Four-component gas/water/oil displacements in one dimension: Part I. structure of the conservation law

This paper presents the first analysis of the mathematical structure of a system of conservation laws modeling compositional flow of four components in three phases. The phase behavior that results from assuming the equilibrium volume ratios of the components in the phases are fixed (constant K-values) when up to three phases may form, is studied. We parameterize the equations in the three-phase region and show that within the three-phase region two of the characteristic curves can be found using three-phase immiscible flow theory. The third eigenvalue can also be found analytically when the K-values are constant. We show that the eigenvalue problem given by the conservation law has a discontinuity at the boundary of the two- and three-phase regions. Finally, the loss of strict hyperbolicity is discussed.     

Four-Component Gas/Water/Oil Displacements in One Dimension: Part III,Development of Miscibility

The structure of the system of conservation laws in fully compositional three-phase, four-component flow is examined for the first time. Two of the eigenvalues can be found analytically for this flow regime, regardless of the equation of state used to model the phase behavior. A cubic equation of state is used to calculate the gas/oil phase behavior and Henry’s law is used to represent the partitioning of hydrocarbons between the hydrocarbon and water phases. Sample analytical solutions are found for Riemann problems modeling the injection of carbon-dioxide and water into an oil reservoir. Finally, the structure of the solutions at the minimum miscibility pressure (MMP) for the hydrocarbon system is studied. We show that when water is injected simultaneously with gas at the MMP, multicontact miscible displacement of the oil by the injected gas develops only if the fraction of water in the injected fluid is below a critical value. For water fractions above the critical value, water flowing at a high velocity forces the composition path of the solution to remain in the three-phase region in which two hydrocarbon phases are present. We study both condensing and vaporizing gas drives to demonstrate that this result is general.     

Four-Component Gas/Oil Displacements in One Dimension: Part II: Analytical Solutions for Constant Equilibrium Ratios

In this paper we derive closed form solutions for composition paths (integral curves of eigenvectors) for three- and four-component systems with constant equilibrium K-values, and we report example solutions that describe gas injection processes. Extensions to systems with an arbitrary number of components are discussed.Author for correspondence: e-mail:wangy2@bp.com     

On thermoelastic fields of a multi-phase inhomogeneity system with perfectly/imperfectly bonded interfaces

The stress fields of cylindrical and spherical multi-phase inhomogeneity systems with perfect or imperfect interfaces under uniform thermal and far-field mechanical loading conditions are investigated by use of the Boussinesq displacement potentials. The radius of the core inhomogeneity and the thickness of its surrounding coatings are arbitrary. The discontinuities in the tangential and normal components of the displacement at the imperfect interfaces are assumed to be proportional to the associated tractions. In this work, for the problems where the phases of the inhomogeneity system are homogeneous, the exact closed-form thermo-elastic solutions are presented. These solutions along with a systematic numerical methodology are utilized to solve various problems of physical importance, where the constituent phases of the inhomogeneity system may be made of a number of different functionally graded (FG) and homogeneous materials, and each interface may have a perfect or imperfect boundary condition, as desired. Also, the effect of the interfacial sliding and debonding on the stress field and elastic energy of an FG-coated inhomogeneity is examined.     

Computation of compaction in compressible granular material

Equations modeling compaction in a mixture of granular high explosive and interstitial gas are solved numerically. Both phases are modeled as compressible, viscous fluids. This overcomes well known difficulties associated with computing shock jumps in the inviscid version of the equations, which cannot be posed in a fully conservative form. One-dimensional shock tube and piston-driven compaction solutions compare favorably with experiment and known analytic solutions. A simple two-dimensional extension is presented.     

