Using cellular automata for porous media simulation

A cellular automata (CA) approach is proposed for simulating a fluid flow through porous materials with tortuous channels at pore level. The approach aims to combine CA methods both for constructing computer representation of porous material morphology and for simulating fluid flow through it. Morphology representation is obtained using CA whose evolution exhibits self-organization and results in a stable configuration. The latter is then used for Lattice Gas CA application to simulate fluid flow through a porous material specimen and compute its permeability properties. Special boundary conditions are introduced allowing for different smoothness of solid pore walls surface. The model has been tested on a small 2D fragment in a PC and then implemented to investigate a porous carbon electrode of a hydrogen fuel cell on 128 processors of a multiprocessor cluster.     

Mesoscale SPH modeling of fluid flow in isotropic porous media

A novel numerical technique—Smoothed Particle Hydrodynamics (SPH) is used to model the fluid flow in isotropic porous media. The porous structure is resolved in a mesoscopic-level by randomly assigning certain portion of SPH particles to fixed locations. A repulsive force, similar in form to the 12-6 Lennard-Jones potential between atoms, is set in place to mimic the interactions between fluid and porous structure. This force is initiated from the fixed porous material particle and may act on its nearby moving fluid particles. In this way, the fluid is directed to pass through the porous structure in physically reasonable paths. For periodic porous systems formed by intersecting solid material with straight parallel fluid channels, the Kozeny formula of permeability was reproduced successfully, which, to a great extent, validates the reliability of the developed SPH model. Further, SPH simulations for the fluid flows induced by an applied streamwise body force in two-dimensional porous structures of different porosities are performed. The macroscopic Darcy's law is confirmed to be valid only in the creeping flow regime. The derived relationship of permeability versus porosity is compared with some existing numerical results/experimental data, which demonstrates that the present SPH model is able to capture the essential features of the fluid flow in porous media.     

Non-newtonian laminar flow machine rotor design by using topology optimization

Flow machines are widely used in industry through devices such as hydraulic turbines and pumps. Most part of these devices work with newtonian fluids, however, there are some specific devices dedicated to work with non-newtonian fluids, such as blood pumps. The main function of a blood pump is to have a suitable hydraulic performance while maintaining good haematological compatibility which consists of avoiding hemolysis (release of hemoglobin from red blood cells) and thrombosis (clotting). However, the challenge of improving the performance of these non-newtonian fluid machines requires the solution of an inverse-based design optimization problem, in which an oriented search must be conducted to obtain the optimized design. The rotor is a main component in the non-newtonian pump and the design of rotor topology can play an important role in the pump performance and its haematological conditions. Thus, performance improvement of these devices can be achieved by using topology optimization techniques. The optimization of pump hydraulic performance can be achieved by minimizing dissipative energy and power consumption and for the improvement of the haematological conditions, it is proposed to minimize the vorticity. Thus, in this work, topology optimization techniques are applied for designing the rotor pump such that the energy dissipation, vorticity, and power consumption are minimized considering non-Newtonian fluid. A two-dimensional finite element derived for a rotating frame is applied to model the rotor flow behavior. The modeling predicts the flow field between relative two blades of a rotor without considering the influence of the volute. A modified Cross model is adopted for the non-Newtonian fluid modeling. It is assumed that the fluid is flowing an idealized porous medium subjected to a friction force, which is proportional to the fluid velocity and the inverse local permeability. A porous flow model is considered with a continuous (gray) permeability design variable for each element that defines the local permeability of the medium and allows the transition between fluid and solid property. The design optimization problem is solved by using the method of moving asymptotes (MMA). Numerical examples are presented to illustrate this methodology aiming blood pump applications. A comparison among designs obtained by considering newtonian and non-newtonian fluid is included. Finally, it is verified that an improvement of the hemolysis index can be achieved by minimizing the vorticity in the rotor.     

