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.     

Heat Transfer and Particle Behaviours in Dispersed Two-Phase Flow with Different Heat Conductivities for Liquid and Solid

Liquid-solid two-phase flow with heat transfer is directly simulated, to investigate the effects of the ratios of heat conductivities (solid to liquid) and bulk solid volume fraction from dense to dilute situations. The interaction between fluid and particles is solved by our original immersed solid approach on a rectangular grid system. A discrete element method with a soft-sphere collision model is applied for particle-particle and particle-wall interactions. Governing equation of temperature is time-updated with an implicit treatment for the diffusion term, which enables robust simulation with particles of very high/low ratios of heat conductivities (from 1/1000 to 1000) to the fluid. The local heat flux at the fluid-solid interface is modelled by a new flux decomposition technique, and incorporated into the implicit scheme of the temperature. The method is applied to a 2-D particulate flow in a natural convection in a square domain at a relatively low Rayleigh number. In the dense condition, for the cases with high ratios of heat conductivity, the heat transfer is promoted by strong convection, while the particles of low ratios of heat conductivity tend to hinder the development of the temperature rise in the flow field, causing a weak convection and low Nusselt number. Under a condition of relatively low solid volume fraction, fixed particles only depress the heat convection as the number of particles and heat conductivity ratio increase. For the cases with freely-moving particles, on the other hand, heat conductivity of particles has a stronger influence on the heat transfer of the system than the number of particles. The above simulation results highlight the effect of temperature distributions within the particles and liquid.     

Transient behavior of heat removal from a cylindrical heat storage vessel packed with spherical porous particles

The transient heat transfer behavior in the case of heat removal from a cylindrical heat storage vessel packed with spherical particles was investigated experimentally for various factors (flow rate, diameter of spherical particles packed, temperature difference between flowing cold air and spherical particles accumulating heat, and physical properties of spherical particles). The experiments were covered in ranges of Reynolds number based on the mean diameter of spherical particles packed Re_d = 10.3–2200, porosity?=0.310 to 0.475, ratio of spherical particle diameter to cylinder diameterd/D = 0.0075–0.177 and ratio of length of the cylinder to cylinder diameterL/D=2.5–10. It was found that especially the flow rate and the dimension of spherical particles played an important role in estimating the transient local heat transfer characteristics near the wall of the cylindrical vessel in the present heat storage system. As flow rate and diameter of spherical particles were increased under a given diameter of the cylinder heat storage vessel, the mean heat transfer coefficient between the flow cold air and the hot spherical particles increased and the time period to finish removing heat from the vessel reduced. In addition, the useful experimental correlation equations of mean heat transfer coefficient between both phases and the time period to finish removing heat from the vessel were derived with the functional relationship of Nusselt numberNu _d=f [modified Prandtl numberPr ^* (d/D), Re_d) and Fourier numberFo = f(d/D, L/D, Pr^*, Re_d).     

Superquadric DEM-SPH coupling method for interaction between non-spherical granular materials and fluids

The research on the coupling method of non-spherical granular materials and fluids aims to predict the particle–fluid interaction in this study. A coupling method based on superquadric elements is developed to describe the interaction between non-spherical solid particles and fluids. The discrete element method (DEM) and the smoothed particle hydrodynamics (SPH) are adopted to simulate granular materials and fluids. The repulsive force model is adopted to calculate the coupling force and then a contact detection method is established for the interaction between the superquadric element and the fluid particle. The contact detection method captures the shape of superquadric element and calculates the distance from the fluid particle to the surface of superquadric element. Simulation cases focusing on the coupling force model, energy transfer, and large-scale calculations have been implemented to verify the validity of the proposed coupling method. The coupling force model accurately represents the water entry process of a spherical solid particle, and reasonably reflects the difference of solid particles with different shapes. In the water entry process of multiple solid particles, the total energy of the water entry process of multiple solid particles tends to be stable. The collapse process of the partially submerged granular column is simulated and analyzed under different parameters. Therefore, this coupling method is suitable to simulate fluid–particle systems containing solid particles with multiple shapes.     

Numerical Study of Heat Transfer in a Rectangular Channel with Porous Covering Obstacles

A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered. The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with the increase of Reynolds number.     

