Granular Temperature Research Articles

Effect of collision, size, and oscillation of RBCs on blood heat transfer in a bifurcated vessel

This study attempts to analyze the effect of red blood cells (RBCs) on blood heat transfer in a three-dimensional bifurcated vessel when treated with hyperthermia procedure. A two-phase granular model is used in this paper to study the various underlying factors that affect the flow dynamics of RBCs in a blood vessel. Separate cases are analyzed to study the effect of RBC size, RBC-RBC, and RBC-wall collision and oscillation on heat transfer in a three-dimensional bifurcated vessel under pulsatile flow condition. Blood temperature and transient Nusselt number are used as heat transfer representative parameters. A good agreement with the experimental results from the existing literature is observed when the numerical model used in this study is compared for accuracy. From this study, it has been found that an increase in the size of RBCs of a blood disorder patient can decrease the temperature of blood compared to a normal patient when subjected to hyperthermia treatment. A change in the nature of collision between RBCs does not affect the heat transfer of blood under pulsatile flow condition in a bifurcated vessel. Also, an increase in granular temperature or oscillation of RBCs slightly increases the blood temperature when exposed to thermal treatment.

Self-diffusion in inhomogeneous granular shearing flows.

In this Letter, we discuss how flow inhomogeneity affects the self-diffusion behavior in granular flows. Whereas self-diffusion scalings have been well characterized in the past for homogeneous shearing, the effect of shear localization and nonlocality of the flow has not been studied. We, therefore, present measurements of self-diffusion coefficients in discrete numerical simulations of steady, inhomogeneous, and collisional shearing flows of nearly identical, frictional, and inelastic spheres. We focus on a wide range of dense solid volume fractions, that correspond to geophysical and industrial shearing flows that are dominated by collisional interactions. We compare the measured values first with a scaling based on shear rate and, then, on a scaling based on the granular temperature. We find that the latter does much better than the former in collapsing the data. The results lay the foundations of diffusion models for inhomogeneous shearing flows, which should be useful in treating problems of mixing and segregation.

On the mean square displacement of intruders in freely cooling granular gases

We compute the mean square displacement (MSD) of intruders immersed in a freely cooling granular gas made up of smooth inelastic hard spheres. In general, intruders and particles of the granular gas are assumed to have different mechanical properties, implying that non-equipartition of energy must be accounted for in the computation of the diffusion coefficient D. In the hydrodynamic regime, the time decay of the granular temperature T of the cooling granular gas is known to be dictated by Haff’s law; the corresponding decay of the intruder’s collision frequency entails a time decrease of the diffusion coefficient D. Explicit knowledge of this time dependence allows us to determine the MSD by integrating the corresponding diffusion equation. As in previous studies of self-diffusion (intruders mechanically equivalent to gas particles) and the Brownian limit (intruder’s mass much larger than the grain’s mass), we find a logarithmic time dependence of the MSD as a consequence of Haff’s law. This dependence extends well beyond the two aforementioned cases, as it holds in all spatial dimensions for arbitrary values of the mechanical parameters of the system (masses and diameters of intruders and grains, as well as their coefficients of normal restitution). Our result for self-diffusion in a three-dimensional granular gas agrees qualitatively, but not quantitatively, with that recently obtained by Blumenfeld [arXiv: 2111.06260] in the framework of a random walk model. Beyond the logarithmic time growth, we find that the MSD depends on the mechanical system parameters in a highly complex way. We carry out a comprehensive analysis from which interesting features emerge, such a non-monotonic dependence of the MSD on the coefficients of normal restitution and on the intruder-grain mass ratio. To explain the observed behaviour, we analyze in detail the intruder’s random walk, consisting of ballistic displacements interrupted by anisotropic deflections caused by the collisions with the hard spheres. We also show that the MSD can be thought of as arising from an equivalent random walk with isotropic, uncorrelated steps. Finally, we derive some results for the MSD of an intruder inmersed in a driven granular gas and compare them with those obtained for the freely cooling case. In general, we find significant quantitative differences in the dependence of the scaled diffusion coefficient on the coefficient of normal restitution for the grain-grain collisions.Graphic abstract

Critical comparison of polydisperse kinetic theories using bidisperse DEM data

Kinetic theories have been developed to describe the hydrodynamics of polydisperse granular flows under different theoretical assumptions. In this study, six species theories are assessed using the DEM data obtained from simple shear flow containing bidisperse particles with low and moderate solid volume fraction (Galvin, 2007). It was shown that (i) only the theories of Iddir and Arastoopour (2005) and Zhao and Wang (2021) can qualitatively capture all of the effects of various parameters on the granular temperature ratio and the normal and shear stresses; (ii) the granular temperature ratio can be predicted accurately either by Iddir and Arastoopour (2005) or Zhao and Wang (2021), depending on the input parameters; and (iii) the predictions of normal and shear stresses by Iddir and Arastoopour (2005) are superior in matching the DEM data for most tested cases. Present study not only discusses the fundamental differences between different species kinetic theories, but also offers a critical assessment of their suitability in modeling simple shear flow.

