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25 pages, 1400 KiB

Open AccessArticle

Dynamics of Thin Film Under a Volatile Solvent Source Driven by a Constant Pressure Gradient Flow

by Mohammad Irshad Khodabocus, Mathieu Sellier and Volker Nock

Fluids 2019, 4(4), 198; https://doi.org/10.3390/fluids4040198 - 29 Nov 2019

Cited by 1 | Viewed by 2300

The evolution of a thin liquid film subject to a volatile solvent source and an air-blow effect which modifies locally the surface tension and leads to Marangoni-induced flow is shown to be governed by a degenerate fourth order nonlinear parabolic h-evolution equation [...] Read more.

The evolution of a thin liquid film subject to a volatile solvent source and an air-blow effect which modifies locally the surface tension and leads to Marangoni-induced flow is shown to be governed by a degenerate fourth order nonlinear parabolic h-evolution equation of the type given by

\partial_{t} h = - {div}_{x} (M_{1} (h) \partial_{x}^{3} h + M_{2} (h) \partial_{x} h + M_{3} (h))

, where the mobility terms

M_{1} (h)

and

M_{2} (h)

result from the presence of the source and

M_{3} (h)

results from the air-blow effect. Various authors assume

M_{2} (h) \approx 0

and exclude the air-blow effect into

M_{3} (h)

. In this paper, the authors show that such assumption is not necessarily correct, and the inclusion of such effect does disturb the dynamics of the thin film. These emphasize the importance of the full definition

\vec{t} \cdot grad (γ) = {grad}_{x} (γ) + \partial_{x} h {grad}_{y} (γ)

of the surface tension gradient at the free surface in contrast to the truncated expression

\vec{t} \cdot grad (γ) \approx {grad}_{x} (γ)

employed by those authors and the effect of the air-blow flowing over the surface. Full article

(This article belongs to the Special Issue Free surface flows)

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20 pages, 5229 KiB

Open AccessFeature PaperArticle

Progress in Phenomenological Modeling of Turbulence Damping around a Two-Phase Interface

by Wenyuan Fan and Henryk Anglart

Fluids 2019, 4(3), 136; https://doi.org/10.3390/fluids4030136 - 18 Jul 2019

Cited by 10 | Viewed by 3180

Abstract

The presence of a moving interface in two-phase flows challenges the accurate computational fluid dynamics (CFD) modeling, especially when the flow is turbulent. For such flows, single-phase-based turbulence models are usually used for the turbulence modeling together with certain modifications including the turbulence [...] Read more.

The presence of a moving interface in two-phase flows challenges the accurate computational fluid dynamics (CFD) modeling, especially when the flow is turbulent. For such flows, single-phase-based turbulence models are usually used for the turbulence modeling together with certain modifications including the turbulence damping around the interface. Due to the insufficient understanding of the damping mechanism, the phenomenological modeling approach is always used. Egorov’s model is the most widely-used turbulence damping model due to its simple formulation and implementation. However, the original Egorov model suffers from the mesh size dependency issue and uses a questionable symmetric treatment for both liquid and gas phases. By introducing more physics, this paper introduces a new length scale for Egorov’s model, making it independent of mesh sizes in the tangential direction of the interface. An asymmetric treatment is also developed, which leads to more physical predictions for both the turbulent kinetic energy and the velocity field. Full article

(This article belongs to the Special Issue Free surface flows)

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10 pages, 572 KiB

Open AccessArticle

Radial Imbibition in Paper under Temperature Differences

by Abel López-Villa, Abraham Medina, F. J. Higuera, Jonatan R. Mac Intyre, Carlos Alberto Perazzo and Juan Manuel Gomba

Fluids 2019, 4(2), 86; https://doi.org/10.3390/fluids4020086 - 11 May 2019

Cited by 2 | Viewed by 2860

Abstract

Spontaneous radial imbibition into thin circular samples of porous material when they have been subjected to radial temperature differences was analyzed theoretically and experimentally. The use of the Darcy equation allowed us to take into account temperature variations in the dynamic viscosity and [...] Read more.

Spontaneous radial imbibition into thin circular samples of porous material when they have been subjected to radial temperature differences was analyzed theoretically and experimentally. The use of the Darcy equation allowed us to take into account temperature variations in the dynamic viscosity and surface tension in order to find the one-dimensional equation for the imbibition fronts. Experiments using blotting paper showed a good fit between the experimental data and theoretical profiles through the estimation of a single parameter. Full article

(This article belongs to the Special Issue Free surface flows)

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Graphical abstract

25 pages, 660 KiB

Open AccessArticle

A Potential Field Description for Gravity-Driven Film Flow over Piece-Wise Planar Topography

by Markus Scholle, Philip H. Gaskell and Florian Marner

Fluids 2019, 4(2), 82; https://doi.org/10.3390/fluids4020082 - 02 May 2019

Cited by 4 | Viewed by 2972

Abstract

Models based on a potential field description and corresponding first integral formulation, embodying a reduction of the associated dynamic boundary condition at a free surface to one of a standard Dirichlet-Neumann type, are used to explore the problem of continuous gravity-driven film flow [...] Read more.

