Gravity-driven Flow Research Articles

Improved treatment of wall boundary conditions for a particle method with consistent spatial discretization

In recent years, consistent spatial discretization schemes for meshfree particle methods to numerically simulate incompressible flow have been studied by many researchers. This study is focused on the treatment of solid wall boundary conditions for one of those schemes, namely the least squares MPS (LSMPS) scheme, and proposes a new technique to deal with no-slip and free-slip wall boundary conditions. With the proposed treatment, wall geometries are expressed by surface meshes, i.e. polygons in 3D and line segments in 2D. Thus, complicated geometries can be handled easily. Based on a Taylor series expansion, wall boundary conditions are incorporated into the differential operators acting on fluid particles located in the vicinity of a wall, through a least squares approach. As a consequence, Neumann boundary conditions can be treated quite efficiently. To verify consistency of the proposed discretization scheme, a convergence study was carried out. As numerical examples, Couette flow, plane Poiseuille flow, gravity-driven flow in a 3D square duct, a rigid rotation problem, Taylor–Green vortices and lid-driven cavity flow have been calculated using the proposed boundary treatment, with both no-slip and free-slip conditions applied. As a result, the present method agreed well with the reference solutions, which verified its computational accuracy.

Simplified physically based models for free-surface flow in karst systems

Most karst aquifers are characterized as a dual-flow system comprised of a highly conductive conduit network embedded in a low porosity matrix. The conduits are hydraulically connected to the matrix and behave either as a drain or a source depending on the recharge conditions. Simplified physically based models are herein employed to simulate the spring outflow for such aquifer systems. The processes consist of a free-surface flow in the conduit that is interacting laterally with a laminar groundwater flow in the surrounding matrix. The conduit is subject to a concentrated recharge at its upstream end while the groundwater aquifer is subject to a diffuse recharge over its contributing surface area. The flow system is described by a coupled system of partial differential equations: the conduit flow is approximated by the kinematic wave equation and the groundwater flow by the linearized Boussinesq equation. The governing equations are solved using the Laplace transform method after an appropriate linearization of the nonlinear coefficient. The derived spring discharge models are a function of three dimensionless parameters: the time lag parameter ξ, the lumped conduit parameter λ, and the aquifer parameter η. The simulation results highlight the contrast between pressure-driven and gravity-driven flows and the importance of the conduit-matrix interaction on the response of the karst system. Application of the models on real karst aquifers demonstrates their effectiveness in simulating the observed spring hydrograph using lumped physical parameters of the karst system.

Experimental Evaluation of Changes in Channel Bed Morphology due to a Defective Pressure Flow Pipe

AbstractThere are two types of flow in underground pipes: gravity-driven flow, such as in sewer pipes, and pressure flow, such as in syphon pipes. Defective pipes can cause extensive economic losse...

Shear force measurement of the hydrodynamic wall position in molecular dynamics.

Flows in nanofluidic systems are strongly affected by liquid-solid slip, which is quantified by the slip length and by the position where the slip boundary condition applies. Here, we show that the viscosity, slip length, and hydrodynamic wall position (HWP) can be accurately determined from a single molecular dynamics (MD) simulation of a Poiseuille flow, after identifying a relation between the HWP and the wall shear stress in that configuration. From this relation, we deduce that in gravity-driven flows, the HWP identifies with the Gibbs dividing plane of the liquid-vacuum density profile. Simulations of a generic Lennard-Jones liquid confined between parallel frozen walls show that the HWP for a pressure-driven flow is also close to the Gibbs dividing plane (measured at equilibrium), which therefore provides an inexpensive estimate of the HWP, going beyond the common practice of assuming a given position for the hydrodynamic wall. For instance, we show that the HWP depends on the wettability of the surface, an effect usually neglected in MD studies of liquid-solid slip. Overall, the method introduced in this article is simple, fast, and accurate and could be applied to a large variety of systems of interest for nanofluidic applications.

Local Rheology Relation with Variable Yield Stress Ratio across Dry, Wet, Dense, and Dilute Granular Flows.

Dry, wet, dense, and dilute granular flows have been previously considered fundamentally different and thus described by distinct, and in many cases incompatible, rheologies. We carry out extensive simulations of granular flows, including wet and dry conditions, various geometries and driving mechanisms (boundary driven, fluid driven, and gravity driven), many of which are not captured by standard rheology models. For all simulated conditions, except for fluid-driven and gravity-driven flows close to the flow threshold, we find that the Mohr-Coulomb friction coefficient μ scales with the square root of the local Péclet number Pe provided that the particle diameter exceeds the particle mean free path. With decreasing Pe and granular temperature gradient M, this general scaling breaks down, leading to a yield condition with a variable yield stress ratio characterized by M.

