Modern kinetic mechanisms are intricate and can comprise tens of substances and hundreds of reactions [46, 95, 96]. For example, paper [97] deals with low-temperature decomposition of hydrocarbons to analyze the combustion mechanism totaling 340 substances and 3400 reactions. The authors of [98] exploited the combustion mechanism including 120 substances and 721 reactions for simulation of n-decane ignition. In the calculation of the oxidation of hydrocarbons described in [99], a mechanism comprising 71 substances and 417 reactions was analyzed.

In numerical analyses aimed at developing high-efficiency combustion chambers for various engines and thermal power systems, it is necessary to have an adequate understanding of hydrodynamic and chemical processes related to flowing, mixing, and combustion of two-phase fuels and oxidizers. The occurrence of such processes is described by the availability of zones differing in type, space, and time scale of these processes in the working volume.

The model of the combustion in the flame front is commonly used for the simulation of operating parameters and emission characteristics of combustion chambers of different combustion systems as one of the main simulation fragments in models of premixed flames. The typical scheme of combustion in the flame front was described in the Section 1.1. Combustion in the flame front predetermines to a considerable extent the further afterburning processes and parameters of reacting flows in the combustion unit and combustion products emission. In accordance with the generally accepted definition, the flame front is identified as a thin layer separating an unburned fresh mixture of the reactants from the combustion products wherein maximum gradients of concentrations of the reactants and reaction products are observed (Figure 4.1). Once the fresh mixture is ignited, a resulting premixed flame propagates in the x direction, consuming the unburned mixture. The chemical interaction in the flame front under conditions of intensive self-acceleration of the processes caused by the transfer of both heat and active catalyzing centers from the products of reactions to the unburned fresh mixture.

Combustion processes (that is, conversion of chemical energy of propellant components into thermal energy of combustion products) are typical for various engineering systems. Working volumes wherein these processes can occur may be represented by combustion chambers of liquid-propellant rocket engines (LPRE), solid-propellant rocket engines (SPRE), air-breathing engines (ABE) steam-gas generators, magnetohydrodynamic generators (MHD generators), boiler furnaces of thermal electric power stations, and cylinders of internal combustion engines (ICEs) [1]. Besides, further conversion of combustion products with chemical conversions can proceed also in aircraft and rocket engine nozzles, ICE exhaust systems, LPRE gas ducts, etc.

The model of the combustion in the flame front is commonly used for the simulation of operating parameters and emission characteristics of combustion chambers of different combustion systems as one of the main simulation fragments in models of premixed flames. The typical scheme of combustion in the flame front was described in the Section 1.1. Combustion in the flame front predetermines to a considerable extent the further afterburning processes and parameters of reacting flows in the combustion unit and combustion products emission. In accordance with the generally accepted definition, the flame front is identified as a thin layer separating an unburned fresh mixture of the reactants from the combustion products wherein maximum gradients of concentrations of the reactants and reaction products are observed (Figure 4.1). Once the fresh mixture is ignited, a resulting premixed flame propagates in the x direction, consuming the unburned mixture. The chemical interaction in the flame front under conditions of intensive self-acceleration of the processes caused by the transfer of both heat and active catalyzing centers from the products of reactions to the unburned fresh mixture.

Evaporation and combustion of dispersed propellants in a high-temperature reacting flow are typical for the most diverse propulsion and power generation systems such as internal combustion engines (ICE), combustors of air breathing engines (ABE), combustion chambers of liquid-propellant rocket engines (LPRE), liquid gas generators (LGG), and steam-gas generators (SGG), combustion chambers of furnaces, etc. Liquid-propellant atomization, spray formation, and droplet evaporation processes are seen to bear strong influence on the efficiency of the combustion process and, hence, the operating and ecological parameters of these combustion systems.

