奥美拉唑对映体的模拟移动床色谱分离过程模拟

模拟移动床色谱已成为一种重要的手性药物制备技术,其技术关键在于最佳运行点的确定。由于其过程复杂,用数学模型来确定最佳运行点,求解难度大,计算时间长。今以考虑传质阻力与轴向弥散的模拟移动床模型为基础,采用线上求解法,将模型方程沿空间方向离散,得到一组常微分方程,然后运用MATLAB提供的常微分求解器求解这一偏微分方程组,模拟了奥美拉唑对映体的模拟移动床色谱分离过程。研究结果表明,线上求解法结合MATLAB常微分求解器可快速、准确地求解模拟移动床模型,用于模拟移动床色谱分离过程的实时控制与优化。     

吸附剂孔内扩散对模拟移动床分离过程的影响

为考察孔内扩散对模拟移动床分离过程的作用,采用综合速率模型对其进行研究,其中流动相模型为轴向扩散活塞流,颗粒相为Fiek定律描述的扩散方程,液相和固相之间的吸附平衡采用改进的Langmuir吸附等温线．对流动相和颗粒相分别采用有限元Galerkin法和正交配置法,沿空间方向离散化后的常微分方程组运用MATI。AB的ODE求解器求解．在验证了模型和离散方法对模拟移动床吸附分离过程计算的可靠性的基础上,模拟了EMD53986对映体的模拟移动床分离过程,跟文献中使用忽略孔内传质过程的模型得到的计算值相比,模拟值与实验值吻合得更好,表明孔内扩散传质过程对模拟移动床模拟计算的重要性．     

SMB色谱分离过程计算机仿真

针对模拟移动床(SMB)综合速率模型，采用有限元法和正交配点法分别对柱向和颗粒径向模型进行离散化，利用MatLab ODE求解器对SMB过程进行数值求解。通过仿真，验证了该方法的可行性。     

结晶性注塑平板制品冷却时间的确定

从传热学基本原理出发,推导出结晶性平板状注塑制品冷却时间的几种计算方法。对于PP,在相同条件下,利用分离变量法对简化的一维传热模型进行求解,得冷却时间τ为7 5s;对一维相变移动边界模型,解析解法采用固相精确求解与液相近似求解相结合的方法,得τ为23s;数值解法采用了焓法,得τ等于23 05s。最后举例讨论了数学模型与实际注塑加工的差距。这些对结晶性聚合物注塑加工具有一定的指导作用。     

填充床电化学反应器普遍化模型方程数值求解方法

以有限差分法与正交配置法联用对填充床电化学反应器的模型方程进行了求解，结果表明该法是一种快速、有效地求解具有较为复杂的边界条件的偏微分方程的计算方法。     

分子筛脱蜡模拟移动床工业过程的模拟计算与分析

针对分子筛脱蜡工业生产的模拟移动床过程,基于TMB建模策略,建立了描述模拟移动床过程的数学模型,模型求解采用有限元配置的数值计算方法PDECOL软件包。结果表明:在验证模型计算正确性的基础上,模型模拟计算值与过程设计值相一致,可以用描述分子筛脱蜡工业生产的模拟移动床过程。探讨了模拟移动床过程中的进料流速、提取液的提取速度、旋转阀的切换周期以及脱附液的用量等操作参数对过程性能的影响,为过程的优化提供了基础。     

基于行波法的段塞流瞬态捕捉模型建立与验证

气液两相流中，准确预测段塞流的特征参数具有重要的现实意义。Renault模型是基于非黏性Kelvin-Helmholtz（IKH）稳定性准则与黏性Kelvin-Helmholtz（VKH）稳定性准则建立的能够捕捉段塞前后界面运动的双流体模型，但该模型在液相单元格之间采用Riemann精确解，求解速度较慢。为简化计算，本文将行波法引入到Renault模型的液相方程求解过程，并对可能出现的干区用薄液膜代替，使行波法适用于所有计算单元，在保证模型精度的条件下，极大地提高了计算速度，运算时间相比Renault模型平均减少28%。对比本模型计算结果与室内小型环道实验数据，持液率与实测结果相一致，压降、段塞长度计算相对误差分别在25%、30%以内，且主要分布在20%以内。说明本文改进的瞬态段塞流模型具备运算快速、计算精度较高的特点，具有一定的工程应用价值。     

