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On flowing soap films as experimental models of 2D Navier–Stokes flows

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Abstract

We show the validity of using a flowing soap film system as a two-dimensional laboratory model of flow past a circular cylinder at low Reynolds numbers through a novel combination of qualitative wake visualizations and quantitative velocity measurements and through a new quantitative method for determining the relative film thickness. We verify the correlation between interference fringe patterns and underlying flow structures by simultaneously obtaining digital particle image velocimetry (DPIV) data and interferograms. We introduce a quantitative soap film thickness measurement method using background-oriented schlieren (BOS) to provide a spatially resolved (relative) thickness field. Vortex cores in the cylinder wake appear as low thickness zones, and the minimum thickness regions identified with BOS are shown to coincide with the vortex centers identified in phase-matched interferograms. The vortex positions and circulations in the soap film correlate well with those reported in the literature for the case of low-Reynolds-number flow past a circular cylinder.

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Notes

  1. A number of other definitions of vortex formation length have been introduced; see, e.g., Yang, Masroor & Stremler (in preparation).

References

  • Abiven C, Vlachos PP (2020) Super spatio-temporal resolution, digital PIV system for multi-phase flows with phase differentiation and simultaneous shape and size quantification, In: 2002 Proceedings of the ASME IMECE

  • Abiven C, Vlachos PP, Papadopoulos G (2002) DPIV strategies for resolving high shear and vortical flows, In: 2002 proceedings of the ASME IMECE

  • Acharya T, Ray AK (2005) Image processing: principles and applications. Wiley, USA

    Google Scholar 

  • Adrian RJ (2005) Twenty years of particle image velocimetry. Exp Fluids 39(2):159–169

    Google Scholar 

  • Auliel MI, Hebrero CF, Sosa R, Artana G (2017) Schlieren technique in soap film flows. Exp Fluids 58(5):38. https://doi.org/10.1007/s00348-017-2311-4

    Article  Google Scholar 

  • Bandi MM, Concha A, Wood R, Mahadevan L (2013) A pendulum in a flowing soap film. Phys Fluids 25:41702

    Google Scholar 

  • Başca CA, Takş M, Brad R (2005) Randomized Hough transform for ellipse detection with result clustering, In: EUROCON 2005 - The International Conference on Computer as a Tool, 2: 1397–1400

  • Berger E (1964) The determination of hydrodynamic parameters of a Karman eddy street from hot-wire measurements at low Reynolds numbers. Zeitschrift Fiir Flugwissenschaften 12:41

    Google Scholar 

  • Bhattacharya S, Charonko JJ, Vlachos PP (2017) Stereo-particle image velocimetry uncertainty quantification. Meas Sci Technol 28(1):015301

    Google Scholar 

  • Bhattacharya S, Charonko JJ, Vlachos PP (2018) Particle image velocimetry (PIV) uncertainty quantification using moment of correlation (MC) plane. Meas Sci Technol 29(11):115301

    Google Scholar 

  • Brindise MC, Vlachos PP (2017) Proper orthogonal decomposition truncation method for data denoising and order reduction. Exp Fluids. https://doi.org/10.1007/s00348-017-2320-3

    Article  Google Scholar 

  • Chen YN (1972) Fluctuating lift forces of the Karman vortex streets on single circular cylinders and in tube bundles: part 1—the vertex street geometry of the single circular cylinder. J Manuf Sci Eng Trans ASME 94:603

    Google Scholar 

  • Chen Y, Fried E (2013) Stability and bifurcation of a soap film spanning an elastic loop. J Elast 116(1):75–100. https://doi.org/10.1007/s10659-013-9458-x

    Article  MATH  Google Scholar 

  • Chomaz JM (2001) The dynamics of a viscous soap film with soluble surfactant. J Fluid Mech 442:387

    MathSciNet  MATH  Google Scholar 

  • Chomaz JM, Cathalau B (1990) Soap films as two-dimensional classical fluids. Phys Rev A 41:2243

    Google Scholar 

  • Chomaz JM, Costa M (1998) Thin Film Dynamics. Free Surface Flows. Springer, Vienna, pp 45–99

    Google Scholar 

  • Chong MS, Perry AE, Cantwell BJ (1990) A general classification of three-dimensional flow fields. Phys Fluids A 2:765

    MathSciNet  Google Scholar 

  • Couder Y (1984) Two-dimensional grid turbulence in a thin liquid film. J Phys Lettres 45:353

    Google Scholar 

  • Couder Y, Basdevant C (1986) Experimental and numerical study of vortex couples in two-dimensional flows. J Fluid Mech 173:225

    Google Scholar 

  • Couder Y, Chomaz JM, Rabaud M (1989) On the hydrodynamics of soap films. Phys D Nonlinear Phenom 37:384

    Google Scholar 

  • Eckstein A, Vlachos PP (2009a) Digital particle image velocimetry (DPIV) robust phase correlation. Meas Sci Technol 20(5):55401

    Google Scholar 

  • Eckstein A, Vlachos PP (2009b) Assessment of advanced windowing techniques for digital particle image velocimetry (DPIV). Meas Sci Technol 20:75402

    Google Scholar 

  • Eckstein AC, Charonko J, Vlachos P (2008) Phase correlation processing for DPIV measurements. Exp Fluids 45(3):485–500

    Google Scholar 

  • Etebari A, Vlachos PP (2005) Improvements on the accuracy of derivative estimation from DPIV velocity measurements. Exp Fluids 39:1040

    Google Scholar 

  • Fujiwara H (2007) Spectroscopic ellipsometry: principles and applications. Wiley, USA

    Google Scholar 

  • Georgiev D, Vorobieff P (2002) The slowest soap-film tunnel in the Southwest. Rev Sci Instrum 73:1177

    Google Scholar 

  • Gharib M, Derango P (1989) A liquid film (soap film) tunnel to study two-dimensional laminar and turbulent shear flows. Phys D 37:406

    Google Scholar 

  • Green RB, Gerrard JH (1993) Vorticity measurements in the near wake of a circular cylinder at low Reynolds numbers. J Fluid Mech 246:675

    Google Scholar 

  • Griffin OM (1971) The unsteady wake of an oscillating cylinder at low reynolds number. J Appl Mech Trans ASME 38:729

    Google Scholar 

  • Griffin OM (1995) A note on bluff body vortex formation. J Fluid Mech 284:217

    Google Scholar 

  • Griffin OM, Ramberg SE (1974) The vortex-street wakes of vibrating cylinders. J Fluid Mech 66:553

    Google Scholar 

  • Griffin OM, Votaw CW (1972) The vortex street in the wake of a vibrating cylinder. J Fluid Mech 55:31

    Google Scholar 

  • Horváth VK, Cressman JR, Goldburg WI, Wu XL (2000) Hysteresis at low reynolds number: onset of two-dimensional vortex shedding. Phys Rev E 61:R4702

    Google Scholar 

  • Hum YC, Lai KW, Mohamad Salim MI (2014) Multiobjectives bihistogram equalization for image contrast enhancement. Complexity 20(2):22–36

    Google Scholar 

  • Hunt JCR (1987) Vorticity and vortex dynamics in complex turbulent flows. Trans Can Soc Mech Eng 11(1):21–35

    Google Scholar 

  • Illingworth J, Kittler J (1988) A Survey of the Hough Transform. Comput Vision, Graph Image Process 44(1):87–116

    Google Scholar 

  • Jaensson N, Vermant J (2018) Tensiometry and rheology of complex interfaces. Curr Opin Colloid Interf Sci 37:136–150

    Google Scholar 

  • Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69

    MathSciNet  MATH  Google Scholar 

  • Jia LB, Yin XZ (2008) Passive oscillations of two tandem flexible filaments in a flowing soap film. Phys Rev Lett 100(22):228104

    Google Scholar 

  • Jia L-B, Yin X-Z (2009) Response modes of a flexible filament in the wake of a cylinder in a flowing soap film. Phys Fluids 21(10):101704

    Google Scholar 

  • Jia L, Xiao Q, Wu H, Wu Y, Yin X (2015) Response of a flexible filament in a flowing soap film subject to a forced vibration. Phys Fluids 27:17101

    Google Scholar 

  • Kellay H (2017) Hydrodynamics experiments with soap films and soap bubbles: a short review of recent experiments. Phys Fluids 29(11):111113

    Google Scholar 

  • Kellay H, Wu XL, Goldburg WI (1995) Experiments with turbulent soap films. Phys Rev Lett 74:3975

    Google Scholar 

  • Kim I, Mandre S (2017) Marangoni Elasticity of Flowing Soap Films. Phys Rev Fluids 2(8):082001

    Google Scholar 

  • Kovasznay LSG (1949) Hot-Wire Investigation of the Wake behind cylinders at low Reynolds numbers. Proc r Soc London Ser a Math Phys Sci 198:174

