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The average residence time of liquid flowing over the surface of a rotating cone was determined numerically. The development and propagation of the free surface flow was simulated using the volume of fluid (VOF) method. The numerical simulations were validated using laboratory experiments using soy‐oil as a model liquid, and approximate analytical solutions of the simplified governing equations. The numerical simulations revealed the importance of the cone rotation frequencies and the minor influence of the cone angles on the residence times. Higher liquid throughputs produced smaller residence times. As expected, an increasing cone size results in proportionally higher residence times. Furthermore, it was established that even for small cones with a characteristic diameter of, e.g. less than 1m, relatively high (∼1 kg/s) throughputs of liquid are possible. It appears that the combination of the decreasing layer thickness and the increasing size of the numerical grid cells with increasing radial cone coordinate hampers the numerical simulation of this system.

The purpose of this paper is to focus on modeling buoyancy driven viscous flow and heat transfer through saturated packed pebble‐beds via a set of homogeneous volume‐averaged conservation equations in which local thermal disequilibrium is accounted for.

The local thermal disequilibrium accounted for refers to the solid and liquid phases differing in temperature in a volume‐averaged sense, which is modeled by describing each phase with its own governing equation. The partial differential equations are discretized and solved via a vertex‐centered edge‐based dual‐mesh finite volume algorithm. A compact stencil is used for viscous terms, as this offers improved accuracy compared to the standard finite volume formulation. A locally preconditioned artificial compressibility solution strategy is employed to deal with pressure incompressibility, whilst stabilisation is achieved via a scalar‐valued artificial dissipation scheme.

The developed technology is demonstrated via the solution of natural convective flow inside a heated porous axisymmetric cavity. Predicted results were in general within 10 per cent of experimental measurements.

This is the first instance in which both artificial compressibility and artificial dissipation is employed to model flow through saturated porous materials.

The volume of fluid (VOF) method is a numerical technique to track the developing free surfaces of liquids in motion. This method can, for example, be applied to compute the liquid flow patterns in a rotating cone reactor. For this application a spherical coordinate system is most suited. The novel derivation of the extended VOF algorithms for this class of applications is presented here. Some practical limitations of this method, that are inherent in the geometry of the described system, are discussed.

This paper aims to propose a new method for robust simulations of passive heat transfer in two-fluid flows with high volumetric heat capacity contrasts.

This paper implements a prediction–correction scheme to evolve the volumetric heat capacity. In the prediction substep, the volumetric heat capacity is evolved together with the temperature. The bounded downwind version of compressive interface capturing scheme for arbitrary meshes and central difference scheme are used for the spatial discretization of the advection and diffusion terms of the heat transfer equation, respectively. In the correction substep, the volumetric heat capacity is updated in accordance with the interface captured by using a coupled level-set and volume-of-fluid method to capture the interface dynamics precisely.

The proposed method is verified by simulating the advection of a hot droplet with high volumetric heat capacity, a stationary air–water tank with temperature variation between top and bottom walls and heat transfer during wave plunging at Re=108. The test results show that the proposed method is practical and accurate for simulating two-fluid heat transfer problems, especially for those feature high volumetric heat capacity contrasts.

To ensure the numerical stability, this paper solves an additional conservative form of volumetric heat capacity equation along with the conservative form of temperature equation by using consistent spatial-discretization and temporal-integration schemes.

The purpose of this paper is to fundamentally develop a mathematical model for predicting the particle size distribution (PSD) in fluidized beds because their hydrodynamics depend on the PSD and its evolution during operation. To predict the gradual PSD change in a fluidized bed by using the population balance method (PBM), the kinetic parameter for agglomerate formation should be known and this parameter, in this work, is determined by the results of computational fluid dynamic–discrete element method (CFD-DEM) simulation.

Momentum and energy conservation equations and soft-sphere DEM are used to simulate the agglomeration phenomenon at high temperature in a two-dimensional air-polyethylene fluidized bed in bubbling regime. The Navier–Stokes equations for motion of gas are solved by the SIMPLE algorithm. Newton’s second law of motion is applied to describe the motion of individual particles. Collision between particles is detected by the no-binary search algorithm.

A correlation is proposed for estimating the kinetic parameter for agglomerate formation based on collision frequency, collision efficiency and inlet gas temperature. Based on the corrected kinetic parameter, the PBM is able to predict the PSD evolution in the fluidized bed in a fairly good agreement with the results of the CFD-DEM.

The results of the agglomeration process cannot be compared quantitatively with experimental results. Because three-dimensional fluidized bed mostly contains millions of particles and simulating them takes a long computing time in DEM. As far as temperature is a dominant parameter in the agglomeration process, effects of inlet gas temperature are examined on the kinetic parameter. On the other hand, wider and deeper insights in which the effect of other parameters, such as velocity and so on will be studied, is one of the goals in the authors’ next works to compensate for the shortcomings in this work.

This study helps to understand the effect of the inlet gas temperature during the agglomeration process on the kinetic parameter and provides fundamental information in dealing with kinetic parameter to attain PSD in fluidized bed by the PBM.

The purpose of this paper is to present a computational fluid dynamic simulation for the investigation of the particles segregation phenomenon in the gas–solid fluidized beds.

