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Nonlinear coupling of interfacial instabilities with resonant wave interactions in horizontal two-fluid plane Couette–Poiseuille flows: numerical and physical observations

Published online by Cambridge University Press:  14 November 2016

Bryce K. Campbell ,
Kelli Hendrickson  and
Yuming Liu
Bryce K. Campbell
Affiliation:
Department of Mechanical Engineering, Center for Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Kelli Hendrickson
Affiliation:
Department of Mechanical Engineering, Center for Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Yuming Liu*
Affiliation:
Department of Mechanical Engineering, Center for Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

We investigate mechanisms governing the initial growth and nonlinear evolution of interfacial waves in horizontal two-fluid plane Couette–Poiseuille flows. Nonlinear coupling of the Kelvin–Helmholtz interfacial instability with resonant wave interactions has been shown to be capable of rapidly generating long waves through the transfer of energy from linearly unstable short waves to stable long-wave components within the context of potential flow theory. The objective of this work is to determine whether that coupled mechanism persists in laminar and turbulent viscous flows. Utilizing both theoretical and computational methods, we analyse the initial Orr–Sommerfeld instability to quantify the frequencies and growth/decay rates of each wave mode for two-fluid laminar and turbulent channel flows. The obtained dispersion relation allows for the identification of resonant and/or near-resonant triads among (unstable and damped) wave components in an interfacial wave spectrum. We perform direct numerical simulations (DNS) of the two-phase Navier–Stokes equations with a fully nonlinear interface to formally establish the validity of our theoretical predictions for viscous flows. DNS results show the existence of a nonlinear energy cascade from unstable short- to damped long-wavelength waves due to resonant subharmonic and/or triadic interactions in both laminar Couette and turbulent Poiseuille flows. Spectral analysis of the interfacial evolution confirms that the combined instability–resonance mechanism persists in the presence of viscosity despite being derived under the assumption of potential flow theory. Finally, we perform a detailed examination of experimentally measured wave power spectra from Jurman et al. (J. Fluid Mech., vol. 238, 1992, pp. 187–219) and carry out a numerical sensitivity study of the flow conditions to demonstrate and verify the existence of the coupled instability–resonance mechanism in physical systems. Our analysis accurately predicts the initial instability and the resulting nonlinear energy cascade through subharmonic and triadic interfacial wave resonances.

JFM classification

Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 809 , 25 December 2016 , pp. 438 - 479
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Copyright
© 2016 Cambridge University Press 

