Lubrication Forces Research Articles

Computational Fluid Dynamics Modeling of Argon–Steel (–Slag) Multiphase Flow in an Ruhrstahl–Heraeus Degasser: A Review of Past Numerical Studies

Many metallurgical functions such as dehydrogenation, decarburization, and inclusion removal are achieved during Ruhrstahl–Heraeus (RH) treatment. The realization of these functions is closely related to argon–steel–slag flow in an RH degasser. Recently, computational fluid dynamics (CFD) methods have been widely adopted to understand such multiphase flow. This review summarizes and analyzes CFD modeling of argon–steel (–slag) flow from the aspect of fundamentals of the numerical approach, focusing on CFD models and validation (homogeneous fluid model, volume of fluid–discrete phase model, and Eulerian model), bubble behaviors (deformation, expansion, coalescence, and breakup), interfacial closure laws (drag, turbulent dispersion, lift, virtual mass, and wall lubrication forces), and turbulence closures (Reynolds‐averaged approach with standard, renormalization group, and realizable k–ε models, and large eddy simulation with Smagorinsky–Lilly model). This review also suggests that future challenge is to further develop a model for coupling the dispersed interface with a wide bubble size distribution and the sharp interface with a large interfacial scale, accompanied by appropriate bubble behaviors and general closure laws of interfacial forces. As a precondition for the development of CFD models, more experiments are required to fully understand the multiphase flow in a real RH degasser.

Synergistic Lubrication for Textured Surfaces Using Polar and Nonpolar Lubricants

Abstract The synergistic effect of surface texturing and lubricants with various viscosity and polarity properties is an attractive and unexplored topic. In this study, surface texturing characterized by circular dimples has been manufactured on steel surfaces in advance, which can improve the lubrication of frictional units compared with the bare disc under different lubricants. Then, three lubricants, low-viscosity and nonpolar white oil, high viscosity and nonpolar silicone oil, and highly viscous and polar castor oil, were used to evaluate the interaction between surface texture and the lubricating oil. The contact angles of each lubricant on the textured and bare surface were measured to investigate the lubricant intermolecular force and wettability. The oil film thickness simulation and tribological experiments were conducted. The tribological results indicate that lubricants with varied characteristics work differently due to their different properties on textured surfaces. Castor oil exhibits the best tribological properties of the three oils used to supply the textured surfaces, which may attribute to its ability to generate strong boundary adsorption films as well as a thickened interfacial layer, and it could reduce the intensity of asperity interaction.

Numerical Research of Dynamical Behavior in Engineering Applications by Using E–E Method

In this research, a general numerical setting has been developed by finite volume approaching for the Eulerian–Eulerian method under OpenFOAM to provide an efficient reference for industrial bubbly flows having various geometrical characteristics under different conditions. Nine different test cases were selected from chemical, nuclear, bio-processing and metallurgical engineering. We compared the predicted results with experimental findings, and the comparison proved that our implementation is correct. The numerical result has good agreement with the experimental result in most testing cases. From the analysis, we found that turbulent dispersion and drag forces were of critical importance and had to be considered in simulations. The turbulent dispersion took into account the turbulence effect, and the drag forces considered two-way coupling and ensured the good position of the Eulerian–Eulerian equations. Wall lubrication and lift forces had to be considered to solve phase fraction accumulation near walls, especially for aspect ratio pipe flows. Under other conditions, lateral forces could be neglected without any problem.

Topological defect-propelled swimming of nematic colloids.

Topological defects on colloids rotating in nematic liquid crystals form far-from-equilibrium structures that perform complex swim strokes in which the defects periodically extend, depin, and contract. These defect dynamics propel the colloid, generating translation from rotation. The swimmer's speed and direction are determined by the topological defect's polarity and extent of elongation. Defect elongation is controlled by a rotating external magnetic field, allowing control over particle trajectories. The swimmers' translational motion relies on broken symmetries associated with lubrication forces between the colloid and the bounding surfaces, line tensions associated with the elongated defect, and anisotropic viscosities associated with the defect elongation adjacent to the colloid. The scattering or effective pair interaction of these swimmers is highly anisotropic, with polarization-dependent dimer stability and motion that depend strongly on entanglement and sharing of their extended defect structures. This research introduces transient, far-from-equilibrium topological defects as a class of virtual functional structures that generate modalities of motion and interaction.

