Time averaged temperature calculations in pulse electrochemical machining, spectral approach

Simulation of the temperature distribution during the Pulse Electrochemical Machining (PECM) process provides information on system design and guidelines for practical use. The pulses that are applied to the PECM system have to be described on a time scale that can be orders of magnitude smaller than the time scale on which the thermal effects evolve. If the full detail of the applied pulses has to be taken into account, the time accurate calculation of the temperature distribution in PECM can become a computationally very expensive procedure. A different approach is used by time averaging the heat sources of the system. Performing this, the time steps used during the calculations are no longer dictated by the pulse characteristics. Using this approach, computationally very cheap, yet satisfying results can be obtained. In previous work of the authors, the hybrid calculation and the Quasi Steady State ShortCut (QSSSC) were introduced. This method allows to perform simplified calculations while getting satisfactory results. The method introduces errors however, which were quantified using analytical solutions and found to be acceptable. The results applied only to rectangular pulses. In this work, the more general case of arbitrary pulse forms is considered using a spectral approach.     

Time averaged calculations in pulse electrochemical machining,using a strongly non-linear model

Simulation of the Pulse Electrochemical Machining (PECM) process can provide information on system design and guidelines for practical use. The pulses that are applied to the PECM system have to be described on a time scale that can be orders of magnitude smaller than the physical time scales in the system. If the full detail of the applied pulses has to be taken into account, the time accurate calculation of the variable distribution evolutions in PECM can become a computationally very expensive procedure. In previous work of the authors, approximate techniques were introduced: the hybrid calculation and the Quasi Steady State Shortcut (QSSSC). In other previous work of the authors a model for PECM of steel in NaNO₃ was introduced. This model contains a changing polarization behaviour of the double layer as a function of the metal ion surface concentration, which brings a strong non-linearity in the system. In this paper a technique is introduced to integrate the non-linear model into the approximate methods. To achieve this, the strategy of the approximate methods is extended. For the QSSSC, the non-linearity is handled using an extra convergence level. For the hybrid calculation, live averaging is used to take care of the non-linear effects. Performing this, the timesteps used during the high level calculations are no longer dictated by the pulse characteristics. Using this approach, computationally very cheap, yet satisfying results can be obtained. The technique is very general and very powerful and can be used in any multi-timescale system.     

Time-averaged concentration calculations in pulse electrochemical machining, spectral approach

Simulation of the species concentrations during the pulse electrochemical machining (PECM) process can provide information on system design and guidelines for practical use. In detailed numerical calculations, the concentrations will be calculated simultaneously with the temperature due to mutual dependencies. The pulses that are applied to the PECM system have to be described on a timescale that can be orders of magnitude smaller than the physical timescales in the system. If the full detail of the applied pulses has to be taken into account, the time accurate calculation of the variable distributions' evolutions in PECM can become a computationally very expensive procedure. A different approach is used by time averaging the pulses applied to the system. Performing this, the timesteps used during the calculations are no longer dictated by the pulse characteristics. Using this approach is computationally very cheap, yet satisfying results can be obtained. In the previous study of the authors (Smets et al., J Appl Electrochem 37(11):1345–1355, 2007 [8]), the hybrid calculation and the quasi-steady-state shortcut (QSSSC) were introduced. These methods introduce errors, however, which were quantified using analytical solutions and found to be acceptable. The results applied only to rectangular pulses. In this study, the more general case of arbitrary pulse forms is considered using a spectral approach. The concentration and the temperature calculation have different requirements for optimal approximated calculations, and a compromise has to be found between them. An analysis is performed on a simplified model, which provides useful guidelines during simulations.     

Time averaged concentration calculations in pulse electrochemical machining

Simulation of the species concentrations during the Pulse Electrochemical Machining (PECM) process can provide information on system design and guidelines for practical use. In detailed numerical calculations the concentrations will be calculated simultaneously with the temperature due to mutual dependencies. The pulses that are applied to the PECM system have to be described on a time scale that can be orders of magnitude smaller than the physical time scales in the system. If the full detail of the applied pulses has to be taken into account, the time accurate calculation of the variables distributions evolutions in PECM can become a computationally very expensive procedure. In previous work (Smets et al. J Appl Electrochem 37(11):1345, 2007), a time averaging approach was introduced. Performing this, the timesteps used during the calculations are no longer dictated by the pulse characteristics. Using this approach, computationally very cheap, yet satisfying results can be obtained. This work focuses on the behaviour of the concentration evolution. The concentration and the temperature calculation have different requirements for optimal approximated calculations, and a compromise has to be found between them. An analysis is performed on a simplified model, which provides useful guidelines during simulations.     