Finite element implementation of stress-jump and stress-continuity conditions at porous-medium, clear-fluid interface

The boundary conditions at the interface between clear-fluid and porous-medium domains are very important for solving flow through an open domain adjoining a porous medium. In this Galerkin finite-element (FE) based simulation of such interface flows employing Stokes and Brinkman equations, the traditional interfacial condition based on the continuity of stress in fluid and porous media is compared with the stress-jump condition proposed by Ochoa-Tapia and Whitaker using the rigorous volume averaging method. A novel FE formulation employing a second-order adjustable tensor is proposed to implement this new stress-jump condition for full three-dimensional flows. The paper also clarifies the hitherto obscure relationship between flow variables in the fluid and porous media for the conventional stress-continuity condition. In the first validation study involving numerical predictions of flow parallel to the interface, our FE implementation of the new stress-jump condition agree very well with the analytical solution for flow parallel to the interface, thereby proving the soundness of our adjustable tensor approach. Similar excellent results were obtained for FE implementation of the stress-continuity condition as well. A good match with analytical solution for a constant cross-flow superimposed on the parallel flow was also achieved while differences in velocity profiles near the interfaces were studied for the two conditions. Lastly a complex 3D flow simulation involving a fluid and porous media interface within the unit-cell of a non-crimp stitched fiber mat, used in liquid composite molding process during the manufacture of composite materials, is undertaken. The permeability of this dual-scale fibrous porous medium, estimated using the newly implemented stress-jump condition, agrees well with the experimental result thereby pointing to the accuracy of the FE implementation of the condition. Our simulations reveal that the stress-jump condition leads to a much smaller boundary layer within porous medium near the interface as compared to the stress-continuity condition, and hence to a lower, more accurate net flow-rate through the unit cell. However the two interfacial conditions yield similar results with a decrease in the porosity.     

Improved scheme of estimating motion blur parameters for image restoration

A motion deblurring algorithm is proposed to enhance the quality of restoration based on the point spread function (PSF) identification in frequency spectrum. An improved blur angle identification algorithm characterized by bilateral-piecewise estimation strategy and the membership function method is presented by formulating the edges of the central bright stripe. Subsequently, the subpixel level image generated with bilinear interpolation is employed in the blur length estimation by calculating the distance between two adjacent dark strips. Through comparison with the existing algorithms, experimental results demonstrate that the proposed PSF estimation scheme could not only achieve higher accuracy for the blur angle and the blur length, but also produce more impressive restoration results. Furthermore, the robustness of our method is also validated in different noisy situations.     

Homotopy perturbation method for couple stresses effect on MHD peristaltic flow of a non-Newtonian nanofluid

Microsystem Technologies - An analytical study is presented for couple stresses effects on MHD peristaltic transport of a non-Newtonian Jeffery nanofluid. The fluid flows through a porous media...     

The Use of Splitting with Respect to Physical Processes for Modeling the Dissociation of Gas Hydrates

The work is devoted to modeling the phase transformations of gas hydrate inclusions in porous media. Studying these problems makes it possible to elaborate various technologies for the development of gas hydrate deposits. A two-block mathematical model of the dissociation of gas hydrates in a porous medium based on splitting with respect to physical processes is proposed and studied. An absolutely stable difference scheme is constructed and implemented in the spatially onedimensional case to numerically analyze the model. The water saturation, thawing, and the thermodynamic parameters (pressure and temperature) are calculated based on this difference scheme. An analysis of the data obtained by the calculations has confirmed the possibility of solving a number of typical problems of gas hydrate fluid dynamics using the above approach, including the problem of the complex dynamics of water and hydrate saturation of a formation.     

Combined Lattice Boltzmann and phase-field simulations for incompressible fluid flow in porous media

A Lattice-Boltzmann method for incompressible fluid flow is coupled with the dynamic equations of a phase-field model for multiple order parameters. The combined model approach is applied to computationally evaluate the permeability in porous media. At the boundaries between the solid and fluid phases of the porous microstructure, we employ a smooth formulation of a bounce-back condition related to the diffuse profile of the interfaces. We present simulations of fluid flow in both, static porous media with stationary non-moving interfaces and microstructures performing a dynamic evolution of the phase and grain boundaries. For the latter case, we demonstrate applications to dissolving grain structures with partial melt inclusions and computationally analyse the temporal evolution of the microporosity under wetting conditions at the melt-grain boundaries. In any development state of the material, the Darcy number and the hydraulic conductivity of the porous medium are evaluated for various types of fluid.     

A microfluidic pore model to study the migration of fine particles in single-phase and multi-phase flows in porous media

Microsystem Technologies - Fine particles within porous media may migrate with the flowing fluid and cause bridging or clogging in the pore space. Bridging and clogging reduce the flow permeability...     

