A numerical study of spatial structure during oscillatory combustion in closed vessels in microgravity

The existence and spatial development of gas-phase, thermokinetic oscillations under the influence of mass and thermal diffusion have been investigated by numerical methods in a 1-dimensional system. The conditions correspond to those that would be experienced under microgravity. The interest arises because there have been recent experimental investigations of oscillatory reactions, involving cool flames during butane oxidation, as part of the NASA, KC135 microgravity flight programme. The Sal'nikov, thermokinetic scheme, which is a two-variable model representing an intermediate chemical species and reactant temperature (taking the form P-->A-->B), forms the basis of the present work. In this model, thermal feedback occurs through the exothermicity of the second step and the non-linearity is derived from its temperature dependence. There are no known chemical examples that satisfy Sal'nikov's formal structure but Griffiths and co-workers conceived an experimental analogue under terrestrial conditions whereby a gaseous reactant was allowed to flow from an external reservoir into a closed, heated reactor at a controlled rate via a capillary tube which fed the reactant to the centre of the vessel. The exothermic reaction that occurred in the vessel satisfied the necessary conditions for the second step and the inflow, with no temperature dependence, represented a physical analogue to the first step of the Sal'nikov scheme. Thermokinetic oscillations were observed and the range of conditions for their existences was investigated. One of the experimental systems was the exothermic reaction between hydrogen and chlorine. To represent the Sal'nikov conditions hydrogen was fed slowly into the reactor, which already contained chlorine. We have exploited this chemical system and its experimental implementation in the present paper to investigate the behaviour when no convection or bulk gas motion occurs and when heat and mass transport is driven solely by diffusion. We study the response of alternative numerical approaches to the way in which the first step of the scheme is simulated. In the first, the precursor (P) is supplied at the same rate simultaneously throughout the cells representing the reactor. This is close to the concept of the Sal'nikov model. In the second method, a fixed rate of supply is applied at the inner boundary of the axisymmetric, 1-dimensional system. This is analogous to the experimental procedure. The numerical results show how oscillatory states can be sustained as a result of heat and mass transport by diffusion. The temporal and spatial evolution of reaction in a range of circumstances is discussed.