Abstract
Theoretically, the combustion stability of solid fuel, which during the combustion process is decomposed according to the “solid phase – liquid phase – gas” scheme, is investigated. The physical and mathematical models for the propagation of small perturbations of combustion are constructed. The medium in all areas of combustion and in combustion products is assumed to be incompressible, and the viscosity of the fuel in the liquid phase is taken into account. Thus, perturbations of hydrodynamic parameters are considered not only in the two-phase gasification zone, but also in the combustion products area and the geometric perturbation of the instantaneous combustion front (flame), distorting the shape of its surface, is also specified. That is the characteristic feature of the presented physical model. The mathematical eigenvalue problem is set and solved. This problem is reduced to an algebraic characteristic equation for a dimensionless complex eigenvalue, which positivity determines the instability. It is proved that in the limiting case of the absence of a liquid phase, absolute instability takes place. At the other limiting case – for perturbations with infinite wavelength – a transition to stability takes place. The latter fact indicates that the presence of a viscous liquid film and changes in the length of the gasification zone under the influence of perturbations have a significant stabilizing effect on solid fuel combustion. In the general case, a sufficient condition for the instability of the roots of the characteristic equation is analytically determined. The physical interpretation of the mathematical results explains the processes of autoturbulization of solid fuel combustion and the possible transition of combustion to deflagration explosion or detonation. The results of the study are in qualitative agreement with experimental data and can additionally be used for theoretical analysis of the stability of the liquid fuel combustion process in the combustion chamber
Highlights
The problem of hydrodynamic stability of combustion waves is a classical theoretical problem of fluid mechanics, which is still topical [1]. This is primarily due to the practical importance of studies of the stability for flames subjected to small perturbations: it is instability that is the main cause of flame autoturbulization [2, 3] and acceleration [4, 5]
Acceleration of the flame can cause its transition to detonation [6,7,8] or to deflagration explosion [9]
A detailed analysis of the evolution of small perturbations [9] for the case of unstable combustion enables us to estimate the time of possible combustion-explosion transition and the length of the so-called detonation induction distance [12]
Summary
The problem of hydrodynamic stability of combustion waves is a classical theoretical problem of fluid mechanics, which is still topical [1] This is primarily due to the practical importance of studies of the stability for flames subjected to small perturbations: it is instability that is the main cause of flame autoturbulization [2, 3] and acceleration [4, 5]. The relevance of studies of the hydrodynamic flame stability is connected with the emergence of new combustible substances and the development of equipment and technology for fuel burning For this reason, new models of the stationary combustion process are constantly being created, and the stability of this process is subsequently investigated. The study of the stability of solid fuel combustion is of special interest, because, in particular, rocket engines use such kinds of fuel [17]
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