Small Density Ratio Research Articles

Numerical investigation of the influence of surface wettability on water entry of spheres

The water-entry problem is a complex multiphase hydrodynamic problem that is directly related to many engineering applications and natural phenomena, such as torpedo airdrops, seaplane landings, and ship slamming. Therefore, studying the influence of the microscopic properties of the object surface on the macroscopic phenomenon during water entry is necessary. In this study, the volume of fluid model and continuum surface force models are coupled to establish a multiphase flow numerical method for the water entry of objects considering surface wettability. The effect of surface wettability on the evolution of the cavity, multiphase flow-field structure, and hydrodynamic force characteristics are analyzed in detail. The results show that the movement of liquid film formed on the surface of the sphere at the early stage is the key to the formation of the cavity. For hydrophobic spheres, the liquid film separates near the equator of the sphere, and air enters it to form a cavity. At the moment of pinch-off, the pressure in the lower cavity increases, which generates a force that pushes the sphere to accelerate the fall, and this force is higher for spheres with a smaller density ratio. The flow-field structure shows that both rotational and shear effects play a dominant role in the evolution of the flow field in the cavity. For hydrophilic spheres, the liquid film follows the contact line along the surface of the sphere and converges at the top to form an upward jet.

A two-way coupling method for simulating wave-induced breakup of ice floes based on SPH

In this paper, a new numerical method for simulating the breakup of ice floes in water waves will be presented. The method is based on Smoothed Particle Hydrodynamics (SPH) but several new numerical techniques are developed to address the challenges associated with wave-ice interaction including breakup. One of them is the new interaction model for fluid-ice interaction, which is not only suitable for small density ratio but also for large density ratio. This model may also be employed by other methods for dealing with general fluid-structure integration. In addition, a technique for modelling the separation of broken ice pieces is developed. Apart from these, a treatment is proposed to rectify the problem caused by unequal time steps in simulating ice and fluid, which is necessary for achieving higher computational efficiency. The numerical method is validated by comparing the numerical results with the experimental data available in literature, which shows that the agreement between them is satisfactory. On this basis, the breakup of ice floes induced by solitary waves and focused waves are studied. To the best of knowledge of the authors, it is the first method which can simulate the ice breaking in waves by two-way coupling approach. The results for ice breaking in solitary and focused waves have not been found so far in previous publications available in literature.

Air/water interfacial waves with a droplet at the tip of their crest

In nature, it is common to observe water wave crests with a droplet at their tip. This fascinating configuration remains unexplained from the physical point of view. The present study explores such a unique local configuration numerically. Solitary waves that propagate at the interface between two layers of irrotational fluids are considered. Extending the work of Guan et al. [“A local model for the limiting configuration of interfacial solitary waves,” J. Fluid Mech. 921, A9 (2021)], the density ratio has been decreased to a very small value equal to 0.001, which is close to the air/water density ratio at sea level (0.0013). A highly accurate solution for the limiting configuration of solitary waves is obtained by solving the irrotational Euler equations using the boundary integral method and Newton's iterations. It is confirmed that the limiting configuration consisting of a droplet sitting on a crest with a 120° angle exists for very small density ratios. This limiting configuration obviously does not exist for surface waves with a void on the top, thus stressing the crucial role played by the air. The droplet is stationary in a frame of reference moving with the wave and experiences intense shear at its tip. From the energy point of view, the formation of a crest with a droplet is accompanied by a remarkable drop of kinetic and potential energies of water in the vicinity of the crest. Furthermore, we present a simple set of scaling relations for the fall of the droplet.