一种求凸多边形宽度的优化算法

提出了一种优化的线性时间算法计算凸多边形的宽度。首先证明了凸多边形的宽度只可能介于“点边式”跨度之间,缩小了宽度的计算范围。其次提出了一种距离比较算法,降低了凸多边形跨度的计算量。最后,在“点边式”基本算法和距离比较算法的基础上,提出了计算宽度的优化算法。仿真分析表明,提出的优化算法提高了计算凸多边形宽度的效率,算法的时间复杂性降为O(n)。     

An evaluation of lattice Boltzmann schemes for porous medium flow simulation

We quantitatively evaluate the capability and accuracy of the lattice Boltzmann equation (LBE) for modeling flow through porous media. In particular, we conduct a comparative study of the LBE models with the multiple-relaxation-time (MRT) and the Bhatnagar–Gross–Krook (BGK) single-relaxation-time (SRT) collision operators. We also investigate several fluid–solid boundary conditions including: (1) the standard bounce-back (SBB) scheme, (2) the linearly interpolated bounce-back (LIBB) scheme, (3) the quadratically interpolated bounce-back (QIBB) scheme, and (4) the multi-reflection (MR) scheme. Three-dimensional flow through two porous media—a body-centered cubic (BCC) array of spheres and a random-sized sphere-pack—are examined in this study. For flow past a BCC array of spheres, we validate the linear LBE model by comparing its results with the nonlinear LBE model. We investigate systematically the viscosity-dependence of the computed permeability, the discretization error, and effects due to the choice of relaxation parameters with the MRT and BGK schemes. Our results show unequivocally that the MRT–LBE model is superior to the BGK–LBE model, and interpolation significantly improves the accuracy of the fluid–solid boundary conditions.     

Time-efficient estimation of conditional mutual information for variable selection in classification

An algorithm is proposed for calculating correlation measures based on entropy. The proposed algorithm allows exhaustive exploration of variable subsets on real data. Its time efficiency is demonstrated by comparison against three other variable selection methods based on entropy using 8 data sets from various domains as well as simulated data. The method is applicable to discrete data with a limited number of values making it suitable for medical diagnostic support, DNA sequence analysis, psychometry and other domains.     

Microfluidic systems for the analysis of viscoelastic fluid flow phenomena in porous media

In this study, two microfluidic devices are proposed as simplified 1-D microfluidic analogues of a porous medium. The objectives are twofold: firstly to assess the usefulness of the microchannels to mimic the porous medium in a controlled and simplified manner, and secondly to obtain a better insight about the flow characteristics of viscoelastic fluids flowing through a packed bed. For these purposes, flow visualizations and pressure drop measurements are conducted with Newtonian and viscoelastic fluids. The 1-D microfluidic analogues of porous medium consisted of microchannels with a sequence of contractions/expansions disposed in symmetric and asymmetric arrangements. The real porous medium is in reality, a complex combination of the two arrangements of particles simulated with the microchannels, which can be considered as limiting ideal configurations. The results show that both configurations are able to mimic well the pressure drop variation with flow rate for Newtonian fluids. However, due to the intrinsic differences in the deformation rate profiles associated with each microgeometry, the symmetric configuration is more suitable for studying the flow of viscoelastic fluids at low De values, while the asymmetric configuration provides better results at high De values. In this way, both microgeometries seem to be complementary and could be interesting tools to obtain a better insight about the flow of viscoelastic fluids through a porous medium. Such model systems could be very interesting to use in polymer-flood processes for enhanced oil recovery, for instance, as a tool for selecting the most suitable viscoelastic fluid to be used in a specific formation. The selection of the fluid properties of a detergent for cleaning oil contaminated soil, sand, and in general, any porous material, is another possible application.     

Visualization of connectivity in octree based models

An interesting problem in the oil and gas industry is the visualization of the movement of oil and gas in porous media. An example of such a medium is a rock sample with some distribution of holes (pores) connected by channels (pore throats), the solid parts of the rock are called grains. In our work we have simulated the porous medium using a pointer-based octree, representing these pores and grains. This data structure allows us to model the connectivity of the pores and thus visualize fluid penetration within the medium. Whereas earlier models represent a serious simplifications or two dimensional homogeneous layers, our model provides us with a statistically accurate distribution in three dimensions and a more accurate representation of the connectivity. In this paper we present our data structure and the techniques which were used to create models of porous media and their porous networks. Next, we present algorithms for connectivity in octrees and we show how to apply them to modelling and visualization of fluid penetration in porous media.     