Particle saltation over rigid bumpy beds in viscous shearing flows

We investigate the steady motion of solid particles through successive jumps over a horizontal, rigid, bumpy bed driven by the shearing of a viscous fluid in the absence of turbulence, lubrication forces and collisions above the bed. We employ a discrete element method for the particles coupled to a mean field continuum model for the fluid to run quasi-two-dimensional simulations that we compare with the predictions of a simple model which assumes that all the particles follow identical periodic trajectories determined by the intensity of the shearing and compatible with previously suggested laws relating the particle velocities before and after the impact with the bed. We solve the periodic model both numerically and analytically, and identify the solutions that are linearly stable to small perturbations. We show that the stable solutions of the periodic model are in qualitative and quantitative agreement with the discrete simulations, as long as the number of moving particles in the system is not too large. The discrete simulations further reveal that there are two distinct families of particle trajectories, and that the simple periodic model is actually a good representation of the more energetic particles, that spend most of their time in the upper flow layers where they can gain momentum from the flow.

Hydrodynamic origin for the suspension viscoelasticity of rough colloids

We report the linear rheology for dense suspensions of sterically stabilized smooth and mesoscopically rough colloids interacting as hard particles. Small amplitude oscillatory measurements reveal that rough colloids at high volume fractions exhibit storage and loss moduli that are orders of magnitude greater than smooth colloids. Frequency-concentration superposition is used to collapse the viscoelasticity data onto a master curve, where shift factors suggest a more elastic microstructure and reduced cage volume for rough particles. A combination of the mode-coupling theory, hydrodynamic modeling, and the activated hopping theory shows that these rough particles with significantly reduced localization lengths tend to become trapped in their glassy cages for extended periods of time. High-frequency data show that rough colloids, but not smooth colloids, display a transition from a free-draining to a fully lubricated state above the crossover volume fraction and, furthermore, exhibit solidlike behavior. Scaling analyses support the idea that lubrication forces between interlocking asperities are enhanced, leading to rotational constraints and stress-bearing structures that significantly elevate the viscoelasticity of dense suspensions. The results provide a framework for how particle surface topology affects the linear rheology in applications such as coatings, cement, consumer products, and shock-absorbing materials.

Squeeze film flow of viscoplastic Bingham fluid between non-parallel plates

Squeeze film flow of a viscoplastic Bingham fluid between non-parallel plates has been analysed. It is assumed that the force applied to the plates is known, therefore, their velocity must be found, and the film thickness decreases then as time proceeds. Moreover, for non-parallel plates, the position along the plates at which flow reverses direction is found as part of the solution. In the Newtonian limit, the thickness of the gap between the plates in the parallel system never quite reaches zero at any finite time, while for the non-parallel case a finite time can be obtained when the plates touch one another at a point. In squeeze flow of a viscoplastic Bingham fluid between parallel and non-parallel plates, under a fixed applied force, a final steady film thickness can sometimes be reached. This final thickness turns out to be sensitive not just to the plate tilt angle but also to the so called Oldroyd number which is defined as the ratio between yield stress and imposed stress. Nevertheless for squeeze film flow of Bingham viscoplastic fluid between non-parallel plates, the results show that other cases exist in which the lubrication force cannot always balance the applied force, leading to the plates approaching and touching at the narrowest end of the gap. Moreover torques that develop within the system have been analysed. • Squeeze flow of fluid between non-parallel plates is considered. • Fluid is considered as Bingham viscoplastic. • In some cases, plates stop at finite height; in other cases, plates touch. • Which case is realised depends on tilt angle and Oldroyd number. • Torque in Bingham fluid is lower than in Newtonian.

