Fluid Velocity Gradient Research Articles

Three-dimensional features of MHD flows turning in a right-angle duct

This study presents a numerical simulation of three-dimensional (3D) Liquid metal (LM) Magnetohydrodynamic (MHD) flows turning in a right-angle duct with a square cross section under a uniform magnetic field applied perpendicular to the plane of the main flow. The 3D features of the flow in a fluid region adjacent to the duct walls of the turning segment are investigated. Cases with different Hartmann numbers and conductance parameters are analyzed using the CFX code. The MHD features of the LM flow are examined in terms of fluid velocity, current density, electric potential, and pressure gradient. The formation of a velocity recirculation is observed in the inner region of the right-angle segment immediately after the turning of the flow because of the inertial force therein, thereby yielding a region of low electric potential with a complicated current distribution. In particular, in the right-angle segment, the axial velocity in the side layer near the outer wall (that is, in the outer side layer) is relatively lower than that in the inflow and outflow channels. In addition, the velocity recirculation region in the right-angle segment decreases and the pressure gradient increases with an increase in conductance parameter.

An interfacial shear term evaluation study for adiabatic dispersed air–water two-phase flow with the two-fluid model using CFD

In commercially available Computational Fluid Dynamics (CFD) codes such as ANSYS CFX and Fluent, the interfacial shear term is missing in the field momentum equations. The derivation of the two-fluid model (Ishii and Hibiki, 2011) indicates the presence of this term as a momentum source in the right hand side of the field momentum equation. The inclusion of this term is considered important for proper modeling of the interfacial momentum coupling between phases. For separated flows, such as annular flow, the importance of the shear term is understood in the one-dimensional (1-D) form as the major mechanism by which the wall shear is transferred to the gas phase (Ishii and Mishima, 1984). For gas dispersed two-phase flow CFD simulations, it is important to assess the significance of this term in the prediction of phase distributions. In the first part of this work, the closure of this term in three-dimensional (3-D) form in a CFD code is investigated. For dispersed gas–liquid flow, such as bubbly or churn-turbulent flow, bubbles are dispersed in the shear layer of the continuous phase. The continuous phase shear stress is mainly due to the presence of the wall and the modeling of turbulence through the Boussinesq hypothesis. In a 3-D simulation, the continuous phase shear stress can be calculated from the continuous fluid velocity gradient, so that the interfacial shear term can be closed using the local values of the volume fraction and the total stress of liquid phase. This form also assures that the term acts as an action-reaction force for multiple phases. In the second part of this work, the effect of this term on the volume fraction distribution is investigated. For testing the model two-phase flow data measured at Purdue University is assessed. The interfacial shear term is assembled in ANSYS CFX. Simulation results are presented to assess the effect of the interfacial shear term on the phase distribution.

Analysis of an augmented mixed-FEM for the Navier-Stokes problem

In this paper we propose and analyze a new augmented mixed finite element method for the Navier-Stokes problem. Our approach is based on the introduction of a “nonlinear-pseudostress” tensor linking the pseudostress tensor with the convective term, which leads to a mixed formulation with the nonlinearpseudostress tensor and the velocity as the main unknowns of the system. Further variables of interest, such as the fluid pressure, the fluid vorticity and the fluid velocity gradient, can be easily approximated as a simple postprocess of the finite element solutions with the same rate of convergence. The resulting mixed formulation is augmented by introducing Galerkin least-squares type terms arising from the constitutive and equilibrium equations of the Navier-Stokes equation and from the Dirichlet boundary condition, which are multiplied by stabilization parameters that are chosen in such a way that the resulting continuous formulation becomes well-posed. Then, the classical Banach's fixed point Theorem and Lax-Milgram's Lemma are applied to prove well-posedness of the continuous problem. Similarly, we establish wellposedness and the corresponding Cea's estimate of the associated Galerkin scheme considering any conforming finite element subspace for each unknown. In particular, the associated Galerkin scheme can be defined by employing Raviart-Thomas elements of degree k for the nonlinear-pseudostress tensor, and continuous piecewise polynomial elements of degree k+1 for the velocity, which leads to an optimal convergent scheme. In addition, we provide two iterative methods to solve the corresponding nonlinear system of equations and analyze their convergence. Finally, several numerical results illustrating the good performance of the method are provided. This contribution is based on joint work with Ricardo Oyarzua (Universidad del Bio-Bio) and Giordano Tierra (Charles University).

Lift force on nanoparticles in shear flows of dilute gases: negative or positive?

