A Generalized Non-Linear Flow Law Based on Modified Zerilli-Armstrong Model and Its Implementation into Abaqus/Explicit FEM Code

Non-linear numerical modeling, widely used in research and development to understand many complex processes such as forming or machining, does not guarantee the success of a study to be performed. Indeed, the numerical simulation uses finite element codes where the models already integrated are not based on shapes adjustable to any type of study. In this study, a new form of non-linear constitutive flow law based on the Modified Zerilli-Armstrong model, which can answer the above problem, has been developed to apply it to the numerical simulation of two different tests (a quasi-static compression test, the necking of a circular bar). This flow law is based on the modified Zerilli-Armstrong model, which, together with the new modified Johnson-Cook model, has been compared to appreciate the relevance of the proposal. For that, an implementation of this new law via the VUHARD subroutine into the Abaqus/Explicit finite element code was made to model the two tests. The comparison of the results obtained (from identification) by our proposed law with those obtained using the NMJC shows that this new law better approaches the experiments than the other one. This is also shown through the numerical results using the Abaqus software. It can be said that this way of formulating a flow law allows highlighting the great performance of the proposed approach. Although this law has been only used for quasi-static tests, we can say that it can also be used in dynamic tests.

GENERALIZED FLOW LAWS OF POLYPHASE ROCKS: AN OVERVIEW

Rheological properties of polyphase rocks play an important role in the dynamics of the lithosphere and asthenosphere. However, such fundamental issues have not been well resolved. A theoretical analysis has been made to develop expressions for the flow laws of polyphase rocks in terms of the volume fractions and flow laws of their constituent phases. The flow strengths predicted by the proposed model for common crustal and upper mantle rocks such as granite, diorite, diabase and lherzolite, and for synthetic two phase composites such as forsterite enstatite and water ice ammonia dehydrate aggregates are in good agreement with previously determined experimental values. The proposed theoretical model allows one to calculate, to the first approximation, the flow laws of a large number of polyphase rocks at geologic conditions based on the experimentally determined flow laws of a relatively small number of monomineralic aggregates.

Non-Darcy Flow in Molding Sands

Darcy’s law is widely used to describe the flow in porous media in which there is a linear relationship between fluid velocity and pressure gradient. However, it has been found that for high numbers of Reynolds this law ceases to be valid. In this work, the Ergun equation is employed to consider the non-linearity of air velocity with the pressure gradient in casting sands. The contribution of non-linearity to the total flow in terms of a variable defined as a non-Darcy flow fraction is numerically quantified. In addition, the influence of the shape factor of the sand grains on the non-linear flow fraction is analyzed. It is found that for values of the Reynolds number less or equal than 1, the contribution of non-linearity for spherical particles is around 1.15%.

Law of nonlinear flow in saturated clays and radial consolidation

It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Re- sults show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.

Propagation law of shock waves and gas flow in cross roadway caused by coal and gas outburst

In order to study the propagation law of shock waves and gas flow during coal and gas outburst,we analyzed the formation process of outburst shock waves and gas flow and established the numerical simulation models of the roadways with 45°intersection and 135°intersection to simulate the propagation of outburst gas flow and the process of gas transport.Based on the analysis of the simulation results,we obtained the qualitative and quantitative conclusions on the characteristics and patterns of propagation and attenuation of outburst shock waves and gas flow.With the experimental models,we investigated the outburst shock waves and gas flow in the roadways with the similar structures to the simulated ones.According to the simulation results,when the angle between the driving roadway and the adjacent roadway increased,the sudden pressure variation range in adjacent roadway and the influencing scope of gas flow increased and the sudden pressure variation duration decreased.The intersection between the driving roadway and the adjacent roadway has no effect on airflow reversal induced by the shock waves and gas flow.

The axisymmetric long-wave interfacial stability of core-annular flow of power-law fluid with surfactant

The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. The analytic solution for the growth rate of perturbation is obtained with long wave approximation. We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability. The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number. For a clean interface, the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall. The converse is true when the interface is close to the pipe centerline. For shear-thickening fluids, the situation is reversed. When the interface is close to the pipe centerline, the capillary instability can be restrained due to the influence of surfactant. A parameter set can be found under which the flow is linearly stable.

Local Scour and the Laws of Scour Pit's Shape Downstream of Debris Flow Sabo Dam

The erosion shape and the law of development of debris flow sabo dam downstream is a weak part in the study on debris flow erosion. The shape and development of scour pit have an important effect on the stability and safety of debris flow sabo dam, which determines the foundational depth of the dam and the design of protective measures downstream. Study on the scouring law of sabo dam downstream can evaluate the erosion range and reasonably arrange auxiliary protective engineering. Therefore, a series of flume experiments are carried out including different debris flow characteristics(density is varying from 1.5 t/m3to 2.1t/m3) and different gully longitudinal slopes. The result shows that the scour pit appears as an oval shape in a plane and deep in the middle while superficial at the ends in the longitudinal section, the position of the maximum depth point moves towards downstream with an increase of flume slope angle.The maximum depth of scour pit is mainly affected by the longitudinal slope of gully, density of debris flow,and the characteristics of gully composition(particle size and the viscosity of soil). The result also indicates that the viscosity of soil will weaken the erosion extent.The interior slopes of scour pit are different between the upstream and the downstream, and the downstream slope is smaller than the upper one. For the viscous and non-viscous sands with the same distribution of gradation, the interior slope of nonviscous sand is smaller than the viscous sand.According to the regression analysis on the experimental data, the quantitative relationship between the interior slope of scour pit, slope of repose under water and the longitudinal slope of gully is established and it can be used to calculate the interior slope of scour pit. The results can provide the basis for the parameter design of the debris flow control engineering foundation.