Geometry-controlled phase transition in vibrated granular media

We report experiments on the dynamics of vibrated particles constrained in a two-dimensional vertical container, motivated by the following question: how to get the most out of a given external vibration to maximize internal disorder (e.g. to blend particles) and agitation (e.g. to absorb vibrations)? Granular media are analogs to classical thermodynamic systems, where the injection of energy can be achieved by shaking them: fluidization arises by tuning either the amplitude or the frequency of the oscillations. Alternatively, we explore what happens when another feature, the container geometry, is modified while keeping constant the energy injection. Our method consists in modifying the container base into a V-shape to break the symmetries of the inner particulate arrangement. The lattice contains a compact hexagonal solid-like crystalline phase coexisting with a loose amorphous fluid-like phase, at any thermal agitation. We show that both the solid-to-fluid volume fraction and the granular temperature depend not only on the external vibration but also on the number of topological defects triggered by the asymmetry of the container. The former relies on the statistics of the energy fluctuations and the latter is consistent with a two-dimensional melting transition described by the KTHNY theory.

Experimental investigation into the wet non-spherical granular segregation and mixing in rotating drums

This paper experimentally investigates the wet non-spherical granular segregation in a quasi-2D rotating drum. The granular mixtures consisted of spherical POM beads and non-spherical red beans. To explore the interlocking effect resulting from particle shape, a long axis ratio was defined. Experimental results reveal that both the long axis ratio and the liquid content play crucial roles in wet non-spherical granular segregation. The steady-state segregation index decreases monotonically with the increase of long axis ratio. As the long axis ratio increases, the average velocity and granular temperature of spherical POM beads increase. Both properties also increase monotonically with liquid content. The dynamic angle of repose increases with the increasing liquid content, whereas the steady-state segregation index decreases. Reverse segregation does occur in a dry non-spherical mixture with a size ratio of 1.42, indicating that the shape effect appears to enhance the degree of reverse segregation appreciably. • Shape effect has a significant influence on granular segregation. • Final segregation index decreases monotonically with the long axis ratio. • Reverse granular segregation occurs at a specific LAR = 0.704. • Reverse granular segregation was mitigated in wet granular systems.

Friction-dependent rheology of dry granular systems

Understanding the rheology of granular assemblies is important for natural and engineering systems, but the relationship between inter-particle friction (or microscopic friction) and macroscopic friction is still not well understood. In this study, using the discrete element method (DEM) with spherical particles and realistic contact laws, we investigate the mechanics of granular systems with a wide range of inter-particle frictional coefficients and aim to establish a friction-dependent rheology for dry granular flows. The corresponding results show that increasing inter-particle friction dramatically increases the effective frictional coefficient, μeff, while decreasing the solid fraction of the system and increasing the transitional inertial number that marks the division of quasi-static regimes and intermediate flow regimes. We further propose a new dimensionless number, $${\cal M}$$ , as a ratio between the inertial effect and frictional effect, which is similar to the effective aspect ratio in granular column collapses, and unifies the influence of inter-particle friction with the inertial number. We then establish a relationship between $${\cal M}$$ and the dimensionless granular temperature, Θ, to further universalize the influence of inter-particle frictions. Such study can broaden the application of the μ(I) rheology in natural and engineering systems and help establish a more general constitutive model for complex granular systems.