Molecular dynamics simulation of annular flow boiling with the modified Lennard-Jones potential function

Molecular dynamics simulation of annular flow boiling in a nanochannel is numerically investigated. In this research, an annular flow model is developed to predict the superheated flow boiling heat transfer characteristics in a nanochannel. To characterize the forced annular boiling flow in a nanochannel, an external driving force F^?_\textext \overrightarrow {F}_{\text{ext}} ranging from 1 to 12 PN (PN = pico newton) is applied along the flow direction to inlet fluid particles during the simulation. Based on an annular flow model analysis, it is found that saturation condition and superheat degree have great influences on the liquid–vapor interface. Also, the results show that due to the relatively strong influence of the surface tension in small channels, the interface between the liquid film and the vapor core is fairly smooth, and the mean velocity along the stream-wise direction does not change anymore. Also, it is found that the heat flux values depend on the boundary conditions. Finally, the Green–Kubo formula is used to calculate the thermal conductivity of liquid Argon. The simulations predict thermal conductivity of liquid Argon quite well.     

Mathematical modelling of two‐phase non‐Newtonian flow in a helical pipe

Governing equations for a two‐phase 3D helical pipe flow of a non‐Newtonian fluid with large particles are derived in an orthogonal helical coordinate system. The Lagrangian approach is utilized to model solid particle trajectories. The interaction between solid particles and the fluid that carries them is accounted for by a source term in the momentum equation for the fluid. The force‐coupling method (FCM), developed by M.R. Maxey and his group, is adopted; in this method the momentum source term is no longer a Dirac delta function but is spread on a numerical mesh by using a finite‐sized envelop with a spherical Gaussian distribution. The influence of inter‐particle and particle–wall collisions is also taken into account. Copyright © 2005 John Wiley & Sons, Ltd.     

Mass and heat transfer during solid sphere dissolution in a non-uniform fluid flow

We studied a nonisothermal dissolution of a solvable solid spherical particle in an axisymmetric non-uniform fluid flow when the concentration level of the solute in the solvent is finite (finite dilution of solute approximation). It is shown that simultaneous heat and mass transfer during solid sphere dissolution in a uniform fluid flow, axisymmetric shear flow, shear-translational flow and flow with a parabolic velocity profile can be described by a system of generalized equations of convective diffusion and energy. Solutions of diffusion and energy equations are obtained in an exact analytical form. Using a general solution the asymptotic solutions for heat and mass transfer problem during spherical solid particle dissolution in a uniform fluid flow, axisymmetric shear flow, shear-translational flow and flow with parabolic velocity profile are derived. Theoretical results are in compliance with the available experimental data on falling urea particles dissolution in water and for solid sphere dissolution in a shear flow.     

Particle shape effect on hydrodynamics and heat transfer in spouted bed: A CFD–DEM study

Spouted bed has drawn much attention due to its good heat and mass transfer efficiency in many chemical units. Investigating the flow patterns and heat and mass transfer inside a spouted bed can help optimize the spouting process. Therefore, in this study, the effects of particle shape on the hydrodynamics and heat transfer in a spouted bed are investigated. This is done by using a validated computational fluid dynamics–discrete element method (CFD–DEM) model, considering volume–equivalent spheres and oblate and prolate spheroids. The results are analysed in detail in terms of the flow pattern, microstructure, and heat transfer characteristics. The numerical results show that the prolate spheroids (Ar = 2.4) form the largest bubble from the beginning of the spouting process and rise the highest because the fluid drag forces can overcome the interlocking and particle–particle frictional forces. Compared with spherical particles, ellipsoidal spheroids have better mobility because of the stronger rotational kinetic energy resulting from the rough surfaces and nonuniform torques. In addition, the oblate spheroid system exhibits better heat transfer performance benefiting from the larger surface area, while prolate spheroids have poor heat transfer efficiency because of their orientation distribution. These findings can serve as a reference for optimizing the design and operation of complex spouted beds.     

A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows

A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid–fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid–fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions.     

Experimental investigation on turbulence modification in a horizontal channel flow at relatively low mass loading

Particle-laden flows in a horizontal channel were investigated by means of a two-phase particle image velocimetry (PIV) technique. Experiments were performed at a Reynolds number of 6 826 and the flow is seeded with polythene beads of two sizes, 60 μm and 110 μm. One was slightly smaller than and the other was larger than the Kolmogorov length scale. The particle loadings were relatively low, with mass loading ratio ranging from 5×10⁻⁴ to 4×10⁻² and volume fractions from 6×10⁻⁷ to 4.8×10⁻⁵, respectively. The results show that the presence of particles can dramatically modify the turbulence even under the lowest mass loading ratio of 5×10⁻⁴. The mean flow is attenuated and decreased with increasing particle size and mass loading. The turbulence intensities are enhanced in all the cases concerned. With the increase of the mass loading, the intensities vary in a complicated manner in the case of small particles, indicating complicated particle-turbulence interactions; whereas they increase monotonously in the case of large particles. The particle velocities and concentrations are also given. The particles lag behind the fluid in the center region but lead in the wall region, and this trend is more prominent for the large particles. The streamwise particle fluctuations are larger than the gas fluctuations for both sizes of particles, however their varying trend with the mass loadings is not so clear. The wall-normal fluctuations increase with increasing mass loadings. They are smaller in the 60 μm particle case but larger in the 110 μm particle case than those of the gas phase. It seems that the small particles follow the fluid motion to certain extent while the larger particles are more likely dominated by their own inertia. Finally, remarkable non-uniform distributions of particle concentration are observed, especially for the large particles. The inertia of particles is proved to be very important for the turbulence modification and particles behaviors and thus should be considered in horizontal channels. The project supported by the National Natural Science Foundation of China (50276021), and Program for New Century Excellent Talents in University, Ministry of Education (NCET-04-0708) The English text was polished by Yunming Chen.     

