The application of homotopy analysis method for 2-dimensional steady slip flow in microchannels

Research on micro flow, especially on micro slip flow, is very important for designing and optimizing the micro electromechanical system (MEMS). In this Letter, similarity transformation for the Navier-Stokes equation for 2-dimensional steady slip flow in microchannels is given. We provide an analytical solution for the slip flow using a powerful, easy-to-use analytic technique for non-linear problems, that is, the homotopy analysis method (HAM). The analytical solution is presented in the form of an infinite series. The effects of the Knudsen number (Kn) is discussed on the velocity profiles. It is found that the results are in excellent agreement with the existing results in the literature for the case of laminar developed flow.     

On the effective viscosity for the Darcy-Brinkman equation

Up-scaling of the Stokes equations with non-slip boundary condition describing the flow in a porous medium, leads to the Darcy-Brinkman equation

?_βμ_βv_D,β=-K_β·(∇P_m,β-ρ_βg)+K_β·μ_β∇²v_D,β.     

A cumulant analysis for non-Gaussian displacement distributions in Newtonian and non-Newtonian flows through porous media

We use displacement encoding pulsed field gradient (PFG) nuclear magnetic resonance to measure Fourier components S(q) of flow displacement distributions P(zeta) with mean displacement (zeta) for Newtonian and non-Newtonian flows through rocks and bead packs. Displacement distributions are non-Gaussian; hence, there are finite terms above second order in the cumulant expansion of ln(S(q)). We describe an algorithm for an optimal self-consistent cumulant analysis of data, which can be used to obtain the first three (central) moments of a non-Gaussian P(zeta), with error bars. The analysis is applied to Newtonian and non-Newtonian flows in rocks and beads. Flow with shear-thinning xanthan solution produces a 15.6+/-2.3% enhancement of the variance sigma(2) of displacement distributions when compared to flow experiments with water.     

Lattice Boltzmann method on quadtree grids for simulating fluid flow through porous media: A new automatic algorithm

During the past two decades, the lattice Boltzmann (LB) method has been introduced as a class of computational fluid dynamic methods for fluid flow simulations. In this method, instead of solving the Navier Stocks equation, the Boltzmann equation is solved to simulate the flow of a fluid. This method was originally developed based on uniform grids. However, in order to model complex geometries such as porous media, it can be very slow in comparison with other techniques such as finite differences and finite elements. To eliminate this limitation, a number of studies have aimed to formulate the lattice Boltzmann on the unstructured grids. This paper deals with simulating fluid flow through a synthetic porous medium using the LB method and on the quadtree grid structure. To this end, the LB method was used on nonuniform grids coupled with a technique for image reconstruction which resulted in the quadtree grids for simulation of fluid flow through porous media. Accuracy and efficiency of this algorithm is compared against the conventional LB method based on uniform grids. While the decrease in computational time in the proposed LB method on nonuniform grids is found to be significant regarding the size of the initial and reconstructed images, the same level of accuracy is obtained when compared with the conventional LB method on uniform grids.     

Influence of partial slip on the peristaltic flow in a porous medium

In this paper, the slip effects are discussed on the peristaltic flow of a viscous fluid in a porous medium. A long wavelength approximation is used in the flow modelling. The solutions for stream function and axial velocity are constructed by employing the Adomian decomposition method. Numerical integration has been used for the pumping and trapping phenomena. Graphs illustrate the physical behavior. It is noted that the size of the trapped bolus decreases and its symmetry disappears for large values of the slip parameter. Further, the peristaltic pumping rate decreases by increasing the slip parameter.     

Three-phase compressible flow in porous media: Total Differential Compatible interpolation of relative permeabilities

We describe the construction of Total Differential (TD) three-phase data for the implementation of the exact global pressure formulation for the modeling of three-phase compressible flow in porous media. This global formulation is preferred since it reduces the coupling between the pressure and saturation equations, compared to phase or weighted formulations. It simplifies the numerical analysis of the problem and boosts its computational efficiency. However, this global pressure approach exists only for three-phase data (relative permeabilities, capillary pressures) which satisfy a TD condition. Such TD three-phase data are determined by the choice of a global capillary pressure function and a global mobility function, which take both saturations and global pressure level as argument. Boundary conditions for global capillary pressure and global mobility are given such that the corresponding three-phase data are consistent with a given set of three two-phase data. The numerical construction of global capillary pressure and global mobility functions by C¹${\text{C}}^1$ and C⁰${\text{C}}^0$ finite element is then performed using bi-Laplacian and Laplacian interpolation. Examples of the corresponding TD three-phase data are given for a compressible and an incompressible case.     

Magnetic resonance velocity imaging of liquid and gas two-phase flow in packed beds

Single-phase liquid flow in porous media such as bead packs and model fixed bed reactors has been well studied by MRI. To some extent this early work represents the necessary preliminary research to address the more challenging problem of two-phase flow of gas and liquid within these systems. In this paper, we present images of both the gas and liquid velocities during stable liquid–gas flow of water and SF₆ within a packing of 5 mm spheres contained within columns of diameter 40 and 27 mm; images being acquired using ¹H and ¹⁹F observation for the water and SF₆, respectively. Liquid and gas flow rates calculated from the velocity images are in agreement with macroscopic flow rate measurements to within 7% and 5%, respectively. In addition to the information obtained directly from these images, the ability to measure liquid and gas flow fields within the same sample environment will enable us to explore the validity of assumptions used in numerical modelling of two-phase flows.     