On the energy transport and heat transfer efficiency in radiatively heated particle-laden Rayleigh–Bénard convection

We investigate the energy transport and heat transfer efficiency in turbulent Rayleigh–Bénard (RB) convection laden with radiatively heated inertial particles. Direct numerical simulations combined with the Lagrangian point-particle mode were carried out in the range of density ratio $854.7\le \rho _p/\rho _0 \le 8547$ and radiation intensity $1\le \phi /\phi _{solar}\le 100$ for both two-dimensional (2-D) and three-dimensional (3-D) simulations. The Rayleigh number ranges from $2\times 10^6$ to $10^8$ for 2-D cases, and is $10^7$ for 3-D cases for $Pr=0.71$ . It is found that particles with small density ratio that encounter strong radiation significantly alter the flow momentum transport and fluid heat transfer, so the fluid temperature of bulk is remarkably heated. We then derived the theoretical relation of the Nusselt number for interphase heat transfer in the heated particle-laden RB convection, which reveals that the heat transfer difference between the top and bottom plates stems from the interphase heat transfer. We further found that both the interphase heat transfer and the interphase thermal energy transport exhibit universal properties. They are both increased linearly with the reciprocal of the normalized density ratio. Additionally, both the interphase heat transfer and the interphase thermal energy transport increase linearly with the increase of radiation intensity. The growth rates exhibit specific scaling relations versus Rayleigh number and density ratio. Two different regimes distinguished by the critical density ratio, i.e. the exothermic particle regime and the endothermic particle regime, are observed. We further derived the power-law relation of the critical density ratios versus Rayleigh number and radiation intensity, i.e. $\rho _p/\rho _c \sim (\phi /\phi _{solar})^{1/2}\,Ra^{1/3}$ , which is in remarkable agreement with the 3-D simulations.

Performance investigation of a novel thermosyphon based trilateral cycle using hydraulic turbine for power generation instead of two-phase expander

The trilateral cycle (TLC) has been viewed as a promising technology for low grade heat to power conversion, while its application in reality is greatly limited by the low efficiency of two-phase expander and high volume flow rate at the expander outlet. This paper suggests a novel thermosyphon based trilateral cycle (TTLC), which uses hydraulic turbine for power generation instead of two-phase expander, avoiding problems in traditional TLC systems and also providing a chance for utilization of pump-as-turbine (PAT) technologies. Thermodynamic model of the novel system is developed, as well as the two-phase flow model for the riser. The system performance of TTLC is investigated based on the first law analysis and the second law analysis, and the results are compared with those of traditional TLC and organic Rankine cycle (ORC). It is found that the extra gravitational pressure drop is the main contributor to the riser efficiency. The working fluids with smaller density ratio and specific heat are more suitable for the proposed system, such as R502, R218, R125 and R115. Increasing heat source temperature is more efficient in energy conversion than decreasing sink temperature for the TTLC system, which generates marginally more power than TLC when the heat source temperature is less than 50 °C, and less power than TLC within the deviation of 10% for the heat source temperature in the range of 50–75 °C. The traditional ORC has the worst performance due to its bad temperature matching. Moreover, the volume flow rate at the turbine outlet of TTLC is only 2–17% of those for TLC and ORC, indicating a much smaller turbine size.

Weak Damping of Propagating MHD Kink Waves in the Quiescent Corona

Abstract Propagating transverse waves are thought to be a key transporter of Poynting flux throughout the Sun’s atmosphere. Recent studies have shown that these transverse motions, interpreted as the magnetohydrodynamic kink mode, are prevalent throughout the corona. The associated energy estimates suggest the waves carry enough energy to meet the demands of coronal radiative losses in the quiescent Sun. However, it is still unclear how the waves deposit their energy into the coronal plasma. We present the results from a large-scale study of propagating kink waves in the quiescent corona using data from the Coronal Multi-channel Polarimeter (CoMP). The analysis reveals that the kink waves appear to be weakly damped, which would imply low rates of energy transfer from the large-scale transverse motions to smaller scales via either uniturbulence or resonant absorption. This raises questions about how the observed kink modes would deposit their energy into the coronal plasma. Moreover, these observations, combined with the results of Monte Carlo simulations, lead us to infer that the solar corona displays a spectrum of density ratios, with a smaller density ratio (relative to the ambient corona) in quiescent coronal loops and a higher density ratio in active-region coronal loops.

