Dense Fluid Flows Research Articles

Investigation of the characteristics of optically dense gray mixed convection fluid flow along a cantilever shape

The goal of the work under consideration is to inspect the steady buoyancy driven flow for a viscous and density independent fluid along a cantilever shape, by considering the optically dense gray fluid. This study examines the characteristics of buoyancy driven convective heat and fluid flow adjacent to the cantilever shape. The governing equations constituting the aforementioned problem are converted into ordinary differential equations by utilizing the stream function formulation. The shooting technique BVP4C along with the MATLAB program is then used to obtain the numerical solutions. The impact of dimensionless cantilever shape parameter n, Prandtl number Pr, Richardson parameter λ, and thermal radiation parameter F on the velocity and temperature profile of the cantilever shape is demonstrated graphically. The tables provide the results for the skin friction and rate of heat transfer coefficient due to the impact of a number of evolving parameters.

Determining dense velocity fields for fluid images based on affine motion.

In this article, we address the problem of estimating fluid flows between two adjacent images containing fluid and non-fluid objects. Typically, traditional optical flow estimation methods lack accuracy, because of the highly deformable nature of fluid, the lack of definitive features, and the motion differences between fluid and non-fluid objects. Our approach captures fluid motions using an affine motion model for each small patch of an image. To obtain robust patch matches, we propose a best-buddies similarity-based method to address the lack of definitive features but many similar features in fluid phenomena. A dense set of affine motion models was then obtained by performing nearest-neighbor interpolation. Finally, dense fluid flow was recovered by applying the affine transformation to each patch and was improved by minimizing a variational energy function. Our method was validated using different types of fluid images. Experimental results show that the proposed method achieves the best performance.

Development of supercritical motion and internal jumps within lock-release radial currents and draining flows

When released from rest in a cylindrical reservoir, relatively dense fluid flows radially and may drain freely over an edge or may propagate along the underlying boundary as a gravity current. Here we show that in both scenarios the unsteady fluid motions develop the same supercritical state, a phenomenon that does not occur in equivalent two-dimensional flows and which strongly influences the ensuing dynamics, even at long times after the release. In particular, we demonstrate the onset and persistence of supercritical outflow when fluid drains over an edge, and the development of internal bores within gravity current flow.

Evolution of a two-layer fluid for solitary waves propagating over a submarine trench

The induced density-stratified fluid motion of a solitary wave propagating over a submarine trench was investigated numerically and experimentally. A new laboratory experiment in a two-dimensional wave flume on dense fluid transport and flow fields inside and around the trench was reported using a measurement framework of laser-induced fluorescence (LIF) and particle image velocimetry (PIV) techniques. A 3D Navier–Stokes numerical model was applied to trace the dense fluid transport using the volume of fluid method. Good agreements were obtained between experiments and computed results. The calibrated model was then used to examine the transport processes of the various dense fluids. Particular attention is paid to the evolution of vortices induced by solitary waves. The results indicate that transported height of dense fluid around the windward trench wall decreases when the dense fluid density increases or wave nonlinearity decreases. The dense fluid is allowed to be transported toward the upstream of the trench when a denser fluid or lower wave nonlinearity is considered. The presence of strong vortical structure and vorticity strength was observed as the dense fluid density decreases or wave nonlinearity increases. Quantitative analyses also demonstrate that either density of dense fluid or wave nonlinearity significantly affects the transport process of the dense fluid.

