Gray-Yang model

One more model scheme is of interest the Gray-Yang model for some aspects of the low temperature oxidation of hydrocarbons [18-21]. This involves the features of chemical and thermal feedback described previously with a chain-carrier X coupled to the temperature T. Four reaction steps are required ... 

Explosion Limits Determination from a Unified Thermal and Chain Theory. In the paper of Gray Yang (Ref 1), a mathematical model was proposed to unify the chain and thermal mechanisms of explosion. It was shown that the trajectories in the phase plane of the coupled energy and radical concentration equations of an explosive system will give the time-dependent behavior of the system when the initial temperature and radical concentration are given. In the 2nd paper of the same investigators (Ref 2), a general equation for explosion limits (P—T relation) is derived from a unified thermal and chain theory and from this equation, the criteria of explosion limits for either the pure chain or pure thermal theory can be deduced. For detailed discussion see Refs... 

A simplified model was used for a study by the analytical methods employed by Gray and Yang [179—182]. Three dimensionless differential... 

Cool flames are difficult subjects for quantitative study since the time scale of events is generally too short to allow the use of conventional sampling. In addition, their non-isothermal character (which implies rate coefficients which change as reaction progresses) makes it difficult to develop theoretical models which satisfactorily describe the more important features (the periodicity and temperature rise). It is outside the scope of this review to discuss the more general theoretical aspects of cool-flame phenomena, and the reader is referred to VoL 2, Chap. 2 of this Series and also to the work of Yang and Gray [113], Halstead et al. [114, 115] and others [112,116,117]. 

The first empirical model for hydrocarbon ignition was created by Gray and Yang [195] in 1965. This simple model, given below, has two variables a single concentration variable x and temperature T. 

In 1969 Gray and Yang [70] formulated an extremely simple scheme which could reproduce these phenomena and it is described in detail in Chapter 5. Its importance lay, not so much in its application to the modelling of practical systems, but in its provision of a conceptual base for further development. It incorporated the essential features of the science, particularly thermokinetic feedback - the interaction between a branched radical chain and the reaction-generated temperature rise. 

In order to amplify these points and to proceed in a more general context it is appropriate to introduce here the most simple, skeleton, thermoKinetic model from which it is possible to predict many of the phenomena observed during the non-isothermal oxidation of organic compounds. The model was devised by B.F. Gray and C.H. Yang about 15 years ago and its properties investigated by them [10,11]. Its representation was reduced to the essential Kinetic features determining the behaviour of an intermediate species x, as follows ... 

Yang, B., X. Wu, and G. Yang. Fault Prediction of Ship Machinery Based on Gray Neural Network Model. Proceedings of the International Conference on Control and Automation, 2007, 1063-1066. 

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