聚合物流动的多尺度模拟

基于聚合物分子运动论,提出了一种新的计算聚合物流体的多尺度方法。该方法在宏观尺度上应用无网格方法求解速度场,在微观尺度上应用随机模拟技术计算聚合物对应力的贡献,从而避免需要本构方程来封闭连续性方程和动量守恒方程。对Hooke哑铃模型、FENE哑铃模型、FENE-P哑铃模型,模拟了突然起动平面Couette流动;对Hooke哑铃模型,模拟了方腔驱动流动。从而验证了该方法的有效性和计算结果的可靠性。     

Decomposition and exact solutions of three-dimensional nonstationary linearized equations for a viscous fluid

A new exact method for solving three-dimensional linear systems of hydrodynamic equations is described based on decomposing these systems into three simpler equations. It is shown that the general solution to three-dimensional Stokes equations (when there are no mass forces) can be expressed by means of solutions to two independent equations: the heat conduction equation and the Laplace equation. A class of solutions with the linear dependence of velocity components on two space variables is studied, and their physical interpretation is given. Axial flows are considered, and certain hydrodynamic problems are solved. A general solution to three-dimensional Oseen equations is constructed. The linearized equations of motion for a viscoelastic Oldroyd fluid are studied     

Systematic coarse graining flowing polymer melts: thermodynamically guided simulations and resulting constitutive model

Complex fluids, such as polymers, colloids, liquid-crystals etc., show intriguing viscoelastic properties, due to the complicated interplay between flow-induced structure formation and dynamical behavior. Starting from microscopic models of complex fluids, a systematic coarse-graining method is presented that allows us to derive closed-form and thermodynamically consistent constitutive equations for such fluids. Essential ingredients of the proposed approach are thermodynamically guided simulations within a consistent coarse-graining scheme. In addition to this new type of multiscale simulations, we reconstruct the building blocks that constitute the thermodynamically consistent coarse-grained model. We illustrate the method for low-molecular polymer melts, which are subject to different imposed flow fields like planar shear and different elongational flows. The constitutive equation for general flow conditions we obtain shows rheological behavior including shear thinning, normal stress differences, and elongational viscosities in good agreement with reference results.     

A finite piece method for simulating polymer melt flows in extrusion sheet dies

A finite piece method is proposed to simulate three‐dimensional slit flows in extrusion sheet dies in this paper. The simulations concern incompressible fluids obeying different constitutive equations: generalized Newtonian (Carreau‐Yasuda law), and viscoelastic Phan‐Thien Tanner (PTT) models. Numerical simulations are carried out for the isothermal and nonisothermal flows of polymer melt through sheet dies. The Picard iteration method is utilized to solve nonlinear equations. The results of the finite piece method are compared with the three‐dimensional (3D) finite element method (FEM) simulation and experiments. At the die exit, the relative error of the volumetric flow between the finite piece method and the 3D FEM is below 1.2%. The discrepancy of the pressure distributions does not exceed 6%. The Maximum error of the uniformity index between the simulations and experiments is about 2.3%. It shows that the solution accuracy of the finite piece method is excellent, and a substantial amount of computing time and memory requirement can be saved. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Modeling and simulation of conditionally volume averaged viscoelastic two‐phase flows

Conditional volume averaging is used to develop a model capable of simulating two‐phase flows of viscoelastic fluids with surface tension effects. The study is started with the single‐phase mass and momentum balances, which are subsequently conditionally volume averaged. In doing so, we arrive at a set of equations having unclosed interfacial terms, for which closure relations for viscoelastic fluids are presented. The resulting equations possess a structure similar to the single‐phase equations; however, separate conservation equations are solved for each phase. As a result, each phase has its own pressure and velocity over the entire domain. Next, our numerical implementation is briefly outlined. We find that a Poiseuille single‐phase flow is predicted correctly. The closure terms are examined by considering a two‐phase shearing flow and a quiescient cylinder with surface tension. A convergence analysis is performed for a steady stratified two‐phase flow with both phases being viscoelastic. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3914–3927, 2013     