Phase-field-based lattice Boltzmann model for ternary fluid flows considering the wettability effect

A phase-field-based lattice Boltzmann model for ternary fluid flows is proposed, where the conservative Allen-Cahn equation for ternary fluids is used to track the interface of fluids. A time derivative term is introduced into the lattice Boltzmann equation for the conservative Allen-Cahn equation and a forcing distribution function is used in the lattice Boltzmann equation for the Navier-Stokes equations. The computational accuracy and capability of the proposed model are verified by benchmark cases related to stationary droplets, spreading of a liquid lens, and phase separation of a ternary fluid mixture. Moreover, a wetting boundary scheme based on the framework of the lattice Boltzmann method applicable to ternary fluid flows is developed. This model performs well in eliminating the undesired numerical artifact after consideration of the wettability effect. Typical wettability problems are simulated to verify the applicability of the wetting boundary scheme, including the spreading of binary droplets and compound droplets on a surface. The numerical results for static contact angles and spreading length show a good fit of the data to the theoretical results within the scope of permissible error. Furthermore, the reliability of this wetting boundary condition for the dynamic case is verified by our modeling the motion of compound droplets subjected to shear flow on a substrate. This boundary scheme performs well for the motion of ternary fluids with a small density ratio and a large density ratio. In conclusion, the phase-field-based lattice Boltzmann model for ternary fluid flows considering the wetting effect has good applicability for modeling ternary fluid flows with a density ratio of 1000.

Pre-impact dynamics of a droplet impinging on a deformable surface

The nonlinear interaction between air and a water droplet just prior to a high-speed impingement on a surface is a phenomenon that has been researched extensively and occurs in a number of industrial settings. The role that the surface deformation plays in an air cushioned impact of a liquid droplet is considered here. In a two-dimensional framework, assuming small density and viscosity ratios between the air and the liquid, a reduced system of integrodifferential equations is derived governing the liquid droplet free-surface shape, the pressure in the thin air film, and the deformation of the surface, assuming the effects of surface tension, compressibility, and gravity to be negligible. The deformation of the surface is first described in a rather general form, based on previous membrane-type models. The coupled system is then investigated in two cases: a soft viscoelastic case where the surface stiffness and (viscous) damping are considered and a more general flexible surface where all relevant parameters are retained. Numerical solutions are presented, highlighting a number of key consequences of surface deformability on the pre-impact phase of droplet impact, such as reduction in pressure buildup, increased air entrapment, and considerable delay to touchdown. Connections (including subtle dependence of the size of entrapped air on the droplet velocity, reduced pressure peaks, and droplet gliding) with recent experiments and a large deformation analysis are also presented.

A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction

This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are benchmarked using a range of test cases and demonstrated using large-scale models of biomedical FSI. The numerical approach developed herein, which we refer to as an immersed Lagrangian-Eulerian (ILE) method, integrates aspects of partitioned and immersed FSI formulations by solving separate momentum equations for the fluid and solid subdomains, as in a partitioned formulation, while also using non-conforming discretizations of the dynamic fluid and structure regions, as in an immersed formulation. A simple Dirichlet-Neumann coupling scheme is used, in which the motion of the immersed solid is driven by fluid traction forces evaluated along the fluid-structure interface, and the motion of the fluid along that interface is constrained to match the solid velocity and thereby satisfy the no-slip condition. To develop a practical numerical method, we adopt a penalty approach that approximately imposes the no-slip condition along the fluid-structure interface. In the coupling strategy, a separate discretization of the fluid-structure interface is tethered to the volumetric solid mesh via stiff spring-like penalty forces. Our fluid-structure coupling scheme relies on an immersed interface method (IIM) for discrete geometries, which enables the accurate determination of both velocities and stresses along complex internal interfaces. Numerical methods for FSI can suffer from instabilities related to the added mass effect, but computational tests indicate that the methodology introduced here remains stable for selected test cases across a broad range of solid-fluid mass density ratios, including extremely small, nearly equal, equal, and large density ratios. Biomedical FSI demonstration cases include results obtained using this method to simulate the dynamics of a bileaflet mechanical heart valve in a pulse duplicator, and to model transport of blood clots in a patient-averaged anatomical model of the inferior vena cava.

