Deletion of nondominant effects in modeling transport in porous media

A methodology for eliminating nondominant effects in models that describe transport phenomena in porous media is presented. The methodology is based on the introduction of dimensionless numbers and on a proper evaluation of the order of magnitude of terms. These dimensionless numbers are redefined as characteristics of transport and transformation phenomena in porous media. It is shown that different time scales and different length scales may have to be employed for different variables. A method for evaluating the order of magnitude of the error of prediction when terms are deleted, is presented.     

Effect of Inertial Terms on Fluid–Porous Medium Flow Coupling

The study considers an effect of the nonlinear inertial terms in the Brinkman filtration equation on the characteristics of coupled flows in a pure fluid and porous medium in the frameworks of two independent problems. The first problem is the forced boundary-layer flow overlying the Darcy–Brinkman porous medium. The Prandtl theory is used, and the self-similar equations are built to describe it. It is shown that the inertial terms have a valuable effect on the boundary-layer structure because of the large velocity gradient in the transition zone. The boundary-layer thickness in a porous medium rapidly grows at large Reynolds numbers. The velocity magnitude and gradient at the interface also change. The second independent problem is an analysis of the inertial terms effect on the flow stability. The neutral curves of the full and linearized flow models are built using the shooting method. They have different short-wave asymptotic, but there are no significant changes in the critical Reynolds numbers and corresponding wave numbers.     

Turbulence characteristics over k-type rib roughened porous walls

To understand the permeability effects on turbulent rib-roughened porous channel flows, particle image velocimetry measurements are performed at the bulk Reynolds number of 5000–20000. Solid impermeable and porous ribs are considered for the rib-roughness whose geometry is categorised in the k-type roughness whose pitch/rib-height is 10. Three isotropic porous media with nearly the same porosity: 0.8, and different permeabilities (0.004, 0.020, 0.033 mm²) are applied. It is observed that the recirculation between the ribs becomes weak and the recirculation vortex submerges into the porous wall as the wall permeability and Reynolds number increase for both solid and porous rib cases while the recirculation vanishes in high permeable cases. These phenomena result in characteristic difference in turbulence quantities. By fitting the mean velocity profiles to the log-law form, the permeability effects of both rib and bottom wall on the log-law parameters and the equivalent sand-grain roughness are discussed. It is concluded that the zero-plane displacement increases while the von Kármán constant and the equivalent sand-grain roughness decrease as the wall and rib permeability increases.     

Transport Mechanism of Interface Turbulence over Porous and Rough Walls

To understand turbulent transport mechanisms of interface turbulence over porous and rough walls, statistical analyses using direct numerical simulation (DNS) data are carried out at a bulk Reynolds number of 3000. The presently considered porous wall, whose porosity is 0.71, consists of interconnected staggered cube arrays and the rough wall has the same surface structure. Through quadrant and budget term analyses, the transport mechanisms of the plane averaged Reynolds stress are investigated and mutual dependency between turbulence and dispersion is elucidated. Moreover, the influence of the Kelvin-Helmholtz instability on turbulent transport is clarified.     

Effects of blowing through a porous strip in a turbulent channel flow

An experimental investigation is performed on a fully developed turbulent channel flow with local injection through a porous strip. The Reynolds number based on the channel half-width was set to 5000. In addition to the no blowing case, measurements are made for three different blowing rates σ = 0.22, 0.36 and 0.58 (where σ is the ratio of momentum flux gain due to the blowing and momentum flux of the incoming channel flow). Measurements carried out with hot-wire anemometry reveal that injection strongly affects both the velocity profiles and the turbulence characteristics. The injection decreases the skin friction coefficient and increases all the Reynolds stresses downstream the blowing strip. The turbulence structure and the bursting phenomena were examined using space-time correlations measurements and conditional analysis. It is found that the injection increases the frequency of occurrence of the bursts.     

Vortex penalization method for bluff body flows

In this work, a penalization method is discussed in the context of vortex methods for incompressible flows around complex geometries. In particular, we illustrate the method in two cases: the flow around a rotating blade for Reynolds numbers 1000 and 10,000 and the flow past a semi‐circular body consisting of a porous layer surrounding a rigid body at Reynolds numbers 550 and 3000. In the latter example, the results are interpreted in terms of control strategy. Copyright © 2015 John Wiley & Sons, Ltd.     

Boundary layer ?ow of Maxwell ?uid due to torsional motion of cylinder: modeling and simulation

This paper investigates the boundary layer ?ow of the Maxwell ?uid around a stretchable horizontal rotating cylinder under the in?uence of a transverse magnetic?eld. The constitutive ?ow equations for the current physical problem are modeled and analyzed for the ?rst time in the literature. The torsional motion of the cylinder is considered with the constant azimuthal velocity E. The partial di?erential equations(PDEs)governing the torsional motion of the Maxwell ?uid together with energy transport are simpli?ed with the boundary layer concept. The current analysis is valid only for a certain range of the positive Reynolds numbers. However, for very large Reynolds numbers, the ?ow becomes turbulent. Thus, the governing similarity equations are simpli?ed through suitable transformations for the analysis of the large Reynolds numbers. The numerical simulations for the ?ow, heat, and mass transport phenomena are carried out in view of the bvp4 c scheme in MATLAB. The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the ?ow penetrates shallower into the free stream ?uid. It is also noted that the phenomenon of stress relaxation, described by the Deborah number, causes to decline the ?ow ?elds and enhance the thermal and solutal energy transport during the ?uid motion. The penetration depth decreases for the transport of heat and mass in the ?uid with the higher Reynolds numbers. An excellent validation of the numerical results is assured through tabular data with the existing literature.     