微通道板电子透射膜工艺的AES研究

用冷基底溅射方法和静电贴膜方法分别在微通道板表面制备了电子透射膜,采用俄歇电子能谱(AES)研究了两种工艺制备的微通道板电子透射膜的薄膜成分,微通道板电子透射膜工艺失败微通道板通道表面的成分和通道内壁的成分随深度的变化.结果表明,冷基底溅射方法制膜工艺的失败对MCP造成了严重的碳污染,污染的MCP不可回收;静电贴膜方法制膜工艺的失败对MCP通道表面没有明显影响,MCP可回收利用.     

A method for rapid characterization of diffusion

This paper describes a method to determine molecular displacements as a function of time in just two scans: one reference scan using the Carr-Purcell-Meiboom-Gill (CPMG) sequence, a second scan using a modified CPMG sequence (KCPMG). Measurements on free diffusion in bulk fluids, and on restricted diffusion in porous rock samples are reported. This technique can also be used for rapid measurement of flow and chemical exchange.     

An efficient S-DDM iterative approach for compressible contamination fluid flows in porous media

In this paper, we develop an efficient splitting domain decomposition method (S-DDM) for compressible contamination fluid flows in porous media over multiple block-divided sub-domains by combining the non-overlapping domain decomposition, splitting, linearization and extrapolation techniques. The proposed S-DDM iterative approach divides the large domain into multiple block sub-domains. In each time interval, the S-DDM scheme is applied to solve the water head equation, in which an efficient local multilevel scheme is used for computing the values of water head on the interfaces of sub-domains, and the splitting implicit scheme is used for computing the interior values of water head in sub-domains; and the S-DDM scheme is then proposed to solve the concentration equation by combining the upstream volume technique. Numerical experiments are performed and analyzed to illustrate the efficiency of the S-DDM iterative approach for simulating compressible contamination fluid flows in porous media. The developed method takes the excellent attractive advantages of both the non-overlapping domain decomposition and the splitting technique, and reduces computational complexities, large memory requirements and long computational durations.     

Post-breakthrough scaling in reservoir field simulation

We study the oil displacement and production behavior in an isothermal thin layered reservoir model subjected to water flooding. We use the CMG’s (Computer Modelling Group  ) numerical simulators to solve mass balance equations. The influences of the viscosity ratio (m≡_μoil/_μwater$m\equiv {\mu }_{oil}/{\mu }_{water}$) and the inter-well (injector-producer) distance r$r$ on the oil production rate C(t)$C\left(t\right)$ and the breakthrough time _tbr$t_{br}$ are investigated. Two types of reservoir configuration are used, namely one with random porosities and another with a percolation cluster structure. We observe that the breakthrough time follows a power-law of m$m$ and r$r$, _tbr∝r^αm^β$t_{br}\propto r^{\alpha }{m}^{\beta }$, with α=1.8$\alpha =1.8$ and β=−0.25$\beta =-0.25$ for the random porosity type, and α=1.0$\alpha =1.0$ and β=−0.2$\beta =-0.2$ for the percolation cluster type. Moreover, our results indicate that the oil production rate is a power law of time. In the percolation cluster type of reservoir, we observe that P(t)∝t^γ$P\left(t\right)\propto t^{\gamma }$, with γ=−1.81$\gamma =-1.81$, where P(t)$P\left(t\right)$ is the time derivative of C(t)$C\left(t\right)$. The curves related to different values of m$m$ and r$r$ may be collapsed suggesting a universal behavior for the oil production rate.     

Porous electrolyte-supported tubular micro-SOFC design

Due to the poor redox cycling resistance of the second generation of μ-SOFCs, a new generation of SOFC has been recently developed using a porous electrolyte-supported structure to overcome this problem. In this research, the porous structure was successfully fabricated with slip casting using calcined YSZ (ZrO₂ + 8 mol% Y₂O₃) with or without graphite as a pore former. Calcination of YSZ powder at 1300-1500 °C prior to making the slip leads to growth of YSZ crystals and particle size which results in a decrease in surface area and powder sinterability. This was found to be an important criterion in developing the porous structure as, due to the high sinterability of non-calcined YSZ, even the addition of graphite is inadequate to generate sufficient open porosity. A dense YSZ electrolyte layer was immediately coated on the porous structure using YSZ calcined at 1300 °C with a sequential slip casting method. Sample thickness was found to be a function of both graphite content as well as YSZ calcination temperature. Physical properties of the porous YSZ supports and SEM analysis of the support and coated electrolyte are presented.     