We theoretically investigate the lift force on spherical nanoparticles in a shear flow of a dilute gas, wherein the non-rigid-body collision between the particle and the gas molecules is considered. The analytical formula of the lift force is derived based on the gas kinetic theory. In the limit of rigid-body collision, the formula is consistent with the theoretical results in the literature (Liu & Bogy,Phys. Fluids, vol. 20, 2008, 107102), which predicts that the lift force is in the opposite direction to the fluid velocity gradient (negative lift force). However, by taking into account gas–particle intermolecular interactions, the direction of the lift force on the nanoparticle is found to be dependent on temperature, i.e. both positive and negative lift forces exist in a certain temperature range. An explanation for the direction change of the lift force is given based on the analysis of the scattering angle under non-rigid-body particle–molecule collisions.

Preferential Sampling and Small-Scale Clustering of Gyrotactic Microswimmers in Turbulence.

Recent studies show that spherical motile microorganisms in turbulence subject to gravitational torques gather in down-welling regions of the turbulent flow. By analyzing a statistical model we analytically compute how shape affects the dynamics, preferential sampling, and small-scale spatial clustering. We find that oblong organisms may spend more time in up-welling regions of the flow, and that all organisms are biased to regions of positive fluid-velocity gradients in the upward direction. We analyze small-scale spatial clustering and find that oblong particles may either cluster more or less than spherical ones, depending on the strength of the gravitational torques.

Bimodal rheotactic behavior reflects flagellar beat asymmetry in human sperm cells

Rheotaxis, the directed response to fluid velocity gradients, has been shown to facilitate stable upstream swimming of mammalian sperm cells along solid surfaces, suggesting a robust physical mechanism for long-distance navigation during fertilization. However, the dynamics by which a human sperm orients itself relative to an ambient flow is poorly understood. Here, we combine microfluidic experiments with mathematical modeling and 3D flagellar beat reconstruction to quantify the response of individual sperm cells in time-varying flow fields. Single-cell tracking reveals two kinematically distinct swimming states that entail opposite turning behaviors under flow reversal. We constrain an effective 2D model for the turning dynamics through systematic large-scale parameter scans, and find good quantitative agreement with experiments at different shear rates and viscosities. Using a 3D reconstruction algorithm to identify the flagellar beat patterns causing left or right turning, we present comprehensive 3D data demonstrating the rolling dynamics of freely swimming sperm cells around their longitudinal axis. Contrary to current beliefs, this 3D analysis uncovers ambidextrous flagellar waveforms and shows that the cell's turning direction is not defined by the rolling direction. Instead, the different rheotactic turning behaviors are linked to a broken mirror symmetry in the midpiece section, likely arising from a buckling instability. These results challenge current theoretical models of sperm locomotion.

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

ABSTRACTThe rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.

On the relationship between the non-local clustering mechanism and preferential concentration

‘Preferential concentration’ (Squires & Eaton,Phys. Fluids, vol. A3, 1991, pp. 1169–1178) refers to the clustering of inertial particles in the high strain, low-rotation regions of turbulence. The ‘centrifuge mechanism’ of Maxey (J. Fluid Mech., vol. 174, 1987, pp. 441–465) appears to explain this phenomenon. In a recent paper, Bragg & Collins (New J. Phys., vol. 16, 2014, 055013) showed that the centrifuge mechanism is dominant only in the regime$St\ll 1$, where$St$is the Stokes number based on the Kolmogorov time scale. Outside this regime, the centrifuge mechanism gives way to a non-local, path history symmetry breaking mechanism. However, despite the change in the clustering mechanism, the instantaneous particle positions continue to correlate with high strain, low-rotation regions of the turbulence. In this paper, we analyse the exact equation governing the radial distribution function and show how the non-local clustering mechanism is influenced by, but not dependent upon, the preferential sampling of the fluid velocity gradient tensor along the particle path histories in such a way as to generate a bias for clustering in high strain regions of the turbulence. We also show how the non-local mechanism still generates clustering, but without preferential concentration, in the limit where the time scales of the fluid velocity gradient tensor measured along the inertial particle trajectories approaches zero (such as white noise flows or for particles in turbulence settling under strong gravity). Finally, we use data from a direct numerical simulation of inertial particles suspended in Navier–Stokes turbulence to validate the arguments presented in this study.

Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence.