Photoelastic study of dense granular free-surface flows.

In this study, we perform experiments that reveal the distribution of dynamic forces in the bulk of granular free-surface flows. We release photoelastic disks from an incline to create steady two-dimensional avalanches. These gravity-driven dry granular flows are in the slow to intermediate regime (I≤1), dense (φ≈0.8), and thin (h≈10d). The transition between solidlike (quasisteady) and fluidlike (inertial) regimes is observable for certain experimental settings. We measure constant density and quasilinear velocity profiles through particle tracking at several points down the chute, for two different basal topographies. The photoelastic technique allows the visualization and quantification of instantaneous forces transmitted between particles during individual collisions. From the measured forces we obtain coarse-grained profiles of all stress tensor components at various positions along the chute. The discreteness of the system leads to highly fluctuating individual force chains which form preferentially in the directions of the bulk external forces: in this case, gravity and shear. The behavior of the coarse-grained stress tensor within a dynamic granular flow is analogous to that of a continuous fluid flow, in that we observe a hydrostatic increase of the mean pressure with depth. Furthermore, we identify a preferential direction for the principal stress orientation, which depends on the local magnitudes of the frictional and gravitational forces. These results allow us to draw an analogy between discrete and continuous flow models.

Falling water films over vertical surfaces due to orthogonal water jet impingement

In AHWR rod bundle assembly, LOCA could cause failure of the system due to overheating. To overcome this problem, it is proposed to introduce holes in the axial and circumferential direction of central water tube so that water discharges through these holes in the form of a jet and strikes the high-temperature fuel rods resulting in their cooling by gravity-driven flow mechanism. This cooling involves a different mechanism of heat transfer such as two-phase flow, single phase jet impingement, droplet impingement, evaporation, natural convection, and radiation due to the high temperature of the fuel rods. Among all these heat transfer mechanisms, the present study focuses on the horizontal water jet impingement on a vertically oriented surface. The scarcity of research in such cases is the motivation to study the hydrodynamics of the water jet impingement on a vertically oriented surface. A proper understanding of hydrodynamics of the water film on a vertical surface is important in the understanding of heat removal processes. Present study discusses the hydrodynamics of falling water films on a flat surface and a curved surface exposed to horizontal water jet impingement. Effect of the jet exit to surface distance (Z/d), Reynolds number, nozzle diameter (d), and the ratio of curvature of the surface to the diameter of the pipe (D/d) were examined on lateral and vertical spread of the water film at vertically oriented flat and curved surface.

Pore-scale hydrodynamics influence the spatial evolution of bacterial biofilms in a microfluidic porous network.

Bacteria occupy heterogeneous environments, attaching and growing within pores in materials, living hosts, and matrices like soil. Systems that permit high-resolution visualization of dynamic bacterial processes within the physical confines of a realistic and tractable porous media environment are rare. Here we use microfluidics to replicate the grain shape and packing density of natural sands in a 2D platform to study the flow-induced spatial evolution of bacterial biofilms underground. We discover that initial bacterial dispersal and grain attachment is influenced by bacterial transport across pore space velocity gradients, a phenomenon otherwise known as rheotaxis. We find that gravity-driven flow conditions activate different bacterial cell-clustering phenotypes depending on the strain’s ability to product extracellular polymeric substances (EPS). A wildtype, biofilm-producing bacteria formed compact, multicellular patches while an EPS-defective mutant displayed a linked-cell phenotype in the presence of flow. These phenotypes subsequently influenced the overall spatial distribution of cells across the porous media network as colonies grew and altered the fluid dynamics of their microenvironment.