Time averaged temperature calculations in pulse electrochemical machining, part II: numerical simulation

Simulation of the temperature distribution and evolution during pulse electrochemical machining can be a computationally very expensive procedure. In a previous part of the work [Smets et al. J Appl Electrochem 37(11):1345, 2007] a new approach to calculate the temperature evolution was introduced: the hybrid method, which combines averaged and pulsed calculations. The averaged calculations are performed by time averaging the boundary conditions and the bulk heat sources of the system. The timesteps used during the averaged calculations are then no longer dictated by the pulse characteristics. Using this approach, computationally very cheap, yet satisfactory results can be obtained. The analysis in the previous part of the work was obtained from analytical solutions on simplified models. In this part, the more general case is solved numerically. Multiple geometries are simulated and analyzed and methods are compared. Very satisfactory, yet cheap results are obtained.     

Mathematical modeling of the full molecular weight distribution in ATRP techniques

In this work the molecular weight distribution (MWD) of several atom transfer radical polymerization (ATRP) techniques has been derived and solved using the Reduced Stiffness by Quasi Steady State Approximation (RSQSSA) methodology. The Quasi Steady State Approximation has been validated on the living radicals for normal, Simultaneous Reversible and Normal Initiation and Activators Regenerated by Electron Transfer (ARGET), and it is shown that the information lost due to its application is negligible. According to these results, RSQSSA shows the best performance in terms of wall‐clock time and required memory in comparison to implicit techniques and Predici. In the case of the ARGET technique, the model predictions show good agreement with experimental data. Finally, an analysis on the impact of the slow and fast activation of the initiator on the MWD using ARGET has been carried out, indicating that the optimal initiator to control the MWD should exhibit activation‐deactivation rates very similar to those of the polymeric equilibrium. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2762–2777, 2016     

Calculation of temperature transients in pulse electrochemical machining (PECM)

Pulse Electrochemical Machining (PECM) is a manufacturing process which provides an economical and effective method for machining hard materials into complex shapes. One important drawback of ECM is the lack of quantitative simulation software to predict the tool shape and machining parameters necessary to produce a given work-piece profile. Calculating temperature distributions in the system allows more accurate simulations, as well as the determination of the thermal limits of the system. In this paper temperature transients over multiple pulses are calculated. It is found that the way the system is modeled has a great impact on the temperature evolution in the thermal boundary layer. The presence of massive electrodes introduces extra time scales which may not be negligible. It is advantageous to identify the thermal time scales in the system, to see whether the heat produced during separate pulses will accumulate or not during the process. The occurring thermal time scales in the system are discussed in detail.     

An analysis of chemical reactor stability and control—XVI: The stochastic stirred pot

A continuous stirred tank reactor subject to random fluctuations in flow rate and inlet temperature was simulated on a hybrid computer. The stochastic response of the reactor about unique stable deterministic steady states was studied as a function of the damping coefficient and response time of the deterministic system and the power spectrum of the stochastic input. It was found that the stochastic response could be classified into categories similar to those used for forced periodic systems according to the relationship between the deterministic system response time and the 90% cut-off frequency of the stachastic input. The nature of the stochastic response is predictable for relatively low frequency inputs but unexpected results may occur at intermediate frequencies. The magnitude of reactor state fluctuations was seen to be dependent on the deterministic damping coefficient. The distribution of reactor states was studied as a function of input process variance and it was found that the distribution can become bimodal even when the associated deterministic steady state is unique.The concept of stochastic stability is discussed and several practical stochastic stability definitions are proposed. The stochastic stability of the random systems was seen to be well described by the stochastic regions of operation predicted by the input process power spectrum and the deterministic system response time. The input variance levels necessary to produce stochastic instability can be estimated in the Quasi Steady region of operation. It was found that exposure of an autonomous limit cycle about a unique unstable deterministic steady state to high frequency random inputs may lead to effective stabilization.     

