Stability of the combustion process in elastic combustion chambers

High-frequency instability phenomena in rigid combustion chambers have been studied theoretically in [1–3]. This phenomenon is attributed to the interaction between the combustion processes and combustion-product fluctuations in the chamber. One of the possible mechanisms of formation of high-frequency instability is examined in [3], where the combustion rate is represented in the form of a retarded pressure functional. In this case, the problem is reduced to studying the stability of a certain distributed self-oscillating time-lag system.If the oscillation frequencies of the combustion products are comparable to the natural vibrations of the shell which forms the combustion chamber, then it is natural to expect that the elasticity of the chamber walls will affect the combustion process. Coupled effects of acoustoelastic instability can arise, in whose development the vibrations of the chamber wall play a substantial role. These effects are particularly undesirable from the point of view of the vibrational stability of combustion chambers.In this paper, a theory of high-frequency instability of stationary combustion is developed with allowance for elastic deformations of the combustion chamber walls. The theory is based on the mechanism of vibrational combustion [1–3], according to which the combustion front is assumed to the concentrated, while the velocity jump at the front is expressed through a retarded pressure functional. It is assumed that the combustion product flow is one-dimensional and isentropic and that the chamber is cylindrical. The deformations of the chamber are described via the moment theory of shells. The existence is revealed of additional instability regions produced by the interaction between the elastic vibrations of the chamber walls and the acoustic oscillations of the combustion products. The influence of the relation between the elastic and acoustic frequencies and of the structural damping factor in the combustion chamber walls on the stability of the stationary combustion process is examined. The problem discussed is treated as a mathematical model for more complex asymmetric problems in which the elastic and acoustic frequencies can be of the same order.     

Behavior of two-layer structures with protective layer swelling

Moscow Institute of Chemistry Machine Construction. Translated from Prikladnaya Mekhanika, Vol. 24, No. 1, pp. 88–96, January, 1988.     

Chemical transformations of 3-aminopyrrolidin-2-ones of the norbornane and cyclopropane series

3-Aminopyrrolidin-2-ones containing a fused norbornane or spirocyclopropane fragment react with benzaldehyde to give azomethines, which can be transformed into N-substituted 3-aminopyrrolidin-2-ones by reduction with sodium borohydride. Diazotization of amino-pyrrolidinones with NaNO₂ in acetic acid results in the elimination of molecular nitrogen and in the formation of acetoxy or unsaturated derivatives (through stabilization of intermediate carbocations). 6-Methylidene4-azaspiro[2.4]heptan-5-one obtained by diazotization of 6-amino-6-methyl-4-azaspiro[2.4]heptan-5-one easily reacts with diazomethane, diazocyclo-propane, and benzonitrile oxide to yield heterocyclic spiranes by means of 1,3-dipolar cycloaddition.     

Instability of an electron beam in a magnetic field

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 10–17, March–April, 1990.     

Surface buckling of a layered medium

The surface buckling of a layer-reinforced medium with the layers arranged at right angles to the surface is investigated on the basis of Bolotin's theory of layered media. The critical load is determined and the buckling mode studied. By means of a simplified approach simple expressions are obtained for the critical loads corresponding to surface buckling.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 4, pp. 648–654, July–August, 1973.     

Optimal design of temperature regimes of reflecting systems

We solve the variational problem of determining the power of additional three-dimensional and surface heat sources to guarantee the minimization of the displacement field at the end of a finite circular cylinder on which a stationary heat flow is prescribed. Four figures. Bibliography: 5 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 73–77.