Modeling fixed bed reactors as porous media using unit cell simulations

The ability to design multi-resonant thermal emitters is essential to the advancement of a wide variety of applications, including thermal management and sensing. These fields would greatly benefit from the development of more efficient tools for predicting the spectral response of coupled, multi-resonator systems. In this work, we propose a semi-analytical prediction tool based on coupled-mode theory. In our approach, a complex thermal emitter is fully described by a set of coupled-mode parameters, which can be straightforwardly calculated from simulations of unit cells containing single and double resonators. We demonstrate the accuracy of our method by predicting and optimizing spectral response in a coupled, multi-resonant system based on hBN ribbons. The approach described here can greatly reduce the computational overhead associated with spectral design tasks in coupled, multi-resonant systems.

The manifold microchannel (MMC) heat sink has been widely studied for liquid-cooling of power-dense electronic components. Conventionally, thermal-fluid performance of an MMC heat sink is analyzed via unit cell simulations and designed by varying the rectangular fin and channel geometries, namely size optimization. To further explore the performance potential of the MMC heat sink, this paper proposes topology optimization (TO) to design the optimal freeform fin/channel geometry to maximize heat transfer performance while minimizing the required pumping power. The heat transfer physics in an MMC heat sink is governed by conjugate heat transfer between an incompressible laminar fluid and a heated conductor. The MMC heat sink fin/channel geometry design is formulated as a material distribution problem in a periodic unit cell. Since TO describes the geometry non-parametrically, it facilitates innovative designs through the exploration of arbitrary shapes. The physics-governed design optimization problem is solved by mathematical programming using design sensitivities and an iterative gradient-based method. The thermal-fluid performance is presented for both conventional size optimization and the proposed TO approach, considering the heat transfer performance versus the required pumping power. It is demonstrated that the TO designed fin/channel geometries outperform those obtained through size optimization. Due to the shape complexity associated with the TO designed fin/channel geometries, they are not readily suitable for conventional manufacturing processes, e.g., machining and metal die-casting. However, such out-of-box designs fully exploit the flexibility offered by the latest advanced manufacturing processes, e.g., additive manufacturing and rapid investment casting.

Micromechanics-based identification of a ductile fracture model for three structural steels

In this study, a polarization‐insensitive and ultra‐wideband transmissive polarization convertor (PC) is proposed. The proposed PC operates at 2.29–6.27 GHz (93.32%) for the same polarization reflection at ≤−10 dB, orthogonally rotated polarization transmission at ≥−1 dB, and a 0.22 λlow thickness at the lowest operating frequency. A dual‐polarized tightly coupled dipole array (TCDA) antenna is introduced for application in the wideband PC, where the operating bandwidth is related to the antenna bandwidth. Additionally, the polarization insensitivity is related to the feeding structure, which allows coupling of the receiving signal to the transmitting antenna. Furthermore, the operating principle is described in detail by showing the surface current on the TCDA and the feeding structure. Finally, unit cell simulations and measurements are presented to demonstrate the performance of the proposed PC.

Elastically-isotropic elementary cubic lattices composed of tailored hollow beams

In this article, we present a high‐gain low‐profile resonant cavity antenna that utilizes a novel metamaterial surface as a superstrate. Due to the low‐reflection phase value of the metamaterial superstrate, the thickness of the resonant cavity antenna is significantly thinner than the operating wavelength. Several important parameters that characterize the metamaterial superstrate are investigated based on the unit cell simulation. The proposed antenna is fabricated and measured. The experimental results show that the prototype can provide a high‐gain at the operating frequency. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 1855–1858, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25336

Dispersion in periodic porous media. Experience versus theory for two-dimensional systems

Vanadium redox flow battery (VRFB) is one of the promising technologies for large scale renewable energy storage due to its long life time and flexible design. Electrolyte flow rate, electrolyte concentration, electrode porosity, temperature and applied magnitude of current have significant effect on the efficiency of VRFB. In the present work, a simplified dynamic lumped parameter model is developed in MATLAB to provide accurate results at unit cell level which can be used to control and optimize the parameters. The proposed model is based on the mass balance and charge conservation of various vanadium species and hydrogen ion concentration in the electrolyte. Major losses such as ohmic losses and activation losses are included in the cell potential. Recirculation of the electrolyte through external reservoirs is also considered. Numerical simulation demonstrates the effect of change in initial vanadium concentration and operating temperature on unit cell performance. It is shown that variations in electrolyte flow rate, magnitude of applied current substantially alter the charge/discharge characteristics and efficiency.