Performance Investigation of a Novel Thermosyphon Based Trilateral Cycle Using Hydraulic Turbine for Power Generation Instead of Two-Phase Expander

The trilateral cycle (TLC) has been viewed as a promising technology for low grade heat to power conversion, while its application in reality is greatly limited by the low efficiency of two-phase expander and high volume flow rate at the expander outlet. This paper suggests a novel thermosyphon based trilateral cycle (TTLC), which uses hydraulic turbine for power generation instead of two-phase expander, avoiding problems in traditional TLC systems and also providing a chance for utilization of pump-as-turbine (PAT) technologies. The system performance of TTLC is theoretically investigated, and the results are compared with those of traditional TLC and ORC. It is found that the slip loss is the main contributor to the riser efficiency. The working fluids with smaller density ratio and specific heat are more suitable for TTLC. TTLC generates more power than TLC when the heat source temperature is less than 50 °C, and less power than TLC within the deviation of 10% for the heat source temperature in the range of 50-75 °C. Moreover, the volume flow rate at the turbine outlet of TTLC is only 2-17% of those for TLC and ORC, indicating a much smaller turbine size.

Experimental investigation on the effect of hole diameter on the leading edge region film cooling of a twist turbine blade under rotation conditions

Film cooling performance on the twist turbine blade leading edge (LE) model has been experimentally investigated employing the thermochromic liquid crystal (TLC) technology under rotation conditions. The novelty of this paper is the earlier study on the effect of film hole diameter (d = 0.4 mm and 0.5 mm) on the LE region of a rotating twist blade. The effects of blowing ratio (M) and density ratio (DR) were also considered. M ranged from 0.5 to 2.0 when DR = 1.56 and M ranged from 0.5 to 1.25 when DR = 1.04. The whole experiment was conducted at the rotating speed of 574 r/min with the Reynolds number of 63,400. Results show that the film hole diameter of leading edge has a significant effect on the spanwise average film cooling effectiveness. The spanwise effectiveness provided by the larger DR (1.56) increases with increasing hole diameter in the whole range of −4.3d to 3.75d at M = 0.5, 1.0 and 1.5. When DR = 1.56, the spanwise effectiveness increases monotonically with increasing blowing ratio in the whole range of −4.3d to 3.75d under the condition of d = 0.4 mm case, and it increases first and then descends with increasing blowing ratio in the whole range except −3.3d to −0.5d with the best M = 1.5 under the condition of d = 0.5 mm case. The area average film cooling effectiveness provided by the larger DR (1.56) is higher than that provided by the smaller DR (1.04) when M = 0.5 and 1.0 for the d = 0.5 mm case. More results on the influence of hole diameter, blowing ratio and density ratio are shown in this paper.

Kinetic Analysis of the Energy Transport of Two‐Flow Components in the Plasma Sheet

AbstractSatellite observations indicate that multiple components often exist in the plasma sheet, particularly during impulsive fast flow events. In this paper, we perform a kinetic analysis of the energy transport of plasma sheet ion flow using a model of two‐component plasma sheet ion flows (Background convection flow represented by subscript “b” and Fast flow represented by subscript “f”) and compare the energy transport calculated by kinetic approach Qk with those obtained from magnetohydrodynamic (MHD) approach QMHD. The ratio of Qk/QMHD is always larger than unity and is positively proportional to the ratios of Vf/Vb and Tf/Tb. The maximum values of Qk/QMHD occur in the low‐speed ranges (i.e., small density ratio Nf/N). When Nf/N exceeds 0.4, the ratio of Qk/QMHD is almost the same for a wide parameter ranges of Vf, Tf, and Vb. Heat flux is important in low‐speed range and is neglectable in the high‐speed range. The adiabatic polytropic index 5/3 cannot correctly describe energy transport rate. A density ratio Nf/N of 0.3% of high‐speed ion flow can make the effective polytropic index obviously deviate from adiabatic polytropic index (5/3). The above theoretic results can well explain previously reported satellite in situ observations.

