Simulation of Surface Instability at the Interface of Two Fluids

Year 2017, , 365 - 377, 30.06.2017

Nurdan Yıldırım , *, Jean-marie Buchlin Carlo Benocci

https://doi.org/10.18466/cbayarfbe.319878

Abstract

In this theoretical and numerical study, the physical
mechanisms leading to the production of surface waves generated at the
interface of two fluids (liquid/gas or liquid/liquid) are investigated.
Particular attention is devoted to the Kelvin-Helmholtz (KH) type instability,
which appears in the area of high shear located at the fluid-fluid interface.
The subsequent disturbances in velocity and pressure associated with the wave
motion are assumed to be 2D and sufficiently small to justify the linearization
of the equations of the motion. The Navier-Stokes (NS), Orr-Sommerfeld (OS) and
KH equations are the primary ones used to investigate of surface instability. During
the study, the main characteristics of a surface instability such as
wavelength, wave number, frequency, amplitude, wave speed and growth rate are
investigated according to fluid viscosity. The effect of gravity is
investigated by 2D simulations without these external forces or with them in
one of the following configurations:

Keywords

Surface wave, surface instability, viscosity, gravity, two-layer fluid flow

References

• [1] Ozgen, S. Two-Layer Flow Instability in Newtoni-an and non-Newtonian Fluids, Universite Libre de Bruxelles and Von Karman Institute, Ph.D. Thesis, 1999.
• [2] Rossi, V. Numerical Modelling of Gas-Jet Wiping, Von Karman Institute, Project Report 17, 2004.
• [3] Philips, O.M. On the generation of waves by tur-bulent wind. J. Fluid Mech. 1957; 2, 417.
• [4] Benjamin, T.B. Shearing Flow Over a Wavy Boundary. J. Fluid Mech. 1959; 6, 161.
• [5] Miles, J.W. On the generation of surface waves by shear flows. J. Fluid Mech. 1957; 3, 185.
• [6] Miles, J.W. On the generation of surface waves by shear flows. Part 4. J. Fluid Mech. 1962; 13, 433.
• [7] Valenzuela, G.R. The Growth of Gravity-Capillary Waves in a Coupled Shear Flow. J. Fluid Mech. 1976; 76, 229-250.
• [8] Kawai, S. Generation of Initial Wavelets by Insta-bility of a Coupled Shear Flow and Their Evolu-tion to Wind Waves. J. Fluid Mech. 1979; 93, 661-703.
• [9] Wheless, G.H.; Csanady, G.T. Instability Waves on the Air-Sea Interface. J. Fluid Mech.. 1993; 248, 363-381. [10] Lock, R. C. Hydrodynamic stability of the flow in the laminar boundary layer between parallel streams. Proc, Cambridge Philos. Soc. 1954; 50, 105-124.
• [11] Tsai, W.T.; Lin, M.Y. Stability Analysis on the Ini-tial Surface-Wave Generation Within an Air-Sea Coupled Shear Flow. Journal of Marine Science and Technology. 2004; 12-3, 200-208.
• [12] Cao, Q.; Sarkar, K.; Prasad, A.K. Direct numerical simulations of two-layer viscosity-stratified flow. International Journal of Multiphase Flow. 2004; 30, 1485–1508.
• [13] Dong L.; Johnson, D. Experimental and theoretical study of the interfacial instability between two shear fluids in a channel Couette flow. Interna-tional Journal of Heat and Fluid Flow. 2005; 26, 133–140.
• [14] Awasthi, M.K.; Asthana, R.; Agrawal, G.S. Viscous correction for the viscous potential flow analysis of Kelvin–Helmholtz instability of cylindrical flow with heat and mass transfer. International Journal of Heat and Mass Transfer. 2014; 78, 251-259.
• [15] Fernandino, M.; Ytrehus, T. Determination of flow sub-regimes in stratified air–water channel flow using LDV spectra. International Journal of Multi-phase Flow. 2006; 32, 436–446.
• [16] Fielding, S.M.; Wilson, H.J. Shear banding and in-terfacial instability in planar Poiseuille flow. J. Non-Newtonian Fluid Mech. 2010; 165, 196-202.
• [17] Cheung L.C.; Zaki, T.A. A nonlinear PSE method for two-fluid shear flows with complex interfacial topology. Journal of Computational Physics. 2011; 230, 6756–6777.
• [18] Tzotzi C.; Andritsos N. Interfacial shear stress in wavy stratified gas–liquid flow in horizontal pipes. International Journal of Multiphase Flow. 2013; 54, 43–54.
• [19] Apsley, D. D. Instability and Transition, Universi-ty of Manchester, School of Mechanical, Aerospace and Civil Engineering http://personalpages.manchester.ac.uk/staff/david.d.apsley/lectures/turbbl/stability.pdf (access in August, 2014)
• [20] Van den Borre, G. Wind Induced Instabilities on a Thin Layer of Aaircraft de or Anti-Icing Fluid. Von Karman Institute, Project Report 32, 1999.
• [21] Fluent 6.1 Documentation, http://jullio.pe.kr/fluent6.1/help/ (access in August, 2014)
• [22] Anthoine, J. Advanced Data Processing. Von Kar-man Institute. Course notes 2005.
• [23] Alexakis, A.; Young, Y.; Rosner, R. Shear Instabil-ity of Fluid Interfaces: Stability Analysis, Physical Review E. 2002; 65, 026313.
• [24] Techet, A. Free-Surface Waves, Massachusetts Insti-tute of Technology, Ocean Engineering, Depart-ment of Mechanical Engineering, http://web.mit.edu/13.012/www/handouts/Free-Surface%20Waves_note.pdf (access in August, 2014)
• [25] Yildirim, N. Simulation of Surface Instability of a Liquid Pool Subjected to a Shear Flow. Von Kar-man Institute, Project Report, 2005.