Simulation of freezing step in vial lyophilization using finite element method

Determination of heat transfer and temperature profile during freezing step is fundamental to predict the final structure of a lyophilized product. The aim of this study was to develop and optimize a dynamic model based on finite element method for simulation of freezing step in order to study final product morphology in both vertical and radial directions. Different factors have been taken into account: chamber pressure, shelf temperature, vial shape, initial solution temperature, nucleation temperature and phase changes. The dynamic axisymmetric model proposed could simulate temperature of each point in the vial and position of liquid-solid interface, without necessity of fitting parameters or questionable assumptions. In addition, the model was extended to predict the average crystal size in each element and the influence of different factors was examined.     

Simulation of packed bed reactors using lattice Boltzmann methods

Lattice Boltzmann (LB) methods are used to simulate hydrodynamics, reaction and subsequent mass transfer in a disordered packed bed of catalyst particles at sub-pore length-scales. In contrast to previous studies, a variety of modifications are introduced in the LB method enabling particle Pe numbers up to 10⁸, and hence realistic values of diffusivity, to be accessed. These include decoupling the hydrodynamics from mass transfer and the use of a rest fraction in the LB formulation of mass transfer. In addition the mass transfer simulations are modified to permit spatially varying values of diffusivity, essential to differentiate between intra- and inter-particle diffusivity (D_intra and D_inter, respectively). The simulation method is applied to both a disordered and ordered 2D packing for a range of Pe (15.6-1557.8) and Re (0.16-1.56) numbers, as well as various ratios of D_intra/D_inter (0-1), whilst simulating an esterfication reaction catalyzed by an ion-exchange resin. The value of D_intra is found to have limited effect, whilst reducing Pe number results in a considerable increase in overall conversion. The simulation method is then applied to a 3D lattice for which experimental conversion data is available. This experimental data is straddled by the simulation case of D_intra=0 and D_intra=D_inter, as expected.     

Simulation in electrochemistry using the finite element method part 2: scanning electrochemical microscopy

The previously introduced adaptive finite element (AFE) algorithm for use in electrochemistry is applied to the simulation of selected multidimensional problems: steady state simulation, chronoamperometric simulation, cyclic voltammetry at microelectrodes, and simulation of arbitrarily shaped scanning electrochemical microscope (SECM) tips. It is shown that the algorithm is suitable for this kind of problems and can be easily extended to the simulation of many types of electrochemical experiments.     

Simulation of adhesive joints using the superimposed finite element method and a cohesive zone model

Adhesive joints have been widely used in various fields because they are lighter than mechanical joints and show a more uniform stress distribution if compared with traditional joining techniques. Also they are appropriate to be used with composite materials. Therefore, several studies were performed for the simulation of the bonded joints mechanical behavior. In general for adhesive joints, there is a scale difference between the adhesive and the substrate in geometry. Thus, mesh generation for an analysis is difficult and a manual mesh technique is needed. This task is not efficient and sometimes some errors can be introduced. Also, element quality gets worse.In this paper, the superimposed finite element method is introduced to overcome this problem. The superimposed finite element method is one of the local mesh refinement methods. In this method, a fine mesh is generated by overlaying the patch of the local mesh on the existing mesh called the global mesh. Thus, re-meshing is not required.Elements in the substrate are generated. Then, the local refinement using the superimposed finite element method is performed near the interface between the substrate and the adhesive layer considering the shape of the element, the element size of the adhesive layer and the quality of the generated elements. After performing the local refinement, cohesive elements are generated automatically using the interface nodes. Consequently, a manual meshing process is not required and a fine mesh is generated in the adhesive layer without the need for any re-meshing process. Thus, the total mesh generation time is reduced and the element quality is improved. The proposed method is applied to several examples.     