Simplified Wave Models Applicability to Shallow Mud Flows Modeled as Power-Law Fluids

Simplified wave models- such as kinematic,diffusion and quasi-steady- are widely employed as a convenient replacement of the full dynamic one in the analysis of unsteady open-channel flows,and especially for flood routing.While their use may guarantee a significant reduction of the computational effort,it is mandatory to define the conditions in which they may be confidently applied.The present paper investigates the applicability conditions of the kinematic,diffusion and quasisteady dynamic shallow wave models for mud flows of power-law fluids.The power-law model describes in an adequate and convenient way fluids that at low shear rates fluids do not posses yield stress,such as clay or kaolin suspensions,which are frequently encountered in Chinese rivers.In the framework of a linear analysis,the propagation characteristics of a periodic perturbation of an initial steady uniform flow predicted by the simplified models are compared with those of the full dynamic one.Based on this comparison,applicability criteria for the different wave approximations for mud flood of power-law fluids are derived.The presented results provide guidelines for selecting the appropriate approximation for a given flow problem,and therefore they may represent a useful tool for engineering predictions.

Mixture flow of particles and power-law fluid in round peristaltic tube

The erythrocyte and blood flowing in the blood vessel can be treated as the two-phase flow of the mixture of particles and a power-law fluid in a peristaltic tube.In the present work, the peristaltic transport of a power-law fluid and the suspension of particles in a tube is investigated by a perturbation method using the long wavelength approximation. The influence of different parameters on the velocity profile and streamlines is explored. Results show that there is a deflection of the flow field when the power-law index n = 0.5 or 1.5 compared with the Newtonian fluid where the trapping zone is symmetric to a certain cross section. The flux rate and reflux of the material are identified,and the conditions under which the reflux appears are determined. Moreover, a reflux phenomenon occurs near the wall. The trapping zone is related to not only the tube geometry and the flow flux but also the fluid properties. Both the length and width of the trapping zone increase with an increase in θ or φ. The trapping zone is more difficult to produce in the shear-thinning fluid than the shear-thickening fluid.

THE TRANSIENT ELLIPTIC FLOW OF POWER-LAW FLUID IN FRACTAL POROUS MEDIA

The steady oil production and pressure distribution formulae of vertically fractured well for power-law non-Newtonian fluid were derived on the basis of the elliptic flow model in fractal reservoirs. The corresponding transient flow in fractal reservoirs was studied by numerical differentiation method: the influence of fractal index to transient pressure of vertically fractured well was analyzed. Finally the approximate analytical solution of transient flow was given by average mass conservation law. The study shows that using elliptic flow method to analyze the flow of vertically fractured well is a simple method.

Computational analysis of the flow of pseudoplastic power-law fluids in a microchannel plate

The flow of pseudoplastic power-law fluids with different flow indexes at a microchannel plate was studied using computational fluid dynamic simulation.The velocity distribution along the microchannel plate and especially in the microchannel slits,flow pattern along the outlet arc and the pressure drop through the whole of microchannel plate were investigated at different power-law flow indexes.The results showed that the velocity profile in the microchannel slits for low flow index fluids was similar to the plug flow and had uniform pattern.Also the power-law fluids with lower flow indexes had lower stagnation zones near the outlet of the microchannel plate.The pressure drop through the microchannel plate showed huge differences between the fluids.The most interesting result was that the pressure drops for power-law fluids were very smaller than that of Newtonian fluids.In addition,the heat transfer of the fluids through the microchannel with different channel numbers in a wide range of Reynolds number was investigated.For power-law fluid with flow index(n=0.4),the Nusselt number increases continuously as the number of channels increases.The results highlight the potential use of using pseudoplastic fluids in the microheat exchangers which can lower the pressure drop and increase the heat transfer efficiency.

Non-Newtonian Power-Law Fluid Flow and Heat Transfer over a Non-Linearly Stretching Surface

The problem of magneto-hydrodynamic flow and heat transfer of an electrically conducting non-Newtonian power-law fluid past a non-linearly stretching surface in the presence of a transverse magnetic field is considered. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. These equations are then solved numerically by an implicit finite-difference scheme known as Keller-Box method. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, velocity exponent parameter, temperature exponent parameter, Modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena.

