Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

Numerical simulation of supersonic flow past reentry capsules

The flow fields over ARD (ESA's atmospheric reentry demonstrator), OREX (orbital reentry experiments) and spherically blunted cone-flare reentry configurations are numerically obtained by solving time-dependent, axisymmetric, compressible Navier–Stokes equations for freestream Mach numbers range of 1.2–6.0. The fluid dynamics are discretized in spatial coordinates employing a finite volume approach which reduces the governing equations to semi discretized ordinary differential equations. Temporal integration is performed using the multistage Runge–Kutta time-stepping scheme. A local time step is used to achieve steady-state solution. The numerical simulation is carried out on a structured grid. The flow-field features around the reentry capsule, such as bow shock wave, sonic line, expansion fan and recirculating flow in the base region are obtained. A good agreement is found between the calculated value of aerodynamic drag coefficient of the spherically blunted cone/fare reentry configuration with the experimental data. The effects of geometrical parameters, such as radius of the spherical cap, half cone angle, with sharp shoulder edge and with smooth shoulder edge on the flow-field have been numerically investigated for various reentry configuration which will be useful for optimization of the reentry capsule. PACS 47.11.Df, 47.40.Ki     

NUMERICAL SIMULATION OF THREE DIMENSIONAL GAS-PARTICLE FLOW IN A SPIRAL CYCLONE

The three-dimension gas-particle flow in a spiral cyclone is simulated numerically in this paper. The gas flow field was obtained by solving the three-dimension Navier-Stokes equations with Reynolds Stress Model (RSM). It is shown that there are two regions in the cyclone, the steadily tangential flow in the spiral channel and the combined vortex flow in the centre. Numerical results for particles trajectories show that the initial position of the particle at the inlet plane substantially affects its trajectory in the cyclone. The particle collection efficiency curves at different inlet velocities were obtained and the effects of inlet flow rate on the performance of the spiral cyclone were presented. Numerical results also show that the increase of flow rate leads to the increase of particles collection efficiency, but the pressure drop increases sharply.     

Numerical study of steady/unsteady flow and heat transfer in porous media using a characteristics-based matrix-free implicit FV method on unstructured grids

In this study, a high-resolution characteristic-based finite-volume (FV) method on unstructured grids [Int. J. Numer. Method Eng. 50 (2001) 11; Int. J. Heat Fluid Flow 21 (2000) 432] is extended by a matrix-free implicit dual-time stepping scheme for the numerical simulation of steady and unsteady flow and heat transfer with porous media. The method has been used to study the characteristics of a complex problem: flow and heat transfer in a channel with multiple discrete porous blocks, which was originally proposed by Huang and Vafai [J. Thermophys. Heat Transfer 8 (3) (1994) 563]. In addition, flow and heat transfer in a channel partially or fully filled with porous layers and containing solid protruding blocks with constant heat flux on its lower surface are also investigated in details. Hydrodynamic and heat transfer results are reported for both steady and transient flow cases. In particular, the effects of Darcy and Reynolds numbers on heat transfer augmentation and pressure loss are studied. An in-depth discussion of the formation and variation of recirculation is presented and the existence of optimum porous insert is demonstrated. At high Reynolds numbers the flow in the porous channel exhibits a cyclic characteristics although unlike the non-porous channel flow, the cyclic vortex development is only restricted to a small area behind the last solid block, while temperature changes more slowly and does not exhibit cyclic variations over a long period of time. It is shown that for all the cases studied altering some parametric values can have significant and interesting effects on both flow pattern as well as heat transfer characteristics.     

Effects of particle size and concentration on bubble coalescence and froth formation in a slurry bubble column

A new approach for simulating the formation of a froth layer in a slurry bubble column is proposed. Froth is considered a separate phase, comprised of a mixture of gas, liquid, and solid. The simulation was carried out using commercial flow simulation software (FIRE v2014) for particle sizes of 60–150 μm at solid concentrations of 0–40 vol%, and superficial gas velocities of 0.02–0.034 m/s in a slurry bubble column with a hydraulic diameter of 0.2 m and height of 1.2 m. Modelling calculations were conducted using a Eulerian–Eulerian multiphase approach with k–ε turbulence. The population balance equations for bubble breakup, bubble coalescence rate, and the interfacial exchange of mass and momentum were included in the computational fluid dynamics code by writing subroutines in Fortran to track the number density of different bubble sizes. Flow structure, radial gas holdup, and Sauter mean bubble diameter distributions at different column heights were predicted in the pulp zone, while froth volume fraction and density were predicted in the froth zone. The model was validated using available experimental data, and the predicted and experimental results showed reasonable agreement. To demonstrate the effect of increasing solid concentration on the coalescence rate, a solid-effect multiplier in the coalescence efficiency equation was used. The solid-effect multiplier decreased with increasing slurry concentration, causing an increase in bubble coalescence efficiency. A slight decrease in the coalescence efficiency was also observed owing to increasing particle size, which led to a decrease in Sauter mean bubble diameter. The froth volume fraction increased with solid concentration. These results provide an improved understanding of the dynamics of slurry bubble reactors in the presence of hydrophilic particles.     

