Thermokinetic feedback oscillations and local stability analysis

6 THERMOKINETIC FEEDBACK OSCILLATIONS AND LOCAL STABILITY ANALYSIS 

In many combustion systems there will be the possibility of both thermal and chemical feedback, with the two processes coupled together through the heat and mass balance equations just for added fun. A simple model 

Another model studied under the name of thermokinetic feedback is due to Salnikov [14,15]. This has two first-order reaction steps which, in general, could both be exothermic and both have an Arrhenius temperature dependence  

The most interesting behaviour can be obtained, however, by taking a slightly simplified version in which only step (S2) is exothermic and has a temperature-dependent rate law, so that the governing equations have the form  

/r is a dimensionless measure of the initial reactant concentration Oo, y is the dimensionless concentration of X and k is the ratio of the Newtonian cooling time to the chemical reaction time at ambient temperature. 

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