Buoyancy-induced turbulent mixing in a narrow tilted tank

We describe a series of experiments in which a constant buoyancy flux $B_{s}$ of salty dyed water of density ${\it\rho}_{s}$ is introduced at the top of a long narrow tank of square cross-section tilted at an angle ${\it\theta}$ to the vertical. The tank is initially filled with fresh clear water of density ${\it\rho}_{0}<{\it\rho}_{s}$, and we investigate the resulting buoyancy-driven turbulent mixing at various tilt angles ${\it\theta}$. Using a light-attenuation image analysis method, we determine the evolution of the reduced gravity $g^{\prime }=g({\it\rho}-{\it\rho}_{0})/{\it\rho}_{0}$ of the mixed fluid in time and space as it propagates towards the bottom of the tank. For all tilt angles tested (${\it\theta}=0^{\circ }$ to ${\it\theta}=45^{\circ }$), we focus exclusively on high-Reynolds-number experiments, where the flow remains turbulent both along the length and across the width of the tank. We find that when ${\it\theta}>0^{\circ }$, the cross-tank component of gravity acts to segregate the dense fluid from the relatively lighter fluid, and a statically stable gradient of $g^{\prime }$ across the width of the tank occurs more frequently than a statically unstable gradient, i.e. $(\partial g^{\prime }/\partial x)<0$ occurs more frequently than $(\partial g^{\prime }/\partial x)>0$. This is in contrast to the case when ${\it\theta}=0^{\circ }$, where instantaneous cross-tank gradients of reduced gravity may be positive or negative, but are equal to zero in an ensemble average. We observe that when ${\it\theta}>0^{\circ }$, the cross-tank gradient of reduced gravity induces a turbulent counterflow where dense fluid flows down the upward-facing surface of the tank and lighter fluid flows in the opposing direction above. We model the evolution of the cross-tank averaged, ensemble averaged reduced gravity $\langle \overline{g^{\prime }}\rangle _{e}$ as a diffusive process using Prandtl’s mixing length theory, building on the model of van Sommeren et al. (J. Fluid Mech., vol. 701, 2012, pp. 278–303) who considered purely vertical tanks. We model the fluctuations (from the cross-tank averaged quantity) of reduced gravity $\langle {\hat{g}}^{\prime }\rangle _{e}$ and counterflow velocity $\langle {\hat{w}}\rangle _{e}$ by characterising the mixing across the width of the tank with a cross-tank turbulent diffusivity ${\it\kappa}_{T,x}$, which we assume is constant in the cross-tank coordinate $x$. We show that the counterflow that exists when ${\it\theta}>0^{\circ }$ acts directly to enhance the effective along-tank turbulent diffusivity ${\it\kappa}_{T,z}$, and from experiments, we find that the mixing length increases approximately linearly with ${\it\theta}$, and that both ${\it\kappa}_{T,x}$ and ${\it\kappa}_{T,z}$ are proportional to $(\partial \langle \overline{g^{\prime }}\rangle _{e}/\partial z)^{1/2}$.

The Graetz–Nusselt problem extended to continuum flows with finite slip

AbstractGraetz and Nusselt studied heat transfer between a developed laminar fluid flow and a tube at constant wall temperature. Here, we extend the Graetz–Nusselt problem to dense fluid flows with partial wall slip. Its limits correspond to the classical problems for no-slip and no-shear flow. The amount of heat transfer is expressed by the local Nusselt number $\mathit{Nu}_{x}$, which is defined as the ratio of convective to conductive radial heat transfer. In the thermally developing regime, $\mathit{Nu}_{x}$ scales with the ratio of position $\tilde{x}=x/L$ to Graetz number $\mathit{Gz}$, i.e. $\mathit{Nu}_{x}\propto (\tilde{x}/\mathit{Gz})^{-{\it\beta}}$. Here, $L$ is the length of the heated or cooled tube section. The Graetz number $\mathit{Gz}$ corresponds to the ratio of axial advective to radial diffusive heat transport. In the case of no slip, the scaling exponent ${\it\beta}$ equals $1/3$. For no-shear flow, ${\it\beta}=1/2$. The results show that for partial slip, where the ratio of slip length $b$ to tube radius $R$ ranges from zero to infinity, ${\it\beta}$ transitions from $1/3$ to $1/2$ when $10^{-4}<b/R<10^{0}$. For partial slip, ${\it\beta}$ is a function of both position and slip length. The developed Nusselt number $\mathit{Nu}_{\infty }$ for $\tilde{x}/\mathit{Gz}>0.1$ transitions from 3.66 to 5.78, the classical limits, when $10^{-2}<b/R<10^{2}$. A mathematical and physical explanation is provided for the distinct transition points for ${\it\beta}$ and $\mathit{Nu}_{\infty }$.