Further contributions on the flow past a stationary and confined cylinder: Creeping and slowly moving flow of Power law fluids

The steady flow of generalized Newtonian fluid around a stationary cylinder placed between two parallel plates was studied numerically. Finite volume method was applied to solve the momentum equations along with the continuity equation and the Power law rheological model within the laminar flow regime for a range of the Reynolds number Re and the Power law index n values. The values of the Reynolds number, based on physical and rheological properties, cylinder radius and bulk velocity, were varied between 0.0001≤Re≤10, while the Power law index values mapped the 0.50≤n≤1.50 range, allowing for the investigation of both shear-thinning and shear-thickening effects at the creeping as well as slowly moving fluid flow conditions. We report accurate results of a systematic study with a focus on the most important characteristics of fluid flow past circular cylinder. It is shown that for the creeping flow regime there exist finite sized redevelopment length, drag and loss coefficient. Last but not least, the present numerical results indicate that the shear-thinning viscous behaviour decreases the onset of flow separation.     

Numerical investigation on flow around circular cylinders in tandem arrangement at a subcritical Reynolds number

Three-dimensional fluid computations have been performed to investigate the flows around two circular cylinders in tandem arrangements at a subcritical Reynolds number, Re=2.2×10⁴. The center-to-center space between the cylinders was varied from twice the cylinder diameter to five times that, and the flows and fluid-dynamic forces obtained from the simulations are compared with the experimental results reported in the literature. Special attention is paid to the characteristics of the vortices shed from the upstream cylinder such as the convection, the impingement onto the downstream cylinder and the interaction with the vortices from the downstream cylinder. The effects of the vortices from the upstream cylinder on the fluid-dynamic forces acting on the downstream cylinder are discussed.     

A computational study of gas flow in a De‐Laval micronozzle at different throat diameters

A numerical study has been carried out to investigate the gas flows in a micronozzle using a continuum model under both slip and no‐slip boundary conditions. The governing equations were solved with a finite volume method. The numerical model was validated with available experimental data. Numerical results of exit thrust showed good agreement with experimental data except at very low Reynolds numbers. For parametric studies on the effect of geometric scaling, the nozzle throat diameter was varied from 10 to 0.1 mm, whereas throat Reynolds number was varied from 5 to 2000. A correlation has also been developed to calculate the specific impulse at specified throat diameter and Reynolds number. The effect of different gases on the specific impulse of the nozzle, such as helium, nitrogen, argon and carbon dioxide, was also examined. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical analysis of respiratory flow patterns within human upper airway

A computational fluid dynamics （CFD） approach is used to study the respiratory airflow dynamics within a human upper airway. The airway model which consists of the airway from nasal cavity, pharynx, larynx and trachea to triple bifurcation is built based on the CT images of a healthy volunteer and the Weibel model. The flow character- istics of the whole upper airway are quantitatively described at any time level of respiratory cycle. Simulation results of respiratory flow show good agreement with the clinical mea- sures, experimental and computational results in the litera- ture. The air mainly passes through the floor of the nasal cavity in the common, middle and inferior nasal meatus. The higher airway resistance and wall shear stresses are distrib- uted on the posterior nasal valve. Although the airways of pharynx, larynx and bronchi experience low shear stresses, it is notable that relatively high shear stresses are distrib- uted on the wall of epiglottis and bronchial bifurcations. Besides, two-dimensional fluid-structure interaction models of normal and abnormal airways are built to discuss the flow-induced deformation in various anatomy models. The result shows that the wall deformation in normal airway is relatively small.     

Numerical and experimental study of an innovative pipeline design in a granular pneumatic-conveying system

During gas–solid mixture conveying in a dense phase, material is conveyed in dunes on the bottom of the pipeline, or as a pulsating moving bed. This phenomenon increases the pressure drop and power consumption. We introduce a new technique to reduce the pressure drop, which is termed the perforated double tube. To validate this new model, the gas–solid flow pattern and pressure drop were studied numerically and experimentally. The power consumption was also studied experimentally. Numerical studies were performed by the Eulerian–Lagrangian approach to predict gas and particle movement in the pipeline. Comparisons between the numerical predictions and the experimental results for the gas–solid flow patterns and pressure drop show good agreement.     