The laminar pulsating flow through porous media was numerically studied. Two-dimensional flows in systems composed of a number of unit cells of generic porous structures were simulated using a computational fluid mechanics tool, with sinusoidal variations in flow with time as the boundary condition. The porous media were periodic arrays of square cylinders. Detailed numerical data for the porosity ranging from 0.64 to 0.84, with flow pulsation frequencies of 20–64 Hz were obtained. Based on these numerical data, the instantaneous as well as the cycle-average permeability and Forchheimer coefficients, to be used in the standard unsteady volume-averaged momentum conservation equation for flow in porous media, were derived. It was found that the cycle-average permeability coefficients were nearly the same as those for steady flow, but the cycle-average Forchheimer coefficients were significantly larger than those for steady flow and were sensitive to the flow oscillation frequency. Significant phase lags were observed between the volume-averaged velocity and the pressure waves. The phase difference between pressure and velocity waves, which is important for pulse tube cryocooling, depended strongly on porosity and the mean-flow Reynolds number.

Local fluid flow (LFF) at the mesoscopic scale is the main dissipation mechanism of seismic waves in heterogeneous porous media within the seismic frequency band. LFF is easily influenced by the structure and boundary conditions of the porous media, which leads to different behaviors of the peak frequency of attenuation. The associated transition frequency can provide detailed information about the trend of LFF; therefore, research on the transition frequency of LFF and its relationship with the peak frequency of the corresponding attenuation (i.e., inverse of quality factor) facilitates the detailed understanding of the effect of inner structures and boundary conditions in porous media. In this study, we firstly obtain the transition frequency of fluid flux based on Biot’s theory of poroelasticity and the fast Fourier transform algorithm in a sample containing one repeating unit cell (RUC). We then analyze changes of these two frequencies in porous media with different porous properties. Finally, we extend our analysis to the influence of the undrained boundary condition on the transition frequency and peak frequency in porous media with multiple RUCs. This setup can facilitate the understanding of the effect from the undrained boundary condition. Results demonstrate that these two frequencies have the same trend at low water saturation, but amplitude variations differ between the frequencies as the amount of saturation increases. However, for cases of high water saturation, both the trend and the amplitude variation of these two frequencies fit well with each other.

The behaviour of non-wetting ganglia undergoing immiscible displacement in a porous medium is studied with the help of a theoretical simulator. The porous medium is represented by a network of randomly sized unit cells of the constricted-tube type. The fluid of a non-wetting ganglion is in contact with the wetting fluid at menisci which are assumed to be spherical cups. The flow in every constricted unit cell occupied by a single fluid is modelled as flow in a sinusoidal tube. The flow in every unit cell that contains a meniscus and portions of both fluids is treated with a combination of a Washburn-type analysis and a lubrication-theory approximation. The flow problem is thus reduced to a system of linear equations the solution of which gives the instantaneous pressures on the nodes, the flowrates through the unit cells, and the velocities of the menisci. The motion of a ganglion is determined by assuming quasi-static flow, taking a small time increment, updating the positions of the menisci, and iterating. The behaviour of solitary ganglia is studied under conditions of quasi-static displacement (Ca slightly larger than critical), as well as dynamic displacement (Ca substantially larger than critical). Shape evolution, rate of flow, mode of break-up, and stranding are examined. The stranding and break-up coefficients are determined as functions of the capillary number and the ganglion size for a 100 × 200 sandpack. The dependence of the average ganglion velocity on ganglion size, capillary number, viscosity ratio and dynamic contact angle is examined for the simple case of motion between straight rows of spheres. It is found, among other things, that when μo < μw the velocity of ganglia can be substantially larger than that of the displacing fluid.

In this work we develop, via volume averaging, the macroscale transport equation \nfor a reactive chemical species undergoing a heterogeneous reaction with first-\norder kinetics. We describe the closure problem required to predict (1) the \neffective macroscale reaction rate, and (2) the effective dispersion tensor from \nthe microscale geometry, chemical, and physical properties of the media. The \neffective parameters are computed for a 3D simple unit cell. Particular attention \nis given to the influence of inertial effects on the flow field and the resulting \neffective parameters.

A pore scale analysis is implemented in this numerical study to investigate the behavior of microscopic inertia and thermal dispersion in a porous medium with a periodic structure. The macroscopic characteristics of the transport phenomena are evaluated with an averaging technique of the controlling variables at a pore scale level in an elementary cell of the porous structure. The Darcy–Forchheimer model describes the fluid motion through the porous medium while the continuity and Navier–Stokes equations are applied within the unit cell. An average energy equation is employed for the thermal part of the porous medium. The macroscopic pressure loss is computed in order to evaluate the dominant microscopic inertial effects. Local fluctuations of velocity and temperature at the pore scale are instrumental in the quantification of the thermal dispersion through the total effective thermal diffusivity. The numerical results demonstrate that microscopic inertia contributes significantly to the magnitude of the macroscopic pressure loss, in some instances with as much as 70%. Depending on the nature of the porous medium, the thermal dispersion may have a marked bearing on the heat transfer, particularly in the streamwise direction for a highly conducting fluid and certain values of the Peclet number.