Shock-wave compression and Joule-Thomson expansion.

Structurally stable atomistic one-dimensional shock waves have long been simulated by injecting fresh cool particles and extracting old hot particles at opposite ends of a simulation box. The resulting shock profiles demonstrate tensor temperature, Txx≠Tyy and Maxwell's delayed response, with stress lagging strain rate and heat flux lagging temperature gradient. Here this same geometry, supplemented by a short-ranged external "plug" field, is used to simulate steady Joule-Kelvin throttling flow of hot dense fluid through a porous plug, producing a dilute and cooler product fluid.

Advection and buoyancy-induced turbulent mixing in a narrow vertical tank

AbstractWe describe new experiments to examine the buoyancy-induced turbulent mixing which results from the injection of a small constant volume flux of dense fluid at the top of a long narrow vertical tank with square cross-section, in which a steady laminar upward flow of less dense fluid is present. To conserve volume of fluid in the tank, fluid leaves the tank through two small openings near the top of the tank. Dense source fluid vigorously mixes with the less dense fluid of the upward flow, such that a dense mixing region of turbulent fluid propagates downwards during the transient mixing phase of the experiment. Eventually, the transport of dense fluid associated with the buoyancy-induced turbulent flow is balanced by the transport of less-dense fluid associated with the steady upward flow, such that the mixing region evolves into a layer of finite extent which stays approximately constant in height during a statistically steady mixing phase of the experiment. With an ideal source of downward constant buoyancy flux ${B}_{s} $ at the top of the tank, tank width $d$, and speed of the upward flow ${u}_{u} $, we perform experiments with Froude numbers $\mathit{Fr}= {u}_{u} {d}^{1/ 3} / { B}_{s}^{1/ 3} $ ranging between $O(0. 01)$ and $O(1)$. The steady-state height of the mixing region and the maximum reduced gravity as found near the source of buoyancy flux at the top of the tank increase with decreasing Froude number. For the experiments with intermediate values of the Froude number, we find that the steady-state mixing region is small enough to be contained in the experimental tank, but large enough not to be dominated by developing turbulence near the source of buoyancy flux. For these experiments, we show that the key buoyancy-induced turbulent mixing properties are not significantly affected by the upward flow. We use a dye-attenuation technique to obtain vertical profiles of the time- and horizontally averaged reduced gravity to show a good agreement between the experimental profiles and the solution of a nonlinear turbulent advection–diffusion equation during the steady mixing phase. Furthermore, we discuss the characteristic time scale of the transient mixing phase. We compare our experimental results with the numerical solution of a time-dependent nonlinear turbulent advection–diffusion equation during the transient mixing phase. We also describe three reduced models for the evolution of the reduced gravity distribution in the mixing region, and we demonstrate these models’ usefulness by comparison with our experimental results and the numerical solution of the time-dependent nonlinear turbulent advection–diffusion equation.

Vehicle Motion in Currents

In this paper, we present a nonlinear dynamic model for the motion of a rigid vehicle in a dense fluid flow that comprises a steady, nonuniform component and an unsteady, uniform component. In developing the basic equations, the nonuniform flow is assumed to be inviscid, but containing initial vorticity; further rotational flow effects may then be incorporated by modifying the angular rate used in the viscous force and moment model. The equations capture important flow-related forces and moments that are absent in simpler models. The dynamic equations are presented in terms of both the vehicle's inertial motion and its flow-relative motion. Model predictions are compared with exact analytical solutions for simple flows. Applications of the motion model include controller and observer design, stability analysis, and simulation of nonlinear vehicle dynamics in nonuniform flows. As illustrations, we use the model to analyze the motion of a cylinder in a plane laminar jet, a spherical Lagrangian drifter, and a slender underwater vehicle. For this last example, we compare predictions of the given model with those of simpler models and we demonstrate its use for flow gradient estimation. The results are applicable to not only underwater vehicles, but also to air vehicles of low relative density such as airships and ultralights.