In this paper, we consider the physical mechanism for the clustering of inertial particles in the inertial range of isotropic turbulence. We analyze the exact, but unclosed, equation governing the radial distribution function (RDF) and compare the mechanisms it describes for clustering in the dissipation and inertial ranges. We demonstrate that in the limit Str≪1, where Str is the Stokes number based on the eddy turnover time scale at separation r, the clustering in the inertial range can be understood to be due to the preferential sampling of the coarse-grained fluid velocity gradient tensor at that scale. When Str≳O(1) this mechanism gives way to a nonlocal clustering mechanism. These findings reveal that the clustering mechanisms in the inertial range are analogous to the mechanisms that we identified for the dissipation regime [see New J. Phys. 16, 055013 (2014)]. Further, we discuss the similarities and differences between the clustering mechanisms we identify in the inertial range and the "sweep-stick" mechanism developed by Coleman and Vassilicos [Phys. Fluids 21, 113301 (2009)]. We show that the idea that initial particles are swept along with acceleration stagnation points is only approximately true because there always exists a finite difference between the velocity of the acceleration stagnation points and the local fluid velocity. This relative velocity is sufficient to allow particles to traverse the average distance between the stagnation points within the correlation time scale of the acceleration field. We also show that the stick part of the mechanism is only valid for Str≪1 in the inertial range. We emphasize that our clustering mechanism provides the more fundamental explanation since it, unlike the sweep-stick mechanism, is able to explain clustering in arbitrary spatially correlated velocity fields. We then consider the closed, model equation for the RDF given in Zaichik and Alipchenkov [Phys. Fluids 19, 113308 (2007)] and use this, together with the results from our analysis, to predict the analytic form of the RDF in the inertial range for Str1, which, unlike that in the dissipation range, is not scale invariant. The results are in good agreement with direct numerical simulations, provided the separations are well within the inertial range.

Analysis of convective heat transfer improved impeller stirred tanks by the lattice Boltzmann method

This paper performs the lattice Boltzmann simulation combined with unknown-index algorithm for the convective heat transfer problems of an impeller stirred tank. Three types of motion of the heating impeller are adopted in this study, including rotation with constant angular velocity, oscillation and oscillating rotation, which are denoted as Types I, II, and III stirrings respectively. Because the flow structures in rotation stirring case are concentric vertical, the heat transfer efficiency of the tank walls is lower than those of the other two types of stirrings. The other two types of stirrings, the flow structures include complex vortices and present better field synergy of the fluid velocity and temperature gradient, which positively contributes to the convective heat transfer efficiency. The results also indicate that a large swing process angle of the impeller with oscillating rotation stirring does not have significant advantage, because the flow phenomena would be similar to that of constant angular velocity stirring case. Basically, the Type III stirred tank can be considered as an improved Type II stirred tank by choosing appropriate process angle.

Gradient correction to photon emission rate at strong coupling

We compute the correction to the photon emission rate in the first order of shear components of fluid velocity gradients, ${\ensuremath{\sigma}}_{ij}$, in near-equilibrium hydrodynamic plasma at the strong coupling regime, using the real-time Schwinger-Keldysh formalism in AdS/CFT correspondence. Our result is an integral of an analytic expression. We observe that the gradient correction to the photon emission rate at strong coupling is about 0.3--0.4 times the equilibrium rate in units of ${\ensuremath{\sigma}}_{ij}/T$.

Lattice Boltzmann simulation of solute transport in a single rough fracture

In this study, the lattice Boltzmann method (LBM) was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. The ability of the developed LBM to simulate the solute transport was validated by Taylor dispersion. The effect of fluid velocity on the solute transport in a single rough fracture was investigated using the LBM. The breakthrough curves (BTCs) for continuous injection sources in rough fractures were analyzed and discussed with different Reynolds numbers (Re). The results show that the rough fracture wall leads to a large fluid velocity gradient across the aperture. Consequently, there is a broad distribution of the immobile region along the rough fracture wall. This distribution of the immobile region is very sensitive to the Re and fracture geometry, and the immobile region is enlarged with the increase of Re and roughness. The concentration of the solute front in the mobile region increases with the Re. Furthermore, the Re and roughness have significant effects on BTCs, and the slow solute molecule exchange between the mobile and immobile regions results in a long breakthrough tail for the rough fracture. This study also demonstrates that the developed LBM can be effective in studying the solute transport in a rough fracture.