Topology optimization applied to the design of 2D swirl flow devices

The design of fluid devices, such as flow machines, mixers, separators, and valves, with the aim to improve performance is of high interest. One way to achieve it is by designing them through the topology optimization method. However, there is a specific large class of fluid flow problems called 2D swirl flow problems which presents an axisymmetric flow with (or without) flow rotation around the axisymmetric axis. Some devices which allow such simplification are hydrocyclones, some pumps and turbines, fluid separators, etc. Once solving a topology optimization problem for this class of problems using a 3D domain results in a quite high computational cost, the development and use of 2D swirl models is of high interest. Thus, the main objective of this work is to propose a topology optimization formulation for 2D swirl flow fluid problem to design these kinds of fluid devices. The objective is to minimize the relative energy dissipation considering the viscous and porous effects. The 2D swirl laminar fluid flow modelling is solved by using the finite element method. A traditional material model is adopted by considering nodal design variables. An interior point optimization (IPOPT) algorithm is applied to solve the optimization problem. Numerical examples are presented to illustrate the application of this model for various 2D swirl flow cases.     

Computational analysis of cartilage implants based on an interpenetrated polymer network for tissue repairing

Interpenetrated polymer networks (IPNs), composed by two independent polymeric networks that spatially interpenetrate, are considered as valuable systems to control permeability and mechanical properties of hydrogels for biomedical applications. Specifically, poly(ethyl acrylate) (PEA)–poly(2-hydroxyethyl acrylate) (PHEA) IPNs have been explored as good hydrogels for mimicking articular cartilage. These lattices are proposed as matrix implants in cartilage damaged areas to avoid the discontinuity in flow uptake preventing its deterioration. The permeability of these implants is a key parameter that influences their success, by affecting oxygen and nutrient transport and removing cellular waste products to healthy cartilage. Experimental try-and-error approaches are mostly used to optimize the composition of such structures. However, computational simulation may offer a more exhaustive tool to test and screen out biomaterials mimicking cartilage, avoiding expensive and time-consuming experimental tests. An accurate and efficient prediction of material's permeability and internal directionality and magnitude of the fluid flow could be highly useful when optimizing biomaterials design processes. Here we present a 3D computational model based on Sussman–Bathe hyperelastic material behaviour. A fluid structure analysis is performed with ADINA software, considering these materials as two phases composites where the solid part is saturated by the fluid. The model is able to simulate the behaviour of three non-biodegradable hydrogel compositions, where percentages of PEA and PHEA are varied. Specifically, the aim of this study is (i) to verify the validity of the Sussman–Bathe material model to simulate the response of the PEA–PHEA biomaterials; (ii) to predict the fluid flux and the permeability of the proposed IPN hydrogels and (iii) to study the material domains where the passage of nutrients and cellular waste products is reduced leading to an inadequate flux distribution in healthy cartilage tissue. The obtained results show how the model predicts the permeability of the PEA–PHEA hydrogels and simulates the internal behaviour of the samples and shows the distribution and quantification of fluid flux.     

基于Dubins路径的无人艇运动规划算法

针对无人艇运动规划问题,通过Dubins路径的理论分析,提出一种利用纯粹几何方法的Dubins路径计算方法。该方法中没有出现解方程组的运算,而是首先根据无人艇运动状态计算转向圆,然后利用几何方法计算转向圆间的公切线,最后通过公切线连接得到Dubins路径。通过5组仿真实验验证了所提方法的有效性。前4组仿真实验分别设计了计算Dubins路径过程中可能出现的各种情形,以验证算法适用于多种情况的Dubins路径计算。最后一组仿真实验用于无人艇的路径规划及运动状态调整,仿真结果表明,基于Dubins路径的无人艇运动规划算法是可行的。     

Space approach to the hydro-magnetic flow of a dusty fluid through a porous medium

The technique of the state space approach and the inversion of the Laplace transformation method are applied to the non-dimensional equations of an unsteady laminar free convection flow of an incompressible, viscous, electrically conducting dusty fluid through a porous medium, which is bounded by an infinite vertical plane surface of constant temperature, in the presence of a constant magnetic field. The technique is applied to the thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. The numerical results of the dimensionless temperature, velocity, and induced magnetic and electric field distributions are given and illustrated graphically. The effects of the material’s parameters such as the Grashof number, the Prandtl number, the permeability parameter, the mass concentration of the particle phase, the Alfven velocity, the thermal relaxation time and the relaxation time of the particle phase on the temperature, velocity and the induced magnetic and electric fields are discussed.     

Local and parallel finite element methods for the mixed Navier–Stokes/Darcy model

In this paper, the mixed Navier–Stokes/Darcy problem which describes a fluid flow filtrating through porous media is considered. Based on two-grid discretizations, two local and parallel finite element algorithms for solving this mixed model are proposed. Numerical analysis and experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithms.