Abstract
In multiphase flows, form drag and viscous shear stress transfer momentum between phases. For numerous environmental and man-made flows, it is of primary importance to predict this transfer at a liquid–gas interface. In its general expression, interfacial shear stress involves local velocity gradients as well as surface velocity, curvature, and surface tension gradients. It is therefore a challenging quantity to measure experimentally or compute numerically. In fact, no experimental work to date has been able to directly resolve all the terms contributing to the shear stress in the case of curved and moving surfaces. In an attempt to fully resolve the interface shear stress when surface tension gradients are negligible, high-resolution particle image velocimetry (PIV) data are acquired simultaneously on both sides of a water–air interface. The flow consists of a well-conditioned uniform and homogeneous water jet discharging in quiescent air, which exhibits two-dimensional surface waves as a result of a shear layer instability below the surface. PIV provides velocity fields in both phases, while planar laser-induced fluorescence is used to track the interface and obtain its curvature. To compute the interfacial shear stress from the data, several processing schemes are proposed and compared, using liquid and/or gas phase data. Vorticity at the surface, which relates to the shear stress through the dynamic boundary condition at the surface, is also computed and provides additional strategies for estimating the shear. The various schemes are in agreement within the experimental uncertainties, validating the methodology for experimentally resolving this demanding quantity.
Similar content being viewed by others
References
Abrahamson S, Lonnes S (1995) Uncertainty in calculating vorticity from 2D velocity fields using circulation and least-squares approaches. Exp Fluids 20(1):10–20
Adrian R, Westerweel J (2011) Particle image velocimetry. Cambridge University Press, Cambridge
André MA, Bardet PM (2012) Experimental investigation of boundary layer instabilities on the free surface of non-turbulent jet. In: Proceedings of the ASME fluids engineering division summer meeting
André MA, Bardet PM (2014) Velocity field, surface profile and curvature resolution of steep and short free-surface waves. Exp Fluids 55(4):1–19
Banner ML, Peirson WL (1998) Tangential stress beneath wind-driven air–water interfaces. J Fluid Mech 364(115–145):21
Bardet P, André M, Neal D (2013) Systematic timing errors in laser-based transit-time velocimetry. In: 10th international symposium on particle image velocimetry (PIV 13), Delft, The Netherlands, July 1–3
Batchelor GK (1967) An introduction to fluid mechanics. Cambridge University Press, Cambridge
Belden J, Techet AH (2011) Simultaneous quantitative flow measurement using PIV on both sides of the air–water interface for breaking waves. Exp Fluids 50(1):149–161
Binks BP (2002) Particles as surfactants—similarities and differences. Curr Opin Colloid Interface Sci 7(1):21–41
Brennen C (1970) Cavity surface wave patterns and general appearance. J Fluid Mech 44:33–49
Danehy P, Tiemsin P, Wohl C, Verkamp M, Lowe T, Maisto P (2012) Fluorescence doped particles for simultaneous temperature and velocity imaging. Technical report TM-2012-217768, NASA
Davies JT, Rideal EK (1963) Interfacial phenomena. Academic Press, New York
Davis E (1969) Interfacial shear measurement for two-phase gas–liquid flow by means of preston tubes. Ind Eng Chem Fundam 8(1):153–159
Desjardins O, Moureau V (2010) Methods for multiphase flows with high density ratio. In: Proceedings of the summer, program
Dumouchel C (2008) On the experimental investigation on primary atomization of liquid streams. Exp Fluids 45(3):371–422
Etebari A, Vlachos PP (2005) Improvements on the accuracy of derivative estimation from DPIV velocity measurements. Exp Fluids 39(6):1040–1050
Fabre J, Masbernat L, Suzanne C (1987) Experimental data set no. 7: stratified flow, part I: local structure. Multiphase Sci Technol 3(1–4):285–301
Faeth G, Hsiang L, Wu P (1995) Structure and breakup properties of sprays. Int J Multiph Flow 21:99–127
Foucaut J, Stanislas M (2002) Some considerations on the accuracy and frequency response of some derivative filters applied to particle image velocimetry vector fields. Meas Sci Technol 13(7):1058
Garbe CS, Degreif K, Jähne B (2007) Estimating the viscous shear stress at the water surface from active thermography. In: Garbe CS, Handler RA, Jähne B (eds) Transport at the air–sea interface. Springer, Berlin, pp 223–239