Influence of drag laws on pressure and bed material recirculation rate in a cold flow model of an 8 MW dual fluidized bed system by means of CPFD

A cold flow model of an 8 MW dual fluidized bed (DFB) system is simulated using the commercial computational particle fluid dynamics (CPFD) software package Barracuda. The DFB system comprises a bubbling bed connected to a fast fluidized bed with the bed material circulating between them. As the hydrodynamics in hot DFB plants are complex because of high temperatures and many chemical reaction processes, cold flow models are used. Performing numerical simulations of cold flows enables a focus on the hydrodynamics as the chemistry and heat and mass transfer processes can be put aside. The drag law has a major influence on the hydrodynamics, and therefore its influence on pressure, particle distribution, and bed material recirculation rate is calculated using Barracuda and its results are compared with experimental results. The drag laws used were energy-minimization multiscale (EMMS), Ganser, Turton–Levenspiel, and a combination of Wen–Yu/Ergun. Eleven operating points were chosen for that study and each was calculated with the aforementioned drag laws. The EMMS drag law best predicted the pressure and distribution of the bed material in the different parts of the DFB system. For predicting the bed material recirculation rate, the Ganser drag law showed the best results. However, the drag laws often were not able to predict the experimentally found trends of the bed material recirculation rate. Indeed, the drag law significantly influences the hydrodynamic outcomes in a DFB system and must be chosen carefully to obtain meaningful simulation results. More research may enable recommendations as to which drag law is useful in simulations of a DFB system with CPFD.     

A novel interface‐tracking method based on Lagrangian particles for deformation analysis of a red blood cell in a capillary

A novel efficient interface‐tracking method is developed to gain an insight into the interface in a multiphase or multifluid system, called the modified particle binary level set (MPBLS) method, in which the binary level set function is defined to distinguish the different phases or fluids and further modified by Lagrangian particles scattered along the interface for achieving higher accuracy. The validation of the MPBLS method is carried out first by simulating the free motion of a red blood cell (RBC) in the rotating, shear and Poiseuille flows, respectively. Subsequently, further validations are performed by comparing with the experimental and numerical results published previously. As one of important applications, the MPBLS method is employed to investigate the deformation behaviors of RBCs with different shapes in a capillary. The simulations show that the healthy RBC gradually changes the geometric shape from a biconcave to a steady parachute shape. It is thus guaranteed that the RBC successfully traverses through the smaller capillaries compared with undeformed RBC. However, the unhealthy RBC with the circular or elliptical shape has different deformation behaviors, in which the steady parachute shape is much less concave at the rear and more convex in the front. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of heat-source geometry on distribution and deposition of particulates in a ventilated chamber

To investigate the effect of near-wall heat-source shape on particulate motion, the particulate distribution and deposition in a ventilated chamber with different heat-source configurations were numerically modeled. Using the discrete random walk model of the Lagrangian method, the trajectories of 3200 mono-disperse particulates ranging from 1 to 10 μm with a density of 1400 kg/m³ were tracked. Airflow pattern, temperature fields, the distribution of particulate concentrations, and deposition patterns are calculated and presented. The results show that the shape of a near-wall heat source has an influence on the airflow as well as the temperature field in the chamber and hence affects the particulate distribution and deposition.     

A dispersion force approach to modelling the effect of lift forces on fibre dispersion

Wood fibres suspended in air were studied whilst flowing through a throttle. Measurements of volume fraction and velocity were compared with results from a two-fluid model simulation. Results from earlier work have shown that the lift forces acting on the individual fibres are of importance for the dispersion of volume fraction. Since the orientation of the individual fibres cannot be determined, a dispersion force was utilised to model the dispersing effect of the lift forces. The addition of a lift dispersion model significantly improved the agreement between measurement and model data.     

Numerical study on local entropy generation in a burner fueled with various fuels

This study considers numerical simulations of the combustions of hydrogen and various hydrocarbons with air, including 21% oxygen and 79% nitrogen, in a burner and the numerical solution of the local entropy generation rate due to the high temperature and velocity gradients in the combustion chamber. The combustion is simulated for the fuel mass flow rates providing the same heat transfer rate to the combustion chamber in the each fuel case. The effects of (only in the case of H₂ fuel) and equivalence ratio () on the combustion and entropy generation rate are investigated for the different (from 5,000 to 10,000 W) and s (from 0.5 to 1.0). The numerical calculation of combustion is performed individually for all cases with the help of the Fluent CFD code. Furthermore, a computer program has been developed to numerically calculate the volumetric entropy generation rate distributions and the other thermodynamic parameters by using the results of the calculations performed with the FLUENT code. The calculations bring out that the maximum reaction rates decrease with the increase of (or the decrease of ). The large positive and negative temperature gradients occur in the axial direction, nonetheless, the increase of significantly reduces them. The calculations bring out also that with the increase of from 0.5 to 1.0, the volumetric local entropy generation rates decrease about 4% and that the merit numbers increase about 16%.     

