On the importance of material frame-indifference and lift forces in multiphase flows

In this paper, we discuss the importance of the Principle of Material Frame-Indifference, sometimes referred to as Objectivity, in multiphase flows. We first give a brief account of the formulation of a two-phase mixture and then indicate where and how this principle should be utilized. We will then give a brief review of the meaning of this principle in continuum mechanics and how it has been used in various fields of physics. We also give examples of frame-indifferent and frame-dependent constitutive relations which have been used in multiphase flow studies. The importance of lift forces is also discussed. Finally, we derive a general constitutive relation which is frame-invariant and general enough to be used in many applications.     

Influence of the lift force on the stability of a bubble column

This work investigates the role of the lift force for the stability of a homogeneous bubble column. Instabilities caused by the lift force may be one important reason for the transition from homogeneous to heterogeneous bubble column. On rising bubbles the lift force acts in a lateral direction, when gradients of the liquid velocity are present. Non-uniform liquid velocity fields may be induced if the gas fraction is not equally distributed, e.g. caused by local disturbances. This feedback mechanism is studied in the paper. It was found, that a positive lift coefficient (small bubbles) stabilizes the flow, while a negative coefficient (large bubbles) leads to unstable gas fraction distributions, and thus it favours the appearance of a heterogeneous bubble column regime. The turbulent dispersion force has always a stabilizing action, i.e., it partially compensates the destabilization induced by a negative lift coefficient. A stability analysis for a mono-dispersed system nevertheless showed, that influence of the lift force is much larger, compared to the influence of the turbulent dispersion force, if only bubble induced turbulence is considered. Thus, the stability condition is practically the positive sign of the lift force coefficient. The extension of the analysis to two bubbles classes, from which one being small enough to have a positive lift coefficient, results in a minimum fraction of small bubbles needed for stability. Finally a generalized criterion for N bubble classes and for a continuous bubble size distribution is given.     

Process intensification of particle separation by lift force in arc microchannel with bifurcation

The present study demonstrates a novel hydrodynamic lift force sieving attained in an arc microchannel with a bifurcation at the downstream end. The fluorescent polystyrene particles with diameter of 10 or 20 μm are dispersed in water or NaCl aqueous solutions so that the particles are completely neutrally buoyant, lighter or denser relative to medium. The slurry is fed into the arc microchannel whose radius, width and depth are 20 mm, 200 and 150 μm, respectively. The fluorescent trajectories of flowing particles are recorded at the bifurcation. It is found that the 20-μm particle is sharply focused to an equilibrium position somewhat distant from the outer wall regardless of the given density difference. As a result, all 20-μm particles report to the outer branch of bifurcation. On the other hand, the 10-μm particles dispersed mostly across the channel width are always recovered from the both branches. The results imply that the arc microchannel with a bifurcation will intensify the process of particle separation since the particles completely neutrally buoyant as well as denser and lighter particles can be simultaneously separated or classified without membrane. Finally, a separation process in a series of arc channels is proposed and the process efficiencies are discussed.     

Influence of the lift force closures on the numerical simulation of bubble plumes in a rectangular bubble column

Numerical Eulerian-Eulerian simulations of the unsteady gas-liquid flow in a centrally aerated two-dimensional bubble column were carried out in order to understand the effect of different formulations of the lift force coefficient (C_L) on the computational results. Three different values of the superficial gas velocity (U_G=2.4, 12.0 and 21.3 mm s⁻¹) that ensure the existence of different flow regimes were experimentally and computationally studied. The validation of the simulated results was based on visual observations and measurements of the global gas hold-up (ε_G) and the plume oscillation period (POP). The results presented reveal that, at U_G=12.0 and 21.3 mm s⁻¹, using C_L<0 results in under- and over-estimation of the ε_G and POP, respectively. On the other hand, taking C_L>0 does not affect the POP while it leads to increasingly higher ε_G values, which are different from those experimentally reported. At U_G=2.4 mm s⁻¹, the effect of the lift force is not so evident, although it slightly improves the prediction of experimental values. Particularly interesting is the case of C_L>0.4 at U_G=21.3 mm s⁻¹, producing a non-symmetric bubble plume oscillation. Since using Tomiyama's lift coefficient correlation does not improve the results, including the lift force into the simulation of bubble plumes is not recommended.     

