Combined Effect of Stress, Pore Pressure and Temperature on Methane Permeability in Anthracite Coal: An Experimental Study

The effects of particle-size distribution on the longitudinal dispersion coefficient ( $D_{\mathrm{L}})$ D L ) in packed beds of spherical particles are studied by simulating a tracer column experiment. The packed-bed models consist of uniform and different-sized spherical particles with a ratio of maximum to minimum particle diameter in the range of 1–4. The modified version of Euclidian Voronoi diagrams is used to discretize the system of particles into cells that each contains one sphere. The local flow distribution is derived with the use of Laurent series. The flow pattern at low particle Reynolds number is then obtained by minimization of dissipation rate of energy for the dual stream function. The value of $D_{\mathrm{L}}$ D L is obtained by comparing the effluent curve from large discrete systems of spherical particles to the solution of the one-dimensional advection–dispersion equation. Main results are that at Peclet numbers above 1, increasing the width of the particle-size distribution increases the values of $D_{\mathrm{L}}$ D L in the packed bed. At Peclet numbers below 1, increasing the width of the particle-size distribution slightly lowers $D_{\mathrm{L}}$ D L .     

固定床化学链燃烧氧化反应的数值模拟

基于Chimera网格采用有限体积法模拟了450个颗粒随机填充固定床中的化学链燃烧的氧化反应过程,并采用三维瞬态N-S方程,结合压力Poisson方程方法,详细分析了床层入口Re=5时的颗粒内部和外部的传质传热过程．模拟结果揭示了在大颗粒的固定床中,颗粒内部有效扩散系数对颗粒内部的传质起着决定性作用,而且颗粒表面的浓度梯度决定了总反应速率;另外,有惰性芯的结构化颗粒能有效地改善颗粒内部总的反应速率,颗粒的转化速率,并且能使床层很快地达到热平衡．模拟结果能更好地帮助我们认识固定床化学链反应器中的反应和组分传递机理．     

Mixed convection film condensation from downward flowing vapors onto a sphere with variable wall temperature

A model is developed for the study of mixed- convection film condensation from downward flowing vapors onto a sphere with variable wall temperature. The model combined natural convection dominated and forced convection dominated film condensation, concerning effects of pressure gradient (P), interfacial vapor shear drag and non-uniform wall temperature variation (A), has been investigated and solved numerically. The effect of pressure gradient on the dimensionless mean heat transfer, NuˉRe^−1/2 will remain almost uniform with increasing P until for various corresponding available values of F. Meanwhile, the dimensionless mean heat transfer, NuˉRe^−1/2 is increasing significantly with F for its corresponding available values of P. Although the non-uniform wall temperature variation has an appreciable influence on the local film flow and heat transfer; however, the dependence of mean heat transfer on A can be almost negligible. Received on 10 October 1996     

Dense particle cloud dispersion by a shock wave

A dense particle flow is generated by the interaction of a shock wave with an initially stationary packed granular bed. High-speed particle dispersion research is motivated by the energy release enhancement of explosives containing solid particles. The initial packed granular bed is produced by compressing loose powder into a wafer with a particle volume fraction of $\phi _\mathrm{p} = 0.48$ . The wafer is positioned inside the shock tube, uniformly filling the entire cross-section. This results in a clean experiment where no flow obstructing support structures are present. Through high-speed shadowgraph imaging and pressure measurements along the length of the channel, detailed information about the particle shock interaction was obtained. Due to the limited strength of the incident shock wave, no transmitted shock wave is produced. The initial solid-like response of the particle wafer acceleration forms a series of compression waves that eventually coalesce to form a shock wave. Breakup is initiated along the periphery of the wafer as the result of shear that forms due to the fixed boundary condition. Particle breakup is initiated by local failure sites that result in the formation of particle jets that extend ahead of the accelerating, largely intact, wafer core. In a circular tube, the failure sites are uniformly distributed along the wafer circumference. In a square channel, the failure sites, and the subsequent particle jets, initially form at the corners due to the enhanced shear. The wafer breakup subsequently spreads to the edges forming a highly non-uniform particle cloud.     