Feeding high-pressure gas into the gas space of the tanks filled with liquids and even solids aims to maintain this gas space at a preselected pressure history bounded by tanks’ structural requirements or required propellant supply pressures, to prevent propellant pump cavitation, to avoid uncontrolled chemical reactions in gas space, etc. The pressurization process and corresponding pressurization systems are used in diverse technical devices. These include apparatus for chemical technology, oil and ore tankers, aircraft fuel tanks, and propellant tanks of LPREs. Processes related to high-pressure and often high-temperature gas feeding are extremely diversified because of the complex flow patterns of gas in the free space of the tanks, possible heat exchange with structural elements and the propellant, mass exchange caused by the evaporation of liquids, the chemical reactions in gas, and liquid phases.

In numerical analyses aimed at developing high-efficiency combustion chambers for various engines and thermal power systems, it is necessary to have an adequate understanding of hydrodynamic and chemical processes related to flowing, mixing, and combustion of two-phase fuels and oxidizers. The occurrence of such processes is described by the availability of zones differing in type, space, and time scale of these processes in the working volume.

Modeling and numerical simulation of combustion in the cylinders of spark-ignition and compression-ignition internal combustion engines (ICEs) provide a considerable contribution in engines engineering and the optimization of engines performance, efficiency, and emissions. This chapter demonstrates the application of the reactor approach and the chemical nonequilibrium model (Chapters 1–3) to the simulation of combustion in the cylinder of the spark-ignition ICE aiming to predict the variation in ionized particle concentration as control variables. It is known that the combustion of hydrocarbon fuels with oxidizers at high pressures and temperatures is accompanied by the output of some ionized substances. Research on the ionization in flames was started in the mid-1950s for the purpose of optimization of magnetohydrodynamic generators as well as the study of ionized particle formation in combustion products of propulsion systems, particularly in the thrust chambers and exhaust plumes of rocket engines [1, 160, 215, 227, 228]. This study was later extended to the combustion in the ICE for the purpose of employing empirical and theoretical data on the ionization of combustion products for engine performance control intended for the optimization of the combustion process, the reduction of fuel consumption, the reduction of exhaust gas emission, the optimization of the exhaust gas recirculation (EGR) process, etc. [292–305].

Gas–liquid reacting flows seem to be one of the most complex and, at the same time, most prevalent fields of application for mathematical simulation of high-temperature processes. Of these processes, the phenomena are fluid atomization polydispersity and droplet secondary fragmentation, droplet heating and evaporation, turbulence, reactions in the gas phase, the difference in the velocity between the gas and droplet phases (slip velocity), and the multidimensional nature of fluid flow. Such flows make the core of processes proceeding in combustion chambers of air-breathing jet engines [216, 231, 239, 240], rocket engines [160, 215, 228, 229, 241, 242], gas generator driving turbopumps, pressurization systems of the LPRE propellant tanks [160, 215, 228, 241–243], vapor-gas generators [50, 55, 56], afterburners of air-breathing jet engines [216, 231, 239, 240], and different furnaces [58].

Combustion processes (that is, conversion of chemical energy of propellant components into thermal energy of combustion products) are typical for various engineering systems. Working volumes wherein these processes can occur may be represented by combustion chambers of liquid-propellant rocket engines (LPRE), solid-propellant rocket engines (SPRE), air-breathing engines (ABE) steam-gas generators, magnetohydrodynamic generators (MHD generators), boiler furnaces of thermal electric power stations, and cylinders of internal combustion engines (ICEs) [1]. Besides, further conversion of combustion products with chemical conversions can proceed also in aircraft and rocket engine nozzles, ICE exhaust systems, LPRE gas ducts, etc.

Equations of gas-phase chemical kinetics (1.85) (see Section 1.3) are valid for a constant volume (V = const) BR, while occurring a reversible chemical reactions. However, in the general case, it is desirable to allow for volume variation (V = var) in the reactor R, or in an assumed reactor of the system of reactors (SR), as well as in occurrences of irreversible reactions herein, feed and discharge of substances and surface reactions [5]. Such reactions reflect the change in gas mass and its composition in the reactor due to a number of processes (for example, evaporation, condensation, combustion of metals and coal, absorption, etc.).