Three-dimensional water entry of a solid body: A computational study

Marine vessels are continuously subject to impulsive loading from impact on the water surface. Understanding and quantifying the hydrodynamics generated by the three-dimensional (3D) water impact of a solid body is central to the design of resilient and performing vessels. Computational fluid dynamics (CFD) constitutes a viable tool for the study of water entry problems, which may overcome some of the drawbacks associated with semi-analytical and experimental methods. Here, we present a new computational study of the 3D water entry of a solid body with multiple curvatures. The method of finite volume is utilized to discretize incompressible Navier-Stokes equations in both air and water, and the method of volume of fluid is employed to describe the resulting free-surface multiphase flow. Computational results are validated against available experimental findings obtained using particle image velocimetry in terms of both the flow kinetics and kinematics. Specifically, we demonstrate the accuracy of our CFD solution in predicting the overall force experienced by the hull, the pile-up phenomenon, the velocity field in the water, the distribution of the hydrodynamic loading, and the energy transfer during the impact. Our approach is expected to aid in the validation of new semi-analytical solutions and to offer a viable means for conducting parametric studies and design optimization on marine vessels.     

Finite-length effects on dynamical behavior of rod-like particles in wall-bounded turbulent flow

Combined Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) measurements have been performed in dilute suspensions of rod-like particles in wall turbulence. PIV results for the turbulence field in the water table flow apparatus compared favorably with data from Direct Numerical Simulations (DNS) of channel flow turbulence and the universality of near-wall turbulence justified comparisons with DNS of fiber-laden channel flow. In order to examine any shape effects on the dynamical behavior of elongated particles in wall-bounded turbulent flow, fibers with three different lengths but the same diameter were used. In the logarithmic part of the wall-layer, the translational fiber velocity was practically unaffected by the fiber length l. In the buffer layer, however, the fiber dynamics turned out to be severely constrained by the distance z to the wall. The short fibers accumulated preferentially in low-speed areas and adhered to the local fluid speed. The longer fibers (l/z > 1) exhibited a bi-modal probability distribution for the fiber velocity, which reflected an almost equal likelihood for a long fiber to reside in an ejection or in a sweep. It was also observed that in the buffer region, high-speed long fibers were almost randomly oriented whereas for all size cases the slowly moving fibers preferentially oriented in the streamwise direction. These phenomena have not been observed in DNS studies of fiber suspension flows and suggested l/z to be an essential parameter in a new generation of wall-collision models to be used in numerical studies.     

Numerical simulation of the head-on reflection of a regular reflection

The head-on collision and subsequent reflection of a Regular Reflection (RR) from the end-wall of a shock tube has been investigated both experimentally and numerically for two different incident shock wave Mach numbers and two different reflecting wedge angles. The agreement between the double-exposure holographic interferograms and the numerical simulations which were obtained using a GRP based numerical code, was found to be excellent in the RR region and very good behind the head-on reflected RR. The overall good agreement between the computed and experimental constant-density contours (isopycnics) constitutes a validation of the computational method, including the oblique-wall boundary condition.     

Influences of the fluidizing and spouting pulsation on particle motion in spout-fluid beds

Effects of variable airflow on particle motion in spout-fluid beds are studied. Computational fluid dynamics using Navier–Stokes equations for the gas phase coupled with the discrete element method using Newton’s laws for the solid phase have been employed. Results indicate that increasing the fluidizing velocity diminishes dead zones and increases both the total height of the bed and the traversed distance by particles in the steady spout-fluid bed. In pulsed airflows, two configurations are investigated, namely, the spouted pulsed-fluidized bed with pulsed flow of the fluidizing velocity, and the pulsed-spouted fluidized bed with pulsed flow of the spouting velocity. The positive effect of pulsation on particle motion is shown and the effects of parameters, such as amplitude and frequency, on the dynamics of the bed are investigated in each configuration. An increase of up to 19% in traversed distance is found for the range studied, which suggests flow pulsation as a promising technique for increasing particle mixing in spout-fluid beds.