Thermal resonant tunneling rates by a generalized flux averaging method

The calculation of the thermal rate constant as a time integral over flux-flux correlation functions is a challenging task when the potential energy along the reaction coordinate cannot be associated with a distinctive single barrier. In the case of resonant tunneling through a double barrier potential, the calculations may become formidable due to the population of long-lived resonance states and the corresponding long time-decay of the flux-flux correlation functions. The flux averaging method was introduced recently in order to circumvent this problem in cases where the long time dynamics is due to a single resonance state with the longest lifetime in the system. In this work we generalize the method for calculations of thermal resonant-tunneling rates in systems of many resonances, where the long time-decay is accompanied by an internal dynamics within the quasi-bound system. This extra complication is handled by additional averaging of flux-flux correlation funcation over the time period of the internal dynamics. The result is an exact expression for the rate constant in terms of a linear combination of time integrals over flux-flux correlation functions, which reaches its asymptotic time limit in a short (direct scattering) time, regardless of the long time-decay of the flux-flux correlation functions. This is derived for an analytic model system, and demonstrated in a numerical simulation of resonant tunneling through a double barrier potential.     

Prioritizing Small Sets of Molecules for Synthesis through in-silico Tools: A Comparison of Common Ranking Methods

Prioritizing molecules for synthesis is a key role of computational methods within medicinal chemistry. Multiple tools exist for ranking molecules, from the cheap and popular molecular docking methods to more computationally expensive molecular-dynamics (MD)-based methods. It is often questioned whether the accuracy of the more rigorous methods justifies the higher computational cost and associated calculation time. Here, we compared the performance on ranking the binding of small molecules for seven scoring functions from five docking programs, one end-point method (MM/GBSA), and two MD-based free energy methods (PMX, FEP+). We investigated 16 pharmaceutically relevant targets with a total of 423 known binders. The performance of docking methods for ligand ranking was strongly system dependent. We observed that MD-based methods predominantly outperformed docking algorithms and MM/GBSA calculations. Based on our results, we recommend the application of MD-based free energy methods for prioritization of molecules for synthesis in lead optimization, whenever feasible.     

气液相平衡计算与教学

气液平衡计算是化学过程中的一项十分重要的计算。但目前的教学中并没得到相应的强调与详细的阐述。本文讨论了低中高压下的气液平衡计算的特点与之间的关系,通过程序设计对双组分系统进行了计算,并将计算结果进行了对比,采用PR方程设计的适于高压下气液平衡计算的方法与程序用于中低压下的计算也得到了较好的一致性。本研究结果可使气液相平衡内容的教学更为丰富与系统。     

MEASUREMENT TECHNIQUES AND DATA INTERPRETATIONS FOR VALIDATING CFD MULTI PHASE REACTOR MODELS

One problem associated with the use of Computational Fluid Dynamics(CFD) in reactor modeling is the proper validation of the models. Proper validation in this context means that the physical fluid dynamic model, the mathematical implementation and the data used for validation must be consistent. The present paper addresses this issue and to provide appropriate relations between experimental method and modeling approach

A critical review of currently used measurement techniques for characterizing multiphase now systems is presented. The interpretation of the data obtained from the various techniques is discussed as well as how these data can be used for validation of various CFD model formulations

Steady state models can be validated using time averaged data, making sure that the averaging time for the experimental data is long enough so that low frequency periodic oscillations also are evened out. If homogeneous systems are considered, then a volume average approach may be used for modeling, If the system cannot be considered homogeneous and steady, as is the most common case, then a dynamic ensemble averaging technique should be preferred. The validation of such models must be done with methods fast enough to resolve periodic fluctuating structures of interest. These methods are cumbersome and tedious to operate and the ergodic hypothesis may be invoked enabling the use of volume or time averaged data for the validation of ensemble averaged models.     