The hydraulics of exchange flow between adjacent confined building zones

Buoyancy driven flow between two finite zones containing fluid of slightly different density is investigated. The two zones are connected through a common rectangular doorway spanning the channel width so that a two-layer exchange flow develops once the barrier is removed. In the zone that initially contained dense fluid, a buoyant plume of light fluid mixes with the dense fluid leading, over time, to the development of non-trivial ambient density stratification. Meanwhile, dense fluid flows as a gravity current into the zone that initially contained light fluid. This gravity current reflects from the end wall and propagates back toward the opening in the form of an internal bore. When the bore reaches the opening the dynamics of the exchange flow (and consequently the source conditions of the buoyant plume) are substantially altered. Such dynamics are modeled using elements of gravity current, internal bore and plume theory. The flow dynamics of the two zones are linked using two-layer exchange flow theory whereby a maximal exchange flow rate is prescribed only before the bore reaches the opening. The velocity and density jump across the first front decrease substantially once the exchange flow becomes sub-maximal. Depending on the geometrical parameters, the terminal elevation of the first front may lie above, at or below the top of the opening; here, we focus on the former scenario. Experiments have been carried out to validate the model. The comparison between theory and experiment plus the application of the research to architectural fluid mechanics is discussed.

A Molecular Dynamics and Lattice Boltzmann Multiscale Simulation for Dense Fluid Flows

A molecular dynamics (MD)-lattice Boltzmann (LB) hybrid scheme has been adopted to simulate dense fluid flows. Based on the domain decomposition method and the Schwarz alternating scheme, the “Maxwell Demon” approach is used to impose boundary conditions from the continuum to the atomistic region, while the “reconstruction operator” is implemented to construct the single-particle distribution function of the LB method from the results of the MD simulation. Couette flows and the flow of a dense fluid argon around a carbon nanotube (CNT) are solved to validate the hybrid method. When the mesh of the LB domain is refined and the size of corresponding sampling cells of the MD domain is reduced, the fluctuations of the results between two successive iterations of the hybrid method become more severe, although the results get closer to the MD reference solutions. To decrease the fluctuation due to the mesh refinement, a new weighting function is proposed for the sampling of MD simulation results. Numerical practice demonstrates its feasibility.

A thermodynamically consistent non-ideal stochastic hard-sphere fluid

A grid-free variant of the direct simulation Monte Carlo (DSMC) method is proposed,named the isotropic DSMC (I-DSMC) method, that is suitable for simulating dense fluidflows at molecular scales. The I-DSMC algorithm eliminates all grid artifacts from thetraditional DSMC algorithm; it is Galilean invariant and microscopically isotropic. Thestochastic collision rules in I-DSMC are modified to yield a non-ideal structure factor thatgives consistent compressibility, as first proposed by Donev et al (2008 Phys. Rev. Lett. 101 075902). The resulting stochastic hard-sphere dynamics (SHSD) fluid is empiricallyfound to have the same pair correlation function as a deterministic Hamiltonian system ofpenetrable spheres interacting with a linear core pair potential, well described by thehypernetted chain (HNC) approximation. We apply a stochastic Enskog kinetic theory tothe SHSD fluid to obtain estimates for the transport coefficients that are in excellentagreement with particle simulations over a wide range of densities and collision rates. Thefluctuating hydrodynamic behavior of the SHSD fluid is verified by comparing itsdynamic structure factor against theory based on the Landau–Lifshitz Navier–Stokesequations. We also study the Brownian motion of a nanoparticle suspended in anSHSD fluid and find a long-time power-law tail in its velocity autocorrelationfunction consistent with hydrodynamic theory and molecular dynamics calculations.