Erratum: “Comment on ‘Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity’” [Phys. Fluids 33, 043321 (2021)

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Effect of crooked drill pipe rotation on cuttings transport in horizontal directional drilling using kinetic theory of granular flow – A numerical perspective

Effective cuttings transportation is essential for trenchless horizontal directional drilling (HDD). Inadequate borehole cleaning is one of the major reasons for drilling problems. Due to complicated mechanical effects accompanying the drilling process, the rotating drill pipe inevitably subjects bending deformation, which has a significant influence on the cuttings-drilling mud two-phase flow in the horizontal borehole, especially in the pilot hole drilling stage when the drill pipe is in a state of full rotation. However, there is a lack of research on the cuttings transport in the borehole where the rotating drill pipe is crooked. In this work, considering the bending deformation of the rotating drill pipe, the cuttings transport has been investigated in horizontal directional drilling based on the kinetic theory of granular flow. Using the dynamic mesh method, the crooked drill pipe is modeled as a sinusoidal form and rotates around the borehole axis. Flow behaviors of cuttings and drilling mud are predicted in pilot holes with a concentrically straight pipe, an eccentrically straight pipe, and a crooked pipe. Modeling results display the complex two-phase flow pattern for the horizontal directional drilling. The rotation of the crooked drill pipe enhances the cuttings spiral flow, where the axial velocity core zones of both cuttings and drilling fluid rotate with the drill pipe. The tangential velocities of the two phases originate from the rotating drill pipe wall, and the secondary flow is generated in the region that closes to the borehole inner wall within the annulus narrow portion. The cuttings transport mechanism is revealed by kinetic theory of granular flow. Predicted granular temperatures confirm more intense collisions between cuttings in the moving bed region due to the high shear rates caused by the pipe rotation. The suspension region contributes most of the cuttings transport velocity, and the fixed bed is formed by cuttings deposition. More uniform distributions of cuttings concentration and axial velocity are found in the borehole with a crooked drill pipe, however, it is found that the average torque of the crooked drill pipe is three times higher than that of the straight drill pipe exerted by the liquid–solid mixture.

A cluster-based drag model of rough sphere for the simulation of fast fluidization

The non-uniform flow caused by cluster greatly influences the performance in fast fluidization systems. Rough particles result in extra energy dissipation by particle rotation, which finally affects the cluster formation and evolution. In this study, the kinetic theory of rough sphere (KTRS) is employed and coupled with the cluster structure-dependent (CSD) drag model to consider the rotation effect on cluster formation, where the total granular temperature is introduced and the cluster-scale effect on the collision is incorporated. The effect of particle roughness on energy consumption is also discussed. The result demonstrates that the cluster-scale pressure plays an important role in the collision. The energy consumption is dependent on the particle roughness or tangential restitution coefficient. Meanwhile, the change of particle roughness also alters mesoscale parameters like cluster size and cluster solid concentration.

Different shear regimes in the dense granular flow in a vertical channel

The steady dense granular flow in a vertical channel bounded by flat frictional walls in one horizontal direction and with periodic boundary conditions in the other horizontal and vertical directions is studied using the discrete element method. The shape of the scaled velocity profile is characterized quantitatively by a universal exponential function, and the ratio of the maximum and slip velocities is independent of the average volume fraction $\bar {\phi }$ and the channel width $W$ . For sufficiently wide channels, the maximum and slip velocities increase proportional to $\sqrt {W}$ , and the thickness of the shearing zones increases proportional to $W$ . There are four zones in the flow, each with distinct dynamical properties. There is no shear in the plug zone at the centre, but there is particle agitation, and the volume fraction $\phi$ is lower than the random close packing volume fraction $\phi _{rcp}$ . In the adjoining dense shearing zone, $\phi$ is greater than the volume fraction for arrested dynamics $\phi _{ad} = 0.587$ , and the granular temperature and shear rate depend on the particle stiffness. Adjacent to the dense shearing zone is the loose shearing zone where $\phi < \phi _{ad}$ . Here, the properties do not depend on the particle stiffness, and the constitutive relations are well described by hard-particle models. The rheology in the loose shearing zone is similar to the dense flow down an inclined plane. There is high shear and a sharp decrease in $\phi$ in the wall shearing zone of thickness about two particle diameters, where the particle angular velocity is different from the material rotation rate due to the presence of the wall.

Phase transition in monodisperse granular materials: How to model it by using a strain hardening visco‐elastic‐plastic constitutive relationship

AbstractDuring heating (loading characterised by a progressive increase in strain rate) and cooling (loading characterised by a progressive decrease in strain rate) numerical tests, performed by using Discrete Element codes, granular materials experience phase transition phenomena, named in this paper ‘dry liquefaction’ (when from solid the material starts behaving like a fluid) and ‘dry resolidification’ (freezing, when the material from fluid starts behaving like a solid). The aim of this paper consists in reproducing phase transition phenomena by using a strain hardening visco‐elastic‐plastic model based on the critical state concept and kinetic theories of granular gases. The authors demonstrate that crucial is the role of isotropic softening/hardening, which describes the size of the elastic domain and the capability of the solid skeleton of storing elastic energy according to permanent force chains. The main ingredients of the model are: (i) the additivity of quasi‐static and collisional stresses, (ii) the energy balance equation governing the evolution of the granular temperature, interpreted this latter as an additional internal variable for the system for the collisional contribution, (iii) the mixed isotropic and kinematic hardening characterising the quasi‐static incremental constitutive relationship. The model has been both calibrated and validated on Discrete Element Method (DEM) numerical results, obtained by testing dry assemblies of monodisperse spheres under true triaxial loading conditions.