Models based on a potential field description and corresponding first integral formulation, embodying a reduction of the associated dynamic boundary condition at a free surface to one of a standard Dirichlet-Neumann type, are used to explore the problem of continuous gravity-driven film flow down an inclined piece-wise planar substrate in the absence of inertia. Numerical solutions of the first integral equations are compared with analytical ones from a linearised form of a reduced equation set resulting from application of the long-wave approximation. The results obtained are shown to: (i) be in very close agreement with existing, comparable experimental data and complementary numerical predictions for isolated step-like topography available in the open literature; (ii) exhibit the same qualitative behaviour for a range of Capillary numbers and step heights/depths, becoming quantitively similar when both are small. A novel outcome of the formulation adopted is identification of an analytic criteria enabling a simple classification procedure for specifying the characteristic nature of the free surface disturbance formed; leading subsequently to the generation of a related, practically relevant, characteristic parameter map in terms of the substrate inclination angle and the Capillary number of the associated flow. Full article

(This article belongs to the Special Issue Free surface flows)

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13 pages, 1742 KiB

Open AccessArticle

The Hydrodynamics of a Micro-Rocket Propelled by a Deformable Bubble

by Giacomo Gallino, Lailai Zhu and François Gallaire

Fluids 2019, 4(1), 48; https://doi.org/10.3390/fluids4010048 - 14 Mar 2019

Cited by 6 | Viewed by 3186

Abstract

We perform simulations to study the hydrodynamics of a conical-shaped swimming micro-robot that ejects catalytically produced bubbles from its inside. We underline the nontrivial dependency of the swimming velocity on the bubble deformability and on the geometry of the swimmer. We identify three [...] Read more.

We perform simulations to study the hydrodynamics of a conical-shaped swimming micro-robot that ejects catalytically produced bubbles from its inside. We underline the nontrivial dependency of the swimming velocity on the bubble deformability and on the geometry of the swimmer. We identify three distinct phases during the bubble evolution: immediately after nucleation the bubble is spherical and its inflation barely affects the swimming speed; then the bubble starts to deform due to the confinement gradient generating a force that propels the swimmer; while in the last phase, the bubble exits the cone, resulting in an increase in the swimmer velocity. Our results shed light on the fundamental hydrodynamics of the propulsion of catalytic conical swimmers and may help to improve the efficiency of these micro-machines. Full article

(This article belongs to the Special Issue Free surface flows)

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19 pages, 5713 KiB

Open AccessArticle

A Three-Dimensional Flow and Sediment Transport Model for Free-Surface Open Channel Flows on Unstructured Flexible Meshes

by Yong G. Lai and Kuowei Wu

Fluids 2019, 4(1), 18; https://doi.org/10.3390/fluids4010018 - 24 Jan 2019

Cited by 17 | Viewed by 4684

Abstract

Three-dimensional (3D) hydrostatic-pressure-assumption numerical models are widely used for environmental flows with free surfaces and phase interfaces. In this study, a new flow and sediment transport model is developed, aiming to be general and more flexible than existing models. A general set of [...] Read more.

Three-dimensional (3D) hydrostatic-pressure-assumption numerical models are widely used for environmental flows with free surfaces and phase interfaces. In this study, a new flow and sediment transport model is developed, aiming to be general and more flexible than existing models. A general set of governing equations are used for the flow and suspended sediment transport, an improved solution algorithm is proposed, and a new mesh type is developed based on the unstructured polygonal mesh in the horizontal plane and a terrain-following sigma mesh in the vertical direction. The new flow model is verified first with the experimental cases, to ensure the validity of flow and free surface predictions. The model is then validated with cases having the suspended sediment transport. In particular, turbidity current flows are simulated to examine how the model predicts the interface between the fluid and sediments. The predicted results agree well with the available experimental data for all test cases. The model is generally applicable to all open-channel flows, such as rivers and reservoirs, with both flow and suspended sediment transport issues. Full article

(This article belongs to the Special Issue Free surface flows)

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19 pages, 6782 KiB

Open AccessArticle

Field Studies and 3D Modelling of Morphodynamics in a Meandering River Reach Dominated by Tides and Suspended Load

by Qiancheng Xie, James Yang and T. Staffan Lundström

Fluids 2019, 4(1), 15; https://doi.org/10.3390/fluids4010015 - 22 Jan 2019

Cited by 12 | Viewed by 3820

Abstract

Meandering is a common feature in natural alluvial streams. This study deals with alluvial behaviors of a meander reach subjected to both fresh-water flow and strong tides from the coast. Field measurements are carried out to obtain flow and sediment data. Approximately 95% [...] Read more.