应用有限元程序ANSYS/LS-DYNA进行结构的屈曲模拟

阐述了利用程序 ANSYS/ L S-DYNA进行屈曲分析的有限元理论 ;讨论了在屈曲分析中 ,使用 ANSYS隐式和 L S-DYNA显式有限元分析的一般属性和方法 ;最后基于该有限元程序模块对一圆柱壳结构进行屈曲模拟     

Simulation of solid-liquid flows using a two-way coupled smoothed particle hydrodynamics-discrete element method model

We introduce a coupled smoothed particle hydrodynamics-discrete element method (SPH-DEM) to describe the two-way interaction between the two phases of a solid-liquid flow. To validate the model, we simulated two test problems: a solid-liquid counter-flow in a periodic box and particle settlement. The simulations correctly predicted the dynamics, and the results showed good agreement with the theory. The developed model was then applied to simulate the slurry coagulation process to examine the coagulation efficiency. When the rotational speed exceeded the normal range, the coagulation rate decreased with time, even though the rate was high during the early stage due to the size separation effect of the particles. Given this result, overly fast stirring appears to have an adverse effect on the coagulation efficiency. The model is applicable to the design of various types of solid-liquid flows.     

Thermodynamic stability of chemical reactors

Reference is made to the general criteria for thermodynamic stability of stationary states far from equilibrium recently established by Glansdorff and Prigogine, in order to find the global sufficient conditions for the continuous well-stirred tank reactor and for the catalytic particle. When the thermodynamic conditions are obtained in a form which permits their being symmetrically compared with the well-known necessary and sufficient kinetic conditions, it appears that the former are in fact more restrictive, but they may be led back to the kinetic conditions by isolating some particular features of the theory of normal modes.     

Simulation of the newtonian flow through an abruptly contracted tube using a mixed finite element method

The solutions of the Navier-Stokes equation for a Newtonian flow through a 4/1 contraction tube were obtained numerically using the Galerkin finite element method with the nine-node Lagrangian element which was believed to be one of the most accurate tools for mixed-type interpolating formulations. It was proved from this study that the vortex occurrence in the entrance corner region were confirmed but its size was gradually decreased with the increase of Reynolds numbers, and that the velocity profiles and pressure distributions along the applied mesh layers were in agreement with the experimental and the previously reported numerical results.     

Current problems in the modelling of chemical reactors

Modelling of chemical reactors is reviewed with an emphasis on process development and scale-up. A distinction is made between modelling of chemical kinetics, of rate processes in volume elements and of whole reactors. Examples are mainly taken from papers presented at the Sixth International Symposium on Chemical Reaction Engineering. Special attention is given to the modelling of single phase reactors, fixed beds, trickle beds, fluid beds, and gas bubble reactors.     

Estimating spectral properties of the thermal instability in packed-bed reactors

In response to transient perturbations, the packed-bed reactor (PBR) can exhibit dynamic thermal instability in the form of resonant amplification of process disturbances. Based on linearized PBR model we derive estimates of the resonance frequency, the frequency range where amplification takes place and the maximum amplification. We also discuss the velocity of perturbation waves and how nonlinearity of reactor response to finite-size perturbations limits the amplification predicted by the linear analysis.     

Stability of chemical reactors in the presence of sustained disturbances

A general method is developed for constructing regions of practical stability for nonlinear lumped-parameter systems. The region of practical stability serves as a bound on the system response for a general class of magnitude-constrained disturbances. The construction method is based on a modified Liapunov approach but is not restricted to a particular type of Liapunov function. The method is applicable to higher order systems in which several disturbance variables are present. Numerical results are presented for a CSTR with magnitude-constrained disturbances in feed composition and feed temperature.     

Modeling and simulation of dynamics of chemical reactors

The rate of the homogenous exothermic hydrolysis reaction of acetic anhydride catalyzed by sulfric acid in solvent acetic acid was estimated from nonisothermal experimental batch reactor transient temperature data. Rate equations based on three different reaction mechanisms of hydrolysis published in the literature were fitted to the experimental rate data. The experimental results on runaway and limit cycle behavior obtained with this reaction were explained by using the mechanism-based rate equations for hydrolysis in the reactor dynamic models, and good agreement was obtained between the predicted and the experimental dynamic data.     