Carbon Dioxide (CO2) injection in geological formations is a potential solution to control anthropogenic greenhouse gas emissions. Value added processes such as CO2 flooding for enhanced oil/gas recovery and disposal processes such as CO2 injection in saline aquifers are among the most promising sequestration processes. Transport, storage, and sequestration of CO2 in these processes involve dispersion and reaction phenomena in porous media. The overall performance of any CO2 injection project depends on the mechanistic aspects of CO2 interaction with the natural porous system at pore scale, core scale, and the heterogeneity of the geological formations. The physics of transport and sequestration of CO2 for different CO2 injection processes in a pore-level scale is first described. These pore-level events are then related to core-scale (gridscale) coefficients using an advanced upscale theory. At the pore-level, a unit cell consists of different sand grains and the interstitial space around them. CO2 enters the unit cell by convection and diffusion and interacts with the interstitial fluid and sand grains. Such local events are transformed into a macro-scale level by adopting periodic boundary conditions for contiguous unit-cells and applying Taylor-Aris dispersion theory. Using this theory, macroscopic coefficient for the transport of CO2 molecules in porous media are determined. These macroscopic coefficients may be used in dispersionreaction constitutive equation to calculate CO2 concentration in time and space. Introduction The three main options for the geological storage of CO2 are saline aquifers, and existing oil and gas fields. These can be divided into two economic end-members. First are purely storage options, whereby the CO2 is injected without any direct financial benefits, e.g. saline aquifers, although carbon tax credits may improve the financial viability of this option. The second are utilization options where the CO2 injection process has additional economic benefits through enhanced hydrocarbon recovery(1). Many of the oil and gas pools in North America have reached the maturity of economic production. CO2 injection is an option to rejuvenate oil or gas production from these reservoirs(2). Miscibility of CO2 and oil improves microscopic displacement efficiency in these pools(3,4). Saline aquifers are defined as aquifers without potable water. Saline aquifers have the potential to store a huge volume of the total CO2 emissions in various locations near the sources of the CO2 emission, e.g. power plants(5–7). For any CO2 storage or utilization process to be successful, it must be technically and economically feasible, effective in significantly reducing CO2 emission for a long period of time, and be safe for people and environment. Reliable mathematical models are needed to predict the success of a CO2 sequestration process in geological formations. The efficiency of a CO2 sequestration process is defined as: Equation (1) (Available in full paper) Mathematical Modelling Suppose that CO2-free fluid flows through the porous bed. At time t=0 let a swarm of CO2 molecules be instantaneously introduced into the bed. Each CO2 molecule will be transported through the interstices by convection and diffusion, with some being interacting (ab/adsorption, reaction) with the interstitial fluid and sand grains.

Dual‐porosity simulation is one of the most used and efficient approaches in modeling fractured porous media. The performance of this approach is highly dependent on the accuracy of the definition of matrix‐fracture transfer shape factor. In this paper, a two‐step computational algorithm is developed to enhance the accuracy of the dual‐porosity method in modeling large‐scale deformable porous media, particularly in the transient stage when the conventional dual‐porosity models are associated with some errors. Moreover, in the proposed finite element method (FEM)‐based algorithm, the interaction between the fluid and solid phases is taken into account using a modified expression for the conventional shape factor. To this end, an extended relationship is derived to calculate the hydro‐mechanical shape factor for deformable saturated porous media. An appropriate unit cell along with the consistent boundary conditions is introduced, and the corresponding hydro‐mechanical shape factor is numerically evaluated for the unit cell at each time step. Finally, the calculated time‐varying shape factors are employed in a dual‐porosity framework to simulate various case studies and investigate the influence of different parameters, including the boundary conditions, the fracture to matrix permeability ratio, and the fracture compressibility coefficient on the hydraulic and hydro‐mechanical time‐varying shape factors. Numerical simulations are carried out by employing the proposed dual‐porosity algorithm through two general problems and the results are compared with the fine‐grid direct numerical simulation. The results are promising and show that the present algorithm effectively and efficiently increases the precision of the dual‐porosity method in modeling large‐scale deformable problems.