Large-eddy simulation (LES) of the large scale bubble plume

A large-eddy simulation of gas-liquid flow in a large scale bubble plume is presented. The Euler-Euler approach is used to describe the equations of motion of the two phase flow. The sub-grid scale modeling is based on the Smagorinsky kernel. All the non-drag forces (turbulent dispersion force (only for RANS), virtual mass force, lift force) and drag force are incorporated in the model. Overall, predictions are in good agreement with the experimental data at higher measurement levels but discrepancies are observed in the region near the injector. The axial mean liquid velocity and gas velocity at all the measurement levels exhibit the expected Gaussian profiles and plume spreading. The predictions of gas void fraction, axial gas and liquid velocity are in good agreement with the experimental data except near the injector. Further, the detailed comparison of LES and RANS predictions along with experimental data is presented and discussed.     

CFD study of non-premixed swirling burners: Effect of turbulence models

This research investigates a numerical simulation of swirling turbulent non-premixed combustion. The effects on the combustion characteristics are examined with three turbulence models: namely as the Reynolds stress model, spectral turbulence analysis and Re-Normalization Group. In addition, the P-1 and discrete ordinate (DO) models are used to simulate the radiative heat transfer in this model. The governing equations associated with the required boundary conditions are solved using the numerical model. The accuracy of this model is validated with the published experimental data and the comparison elucidates that there is a reasonable agreement between the obtained values from this model and the corresponding experimental quantities. Among different models proposed in this research, the Reynolds stress model with the Probability Density Function (PDF) approach is more accurate (nearly up to 50%) than other turbulent models for a swirling flow field. Regarding the effect of radiative heat transfer model, it is observed that the discrete ordinate model is more precise than the P-1 model in anticipating the experimental behavior. This model is able to simulate the subcritical nature of the isothermal flow as well as the size and shape of the internal recirculation induced by the swirl due to combustion.     

浆体管道中大颗粒干涉力研究

为了研究输送大颗粒的垂直浆体管道中固体颗粒所受的干涉力,采用相关专家的实验数据,发现大颗粒垂直浆体管道中大颗粒受到的干涉力要大于小颗粒所受的干涉力。在此基础上,采用数据拟合方式给出了干涉力修正系数的表达形式。将得到的干涉力应用于管道中颗粒受力分析中,并运用在大颗粒垂直管道阻力损失的计算模型中,通过实验数据验证了干涉力对阻力的影响。     

Influence of normal contact force model on simulations of spherocylindrical particles

How the choice of elastic normal contact force model affects predictions from discrete element method simulations of spherocylindrical particles is investigated in this article. Three force models were investigated: (1) a Hertzian force model (HFM) which assumes a circular contact area; (2) a linear force model (LFM) with a constant stiffness; and (3) a modified HFM (MFM) that accounts for various contact areas and contact transitions. With the MFM, transitions between contact area types must be accounted for otherwise discontinuities in the contact force can occur. It is found that simple force models (HFM, LFM) can be substituted for more accurate force models if only force data and bulk properties are of interest. However, if more detailed contact information, such as contact area, contact overlap, contact duration, or collision frequency, are needed, for example, in population balance models and transient liquid bridge modeling, then a more accurate force model should be used. © 2018 American Institute of Chemical Engineers AIChE J, 64: 1986–2001, 2018     

Analytical solution for the problem of frictional-elastic collisions of spherical particles using the linear model