Path instabilities of oblate spheroids

In the present paper, we investigate the path instabilities and the transition scenario for oblate homogeneous spheroids falling (or ascending) freely in a quiescent and unconfined Newtonian fluid under the action of gravity, buoyancy and hydrodynamic forces. The problem depends on three independent external parameters: the aspect ratio $\unicode[STIX]{x1D712}=d/a$, where $d$ is the diameter and $a$ the length of the axisymmetry axis of the spheroid; the non-dimensionalized mass $m^{\ast }=m/(\unicode[STIX]{x1D70C}d^{3})$, $m$ being the mass of the spheroid and $\unicode[STIX]{x1D70C}$ the fluid density; and the Galileo number, defined as $G=\sqrt{(m^{\ast }-V^{\ast })gd^{3}}/\unicode[STIX]{x1D708}$. In the definition of the Galileo number, $V^{\ast }=V/d^{3}$ is the non-dimensionalized volume, $g$ the gravitational acceleration and $\unicode[STIX]{x1D708}$ is the kinematic viscosity. Asymptotic solutions (regimes) are investigated in seven $\unicode[STIX]{x1D712}=\text{const}.$ parameter planes going from $\unicode[STIX]{x1D712}=10$ (very flat spheroid) to $\unicode[STIX]{x1D712}=1.1$ (an almost spherical shape), for $m^{\ast }$ going from 0 to 5 and Galileo numbers up to 300 (i.e. Reynolds numbers roughly up to 500). The obtained results provide a link between the known scenario of a homogeneous disk and that, well known, of a sphere. The scenario of the flat spheroid of aspect ratio 10 has many common features with that of an infinitely thin disk, but the finite thickness brings about significant quantitative differences. At the opposite side of the investigated aspect ratio interval, the dynamics of the spheroid of aspect ratio 1.1 is found very close to that of a perfect sphere except for small density ratios (smaller than approximately 0.5). Very light spheroids of aspect ratio 1.1 move along vertical zig-zagging trajectories. At intermediate aspect ratios, the strong subcritical effects and the characteristic zig-zagging and fluttering motion, typical for flat bodies, progressively disappear. The tumbling regime remains remarkably stable and is shown to be present down to $\unicode[STIX]{x1D712}=2$. An interesting result consists in the evidence of the first two bifurcations typical for the sphere scenario (leading to steady oblique and oblique oscillating trajectories) present both for very flat and thick spheroids but absent at intermediate aspect ratios. The results pertaining to spheroids might be more useful in practical applications than those obtained for too idealized thin disks and perfect spheres.

Impact of red giant/AGB winds on active galactic nucleus jet propagation

Dense stellar winds may mass-load the jets of active galactic nuclei, although it is unclear what are the time and spatial scales in which the mixing takes place. We study the first steps of the interaction between jets and stellar winds, and also the scales at which the stellar wind may mix with the jet and mass-load it. We present a detailed two-dimensional simulation, including thermal cooling, of a bubble formed by the wind of a star. We also study the first interaction of the wind bubble with the jet using a three-dimensional simulation in which the star enters the jet. Stability analysis is carried out for the shocked wind structure, to evaluate the distances over which the jet-dragged wind, which forms a tail, can propagate without mixing with the jet flow. The two-dimensional simulations point at quick wind bubble expansion and fragmentation after about one bubble shock crossing time. Three-dimensional simulations and stability analysis point at local mixing in the case of strong perturbations and relatively small density ratios between the jet and the jet dragged-wind, and to a possibly more stable shocked wind structure at the phase of maximum tail mass flux. Analytical estimates also indicate that very early stages of the star jet-penetration time may be also relevant for mass loading. The combination of these and previous results from the literature suggest highly unstable interaction structures and efficient wind-jet flow mixing on the scale of the jet interaction height, possibly producing strong inhomogeneities within the jet. In addition, the initial wind bubble shocked by the jet leads to a transient, large interaction surface. The interaction structure can be a source of significant non-thermal emission.