Towards high-fidelity erosion prediction: On time-accurate particle tracking in turbomachinery

Erosion and fouling caused by ingested particles causes performance degradation and safety issues in turbomachinery components. Simulating these processes is a complex multiphysics and multiscale problem which has not reached a satisfactory level of maturity yet. The current state of the art approach is based on RANS solutions, which provide an averaged carrier phase on which the particles are advanced in an a posteriori manner. Upon wall impact, the particle quantities are then fed to the erosion and rebound models. In this work, we present as an alternative to this approach an Eulerian/Lagrangian simulation framework of high-order accuracy in space and time for the time-resolved prediction of particle motion in complex flows. We apply it to the LES of a particle-laden flow over a T106C low pressure turbine linear cascade. We then contrast time-averaged and time-accurate flow fields as carrier phases for the particles and highlight how the associated modeling assumptions influence the solution. Based on the particle Stokes number, we identify characteristic regimes and their interaction with the flow phase. By a detailed comparison of the particle statistics, we highlight the effects of turbulent small scale behavior and define the modeling challenges associated with finding accurate particle closure models for time-averaged simulations. This framework constitutes a first step towards high-fidelity erosion prediction for turbomachinery applications.     

Effect of bulk deformation and surface tension on the growth of a coherent inclusion

The object of this paper is the study of the moving boundary problem modeling the growth of a spherical solid inclusion in an infinite solid matrix. The displacement in bulk is assumed infinitesimal, while the phases are modeled as isotropic elastic bodies, and the interface structure is described by a constant surface tension. Existence of solutions is proved, and their asymptotic behavior in time is studied, with particular attention to the competition between surface tension and bulk deformation.     

Stability of multiple solutions in inclined gas/shear-thinning fluid stratified pipe flow

This work provides an investigation on multiple solutions in gas/shear-thinning fluid inclined stratified pipe flows. Multiple solution operative conditions are studied investigating the effect of the interfacial shear stress modeling and the rheology of the shear-thinning fluid. The modeling of the interfacial shear stress in counter-current has a strong influence of multiple solutions regions. The stability of multiple hold-up solutions is studied considering the structural stability, the interfacial stability, and the minimization of the dissipation approaches. The results of the three different approaches are commented both for concurrent and counter-current flows, giving the same conclusions only for upward inclined flows.     

Application of Modelica/MWorks on modeling,simulation and optimization for electro-hydraulic servo valve system

Electro-hydraulic servo valve is a typical complicated multi-domain system constituted by mechanical, electric, hydraulic and magnetic components, which is widely used in electro-hydraulic servo systems such as construction machinery, heavy equipment, weapon and so forth. The traditional method of modeling and simulation of servo valve is based on block diagram or signal flow, which cannot describe the servo valve system from components level nor be used in modeling and simulation of overall servo systems. In the procedure of traditional method, computational causality must be involved in modeling of servo valve, which is inconvenient to execute modification on components or parameters. Modelica is an object-oriented modeling language which is suited for large, complex, heterogeneous and multi-domain systems. The key features of Modelica are multi-domain, object-oriented and non-causal, which are suitable for modeling of servo valve and make the model readable, reusable, and easy to modify. The simulation results show similar curves with traditional method. This new servo valve modeling and simulation method can provide the engineers a more efficient way to design and optimize a servo valve and an overall servo system.     

Effect of Allowance for Small‐Scale Perturbations of the Carrier Phase on Properties of the System of Equations of a Two‐Fluid Flow with Incompressible Phases

The effect of the fluctuating components of kinetic energy and stress tensor of the carrier phase, which were previously obtained by the cell technique, on the properties of the system of equations of a gas–liquid flow with incompressible phases is considered. It is shown that the characteristic properties of this system and also the possibility of modeling the Zuber–Findlay empirical relation are determined by the tensor of fluctuating stresses of the carrier phase.     

Numerical modeling of slug flow initiation in a horizontal channels using a two-fluid model

This paper presents a methodology for modeling slug initiation and growth in horizontal ducts. Transient two-fluid equations are solved numerically using a class of high-resolution shock capturing methods. The advantage of this method is that slug formation and growth in a stratified regime can be calculated directly from the solutions to the flow field differential equations. In addition, by using high-resolution shock capturing methods that do not contain numerical diffusion, the discontinuity generated by slugging in the flow field can be modeled with good accuracy. The two-fluid model is shown to be well-posed mathematically only under certain conditions. Under these circumstances, the two-fluid model is capable of correctly predicting and modeling the flow physics. When ill-posed, an unbounded instability occurs in the flow field solution, and the instability amplitude increases exponentially with decreasing mesh sizes. This work shows that there are three zones associated with slug formation. In addition, long wavelength slugs are shown to initiate from short wavelength waves. These short waves are generated at the interface of the two phases by the Kelvin-Helmholtz hydrodynamic instability. The results obtained through numerical modeling show good agreement with experimental results.     

