6 results
Gas-sheared falling liquid films beyond the absolute instability limit
- Misa Ishimura, Sophie Mergui, Christian Ruyer-Quil, Georg F. Dietze
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- Journal:
- Journal of Fluid Mechanics / Volume 971 / 25 September 2023
- Published online by Cambridge University Press:
- 25 September 2023, A37
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We study the effect of a confined turbulent counter-current gas flow on the waviness of a weakly inclined falling liquid film. Our study is centred on experiments in a channel of 13 mm height, using water and air, where we have successively increased the counter-current gas flow rate until flooding. Computations with a new low-dimensional model and linear stability calculations are used to elucidate the linear and nonlinear wave dynamics. We find that the gas pressure gradient plays an important role in countering the stabilizing effect of the tangential gas shear stress at the liquid–gas interface. At very low inclination angles, the latter effect dominates and can suppress the long-wave Kapitza instability unconditionally. By contrast, for non-negligible inclination, the gas effect is linearly destabilizing, amplifies the height of nonlinear Kapitza waves, and exacerbates coalescence-induced formation of large-amplitude tsunami waves. Kapitza waves do not undergo any catastrophic transformation when the counter-current gas flow rate is increased beyond the absolute instability (AI) limit. On the contrary, we find that AI is an effective linear wave selection mechanism in a noise-driven wave evolution scenario, leading to highly regular downward-travelling nonlinear wave trains, which preclude coalescence events. In our experiments, where Kapitza waves develop in a protected region before coming into contact with the gas, flooding is eventually caused far beyond the AI limit by upward-travelling short-wave ripples. Based on our linear stability calculations for arbitrary wavenumbers, we have uncovered a new short-wave interfacial instability mode with negative linear wave speed, causing these ripples.
Modelling falling film flow: an adjustable formulation
- Sanghasri Mukhopadhyay, Christian Ruyer-Quil, R. Usha
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- Journal:
- Journal of Fluid Mechanics / Volume 952 / 10 December 2022
- Published online by Cambridge University Press:
- 29 November 2022, R3
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A new two-equation model for gravity-driven liquid film flow based on the long-wave expansion has been derived. The novelty of the model consists in using a base velocity profile combining parabolic (Ruyer-Quil & Manneville, Eur. Phys. J. B, vol. 15, issue 2, 2000, pp. 357–369) and ellipse (Usha et al., Phys. Fluids, vol. 32, issue 1, 2020, 013603) profile functions in the wall-normal coordinate. The dependence on a free parameter $A$ related to the eccentricity of an ellipse serves as an adjustable parameter. The resulting models are consistent at $O(\varepsilon )$ for inertia terms and at $O(\varepsilon ^2)$ for viscous diffusion effects, and predict accurately the primary instability. Appropriate tuning of the adjustable parameter helps to recover accurate predictions for the asymptotic wave celerity of nonlinear solitary waves. Further, the model is shown to capture the closed separation vortices that can form underneath the troughs of precursory capillary ripples.
Falling film on an anisotropic porous medium
- Sanghasri Mukhopadhyay, Nicolas Cellier, Usha R, Marx Chhay, Christian Ruyer-Quil
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- Journal:
- Journal of Fluid Mechanics / Volume 947 / 25 September 2022
- Published online by Cambridge University Press:
- 25 August 2022, A26
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The stability and dynamics of a falling liquid film over an anisotropic porous medium are studied using a one-domain approach. Our stability analysis shows a significant departure from the effective no-slip boundary condition in the isotropic case. Anisotropy does not affect the threshold of linear instability. However, a non-trivial dual effect of anisotropy on the film stability is observed depending on the permeability of the porous medium. This dual effect results from the net balance of the enhancement of viscous diffusion at the top Brinkman sublayer and the mitigation of viscous damping in the core Darcy sublayer. Three-equation models have been derived from the lubrication theory approximation in terms of the exact mass balance and averaged momentum balances in the porous and liquid layers. In the nonlinear regime, anisotropy has a dual effect by damping capillary waves at large permeabilities and enhancing them at low permeabilities. Anisotropy also affects wave speeds and shapes, modifies travelling-wave branches of solutions, affects the development of a time-periodic wavetrain by inlet forcing and alters the noise-driven dynamics of the flow. These effects result from the mitigation of mass exchange at the liquid–porous interface and the contribution of the cross-stream permeability in the Brinkman top sublayer to the viscous diffusion.