Numerical investigation of rising bubbles bursting at a free surface through a multiphase SPH model

As a Lagrangian meshless method, smoothed particle hydrodynamics (SPH) method is robust in modelling multi-fluid flows with interface fragmentations. However, the application for the simulation of a rising bubble bursting at a fluid surface is rarely documented. In this paper, the multiphase SPH model is extended and applied to simulate this challenging phenomenon. Different numerical techniques developed in different SPH models are combined in the present SPH model. The adoption of a background pressure determined based on the surface tension can help to avoid tensile instability and interface penetrations. An accurate surface tension model is employed. This model is suitable for bubble rising problems of small scales and high density ratios. An interface sharpness force is adopted to achieve a smoother bubble surface. A suitable formula of viscous force, which is proven to be able to accurately capture the bubble splitting and small bubble detachment, is employed. Moreover, a modified prediction-correction time-stepping scheme for a better numerical stability and allows a relatively larger CFL factor is adopted. It is also worthwhile to mention that the particle shifting technique, which helps to make the particle distribute in an arrangement of lower disorder, can significantly improve the numerical accuracy. Regarding the treatment of the fluid surface, particles of lighter phase are arranged above the free surface of the denser phase to avoid the kernel truncation in the density approximation. Furthermore, this technique also allows an accurate calculation of the surface tension on the fluid surface. A number of cases of bubbly flows are presented, which confirms the capability of the present multiphase SPH model in modelling complex bubble-surface interactions with the density ratio and viscosity ratio up to 1000 and 100 respectively.

Suppression of vortex-induced vibration of a circular cylinder using thermal effects

Transverse vortex-induced vibration (VIV) of a cylinder with various body-to-fluid density ratio and stiffness is studied. The cylinder is elastically mounted and heated, and the flow direction is aligned with the direction of the thermal induced buoyancy force. Amplitude of VIV can be reduced as the thermal control parameter Richardson number (Ri) increases, or even be fully suppressed when Ri is above a critical value. This critical Richardson number depends on both body-to-fluid density and structural stiffness. A higher critical Richardson is required to fully suppress the VIV of a structure with smaller density ratio. With the same density or mass, a structure with intermediate stiffness vibrating in lock-in regime needs higher critical Ri to suppress VIV than either rigid or flexible structures. Drag experienced by the body is also studied. It is found that for a flexible body, drag gradually increases with the Richardson number. For a body with intermediate stiffness, both drag and amplitude of VIV can be reduced until the Richardson number reaches the critical value, after which drag builds up if the Richardson number is further increased. A drag reduction of 30%–40% can be obtained at the critical Richardson number.

Magnetorotational instability of weakly ionized and magnetized electron-positron-ion plasma

The magnetorotational instability in a differential rotating weakly ionized and magnetized plasma consisting of electron, positron, ion, and neutral particles has been investigated by using the multi-fluid model. Satisfying the current neutrality and homogeneity of the system in the equilibrium state by assuming the same unperturbed angular velocity for charge species and neutrals, the general local dispersion relation (DR) has been derived by taking into account the collision effects. By analytical examination of the obtained DR in the arbitrary and high frequency regimes, the instability conditions have been found in which the presence of light positive species (positrons) plays an important role in the instability criteria. Moreover, numerical investigation shows the broadening of instability range as well as increasing the maximum growth rate of instability (especially for the small number density ratio of light to heavy positive species) in the presence of positrons. The obtained results of the present investigation will greatly contribute to the understanding of the particles' dynamics as well as dissipation mechanism in some astrophysical environments, such as the region of accretion disks surrounding the central of black holes and protoplanetary disks.