In the present paper, the problem of a frictional-elastic impact of two spheres is addressed with a novel approach. The set of equations arising from the linear model of the contact mechanics is analytically integrated considering the combined effects of the elastic and frictional mechanisms. The linear model is very commonly used in simulations based on the soft-sphere distinct element method (DEM) (Geotechnique 29 (1979) 47), where numerical methods are used for the integration of the equations of motion of the particles. The analytical approach presented in this work allows the examination of many important aspects related to the use of the linear model in dynamic simulation of multi-particle systems. The impact characteristics, in terms of the mechanisms governing the evolution of the force-displacement relation, can be classified in terms of the initial conditions, showing the same subdivision as that obtained with the more complex model of Maw et al. (Wear 38 (1976) 101). It is demonstrated how the values of many interesting variables at the end of the impact can be directly related to the impact initial conditions through a one-step calculation procedure. The model results of the tangential coefficient of restitution, rebound angles of the contact point and center of mass are validated with the experimental data on frictional-elastic collisions of Kharaz et al. (Powder Technol. 120 (2001) 281), showing, despite the simplicity of the considered model, an excellent agreement. However, it is demonstrated that the force evolution and time duration of the collisions strongly depend on the model parameters and can be improperly evaluated with incorrect material constants. Further analyses are carried out, for various impact angles, on the amount of energy loss due to the frictional mechanism. Also, an analysis of the direct influence of each model parameter on the properties of the particles at the end of the collision is carried out, with special emphasis on the normal elastic spring constant K_n. This helps clarifying why, in the literature, realistic macroscopic results were obtained even with very small values of K_n.     

Effect of particle orientation on the drag force in random arrays of prolate ellipsoids in low-Reynolds-number flows

Direct numerical simulations are performed to study the effect of particle orientation on flows through fixed random arrays of prolate ellipsoids at low Reynolds numbers. The Hermans orientation factor and Beta distribution are introduced to quantify the mean orientation and orientation deviation of the particles. The simulation results show that the effect of particle orientation is profound especially when the solid volume fraction and the aspect ratio are large. With the increase of Hermans orientation factors, the drag force decreases when the flow follows a reference direction defined by the average direction of all particles' semi-major axes, while increases when the flow is perpendicular to the reference direction. Comparisons show that the traditional drag force correlations for ellipsoidal particles significantly under-predict the drag force. Based on current simulation results, new drag relations are proposed for prolate ellipsoidal particles at arbitrary aspect ratios, Hermans orientation factors and solid volume fractions.     

Determination of the adhesion force between particles and a flat surface, using the centrifuge technique

By using a centrifuge technique, the influence of powdery material particle size on the adhesion force particle-surface was determined. In order to achieve this, the adhesion of phosphatic rock (ρ_p = 3.090 kg m^− 3) and of manioc starch particles (ρ_p = 1.480 kg m^− 3) on a steel surface were studied. A microcentrifuge that reached a maximum speed rotation of 14000 rpm and which contained specially designed centrifuge tubes was used. There tubes contained the flat surface where the test particles were deposited. The powder particles were dispersed on these disks and the particles detachment were performed using diverse centrifugal speeds. The graphics of particle percentages still adhering on the surface of the disks as a function of the applied detachment force showed that the profile of adhesion force followed a log-normal distribution. The adhesion force increased with particle size. The manioc starch particles presented adhesion forces greater than those for the phosphatic rock particles for all particle sizes studied. The results obtained were compared with the theory proposed by Derjaguin, Muller and Toporov whose theoretical adhesion presented values close to the experimental data for the phosphatic rock particles adhesion on the stainless steel surface. On the contrary, the theoretical values were lower than the experimental ones for the manioc starch particles maybe due to the small roughness of these particles, their physical properties (softer and deformable material) and/or specific chemical interactions since the organic composition of the manioc starch particles that can dominate the adhesion force. Finally, the separation distance among the surfaces in contact (Z₀) was estimated in approximately 1.0 × 10^− 9 m for the phosphatic rock and 5.0 × 10^− 10 m for the manioc starch. These results were weakly dependent on the particle size range.     

