Limitations of mathematical modelling and numerical simulation of industrial and laboratory high-pressure processes

High pressures up to several hundreds of MPa are utilised in a wide range of applications in chemical engineering, bioengineering, and food engineering, aiming at selective control of (bio-)chemical reactions. Non-uniformity of process conditions may threaten the safety and quality of the resulting products as the process conditions such as pressure, temperature, and treatment history are crucial for the course of (bio-)chemical reactions. Therefore, thermofluid dynamical phenomena during the high-pressure process have to be examined, and tools to predict process uniformity and to optimise the processes have to be developed. Recently, mathematical models and numerical simulations of laboratory and industrial scale high-pressure processes have been set up and validated by experimental results. This contribution deals with the assumption of the modelling that relevant (bio-)chemical compounds are ideally dissolved or diluted particles in a continuum flow. By considering the definition of the continuum hypothesis regarding the minimum particle population in a distinct volume, limitations of this modelling and simulation are addressed.     

Gasdynamic characteristics of toroidal shock and detonation wave converging

The modified CCW relation is applied to analyzing the shock, detonation wave converging and the role of chemical reactions in the process. Results indicate that the shock wave is strengthened faster than the detonation wave in the converging at the same initial Mach number. Euler equations implemented with a detailed chemical reaction model are solved to simulate toroidal shock and detonation wave converging. Gasdynamic characteristics of the converging are investigated, including wave interaction patterns, observable discrepancies and physical phenomena behind them. By comparing wave diffractions, converging processes and pressure evolutions in the focusing area, the different effects of chemical reactions on diffracting and converging processes are discussed and the analytic conclusion is demonstrated through the observation of numerical simulations.     

Gasdynamic characteristics of toroidal shock and detonation wave converging

Shock wave focusing is a fundamental problem in the shock wave research and the instantaneous impulse of high temperature and pressure generated at the focal points has been applied recently in industrial and medical researches[1]. There are several methods to create shock wave focusing, among which the more commonly-used one is to make a planar shock wave reflect from a concave surface, such as the elliptical or parabolic re- flector. Toroidal shock wave focusing has been proposed and investi…     

The importance of chemical mechanisms in sonochemical modelling

A state-of-the-art chemical mechanism is introduced to properly describe chemical processes inside a harmonically excited spherical bubble placed in water and saturated with oxygen. The model uses up-to-date Arrhenius-constants, collision efficiency factors and takes into account the pressure-dependency of the reactions. Duplicated reactions are also applied, and the backward reactions rates are calculated via suitable thermodynamic equilibrium conditions. Our proposed reaction mechanism is compared to three other chemical models that are widely applied in sonochemistry and lack most of the aforementioned modelling issues. In the governing equations, only the reaction mechanisms are compared, all other parts of the models are identical. The chemical yields obtained by the different modelling techniques are taken at the maximum expansion of the bubble. A brief parameter study is made with different pressure amplitudes and driving frequencies at two equilibrium bubble sizes. The results show that due to the deficiencies of the former reaction mechanisms employed in the sonochemical literature, several orders of magnitude differences of the chemical yields can be observed. In addition, the trends along a control parameter can also have dissimilar characteristics that might lead to false optimal operating conditions. Consequently, an up-to-date and accurate chemical model is crucial to make qualitatively and quantitatively correct conclusions in sonochemistry.     

A study of the Soret effect in laser-induced chemical vapor deposition

This paper presents an investigation of the modeling of the process of pyrolytic laser-induced chemical vapor deposition (LCVD) applied to study the Soret effect. LCVD is a thermally activated process characterized by strongly coupled mass and energy transport phenomena, together with chemical reactions, which are difficult to investigate experimentally. A physical and numerical model based on a commercial computational fluid dynamics package is developed and used to simulate a reactor operating at conditions of room temperature and pressure. The proposed numerical methodology will allow us to assess and analyze the effect of various factors controlling the process, and in particular the Soret effect. This numerical model is validated by comparison with the measured growth rate of the fiber. While several studies have proposed simulations of the LCVD process, this is among the first attempts at including the Soret effect in the numerical modeling at the micro-scale level. It is expected that the fundamental insights thus obtained will guide experimental investigations which can be applied to establish reactor design and process control guidelines.     