Meandering is a common feature in natural alluvial streams. This study deals with alluvial behaviors of a meander reach subjected to both fresh-water flow and strong tides from the coast. Field measurements are carried out to obtain flow and sediment data. Approximately 95% of the sediment in the river is suspended load of silt and clay. The results indicate that, due to the tidal currents, the flow velocity and sediment concentration are always out of phase with each other. The cross-sectional asymmetry and bi-directional flow result in higher sediment concentration along inner banks than along outer banks of the main stream. For a given location, the near-bed concentration is 2−5 times the surface value. Based on Froude number, a sediment carrying capacity formula is derived for the flood and ebb tides. The tidal flow stirs the sediment and modifies its concentration and transport. A 3D hydrodynamic model of flow and suspended sediment transport is established to compute the flow patterns and morphology changes. Cross-sectional currents, bed shear stress and erosion-deposition patterns are discussed. The flow in cross-section exhibits significant stratification and even an opposite flow direction during the tidal rise and fall; the vertical velocity profile deviates from the logarithmic distribution. During the flow reversal between flood and ebb tides, sediment deposits, which is affected by slack-water durations. The bed deformation is dependent on the meander asymmetry and the interaction between the fresh water flow and tides. The flood tides are attributable to the deposition, while the ebb tides, together with run-offs, lead to slight erosion. The flood tides play a key role in the morphodynamic changes of the meander reach. Full article

(This article belongs to the Special Issue Free surface flows)

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Review

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23 pages, 3922 KiB

Open AccessReview

Steady Two-Dimensional Free-Surface Flow Past Disturbances in an Open Channel: Solutions of the Korteweg–De Vries Equation and Analysis of the Weakly Nonlinear Phase Space

by Benjamin J. Binder

Fluids 2019, 4(1), 24; https://doi.org/10.3390/fluids4010024 - 04 Feb 2019

Cited by 7 | Viewed by 3613

Abstract

Two-dimensional free-surface flow past disturbances in an open channel is a classical problem in hydrodynamics—a problem that has received considerable attention over the last two centuries (e.g., see Lamb’s Treatise, 1879). With traces back to Russell’s experimental observations of the Great Wave of [...] Read more.

Two-dimensional free-surface flow past disturbances in an open channel is a classical problem in hydrodynamics—a problem that has received considerable attention over the last two centuries (e.g., see Lamb’s Treatise, 1879). With traces back to Russell’s experimental observations of the Great Wave of Translation in 1834, Korteweg and de Vries (1895), and others, derived an unforced equation to describe the balance between nonlinearity and dispersion required to model the solitary wave. More recently, Akylas (1984) derived a forced KdV equation to model a pressure distribution on the free-surface (e.g., a ship). Since then, the forced KdV equation has been shown to be a useful model approximation for two-dimensional flow past disturbances in an open channel. In this paper, we review the stationary solutions of the forced KdV equation for four types of localised disturbances: (i) a flat plate separating two free surfaces; (ii) a compact bump, or dip in the channel bottom topography; (iii) a compact distribution of pressure on the free surface and (iv) a step-wise change in the otherwise constant horizontal level of the channel bottom topography. Moreover, Dias and Vanden-Broeck (2002) developed a phase plane method to analyse flow over a bump, and this general approach has also been applied to the three other types of forcing (see Binder et al., 2005–2015, and others). In this study, we use eleven basic flow types to classify the steady solutions of the forced KdV equation using the phase plane method. Additionally, considering solutions that are wave-free both far upstream and far downstream, we compare KdV model approximations of the uniform flow conditions in the far-field with exact solutions of the full problem. In particular, we derive a new KdV model approximation for the upstream dimensionless flow-rate which is conveniently given in terms of the known downstream dimensionless flow-rate. Full article

(This article belongs to the Special Issue Free surface flows)

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15 pages, 43096 KiB

Open AccessReview

The Past and Present of Discharge Capacity Modeling for Spillways—A Swedish Perspective

by James Yang, Patrik Andreasson, Penghua Teng and Qiancheng Xie

Fluids 2019, 4(1), 10; https://doi.org/10.3390/fluids4010010 - 13 Jan 2019

Cited by 15 | Viewed by 5197

Abstract

Most of the hydropower dams in Sweden were built before 1980. The present dam-safety guidelines have resulted in higher design floods than their spillway discharge capacity and the need for structural upgrades. This has led to renewed laboratory model tests. For some dams, [...] Read more.

Most of the hydropower dams in Sweden were built before 1980. The present dam-safety guidelines have resulted in higher design floods than their spillway discharge capacity and the need for structural upgrades. This has led to renewed laboratory model tests. For some dams, even computational fluid dynamics (CFD) simulations are performed. This provides the possibility to compare the spillway discharge data between the model tests performed a few decades apart. The paper presents the hydropower development, the needs for the ongoing dam rehabilitations and the history of physical hydraulic modeling in Sweden. More than 20 spillways, both surface and bottom types, are analyzed to evaluate their discharge modeling accuracy. The past and present model tests are compared with each other and with the CFD results if available. Discrepancies do exist in the discharges between the model tests made a few decades apart. The differences fall within the range −8.3%–+11.2%. The reasons for the discrepancies are sought from several aspects. The primary source of the errors is seemingly the model construction quality and flow measurement method. The machine milling technique and 3D printing reduce the source of construction errors and improve the model quality. Results of the CFD simulations differ, at the maximum, by 3.8% from the physical tests. They are conducted without knowledge of the physical model results in advance. Following the best practice guidelines, CFD should generate results of decent accuracy for discharge prediction. Full article

(This article belongs to the Special Issue Free surface flows)

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