Four-Component Gas/Oil Displacements in One Dimension: Part I: Global Triangular Structure

This paper presents an analysis of the mathematical structure of three-component and four-component gas displacements. The structure of one-dimensional flows in which components partition between two phases is governed by the geometry of a set of equilibrium tie lines. We demonstrate that for systems of four components, the governing mass conservation laws for the displacement can be represented by an eigenvalue system whose coefficient matrix has a global triangular structure, which is defined in the paper, for only specific types of phase behavior. We show that four-component systems exhibit global triangular structure if and only if (1) tie lines meet at one edge of the quaternary phase diagram or (2) if tie lines lie in planes. For such systems, shock and rarefaction surfaces coincide and are planes. We prove that systems are of category (2) if equilibrium ratios (K-values) are independent of mixture composition. In particular, for such systems shock and rarefaction curves will coincide. We also show that for systems with variable K-values, the rarefaction surfaces are almost planar in a precise sense, which is described in the paper. Therefore, systems with variable K-values may be well approximated by assuming shock and rarefaction surfaces do coincide. For these special systems the construction of solutions for one-dimensional, two-phase flow with phase behavior simplifies considerably. In Part II, we describe an application of these ideas to systems in which K-values are constant.     

A two-dimensional,higher-order,elasticity-based micromechanics model

A new, two-dimensional (2D) homogenization theory is proposed. The theory utilizes a higher-order, elasticity-based cell model (ECM) analysis. The material microstructure is modeled as a 2D periodic array of unit cells where each unit cell is discretized into four subregions (or subcells). The analysis utilizes a (truncated) eigenfunction expansion of up to fifth order for the displacement field in each subcell. The governing equations for the theory are developed by satisfying the pointwise governing equations of geometrically linear continuum mechanics exactly up through an order consistent with the order of the subcell displacement field. The formulation is carried out independently of any specified constitutive models for the behavior of the individual phases (in the sense that the general governing equations hold for any constitutive model). The fifth order theory is subsequently specialized to a third order theory. Additionally, the higher order analyzes reduce to a theory equivalent to the original 2D method of cells (MOC) theory when all higher order terms are eliminated. The proposed 2D theory is the companion theory to an equivalent 3D theory [T.O. Williams, A three-dimensional, higher-order, elasticity-based micromechanics model, Int. J. Solids Struc., in press].Comparison of the predicted bulk and local responses with published results indicates that the theory accurately predicts both types of responses. The high degree of agreement between the current theory results and published results is due to the correct incorporation of the coupling effects between the local fields.The proposed theory represents the necessary theoretical foundations for the development of exact homogenization solutions of generalized, two-dimensional microstructures.     

Fluid–structure interaction with viscoelastic supports during waterhammer in a pipeline

Waterhammer modeling with fluid–structure interaction (FSI) in a pipeline with axial viscoelastic supports is the aim of this research. The viscoelastic materials of supports (or the pipe wall) were described using the generalized Kelvin–Voigt model. Hydraulic governing equations were solved by the method of characteristic (MOC) and axial vibration equation of the pipe wall was solved using the finite element method (FEM) in the time domain. For a typical case study, four different types for supporting the pipeline in the axial direction: fully free to move; fixed (rigid support); elastic and viscoelastic supports, subject to a waterhammer are analyzed and the results are scrutinized. The results quantitatively confirm that the use of supports with viscoelastic behavior in the axial direction of the pipeline can significantly reduce axial-pipe vibrations (displacements and stresses). The consequences of this structural damping on the attenuation of the internal fluid pressure are further demonstrated.     