Spurious velocity from the cutoff and magnification equation in free energy-based LBM for two-phase flow with a large density ratio

The spurious velocity resulting from the cutoff and magnification equation in the free-energy-based one-component-two-phase flow lattice Boltzmann method (LBM) for a large density ratio proposed by Inamuro et al. [34] is investigated. In Inamuro’s model, the phase interface is tracked by the order parameter, which is the dimensionless density of a two-phase flow system with a small density ratio. The velocity field is calculated based on the density profile of a two-phase system with a large density ratio, which is derived from the order parameter profile through a sine type of cutoff and magnification equation; this velocity field is then used to drive the movement of a phase interface described by the order parameter. The implementation of the cutoff and magnification equation causes the density profiles in the two systems to differ from each other such that force balances across the interfaces break from the ideal state and lead to spurious velocity. Three measures: (1) the linear cutoff and magnification equation which equalizes the density profiles in the interface region, (2) a new scheme which enhances the smoothness of the density profile around the cutoff points in the large density ratio system and (3) a special method that increases the interface thickness of the large density ratio system are adopted to reduce the magnitude of the spurious velocity from the profile difference, respectively. We show that all of these measures can successfully reduce the magnitude of the spurious velocity to some degree; and the scheme that enhances the smoothness of the density profile around the cutoff points reduces the spurious velocity of the original scheme by one order of magnitude.

Contact angle adjustment in equation-of-state-based pseudopotential model

The single component pseudopotential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many studies, it has been claimed that this model can be stable for density ratios larger than 1000. However, the application of the model is still limited to small density ratios when the contact angle is considered. The reason is that the original contact angle adjustment method influences the stability of the model. Moreover, simulation results in the present work show that, by applying the original contact angle adjustment method, the density distribution near the wall is artificially changed, and the contact angle is dependent on the surface tension. Hence, it is very inconvenient to apply this method with a fixed contact angle, and the accuracy of the model cannot be guaranteed. To solve these problems, a contact angle adjustment method based on the geometry analysis is proposed and numerically compared with the original method. Simulation results show that, with our contact angle adjustment method, the stability of the model is highly improved when the density ratio is relatively large, and it is independent of the surface tension.

Particle dispersion in a partially filled rotating cylindrical tank

Particles-liquid flow involving a free surface in partially filled rotating cylindrical tank is common in chemical engineering, which attracts numerical studies on it in an effort to provide useful information for the design and optimization of operational conditions in the real application. However, the dynamics of particles dispersion in partially filled rotating cylindrical tank under small particles-liquid density ratio has not been fully understood by performing a reasonable 3D numerical simulation. A three-dimensional unsteady model of a solid–liquid dispersed flow involving a free surface has been developed and numerically analyzed to investigate the particle dispersion in a partially filled rotating cylindrical tank. In the model, the discrete element method (DEM) and the volume of fluid (VOF) method have been applied. The flow field and the particle dispersion process in a rotational cylindrical tank have been presented. The effects of the tank rotation speed and the liquid height on the dispersion behaviors of particles are examined and analyzed. The results indicate that vortexes have formed in the liquid phase that entrain the particles and induce their gradual dispersion throughout the entire region of the liquid phase. The average mass concentration of particles is high in the rotating-out side of the liquid phase and in the liquid–wall contact region, while it is low in the rotating-in side of the liquid phase and in the vortex generation region. In addition, as the rotation speed increases, the entrainment capability of the liquid phase has been enhanced, which improves the dispersion performance of the particles. The selection of an appropriate liquid height is beneficial for the enhancement of particle dispersion in a partially filled rotating cylindrical tank.