Combining hydrodynamics, hydrochemistry, and environmental isotopes to understand the hydrogeological functioning of evaporite-karst springs. An example from southern Spain

This work adopts a multicriteria approach, combining diverse karst hydrogeology techniques, to investigate the functioning of evaporite-karst systems, which are normally less studied due to the poor quality of their water resources. The applicability of using several methods was also verified. In view of previous experience at a pilot site within southern Spain, the natural responses of the main discharge point of the system of study (Lower Anzur spring) were controlled by continuous monitoring of the discharge rate, water temperature, and electrical conductivity. Water samples were collected for chemical analysis and for the determination of intrinsic fluorescence, water stable isotopes (δ18O, δ2H) and tritium (3H) concentrations. Physico-chemical data were statistically examined applying principal component analysis (PCA) and trend analysis tests (Mann-Kendall and Sen’s slope). The system shows a clear karstic functioning, highly dependent on concentrated recharge, and influenced by a limited drainage capacity of the conduit network. The piston-flow effects at the beginning of floods indicate a contribution to the drainage of deep ascending flows through the saturated zone. Subsequent drops in temperature and mineralization values in the water drained by the spring, as well as a recent infiltration deduced from the signature of intrinsic fluorescence and stable isotopes, point to a good hydrogeological connection from the recharge areas to the spring. Later restoration of the initial values of mineralization —in a much shorter time than those of temperature— reveals a faster geochemical evolution of the recently infiltrated groundwater, which may be a distinctive trait of evaporite karst aquifers. Lastly, the high solute content of the spring water in depletion conditions, with ascending trends of mineralization and temperature observed during several dry years as a consequence of lower recharge contribution, together with the tritium activity of selected samples, suggest the existence of an old component partly responsible for the spring base flow. Thus, groundwater would be linked to gravity-driven regional flows, but also to recent conduit flows. All the results obtained led us to devise a hydrogeological conceptual model to precisely reflect the functioning of the studied system. The results presented here demonstrate the advantages of using diverse techniques when investigating evaporite karst aquifers.

Numerical analysis of flow pattern transition in a conical silo with ellipsoid particles

Gravity-driven discharge flow in conical silos is ubiquitous in manufacturing processes for numerous industries such as food, pharmaceutical and chemical industries, wherein flow pattern is the key topic to be studied. In this work, discrete element method was used to study discharge flow behaviors in a special conical silo. This work aims to understand the dynamic evolution of discharge flow pattern and establish methods for regional determination of flow pattern transition. The results indicated that both mass flow and funnel flow patterns coexist in the silo at the initial stage of discharge, and there is a definite transition process from mass flow to funnel flow. Furthermore, the flow pattern transition is revealed by the change in discharge flow characteristics. Specifically, the change in force acting on particles leads to the change of particle orientation and particle velocity field, macroscopically resulting in the flow pattern transition. Finally, based on the kinetic stress field and shear rate, the height and radial region of flow pattern transition were determined, respectively. Understanding of the flow pattern transition is useful to the design, scale-up and optimization of silos and similar structural devices.

A two-phase SPH model for massive sediment motion in free surface flows

Massive sediment motion in water with a free surface is an important kind of geophysical flows such as hyper-concentrated sediment laden river flows discharging into estuarine delta and turbidity currents generated by subaqueous landslides. One of the key and common characteristics of such flows is that interactions between water and sediment as well as those among sediment particles are equally important in affecting the sediment motion and the fluid flow. This paper presents a numerical model that builds on and extends an earlier two-phase SPH model based on a continuum formulation of solid-liquid mixtures (Shi et al., 2017) to provide a unified description of massive sediment motion in free surface flows. In the model, a constitutive law based on the rheology of dense granular flow is introduced to express the intergranular stresses while the interphase drag force is determined by combining the Ergun equation for dense solid-fluid mixtures and the power law for dilute suspensions. The proposed model is firstly applied to the study of collapse of loosely or densely packed granular columns submerged in water. The computed surface profiles of the granular column are found to be in good agreement with the experimental data. It shows that the loosely packed and the densely packed columns behave rather differently due to the differences in water-sediment interaction processes. The model is then used to simulate a dam-break flow over a mobile sediment bed. The computed configurations of the flow and the movable bed also agree well with the measured data. The predicted position on the leading edge of the flow has a mean error of 0.8% while the mean error for the maximum bed height is 12.9%. To further identify the dynamic processes involved, effects of water-sediment interactions on the motion of bed materials are investigated by examining the spatial and temporal variations of pressure and flow velocity. As shown in the applications, the proposed two-phase SPH model can successfully represent both the gravity-driven underwater granular flows and the shear flow driven intense sediment transport, implying its potential use in practical scenarios in which the two kinds of flows exist simultaneously, such as landslides triggered by storm in shallow sea and flows resulted in barrier or dam breaks.