A three phase model of a batch fluidized bed

A three phase mathematical model of simultaneous heat and mass transfer of a batch operation for a fluidized bed is presented. The three phases are a solid free bubble, emulsion and solid phases. The model employs an elaborate five equations porosity model. Various correlations for the minimum fluidization parameters are surveyed and compared with the adequate one is being adopted in the model. The governing equations together with the boundary and initial conditions are presented for a cyclic operation of the bed. These are numerically solved for a test case where the bed is charged with silica gel particles to dehumidify a process air stream. Thus the bed works in an air dehumidification mode/bed regeneration mode cyclic operation with matching conditions.Results for the bed operation are presented as the temperature and humidity ratio variations for the test case. The results indicate the ability of the developed model to provide the␣required data for the concerned batch operated fluidized bed. Received on 11 May 1998     

Numerical Simulation of Forced Convective Heat Transfer Past a Square Diamond-Shaped Porous Cylinder

Fluid flow and heat transfer around and through a porous cylinder is an important issue in engineering applications. In this paper a numerical study is carried out for simulating the fluid flow and forced convection heat transfer around and through a square diamond-shaped porous cylinder. The flow is two-dimensional, steady, and laminar. Conservation laws of mass, momentum, and heat transport equations are applied in the clear region and Darcy–Brinkman–Forchheimer model for simulating the flow in the porous medium has been used. Equations with the relevant boundary conditions are numerically solved using a finite volume approach. In this study, Reynolds and Darcy numbers are varied within the ranges of $1<Re<45$ and $10^{-6}<Da<10^{- 2}$ , respectively. The porosity $(\varepsilon )$ is 0.5. This paper presents the effect of Reynolds and Darcy numbers on the flow structure and heat transfer characteristics. Finally, these parameters are compared among solid and porous cylinder. It was found that the drag coefficient decreases and flow separation from the cylinder is delayed with increasing Darcy number. Also the size of the thermal plume decreases by decreasing Darcy number.     

Fluid Permeability in Stratified Unconsolidated Particulate Bed

Fluid permeability of polydisperse particulate bed with finite thickness has been examined. On the assumption of creeping flow, the permeability of monodisperse particles with arbitrary arrangement is calculated by means of Stokesian dynamics approach in which the interaction between individual particles and interstitial fluid is described by multipole expansion of the Oseen tensor. We have extended such calculation method to polydisperse particulate systems which have not so dense structures (up to particle volume fraction ${\phi \sim}$ 0.2). The particles are located infinitely in space and their interaction has been taken into account by Ewald summation technique. For the spatial distribution of polydisperse particles, we consider locally stratified particulate beds and define stratification degree as a parameter which apparently and mathematically represents the thickness of the mixing region of different-sized particles. The permeability profiles in the particulate beds with different stratification degree show the dependence of local permeability on the spatial and size distribution of particles. Consequently, the calculation results indicate that the permeability of non-uniform polydisperse particulate bed can be predicted by integrating the local permeation resistance which is determined by the local specific surface area.     

Mixed convection film condensation from downward flowing vapors onto a sphere with uniform wall heat flux

A model is developed for the study of mixed convection film condensation from downward flowing vapors onto a sphere with uniform wall heat flux. The model combined natural convection dominated and forced convection dominated film condensation, including effects of pressure gradient and interfacial vapor shear drag has been investigated and solved numerically. The separation angle of the condensate film layer, φ _s is also obtained for various pressure gradient parameters, P ^* and their corresponding dimensionless Grashof?'s parameters, Gr ^*. Besides, the effect of P ^* on the dimensionless mean heat transfer, will remain almost uniform with increasing P ^* until for various corresponding available values of Gr ^*. Meanwhile, the dimensionless mean heat transfer, is increasing significantly with Gr ^* for its corresponding available values of P ^*. For pure natural-convection film condensation, is obtained.     

Experimental and numerical investigations on the performance of dehumidifying desiccant beds composed of silica-gel and thermal energy storage particles

Enhanced efficiency of the adsorption process in the dehumidifier is a key element for improved performance of desiccant cooling systems. Due to the exothermic nature of the adsorption process, the dehumidification and cooling capacity are limited by significant temperature changes in the adsorption column. In the present study, the effects of integration of sensible and latent heat storage particles in the desiccant bed for in situ management of released adsorption heat are investigated. For this purpose, column experiments are performed using an initially dry granular bed made of silica-gel particles or a homogeneous mixture of silica gel and inert sensible or latent heat storage particles. The packed bed is subject to a sudden uniform air flow at selected values of temperature and humidity. Also, a packed bed numerical model is developed that includes the coupled non-equilibrium heat and moisture transfer in the solid and gas phases. Investigations of the heat and mass transfer characteristics are reported using the composite structure and the results are compared with the base case of simple silica gel bed. Improved desiccant cooling system performance can be obtained by appropriate adjustment of desiccant cycle operation and proper choice of the volume ratio of thermal energy storage particles.     