双柱状颗粒在线性剪切流场中的动力学分析

为研究柱状颗粒在线性剪切流场中的运动状态和受力情况，本文以颗粒长径比为2，颗粒之间的初始距离ΔS_Py=4D为例，基于直接力浸入边界法数值模拟了双柱状颗粒在三维线性剪切流场中的运动过程。根据模拟结果分析了柱状颗粒周围流场参数分布，在考虑壁面对颗粒的影响和颗粒之间相互影响的条件下，研究了颗粒的受力和运动的变化，探索了流体曳力导致柱状颗粒迁移和转动的规律。研究结果表明，双柱状颗粒在线性剪切流场中易向速度大的流体区域运动；前后两颗粒运动状态和轨迹不同，颗粒之间距离较近时，曳力会产生较大的波动；只有当颗粒在壁面附近时，滞后颗粒才能追上领先颗粒，两颗粒发生牵引、翻滚和分离过程。     

Heat transfer effects on particle motion under rarefied conditions

Gas–solid flows occurring on very small spatial scales (of the order of micro and nanometres) are of great relevance in a number of industrial applications. It is currently not well established how particle motion and filtration are affected by non-isothermal conditions at such scales. Furthermore, when the particle size is comparable to the mean free path of the gas, rarefaction effects become important. In the present work we investigate the effects of heat transfer and non-isothermal conditions on the motion of small particles in rarefied flow. For that purpose, a suitable framework is developed here as a generic multiphase DNS method for rarefied flows. The resulting model is valid for low particle Reynolds number flows, irrespective of the Biot number, and for particle Knudsen numbers up to unity in unbounded flow. Using this model, we show that there is different settling behaviour of particles with an internal heat source in rarefied and continuum cases of the carrier gas respectively. It is shown that the chances for thermal levitation and/or lifting up of a particle due to buoyancy effects are significantly reduced under rarefied conditions.     

Conjugate heat transfer within a concentric annulus filled with micropolar fluid

This paper investigates numerically the conjugate heat transfer in an annulus between two concentric cylinders. The annulus contains micropolar fluid and is heated isothermally from its inner wall. The effect of Rayleigh number, thickness of inner wall, inner wall-fluid thermal conductivity ratio, and material parameters of micropolar fluid on heat transfer rate within the annulus has been investigated. The study has shown that for low Rayleigh number regimes and for thermal conductivity of the inner wall greater than that of the fluid, the increase of inner wall thickness increases the heat transfer rate through the annulus and vice versa. While for convection dominating regimes Ra ≥ 10⁴ the increase of inner wall thickness decreases the heat transfer rate. Moreover, the study has shown that for fixed geometrical and flow parameters the heat transfer decreases in case of micropolar fluids in comparison with that of Newtonian fluids.     

Unsteady hydromagnetic Couette flow of dusty fluid with temperature dependent viscosity and thermal conductivity

In the present paper the unsteady Couette flow and heat transfer of a dusty conducting fluid between two parallel plates with temperature dependent viscosity and thermal conductivity are studied. A constant pressure gradient and an external uniform magnetic field are applied. The governing coupled momentum and energy equations are solved numerically using finite differences. The effect of the variable viscosity and thermal conductivity of the fluid and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed.     

Transient heat transfer behaviors in cylindrical porous beds at relatively large Reynolds numbers

The transient behavior of heat transfer in a cylindrical porous bed was examined experimentally under various factors (flow rate, diameter of spherical solid particle, temperature of flowing fluid and physical properties of porous bed). In these factors, it was understood that especially flow rate and the diameter of the particled have important role in evaluating the transient behavior of heat transfer in the porous bed. That is, as the flow rate and the diameter of the particle under a constant diameterD of the cylindrical bed are increased, mean heat transfer coefficient between flowing fluid and the solid particles is increased and the time period to reach a thermally steady state is decreased. The useful experimental correlation equations of mean heat transfer coefficient and the time period to reach the steady state were derived with the functional relationships of Nusselt numberNu _d =f(d/D, Reynolds numberRe _d ) and Fourier numberFo =f (modified Prandtl numberPr*, d/D, Re _d ).     

