Major research interests of Professor V.B. Novozhilov include combustion (solid propellants, combustion theory and fire research) and the theory of heat transfer. He is a leading expert in theoretical and computational methods in the areas of combustion and fire research, in particular, computational fluid dynamics modelling of compartment fires. He has also made important contributions to the application of dynamical system methods in fire dynamics, and has also been greatly involved with analytical methods of the heat transfer theory in application to ultra‐fast heat transfer processes.
Professor V.B. Novozhilov is the author of over 60 journal papers and four book chapters. He was a Keynote Speaker at the 68th International Astronautical Congress (2017) delivering an overview of the fundamentals of the Zeldovich–Novozhilov propellant combustion theory, as well as of other contributions by Professor B.V. Novozhilov to the physics of combustion.
Preface
Nonsteady operating regimes, where fuel burning rates vary in time, are common for solid rocket motors. Under such conditions, combustion chamber pressure and, consequently, specific impulse are also functions of time. Some examples of such processes are combustion under variable pressure, a transition from one operating regime to another, oscillating combustion, erosion combustion in a dynamical regime, and propellant charge ignition and extinction under rapid depressurization.
In contrast to a steady‐state regime, propellant burning rate in such situations depends not only on instantaneous parameters (initial pressure, temperature, and the velocity of a tangential gas stream), but is also determined by the full history of the process. This is due to the inertia of the combustion wave, which includes a heated layer of the condensed phase, a chemical reaction zone, and a certain region in space that is occupied by combustion products.
The natural way of describing nonsteady propellant combustion would be to use the theory of steady‐state burning regimes. The transition to unsteady theory would require a simple addition of time derivatives into the relevant set of differential equations. At the current level of available computational resources, this additional mathematical complexity does not present a problem. However, the described hypothetical approach is not possible for a very simple reason: the consistent and universal theory of steady‐state propellant combustion describing experimental observations does not exist.
Each physical and chemical process which occurs during the combustion of propellants is immensely complex. For the overwhelming majority of substances, the burning rate is determined by chemical kinetics. Therefore, the kinetic parameters of reactions are a substantial part of practically any combustion theory. However, with some exception, this knowledge of the kinetics of combustion reactions is as yet incomplete. In particular, information on chemical transformations which occur during the combustion of condensed substances is very scarce so it is necessary to involve model kinetic schemes, which only remotely resemble real chemical processes (typically, Arrhenius dependence on temperature and power dependence on reactant concentration are adopted).
There is a large body of steady‐state homogeneous and composite propellant combustion models presented within this work. Naturally, such models contain a large number of parameters (reaction rate constants, activation energies, heat of combustion, transfer coefficients, thermophysical properties of gas, condensed phases, etc.) which are unknown in most cases. Evidently, an adjustment of numerous parameters allows the experimental data to be approximated, which of course does not imply a proper description of real fuel. Such studies are therefore of qualitative nature only, and are hardly suitable for comparison with experiments. Moreover, it would probably be impossible to develop a quantitative steady‐state combustion theory applicable to a wide range of substances due to the large variation in their properties.
A drastically different approach to the development of nonsteady theory (avoiding the necessity to create a detailed description of the steady‐state regime) was proposed by Ya.B. Zeldovich in 1942. It invokes an elegant and powerful idea of using the experimentally determined steady‐state dependence of a propellant burning rate on pressure and an initial temperature for studying nonsteady combustion regimes. It was demonstrated that this is only possible taking into account the thermal inertia of the condensed phase. The idea was formulated in the original paper by Zeldovich (1942) in the following way: ‘Since the relaxation time of combustion in gas is very small, we have the right to consider gaseous combustion as determined by the thermal condition of the thin condensed phase layer adjacent to the interface; the temperature distribution within deeper layers does not have a direct effect on the processes near the surface. The conditions of gas must be fully determined by instantaneous values of the surface temperature, and a temperature gradient in the condensed phase at the surface. Consider the surface temperature as being constant.’
Thus, the nonsteady propellant combustion theory was reduced to a consideration of a relatively slow variation of temperature distribution in the condensed phase. This is achieved by the solution of the heat transfer equation, combined with the known dependency of the burning rate on instantaneous values of pressure and the temperature gradient in a condensed phase at the surface. The latter may be obtained from the (theoretical or experimental) steady‐state dependency of the burning rate on pressure and initial temperature.
This theory explained some nonsteady combustion phenomena qualitatively, but its quantitative comparison with experimentation leads to contradiction. Most remarkably, this contradiction manifests itself in the conclusion that, according to this theory, a steady‐state burning regime of real systems is actually unstable. The reason for this discrepancy is an oversimplification of the theory, which considered propellant surface temperature as constant.
For all practically used compositions, the temperature at the interface between the condensed and gas phases depends on external conditions: the pressure, initial temperature, and velocity of the tangential gas stream. The theory proposed by Zeldovich (1942) was generalized and transformed to its contemporary state by B.V. Novozhilov in 1965 (Novozhilov 1965a,b). An additional function characterizing the steady‐state regime was introduced: the dependence of the propellant surface temperature on external parameters. Such a generalization of the Zeldovich theory allowed the majority of phenomena related to nonsteady combustion regimes to be explained.
It is important to note that this generalization of the theory by Zeldovich (1942) preserved its main idea, that is, the possibility of investigating nonsteady phenomena using steady‐state dependencies. The theory contains experimental dependencies related to a steady‐state combustion regime. These dependencies carry all the information on kinetics of chemical reactions as well as on various physical processes (thermal conduction and diffusion in the gas phase, devolatilization of the fuel, etc.).
Even in the absence of such dependencies, the theory still turns out to be helpful when considering a comparison of its conclusions with experimental data on nonsteady combustion. Thus, the comparison of theoretical and experimental data on acoustic combustion instability enables prediction of the behaviour of the same fuel under different nonsteady conditions, such as during combustion in a semi‐enclosed volume.
Moreover, the theory allows some fuel parameters, related to the kinetics of reactions at its surface, to be extracted from experimental data. For example, it is possible to obtain the effective activation energy of the chemical reaction at the fuel surface from the data on acoustic admittance.
The theory developed on the basis of results by Zeldovich (1942) and Novozhilov (1965a,b) is usually called the Zeldovich–Novozhilov theory (the ZN theory). The other titles that are used include the phenomenological theory of nonsteady combustion or the tc approximation. The latter emphasizes that the time of thermal relaxation of the condensed phase is the only fuel characteristic time.