Diffusion-Thermo and Radiation Effects on Unsteady MHD Flow Through Porous Medium Past an Impulsively Started Infinite Vertical Plate with Variable Temperature and Mass Diffusion

The objective of this study is to investigate diffusion-thermo (Dufour effect) and radiation effects on unsteady MHD free convection flow past an impulsively started infinite vertical plate with variable temperature and uniform mass diffusion in the presence of transverse applied magnetic field through porous medium. At time t > 0, the plate is given an impulsive motion with constant velocity u ₀ in the vertical upward direction against to the gravitational field. At the same time, the plate temperature is raised linearly with time t and the level of concentration near the plate is raised to ${{C}_{\rm w}^{\prime}}$ . A magnetic field of uniform strength B ₀ is applied normal to the direction to the flow. The dimensionless governing equations are solved in closed form by Laplace transform technique. The effect of flow parameters on velocity, temperature, concentration, the rate of heat transfer and the rate of mass transfer are shown through graphs.     

Boiling in particle beds in a two dimensional configuration

 The work presented here concentrates on the boiling heat transfer from a porous bed with internal heat sources. This configuration can occur, when in the progress of a hypothetical accident the core melt relocates to the lower plenum of a nuclear reactor pressure vessel and gets partially fragmented. The coolability and the boiling heat transfer are experimentally investigated for two- dimensional particle beds. Experiments are discussed with particles of an uniform diameter of 2 mm as well as mixtures of 4 mm and 1 mm particles. The bed was placed in a glass container with an inclined bottom to represent a section of the lower plenum of a reactor pressure vessel. The refrigerant R134a was used for tests with a pressure up to 1.8 MPa. The particle bed was equipped with thermocouples and capacitive local void fraction probes to map the temperatures and the distribution of liquid and steam. In the following the basic effects and the parameters influencing the coolability of such a configuration will be discussed. Received on 1 March 2001     

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.     

Unsteady MHD double-diffusive convection boundary-layer flow past a radiate hot vertical surface in porous media in the presence of chemical reaction and heat sink

This paper presents an analytical study of the unsteady MHD free convective heat and mass transfer flow of a viscous, incompressible, gray, absorbing-emitting but non-scattering, optically-thick and electrically conducting fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity. We employ a Darcian viscous flow model for the porous medium the Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. The homogeneous chemical reaction of first order is accounted in mass diffusion equation. The governing equations are solved in closed form by Laplace-transform technique. A parametric study of all involved parameters is conducted and representative set of numerical results for the velocity, temperature, concentration, shear stress function $\frac{\partial u}{\partial y} \vert_{y=0}$ , temperature gradient $\frac{\partial \theta }{ \partial y}\vert_{y=0}$ , and concentration gradient $\frac{ \partial \phi }{\partial y}\vert_{y=0}$ is illustrated graphically and physical aspects of the problem are discussed.     

Direct measurements of local bed shear stress in the presence of pressure gradients

This paper describes the development of a shear plate sensor capable of directly measuring the local mean bed shear stress in small-scale and large-scale laboratory flumes. The sensor is capable of measuring bed shear stress in the range \(\pm\) 200 Pa with an accuracy up to \(\pm\) 1 %. Its size, 43 mm in the flow direction, is designed to be small enough to give spatially local measurements, and its bandwidth, 75 Hz, is high enough to resolve time-varying forcing. Typically, shear plate sensors are restricted to use in zero pressure gradient flows because secondary forces on the edge of the shear plate caused by pressure gradients can introduce large errors. However, by analysis of the pressure distribution at the edges of the shear plate in mild pressure gradients, we introduce a new methodology for correcting for the pressure gradient force. The developed sensor includes pressure tappings to measure the pressure gradient in the flow, and the methodology for correction is applied to obtain accurate measurements of bed shear stress under solitary waves in a small-scale wave flume. The sensor is also validated by measurements in a turbulent flat plate boundary layer in open channel flow.     