A hybrid CFD—reaction engineering framework for multiphase reactor modelling: basic concept and application to bubble column reactors

The coupling of turbulent mixing and chemical phenomena lies at the heart of multiphase reaction engineering, but direct CFD approaches are usually confronted with excessive computational demands. In this hybrid approach, the quantification of mixing is accomplished through averaging the flow and concentration profiles resulting from a CFD flow field calculation and a computational (“virtual”) tracer experiment. Based on these results, we construct a mapping of the CFD grid into a generalised compartmental model where the chemistry calculations can be efficiently carried out. In contrast to the empirical models used in the residence time distribution (RTD) approach, the compartmental model in this methodology, owning to its CFD origins, retains the essential features of the equipment geometry and flow field. A procedure for extracting the mixing information from k-ε based CFD codes is outlined, but the main concept of the approach is not restricted to any particular type of turbulence modelling, and will therefore benefit from future developments. A phenomenological model of mass transfer and chemical reaction, based on the penetration theory, is employed to simulate the interfacial phenomena in gas-liquid reactors, and a study of CO₂ absorption into alkali solution is presented to demonstrate the method.     

Mathematical simulation of wet spinning coagulation process: Dynamic modeling and numerical results

A dynamic model of polymer wet spinning coagulation process is proposed in this article. The model is based on the double diffusion phenomenon, phase separation process, continuity balance, and momentum balance of the entire coagulation process. The uniqueness of the model lies in its dynamic feature. The model can simulate the system's dynamic response to variations in system inputs/parameters. Steady‐state system solutions can also be produced as the long‐time solutions of the dynamic model; a settling time can be observed at the same time. This paper employs a computationally efficient method of lines numerical algorithm for solving the dynamic model. A simulation experiment on a selected non‐solvent‐solvent‐polymer ternary system is carried out to verify the model as well as the numerical method. The dynamic simulation results are analyzed and discussed. At the end of the article, h‐refinement and p‐refinement are used to confirm the spatial convergence of the numerical solutions. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3432–3440, 2016     

A unified Eulerian theory of turbulent deposition to smooth and rough surfaces

This paper presents a simple, unified theory of deposition that is applicable for particles of any size, and reproduces very closely experimentally measured variation in deposition velocity with particle relaxation time. Apart from providing physical insight, the theory offers a simple, fast and reliable computational tool of practical use to aerosol engineers. The predictions are at least as accurate as the state-of-the-art particle-tracking calculations but require much less computational time. The theory includes the effects of thermophoresis, turbophoresis, electrostatic forces, gravity, lift force and surface roughness. The theory consists of writing the particle continuity and momentum conservation equations in their proper form and then performing Reynolds averaging. This procedure results in an expression for the particle flux which consists of three distinct terms for each of which a clear physical interpretation is available. The first term is a diffusive flux due to Brownian motion and turbulent fluctuation, the second is a diffusive flux due to temperature gradient (thermophoresis), and the third is a convective flux that arises primarily as an interaction between particle inertia and the inhomogeneity of the fluid turbulence field (turbophoresis). The lift force and electrostatic forces also contribute to this convective flux. It is shown that it is crucial to include the particle momentum equation in the analysis as this gives an estimate of the mentioned convective slip velocity of the particles. Absence of this equation in many previous studies which included only the particle continuity equation necessitated postulations such as stopping distance models. Only the dominant terms in the continuity and momentum equations are retained in the present analysis which give almost the same answer as with a calculation retaining all terms, but the former is more amenable to direct physical interpretation. The method of Reynolds averaging is general, and other effects not included in this study, e.g. pressure diffusion can easily be incorporated by including the appropriate forces in the particle momentum equation. The present study includes the effects of surface roughness, and the calculations show that the presence of small surface roughness even in the hydraulically smooth regime significantly enhances deposition especially of small particles. Thermophoresis can have equally strong effects, even with a modest temperature difference between the wall and the bulk fluid. For particles of the intermediate size range, turbophoresis, thermophoresis and roughness are all important contributors to the overall deposition rate.     