气化炉炉体关键部位温度分布研究

从通用传热模型出发，研究了气化炉炉体的传热模型。应用有限单元法进行了求解，以德士古气化炉炉体为具体实例，计算了气化炉炉体关键部位的温度分布，结果表明，该方法可以有效的计算出气化炉炉体上任意一点的温度，以气化炉的设计。运行和维护提供理论依据。     

聚合物稀溶液的微观-宏观确定性模拟

采用确定性方法数值求解了聚合物稀溶液的微观-宏观模型,其中,宏观尺度上用有限体积法求解守恒方程,介观尺度上用谱方法求解Fokker-Planck方程和聚合物对偏应力张量的贡献,模拟了聚合物稀溶液FENE哑铃模型的平板Couette流动,给出了速度随时间变化的剖面图,分析了移动平板速度、哑铃的量纲1有限拉伸参数和Deborah数对流动的影响,同时也验证了有限体积法与谱方法结合求解聚合物微观-宏观模型的有效性。     

石蜡在管外凝固过程的理论和实验分析

对使用水作为传热流体的蛇形管式换热器中，进口水温对石蜡在管外凝固过程的影响进行了研究。建立了水温沿流向变化，石蜡温度沿径向变化的传热模型。使用控制容积法及焓法建立了求解水和石蜡耦合温度场的数值方程，这两个温度场的计算结果与实验结果能很好吻合。冷却水进口温度不同，靠近铜管已凝固石蜡中的温度场存在显著差别，离铜管较远石蜡中的温度几乎不受进口水温影响，石蜡的无量纲温度场在离相界面较远处具有相似分布的特点。相界面移动具有先快后慢，然后再变快的特征。研究可为保证蛇形管外石蜡凝固速率选择恰当的进口水温提供计算方法。     

第一类边界条件下板状多孔物质中分子扩散型传质时升华问题的摄动解

本文用摄动方法分析了板状多孔介质在第一类边界条件下Fick分子扩散传质时的升华干燥问题.基于对问题本质特征的分析,提出了运动界面处边界条件的处理的新方法,得到了无量纲形式的温度、浓度及运动界面位置的解析表达式.理论与实验结果的比较表明,摄动解比准稳态解更接近于实验结果.     

Solution of moving boundary problems for gas—solid noncatalytic reactions by orthogonal collocation

An integral transformation, a coordinate transformation for immobilization of the moving boundary, and orthogonal collocation are used to reduce a nonlinear initial-boundary value problem in time and space to a set of ordinary differential equations in time with given initial conditions. The method is developed for solution of models for gas—solid noncatalytic reactions and is especially useful for moving boundary, two-stage reaction problems. The method represents an advantage and an alternative to the available finite difference techniques. Results of various gas—solid reaction models are analyzed.     

Analysis of moving boundary problem of growth of Bismuth germanate crystal by heat exchanger method

Transient two-dimensional model of the growth of BGO crystal by heat exchanger method has been developed. A finite element method with nonorthogonal mapping technique for the solution of the moving boundary problem is developed where the melt/solid interface shape changes from hemispherical to planar. The moving boundary problems for the melt/solid interface location and the temperature field were solved by two mapping rule method which enables the computation of interface shape changing from hemispherical to planar. The maximum deflection of interface is shown when the melt/solid interface meets the corner of crucible. As the excess heating temperature and the heat exchanger temperature were increased, more growth time for whole process is required but the quality of BGO crystal may be improved. The ratio of the height to the radius of crucible hardly affects the deflection of BGO melt/solid interface when it is greater than 1.5. As the cooling zone radius is decreased, maximum deflection is decreased. The heat transfer between the crucible and the heating element should be suppressed to maximize planarity of the interface shape.     

Modeling of Diffusion with Shrinkage and Quality Investigation of Banana Foam Mat Drying

A diffusion model including shrinkage has been developed for predicting the change of moisture content in banana foam mats during drying. Two solution methods, moving boundary using variable grid and immobilizing boundary using the Lagrangian referential coordinate, were used in exploring their capabilities to predict the moisture change. Banana foam mats with initial foam densities of 0.3, 0.5, and 0.7 g/cm³ were dried at 60, 70, and 80°C and superficial air velocity of 0.5 m/s. The qualities of the final products in terms of texture and microstructure were determined. The moving boundary method can predict the moisture content more accurately than the immobilizing boundary method especially in the case of low-density foam. The quality determinations showed that the initial foam density strongly affected hardness, crispness, and morphology of dried banana foam mats, whereas the drying temperature had no significant effect on those qualities.     