Influence of the ignition delay time on the explosion parameters of hydrocarbon–air–oxygen mixtures at elevated pressure and temperature

Combustion phenomena change as the conditions in which they are occurring change. Proper understanding and reliable prediction of these phenomena, including important explosion indexes (e.g., flammability limits, explosion pressures), are required for achieving safe and optimal performance of industrial processes and creating new applications. To this end, we investigated the influence of the residence time on aforementioned parameters of n-butane–oxygen mixture and a typical mixture for ethylene oxide production: methane–ethylene–oxygen, focusing on how elevated conditions affect the upper explosion limit and the explosion pressure. Elevated initial conditions (T = 230 °C, P = 4–16 bar) cause pre-ignition reactions to occur in the regime of the low temperature oxidation mechanism (LTOM). These reactions change the mixture composition prior to ignition. For both mixtures investigated, these changes in the initial mixture composition, due to pre-ignition reactions, result in a different explosion pressure. This is significant, because pressure rise is used as the ignition criterion. Consequently, a different classification of the investigated mixtures, as flammable or non-flammable, is possible, depending on the residence time prior to ignition. The experimental results are compared with theoretical calculations performed using detailed reaction kinetic models.     

A class of collision processes with memory and application to simple chemical reactions in a solvent

We apply the general formalism of a class of non-Markovian processes which we have studied elsewhere to three simple models of chemical reactions: dissociation, isomerization, and diffusion in a double-well potential. Our method leads to explicitly solvable models and numerical computations. The results are in agreement with numerical simulation and stochastic dynamics studies of other authors.     

Combustion in the future: The importance of chemistry

Combustion involves chemical reactions that are often highly exothermic. Combustion systems utilize the energy of chemical compounds released during this reactive process for transportation, to generate electric power, or to provide heat for various applications. Chemistry and combustion are interlinked in several ways. The outcome of a combustion process in terms of its energy and material balance, regarding the delivery of useful work as well as the generation of harmful emissions, depends sensitively on the molecular nature of the respective fuel. The design of efficient, low-emission combustion processes in compliance with air quality and climate goals suggests a closer inspection of the molecular properties and reactions of conventional, bio-derived, and synthetic fuels. Information about flammability, reaction intensity, and potentially hazardous combustion by-products is important also for safety considerations. Moreover, some of the compounds that serve as fuels can assume important roles in chemical energy storage and conversion. Combustion processes can furthermore be used to synthesize materials with attractive properties.A systematic understanding of the combustion behavior thus demands chemical knowledge. Desirable information includes properties of the thermodynamic states before and after the combustion reactions and relevant details about the dynamic processes that occur during the reactive transformations from the fuel and oxidizer to the products under the given boundary conditions. Combustion systems can be described, tailored, and improved by taking chemical knowledge into account. Combining theory, experiment, model development, simulation, and a systematic analysis of uncertainties enables qualitative or even quantitative predictions for many combustion situations of practical relevance.This article can highlight only a few of the numerous investigations on chemical processes for combustion and combustion-related science and applications, with a main focus on gas-phase reaction systems. It attempts to provide a snapshot of recent progress and a guide to exciting opportunities that drive such research beyond fossil combustion.     

Molecular phase space transport in water: Non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).     

Geometrical study of spark ignition in two dimensions

Spark ignition, as the first step during the combustion in Otto engines, has a profound impact on the further development of the flame kernel. Over the last ten years growing concern for environment protection, including low emission of pollutants has increased the interest in the numerical simulation of ignition phenomena to guarantee successful flame kernel development even for lean mixtures.

However, the process of spark ignition in a combustible mixture is not yet fully understood. The use of detailed reaction mechanisms, combined with electrodynamical modelling of the spark, is necessary to optimize ignition of lean mixtures.

This work presents simulations of the coupling of flow, chemical reactions and transport with discharge processes in order to investigate the development of a stable flame kernel initiated by an electrical spark. A two-dimensional code to simulate the early stages of flame kernel formation, shortly after the breakdown discharge, has been developed. The model includes Joule heating. The spark plasma channel formed as a consequence of the breakdown is incorporated into the initial conditions. The computations include the initial phase (1–5 µs), which is governed by pressure wave formation, but also the transition to flame propagation. A thorough study of the influence of the electrodes' geometry, i.e. shape and size, and gap width, has been performed for air and a lean H₂–air mixture. Also a detailed methane-air mechanism was chosen as another example including combustion.

Due to the fast expansion of the plasma channel, together with the geometrical complexity of the electrodes, a complicated flow field develops after the emission of a pressure wave by the expanding channel. Special numerical methods, including artificial viscosity, are required to resolve the complicated flow field during these first 1–5 µs. The heat release through chemical reactions and transport processes is almost negligible during this short phase. The second phase, i.e. the development of a propagating flame and the flame kernel expansion, can last up to several milliseconds and is dominated by diffusive processes and chemical reactions. It has been found that the geometry greatly influences the developing flame kernel and the flow field. As soon as chemical reactions begin to contribute significantly to the heat release, the effect becomes smaller.     

Atomic description of elementary surface processes: diffusion and dynamics

A large fraction of processes which are at the foundation of our technological society involve physical and chemical properties of surfaces. Catalytic reactions and semiconductor devices production are two of the most important ones.