    Google Scholar 

  • Leavers VF (1993) Which Hough transform? CVGIP Image Underst 58:250

    Google Scholar 

  • MaskellE C (1963) A Theory of the Blockage Effects on, Bluff Bodies and Stalled Wings in a Closed Wind Tunnel, Reports Memo. 1

  • Matsui T, Okude M (1980) Rearrangement of Kármán Vortex Street at Low Reynolds Numbers. XVth International Congress of Theoretical and Applied Mechanics. University of Toronto, Toronto, pp 1–27

    Google Scholar 

  • Mysels KJ, Frankel S, Shinoda K (1959) Soap films: studies of their thinning and a bibliography, Pergamon Press

  • Nishioka M, Sato H (1978) Mechanism of determination of the shedding frequency of vortices behind a cylinder at low Reynolds numbers. J Fluid Mech 89:49

    Google Scholar 

  • Raffel M (2015) Background-oriented schlieren (BOS) techniques. Exp Fluids 56:60

    Google Scholar 

  • Raffel M, Willert CE, Wereley ST, Kompenhans J, Willert S, Wereley ST, Kompenhans J (2007) Particle image velocimetry: a practical guide. Springer, Berlin, Heidelberg

    Google Scholar 

  • Rai-Choudhury P, Benton JL, Shroder DK, Shaffner TF (1997) Diagnostic techniques for semiconductor materials and devices, in diagnostic techniques for semiconductor materials and devices, Vol. 3322

  • Rajendran L, Zhang J, Bane S, Vlachos P (2020a) Uncertainty-based weighted least squares density integration for background-oriented schlieren. Exp Fluids 61:239

    Google Scholar 

  • Rajendran LK, Zhang J, Bhattacharya S, Bane SPM, Vlachos PP (2020b) Uncertainty quantification in density estimation from background-oriented schlieren measurements. Meas Sci Technol 31(5):054002

    Google Scholar 

  • Rivera M, Wu XL (2000) External dissipation in driven two-dimensional turbulence. Phys Rev Lett 85:976

    Google Scholar 

  • Rivera M, Vorobeiff P, Ecke R (1998) Turbulence in flowing soap films: velocity, vorticity, and thickness fields. Phys Rev Lett 81:1417

    Google Scholar 

  • Rosenhead L (1930) An Experimental Investigation of the Flow behind Circular Cylinders in Channels of Different Breadths. Proc R Soc Lond Series A, Contain Papers Math Phys Charact 129(809):115–135. https://doi.org/10.1098/rspa.1930.0146

    Article  MATH  Google Scholar 

  • Roushan P, Wu XL (2005) Structure-based interpretation of the Strouhal-Reynolds number relationship. Phys Rev Lett 94:54504

    Google Scholar 

  • Rutgers MA, Wu X, Bhagavatula R, Petersen AA, Goldburg WI (1996) Two-dimensional velocity profiles and laminar boundary layers in flowing soap films. Phys Fluids 8:2847

    Google Scholar 

  • Sallet DW (1969) On the spacing of Karman vortices. J Appl Mec 36(2):370–372. https://doi.org/10.1115/1.356465

    Article  Google Scholar 

  • Schaefer JW, Eskinazi S (1959) An analysis of the vortex street generated in a viscous fluid. J Fluid Mech 6:241

    MathSciNet  MATH  Google Scholar 

  • Schnipper T, Andersen A, Bohr T (2009) Vortex wakes of a flapping foil. J Fluid Mech 633:411

    MATH  Google Scholar 

  • Soloff SM, Adrian RJ, Liu Z-C (1997) Distortion compensation for generalized stereoscopic particle image velocimetry. Meas Sci Technol 8(12):1441–1454. https://doi.org/10.1088/0957-0233/8/12/008

    Article  Google Scholar 

  • Tchoukov P, Yang F, Xu Z, Dabros T, Czarnecki J, Sjöblom J (2014) Role of asphaltenes in stabilizing thin liquid emulsion films. Langmuir 30:3024

    Google Scholar 

  • Thom A (1933) The flow past circular cylinders at low speeds. Proc R Soc A Math Phys Eng Sci 141(845):651–669

    MATH  Google Scholar 

  • Timme A (1957) On the velocity distribution in eddies. Fundamentals 25:205

    MATH  Google Scholar 

  • Venkatakrishnan L, Meier GEA (2004) Density measurements using the background oriented schlieren technique. Exp Fluids 37:237