Lubrication Force Saturation Matters for the Critical Separation Size of the Non-Colloidal Spherical Particle in the Deterministic Lateral Displacement Device

Deterministic lateral displacement (DLD) is a popular technique for separating micro-scale and nano-scale particles continuously. In this paper, an efficient three-dimensional fictitious domain method is developed for the direct numerical simulation of the motion of a non-colloidal spherical particle in the DLD device (i.e., cylinder array), based on substantial modification of our previous FD method. A combination of the fast Fourier transformation (FFT) and a tri-diagonal solver is developed to efficiently solve the pressure Poisson equation for a DLD unit with a shifted periodic boundary condition in the streamwise direction. The lubrication force correction is adopted in the fictitious domain method to correct the unresolved hydrodynamic force when the particle is close to the cylinder with the gap distance below one mesh, and the lubrication force is assumed to saturate at a smaller critical gap distance as a result of the surface roughness effect. The proposed method is then employed to investigate the effect of the critical gap distance of the lubrication force saturation on the motion mode (i.e., separation size) of the particle in the DLD device. Our results indicate that the lubrication force saturation is important to the particle critical separation size, and a smaller saturation distance generally makes the particle more prone to the zigzag mode.

Modelling of Lubricated Electrical Contacts

Electrical contacts, although critically important for a wide range of applications, are susceptible to degradation due to fretting corrosion, especially when sliding and vibrations occur. To overcome fretting corrosion and sliding wear, lubricants are often used. However, the use of lubricants can cause other detrimental issues. Lubricants usually consist of non-conductive fluids such as hydrocarbons and fluorocarbons. Due to fluid dynamics, when sliding, vibration or other excitation occurs, these fluids can cause prolonged gaps between the conducting metal surfaces. Practically, this has been observed in data centers where vibrations due to technician maintenance or even earthquakes can occur. Depending on the viscosity and roughness of the surfaces, the time it takes these connector surfaces to return to solid conductive contact can be many seconds or longer. This work uses a novel theoretical model of the coupled fluid and solid mechanics between the rough metallic surfaces to evaluate these intermittent breaks in contact due to sliding. The influence of variation in lubricant properties, roughness, contact radius and contact force are considered by the model.

A simple and efficient parallel immersed boundary-lattice Boltzmann method for fully resolved simulations of incompressible settling suspensions

This study presents an efficient and parallel fully resolved direct numerical simulation (FR-DNS) of settling suspensions on multiple CPU cores based on the boundary-thickening direct forcing immersed boundary method (BTDF-IBM) and incompressible lattice Boltzmann method (LBM). The simple BTDF-IBM is used to meet the no-slip and no-penetration conditions on particle boundaries, and the incompressible LBM is used to achieve the capability of large pressure fluctuations in suspensions. In addition, a theoretical force model is used to compensate for the unresolved lubrication force between the two approaching particles. A swap strategy for the streaming step is used to reduce the memory storage of the LBM particle density functions to half. A distribution and communication strategy is proposed to handle the IBM computing and complete the immersed boundary (IB) force of the particles residing in the interface region between adjacent subdomains. The developed BTDF-IBM-LBM solver “PFlows” can simulate large particle-laden flows with more than O(106) particles and with a particle volume fraction of up to 0.4. An almost linear parallel speedup and efficiency of higher than 0.8 are obtained by testing three-dimensional (3D) cases (up to 1.0 billion fluid grids and 0.45 million particles) and two-dimensional (2D) cases (up to 1.2 billion fluid grids and 2.39 million particles). Finally, the framework is applied to three large-scale real simulations involving 50,000 particles settling in 2D and 3D bounded and unbounded domains for qualitative and quantitative validations. The particle settling behaviors and disturbed complex fluid flows in the vertical channel are demonstrated. The Boycott effect in the inclined channel is uncovered by a new mechanism that combines particle sliding at the lower sidewall with fluid convection in the upper region. The hindered settling of particles in the 3D periodic domain, which is affected by the strong particle-fluid hydrodynamic interactions and particle-particle many-body interactions at a high solid volume fraction, are analyzed. The complex behaviors and statistical characteristics of the suspensions are preliminarily revealed and analyzed, which demonstrates the prospective capability of the present framework for FR-DNS of large-scale 2D and 3D suspension flows that are relevant to many industrial applications by IB-LBM.