Gorokhovski M, Herrmann M (2008) Modeling primary atomization. Annu Rev Fluid Mech 40:343–366
Gueyffier D, Li J, Nadim A, Scardovelli R, Zaleski S (1999) Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J Comput Phys 152(2):423–456
Hirsa A, Korenowski G, Logory L, Judd C (1997) Determination of surface viscosities by surfactant concentration and velocity field measurements for an insoluble monolayer. Langmuir 13(14):3813–3822
Hochareon P, Manning KB, Fontaine AA, Tarbell JM, Deutsch S (2004) Wall shear-rate estimation within the 50 cc penn state artificial heart using particle image velocimetry. J Biomech Eng 126(4):430–437
Ishii M, Hibiki T (2010) Thermo-fluid dynamics of two-phase flow. Springer, Berlin
Jähne B, Haußecker H (1998) Air–water gas exchange. Annu Rev Fluid Mech 30(1):443–468
Kawaji M (1998) Two-phase flow measurements using a photochromic dye activation technique. Nucl Eng Des 184(2):379–392
Komori S, Nagaosa R, Murakami Y (1993) Turbulence structure and mass transfer across a sheared air–water interface in wind-driven turbulence. J Fluid Mech 249:161–183
Kowalski J (1987) Wall and interfacial shear stress in stratified flow in a horizontal pipe. AIChE J 33(2):274–281
Lishchuk S, Halliday I (2009) Effective surface viscosities of a particle-laden fluid interface. Phys Rev E 80(1):1–7, Art. ID 016306
Longuet-Higgins M (1992) Capillary rollers and bores. J Fluid Mech 240:659–679
Lugt HJ (1987) Local flow properties at a viscous free surface. Phys Fluids 30(12):3647–3652
Lundgren T, Koumoutsakos P (1999) On the generation of vorticity at a free surface. J Fluid Mech 382(1):351–366
Okuda K, Kawai S, Toba Y (1977) Measurement of skin friction distribution along the surface of wind waves. J Oceanogr Soc Jpn 33(4):190–198
Otsu N (1975) A threshold selection method from gray-level histograms. Automatica 11(285–296):23–27
Peirson W (1997) Measurement of surface velocities and shears at a wavy air–water interface using particle image velocimetry. Exp Fluids 23:427–437
Peirson WL, Walker JW, Banner ML (2014) On the microphysical behaviour of wind-forced water surfaces and consequent re-aeration. J Fluid Mech 743:399–447
Raben JS, Hariharan P, Robinson R, Malinauskas R, Vlachos PP (2014) Time-resolved particle image velocimetry measurements with wall shear stress and uncertainty quantification for the FDA benchmark nozzle model. arXiv:1405:3125 (preprint)
Raffel M, Willert C, Kompenhans J (1998) Particle image velocimetry: a practical guide. Experimental fluid mechanics series. Springer, Berlin
Saffman P (1993) Vortex dynamics. Cambridge University Press, Cambridge
Scarano F, Riethmuller M (2000) Advances in iterative multigrid PIV image processing. Exp Fluids 29(1):S051–S060
Scardovelli R, Zaleski S (1999) Direct numerical simulation of free-surface and interfacial flow. Annu Rev Fluid Mech 31(1):567–603
Schlichting H, Gersten K (2000) Boundary-layer theory. Springer, Berlin
Slattery JC, Sagis L, Oh ES (2007) Interfacial transport phenomena. Springer, Berlin
Techet A, McDonald A (2005) High speed PIV of breaking waves on both sides of the air-water interface. In: 6th international symposium on particle image velocimetry, Pasadena, CA, USA, pp 1–14
Tiemsin P, Wohl C (2012) Refined synthesis and characterization of controlled diameter, narrow size distribution microparticles for aerospace research applications. Technical report TM-2012-217591, NASA
Veron F, Saxena G, Misra S (2007) Measurements of the viscous tangential stress in the airflow above wind waves. Geophys Res Lett 34(19):1–5
Ward A, Tordai L (1946) Time-dependence of boundary tensions of solutions i. the role of diffusion in time-effects. J Chem Phys 14(7):453–461
Whalley P (1996) Two-phase flow and heat transfer. Oxford University Press, Oxford
Yecko P, Zaleski S (2000) Two-phase shear instability: waves, fingers, and drops. Ann NY Acad Sci 898(1):127–143
Acknowledgments
This work was initiated using start-up funding from the George Washington University to Dr. Bardet and partially sponsored by US Office of Naval Research, under the leadership of Drs. Thomas C. Fu and Ki-Han Kim. The authors would also like to acknowledge Patsy I. Tiemsin and Dr. Christopher J. Wohl from NASA Langley Research Center for providing the un-doped and Kiton red-doped polystyrene microspheres.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
André, M.A., Bardet, P.M. Interfacial shear stress measurement using high spatial resolution multiphase PIV. Exp Fluids 56, 132 (2015). https://doi.org/10.1007/s00348-015-2006-7
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-015-2006-7