注塑结晶性塑料平板冷却时间的讨论

对注塑结晶性塑料平板的冷却问题进行了分析。注塑结晶性塑料平板的冷却模型实质是伴有相变的不稳定一维导热。通过Neumann方法求得了这一模型冷却时间的数值解，并与其他方法进行了比较。     

中空吹塑成型过程数值分析技术的进展

论文对塑料中空吹塑成型过程数值分析的研究和发展状况进行了全面的阐述，针对成型过程的三个阶段：型坯形成，型坯吹胀以及冷却与固化阶段因内外研究者进行数值分析的具体谅才理论依据进行了较详细的论述，并指出毛坯熔融挤出，吹胀成型、冷却和固化是成型周期中紧密衔接的三个过程，目前对各个阶段分别进行研究的较多，而综合考虑气压、温度、冷却时间、高分子材料性能等因素对全过程进行数值模拟的较少见报道，因此还有许多研究工     

聚丙烯保压注射成型冷却过程温度场的研究

采用数值模拟结合实验验证的方法,对聚丙稀（PP）注射成型（保压和不保压）冷却过程实验和数值模拟进行分析。用数据采集器对不同共混物注射冷却过程中的温度变化进行数据采集,并将采集所得温度的实验值与根据改进焓法用Matlab软件对聚丙烯冷却过程中温度分布进行数值模拟计算所得的值进行了比较分析,结果表明聚丙烯在液体冷却段温度分布的实验值与理论值几乎完全吻合,在结晶段和固体冷却段实验值略有不同。     

注塑模温度场的计算机模拟

本文运用有限元法，采用二次等参单元，对注塑模二维非稳态温度场进行了数值分析，推导了有限元数值求解方程并研制了有限元求解程序软件。实例所得温度场等温线与实验所得结果基本相符，验证了计算机求解的可靠性。通过计算机模拟分析，可了解各瞬时模具温度场的分布状态，观察模具体能否使塑件均匀冷却，如不合理，可通过改变冷却管道参数，达到温度场均匀一致，从而提高塑件质量。通过程序运转，根据塑件的热定型温度，可以预知最短冷却时间，从而缩短冷却周期，提高塑件生产率     

螺杆冷却时的单螺杆挤出熔融理论研究

利用可视化挤出实验对螺杆冷却情况下的单螺杆挤出熔融机理进行了研究。实验表明，挤出过程中固体床始终保持连续而不会出现固体床破碎现象，螺槽表面会出现聚合物的亚稳态相转变行为。通过建立螺杆冷却时熔融理论的数学模型，用数值方法获得了熔融段聚合物流场的数值解，结果表明，理论预测的固体床宽度和机筒压力与实验结果基本吻合。     

基于自动控制概念的干熄炉传热一维模型

根据多孔介质理论，采用非局域热平衡方法，建立了干熄炉内传热的一维数学模型。通过数值求解，得到了干熄炉内气体和焦炭的温度分布规律，通过干熄炉内冷却段焦炭和气体的温度分布可以判断熄焦量与冷却风量是否合理匹配。     

挤出成型塑料管材冷却过程的建模与温度场数值模拟

基于传热学理论，对挤出成型塑料管材的冷却过程进行了分析并建立了数学模型。引入聚合物的比热容和热导率对温度的依赖关系，运用有限差分数值方法，求解变物性参数条件下一维非稳态传热方程，模拟了塑料管材在定型冷却过程中的温度场，并由此确定冷却段的合理长度。     

平板塑件瞬态传热解析解及其在冷却分析中的应用

简要介绍了建立冷却分析数学模型的两种方法，指出了循环迭代模型的不足，推导了平板塑件瞬态传热解析解，找出循环平均热流与边界温度的线性关系表达式，并将它应用于注塑冷却分析，建立了冷却分析的迭代模型，取代原来的循环迭代模型，从而取消了原冷却分析中的中间迭代计算，有效地减少了冷却分析的迭代次数，提高了运算效率。另外，循环迭代求解平板塑件温度场采用的是有限差分法，即近似数值解，而迭代模型采用的是解析解，从理论上讲结果更精确，所以对提高计算结果的精度有一定的改善作用。     

结晶型塑料注塑平板冷却模型的研究

从注塑的实际出发，针对注塑结晶型塑料平板的冷却本质，利用有限厚度区域内注塑平板的冷却模型，运用数值分析的常用算法和多项式拟合的方法进行计算机精确分析求解。进行了详细的理论推导，求得了固液两相内的温度分布，凝固系数的函数以及平板中心层温度冷却至熔点所需的时间。     