Local deformation and coalescence between two equal-sized droplets in a cross-focused microchannel

• Three flow patterns of head-on coalescence of droplets are observed. • Effects of viscosity ratio and surfactant are explored. • Local nipple of droplet is conductive to coalescence. • Influence factors of the nipple are investigated systematically. • A novel model and a predictive equation of the nipple are proposed. The local deformation and the head-on coalescence dynamics of droplets in a cross-focused microchannel are experimentally investigated. The dynamic process of droplets after collision is divided into squeezing stage and decompressing stage, and the flow patterns are divided into squeezing coalescence, decompressing coalescence and non-coalescence based on the moment when the liquid film ruptures. The local nipples caused by the lubrication force in the thin film arise in the decompressing stage and facilitate coalescence. The effects of the dispersed to continuous-phase viscosity ratio and the concentration of surfactant to the dynamic process, operating range of each flow pattern, and the extent of local deformation are investigated, and the predictive equation of the nipple angle is proposed. This research combines the local deformation with coalescence and provides a reference for further understanding the mechanism of droplet coalescence.

Dynamic stiffness and vibration analysis model of angular contact ball bearing considering vibration and friction state variation

Force and thermal effect are dominant in giving rise to variation of bearing dynamic stiffness and vibration. On the basis of test and theoretical analysis, the dynamic stiffness and vibration model of angle contact ball bearing considering vibration and friction state variation is established. Firstly, based on the quasi-statics of bearing and hydrodynamic lubrication theory, the motion and force relation between each parts are determined by considering the force and thermal effect. Secondly, the friction power consumption of bearing is calculated adopting integrated method, besides, the conduction heat resistance and convection heat resistance in the bearing system are achieved. A steady-state temperature calculation model of angle contact ball bearing-shaft-house system is built based on thermal network method. Finally, the dynamic stiffness and vibration model of angular contact ball bearing including the thermal-solid coupling effect is obtained, which is employed to realize the theoretical analysis of bearing dynamic stiffness and vibration, its accuracy is verified through typical test results. The calculation results shows that there is a good agreement between house test temperature and calculation temperature. The evolution rule of contact deformation and contact stiffness between ball and outer/inner ring over the whole life under excessive preload is the same. So does the oil film thickness and oil film stiffness. However, the curve shape and amplitude of contact angular between ball and outer/inner ring over the whole life is different. Bearing radial stiffness value has a more significant change than axial stiffness value, both of them represent an overall upward tendency. The radial clearance holds a negative correlation with house temperature, however, the radial displacement has a positive correlation with house temperature. The evolvement curve of contact angular affected by various preload and speed is opposite. The contact load between ball and outer/inner ring has the same trend influenced by preload and speed with EHL. The variation of preload has bigger effect on temperature rise than speed change. The oil film has little influence on contact angular, contact load and temperature under dry-lubricated or lightly lubricated condition.

An Eulerian-based immersed boundary method for particle suspensions with implicit lubrication model

We describe an immersed boundary method in which the fluid–structure coupling is achieved in an Eulerian framework. The method is an improved extension of the immersed boundary method originally developed by Kajishima et al. (2001), which accounts for the inertia of the fictitious fluid inside the particle volume and is thus able to reproduce the behavior of particles both in the case of neutrally-buoyant objects and in the presence of density difference between the particles and the fluid. The method is capable to handle the presence of multiple suspended objects, i.e., a suspension, by including a soft-sphere normal collision model, while the lubrication correction typically added to similar immersed boundary methods in order to capture the sub-grid unresolved lubrication force is here treated implicitly, i.e., naturally obtained without any explicit expression, thus no additional computation is required. We show that our methodology can successfully reproduce the rheology of a particle suspension in a shear flow up to a dense regime (with a maximum particle volume fraction around 46%) without any additional correction force. The applicability of this methodology is also tested in a turbulent pressure-driven duct flow at high Reynolds number in the presence of non-negligible inertia and non-uniform shear-rate, showing good agreement with experimental measurements.

