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.).

The evaporation of droplets is one of the major stages of the working process that defines the combustion efficiency in the propulsion and power generation systems. Droplets of different sizes moving relative to gas flow and distributed in a complicated manner evaporate in the medium with variable gas dynamic and thermodynamic parameters. The evaporation process is very complicated, which is why whatever actual problem reduces in its theoretical analyses to an approximate model, allowing one to obtain an analytical or numerical solution. For instance, the chemical nonequilibrium model of evaporation of a single-component droplet in high-temperature flow illuminated in Chapter 5 comprises dozens of assumptions. A large number of theoretical and experimental studies are dedicated to the problems of droplets evaporation and combustion.