浮法退火窑辐射间接冷却区内冷却风量及其分布的研究

建立了浮法玻璃退火窑辐射间接冷却区内冷却风量及其分布计算的一个数学模型,并用分区方法在计算机上进行了数值计算。借助所建立的模型研究了冷却风量及其分布与冷却风进口温度、玻璃带运动速度(产量)之间的关系。计算结果可供浮法玻璃退火窑设计与控制参考。     

Analysis of non-linear consolidation of soft clay by differential quadrature method

Due to the complexity of the non-linear consolidation of soft clay, numerical method is always adopted to its solution. The differential quadrature method (DQ method) equaling to a high precision finite difference method can obtain highly accurate numerical solutions of differential equations using less grid points. This numerical method is always used to solve the complicated nonlinear physical problem governed by partial equations. In this paper, DQ method is implemented to one dimensional non-liner consolidation equation and the boundary conditions. Euler forward scheme is used to solve the discrete equation, and the pore pressure and consolidation curves are prepared. The present numerical results are compared with the analytical solutions. Compared with the other numerical method, the method of solving the non-linear consolidation equation by the DQ method in this paper is very simple and reasonable. The DQ method is successfully implemented to the soft clay consolidation analysis and can assure satisfied numerical results with less grid points.     

Dense particulate flow model on unstructured mesh

A numerical method based on two-dimensional (2D) unstructured meshes is developed to solve the discrete particle model (DPM). Inter-particle interactions are taken into account for dense particulate flows, which are described by binary collisions in a hard-sphere model. The particle volume fraction is calculated accurately and physical scalars from the Eulerian grid to the Lagrangian particle positions are mapped through gradient interpolations. The governing equations for the continuous phase are discretized using a finite volume method on an unstructured grid and solved by the algebraic multi-grid (AMG) method. The SIMPLE algorithm employed to solve single-phase flows on unstructured meshes is extended to the pressure-velocity equations. Momentum coupling between the two phases is strongly implicit resulting in a very robust convergence of the AMG solver. Data structuring and mapping techniques for further enhancement of the flexibility and computational efficiency of the numerical model are introduced. Several test cases confirm that the numerical method can be applied to gas-solid and gas-liquid flows in irregular domains without regard to element types of the mesh. The numerical model presented in this paper partly overcomes the difficulties in simulating dense particulate flows using the DPM in 2D irregular domains.     

Solution of population balances with growth and nucleation by high order moment-conserving method of classes

The high order method of classes, developed in our earlier work [Alopaeus, V., Laakkonen, M., Aittamaa J., 2006a. Solution of population balances with breakage and agglomeration by high order moment-conserving method of classes. Chemical Engineering Science 61, 6732-6752] for solution of population balances (PBs), is extended to problems with growth and primary nucleation. The growth problem leads to a hyperbolic partial differential equation with fundamentally different numerical characteristics than the PB with breakage and agglomeration only. However, we show that the principle of moment conservation in the numerical solution can also be applied to this advection-type problem, leading to extremely accurate numerical solutions. The method is tested for two numerical cases. The first one is mass transfer induced particle growth, and the second one is primary nucleation with constant growth (similar to the Riemann advection problem). For mass transfer induced growth, we first analyze functional form of the growth rate from mass transfer correlation viewpoint, and derive a general analytical solution for the power-law growth. The numerical results from the moment conserving method are also compared to one well established high resolution numerical method for advection problems, namely the Lax-Wendroff method with van Leer flux limiter. It was shown that the present method is far superior by predicting the distribution moments with several order of magnitudes lower numerical error. For the Riemann problem with constant growth rate, the present method predicts the shock front location exactly without any numerical diffusion.     