Simulation studies on the transport properties of Cu-H2O nanofluids based on water continuum assumption

Nanofluid is a kind of new engineering medium which is created by dispersing small quantity of nano-sized particles in the base fluid. The dispersion of solid nanoparticles in conventional fluids changes their transport properties remarkably. Molecular dynamics simulation (MDS) is an important approach to study the transport properties of nanofluids. However, the computation amount is huge, and it is very difficult to use the normal MDS to capture the transient flow and heat processes in Cu-H2O nanofluids if the regions in the simulation reach 149.6443 nm3 or 299.2883 nm3, and the number of Cu nano-particles reaches 6-64. Further study by means of simulation on the effects on effective transport properties of nanofluids is also difficult. In this paper, the water-based fluid region of 149.6443 nm3 or 299.2883 nm3 is assumed as continuum phase because of the very low Knudsen number of fluid, and the effects of water on nano-particles are fitted into the Cu-Cu potential parameters. Using the proposed method, the computation amount is significantly reduced. The effective thermal conductivity and dynamic viscosity coefficient of Cu-H2O nanofluids under the stationary condition are simulated and the results are verified with existing experimental data. The motion and aggregation processes of nano-particles in the water-based fluids at different velocity shear rate are simulated. Effects of velocity shear rate, fluid velocity, temperature gradient, and average temperature on the effective thermal conductivity and the dynamic viscosity of Cu-H2O nanofluids in the processes of flow and heat transfer are studied. Three conclusions can be drawn from the obtained results. Firstly, the proposed method is feasible to capture the transient flow and heat processes in Cu-H2O nanofluids, and is also capable to further study the transport properties of Cu-H2O nanofluids. Secondly, the velocity shear rate acting on a nanofluid can effectively prevent the aggregating process of nano-particles, and therefore reduce the diameter of particle-aggregations. Finally, the velocity shear rate and the average temperature of Cu-H2O nanofluids have much more effects on the transport properties, while the fluid velocity and temperature gradient have less effects; the velocity shear rate increases the effective thermal conductivity of a nanofluid but decreases its dynamic viscosity. A rise of average temperature increases the effective thermal conductivity but decreases the dynamic viscosity.

Vorticity and magnetic field production in relativistic ideal fluids

In the framework of relativistic ideal hydrodynamics, we study the production mechanism for vorticity and magnetic field in relativistic ideal fluids. It is demonstrated that in the uncharged fluids the thermal vorticity will always satisfy the Kelvin's theorem and the circulation must be conserved. However, in the charged fluids, the vorticity and magnetic field can be produced by the interaction between the entropy gradients and the fluid velocity gradients. Especially, in the multiple charged fluids, the vorticity and magnetic field can be produced by the interaction between the inhomogenous charge density ratio and the fluid velocity gradients even if the entropy distribution is homogeneous, which provides another mechanism for the production of vorticity and magnetic field in relativistic plasmas or in the early universe.

Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence

AbstractSmall droplets in turbulent flows can undergo highly variable deformations and orientational dynamics. For neutrally buoyant droplets smaller than the Kolmogorov scale, the dominant effects from the surrounding turbulent flow arise through Lagrangian time histories of the velocity gradient tensor. Here we study the evolution of representative droplets using a model that includes rotation and stretching effects from the surrounding fluid, and restoration effects from surface tension including a constant droplet volume constraint, while assuming that the droplets maintain an ellipsoidal shape. The model is combined with Lagrangian time histories of the velocity gradient tensor extracted from direct numerical simulations (DNS) of turbulence to obtain simulated droplet evolutions. These are used to characterize the size, shape and orientation statistics of small droplets in turbulence. A critical capillary number is identified associated with unbounded growth of one or two of the droplet’s semi-axes. Exploiting analogies with dynamics of polymers in turbulence, the critical capillary number can be predicted based on the large deviation theory for the largest finite-time Lyapunov exponent quantifying the chaotic separation of particle trajectories. Also, for subcritical capillary numbers near the critical value, the theory enables predictions of the slope of the power-law tails of droplet size distributions in turbulence. For cases when the viscosities of droplet and outer fluid differ in a way that enables vorticity to decorrelate the shape from the straining directions, the large deviation formalism based on the stretching properties of the velocity gradient tensor loses validity and its predictions fail. Even considering the limitations of the assumed ellipsoidal droplet shape, the results highlight the complex coupling between droplet deformation, orientation and the local fluid velocity gradient tensor to be expected when small viscous drops interact with turbulent flows. The results also underscore the usefulness of large deviation theory to model these highly complex couplings and fluctuations in turbulence that result from time integrated effects of fluid deformations.

Effects of fluid velocity gradients on heavy quark energy loss

We use holographic duality to analyze the drag force on, and consequent energy loss of, a heavy quark moving through a strongly coupled conformal fluid with non-vanishing gradients in its velocity and temperature. We derive the general expression for the drag force to first order in the fluid gradients. Using this general expression, we show that a quark that is instantaneously at rest, relative to the fluid, in a fluid whose velocity is changing with time feels a nonzero force. And, we show that for a quark that is moving ultra-relativistically, the first order gradient "corrections" become larger than the zeroth order drag force, suggesting that the gradient expansion may be unreliable in this regime. We illustrate the importance of the fluid gradients for heavy quark energy loss by considering a fluid with one-dimensional boost invariant Bjorken expansion as well as the strongly coupled plasma created by colliding sheets of energy.