Hydrodynamic Predictions of the Ultralight Particle Dispersions in a Bubbling Fluidized Bed

Particle and gas flow characteristics are numerically simulated by means of a proposed gas–particle second-order moment two-fluid model with particle kinetic–friction stress model in a bubbling fluidized bed. Anisotropic behaviors of gas–solid two-phase stresses and their interactions are fully considered by the two-phase Reynolds stress model and their closure correlations. The dispersion behaviors of the non-spherical expand graphite and spherical heavy particles are predicted by using the parameters of distributions of particle velocity, porosity, granular temperature, and dominant frequency. Compared to particles density 2700 kg/m3, ultralight particles exhibit the higher voidages with big bubbles and larger axial-averaged velocity of particles and stronger dispersion behaviors. Maximum granular temperature is approximately 3.0 times greater than that one, and dominant frequency for axial porosity fluctuations is 1.5 Hz that is 1/3 time as larger as that heavy particle.

Research on size segregation dynamics and processes of a binary mixture dense granular flow

This study employed an experimental approach to investigate the effects of various filling degrees of the granular bed and the rotation speed on size-induced particle segregation behavior in an almost fully filled double-walled rotating drum. The distributions of the concentrations of bicolor particles in the system were obtained via image processing to determine the segregation state. The dynamics of the mixture flow including the statistical distribution, the azimuthal angle and radial direction granular temperature profiles were measured and calculated via particle-tracking velocimetry (PTV). The results were similar for the Brazil-nut effect and its reverse in the radial direction at high or low rotation speeds. When the rotation speed or filling degree was changed, the effect on two different particle sizes in the binary mixture system was inconsistent, and different flow mechanisms led to different segregation patterns. Two phase diagrams with the rotation speed and filling degree and the magnitude and position of the maximum granular temperature as the space enabled the prediction of segregation states.

Wet mono-sized granular packing: effects of initial clusters and filling strategy

Cohesive particles have been demonstrated to affect packing structures that sometimes inhibit applications while helpful in others. Therefore, accurately tailoring the cohesive granular packing, e.g., wet particles, is very rewarding nowadays. We adopt the discrete element method (DEM) and present a packing strategy by falling different size clusters containing mono-sized particles with varying cohesion to tailor the packing structure. We demonstrate the strategy's effectiveness by comparing the result with previous experiments, and we found the larger cluster tends to form a looser packing. We evidence that a dimensionless number, l⁎, evaluating the competing importance between kinetic energy and capillary potential, can precisely describe the cohesion effect. We combine l⁎ with several key indices, e.g., packing fraction, granular temperature, coordination number and force network distribution, to describe packing formation. Meantime, we found the different characterisation of cohesion effect throughout packing stages, which can shed light on the understanding of wet granular packing.

Kinetic Theory of Polydisperse Granular Mixtures: Influence of the Partial Temperatures on Transport Properties-A Review.

It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently adapted to account for inelastic collisions. A surprising result (compared to its molecular gas counterpart) for granular mixtures is the failure of the energy equipartition, even in homogeneous states. This means that the partial temperatures (measuring the mean kinetic energy of each species) are different to the (total) granular temperature T. The goal of this paper is to provide an overview on the effect of different partial temperatures on the transport properties of the mixture. Our analysis addresses first the impact of energy nonequipartition on transport which is only due to the inelastic character of collisions. This effect (which is absent for elastic collisions) is shown to be significant in important problems in granular mixtures such as thermal diffusion segregation. Then, an independent source of energy nonequipartition due to the existence of a divergence of the flow velocity is studied. This effect (which was already analyzed in several pioneering works on dense hard-sphere molecular mixtures) affects to the bulk viscosity coefficient. Analytical (approximate) results are compared against Monte Carlo and molecular dynamics simulations, showing the reliability of kinetic theory for describing granular flows.