The Research of the Flow of Bodies with Use of the Vector Form of the Newton’s Law for the Viscous Liquid

On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.

Variation law of gas holdup in an autoclave during the pressure leaching process by using a mixed-flow agitator

The multiphase reaction process of pressure leaching is mainly carried out in the liquid phase. Therefore, gas holdup is essential for the gas–liquid–solid phase reaction and the extraction rate of valuable metals. In this paper, a transparent quartz autoclave, a six blades disc turbine-type agitator, and a high-speed camera were used to investigate the gas holdup of the pressure leaching process. Furthermore, experiments determining the effects of agitation rate, temperature, and oxygen partial pressure on gas holdup were carried out. The results showed that when the agitation rate increased from 350 to 600 r/min, the gas holdup increased from 0.10% to 0.64%. When the temperature increased from 363 to 423 K, the gas holdup increased from 0.14% to 0.20%. When the oxygen partial pressure increased from 0.1 to 0.8 MPa, the gas holdup increased from 0.13% to 0.19%. A similar criteria relationship was established by Homogeneous Principle and Buckingham's theorem. Comprehensively, empirical equation of gas holdup was deduced on the basis of experimental data and the similarity theory, where the criterion equation was determined as ε=4.54×10^(-11)n^(3.65)T^(2.08)P_g^(0.18). It can be seen from the formula that agitation rate made the most important impact on gas holdup in the pressure leaching process using the mixed-flow agitator.

Similarity solutions for non-Newtonian power-law fluid flow

The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva- ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 〈 n ≤ 1, the solution has a positive curvature, while for n 〉 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

A Numerical Simulation of Air Flow in the Human Respiratory System Based on Lung Model

The lung is an important organ that takes part in the gas exchange process. In the study of gas transport and exchange in the human respiratory system, the complicated process of advection and diffusion (AD) in airways of human lungs is considered. The basis of a lumped parameter model or a transport equation is modeled during the inspiration process, when oxygen enters into the human lung channel. The quantitative measurements of oxygen are detached and the model equation is solved numerically by explicit finite difference schemes. Numerical simulations were made for natural breathing conditions or normal breathing conditions. The respiratory flow results for the resting conditions are found strongly dependent on the AD effect with some contribution of the unsteadiness effect. The contour of the flow rate region is labeled and AD effects are compared with the variation of small intervals of time for a constant velocity when breathing is interrupted for a negligible moment.

通道压裂支撑剂缝内分布规律研究

通道压裂是低渗透致密油气藏高效、低成本开发的关键技术,通过采用非连续簇团铺砂的方式,使裂缝中形成具有高导流能力的通道,但目前关于通道压裂的理论研究仍然处于起步阶段.因此,基于计算流体力学建立欧拉-欧拉固液两相流模型,对通道压裂过程中支撑剂的分布状态进行模拟,通过与实验结果进行对比,证明了所建立模型的有效性,并系统研究了不同中顶压裂液(纯压裂液脉冲段)黏度、支撑剂密度、泵注排量对通道压裂通道率的影响.结果表明,中顶压裂液的黏度从1 mPa·s增加到20 mPa·s,通道内平均通道率增加5%;支撑剂密度从1400 kg/m^(3)增加到2000 kg/m^(3)时,缝内通道率减小了7%;排量由3 m^(3)/min增加到7 m^(3)/min时,通道率由28%增加到33.5%后减小到31%.现场应用过程中应使用较高黏度中顶压裂液、较低密度支撑剂和合理的泵注排量以保证裂缝中形成有效支撑通道.

Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat trans- fer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two- and three-dimensional flow phenom- ena are also shown through graphical results.

A HYPERBOLIC SYSTEM OF CONSERVATION LAWS FOR FLUID FLOWS THROUGH COMPLIANT AXISYMMETRIC VESSELS

We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling fluid flows such as the blood flow through compliant axisyminetric vessels. Early models derived are nonconservative and/or nonho- mogeneous with measure source terms, which are endowed with infinitely many Riemann solutions for some Riemann data. In this paper, we derive a one-dimensional hyperbolic system that is conservative and homogeneous. Moreover, there exists a unique global Riemann solution for the Riemann problem for two vessels with arbitrarily large Riemann data, under a natural stability entropy criterion. The Riemann solutions may consist of four waves for some cases. The system can also be written as a 3 × 3 system for which strict hyperbolicity fails and the standing waves can be regarded as the contact discontinuities corresponding to the second family with zero eigenvalue.

环境规制与资本跨地区流动——来自新《环保法》实施的证据

本文利用2010—2020年中国上市工业企业的异地投资数据,实证检验了新《环保法》的实施对资本流动的影响。研究发现,新《环保法》的实施能够显著减少重污染企业异地投资的策略性行为,主要作用途径是加强外部资源约束和推动内部策略合规。进一步研究表明,新《环保法》的实施在减少污染转移的基础上,提高了重污染企业的创新效率和创新数量。本文在全面畅通国内大循环的战略背景下,为构建高质量的资本流动格局提供了政策启示。