Green altered sandstone related to hydrocarbon migration from the uranium deposits in the northern Ordos Basin, China

The formation of sandstone-hosted uranium deposits has been linked to upward migration of hydrocarbons in many sedimentary basins. However, hydrocarbon-induced diagenetic alterations associated with uranium mineralization and preservation are rarely discussed. Here, we report the bleaching of red sandstone to green in the Middle Jurassic Zhiluo Formation from the uranium deposits in the northern Ordos Basin, China. The original gray sandstone underwent oxidation and was reddened by the downward flow of meteoric water from the northern margin of the basin during the Late Cretaceous–Cenozoic uplift. This process resulted in the leaching of preore-stage uranium concentration and oxidation of preore pyrite in the organic matter-rich sandstone. Uranyl and sulfate ions were carried downward through the host sandstone by oxygenated groundwater. Meanwhile, hydrocarbons migrated upward and reacted with the downward flowing oxidizing fluids, which induced uranium mineralization at the redox interface between the red and gray sandstone where iron was reduced to Fe2+ and incorporated into pyrite cement. The highly negative 34S values (−58.0‰ to −33.4‰ V-CDT) of the pyrite indicate that it originated from bacterial sulfate reduction during hydrocarbon biodegradation. Abundant organic acids and CO2 were generated from hydrocarbon oxidation, resulting in the dissolution of feldspars and the precipitation of kaolinite in the mineralized sandstone. With the formation of the Cenozoic Hetao graben to the north, the gravity-driven flow of meteoric water was limited, resulting in progressive halting of epigenetic uranium mineralization. Then, the upward hydrocarbons dominated the fluid system throughout the northern slope of the basin and bleached the previous red sandstone updip, which set up a strong reducing environment and protected the early formed uranium deposits at the paleo-redox front from oxidation and remobilization. Due to the oxygen and sulfur supply absence, the iron released from hematite during bleaching was immobilized and incorporated into Fe-rich chlorite that imparts the green color, rather than into pyrite or reprecipitation as hematite. This study provides insights for the processes of hydrocarbon-water-rock interactions associated with uranium mineralization and preservation, which can serve as exploration guides for sandstone-hosted uranium deposits.

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

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.

Transition of regular wave fronts to irregular wave fronts in gravity-driven thin films over topography

This article contributes to an understanding of the pathway from regular to chaotic traveling wave fronts over periodically undulated inclines in thin films. In order to investigate the transition from regular to chaotic waves, we used various undulation forms and varied the Reynolds number and the inclination angle in the measurements. Thereby, we revealed the first partially chaotic waves on a gravity-driven thin film channel flow. The wave is subdivided into: (i) the chaotic wave front and (ii) a regular wave tail. The area of the chaotic part can be increased by increasing the inertia of the system. Various phenomena on the flow were revealed: (a) bubble formation, (b) fingering, (c) splashes, and (d) pinch-offs. Our investigation leads to the conclusion that wave breaking over obstacles is a necessary condition for the transition from regular to chaotic wave fronts.

Tubing-Free Microfluidic Microtissue Culture System Featuring Gradual, in vivo-Like Substance Exposure Profiles.

In vitro screening methods for compound efficacy and toxicity to date mostly include cell or tissue exposure to preset constant compound concentrations over a defined testing period. Such concentration profiles, however, do not represent realistic in vivo situations after substance uptake. Absorption, distribution, metabolism and excretion of administered substances in an organism or human body entail gradually changing pharmacokinetic concentration profiles. As concentration profile dynamics can influence drug effects on the target tissues, it is important to be able to reproduce realistic concentration profiles in in vitro systems. We present a novel design that can be integrated in tubing-free, microfluidic culture chips. These chips are actuated by tilting so that gravity-driven flow and perfusion of culture chambers can be established between reservoirs at both ends of a microfluidic channel. The design enables the realization of in vivo-like substance exposure scenarios. Compound gradients are generated through an asymmetric Y-junction of channels with different hydrodynamic resistances. Six microtissues (MTs) can be cultured and exposed in compartments along the channel. Changes of the chip design or operation parameters enable to alter the dosing profile over a large range. Modulation of, e.g., the tilting angle, changes the slope of the dosing curves, so that concentration curves can be attained that resemble the pharmacokinetic characteristics of common substances in a human body. Human colorectal cancer (HCT 116) MTs were exposed to both, gradually decreasing and constant concentrations of Staurosporine. Measurements of apoptosis induction and viability after 5 h and 24 h showed different short- and long-term responses of the MTs to dynamic and linear dosing regimes

Flow of a thin liquid-metal film in a toroidal magnetic field

We investigate the gravity-driven flow of a thin film of liquid metal on a conducting conical substrate in the presence of a strong toroidal magnetic field (transverse to the flow and parallel to the substrate). We solve the leading-order governing equations in a physically relevant asymptotic limit to find the free-surface profile. We find that the leading-order fluid flow rate is a non-monotonic bounded function of the film height, and this can lead to singularities in the free-surface profile. We perform a detailed stability analysis and identify values of the relevant geometric, hydrodynamic and magnetic parameters such that the flow is stable.

