Showing papers on "Streamlines, streaklines, and pathlines published in 2014"

Mixed convection of copper-water nanofluid in a shallow inclined lid driven cavity using the lattice Boltzmann method

Abstract: The goal of this work is to study the laminar mixed convection of water–Cu nanofluid in an inclined shallow driven cavity using the lattice Boltzmann method. The upper lid of the cavity moves with constant velocity, U 0 , and its temperature is higher than that of the lower wall. The side walls are assumed to be adiabatic. The effects of different values of the cavity inclination angle and nanoparticles volume fraction at three states of free, force and mixed convection domination are investigated while the Reynolds number is kept fixed as Re = 100 and Re = 10 . Validation of present results with those of other available ones shows a suitable agreement. Streamlines, isotherms, Nusselt numbers, and velocity and temperature profiles are presented. More Nusselt numbers can be achieved at larger values of the inclination angle and nanoparticles volume fraction at free convection domination. Results imply the appropriate ability of LBM to simulate the mixed convection of nanofluid in a shallow inclined cavity.

Pore-scale intermittent velocity structure underpinning anomalous transport through 3-D porous media

Abstract: We study the nature of non-Fickian particle transport in 3-D porous media by simulating fluid flow in the intricate pore space of real rock. We solve the full Navier-Stokes equations at the same resolution as the 3-D micro-CT (computed tomography) image of the rock sample and simulate particle transport along the streamlines of the velocity field. We find that transport at the pore scale is markedly anomalous: longitudinal spreading is superdiffusive, while transverse spreading is subdiffusive. We demonstrate that this anomalous behavior originates from the intermittent structure of the velocity field at the pore scale, which in turn emanates from the interplay between velocity heterogeneity and velocity correlation. Finally, we propose a continuous time random walk model that honors this intermittent structure at the pore scale and captures the anomalous 3-D transport behavior at the macroscale.

Natural Convection in a Square Porous Cavity with Sinusoidal Temperature Distributions on Both Side Walls Filled with a Nanofluid: Buongiorno’s Mathematical Model

Abstract: Natural convection in a two-dimensional, square porous cavity filled with a nanofluid and with sinusoidal temperature distributions on both side walls and adiabatic conditions on the upper and lower walls is numerically investigated. The flow is assumed to be slow so that advective and Forchheimer quadratic terms are ignored in the momentum equation. The applied sinusoidal temperature is symmetric with respect to the midplane of the enclosure. Numerical calculations are produced for Rayleigh numbers in the range of 10– $$10^{4}$$ in comparison with other authors. The present models, in the form of an in-house computational fluid dynamics code, have been validated successfully against the reported results from the open literature. It is found that the results are in very good agreement. Results are presented in the form of streamlines, isotherm contours, and distributions of the average Nusselt number.

Interaction of nanoparticles for the peristaltic flow in an asymmetric channel with the induced magnetic field

Abstract: In the present investigation, we examined the interaction of nanoparticle copper with the base fluid water in an asymmetric channel in the presence of an induced magnetic field. The complexity of equations describing the flow of the nanofluid is reduced by applying the low-Reynolds number and long-wavelength approximations. The resulting equations are solved exactly. The obtained expressions for the velocity and temperature phenomenon are sketched in graphs. The resulting relations for pressure gradient and pressure rise are plotted for various pertinent parameters. The streamlines are drawn for some physical quantities to discuss the trapping phenomenon.

Anomalous hydrodynamics of two-dimensional vortex fluids.

Abstract: A dense system of vortices can be treated as a fluid and itself could be described in terms of hydrodynamics We develop the hydrodynamics of the vortex fluid This hydrodynamics captures characteristics of fluid flows averaged over fast circulations in the intervortex space The hydrodynamics of the vortex fluid features the anomalous stress absent in Euler's hydrodynamics The anomalous stress yields a number of interesting effects Some of them are a deflection of streamlines, a correction to the Bernoulli law, and an accumulation of vortices in regions with high curvature in the curved space The origin of the anomalous stresses is a divergence of intervortex interactions at the microscale which manifest at the macroscale We obtain the hydrodynamics of the vortex fluid from the Kirchhoff equations for dynamics of pointlike vortices

Lateral migration and focusing of microspheres in a microchannel flow of viscoelastic fluids

Abstract: The lateral migration of microspheres across streamlines induced by elasticity and inertia in a square microchannel flow of viscoelastic fluids is investigated using a holographic microscopy technique. We experimentally demonstrate the exact particle positions driven by the elasticity of fluid in the channel cross-section. The effects of the blockage ratio, flow rate, and shear-thinning property of the viscoelastic fluids on particle migration are evaluated. In particular, the focusing patterns of microspheres in three-dimensional volume are analyzed under different conditions, namely, dominant inertia, dominant elasticity, and the combined effects of inertia and elasticity.

