y. L. 2019 Cloud cavitation behavior on a hydrofoil due to fluid–structure interaction. Trans. ASME J. Fluids Engng 141 (4), 041105.CrossRefGoogle Scholar
Smith, S. M., Venning, J. A., Pearce, B. W., Young, Y.-L. & Brandner, P. A. 2020 The influence of fluid–structure interaction on cloud cavitation about a flexible hydrofoil. Part 2. J. Fluid Mech; doi:10.1017/jfm.2020.323.Google Scholar
Stutz, B. & Reboud, J. L. 1997 Experiments on unsteady cavitation. Exp. Fluids 22 (3), 191–198.CrossRefGoogle Scholar
Torrence, C. & Compo, G. P. 1998 A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79 (1), 61–78.2.0.CO;2>CrossRefGoogle Scholar
Towne, A., Schmidt, O. T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821–867.CrossRefGoogle Scholar
Venning, J. A., Giosio, D. R., Pearce, B. W. & Brandner, P. A. 2018a Global mode visualization in cavitating flows. In Proceedings of the 10th International Symposium on Cavitation (CAV2018). ASME Press.Google Scholar
Venning, J. A., Giosio, D. R., Smith, S. M. P., Bryce, W. & Brandner, P. A. 2018b The influence of nucleation on the spectral content of cloud cavitation about a hydrofoil. In Proceedings of the 10th International Symposium on Cavitation (CAV2018), ASME Press.Google Scholar
Venning, J. A., Khoo, M. T., Pearce, B. W. & Brandner, P. A. 2018c Background nuclei measurements and implications for cavitation inception in hydrodynamic test facilities. Exp. Fluids 59 (4), 71.CrossRefGoogle Scholar
Venning, J. A., Smith, S. M., Brandner, P. A., Giosio, D. R. & Pearce, B. W. 2017 The influence of nuclei content on cloud cavitation about a hydrofoil. In 17th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC 2017.Google Scholar
Welch, P. 1967 The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15 (2), 70–73.CrossRefGoogle Scholar
Wu, J., Ganesh, H. & Ceccio, S. 2019 Multimodal partial cavity shedding on a two-dimensional hydrofoil and its relation to the presence of bubbly shocks. Exp. Fluids 60 (4), 66.CrossRefGoogle Scholar
Young, Y. L., Garg, N., Brandner, P. A., Pearce, B. W., Butler, D., Clarke, D. & Phillips, A. W. 2018 Material bend-twist coupling effects on cavitating response of composite hydrofoils. In 10th International Cavitation Symposium (CAV2018). ASME Press.Google Scholar
Zarruk, G. A., Brandner, P. A., Pearce, B. W. & Phillips, A. W. 2014 Experimental study of the steady fluid-structure interaction of flexible hydrofoils. J. Fluids Struct. 51, 326–343.CrossRefGoogle Scholar
Supplementary material: File

Smith et al. supplementary movie 1

At σ = 1.2, the hydrofoil is seen to experience sheet cavitation where the attached cavity is confined to a small portion of the chord towards the leading edge with length of Lc/c ~ 0.2. The cavity is broken-up into small scale structures driven primarily by inter-facial instabilities such as Kelvin-Helmholtz driven spanwise vorticity lines and turbulent transition.

Download Smith et al. supplementary movie 1(File)
File 6.2 MB
Supplementary material: File

Smith et al. supplementary movie 2

As σ is reduced to 1.0, cloud cavitation is seen to occur with the conditions allowing a re-entrant jet to form and reach the upstream extent of the cavity, causing periodic detachment and the formation of a cavitation cloud. This is seen to be confined to around the mid-span with only the detachment of small bubbly vortices occurring towards the spanwise extents.

Download Smith et al. supplementary movie 2(File)
File 6.2 MB
Supplementary material: File

Smith et al. supplementary movie 3

Multiple stable shedding modes form along the span of the hydrofoil as σ reaches 0.8 with the Type IIa mode shedding at St = 0.408 in the upper portion of the span (0.0 < y/b < 0.4), while the Type IIb mode sheds at St = 0.500 in the lower portion (0.6 < y/b < 0.8).

Download Smith et al. supplementary movie 3(File)
File 10.1 MB
Supplementary material: File

Smith et al. supplementary movie 4

Further reduction in σ to 0.7 sees the hydrofoil enter lock-in where the Type IIa shedding frequency matches a sub-harmonic of the hydrofoil leading to amplified structural excitations. The Type IIa shedding is seen to occur across majority of the span with only small broken-up clouds shed towards the tip.

Download Smith et al. supplementary movie 4(File)
File 10.1 MB
Supplementary material: File

Smith et al. supplementary movie 5

As σ reaches 0.6, the attached cavity now extends to the trailing edge of the hydrofoil with both re-entrant jet and shockwave instabilities present in the flow. The re-entrant jet can be seen slowing down as it approaches the upstream extent of the cavity, stalling before causing detachment. This leads to perturbations to form over the cavity, resulting in small-scale break-up generating a bubbly flow of high void-fraction. This preconditions the flow to allow shockwave propagation that cause the shedding of the cloud cavitation where the re-entrant jet instability drives the frequency that the shedding occurs.

Download Smith et al. supplementary movie 5(File)
File 8.6 MB
Supplementary material: File

Smith et al. supplementary movie 6

With σ reducing to 0.4, the cavity extends beyond the hydrofoil trailing edge with a re-entrant jet still forming but lacking momentum to reach the upstream extent of the cavity. The shockwave instability is prevalent in this condition which is characterized by alternate shedding from the upper and middle portion of the span with this sequence featuring an irregular shedding event in the lower portion.

Download Smith et al. supplementary movie 6(File)
File 9 MB
Supplementary material: File

Smith et al. supplementary movie 7

At σ = 0.3, the shedding is solely driven by shockwave propagation where a re-entrant jet still forms but lacks sufficient time and momentum to reach the upstream extent of the cavity. This results in the shockwave driving the shedding frequency at a rate of St = 0.091 where a cycle consists of a large-scale cloud is shed from the upper portion of the span, followed by two smaller scale clouds in quick succession.

Download Smith et al. supplementary movie 7(File)
File 8.7 MB
Supplementary material: File

Smith et al. supplementary movie 8

As σ reaches 0.2, the cavity grows to a length of Lc/c ~ 1.5, thus forming a supercavity. Closing far downstream of the trailing-edge with no strong adverse pressure gradient present, the supercavity becomes more stable than partial cavities as no substantial shedding mechanisms can form.

Download Smith et al. supplementary movie 8(File)
File 4.9 MB