A hybrid finite element/finite difference algorithm for compressible/incompressible viscoelastic liquids

A unified formulation is proposed for modelling compressible/incompressible viscoelastic liquids. The pure hyperbolic nature of the model overcomes some of the drawbacks of available models. The most important of these drawbacks is the mixed nature of the resulting systems of equations, with the subsequent consequence of having no general numerical algorithm for the solution. A new non‐dimensionalisation procedure is adopted. A hybrid least‐squares finite element/finite difference scheme coupled with a Newton‐Raphson's algorithm is used to solve the resulting system of equations. The method is used to predict the velocity and stress fields for different Weissenberg numbers for two benchmark problems.     

Simple calculation technique to solve the leung/wiles equations for the choking load of multisize particles in pneumatic transport lines

Leung and Wiles (1976) proposed a quantitative procedure to calculate the maximum flowrate or “choking load” of solids which can be conveyed by a gas flowing at a given velocity in a vertical pneumatic transport line. However, no simple way of solving their equations was given by them. A new calculation method is proposed here to solve their equations to obtain the choking load of multisize particles.     

A Method for Calculation of Final Film Thickness in Free Coating of Viscoelastic Fluids onto a Vertical Surface

A method for the calculation of the final film thickness in free coating of a viscoelastic fluid onto a vertical surface withdrawn from its vessel is developed. The method is based on the definition of an objective function, the minimization of which guarantees that the kinematic as well as the dynamic conditions at the lower boundary of the dynamic meniscus region are simultaneously satisfied. A systematic approach is provided in order to localize the optimum value of the final film thickness within the optimization interval. It was observed that there was a clear relationship between the estimated final film thickness and the value of a parameter A. The closeness of this parameter to zero corresponds to the dynamic constraint being fulfilled at the lower boundary of the dynamic meniscus region. This relationship is used as an objective means of determining the direction to update the interval of optimization to obtain the final thickness of the film. The results of the proposed method are compared to the previous works on the free coating of viscoelastic fluids, which are based on a trial‐and‐error method. The performance of the previously applied rheological models to the formulation of the free coating process, mainly the modified Oldroyd models, is also compared by introducing the present method.     

A new splitting wavelet method for solving the general aerosol dynamics equation

In this paper, a new and robust splitting wavelet method has been developed to solve the general aerosol dynamics equation. The considered models are the nonlinear integro-partial differential equations on time, size and space, which describe different processes of atmospheric aerosols including condensation, nucleation, coagulation, deposition, sources as well as turbulent mixing. The proposed method reduces the complex general aerosol dynamic equation to two one-dimensional splitting equations in each time interval, and further the wavelet method and the upstream finite difference method are proposed for solving the particle size directional and the spatial directional splitting equations. By the method, the aerosol size spectrum is represented by a combination of Daubechies’ wavelets and substituted into the size-directional splitting equation at each time step. The class of Daubechies’ wavelets in the wavelet-Galerkin scheme as trial and weight functions has the advantages of both compact support and orthonormality which can efficiently simulate the sharp shape distribution of aerosols along the particle size direction. Numerical experiments are given to show the efficient performance of the method.     

黏弹性表面活性剂溶液中颗粒沉降特性研究

黏弹性表面活性剂溶液悬浮颗粒流广泛存在于自然界和工业生产中,黏弹性表面活性剂溶液的非线性流变性质及应力松弛效应对其中颗粒沉降有着显著影响。采用FENE-P和Giesekus黏弹性本构模型对表面活性剂溶液中颗粒沉降特性进行研究,发现两种本构模型不仅表现出剪切稀化,而且出现拉伸硬化。颗粒在沉降初期的不稳定性主要是由溶液自身的弹性效应引起,弹性效应越强,颗粒沉降速度不稳定性越强,而剪切稀化效应会减弱颗粒沉降速度的不稳定。颗粒沉降过程中在其尾部形成一个“负尾迹”,随着剪切稀化和拉伸硬化效应增强,负尾迹区增大,弹性效应增加,负尾迹增强,负尾迹区流体内部反向速度分布导致的表面活性剂溶液中微观胶束的拉伸断裂和重构可能是引起颗粒沉降速度持续波动的原因。     