Tensor Products, Positive Linear Operators, and Delay-Differential Equations

We develop the theory of compound functional differential equations, which are tensor and exterior products of linear functional differential equations. Of particular interest is the equation $$\begin{aligned} \dot{x}(t)=-\alpha (t)x(t)-\beta (t)x(t-1) \end{aligned}$$ with a single delay, where the delay coefficient is of one sign, say $\delta \beta (t)\ge 0$ with $\delta \in \{-1,1\}$ . Positivity properties are studied, with the result that if $(-1)^k=\delta $ then the $k$ -fold exterior product of the above system generates a linear process which is positive with respect to a certain cone in the phase space. Additionally, if the coefficients $\alpha (t)$ and $\beta (t)$ are periodic of the same period, and $\beta (t)$ satisfies a uniform sign condition, then there is an infinite set of Floquet multipliers which are complete with respect to an associated lap number. Finally, the concept of $u_0$ -positivity of the exterior product is investigated when $\beta (t)$ satisfies a uniform sign condition.     

The Motion of a Fluid-Rigid Ball System at the Zero Limit of the Rigid Ball Radius

We study the limiting motion of a system of rigid ball moving in a Navier–Stokes fluid in ${\mathbb{R}^3}$ as the radius of the ball goes to zero. Recently, Dashti and Robinson solved this problem in the two-dimensional case, in the absence of rotation of the ball (Dashti and Robinson in Arch Rational Mech Anal 200:285–312, 2011). This restriction was caused by the difficulty in obtaining appropriate uniform bounds on the second order derivatives of the fluid velocity when the rigid body can rotate. In this paper, we show how to obtain the required uniform bounds on the velocity fields in the three- dimensional case. These estimates then allow us to pass to the zero limit of the ball radius and show that the solution of the coupled system converges to the solution of the Navier–Stokes equations describing the motion of only fluid in the whole space. The trajectory of the centre of the ball converges to a fluid particle trajectory, which justifies the use of rigid tracers for finding Lagrangian paths of fluid flow.     

Mixed Convection Boundary-Layer Flow Over a Vertical Surface Embedded in a Porous Material Subject to a Convective Boundary Condition

The mixed convection boundary-layer flow on one face of a semi-infinite vertical surface embedded in a fluid-saturated porous medium is considered when the other face is taken to be in contact with a hot or cooled fluid maintaining that surface at a constant temperature $T_\mathrm{{f}}$ . The governing system of partial differential equations is transformed into a system of ordinary differential equations through an appropriate similarity transformation. These equations are solved numerically in terms of a dimensionless mixed convection parameter $\epsilon $ and a surface heat transfer parameter $\gamma $ . The results indicate that dual solutions exist for opposing flow, $\epsilon <0$ , with the dependence of the critical values $\epsilon _\mathrm{{c}}$ on $\gamma $ being determined, whereas for the assisting flow $\epsilon >0$ , the solution is unique. Limiting asymptotic forms for both $\gamma $ small and large and $\epsilon $ large are also discussed.     

Mechanism of the Impact of Particle Size Distribution to Bed-Inventory Overturn for Pant-Leg Circulating Fluidized Bed

An improved two particle sizes numerical model based on a uniform size model was established to investigate the influence of the average particle size on bed-inventory overturn inside a pant-leg circulating fluidized bed (CFB). The new model successfully simulated the dynamic performance of a pant-leg CFB that as average particle size shrank, the pant-leg CFB tended to overturn, while the uniform size model showed a contradicted trend. The success was attributed to the difference of the flow pattern with different particle size. The smaller particles tend to stay the upper furnace after fluidized by the primary air flow while the larger particles tend to fall back to the bottom soon after being carried to upper furnace by the primary air flow and smaller particles. As pointed out in our previous work, the lateral mass transfer resulted in a lateral pressure difference at the upper finance and inhibited further lateral mass transfer, which was regarded as a self-balancing process. The quick fall down of the large particles somehow weaken the lateral pressure different built-up at the upper furnace. Therefore, as the average particle size shrink, the weaken effect of the large particles on self-balancing ability of the pant-leg CFB increase, resulting a more tendency for bed-inventory overturn. It was such a characteristic behavior of the large particles, which was neglected in the uniform particle size model, caused the difference between the results of the two models described above.