假瞬态洁求解中温变换B109催化剂效率因子

建立了描述工业催化剂粒内浓度和温度分布的扩散数学模型.借助假瞬态法,提出了非等温扩散模型的有效解法.本文对16组宏观实验速率,获得了各组分的浓度和温度分布,及中温变换B109催化剂效率因子的数值解.采用该法能在不修改边界条件的情况下,求解催化剂颗粒内存在“死区”的定解问题.计算结果合理,计算速度快.     

Model for drying during fluidized-bed combustion of wet low-rank coals

An unsteady state heat conduction model with a convective boundary condition is proposed for the drying of low-rank, high-porosity coals, such as lignites, during fluidized-bed combustion. The drying front is assumed to be the receding surface of a wet core. The solution technique for this moving boundary problem is based on the heat balance integral approach with immobilization of the moving boundary by a change in space variable. The governing cubic equation describing the drying curve in dimensionless form may be solved easily by the Newton—Raphson method. The model predictions are compared with experimental data for Mississippi lignite with excellent agreement. A correlation for estimation of total drying time is proposed. The temperature profiles obtained may be used for the study of the coupled drying and devolatilization in fluidized-bed combustors. The profiles could also be of importance in the study of formation of fissures/cracks in lignites subjected to intense heating conditions encountered during fluidized-bed combustion.     

Perturbation solutions of spherical moving boundary problems—I Slow growth or dissolution rates

A perturbation solution is developed for the moving boundary problem involving the slow growth or dissolution of an isolated sphere. This solution resolves the difficulties associated with singular behavior in both space and time, and a space—time matching scheme is used to form uniformly valid composite solutions for temperature or concentration and for the radius of the sphere. The predictions of the new solution are compared with a previous analytical solution and with the predictions of finite-difference solutions.     

固定床反应激波运动数学模拟

浓度激波现象是固定床中非线性吸附-反应过程的重要特征。本文将激波面考虑为分割空间光滑区域的运动边界,将激波间断条件作为相应的边界条件,采用移动坐标系中的试验函数来近似浓度剖面,将双组分吸附反应问题化为4个简单的一阶常微分方程的求解,获得了问题的完整解答,据此讨论了浓度激波的运动特征。     

Implementation of the DSPM model using a commercial finite element system

A solution procedure based on the use of the finite element method (FEM) was developed to solve the Donnan steric-partioning pore model (DSPM) for a nanofiltration membrane coupled with a boundary layer. The numerical solution of nanofiltration models like DSPM is usually carried out by combining an integration method like Runge-Kutta with an iterative procedure that starts from guessed permeate concentrations values. However, this approach may have problems of lack of convergence. As an alternative procedure, a finite element system is used to easily implement the transport equation for the membrane and the boundary layer with Donnan-steric conditions in both membrane sides. To test the solution method, an analytical solution was developed for the transport of an uncharged solute across a membrane with boundary layer. Afterwards, the method was applied to the calculation of binary and ternary ionic systems and its performance was compared with that obtained with the classical iterative method. The developed methodology benefits from the accuracy of FEM and the representation and analysis capabilities of the software used.     

Simulation of melting of ice in a porous media under multiple constant temperature heat sources using a combined transfinite interpolation and PDE methods

A numerical study is made of the melting of ice in a rectangular cavity filled with a porous medium subjected to multiple constant temperature heat sources. Focus is placed on establishing a computationally efficient approach for solving moving boundary heat transfer problem in a two-dimensional structured grids. Specific application to multidimensional melting problem with a complicated moving boundary condition is considered. Preliminary grids are first generated by an algebraic method, based on a transfinite interpolation method, with subsequent refinement using a PDE mapping (parabolic grid generation) method. A preliminary case study indicates successful implementation of the numerical procedure. A two-dimensional melting model is then validated against available analytical solution and experimental results and subsequently used as a tool for efficient computational prototyping.