A variational principle for three-dimensional interactions between water waves and a floating rigid body with interior fluid motion

A variational principle is given for the motion of a rigid body dynamically coupled to its interior fluid sloshing in three-dimensional rotating and translating coordinates. The fluid is assumed to be inviscid and incompressible. The Euler–Poincaré reduction framework of rigid body dynamics is adapted to derive the coupled partial differential equations for the angular momentum and linear momentum of the rigid body and for the motion of the interior fluid relative to the body coordinate system attached to the moving rigid body. The variational principle is extended to the problem of interactions between gravity-driven potential flow water waves and a freely floating rigid body dynamically coupled to its interior fluid motion in three dimensions.

Flow dynamics of spherical grains through conical cardboard hoppers

The gravity-driven flow of monodisperse spherical grains of different nature and diameter d, through conical cardboard hoppers, has been studied as function of the orifice diameter D for different values of the aperture angle α (~ 3° ÷ 15°) at large grains conditions (D ≤ 10d). The mass flow rate trend function has displayed, at the lowest angles, a series of linear tracts, with increasing slope, delimited by approximately odd integers of the grains diameter. The linear tracts have been associated to different flow rate regimes, governed by the formation, at the bottom of the granular column, of short-lived arches of “quantized” size (~ 5d, ~ 7d, ~ 9d, …), acting as brakes to flow, by their detachment and ejection from the hopper. This mechanism of events should give rise to a modulation of the flow whose frequency was effectively measured, for the arches of ~ 5d size, by analyzing the signal produced by the falling grains on a microphone. The data of mass flow rate W, as function of the orifice diameter D, have shown, on average, a growth following the 5/2 power-law function, as foreseen by the well-known Beverloo law. Here we analyze the simplified expression of the mass flow rate with the dimension of the square root of the acceleration of gravity, which shows only a slight dependence on the aperture angle of the hopper. The jamming of grains at the outlet opening has been also investigated throughout the transition region at D ~ 3d ÷ 4d, which characterizes the passage from the blocked to the continuous flow for few tens thousand grains, by an optical method and by measuring the frequency of the clogging events.

Understanding the local flow rate peak of a hopper discharging discs through an obstacle using a Tetris-like model

Placing a round obstacle above the orifice of a flat hopper discharging uniform frictional discs has been experimentally and numerically shown in the literature to create a local peak in the gravity-driven hopper flow rate. Using frictionless molecular dynamics (MD) simulations, we show that the local peak is unrelated to the interparticle friction, the particle dispersity, and the obstacle geometry. We then construct a probabilistic Tetris-like model, where particles update their positions according to prescribed rules rather than in response to forces, and show that Newtonian dynamics are also not responsible for the local peak. Finally, we propose that the local peak is caused by an interplay between the flow rate around the obstacle, greater than the maximum when the hopper contains no obstacle, and a slow response time, allowing the overflowing particles to converge well upon reaching the hopper orifice.

An adaptive moving mesh method for two-dimensional thin film flow equations with surface tension

In this paper, we extend our previous work (Alharbi and Naire, 2017) on a one-dimensional r -adaptive moving mesh technique based on a mesh density function and moving mesh partial differential equations (MMPDEs) to two dimensions. As a test problem, we consider the gravity-driven thin film flow down an inclined and pre-wetted plane including surface tension and a moving contact line. This technique accurately captures and resolves the moving contact line and associated fingering instability. Moreover, the computational effort is hugely reduced in comparison to a fixed uniform mesh. • To our knowledge this this the first attempt to implement r -adaptive scheme to a fourth order parabolic PDE. • This technique accurately resolves the moving contact line and fingering instability associated with the prototype flow problem. • This technique hugely reduces the computational effort in comparison to the numerical solution on a fixed uniform mesh.