饱和-非饱和土壤中污染物运移过程的数值模拟

本文提出了一个模拟饱和 非饱和土壤中溶和污染物运移过程的数值模型．模拟的控制污染物运移的物理 化学现象包括：对流，机械逸散，分子弥散，吸附，蜕变，不动水效应．发展了一个修正的特征线Ｇａｌｅｒｋｉｎ方法以离散污染物运移过程的控制方程并导出了一个用于有限元方程求解的显式算法．数值例题结果表明所提出模型和算法的功能     

Boundary layer flow of Maxwell fluid due to torsional motion of cylinder: modeling and simulation

This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field. The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature. The torsional motion of the cylinder is considered with the constant azimuthal velocity E. The partial differential equations (PDEs) governing the torsional motion of the Maxwell fluid together with energy transport are simplified with the boundary layer concept. The current analysis is valid only for a certain range of the positive Reynolds numbers. However, for very large Reynolds numbers, the flow becomes turbulent. Thus, the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers. The numerical simulations for the flow, heat, and mass transport phenomena are carried out in view of the bvp4c scheme in MATLAB. The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid. It is also noted that the phenomenon of stress relaxation, described by the Deborah number, causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion. The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers. An excellent validation of the numerical results is assured through tabular data with the existing literature.     

Extension of the Darcy�CForchheimer Law for Shear-Thinning Fluids and Validation via Pore-Scale Flow Simulations

Flow of non-Newtonian fluids through porous media at high Reynolds numbers is often encountered in chemical, pharmaceutical and food, as well as petroleum and groundwater engineering, and in many other industrial applications. Under the majority of operating conditions typically explored, the dependence of pressure drops on flow rate is non-linear and the development of models capable of describing accurately this dependence, in conjunction with non-trivial rheological behaviors, is of paramount importance. In this work, pore-scale single-phase flow simulations conducted on synthetic two-dimensional porous media are performed via computational fluid dynamics for both Newtonian and non-Newtonian fluids and the results are used for the extension and validation of the Darcy?CForchheimer law, herein proposed for shear-thinning fluid models of Cross, Ellis and Carreau. The inertial parameter ?? is demonstrated to be independent of the viscous properties of the fluids. The results of flow simulations show the superposition of two contributions to pressure drops: one, strictly related to the non-Newtonian properties of the fluid, dominates at low Reynolds numbers, while a quadratic one, arising at higher Reynolds numbers, is dependent on the porous medium properties. The use of pore-scale flow simulations on limited portions of the porous medium is here proposed for the determination of the macroscale-averaged parameters (permeability K, inertial coefficient ?? and shift factor ??), which are required for the estimation of pressure drops via the extended Darcy?CForchheimer law. The method can be applied for those fluids which would lead to critical conditions (high pressures for low permeability media and/or high flow rates) in laboratory tests.     

Numerical Simulation of Turbulent Flow and Heat Transfer in a Three-Dimensional Channel Coupled with Flow Through Porous Structures

This study investigates numerically the turbulent flow and heat transfer characteristics of a T-junction mixing, where a porous media flow is vertically discharged in a 3D fully developed channel flow. The fluid equations for the porous medium are solved in a pore structure level using an Speziale, Sarkar and Gatski turbulence model and validated with open literature data. Overall, two types of porous structures, consisted of square pores, are investigated over a wide range of Reynolds numbers: an in-line and a staggered pore structure arrangement. The flow patterns, including the reattachment length in the channel, the velocity field inside the porous medium as well as the fluctuation velocity at the interface, are found to be strongly affected by the velocity ratio between the transversely interacting flow streams. In addition, the heat transfer examination of the flow domain reveals that the temperature distribution in the porous structure is more uniform for the staggered array. The local heat transfer distributions inside the porous structure are also studied, and the general heat transfer rates are correlated in terms of area-averaged Nusselt number accounting for the effects of Reynolds number, velocity ratio as well as the geometrical arrangement of the porous structures.     

Multiscale Structures to Describe Porous Media Part II: Transport Properties and Application to Test Materials

A renormalization method for the computation of the transport properties of a porous medium modelled as a multiscale random network is proposed. The method applies to electrical conduction, molecular diffusion, hydraulic transport under low Reynolds number, transport of condensable vapour, in the medium fully or partially saturated by one or two immiscible fluids. For 31 test materials, the method previously exposed by the authors for the reconstitution of the pore structure from the mercury intrusion curve is applied. Then, the intrinsic permeability is computed. The results are in good agreement with the measured permeability.     