Time-analyticity of Lagrangian particle trajectories in ideal fluid flow

Abstract: It is known that the Eulerian and Lagrangian structures of fluid flow can be drastically different; for example, ideal fluid flow can have a trivial (static) Eulerian structure, while displaying chaotic streamlines. Here, we show that ideal flow with limited spatial smoothness (an initial vorticity that is just a little better than continuous) nevertheless has time-analytic Lagrangian trajectories before the initial limited smoothness is lost. To prove these results we use a little-known Lagrangian formulation of ideal fluid flow derived by Cauchy in 1815 in a manuscript submitted for a prize of the French Academy. This formulation leads to simple recurrence relations among the time-Taylor coefficients of the Lagrangian map from initial to current fluid particle positions; the coefficients can then be bounded using elementary methods. We first consider various classes of incompressible fluid flow, governed by the Euler equations, and then turn to highly compressible flow, governed by the Euler–Poisson equations, a case of cosmological relevance. The recurrence relations associated with the Lagrangian formulation of these incompressible and compressible problems are so closely related that the proofs of time-analyticity are basically identical.

Magnetohydrodynamic Modeling and Experimental Validation of Convection Inside Electromagnetically Levitated Co-Cu Droplets

Abstract: A magnetohydrodynamic model of internal convection of a molten Co-Cu droplet processed by the ground-based electromagnetic levitation (EML) was developed. For the calculation of the electromagnetic field generated by the copper coils, the simplified Maxwell’s equations were solved. The calculated Lorentz force per volume was used as a momentum source in the Navier–Stokes equations, which were solved by using a commercial computational fluid dynamics package. The RNG k-e model was adopted for the prediction of turbulent flow. For the validation of the developed model, a Co16Cu84 sample was tested using the EML facility in the German Aerospace Center, Cologne, Germany. The sample was subjected to a full melt cycle, during which the surface of the sample was captured by a high-speed camera. With a sufficient undercooling, the liquid phase separation occurred and the Co-rich liquid phase particles could be observed as they were floating on the surface along streamlines. The convection velocity was estimated by the combination of the displacement of the Co-rich particles and the temporal resolution of the high-speed camera. Both the numerical and experimental results showed an excellent agreement in the convection velocity on the surface.

A LES study of the flow interference between tandem square cylinder pairs

Abstract: The results of an investigation on the interference effects of the tandem square cylinders exposed to a uniform flow are presented in this paper. Time-dependent and three-dimensional flow simulations are carried out using large eddy simulation with a one-equation subgrid model. An incompressible three-dimensional finite volume code with a collocated grid arrangement is used for solving filtered Navier–Stokes equations. These equations are solved with an implicit fractional two-step method. Simulations are conducted with different Reynolds numbers between 103 and 105. The longitudinal spacing between the cylinders is selected 4D for the chosen Reynolds numbers, where D is the side of the cylinders. Also the effect of the spacing between cylinders, ranging from 1D to 12D, is studied for the selected Reynolds numbers. The instantaneous flow field is studied by analyzing the vortices, pressure, streamlines and Q-criterion to assist understanding of the various flow patterns, vortical structures and Kelvin–Helmholtz vortices in the separating shear layers. The hysteresis is observed in a certain range of the gap spacing, which this range depends on the selected Reynolds number. The global results are also computed and compared with available experimental results. The results indicate that there is a satisfactory agreement between the predictions and available experimental data considering the fine grid adopted.

Numerical modeling of flow around and through a porous cylinder with diamond cross section

Abstract: Fluid flow across a porous cylinder has various engineering applications. In this paper, a two-dimensional, steady, and laminar flow around and through a porous diamond-square cylinder is studied numerically. The governing equations are written for two zones: the clear fluid zone and the porous zone. For the clear fluid zone, the regular Navier–Stokes equation is used; and the Darcy–Brinkman–Forchheimer model is used for simulating flow in the porous zone. The governing equations, together with the relevant boundary conditions, are solved numerically using the finite-volume method (FVM). In this study, the ranges of Reynolds and Darcy numbers are 1–45 and 10−6–10−2, respectively. The effects of the Darcy and Reynolds numbers on several hydrodynamics parameters such as pressure coefficient, wake structure, and streamlines are explored. Finally, these parameters are compared with the solid and porous diamond-square cylinders. The numerical results indicate that the wake length and pressure coefficient decrease when Darcy number increases.

Effects of heat and mass transfer on peristaltic flow of a nanofluid between eccentric cylinders

Abstract: In the present investigation, we examined the heat and mass transfer analysis for the peristaltic flow of nanofluid through eccentric cylinders. The complexity of equations describing the flow of nanofluid is reduced through applying the low Reynolds number and long wavelength approximations. The resulting equations are highly nonlinear, coupled and nonhomogeneous partial differential equations. These complicated governing equations are solved analytically by employing the homotopy perturbation method. The obtained expressions for velocity, temperature and nanoparticle phenomenon are sketched through graphs for two as well as three dimensions. The resulting relations for pressure gradient and pressure rise are plotted for various pertinent parameters. The streamlines are drawn for some physical quantities to discuss the trapping phenomenon.

