Calculation of Equilibrium Composition of Complex Thermodynamic Systems using Julia Language and Ipopt Library

The article considers the possibility of using the Ipopt optimization package for the calculating the phase and equilibrium compositions of a multicomponent heterogeneous thermodynamic system. Two functions are presented for calculating the equilibrium composition and properties of complex thermodynamic systems, written in the Julia programming language. These functions are the key ones in the program integrated with the IVTANTERMO database on thermodynamic properties of individual substances and used for conducting test calculations. The test calculations showed that Ipopt package allows determining the phase and chemical compositions of simple and complex thermodynamic systems with a fairly high speed. Using the JuMP modeling language significantly simplifies the preparation of the initial data for the Ipopt package, therefore the functions presented in this article are very compact. It is shown how the Ipopt package can be used when the temperature of the thermodynamic system is unknown. The approach proposed in this work is applicable both for analyzing the equilibrium of individual chemical reactions and for calculating the equilibrium composition of complex chemically reacting systems. The simplicity of the proposed functions allows their easy integrating into application programs, embedding them into more complex applications, using them in combination with more complex models (real gas, nonideal solutions, constrained equilibria), and, if necessary, modifying them. It should be noted that the versatility of the JuMP modeling language makes it possible to replace the Ipopt package with another one without significant modification of the program text

Mathematical Simulation of the Behavior of a Cumulative Jet with Inert and Reactive Components

The purpose of the research was to investigate the processes associated with the free flight of a cumulative jet formed from a composite liner of a cumulative charge. We mathematically simulated the process from the perspective of continuum mechanics using numerical methods for solving the corresponding equations. The cumulative jet was simulated in the quasi-two-dimensional nonstationary approximation as a high-gradient cylindrical compressible elastoplastic or liquid rod. The material of the jet was considered as a one-speed three-phase medium. The compressibility of each phase was described by its inherent barotropic dependence of pressure on density. The resulting pressure in a multiphase mixture of particles of the cumulative jet, considered as a composite material, was determined on the basis of the additivity condition of the volumes. When assessing the composition of the jet, we determined the initial concentrations of the components using a software package for thermo-dynamic simulation of chemically reacting systems. To find the numerical solution of the multi-phase, i.e., composite, jet extension problem, we used a finite-difference method based on Neumann --- Richtmyer scheme. The numerical analysis of the process under study was carried out on the example of a laboratory cumulative charge. Within the research, we found the characteristic features and possible variations in the behavior of the jet depending on the presence of the components of the composite liner, i.e., matrix, inert and reactive additives, and their properties. Finally, we estimated the change in the penetrating power of the jet compared to the reference variant of the cumulative liner of a homogeneous single-phase monolithic material.

Chemical Reaction Stoichiometry: A Key Link between Thermodynamics and Kinetics, and an Excel Implementation

<div>The Law of Conservation of Mass (LCM) is one of the most important principles in chemistry. It applies to both closed and steady-state open flow systems undergoing chemical change. Various special methods are generally taught for its implementation, including inspection, oxidation-reduction, and ion-electron approaches, which typically fall under the topic of "balancing a chemical equation". However, apart from the simplest case described by a single such equation, only matrix methods are applicable.</div><div><br></div><div>This paper describes Chemical Reaction Stoichiometry (CRS), and its implementation of the LCM for chemically reacting systems by its expression in terms of a nonunique set of independent chemical equations of the appropriate number. Such equations have the superficial appearance of, but are distinct from, an actual chemical reaction mechanism. The underlying matrix method is based on ideas from basic linear algebra; in addition to being generally applicable to systems of any complexity, it obviates the need for the aforementioned special methods in single-reaction systems.</div><div><br></div><div>We provide an easy-to-use spreadsheet implementation of CRS that includes many worked examples.</div>

Chemical Reaction Stoichiometry: A Key Link between Thermodynamics and Kinetics, and an Excel Implementation

<div>The Law of Conservation of Mass (LCM) is one of the most important principles in chemistry. It applies to both closed and steady-state open flow systems undergoing chemical change. Various special methods are generally taught for its implementation, including inspection, oxidation-reduction, and ion-electron approaches, which typically fall under the topic of "balancing a chemical equation". However, apart from the simplest case described by a single such equation, only matrix methods are applicable.</div><div><br></div><div>This paper describes Chemical Reaction Stoichiometry (CRS), and its implementation of the LCM for chemically reacting systems by its expression in terms of a nonunique set of independent chemical equations of the appropriate number. Such equations have the superficial appearance of, but are distinct from, an actual chemical reaction mechanism. The underlying matrix method is based on ideas from basic linear algebra; in addition to being generally applicable to systems of any complexity, it obviates the need for the aforementioned special methods in single-reaction systems.</div><div><br></div><div>We provide an easy-to-use spreadsheet implementation of CRS that includes many worked examples.</div>

Errors in nanoparticle growth rates inferred from measurements in chemically reacting aerosol systems

In systems in which aerosols are being formed by chemical transformations, individual particles grow due to the addition of molecular species. Efforts to improve our understanding of particle growth often focus on attempts to reconcile observed growth rates with values calculated from models. However, because it is typically not possible to measure the growth rates of individual particles in chemically reacting systems, they must be inferred from measurements of aerosol properties such as size distributions, particle number concentrations, etc. This work discusses errors in growth rates obtained using methods that are commonly employed for analyzing atmospheric data. We analyze “data” obtained by simulating the formation of aerosols in a system in which a single chemical species is formed at a constant rate, R. We show that the maximum overestimation error in measured growth rates occurs for collision-controlled nucleation in a single-component system in the absence of a preexisting aerosol, wall losses, evaporation or dilution, as this leads to the highest concentrations of nucleated particles. Those high concentrations lead to high coagulation rates that cause the nucleation mode to grow faster than would be caused by vapor condensation alone. We also show that preexisting particles, when coupled with evaporation, can significantly decrease the concentration of nucleated particles. This can lead to decreased discrepancies between measured growth rate and true growth rate by reducing coagulation among nucleated particles. However, as particle sink processes become stronger, measured growth rates can potentially be lower than true particle growth rates. We briefly discuss nucleation scenarios in which the observed growth rate approaches zero while the true growth rate does not.