Monte Carlo Simulation of Multicomponent Aerosols Undergoing Simultaneous Coagulation and Condensation

A Monte Carlo method was developed to simulate multicomponent aerosol dynamics, specifically with simultaneous coagulation and fast condensation where the sectional method suffers from numerical diffusion. This method captures both composition and size distributions of the aerosols. In other words, the composition distribution can be obtained as a function of particle size. In this method, particles are grouped into bins according to their size, and coagulation is simulated by statistical sampling. Condensation is incorporated into the Monte Carlo method in a deterministic way. If bins with fixed boundaries are used to simulate the condensation process numerical dispersion occurs, and thus a moving bins approach was developed to eliminate numerical dispersion. The method was validated against analytical solutions, showing excellent agreement. An example of the usefulness of this model in understanding aerosol evolution is presented. The effects of the number of particles and number of bins on the accuracy of the numerical results are also discussed. It was found that with 20 bins per decade and 105particles in the control volume results with less than 5%error can be obtained. The results are further improved to within 2%error by filtering the statistical noise with a cubic spline algorithm.     

Numerical Solution for Fractional-Order Differential Systems with Time-Domain and Frequency-Domain Methods

For a general nonlinear fractional-orderdifferential equation, the numerical solution is a goodway to approximate the trajectory of such systems. Inthis paper, a novel algorithm for numerical solution offractional-order differential equations based on thedefinition of Grunwald-Letnikov is presented. Theresults of numerical solution by using the novel methodand the frequency-domain method are compared, and the limitations of frequency-domain method arediscussed.     

Mathematical modelling of hydrothermal performance for Kenics type static mixer using power law obeying fluids

In this study, analytical, numerical, and experimental works are presented to demonstrate hydrothermal characteristics of a flow choosing non-Newtonian behaviour through a Kenics type static mixer. Experiments are conducted by varying the superficial fluid velocities of the heterogeneous mixture oil with Sudan dye and water, as well as for the homogeneous aqueous system, consisting of CMC (2 wt%) in water. Six static mixing elements are placed in series, and the corresponding wall temperatures of the inline pipe are varied over a range of 293–363 K. In the context of hydrodynamic study, analytical models are solved using the Bessel function and Laguerre function and validated with the in-house experimental results and numerical results. In the thermal performance study, mathematical models are formulated based on differential transformation method (DTM) and homotopy perturbation method (HPM), and have been validated with the numerical results. The deviation among the experimentally measured average pressure drops estimated from our experiment and that predicted by analytical models is found to be as low as ±8.1%. The deviation between the analytical results obtained from the HPM and DTM method and numerical results based on the finite volume method solution of the same equation is observed as low as ±4%. Additionally, both proposed analytical methods used are compared with each other to evaluate the dimensionless swirl flow velocity and temperature gradient of the inline Kenics Static mixer. In the thermal performance study, we observe that the DTM is in good agreement with the numerical method as compared to HPM.     

A new method for solving initial value problems

A more accurate method (comparing to the Euler, Runge–Kutta, and implicit Runge–Kutta methods) for the numerical solutions of ordinary differential equations (ODEs) is presented in this paper. The coefficients in the approximate solution for the ODE using the proposed method are divided into two groups: the fixed coefficients and the free coefficients. The fixed coefficients are determined by using the same way as in the traditional Taylor series method. The free coefficients are obtained optimally by minimizing the error of the approximate solution in each time interval. Examples are presented to compare the numerical solutions of the Rahmanzadeh, Cai, and White's method (RCW) to those of other popular ODEs methods.     

Studies in constrained optimization of chemical process problems

The application of three constrained, nonlinear optimization methods (method of multipliers, complex method and adaptive random search method) to six chemical process problems is described. Based on the numerical results, salient characteristics of the problems and the specific advantages of the methods are discussed. The multiplier method was implemented with numerical approximation to derivatives; the results show that both the increment (or perturbation) and the accuracy of floating-point numbers are important in determining the effect of numerical approximations on the performance of the method.     

化工原理教学中数值方法和程序设计的训练和实践

化工原理课程中涉及众多数值或试差计算问题,但教材对该方面内容的介绍不够深入.为了激发和培养学生的学习兴趣,本文拟介绍在教学中如何运用计算机进行简单工程计算的训练和实践方法.教学实践表明,通过循序渐进的训练和培养,学生不仅对问题的理解更深刻,同时拓展了知识面,收获甚丰.     

CFD 在食品干燥过程及其干燥设备设计中的应用

CFD是通过计算机数值计算和图像显示以定量描述流场的数值解,从而对物理问题进行分析研究。CFD兼有理论性和实践性的双重特点,其主要用途是对流态进行数值仿真模拟计算,能够对流态的温度场、速度场、浓度场等进行有效的指导和预测。本文综述了CFD数值模拟在食品干燥过程中以及干燥设备设计中的应用和发展前景。