Influence of heat generation and heat flux on peristaltic flow with interacting nanoparticles

Abstract: In the current study, we have examined the peristaltic flow of three different nanoparticles with water as base fluid under the influence of slip boundary conditions through a vertical asymmetric porous channel in the presence of MHD. The selected nanoparticles are titanium dioxide ( TiO2 , copper oxide (CuO) and silicon dioxide ( SiO2 . The Brownian motion shows that the effective conductivity increases to result in a lower temperature gradient for a given heat flux. To examine these transport phenomena thoroughly, we also consider the thermal conductivity model of Brownian motion for nanofluids, this increases the effect of the particle size, particle volume fraction and temperature dependence. The mathematical formulation is presented. Exact solutions are obtained from the resulting equations. The obtained expressions for pressure gradient, temperature and velocity profile are described through graphs for the various relevant parameters. The streamlines are drawn for some physical quantities to discuss the trapping phenomenon.

Stability of Dissipation Elements: A Case Study in Combustion

Abstract: Recently, dissipation elements have been gaining popularity as a mechanism for measurement of fundamental properties of turbulent flow, such as turbulence length scales and zonal partitioning. Dissipation elements segment a domain according to the source and destination of streamlines in the gradient flow field of a scalar function f: M → R. They have traditionally been computed by numerically integrating streamlines from the center of each voxel in the positive and negative gradient directions, and grouping those voxels whose streamlines terminate at the same extremal pair. We show that the same structures map well to combinatorial topology concepts developed recently in the visualization community. Namely, dissipation elements correspond to sets of cells of the Morse-Smale complex. The topology-based formulation enables a more exploratory analysis of the nature of dissipation elements, in particular, in understanding their stability with respect to small scale variations. We present two examples from combustion science that raise significant questions about the role of small scale perturbation and indeed the definition of dissipation elements themselves.

Low-order modeling of wind farm aerodynamics using leaky Rankine bodies

Abstract: We develop and characterize a low-order model of the mean flow through an array of vertical-axis wind turbines (VAWTs), consisting of a uniform flow and pairs of potential sources and sinks to represent each VAWT. The source and sink in each pair are of unequal strength, thereby forming a “leaky Rankine body” (LRB). In contrast to a classical Rankine body, which forms closed streamlines around a bluff body in potential flow, the LRB streamlines have a qualitatively similar appearance to a separated bluff body wake; hence, the LRB concept is used presently to model the VAWT wake. The relative strengths of the source and sink are determined from first principles analysis of an actuator disk model of the VAWTs. The LRB model is compared with field measurements of various VAWT array configurations measured over a 3-yr campaign. It is found that the LRB model correctly predicts the ranking of array performances to within statistical certainty. Furthermore, by using the LRB model to predict the flow around two-turbine and three-turbine arrays, we show that there are two competing fluid dynamic mechanisms that contribute to the overall array performance: turbine blockage, which locally accelerates the flow; and turbine wake formation, which locally decelerates the flow as energy is extracted. A key advantage of the LRB model is that optimal turbine array configurations can be found with significantly less computational expense than higher fidelity numerical simulations of the flow and much more rapidly than in experiments.

Hoop stress-assisted three-dimensional particle focusing under viscoelastic flow

Abstract: Three-dimensional particle focusing is a prerequisite for a wide range of lab-on-a-chip applications such as cell counting and sorting. We have demonstrated that when side-wells are inserted in a rectangular channel, the particles form an almost single stream (>99 %) within ±0.9× particle diameter from the channel centerline under viscoelastic flow. Recently, viscoelasticity-based particle focusing technique has attracted much attention since it operates by flowing particles in extremely simple channels. However, the particles move along multiple equilibrium positions in rectangular channels under elasticity-dominant flow, and this is not favorable for practical applications. We show that the hoop stress along curved streamlines in side-wells can be engineered to reduce the multiple particle lanes to a single stream. Further, we achieve highly efficient focusing under inertialess viscoelastic flow with high throughput (>2000/s). We expect that our novel method will find applications in accurate cell counting, sorting, and deformability measurement.

Pressure beneath a traveling wave with constant vorticity

Abstract: The main focus of this paper is to derive a direct relationship between the surface of an inviscid traveling gravity wave in two dimensions, and the pressure at the bottom of the fluid without approximation, including the effects of constant vorticity. Using this relationship, we reconstruct both the pressure and streamlines throughout the fluid domain. We compare our numerical results with various analytical results (such as the bounds presented in [7-10])as well as known numerical results (see [16]).

A theoretical study of Prandtl nanofluid in a rectangular duct through peristaltic transport

Abstract: In the current study, peristaltic transport of Prandtl nanofluid is investigated in a uniform rectangular duct. Interaction of peristaltic flow of non-Newtonian fluid model with nano particles is investigated under the long wave length and low Reynolds number approximations. The governing equations are solved by homotopy perturbation method to get the convergent series solution. Effects of all emerging physical parameters are demonstrated with the help of graphs for temperature distribution, nano particles concentration, pressure rise and pressure gradient. Trapping scheme is also described through streamlines.