These particles have the same size and different densities. The k–ε model and multiphase particle-in-cell method have been utilized for modeling the turbulent fluid flow and solid particles behaviors, respectively. The coupled equations of the velocity and pressure have been solved by using a combination of SIMPLE and PISO algorithms. After validating the simulation, different mixing indices, with different calculation bases, have been investigated, and it has been found that the Lacey mixing index, which was defined based on statistical concepts, is suitable to investigate the segregation/mixing phenomena of this bed in different conditions. Finally, the effects of parameters such as velocity, particle density ratio, jetsam concentration, and initial arrangement on the segregation/mixing behaviors of the bed have been studied.

The results show that the increase in the superficial gas velocity decreases the mixing index to a minimum value and then increases this index in the beds with mixed initial condition, unlike the beds with separated initial condition. Moreover, an increase in the particle density ratio increases the minimum fluidization velocity of the bed, and also the amount of segregation, and increase in the jetsam concentration increases the value of the mixing index.

A computational fluid dynamics simulation has been presented for the particles segregation phenomenon in the gas–solid fluidized beds.

This study aims to provide discussions of the numerical method and the bubbly flow characteristics of an annular bubble plume.

The bubbles, released from the annulus located at the bottom of the domain, rise owing to buoyant force. These released bubbles have diameters of 0.15–0.25 mm and satisfy the bubble flow rate of 4.1 mm³/s. The evolution of the three-dimensional annular bubble plume is numerically simulated using the semi-Lagrangian–Lagrangian (semi-L–L) approach. The approach is composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase.

First, a new phenomenon of fluid dynamics was discovered. The bubbly flow enters a transition state with the meandering motion of the bubble plume after the early stable stage. A vortex structure in the form of vortex rings is formed because of the inhomogeneous bubble distribution and the fluid-surface effects. The vortex structure of the flow deforms as three-dimensionality appears in the flow before the flow fully develops. Second, the superior abilities of the semi-L–L approach to analyze the vortex structure of the flow and supply physical details of bubble dynamics were demonstrated in this investigation.

The semi-L–L approach is applied to the simulation of the gas–liquid two-phase flows.

The purpose of this paper is to develop a corrected unresolved CFD-DEM method that can reproduce the wake effects in modeling particulate flows at moderate Reynolds number.

First, the velocity field in the wake behind a settling particle is numerically investigated by a resolved method, in which the finite volume method (FVM) is applied to model the fluid flow, discrete element method (DEM) is applied to simulate the motion of particles and immersed boundary method (IBM) is used to tackle fluid solid interaction. Second, an analytical scaling law is given, which can effectively describe the velocity field in the wake behind the settling particle at low and middle Reynolds numbers. Third, this analytical expression is incorporated into unresolved modeling to correct the relative velocity between the particle and its surrounding fluid and enable the influence of the wake of the particle on its neighboring particles.

Two numerical examples, the sedimentation of dual particles, a list of particles and even more particles are provided to show the effectiveness of the presented velocity corrected unresolved method (VCUM). It is found that, in both examples simulated with VCUM, the relative positions of the particles changed, and drafting & kissing phenomenon and particle clustering phenomenon were clearly observed.

The developed VCUM can be highly beneficial for modeling industrial particulate flows with DKT and particle clustering phenomena.

VCUM innovatively incorporates the wake effects into unresolved CFD-DEM method. It improves the computational accuracy of conventional unresolved methods with comparable results from resolved modeling, while the computational cost is greatly reduced.

The purpose of this paper is to show how particle scale simulation of industrial particle flows using DEM (discrete element method) offers the opportunity for better understanding of the flow dynamics leading to improvements in equipment design and operation.

The paper explores the breadth of industrial applications that are now possible with a series of case studies.

The paper finds that the inclusion of cohesion, coupling to other physics such fluids, and its use in bubbly and reacting flows are becoming increasingly viable. Challenges remain in developing models that balance the depth of the physics with the computational expense that is affordable and in the development of measurement and characterization processes to provide this expanding array of input data required. Steadily increasing computer power has seen model sizes grow from thousands of particles to many millions over the last decade, which steadily increases the range of applications that can be modelled and the complexity of the physics that can be well represented.

The paper shows how better understanding of the flow dynamics leading to improvements in equipment design and operation can potentially lead to large increases in equipment and process efficiency, throughput and/or product quality. Industrial applications can be characterised as large, involving complex particulate behaviour in typically complex geometries. The critical importance of particle shape on the behaviour of granular systems is demonstrated. Shape needs to be adequately represented in order to obtain quantitative predictive accuracy for these systems.

Understanding the interaction of turbulence and cavitation is an essential step towards better controlling the cavitation phenomenon. The purpose of this paper is to bring out the efficacy of different modelling approaches to predict turbulence and cavitation-induced phase changes.

This paper compares the dynamic cavitation (DCM) and Schnerr–Sauer models. Also, the effects of different modelling methods for turbulence, unsteady Reynolds-averaged Navier–Stokes (URANS) and detached eddy simulations (DES) are also brought out. Numerical predictions of internal flow through a venturi are compared with experimental results from the literature.

The improved predictive capability of cavitating structures by DCM is brought out clearly. The temporal variation of the cavity size and velocity illustrates the involvement of re-entrant jet in cavity shedding. From the vapour fraction contours and the attached cavity length, it is found that the formation of the re-entrant jet is stronger in DES results compared with that by URANS. Variation of pressure, velocity, void fraction and the mass transfer rate at cavity shedding and collapse regions are presented. Wavelet analysis is used to capture the shedding frequency and also the corresponding occurrence of features of cavity collapse.

Based on the performance, computational time and resource requirements, this paper shows that the combination of DES and DCM is the most suitable option for predicting turbulent-cavitating flows.