A Review on Contact and Collision Methods for Multi-Body Hydrodynamic Problems in Complex Flows

Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the combustion process, to aerosol deposition in spray medication, along with many others. Due to their strongly nonlinear and multiscale nature, the above complex phenomena still raise a very steep challenge to the most computational methods. In this review, we provide comprehensive coverage of multibody hydrodynamic (MBH) problems focusing on particulate suspensions in complex fluidic systems that have been simulated using hybrid Eulerian-Lagrangian particulate flow models. Among these hybrid models, the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) provides mathematically simple and computationally-efficient algorithms for solid-fluid hydrodynamic interactions in MBH simulations. This paper elaborates on the mathematical framework, applicability, and limitations of various 'simple to complex' representations of close-contact interparticle interactions and collision methods, including short-range inter-particle and particle-wall steric interactions, spring and lubrication forces, normal and oblique collisions, and mesoscale molecular models for deformable particle collisions based on hard-sphere and soft-sphere models in MBH models to simulate settling or flow of nonuniform particles of different geometric shapes and sizes in diverse fluidic systems.

Viscous peeling of a nanosheet.

Combining molecular dynamics (MD) and continuum simulations, we study the dynamics of propagation of a peeling front in a system composed of multilayered graphene nanosheets completely immersed in water. Peeling is induced by lifting one of the nanosheet edges with an assigned pulling velocity normal to the flat substrate. Using MD, we compute the pulling force as a function of the pulling velocity, and quantify the viscous resistance to the advancement of the peeling front. We compare the MD results to a 1D continuum model of a sheet loaded with modelled hydrodynamic loads. Our results show that the viscous dependence of the force on the velocity is negligible below a threshold velocity. Above this threshold, the hydrodynamics is mainly controlled by the viscous resistance associated to the flow near the crack opening, while lubrication forces are negligible owing to the large hydrodynamic slip at the liquid-solid boundary. Two dissipative mechanisms are identified: a drag resistance to the upward motion of the edge, and a resistance to the gap opening associated to the curvature of the flow streamlines near the entrance. Surprisingly, the shape of the sheet was found to be approximately independent of the pulling velocity even for the largest velocities considered.

Microstructure of the fluid particles around the rigid body at the shear-thickening state toward understanding of the fluid mechanics

We studied the shear-thickening behavior of systems containing rigid spherical bodies immersed in smaller particles using non-equilibrium molecular dynamics simulations. We generated shear-thickening states through particle mass modulation of the systems. From the microstructures, i.e., two-dimensional pair distribution functions, we found anisotropic structures resulting from shear thickening, that are explained by the difference between the velocities of rigid bodies and fluid particles. The increasing viscosity in our system originated from collisions between fluid particles and rigid bodies. The lubrication forces defined in macroscale physics are then briefly discussed.

Dynamic modeling and responses investigation of spatial parallel robot considering lubricated spherical joint

Lubricated spherical joint is widely used in spatial parallel robots, which significantly influences the dynamic response of the mechanism. Current research of mechanism dynamics considering lubricated kinematic joint mainly focuses on the plane mechanism with revolute joint, while that involves lubricated spherical joint of spatial mechanism is very few, especially, spatial parallel robot has not been reported. Dynamic modeling and responses investigation of spatial parallel robot considering lubricated spherical joint is realized in this paper. Combined with Reynolds' equation and Gumbel's boundary condition, dynamic modeling method of spatial parallel robot with lubricated spherical joint is proposed. The dynamic model of 4-UPS/RPS parallel robot with lubricated spherical joint is developed. Lubrication force model has been improved to provide better numerical stability for spatial parallel robots. The influences of lubricated joint and dry contact joint on dynamic response of the parallel robot are simulated by adjusting clearance size and driving speed. Results demonstrate that contact-impact at clearance joint is closely related to impact response of moving platform, and lubricated joint effectively weakens this effect. The deviation degree of acceleration is weak when clearance size is less than 0.4 mm, which means that the robot has good performance. It is of great significance to investigate influences of lubricated spherical joint on performance of parallel robots for dynamic prediction and structural optimization design of the system.