柔性多体系统的计算策略

对柔性多体系统计算建模的研究现状和近期进展进行了总结. 重点讨论了柔性多体 动力学的以下内容: 柔性构件的建模, 约束建模, 求解技术, 控制策略, 耦合问 题, 设计和实验的研究. 对柔性多体系统建模的浮动坐标系,转动坐标系和惯性系 等3种坐标系的特点进行了对比. 指出了未来的研究方向, 包括柔性多体系统的新 的应用,如微观力学系统和超微观力学系统等; 提高这些模型的计算精度和效率的 技巧和策略; 以及可以用于改善柔性多体系统的工具. 本综述文章引用了877篇参 考文献.     

多体系统动力学Kane方法的改进

基于Kane方法, 针对约束多体系统, 建立了一种新型的自动组集系统动力学方程的方法. 首先提出偏速度矩阵和偏角速度矩阵的概念, 将各体对系统广义惯性力的贡献用简洁、统一的数学形式表达. 然后引入各个运动学变量的递推关系以提高建模效率.最后对新型的Kane方程进行扩展, 用于处理多体系统中的运动约束. 该算法适用于任意多体系统, 建立的动力学模型不含待定乘子, 维数与系统广义速率相同, 利于控制系统设计.对带有闭环约束的空间多机械臂系统的数值仿真验证了方法的正确性.      

Numerical modeling of carbon/carbon composites with nanotextured matrix and 3D pores of irregular shapes

A multiscale modeling approach is utilized to evaluate the contribution of irregularly shaped three-dimensional pores to the overall elastic properties of carbon/carbon composites. The degree of anisotropy of a carbon matrix depends on nanotexture, which is defined by manufacturing conditions. Elastic properties of the matrix are predicted assuming a Fisher distribution of orientations of graphene planes with respect to the pyrolytic carbon deposition direction. X-ray computed microtomography is employed to identify pores in a sample of carbon/carbon composite. The pores have highly irregular shapes so that micromechanical modeling based on the analytical solutions of elasticity becomes inapplicable. Thus, the cavity compliance tensor of an individual pore is found numerically by finite element method, and then used in a micromechanical modeling procedure. Examples of pores in isotropic and transversely isotropic pyrolytic carbon matrices are considered. The accuracy of pore approximation by ellipsoidal shapes is evaluated.     

Gravitational forces in dual-porosity systems: I. Model derivation by homogenization

We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effects. In particular, gravitational forces pose special problems. In this paper we develop a general understanding of how to incorporate gravitational forces into the dual-porosity concept. We accomplish this through the mathematical technique of formal two-scale homogenization. This technique enables us to average the single-porosity, Darcy equations that govern the flow on the finest (fracture thickness) scale. The resulting homogenized equations are of dual-porosity type. We consider three flow situations, the flow of a single component in a single phase, the flow of two fluid components in two completely immiscible phases, and the completely miscible flow of two components.This work was supported in part by the National Science Foundation and by the State of Texas Governor's Energy Office.     

A 2D+t SPH model to study the breaking wave pattern generated by fast ships

A 2D+t approach is applied to study the wave pattern generated by high speed slender ships with a sharp stem. This allows approximating the ship motion through a set of equations which are mathematically equivalent to those governing the unsteady 2D free-surface flow generated by a deformable body in the vertical plane transverse to the ship. To describe the body deformation, a proper modeling of the solid boundaries is needed. To this purpose the fixed ghost particle technique recently developed by the authors for 2D SPH schemes is adopted. Then, an in-depth analysis of the bow breaking wave evolution is provided focusing on the different features of the plunging jet as function of the ship forward velocity. The comparison with experimental data proves the proposed SPH scheme to be robust and accurate.     

The structural instability of transonic flow associated with amalgamation/splitting of supersonic regions

We study inviscid transonic flow in a channel with a bump modeling an airfoil at zero incidence. A few simple bump configurations are considered. Numerical simulations show the existence of singular free-stream Mach numbers, which trigger the splitting/amalgamation of local supersonic regions. An analysis of this phenomenon contributes to the understanding of the nonuniqueness of transonic solutions at certain free-stream conditions.