An analytical model for bedload layer thickness

A theoretical study has been carried out to determine the thickness of the bedload layer in an open channel turbulent flow with non-cohesive sediment, which is very crucial in sediment transport problems as this is treated as saltation height of a sediment particle and the reference level in suspension studies. A new expression of viscous shear stress is proposed, which is a function of effective viscosity of sediment–fluid mixture, velocity gradient and volumetric concentration of sediment particles. During particle collisions, impact shear stress is generated, which is another important parameter near the sediment bed. By including both the shear stresses, an expression for the thickness of the bedload layer is developed. The predicted bedload layer thickness is a function of viscous coefficient, impact coefficient, particle diameter, relative mass density of sediment particle, maximum bed concentration and non-dimensional shear stress. It agrees reasonably well when compared with a wide class of experimental data under different hydraulic conditions.

Floc Roll-Up and Its Implications for the Spacing of Inclined Settling Devices

Inclined plate and tube settlers are commonly used to make sedimentation tanks more compact. Conventional design equations for inclined settling devices are based on obtaining a desired particle capture velocity; these equations suggest that a suitable capture velocity can be achieved by reducing plate settler spacing or tube settler diameter below that specified in conventional design guidelines. Smaller spacing would reduce capital costs by decreasing the sedimentation tank volume. However, existing literature does not explain why smaller values of plate or tube spacing cannot be used, and failure mechanisms that set the minimum spacing recommended in design practice have not been documented. This research shows that the fluid velocity gradient at the tube or plate surface is the limiting constraint for spacing, and for very small spacing, particles that settle on the solid surface are carried up the incline. This failure mode, termed “floc roll-up,” occurs when the terminal velocity of a floc along the incline is less than the upward velocity of the fluid at the center of the floc. This article presents an experimental and theoretical investigation of the floc roll-up failure mode and its implications for plate settler design. A model was developed to explain the physics of floc roll-up, and experiments in a bench-scale water treatment apparatus demonstrated its effects on sedimentation performance. When subject to an increasing velocity gradient between the surfaces, turbidity removal in an experimental tube settler decreased from 90% to near zero, even when the traditional design equations would predict no degradation in performance. Both the model predictions and experimental results show that under some conditions, inclined settlers can employ closer spacing than the typical 5-cm design value without sacrificing turbidity removal performance.

Fabrication of Robust Hierarchical Micro/Nanostructures on Tin-Bronze Substrate

To reduce the generated heat due to fluid friction, it is desirable to minimize the drag force at the solid–liquid interface. The boundary slip facilitates fluid velocity gradient and then the drag reduction. This endeavor intends to seek a practical process for fabrication robust hierarchical structures on tin-bronze substrate. The ordered structures at micrometer scale are successfully fabricated by through-mask electrochemical micromachining (TM-EMM) and three candidate fabrication processes involving electroless galvanic deposition, surface oxidation and ZnO nanostructures growth via wet-chemical route for structures at nanometer scale on metal surface are investigated. The fabricated results have been demonstrated and their properties of stability and wettability were evaluated. Experimental study results show that combining TH-EMM with ZnO nanostructures growth presents an effective process for fabrication of firm multi-level structures on metal surface.

Development of a Fluorescent Molecular Rotor‐Based Approach for Concurrent Measurement of Blood Viscosity and Hemodynamics

Shear stress measurements are routinely calculated using local fluid velocity gradients and estimated static viscosity values. However, since blood viscosity is dependent on local hematocrit and is affected by non‐Newtonian shear‐thinning, a methodology allowing concurrent blood velocity and viscosity measurement should improve intracardiac shear mapping accuracy. Our objective was to develop such a methodology using viscosity‐sensitive fluorescent molecular rotors coupled to inert microspheres and validate the approach in a zebrafish model. Microinjection parameters have been optimized for effective delivery of rotors into the zebrafish vascular bed. Age‐dependent injection targets have been identified to facilitate reproducible bolus delivery. Finally, FCVJ reflect local hemodynamic profiles demonstrating a functionality consistent with their in vitro performance. Taken together, our data indicate that fluorescent molecular rotors provide the spatial and temporal resolution required for use in planar and volumetric digital defocusing particle image velocimetry (DDPIV) technology to facilitate real‐time 3‐dimensional in vivo shear mapping. (This work funded by AHA 10IRG4020025.)