A novel methodology to model the creep behavior of polymers at different temperatures

A new methodology for modeling the creep behavior of polymers at different temperatures, by using phenomenological constitutive models, is presented in this paper. The viscoelastic model is given by a combination of springs and dashpots and is used to describe the nonlinear response of polymers, and the viscoplastic formulation is given by a power-law equation. The approach proposed in this work is based on building master curves for different stress levels, and finding the dependency of the constitutive parameters with the temperature. After fitting the equations to the tensile creep tests at different temperatures, the final constitutive formulation is capable of modeling the behavior of polymers at any stress level and temperatures. Poly methyl metacrytale (PMMA) was used to investigate the accuracy of this proposal, and the results showed good agreement with the experimental data.     

A GENERALIZED EQUATION OF STATE FOR POLAR AND NON-POLAR FLUIDS BASED ON FOUR-PARAMETER CORRESPONDING STATES THEOREM

A new generalized equation of state for polar and non-polar fluids based on the corresponding states theorem is developed, f n addition to two critical parameters, four parameters are required; two for the calculation of volumetric properties and two for the calculation of pressure and departure functions. Parameteres for more than 100 polar and non-polar fluids are given. Comparison with the existing generalized state equations showed that the new method, in general, shows a better agreement with the experimental data. The absolute average deviation is 0.48% for the vapor pressure and 0.32% for the saturated liquid volume.     

Globally optimal synthesis of heat exchanger networks. Part III: Non-isothermal mixing in minimal and non-minimal networks

In this work, the enumeration algorithms presented in Parts I and II for the globally optimal synthesis of minimal and non-minimal heat exchanger networks are extended to consider non-isothermal mixing. New mathematical models, including non-isothermal mixing constraints, are proposed to target the bounds of energy consumption and the binding exchanger minimum approximation temperature. These models are solved using the algorithms, which involve solving systems of equations instead of mathematical programming. Three global optimization strategies are proposed to optimize each enumerated structure, involving the use of a global solver directly, or the use of a Golden Search based on energy consumption and a flowrate optimization model considering non-isothermal mixing. The flowrate optimization model is reformulated as a convex problem, which is solved by using nonlinear programming or a mathematical programming-free methodology, that is, solving Karush–Kuhn–Tucker equations. A new Global Optimum Search Algorithm is developed and examples are tested comparing different optimization strategies.     

Two-Dimensional Elasticoviscous Boundary Layer Flows Near a Stagnation Point

At present many new fluids not obeying the Newtonian laws are being studied by scientists because of their industrial importance [1]. The constitutive equations of these fluids have been given by different researchers, for example, Oldroyd [2] and Walters [3]. Beard and Walters [4] solved the two-dimensional boundary layer flow for an elasticoviscous fluid, near a stagnation point for the case of Walter's liquid B″, when the elasticoviscous parameter is very small. A new method is now proposed for determination of the two-dimensional boundary layer flow near a stagnation point for Walter's liquid B″ I, which is valid not only for very small positive elasticoviscous parameters but also for positive elasticoviscous parameters.     

Stability of isothermal spinning of viscoelastic fluids

The stability of isothermal spinning of viscoelastic fluids which have strain-rate dependent relaxation time has been investigated using the linear stability analysis method. The instability known as draw resonance of the system was found to be dependent upon the material functions of the fluids like fluid relaxation time and the strain-rate dependency of the relaxation time as well as upon the draw-down ratio of the process. Utilizing the fundamental physics of the system characterized by the traveling kinematic waves, we also have developed a simple, approximate method for determining this draw resonance instability; it requires only the steady state velocity solutions of the system, in contrast to the exact stability analysis method which requires solving the transient equations. The stability curves produced by this simple, fast method agree well with those by the exact stability method, proving the utility of the method. The stability of other extensional deformation processes such as film casting and film blowing can also be analyzed using the method developed in this study.     

