Instability chemical kinetic

T.C. Lieuwen, Y. Neumeier, and B.T. Zinn. The role of unmixedness and chemical kinetics in driving combustion instabilities in lean premixed combustors. Combustion Science and Technology, 135 193-211,1998. 

Instabilities and dissipative structures play a basic role in our understanding of chemical kinetics in far from equilibrium situations. Through dissipative structures the characteristics of the system become explicitly dependent on macroscopic parameters (dimensions, boundary conditions) that relate it to its environment. 

P. Gray and S. K. Scott Chemical oscillations and instabilities non-linear chemical kinetics... 

P. Gray and S. K. Scott. Chemical Oscillations and Instabilities Nonlinear Chemical Kinetics. Oxford Clarendon Press, 1990. See also the Review Lecture by P. Gray. Instabilities and oscillations in chemical reactions in closed and open systems. Proc. Roy. Soc. Lond. A 415, 1-34 (1988). 

The problems of phase transition always deeply interested Ya.B. The first work carried out by him consisted in experimentally determining the nature of memory in nitroglycerin crystallization [8]. In the course of this work, questions of the sharpness of phase transition, the possibility of existence of monocrystals in a fluid at temperatures above the melting point, and the kinetics of phase transition were discussed. It is no accident, therefore, that 10 years later a fundamental theoretical study was published by Ya.B. (10) which played an enormous role in the development of physical and chemical kinetics. The paper is devoted to calculation of the rate of formation of embryos—vapor bubbles—in a fluid which is in a metastable (superheated or even stretched, p < 0) state. Ya.B. assumed the fluid to be far from the boundary of absolute instability, so that only embryos of sufficiently large (macroscopic) size were thermodynamically efficient, and calculated the probability of their formation. The paper generated extensive literature even though the problem to this day cannot be considered solved with accuracy satisfying the needs of experimentalists. Particular difficulties arise when one attempts to calculate the preexponential coefficient. 

Gray P, Scott SK (1994) Chemical oscillations and instabilities. Non-linear chemical kinetics. Clarendon, Oxford... 

Combustion instability that leads to performance deterioration and excessive mechanical loads, which could result in reduced life and premature failure, is an important issue with modern gas turbine engines and ramjet and scramjet combustors. Various techniques of passive and active control to reduce combustion instabilities and improve performance are addressed. Since extensive, promising research is being carried out to develop sensors and actuators, these techniques can be used in practical combustors in the near future. The topics covered in Section 3 provide the required chemical, kinetic, and fluid dynamic understanding to help the designer who is involved in active feedback control for combustion systems. 

Both in hydrodynamics and in chemical kinetics, instability may occur due to nonlinear conditions far from equilibrium. In hydrodynamic systems, nonlinear conditions are produced by the inertia terms, such as the critical Reynolds number or Rayleigh number. However, nonequilibrium kinetic conditions may lead to a variety of structures. In chemical systems, some autocatalytic effect is required for instability. 

Instabilities arise in combustion processes in many different ways a thorough classification is difficult to present because so many different phenomena may be involved. In one approach [1], a classification is based on the components of a system (such as a motor or an industrial boiler) that participate in the instability in an essential fashion. Three major categories are identified intrinsic instabilities, which may develop irrespective of whether the combustion occurs within a combustion chamber, chamber instabilities, which are specifically associated with the occurrence of combustion within a chamber, and system instabilities, which involve an interaction of processes occurring within a combustion chamber with processes operative in at least one other part of the system. Within each of the three major categories are several subcategories selected according to the nature of the physical processes that participate in the instability. Thus intrinsic instabilities may involve chemical-kinetic instabilities, diffusive-thermal instabilities, or hydrodynamic instabilities, for example. Chamber instabilities may be caused by acoustic instabilities, shock instabilities, or fiuid-dynamic instabilities within chambers, and system instabilities may be associated with feed-system interactions or exhaust-system interactions, for example, and have been assigned different specific names in different contexts. 

Among the areas not covered here is that of intrinsic instabilities associated with chemical-kinetic mechanisms, as exhibited in cool-flame phenomena, for example these subjects are touched briefly in Section B.2.5.3. Intrinsic instabilities of detonations were considered in Section 6.3.1 and will not be revisited. Certain aspects of intrinsic instabilities of diffusion flames were mentioned briefly in Section 3.4.4 diffusion flames appear to exhibit fewer intrinsic instabilities than premixed flames, although under appropriate experimental conditions their effects can be observed, as indicated at the end of Section 9.5.2. Certain chamber instabilities that are not related to acoustic instabilities (such as Coanda effects—oscillatory attachment of flows to different walls) will not be discussed here, but reviews are available [1]. 

Golikeri, S. V., and Luss, D. Diffusional effects in reacting mixtures. Chem. Eng. Sci. 26,237 (1971). Gray, P., and Scott, S. P., Chemical Oscillations and Instabilities. Nonlinear Chemical Kinetics. Oxford Science Publications, Oxford, 1990. 

The steady state spatial correlations in reaction-diffusion systems involving many reversible chemical reactions are examined. It has been cJready discussed that the spatial correlations are related to the breaking of detailed balance in chemical kinetics for both one species and for two species reversible reactions. Here, we focus our attention on how the spatial correlations of concentration fluctuations in a macroscopically homogeneous systems approach to the instability point. The spatial correlations depend strongly on the stability of systems for two species reactions compared to one species reactions. 

Gray, P., and Scott, S. K., Chemical Oscillations and Instabilities Non-Linear Chemical Kinetics. Clarendon Press, Oxford, 1990. 

A further complication arises in the case of heterogeneous catalysis where the activity of the catalyst can change with time on stream or with reactant composition. Changes of this kind are themselves time-dependent processes that are overlaid on the time-dependent kinetics of the chemical transformations. The untangling of all these effects so that pure chemical kinetics can be studied is an important aspect of mechanistic studies using kinetics. See section on catalyst instabilities later in this chapter.)... 

P. Grey and S.K. Scott, Chemical Oscillations and Instabilities in Non-linear Chemical Kinetics, Clarendon, Oxford, 1994. 

Both deterministic and stochastic models can be defined to describe the kinetics of chemical reactions macroscopically. (Microscopic models are out of the scope of this book.) The usual deterministic model is a subclass of systems of polynomial differential equations. Qualitative dynamic behaviour of the model can be analysed knowing the structure of the reaction network. Exotic phenomena such as oscillatory, multistationary and chaotic behaviour in chemical systems have been studied very extensively in the last fifteen years. These studies certainly have modified the attitude of chemists, and exotic begins to become common . Stochastic models describe both internal and external fluctuations. In general, they are a subclass of Markovian jump processes. Two main areas are particularly emphasised, which prove the importance of stochastic aspects. First, kinetic information may be extracted from noise measurements based upon the fluctuation-dissipation theorem of chemical kinetics second, noise may change the qualitative behaviour of systems, particularly in the vicinity of instability points. 

Gray, P Scott, SK. Chemical Oscillations and Instabilities, Non-linear Chemical Kinetics, Claredon Press Oxford, U.K., 1990. 

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