The interaction of a gravity current with a circular cylinder mounted above a wall: Effect of the gap size

Abstract The flow of a gravity current past a circular cylinder mounted above a bottom wall is studied by means of two-dimensional Navier–Stokes simulations. The investigation focuses on the effects of the gap size on the forces acting on the cylinder. The interaction of the current with the cylinder can be divided into an impact, a transient, and a quasisteady stage. During the impact stage, the gravity current meets the cylinder, and the drag increases towards a maximum, while the lift undergoes a drastic fluctuation which increases noticeably with the gap size. During the quasisteady stage, the flow past the cylinder resembles that observed in constant-density boundary layer flows past cylinders: Karman vortex shedding is observed for sufficiently large gap sizes, while a vorticity cancellation mechanism is responsible for the suppression of vortex shedding at small gap sizes. On the other hand, interesting differences that distinguish the gravity current case from the constant-density case are the presence in the gravity current flow of a component of the mean quasisteady lift due to buoyancy, and another component from the deflection of the wake towards the wall by the constriction of the dense fluid flow downstream of the cylinder, as well as the cancellation of vortex shedding for all gap sizes when the ratio of the channel depth to lock height is decreased from 5 to 1.

LATTICE–BOLTZMANN SIMULATION OF DENSE NANOFLOWS: A COMPARISON WITH MOLECULAR DYNAMICS AND NAVIER–STOKES SOLUTIONS

In a recent work, a dense fluid flow across a nanoscopic thin plate was simulated by means of Molecular Dynamics (MD) and Lattice Boltzmann (LB) methods. It was found that in order to recover quantitative agreement with MD results, the LB simulation must be pushed down to sub–nanoscopic scales, i.e. fractions of the range of molecular interactions. In this work, we point out that in this sub–nanoscopic regime, the LB method works outside the hydrodynamic limit at the level of a single cell spacing. A quantitative comparison with the Navier–Stokes (NS) solution shows however that LB and NS results are quite similar, thereby indicating that, apart for a small region past the plate, this nanoflow is still well described by hydrodynamic equations.

Simulation of fluid flows in the nanometer: kinetic approach and molecular dynamic simulation

Slip phenomenon usually occurs at the fluid–solid interface as a fluid flows in a nanometer device. The slip length that characterizes the slip behavior depends on a variety of factors. In this work, the influences of the fluid–wall interaction and system temperature on the slip length for dense fluid flows are studied using a kinetic model and the molecular dynamic (MD) simulation. It is found that the results predicted by the both approaches agree with each other qualitatively.

Fluidized piston model for molecular dynamics simulations of hydrodynamic flow

We have developed a new method, the fluidized piston model (FPM), to drive dense fluid flow in molecular dynamics (MD) simulations. Fluid in the upstream region acts as a fluidized piston (FP) that continuously presses and supplies the downstream fluid. The FPM can treat dense and polyatomic fluid flow driven by a pressure gradient efficiently with the prescribed inlet streaming velocity at high speed, which is usually used for hydrodynamic MD studies. Furthermore, the temperature inside the sampling region is kept constant without direct control. We apply the FPM to the 100 m s−1 water flow inside (20, 20), (12, 12), (10, 10), (8, 8) and (6, 6) carbon nanotubes (CNTs). The results show that the appropriate density in the sampling region is adaptively obtained during the simulation and the desired streaming velocity is obtained except inside the (6,6) CNT. The deviation of the obtained streaming velocity from the desired value inside the (6,6) CNT is related to the current technical limit of the temperature control method applied in the upstream FP region and the highly discrete nature of the single-file water flow.