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.     

多孔介质中流固作用力的动量交换计算

流经多孔介质的流动广泛存在于化工生产、多孔颗粒悬浮流等领域,如何准确计算流体与多孔介质之间的作用力是研究此类流动的一个关键因素. 作为一种有效的流体计算方法,格子波尔兹曼方法（lattice Boltzmannmethod,LBM）常采用动量交换法计算流体与固体之间相互作用力. 分析了流体流经多孔介质时两者的动量交换过程,提出了一种高效的动量交换法来计算流固作用力,并在孔隙尺度下对其进行了验证,结果表明该方法是可行的. 进而将该方法推广到计算表征体元（表征体元）尺度下的流-固相互作用,并对不同雷诺数（Re）下的多孔方柱绕流问题进行了模拟和验证.      

Prediction of nanoparticle transport and deposition in bends

Nanoparticle transport and deposition in bends with circular cross-section are solved for different Reynolds numbers and Schmidt numbers. The perturbation method is used in solving the equations. The results show that the particle transport patterns are similar and independent of the particle size and other parameters when suspended nanoparticles flow in a straight tube. At the outside edge, particle deposition is the most intensive, while deposition at the inside edge is the weakest. In the upper and lower parts of the tube, depositions are approximately the same for different Schmidt numbers. Curvatures of tube, Reynolds number, and Schmidt number have second-order, forth-order, and first-order effects on the relative deposition efficiency, respectively.     

FORCE EVALUATION USING MOMENTUM-EXCHANGEMETHOD IN POROUS MEDIA

流经多孔介质的流动广泛存在于化工生产、多孔颗粒悬浮流等领域,如何准确计算流体与多孔介质之间的作用力是研究此类流动的一个关键因素. 作为一种有效的流体计算方法,格子波尔兹曼方法（lattice Boltzmannmethod,LBM）常采用动量交换法计算流体与固体之间相互作用力. 分析了流体流经多孔介质时两者的动量交换过程,提出了一种高效的动量交换法来计算流固作用力,并在孔隙尺度下对其进行了验证,结果表明该方法是可行的. 进而将该方法推广到计算表征体元（表征体元）尺度下的流-固相互作用,并对不同雷诺数（Re）下的多孔方柱绕流问题进行了模拟和验证.     

Investigation of generalized Fick’s and Fourier’s laws in the second-grade fluid flow

The second-grade fluid flow due to a rotating porous stretchable disk is modeled and analyzed. A porous medium is characterized by the Darcy relation. The heat and mass transport are characterized through Cattaneo-Christov double diffusions. The thermal and solutal stratifications at the surface are also accounted. The relevant nonlinear ordinary differential systems after using appropriate transformations are solved for the solutions with the homotopy analysis method (HAM). The effects of various involved variables on the temperature, velocity, concentration, skin friction, mass transfer rate, and heat transfer rate are discussed through graphs. From the obtained results, decreasing tendencies for the radial, axial, and tangential velocities are observed. Temperature is a decreasing function of the Reynolds number, thermal relaxation parameter, and Prandtl number. Moreover, the mass diffusivity decreases with the Schmidt number.     

Modelling of Power-law Fluid Flow Through Porous Media Using Smoothed Particle Hydrodynamics

The flow of non-Newtonian fluids through two-dimensional porous media is analyzed at the pore scale using the smoothed particle hydrodynamics (SPH) method. A fully explicit projection method is used to simulate incompressible flow. This study focuses on a shear-thinning power-law model (n < 1), though the method is sufficiently general to include other stress-shear rate relationships. The capabilities of the proposed method are demonstrated by analyzing a Poiseuille problem at low Reynolds numbers. Two test cases are also solved to evaluate validity of Darcy’s law for power-law fluids and to investigate the effect of anisotropy at the pore scale. Results show that the proposed algorithm can accurately simulate non-Newtonian fluid flows in porous media.     

Simulating bubble dynamics in a buoyant system

Multiphase flows are critical components of many physical systems; however, numerical models of multiphase flows with large parameter gradients can be challenging. Here, two different numerical methods, volume of fluid (VOF) and smoothed particle hydrodynamics (SPH), are used to model the buoyant rise of isolated gas bubbles through quiescent fluids for a range of Bond and Reynolds numbers. The VOF is an Eulerian grid–based method, whereas the SPH is Lagrangian and mesh free. Each method has unique strengths and weaknesses, and a comparison of the two approaches as applied to multiphase phenomena has not previously been performed. The VOF and SPH simulations are compared, verified, and validated. Results using two-dimensional VOF and SPH simulations are similar to each other and are able to reproduce numerical benchmarks and experimental results for sufficiently large Morton and Reynolds numbers. It is also shown that at low Reynolds numbers, the two methods, SPH and VOF, diverge in the transient regime of the bubble rise. Regimes that require simulations capable of representing three-dimensional drag are identified as well as regimes in which results from VOF and SPH diverge.