Films in narrow tubes
- Georg F. Dietze, Christian Ruyer-Quil
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- Journal:
- Journal of Fluid Mechanics / Volume 762 / 10 January 2015
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- 27 November 2014, pp. 68-109
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We consider the axisymmetric arrangement of an annular liquid film, coating the inner surface of a narrow cylindrical tube, in interaction with an active core fluid. We introduce a low-dimensional model based on the two-phase weighted residual integral boundary layer (WRIBL) formalism (Dietze & Ruyer-Quil, J. Fluid Mech., vol. 722, 2013, pp. 348–393) which is able to capture the long-wave instabilities characterizing such flows. Our model improves upon existing works by fully representing interfacial coupling and accounting for inertia as well as streamwise viscous diffusion in both phases. We apply this model to gravity-free liquid-film/core-fluid arrangements in narrow capillaries with specific attention to the dynamics leading to flooding, i.e. when the liquid film drains into large-amplitude collars that occlude the tube cross-section. We do this against the background of linear stability calculations and nonlinear two-phase direct numerical simulations (DNS). Due to the improvements of our model, we have found a number of novel/salient physical features of these flows. First, we show that it is essential to account for inertia and full interphase coupling to capture the temporal evolution of flooding for fluid combinations that are not dominated by viscosity, e.g. water/air and water/silicone oil. Second, we elucidate a viscous-blocking mechanism which drastically delays flooding in thin films that are too thick to form unduloids. This mechanism involves buckling of the residual film between two liquid collars, generating two very pronounced film troughs where viscous dissipation is drastically increased and growth effectively arrested. Only at very long times does breaking of symmetry in this region (due to small perturbations) initiate a sliding motion of the liquid film similar to observations by Lister et al. (J. Fluid Mech., vol. 552, 2006, pp. 311–343) in thin non-flooding films. This kickstarts the growth of liquid collars anew and ultimately leads to flooding. We show that streamwise viscous diffusion is essential to this mechanism. Low-frequency core-flow oscillations, such as occur in human pulmonary capillaries, are found to set off this sliding-induced flooding mechanism much earlier.
Wavy liquid films in interaction with a confined laminar gas flow
- Georg F. Dietze, Christian Ruyer-Quil
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- Journal:
- Journal of Fluid Mechanics / Volume 722 / 10 May 2013
- Published online by Cambridge University Press:
- 28 March 2013, pp. 348-393
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A low-dimensional model capturing the fully coupled dynamics of a wavy liquid film in interaction with a strongly confined laminar gas flow is introduced. It is based on the weighted residual integral boundary layer approach of Ruyer-Quil & Manneville (Eur. Phys. J. B, vol. 15, 2000, pp. 357–369) and accounts for viscous diffusion up to second order in the film parameter. The model is applied to study two scenarios: a horizontal pressure-driven water film/air flow and a gravity-driven liquid film interacting with a co- or counter-current air flow. In the horizontal case, interfacial viscous drag is weak and interfacial waves are primarily driven by pressure variations induced by the velocity difference between the two layers. This produces an extremely thin interfacial shear layer which is pinched at the main and capillary wave humps, creating several elongated vortices in the wave-fixed reference frame. In the capillary wave region preceding a large wave hump, flow separation occurs in the liquid in the form of a vortex transcending the liquid–gas interface. For the gravity-driven film, a twin vortex (in the wave-fixed reference frame) linked to the occurrence of rolling waves has been identified. It consists of the known liquid-side vortex within the wave hump and a previously unknown counter-rotating gas-side vortex, which are connected by the same interfacial stagnation points. At large counter-current gas velocities, interfacial waves on the falling liquid film are amplified and cause flooding of the channel in a noise-driven scenario, while this can be delayed by forcing regular waves at the most amplified linear wave frequency. Our model is shown to exactly capture the long-wave linear stability threshold for the general case of two-phase channel flow. Further, for the two considered scenarios, it predicts growth rates and celerity of linear waves in convincing agreement with Orr–Sommerfeld calculations. Finally, model calculations of nonlinear interfacial waves are in good agreement with film thickness and velocity measurements as well as streamline patterns in both phases obtained from direct numerical simulations.
Wave patterns in film flows: modelling and three-dimensional waves
- BENOIT SCHEID, CHRISTIAN RUYER-QUIL, PAUL MANNEVILLE
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- Journal:
- Journal of Fluid Mechanics / Volume 562 / 10 September 2006
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- 14 August 2006, pp. 183-222
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In a previous work, two-dimensional film flows were modelled using a weighted-residual approach that led to a four-equation model consistent at order $\epsilon^2$. A two-equation model resulted from a subsequent simplification but at the cost of lowering the degree of the approximation to order $\epsilon$ only. A Padé approximant technique is applied here to derive a refined two-equation model consistent at order $\epsilon^2$. This model, formulated in terms of coupled evolution equations for the film thickness $h$ and the flow rate $q$, accounts for inertia effects due to the deviations of the velocity profile from the parabolic shape, and closely follows the asymptotic long-wave expansion in the appropriate limit. Comparisons of two-dimensional wave properties with experiments and direct numerical simulations show good agreement for the range of parameters in which a two-dimensional wavy motion is reported in experiments.
The stability of two-dimensional travelling waves to three-dimensional pertur-bations is investigated based on the extension of the models to include spanwise dependence. The secondary instability is found to be not very selective, which explains the widespread presence of the synchronous instability observed in the experiments by Liu et al.(1995) whereas Floquet analysis predicts a subharmonic scenario in most cases. Three-dimensional wave patterns are computed next assuming periodic boundary conditions. Transition from two- to three-dimensional flows is shown to be strongly dependent on initial conditions. The herringbone patterns, the synchronously deformed fronts and the three-dimensional solitary waves observed in experiments are recovered using our regularized model, which is found to be an excellent compromise between the complete model, which has seven equations, and the simplified model, which does not include the second-order inertia corrections. Those corrections are found to play a role in the selection of the type of secondary instability as well as of the spanwise wavelength of the emerging pattern.