Uncertainty and models for creep of concrete

An engineer involved in practical design must often choose between using approximate rules of thumb, and more rigorous analyses. The problem may be tackled using decision theory. An important element in this analysis is the estimation of probabilities of future values of creep. Some factors that contribute to one's uncertainty are discussed and ranked. If it is decided to carry out a detailed structural analysis, it is necessary to have constitutive equations for creep. The importance of heterogeneity of concrete and cement paste is emphasized, together with the implications of this in the analysis of time-dependent movements using the activation energy approach. A qualitative interpretation of the dashpot elements in viscoelastic models from a thermodynamic standpoint is given; this relates primarily to an increase in configurational entropy. Lastly the effects of ageing and some disadvantages of the linear viscoelastic models are discussed.     

A new concept for augmented van der Waals equations of state

A novel approach to perturbed equations of state for simple fluids is presented and its advantages over the traditional perturbed hard sphere equations are demonstrated by its application to several model fluids. The approach is based on a short range Yukawa reference which incorporates, in addition to repulsive interactions, also attractive interactions at short separations. The considered models of common interest are the Sutherland, Lennard-Jones, and EXP6 fluids. It is shown that using the proposed approach the reference system captures a good deal of properties of the studied fluids and that an accurate equation of state can be obtained using only the crude mean field (augmented van der Waals) approach.     

NATURAL CONVECTION FLOW OF SECOND-GRADE FLUID ALONG A VERTICAL HEATED SURFACE WITH POWER-LAW TEMPERATURE

In this study we investigated the effects of free convection flow of a viscoelastic second-grade fluid along a vertical flat surface with power-law temperature distribution. The boundary layer equations for the momentum and the energy transport have been reduced to local similarity equations using appropriate transformations. Solutions of the reduced equations are obtained employing the local non-similarity method as well as the implicit finite difference method against ξ (the local Deborah number) in the range [0, 10] for fluids having Prandtl numbers of 10, 50, and 100. The regular perturbation solutions are also been obtained for smaller values of ξ together with the Padé approximation. Results thus obtained are discussed in terms of the local skin friction and local rate of heat transfer for different values of the physical parameters, like n and Pr. Effect of the Deborah number, De, on the velocity and temperature profiles has also been shown graphically. It is observed that both the local skin friction and heat transfer coefficients decrease with increase in the value of De for given values of n and Pr.     

注塑制品内应力计算的非线性黏弹性本构方程

在聚合物黏弹性理论的基础上,构建了新的注塑制品内应力计算的四元件串联力学模型,并推导了其瞬态黏弹性响应的非线性本构方程,给出了聚合物材料参数弹性模量和黏壶系数的计算公式,并对PS平板注塑制件脱模前的内应力进行了模拟计算。计算结果与固体高聚物的结构和力学性能的相关研究结论相一致,所建计算模型合理可靠。     

Modeling and simulation of solvent extraction processes for purifying rare earth metals with PC88A

A new simulation logic and thermodynamic equilibrium analysis algorithm combined with a new model simplification technique was developed to simulate the solvent extraction process for purifying rare earth metals from chloride solution with 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (PC88A) as a solvent. The proposed model simplification method significantly reduces the number of the nonlinear equilibrium equations to be simultaneously solved to overcome the initial guess problem and obtain numerically stable convergence pattern in solving the equilibrium analysis problem and performing the rigorous simulation of the extraction process. A new equilibrium analysis algorithm on the basis of the simplified nonlinear equilibrium equations is also proposed to estimate the equilibrium concentrations by solving the rigorous first principle extraction model. Finally, a solvent extraction simulator is developed to estimate all the concentrations of all the stages of the solvent extraction process by solving the equilibrium analysis problem at each stage in a sequential way. The proposed simulator doe not suffer from the initial guess problem and shows very robust convergence pattern without any numerical problems.