CFD modeling for slurry flow through a horizontal pipe bend at different Prandtl number

The present work shows the slurry flow characteristics of bottom ash particulates having density 2219 kg/m3 at different Prandtl number through horizontal pipe bend. The simulation is carried out by adopting Eulerian two-phase model in conjunction with RNG k-ε turbulence model using available commercial software ANSYS Fluent. The transportation of solid particulates has the settling behaviour in the slurry pipeline and that leads to the sedimentation and blockage of the pipeline resulting more power and pressure drop in the pipeline. Therefore, it is important to know the transport capability of the solid particulates at different Prandtl fluids to minimise the pressure loss. The fluid properties at four Prandtl numbers i.e., 1.34, 2.14, 3.42 and 5.83 are used to carry the bottom ash concentration ranging from 40 to 60% (by weight) at mean flow-velocity ranging from 1 to 5 ms−1. The obtained computational results for pressure drop are validated with the published data in the literature and found in good agreement. The findings show that the pressure drop rises with escalation in flow velocity and Prandtl number for chosen efflux concentration range. The bottom ash particulates flowing at higher Prandtl fluid experiences less pressure drop through bend cross section in comparison to bottom ash particulates flowing at low Prandtl fluid. Finally, the contours of granular pressure, granular temperature and wall shear stress are predicted and discussed in details through the bend cross section to understand the complex slurry flow for chosen Prandtl numbers.

Kinetic theory of granular particles immersed in a molecular gas

The transport coefficients of a dilute gas of inelastic hard spheres immersed in a gas of elastic hard spheres (molecular gas) are determined. We assume that the number density of the granular gas is much smaller than that of the surrounding molecular gas, so that the latter is not affected by the presence of the granular particles. In this situation, the molecular gas may be treated as a thermostat (or bath) of elastic hard spheres at a fixed temperature. The Boltzmann kinetic equation is the starting point of the present work. The first step is to characterise the reference state in the perturbation scheme, namely the homogeneous state. Theoretical results for the granular temperature and kurtosis obtained in the homogeneous steady state are compared against Monte Carlo simulations showing a good agreement. Then, the Chapman–Enskog method is employed to solve the Boltzmann equation to first order in spatial gradients. In dimensionless form, the Navier–Stokes–Fourier transport coefficients of the granular gas are given in terms of the mass ratio$m/m_g$($m$and$m_g$being the masses of a granular and a gas particle, respectively), the (reduced) bath temperature and the coefficient of restitution. Interestingly, previous results derived from a suspension model based on an effective fluid–solid interaction force are recovered in the Brownian limit ($m/m_g \to \infty$). Finally, as an application of the theory, a linear stability analysis of the homogeneous steady state is performed showing that this state is always linearly stable.

Evaluation of hydrodynamic behavior of urea granules in a pseudo-2D fluidized bed using drag models and comparison with PIV technique

The urea fluidized bed hydrodynamics were simulated using computational fluid dynamics (CFD) vs. image processing technique. To identify the suitable model, sensitivity analyses on time step, number of nodes, and drag force coefficient were performed, and accordingly, Gidaspow and Syamlal–OˈBrien drag models were selected to simulate the fluidized bed for - particles categorized under Geldart-D. The CFD data were validated against the determined particle velocity using an image processing technique. Results indicate that Gidaspow model predictions for particles velocity and granular temperature are in good agreement whereas the Syamlal–OˈBrien model resulted in underestimated predictions. Further analysis using Gidaspow model, the particle velocity increased by 12.5%, when the air inlet velocity is increased from 2 to 3 m/s and decreased by 87.5% when the particle sizes are changed from 2 to 4 mm. Although the primary loading height and pressure showed no effect, but at high pressures, it is important to consider humidity to avoid the negative impact on the granulation performance.

Fluid-mediated sources of granular temperature at finite Reynolds numbers

We derive analytical solutions for hydrodynamic sources and sinks to granular temperature in moderately dense suspensions of elastic particles at finite Reynolds numbers. Modelling the neighbour-induced drag disturbances with a Langevin equation allows an exact solution for the joint fluctuating acceleration–velocity distribution function $P(v^{\prime },a^{\prime };t)$ . Quadrant-conditioned covariance integrals of $P(v^{\prime },a^{\prime };t)$ yield the hydrodynamic source and sink that dictate the evolution of granular temperature that can be used in Eulerian two-fluid models. Analytical predictions agree with benchmark data from particle-resolved direct numerical simulations and show promise as a general theory from gas–solid to bubbly flows.