This paper describes a sample of some of the most relevant surface science experiments which have been recently performed, in order to understand elementary surface processes of model catalytic reactions and in semiconductor technology at the atomic level. The focus is on experiments performed with scanning tunneling microscopy and atomic force microscopy which have represented, in some cases, real breakthroughs in our understanding of these phenomena.

We then present an overview of possible experimental technique developments that can be foreseen for the future and that may give us a more in-depth understanding of the elementary processes which form the basis of important complex surface phenomena. Finally, some of the challenging tasks that lie ahead for surface scientists and the collateral opportunities are discussed.     

High pressure rheology and the impact on process homogeneity

The impact of different viscous substances on homogeneous thermal treatment during high pressure processes is exemplified for a cylinder piston system. Therefore, the relevant equations of thermofluid dynamics have been examined and conditions for homogeneous thermal processing have been set up. Furthermore, the analysis of an n-order inactivation kinetic delivers criteria for insensitivity of reactions to spatial temperature heterogeneities. The findings have been applied to a short time high pressure process and compared with results of numerical simulations. Good agreement could be achieved.     

模板对异构体选择性生长的动力学控制作用与化学气相沉积金刚石的生长机理

阐述了模板的动力学控制作用对大尺度有序结构特别是亚稳相的生长，对自由能相差很小的异构体的选择生长所具有的重要作用.汲取现有金刚石生长理论的合理思想，以模板概念为基础给出了对化学气相沉积(CVD)过程的动力学热力学综合描述：1)碳原子在碳氢化合物中的化学势高于固相碳，气相碳氢化合物的碳原子有可能落到化学势较低的固态碳的各种异构体.2)气相碳通过表面反应实现向固相碳的转化.3)表面的模板作用是控制气相碳原子转换方式的主要动力学因素，不同的表面(石墨各种取向的表面及金刚石不同取向的表面)选择了落入其上的碳原子的结构方式及能量状态.4)因此,衬底的不同区域可发生几种不同的独立的表面反应过程,这些反应对应于不同表面的生长.5）而这些表面反应的方向性及速度受表面临域热力学因素的影响，反应的方向性决定了某种晶面是生长或刻蚀，在特定的温度、压强及各种气体分压下可以实现金刚石的生长和石墨的刻蚀.6)衬底局域晶格结构及键价结构和衬底表面气相的温度、压强及各种气体分压等热力学条件共同决定了成核的临界条件.7）与外界有能量和物质交换的等离子体系统，以及气相中发生的一系列化学反应，仅起到了维持某种固相表面生长所需要的非平衡热力学条件和化学条件的作用.金刚石和石墨表面具有的模板动力学控制作用，在特定热力学条件下主导自身外延层的生长方式；异质衬底的某些局域微观结构可以作为新相生长成核的局域模板；不同材料、不同的处理方法、及不同的化学环境下的衬底具有不同的局域微观结构，从而决定了多晶薄膜的取向优势. 关键词： 模板 异构体 选择性生长 金刚石薄膜     

Guest-host interaction in energy storage systems

Charge transfer reactions are the most frequent processes met during the conversion of chemical energy into electrical one. Intercalation/insertion processes are the best examples of these phenomena. The type of interaction/binding between guest species and host material decides about the reversibility of the processes. The important drawback of the carbon anode in Li-ion cells is often its irreversible capacity. It correlates with the active surface area and it can be significantly diminished through pyrolytic carbon coating. In situ⁷Li-NMR measurement is a perfect method for monitoring the type of Li-C bonding during the insertion/deinsertion process. Supercapacitor is the second category of attractive energy storage system. The main operation of a capacitor is based on an electrostatic attraction; however, very often pseudocapacitance effects take place. Intensive research is devoted to electrochemical hydrogen storage where the type of C-hydrogen bonding is crucial for practical application of this process. The reversibility of hydrogen insertion into the carbon network is ensured by a weak chemical bonding. Carbon materials with electrosorbed hydrogen play a perfect role of negative electrode in supercapacitor. Attractive host-guest interactions take place during the performance of various supercapacitor electrode materials, e.g. nitrogen-doped carbons with modified electronic structure, layered double hydroxides, conducting polymers, etc.     

Computational analysis of the roles of biochemical reactions in anomalous diffusion dynamics

Most biochemical processes in cells are usually modeled by reaction–diffusion(RD) equations. In these RD models,the diffusive process is assumed to be Gaussian. However, a growing number of studies have noted that intracellular diffusion is anomalous at some or all times, which may result from a crowded environment and chemical kinetics. This work aims to computationally study the effects of chemical reactions on the diffusive dynamics of RD systems by using both stochastic and deterministic algorithms. Numerical method to estimate the mean-square displacement(MSD) from a deterministic algorithm is also investigated. Our computational results show that anomalous diffusion can be solely due to chemical reactions. The chemical reactions alone can cause anomalous sub-diffusion in the RD system at some or all times.The time-dependent anomalous diffusion exponent is found to depend on many parameters, including chemical reaction rates, reaction orders, and chemical concentrations.     