A spectral‐element discontinuous Galerkin thermal lattice Boltzmann method for conjugate heat transfer applications

We present a spectral‐element discontinuous Galerkin thermal lattice Boltzmann method for fluid–solid conjugate heat transfer applications. Using the discrete Boltzmann equation, we propose a numerical scheme for conjugate heat transfer applications on unstructured, non‐uniform grids. We employ a double‐distribution thermal lattice Boltzmann model to resolve flows with variable Prandtl (Pr) number. Based upon its finite element heritage, the spectral‐element discontinuous Galerkin discretization provides an effective means to model and investigate thermal transport in applications with complex geometries. Our solutions are represented by the tensor product basis of the one‐dimensional Legendre–Lagrange interpolation polynomials. A high‐order discretization is employed on body‐conforming hexahedral elements with Gauss–Lobatto–Legendre quadrature nodes. Thermal and hydrodynamic bounce‐back boundary conditions are imposed via the numerical flux formulation that arises because of the discontinuous Galerkin approach. As a result, our scheme does not require tedious extrapolation at the boundaries, which may cause loss of mass conservation. We compare solutions of the proposed scheme with an analytical solution for a solid–solid conjugate heat transfer problem in a 2D annulus and illustrate the capture of temperature continuities across interfaces for conductivity ratio γ > 1. We also investigate the effect of Reynolds (Re) and Grashof (Gr) number on the conjugate heat transfer between a heat‐generating solid and a surrounding fluid. Steady‐state results are presented for Re = 5?40 and Gr = 10⁵?10⁶. In each case, we discuss the effect of Re and Gr on the heat flux (i.e. Nusselt number Nu) at the fluid–solid interface. Our results are validated against previous studies that employ finite‐difference and continuous spectral‐element methods to solve the Navier–Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd.     

Mixed convective heat transfer characteristics and mechanisms in structured packed beds

The structured packed bed is considered a promising reactor owing to its low pressure drop and good heat transfer performance. In the heat transfer process of thermal storage in packed beds, natural convection plays an important role. To obtain the mixed convective heat transfer characteristics and mechanisms in packed beds, numerical simulations and coupling analyses were carried out in this study on the unsteady process of fluid flow and heat transfer. A three-dimensional model of the flow channel in the packed bed was established, and the Navier–Stokes equations and Laminar model were adopted for the computations. The effects of the driving force on fluid flow around a particle were studied in detail. The differences in velocity and density distributions under different flow directions due to effect of the aiding flow or opposing flow were intuitively demonstrated and quantitatively analyzed. It was found that the driving force strengthens the fluid flow near the particle surface when aiding flow occurs and inhibits the fluid flow when opposing flow occurs. The boundary layer structure was changed by the natural convection, which in turn influences the field synergy angle. For the aiding flow, the coordination between the velocity and density fields is higher than that for the opposing flow. By analysis the effects of physical parameters on mixed convective heat transfer, it is indicated that with an increase in the fluid-solid temperature difference or the particle diameter, or a decrease in the fluid temperature, the strengthening or inhibiting effect of natural convection on the heat transfer became more significant.     

A single-camera technique for simultaneous measurement of large solid particles transported in rapid shallow channel flows

This paper describes a measurement technique that was successfully applied in a study of bed load transport of large spherical solid particles in a shallow and supercritical flow (Fr?=?2.59–3.17) down a steep slope. The experimental condition was characterized by the relatively large solid particle size compared to the flow depth (d _p /h?=?0.23–0.35), and compared to the tracer diameter (d _p /d _t ?≈?130). The technique incorporated particle image velocimetry and particle tracking velocimetry (PTV) to simultaneously measure the characteristics of the two phases. In order to detect true solid particles and to distinguish them from each other and the unwanted objects, a particle characterization (PCR) algorithm based on Hough transform was employed. The output from the PCR process was utilized for PTV, as well as to generate the corresponding tracer images for special needs. Validation tests have confirmed the pixel accuracy and high reliability of the combined technique. Experimental results obtained with the developed technique include flow velocities, particle velocities, and concentration. The analysis has shown that the particle concentration profile followed an exponential relationship of the form similar to that of Rouse’s profiles, despite the large d _p /h ratio. It also revealed the effect of phase interaction, as a low loading rate of light particles on the order of O(10^?3) could yield a noticeable slowdown in the streamwise fluid velocity.