Gravitational collision efficiencies of small viscous drops at finite Stokes numbers and low Reynolds numbers

Collision efficiencies are calculated for two sedimenting spherical drops of different radii with internal circulation under conditions such that drop inertia can be significant while the surrounding fluid inertia remains negligible. A trajectory analysis is employed with exact methods for determining the hydrodynamic forces. When the Reynolds number is small, fluid inertia is negligible, and the hydrodynamic forces are linear functions of the velocities of the drops. However, at nonzero Stokes numbers, drop inertia must be taken into account, and the hydrodynamic forces do not balance the applied forces. For drops in close approach, lubrication forces, slip and attractive molecular forces are considered. Comparison is made between the effects of unretarded and retarded van der Waals forces and Maxwell slip on collision efficiencies. Slip is calculated exactly for viscous drops using bispherical coordinates for motion along the drops’ line of centers. For water droplets in air, at drop radii between 10 and 30μm, drop inertia is important while the Reynolds based on the surrounding air is still small. The collision efficiency goes through a minimum and then approaches the Smoluchowski limit of no hydrodynamic interactions as the drop size and Stokes number become increasingly large. Viscous effects are most important at drop radii of about 15μm. For drops with a radius less than 10μm, the most significant factors are unretarded van der Waals forces, Maxwell slip, and retarded van der Waals forces, respectively. When van der Waals forces and slip are combined, the collision efficiencies for drops with radii of 10μm are significantly greater than the results of previous researchers. At an intermediate drop radius of 20μm, surrounding fluid inertia, as considered in earlier work, appears to lead to greater collision efficiencies at intermediate size ratios, while van der Waals forces, incorporated in the present study, cause larger values at smaller and larger size ratios. At a drop radius of 30μm, drop inertia dominates interactions, and similar results occur for both the current and prior investigations. Since temperature affects both density and viscosity, collision efficiencies can differ by a factor of two or more between 0 °C and 100 °C at certain drop radii. Change in the viscosity ratio itself leads to about a 7% difference in the collision efficiency between drops with internal circulation and solid spheres at room temperature.

Nonlinear dynamic behavior analysis of multi-linkage mechanism with multiple lubrication clearances

Clearance exists in mechanical equipment, which aggravates the friction and wear in moving pairs and reduces the use accuracy of mechanism. So as to reduce the impact of clearance on industrial equipment, lubricating oil is usually added to the clearance of moving pair. The lubricating oil can effectively reduce the collision and vibration between components and reduce noise. Previous studies mainly concentrated on the research of dry clearance joints, but less on clearance lubrication. At the same time, there is little research on nonlinear characteristic of lubrication clearance. For the sake of studying the impact of lubrication clearance with multiple revolute joints on mechanical system, the dynamic response and nonlinear characteristic of planar six-bar linkage are analyzed. The movement model of lubrication clearance is developed, and lubrication force of lubrication clearance is modeled by modified Pinkus–Sternlicht model. Dynamical model of lubrication clearance of planar six-bar linkage is established by Lagrange multiplier method. The impacts of lubrication, viscosity coefficient, clearance value and driving speed on dynamic of mechanism with lubrication clearance are explored. By drawing bifurcation diagram, phase trajectory diagram and Poincare map, the nonlinear characteristic of mechanism with lubrication clearance is studied.

Experimental Study on the Behavior of Single Rising Bubbles in a Confined Rectangular Channel

The influence of the walls on the dynamics of single bubbles rising through a vertical water channel was experimentally investigated by using the shadowgraph technique. A tank equipped with two moving glass sheets was used to vary the internal section of the container. The obtained wall-to-wall distances ranged between 3.5 and 80 mm. Bubbles with sizes in the range of 1.2 mm to 3.6 mm were employed. The terminal velocities of the bubbles, their shapes and paths were analyzed for the different channel widths. The distance between walls (GAP) to bubble diameter ratio (D), leads to GAP/D values of 1.1 to 58. In order to classify a system as confined or non-confined, the deformation degree of the bubbles and terminal velocities were observed and analyzed. The aspect ratio of the bubbles begins to decay at a 12-mm gap, but for the 8.5-mm gap the bubble terminal velocity decays drastically. The inertial criterion was selected as a limiting value to define a confined system. The velocity reduction for smaller gaps is a result of the increased drag due to stronger bubble-wall interactions. Moreover, these interactions induce larger shear stresses over the surfaces of the bubbles, which together with the wall lubrication forces are responsible for the small deformations of the bubbles. The attractive lift force caused by the presence of the walls is responsible for a zigzag path for low inertial regimes (Re∼200). These instabilities also contribute to vortex shedding and more oscillating trajectories. In addition, velocity and drag coefficient correlations were proposed as functions of the confinement parameter.