Predicting the flow mode from hoppers using the discrete element method

In this work, the discrete element method (DEM) is used to assess powder flow from hoppers and the results are compared to widely-used hopper design charts. These design charts delineate mass-flow and funnel-flow behavior based on the hopper wall angle and a given set of material properties. The modeled system consists of hoppers with various wall angles and frictional, non-cohesive, spherical particles. The performance is assessed by measuring the particle residence times, particle velocities, and the extent of segregation during discharge. A Mass Flow Index (MFI) based on the velocity profile data is used to quantitatively characterize the nature of the flow pattern as mass-flow, funnel-flow, or some intermediate. The DEM predictions are generally in very good agreement with the Jenike design charts. The level of agreement shown here indicates that DEM cannot only reproduce the current estimates of hopper performance, but also provide additional insight into the flow-such as the internal granular structure-that may be difficult to obtain otherwise.     

Study of cold powder compaction by using the discrete element method

The discrete element method (DEM), based on a soft-sphere approach, is commonly used to simulate powder compaction. With these simulations a new macroscopic constitutive relation can be formulated. It is able to de-scribe accurately the constitutive material of powders during the cold compaction process. However, the force-law used in the classical DEM formulation does not reproduce correctly the stress evolution during the high density compaction of powder. To overcome this limitation at a relative density of about 0.85, the high density model is used. This contact model can reproduce incompressibility effects in granular media by implementing the local solid fraction into the DEM software, using Voronoi cells. The first DEM simulations using the open-source YADE software show a fairly good agreement with the multi-particle finite element simulations and experimental results.     

Ratio-integral objective functions in the optimal operation of chemical reactors

The efficiency of a broad class of continuous processes operated under unsteady-state conditions must often be expressed as the ratio of two integrals: in chemical reactor problems this may represent either the yield or the selectivity of a desired product in a complex reaction scheme.Objective functions taking this form are included in the formulation of the problem for solution using the Maximum Principle of Pontryagin; the resultant additional necessary condition of optimality appears in a particularly convenient form so that the complexity of the problem is only marginally increased.     

Simulation of systems with chaos in the chemical composition using stochastic methods

As a result of the simulation of the functions of the probability distribution in systems with chaos in the chemical composition, which also includes difficult natural and technogenic mixes, e.g., oil hydrocarbonic systems, it is established that the normal distribution of the composition is observed with the probability of differences in the components in the range of 0.2–0.8. This means that the normal distribution of free energy, and the boiling temperatures are achievable in systems where the ratio of the number of components with different properties to the total number of components is 20–80%. The borders of the difference probability are established, which define the belonging of systems to different types of distribution. At a share of the differing on properties components of 1–8.5%, the distribution is close to Poisson’s distribution. When the differences in the probability components in range of 0.085–0.2, a region of unstable distribution is observed.     

Nanoscale sensor analysis using the immersed molecular electrokinetic finite element method

The concentration and detection of molecular biomarkers remain as a challenge to develop point-of-care diagnostic devices. An electric field induced concentration has been studied for such purposes but with limited success due to limited efficacy. This paper presents a computational study for investigating the molecular concentration and retention efficacy of single nanowire (SNW) and dendritic nanotip (DNT) sensors. Our computational results indicate that compared to a DNT, the SNW sensor produces higher dielectrophoretic (DEP) forces in the vicinity of the terminal end of the tip. Furthermore, the magnitude of the DEP force increases exponentially as the diameter of the SNW is decreased, resulting in a further improved retention efficacy of NPs. However, the SNW sensor's concentration efficacy was not much improved for NPs smaller than 10 nm diameter when the nanowire diameter was reduced from 500 to 50 nm. Compared to the SNW, the DNT sensor showed improved concentration efficacy due to multiple points of electric field concentrations, which retard the exponential decay of the DEP force resulting in a greater widespread region where the DEP force dominates the Brownian motion forces. When oligonucleotides are used as a target particle, the DEP force can be used to elongate oligonucleotides to further enhance the concentration and retention efficacy.