Phenomenological nuclear-reaction description in deuterium-saturated palladium and synthesized structure in dense deuterium gas under γ-quanta irradiation

The observed phenomena of changes of chemical compositions in previous reports [1, 2] allowed us to develop a phenomenological nuclear fusion-fission model with taking into consideration the elastic and inelastic scattering of photoprotons and photoneutrons, heating of surrounding deuterium nuclei, following d-d fusion reactions and fission of middle-mass nuclei by “hot” protons, deuterons and various-energy neutrons. Such chain processes could produce the necessary number of neutrons, “hot” deuterons for explanation of observed experimental results [1, 2]. The developed approach can be a basis for creation of deuterated nuclear fission reactors (DNFR) with high-density deuterium gas and the so-called deuterated metals. Also, this approach can be used for the study of nuclear reactions in high-density deuterium or tritium gas and deuterated metals.     

Imaging of dynamic processes on surfaces by light

This work focuses on imaging of dynamic processes on surfaces, using light to illuminate the area of interest. The methods discussed here are those in which the photoelectrons emitted from or the light reflected off the surface are measured. While the first approach is well-known since electron microscopy was invented and has been used in surface science applications for a decade, genuine optical microscope methods using polarized light were first developed in 1995 for imaging surface reactions.

The results discussed here are from different fields of surface research. These include the imaging of adsorption phenomena, surface diffusion and growth processes. The main emphasis will be on pattern formation of surface reactions under strictly controlled parameters. The most recent techniques expand the range of observable pressure conditions by many orders of magnitude, thus bridging the pressure gap in imaging surface reactions.     

Ultrasound technology for food fermentation applications

Fermentation processes involve the participation of enzymes and organic catalysts, generated by range of microorganisms to produce chemical transformations. Ultrasound can be used in such processes to either monitor the progress of fermentation or to influence its progress. High frequency ultrasound (>2 MHz) has been extensively reported as a tool for the measurement of the changes in chemical composition during fermentation providing real time information on reaction progress. Low frequency ultrasound (20–50 kHz) can influence the course of fermentation by improving mass transfer and cell permeability leading to improved process efficiency and production rates. It can also be used to eliminate micro-organisms which might otherwise hinder the process. This review summarises key applications of high and low frequency ultrasound in food fermentation applications.     

A novel linear transformation model for the analysis and optimisation of chemical kinetics

In this study, a novel model for the analysis and optimisation of numerical and experimental chemical kinetics is developed. Concentration–time profiles of non-diffusive chemical kinetic processes and flame speed profiles of fuel–oxidiser mixtures can be described by certain characteristic points, so that relations between the coordinates of these points and the input parameters of chemical kinetic models become almost linear. This linear transformation model simplifies the analysis of chemical kinetic models, hence creating a robust global sensitivity analysis and allowing quick optimisation and reduction of these models. Firstly, in this study the model is extensively validated by the optimisation of a syngas combustion model with a large data set of imitated ignition experiments. The optimisation with the linear transformation model is quick and accurate, revealing the potential for decreasing the numerical costs of the optimisation process by at least one order of magnitude compared to established methods. Additionally, the optimisation on this data set demonstrates the capability of predicting reaction rate coefficients more accurately than by currently known confidence intervals. In a first application, methane combustion models are optimised with a small experimental set consisting of OH(A) and CH(A) concentration profiles from shock tube ignition experiments, species profiles from flow reactor experiments and laminar flame speeds. With the optimised models, especially the predictability for the flame speeds of mixtures of hydrogen, carbon monoxide and methane can be increased compared to established models. With the analysis of the optimised models, new information on the low pressure reaction coefficient of the fall-off reaction H+CH₃(+M)?CH₄(+M) is determined. In addition, the optimised combustion model is quickly and efficiently reduced to validate a new rapid reduction scheme for chemical kinetic models.     

Stationary diffusion in the membrane systems with the ongoing reversible chemical reactions

The diffusion phenomena were analyzed using the phenomenological equations of the thermodynamics of irreversible processes. The diffusion coefficient was thought to be dependent on local concentrations and pressure, unlike it was done in the linear theories. The reversible chemical reactions were modeled as intermolecular interaction. The ideal and regular solutions and solutions, described by the Margules's and Sketchard–Hammer's equations, were investigated and analytical solutions were found.