对流梯形微通道内气液两相流动的数值研究

采用VOF方法,对梯形微通道内不可压缩气液两相流动进行了数值模拟研究,详细分析了气泡形成过程,以及当量直径、截面形状、液体表面张力和粘度等对气泡液柱形成过程和长度的影响,拟合出微通道气泡液柱长度计算公式。结果表明:气泡液柱的长度受表观气速和表观液速的影响较大;表面张力对气泡尺寸的影响较小,当液体粘度增加为水粘度的10倍时,形成的气泡形状不规则。增大表面张力,形成气泡的时间增加;增大粘度,形成气泡的时间减小。     

Conditional methods for continuum reacting flows in porous media

A special version of conditional moment closure—PCMC—is suggested for modeling reacting flows in porous media. The model involves conditioning on a special tracer scalar, which is introduced to characterize scalar transport in the gaseous phase. (i.e., for the flow in the interparticle space or in the pores). The model accounts for interparticle variations of species concentrations and emulates diffusion in the interparticle space. Special boundary conditions that are consistent with conventional conditions at the phase interface are obtained for the PCMC model. The model is tested against complete direct simulation of a reacting flow in porous media with favourable results.     

Transition in the propagation mechanism during flame acceleration in porous media

The combustion of stoichiometric hydrogen-air at various initial pressures was investigated in a 7.62 cm square cross-section channel filled with 1.27 cm diameter beads. The flame time-of-arrival and pressure time history along the channel were obtained by ionization probes and piezoelectric pressure transducers. Flame acceleration was found to be very rapid, e.g. at an initial pressure of 45 kPa the flame achieves a velocity of over 600 m/s in roughly 0.3 m. It was determined that at this high speed a well defined planar shock wave precedes a thick reaction zone. It was also shown that there is a transition in the flame propagation mechanism, similar to that observed in an obstacle laden channel [G. Ciccarelli and C. Johansen, The role of shock-flame interactions on flame acceleration in an obstacle laden channel, Proc. 22nd International Colloquium on the Dynamics of Explosions and Reactive Systems, Minsk, 2009]. By varying the initial pressure of the mixture, changes in the axial location of the transition between combustion propagation regimes was also observed. A soot foil technique was used to identify the transition in the propagation mechanism, as well as to provide information concerning the local flow field around the beads and the overall average flow direction.     

Electrical discharge characteristics of a dielectric liquid under external flow in a microchannel with planar electrode configuration

The effect of fluid flow on discharge characteristics in a dielectric liquid was determined. Tests were performed for flow in a 100 micron high, 5 mm wide, 50 mm long microchannel at Reynolds numbers up to 13 and applied DC potentials up to 1.5 kV through 100 micro planar electrode pairs along the floor of the channel. The current within the conduction regime increased as the flow rate increased for the case where the flow was in the same direction as the applied electric field. In the injection regime, there was an optimum flow rate for maximum current.     

Direct pore-level modeling of incompressible fluid flow in porous media

We present a dynamic particle-based model for direct pore-level modeling of incompressible viscous fluid flow in disordered porous media. The model is capable of simulating flow directly in three-dimensional high-resolution micro-CT images of rock samples. It is based on moving particle semi-implicit (MPS) method. We modify this technique in order to improve its stability for flow in porous media problems. Using the micro-CT image of a rock sample, the entire medium, i.e., solid and fluid, is discretized into particles. The incompressible Navier–Stokes equations are then solved for each particle using the MPS summations. The model handles highly irregular fluid–solid boundaries effectively. An algorithm to split and merge fluid particles is also introduced. To handle the computational load, we present a parallel version of the model that runs on distributed memory computer clusters. The accuracy of the model is validated against the analytical, numerical, and experimental data available in the literature. The validated model is then used to simulate both unsteady- and steady-state flow of an incompressible fluid directly in a representative elementary volume (REV) size micro-CT image of a naturally-occurring sandstone with 3.398 μm resolution. We analyze the quality and consistency of the predicted flow behavior and calculate absolute permeability using the steady-state flow rate.     

A numerical simulation method for dissolution in porous and fractured media

We describe an algorithm for simulating reactive flows in porous media, in which the pore space is mapped explicitly. Chemical reactions at the solid–fluid boundaries lead to dissolution (or precipitation), which makes it necessary to track the movement of the solid–fluid interface during the course of the simulation. We have developed a robust algorithm for constructing a piecewise continuous (C₁) surface, which enables a rapid remapping of the surface to the grid lines. The key components of the physics are the Navier–Stokes equations for fluid flow in the pore space, the convection–diffusion equation to describe the transport of chemical species, and rate equations to model the chemical kinetics at the solid surfaces. A lattice-Boltzmann model was used to simulate fluid flow in the pore space, with linear interpolation at the solid boundaries. A finite-difference scheme for the concentration field was developed, taking derivatives along the direction of the local fluid velocity. When the flow is not aligned with the grid this leads to much more accurate convective fluxes and surface concentrations than a standard Cartesian template. A robust algorithm for the surface reaction rates has been implemented, avoiding instabilities when the surface is close to a grid point. We report numerical tests of different aspects of the algorithm and assess the overall convergence of the method.