    Google Scholar 

  • Von Kármán T (1912) On the mechanism of resistance produced by moving body in liquid, Nachrichtungen Des Gesellschaft Wiss

  • Vorobieff P, Ecke RE (1999) Cylinder wakes in flowing soap films. Phys Rev E 60:2953

    Google Scholar 

  • Vorobieff P, Rivera M, Ecke RE (1999) Soap film flows: statistics of two-dimensional turbulence. Phys Fluids 11:2167

    MathSciNet  MATH  Google Scholar 

  • Vorobieff P, Rivera M, Ecke RE (2001) Imaging 2D Turbulence. J vis 3:323

    Google Scholar 

  • Walton ETS (1928) The formation of vortices behind a cylinder moving through a fluid. Sci Proc Royal Dublin Soc 18:521–534

    Google Scholar 

  • Wen C-Y, Lin C-Y (2001) Two-dimensional vortex shedding of a circular cylinder. Phys Fluids 13:557

    MATH  Google Scholar 

  • West GS, Apelt CJ (1982) The effects of tunnel blockage and aspect ratio on the mean flow past a circular cylinder with Reynolds numbers between 104 and 105. J Fluid Mech 114:361

    Google Scholar 

  • Westerweel J, Scarano F (2005) Universal outlier detection for PIV data. Exp Fluids 39:1096

    Google Scholar 

  • Wieneke B (2005) Stereo-PIV using self-calibration on particle images. Exp Fluids 39:267

    Google Scholar 

  • Williamson CHK, Brown GL (1998) A series in 1/√ Re to represent the Strouhal-Reynolds number relationship of the cylinder wake. J Fluids Struct 12:1073

    Google Scholar 

  • Wu XL, Levine R, Rutgers M, Kellay H, Goldburg WI (2001) Infrared technique for measuring thickness of a flowing soap film. Rev Sci Instrum 72:2467

    Google Scholar 

  • Wu MH, Wen CY, Yen RH, Weng MC, Wang AB (2004) Experimental and numerical study of the separation angle for flow around a circular cylinder at low reynolds number. J Fluid Mech 515:233

    MATH  Google Scholar 

  • Yang W, Stremler MA (2019) Critical spacing of stationary tandem circular cylinders at Re≈ 100. J Fluids Struct 89:49–60. https://doi.org/10.1016/j.jfluidstructs.2019.02.023

    Article  Google Scholar 

  • Yang TS, Wen CY, Lin CY (2001) Interpretation of color fringes in flowing soap films. Exp Therm Fluid Sci 25:141

    Google Scholar 

  • Yonghong X, Qiang J (2002) A new efficient ellipse detection method, proceedings - international conference on. Pattern Recogn 16:957–960

    Google Scholar 

  • Yuen HK, Princen J, Illingworth J, Kittler J (1990) Comparative study of Hough transform methods for circle finding. Image vis Comput 8:71

    Google Scholar 

  • Zdravkovich MM (1997) Flow around circular cylinders. Fundamentals 1:566

    MATH  Google Scholar 

  • Zhang J, Childress S, Libchaber A, Shelley M (2000) Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408:835

    Google Scholar 

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Acknowledgements

The authors thank Emad Masroor for his assistance in reviewing the historical works on the wake of cylinders.

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Authors and Affiliations

  1. Purdue University, West Lafayette, IN, 47907, USA

    Javad Eshraghi, Lalit K. Rajendran & Pavlos P. Vlachos

  2. Queen’s University, Kingston, ON, K7L 3N6, Canada

    Wenchao Yang

  3. Virginia Tech, Blacksburg, VA, 24061, USA

    Mark A. Stremler

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  1. Javad Eshraghi
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  2. Lalit K. Rajendran
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Contributions

Javad Eshraghi was involved in methodology, software, formal analysis, data curation, investigation, visualization, and writing—original draft. Lalit K. Rajendran was involved in methodology, software, investigation, and writing—original draft. Wenchao Yang was involved in methodology and writing—review and editing. Mark A. Stremler was involved in conceptualization, methodology, investigation, supervision, and writing—original draft, review, and editing. Pavlos P. Vlachos was involved in conceptualization, methodology, investigation, supervision, project administration, funding acquisition, and writing—original draft, review, and editing.

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Correspondence to Pavlos P. Vlachos.

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Eshraghi, J., Rajendran, L.K., Yang, W. et al. On flowing soap films as experimental models of 2D Navier–Stokes flows. Exp Fluids 62, 162 (2021). https://doi.org/10.1007/s00348-021-03238-z

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