Mixing regimes for the flow of dense fluid down slopes into stratified environments

Downslope flows into density-stratified environments have been observed to have the character of detraining gravity currents on small slopes, and of entraining plumes on steep slopes. In this paper, observations of flows on slopes of intermediate (20) steepness are described, and their mixing properties quantified. Both gravity-current-like and plume-like flows are observed, and an observational boundary between these two types is identified. Theoretical models for the bulk properties of these flows are presented, and their predictions are compared with the observations. A theoretical criterion is derived for the limit of applicability of the gravity-current model in terms of the Buoyancy number, the bottom slope and the bottom drag coefficient. This provides a criterion for the boundary between the plume-like and gravity-current-like flows, which is consistent with the observations. These results have implications for the modelling of downslope flows in nature, and indicate where the appropriate dynamical model may change from one type to the other.

Hybrid atomistic–continuum method for the simulation of dense fluid flows

We present a hybrid atomistic–continuum method for multiscale simulations of dense fluids. In this method, the atomistic part is described using a molecular dynamics description, while the continuum flow is described by a finite volume discretization of the incompressible Navier–Stokes equations. The two descriptions are combined in a domain decomposition formulation using the Schwarz alternating method. A novel method has been proposed in order to impose non-periodic velocity boundary conditions from the continuum to the atomistic domain, based on an effective boundary potential, consistent body forces, a particle insertion algorithm and specular walls. The extraction of velocity boundary conditions for the continuum from the atomistic domain is formulated by taking into account the associated statistical errors. The advantages and drawbacks of the proposed Schwarz decomposition method as compared to related flux-based schemes are discussed. The efficiency and applicability of the method is demonstrated by considering hybrid and full molecular dynamics simulations of the flow of a Lennard–Jones fluid past a carbon nanotube.

New molecular approach to theoretical investigations of fluid flows in narrow pores

Abstract A new approach has been offered to calculate dense fluid flows in narrow pores. The local properties of fluids are calculated on the basis of the simple molecular model—the lattice-gas model. Molecular interactions are taken into account in quasi-chemical approximation, preserving effects of correlation between nearest neighbours. The model covers a wide range of changes of fluid density (from gaseous up to a liquid state) and temperature including the critical range that permits to consider dynamics of fluid flows at the presence of the capillary condensation, A system of equations has quasi-hydrodynamic type and the approach can be considered as micro-hydrodynamic one. Numerical analysis of the Navier–Stokes type equations predicted by the model was performed by a ‘relaxation’ method with second order accuracy in the temporal and spatial domains. The approach was used for the analysis of dynamic modes of flows for argon gas in carbon slit-like pores. Possibilities of the new approach are demonstrated for four types of steady-state and non-steady-state regimes of molecular flows in narrow slit-like pores.

Mixing in flows down gentle slopes into stratified environments

Observations of the flow of dense fluid into uniformly density-stratified environments down plane slopes with small inclination to the horizontal ([les ] 20°) are described, and a quantitative model for such flows is presented. In these experiments the dense fluid is released at the top of the slope for a finite period of time. The resulting downslope gravity current, or downflow, has uniform thickness with a distinct upper boundary, until it approaches its level of neutral density where the fluid leaves the proximity of the slope. Turbulent transfers of mass and momentum occur across the upper boundary, causing a continuous loss of fluid from the downflow in most cases, and associated loss of momentum. The flow may be characterized by the local values of the Richardson number Ri, the Reynolds number Re (generally large), and of M = QN3/g′2, where Q is the (two-dimensional) volume flux, N the buoyancy frequency and g′ the (negative) buoyancy of the dense fluid. The model for the downflow describes the turbulent transfers in terms of entrainment, detrainment and drag coefficients, Ee, Ed and k respectively, and the observations enable the determination of these coefficients in terms of the local values of M and Ri. The model may be regarded as an extension of that Ellison & Turner (1959) to stratified environments, describing the consequent substantial changes in mixing and distribution of the inflow. It permits the modelling of the bulk properties of these flows in geophysical situations, including shallow and deep flows in the ocean.