Analysis of the Particle Clustering Phenomenon in the Fluid Catalytic Cracking of Gasoil in a Downer Reactor

A large eddy simulation (LES)‐discrete element method (DEM) investigation was carried out to study particle clusters in a canonical downer reactor during the fluid catalytic cracking of gasoil. The analysis considered two cases: with and without chemical reactions. The results of the system under cold‐flow conditions for the frequency and mean lifetime of clusters were in good agreement with experimental data. The changes in the hydrodynamic conditions generated by the cracking reactions led to clusters with shorter mean lifetime but higher frequency compared to the system without chemical reactions. Additionally, the frequency and mean lifetime of clusters were successfully correlated to an empirical expression as a function of the particle Reynolds number and the Stokes number, which summarize the hydrodynamic conditions of the downer.     

Deposition of ultrafine aerosol particles on wire screens by simultaneous diffusion and image force

This paper presents the results of an experimental investigation on the deposition of multiply charged particles on wire screens by the combined mechanisms of diffusion and image force. Experiments were performed with particles having diameters between 25 and 65 nm (transition regime), carrying 0, +1, +2 or +3 elementary charges, and using three different flow rates, two types of wire screen, and two types of test aerosol. The single fiber efficiencies for the mechanisms of image force, η_IM, and diffusion, η_D, are of the same order of magnitude and, furthermore, they are both much smaller than one. Under these conditions, the total capture efficiency can be approximated as the sum of the efficiencies by diffusion and image force deposition. Theoretically, η_IM is proportional to the square root of a dimensionless number, K_IM, which includes all the relevant parameters cited above (i.e., particle size and charge, aerosol flow rate and screen geometry). The available correlations for η_IM, obtained from experiments with particles carrying a large number of elementary charges (K_IM>10^-5), predict that image force should not have any effect in the case of the small particles with very few number of charges that we have tested in our experiments (in our experimentation, K_IM ranged between 10^-7 and 10^-5). Our results, the only ones available to date for this particle size range, show that there is indeed a clear, measurable effect. Although our experimental results are best fitted by the correlation , it is shown that the expression , which is in agreement with the theoretical 1/2 exponent for K_IM, also reproduces reasonably well the measured values.     

Atomic force microscopy study on structure and properties of irradiation grafted silica particles in polypropylene‐based nanocomposites

Nanosilica particles treated by irradiation grafting polymerization can effectively improve the strength and toughness of a thermoplastic polymer at a rather low filler content. A detailed investigation on the modified nanoparticles in the absence and presence of a polypropylene matrix is carried out by using atomic force microscopy. The results indicate that the loosen agglomerates of the untreated SiO₂ became more compact due to the linkage between the nanoparticles offered by the grafting polymer. In addition, the molecules of the polypropylene matrix are able to diffuse into the modified nanoparticle agglomerates during the melt processing. Entanglement between the molecules of the grafting polymer and the matrix is thus available, which in turn facilitates a strong particle–matrix interfacial interaction. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 2218–2227, 2001     

Shape dependence of resistance force exerted on an obstacle placed in a gravity‐driven granular silo flow

Resistance force exerted on an obstacle in a gravity‐driven slow granular silo flow is studied by experiments and numerical simulations. In a two‐dimensional granular silo, an obstacle is placed just above the exit. Then, steady discharge flow is made and its flow rate can be controlled by the width of exit and the position of obstacle. During the discharge of particles, flow rate and resistance force exerting on the obstacle are measured. Using the obtained data, a dimensionless number characterizing the force balance in granular flow is defined by the relation between the discharge flow rate and resistance‐force decreasing rate. The dimensionless number is independent of flow rate. Rather, we find the weak shape dependence of the dimensionless number. This tendency is a unique feature for the resistance force in granular silo flow. It characterizes the effective flow width interacting with the obstacle in granular silo flow. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3849–3856, 2018     

A novel strategy to determine the optimal clamping force based on the clamping force change during injection molding