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References

Andritsos, N., Williams, L. & Hanratty, T. J. 1989 Effect of liquid viscosity on the stratified-slug transition in horizontal pipe flow. Intl J. Multiphase Flow 15 (6), 877–892.Google Scholar
Boomkamp, P. A. M. & Miesen, R. H. M. 1996 Classification of instabilities in parallel two-phase flow. Intl J. Multiphase Flow 22, 67–88.Google Scholar
Bruno, K. & McCready, M. J. 1988 Origin of roll waves in horizontal gas–liquid flows. AIChE J. 34 (9), 1431–1440.Google Scholar
Campbell, B. K.2009 Nonlinear effects on interfacial wave growth into slug flow. Master’s thesis, Massachusetts Institute of Technology.Google Scholar
Campbell, B. K.2015 A mechanistic investigation of nonlinear interfacial instabilities leading to slug formation in multiphase flows. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Campbell, B. K. & Liu, Y. 2013 Nonlinear resonant interactions of interfacial waves in horizontal stratified channel flows. J. Fluid Mech. 717, 612–642.Google Scholar
Campbell, B. K. & Liu, Y. 2014 Sub-harmonic resonant interactions in the presence of a linear interfacial instability. Phys. Fluids 26, 082107.Google Scholar
Coward, A. V., Renardy, Y. Y., Renardy, M. & Richards, J. R. 1997 Temporal evolution of periodic disturbances in two-layer Couette flow. J. Comput. Phys. 132 (2), 346–361.Google Scholar
Falgout, R. D., Jones, J. E. & Yang, U. M. 2006 The design and implementation of hypre, a library of parallel high performance preconditioners. Numerical Solution of Partial Differential Equations on Parallel Computers. Springer.Google Scholar
Falgout, R. D. & Yang, U. M. 2002 Hypre: a library of high performance preconditioners. Computational Science ICCS 2002. Springer.Google Scholar
Fan, Z., Lusseyran, F. & Hanratty, T. J. 1993 Initiation of slugs in horizontal gas–liquid flows. AIChE J. 39 (11), 1741–1753.Google Scholar
Fulgosi, M., Lakehal, D., Banerjee, S. & Angelis, V. D. 2003 Direct numerical simulation of turbulence in a sheared air–water flow with a deformable interface. J. Fluid Mech. 482, 319–345.Google Scholar
Hunt, J. C. R., Stretch, D. D. & Belcher, S. E. 2011 Viscous coupling of shear-free turbulence across nearly flat fluid interfaces. J. Fluid Mech. 671, 96–120.Google Scholar
Hurlburt, E. T. & Hanratty, T. J. 2002 Prediction of the transition from stratified to slug and plug flow for long pipes. Intl J. Multiphase Flow 28 (5), 707–729.CrossRefGoogle Scholar
Jurman, L. A., Deutsch, S. E. & McCready, M. J. 1992 Interfacial mode interactions in horizontal gas–liquid flows. J. Fluid Mech. 238, 187–219.Google Scholar
Jurman, L. A. & McCready, M. J. 1989 Study of waves on thin liquid films sheared by turbulent gas flows. Phys. Fluids 1, 522–536.Google Scholar
King, M. & McCready, M. J. 2000 Weakly nonlinear simulation of planar stratified flows. Phys. Fluids 12 (1), 92–102.CrossRefGoogle Scholar
Lin, M.-Y., Moeng, C.-H., Tsai, W.-T., Sullivan, P. P. & Belcher, S. E. 2008 Direct numerical simulation of wind-wave generation processes. J. Fluid Mech. 616, 1–30.Google Scholar
Liu, S., Kermani, A., Shen, L. & Yue, D. K. P. 2009 Investigation of coupled air–water turbulent boundary layers using direct numerical simulations. Phys. Fluids 21, 062108.Google Scholar
Lombardi, P., Angellis, V. D. & Banerjee, S. 1996 Direct numerical simulation of near-interface turbulence in coupled gas–liquid flow. Phys. Fluids 8, 1643–1665.CrossRefGoogle Scholar
Moler, C. B. & Stewart, G. W. 1972 An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 19 (1), 241–256.Google Scholar
Naraigh, L. O., Spelt, P. D. M., Matar, O. K. & Zaki, T. A. 2011 Interfacial instability in turbulent flow over a liquid film in a channel. Intl J. Multiphase Flow 37 (7), 812–830.CrossRefGoogle Scholar
Pan, Y. & Yue, D. K. P. 2014 Direct numerical investigation of turbulence of capillary waves. Phys. Rev. Lett. 113, 094501.Google Scholar
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude 1. The elementary interactions. J. Fluid Mech. 9 (2), 193–217.Google Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 5838–5866.CrossRefGoogle Scholar
Tryggvason, G., Scardovelli, R. & Zaleski, S. 2011 Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press.Google Scholar
Ujang, P. M., Lawrence, C. J., Hale, C. P. & Hewitt, G. F. 2006 Slug initiation and evolution in two-phase horizontal flow. Intl J. Multiphase Flow 32 (5), 527–552.Google Scholar
Valluri, P., Spelt, P. D. M., Lawrence, C. J. & Hewitt, G. F. 2008 Numerical simulation of the onset of slug initiation in laminar horizontal channel flow. Intl J. Multiphase Flow 34 (2), 206–225.Google Scholar
Weymouth, G. D. & Yue, D. K. P. 2010 Conservative volume-of-fluid method for free-surface simulations on cartesian-grids. J. Comput. Phys. 229 (8), 2853–2865.Google Scholar
Woods, B. D., Fan, Z. & Hanratty, T. J. 2006 Frequency and development of slugs in a horizontal pipe at large liquid flows. Intl J. Multiphase Flow 32, 902–925.Google Scholar
Woods, B. D. & Hanratty, T. J. 1999 Influence of Froude number on physical processes determining frequency of slugging in horizontal gas–liquid flows. Intl J. Multiphase Flow 25, 1195–1223.Google Scholar
Yih, C. S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337–352.Google Scholar
Zonta, F., Soldati, A. & Onorato, M. 2015 Growth and spectra of gravity-capillary waves in countercurrent air/water turbulent flow. J. Fluid Mech. 777, 245–259.Google Scholar