Towards more realistic computational modeling of homogenous catalysis by density functional theory: combined QM/MM and ab initio molecular dynamics

The combined quantum mechanics/molecular mechanics (QM/MM) and the ab initio molecular dynamics methods (AIMD) are fast emerging as viable computational molecular modeling tools. Both methods allow for the incorporation of effects that are often ignored in high level calculations, but may be critical to the real chemistry of the simulated system. In the combined QM/MM method part of the system, say the active site, is treated quantum mechanically whereas the remainder of the system is treated with a faster molecular mechanics force field. This allows high level calculations to be performed where the effects of the environment are incorporated in a computationally tractable manner. With the ab initio molecular dynamics methods, the system is simulated at a finite temperature with no empirical force field. Rather, the forces at each time step are determined with a full electronic structure calculation at the density functional level. Thus, simulations of chemical reactions can be performed where finite temperature effects are realistically represented. In this paper a brief introduction to both methods is given. The methods are further demonstrated with specific applications to modeling homogenous catalytic processes at the molecular level. These applications are our latest efforts to build more realistic computational models of catalytic systems at the density functional level.     

Speed-up of computing time for numerical analysis of particle charging process by using discrete element method

The objective of this paper is to improve the computing time for numerical analysis of particle charging process by using discrete element method. The rule for ignoring the calculations of contact forces and updating trajectories of unmoved particles were discussed. When the relative displacement of a particle within certain calculation steps became less than 0.1% of particle radius, this particle was determined to be unmoved and the calculations of this particle were ignored. The computing time was improved significantly when this new method was used, and its calculation speed was more than two times faster than that of original. It was found that this speed-up method is more useful for the cases that the particle becomes unmoved in short time or the height of charged bed is large. The simulation of charging process in an industrial-scale surge hopper was studied by using new method, the calculation speed became 2.88 times faster than that of original, and the quite similar particle size segregation between original and new methods was given. This new method for speed-up of the charging process in DEM is very useful, and the charging processes of the industrial scale storages can be simulated by using this method.     

Advanced trust region optimization strategies for glass box/black box models

We present an improved trust region filter (TRF) method for optimization of combined glass box/black box systems. Glass box systems refer to models that are easily expressed in an algebraic modeling language, providing cheap and accurate derivative information. By contrast, black box systems may be computationally expensive and derivatives are unavailable. The TRF method, as first introduced in our previous work (Eason and Biegler, AIChE J. 2016; 62:3124–3136), is able to handle hybrid systems containing both glass and black box components, which can frequently arise in chemical engineering, for example, when a multiphase reactor model is included in a flow sheet optimization problem. We discuss several recent modifications in the algorithm such as the sampling region, which maintains the algorithm's global convergence properties without requiring the trust region to shrink to zero in the limit. To benchmark the development of this optimization method, a test set of problems is generated based on modified problems from the CUTEr and COPS sets. The modified algorithm demonstrates improved performance using the test problem set. Finally, the algorithm is implemented within the Pyomo environment and demonstrated on a rigorous process optimization case study for carbon capture. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3934–3943, 2018     

应用广义简约梯度算法增强遗传算法求解化工冶金相平衡

研究可靠的相平衡计算对化工冶金过程有很重要意义,本文采用广义简约梯度法（GRG）来增强遗传算法（GA）用于相平衡计算过程,在遗传算法演化快结束时引入GRG算子,演化结束后使用GRG精修结果,克服了GA局部搜索能力不强的缺点,加快了搜索速度.KCl-FeCl₂体系相平衡计算结果显示这种混合算法（Hybrid Algorithms）能够提高GA效率的同时保留了全局收敛的优点,因此其在化工冶金相平衡计算中将有广泛的应用前景.     

Characterization of hybrid copolymer containing thermosensitive and polypeptide blocks by thermogravimetric analysis

Thermogravimetric studies of polypeptide-based hybrid copolymer (PNIPAm-g-PEG)-b-PLys in a flow of nitrogen were carried out at four rates of linear increase of the temperature. The kinetics and mechanism of the degradation process were evaluated from the TG data using the iso-conversional calculation procedure of Kissinger–Akahira–Sunose recommended by the ICTAC kinetics committee. It is very important to determine the most probable function of the mechanism, because the kinetic parameters of the process depend on its selection. In this respect, the iso-conversion calculation procedure turned out to be the most appropriate one. In the present work, the kinetic triplet (E, A and the shape of the most appropriate f(α)-function) of this process, as well as the kinetic parameters for the formation of the activated complex from the reagent, was calculated. All the calculations were performed using programs developed by us.