Injection molding machines are widely used to fabricate plastic products with complex geometries and structures. They consist of an injection unit and a clamping unit. To withstand the pressure of the mold cavity, the clamping unit needs a high clamping force to hold the mold halves. Unfortunately, the clamping force is among the overlooked parameters of the injection molding parameters. Setting the clamping force at max is needed in practice to avoid flash defects for most operators. However, excessive clamping force creates problems for the machine. This study proposes a verification method for determining optimal clamping force based on the clamping force change ΔCF. When ΔCF becomes zero, the current set value of the clamping force is appropriate. A positive and negative ΔCF corresponds to an excessive and insufficient set value of the clamping force, respectively. Verification experiments are implemented on an electric injection molding machine with polypropylene (PP). The experimental results show that the novel strategy can basically calculate and identify the optimal clamping force with iteration method. The optimal clamping force value for current working conditions (620kN) is acquired after several automatic molding trials, which provides a direction for further research.     

原子力显微镜在聚氨酯材料性能分析中的应用

简述了原子力显微镜（AFM）探测物体表面形貌的工作原理和操作模式，介绍了AFM在观察聚氨酯（PU）材料微相分离、复合树脂的相容性的应用情况，综述了AFM应用于PU材料研究的新进展。     

Experimental analysis of the influence of surface topography on the adhesion force as measured by an AFM

Force curves have been acquired using an atomic force microscope (AFM) on homogeneous microspheres of three different materials (latex, glass and yttria), in order to study the possible influence of the surface topography/geometry on the adhesion force as measured by an AFM. Forces were measured in regions at the top of the spheres ( ≈ 90°), at half-heights ( ≈ 0°) and in an intermediate region between these two ( ≈ 45°), where the angle is measured from the equatorial plane of the sphere to its polar axis. A very irregular and non-reproducible behaviour was found at ≈ 0°, so only the other two regions were quantitatively analysed. For all the three materials, a much smaller adhesion force was obtained in the region corresponding to ≈ 45° as compared to ≈ 90°. Moreover, a quite similar adhesion decrease ratio of about 1.60 ± 0.5 was obtained for all the three materials, which may suggest that the observed behavior might be due to geometrical factors. This observed influence could, in part, explain the observed heterogeneity in adhesion maps of microbial cells reported in the literature. The influence of the surface roughness is also discussed and it seems to result in a poor reproducibility of force curves.     

Influences of various vortex structures on the dispersion and deposition of small ash particles

Numerical simulations were conducted to study the influences of various vortex structures on the dispersion and deposition processes of 1 μm to 10 μm diameter fly ash particles on the rear side surface of a boiler tube. Turbulent gas flow was simulated with detached eddy simulation (DES) method and vortex structures in the wakes were modeled. Results suggested that the motions of particles in the near wake region were controlled by different vortex structures, and the impact efficiency and deposit concentration on the rear side surface induced by the vortices varied considerably at different velocities. The results of volume percentages distribution of the deposited particles with various diameters simulated were in good agreement with the experimental data.     

Numerical studies on effects of bubbles regular array on the liquid‐phase turbulence

It is well known that additive drag‐reducing methods have broadly developing prospects, so studies on mechanisms of additive drag reduction are very necessary. We hypothesised that the main reason for bubbles induced drag reduction is the modification on liquid‐phase turbulence structure by the addition of bubbles, and therefore such modification is the focus of our investigation. In this paper, effects of bubbles on liquid‐phase turbulence under the circumstance of regular bubble array were investigated by using Euler–Lagrange two‐way numerical simulations. The liquid‐phase velocity field was solved by using direct numerical simulations (DNS) in Euler frame of reference, and the bubble motion was tracked by using Newtonian motion equations that took into account interaction forces including drag force, shear lift force, gravity force, buoyant force, and inertia force in Lagrange frame of reference. The coupling between the phases was realised by regarding the interphase forces as momentum source terms of the continuous phase. Similarities and differences for effects of bubbles and surfactants on liquid turbulent flows were also analysed. The study indicated that addition of bubbles enhances the mean streamwise velocity, greatly reduces the Reynolds stress, and shows anisotropic suppression to the velocity fluctuations. The interphase force has a great influence on budget of energy balance. It is a gain term near the wall and is a loss term in a wide range of the channel core.