Oscillatory combustion in closed vessels under microgravity

The existence and spatial development of gas-phase, thermokinetic oscillations in a spherical reactor under the influence of mass and thermal diffusion have been investigated by numerical methods. The conditions correspond to those that would be experienced under microgravity, as has been recently put to experimental test in studies of n-butane oxidation. Comparisons and contrasts with responses under perfectly mixed conditions are made. The numerical simulation was based on the Sal'nikov skeleton thermokinetic scheme, which is a two-variable model representing an intermediate chemical species and reactant temperature (taking the form P - A - B). Dirichlet and Neumann boundary conditions could be variously selected. The equations were cast in one dimension (spherical symmetry) and integrated using the NAG routine D03PSF. Approximate analytical forms of the solutions to the equations are also presented, and the relationship of numerical solutions to the equations under Dirichlet boundary conditions to these solutions are discussed. Both sustained oscillatory and damped oscillatory reaction were predicted to exist under spatially uniform conditions, and the phase relationship between the intermediate chemical species and temperature during sustained oscillation is demonstrated. The numerical results are compared with analytical predictions under spatially uniform conditions. No sustained oscillations were predicted to occur under the effect of diffusive fluxes at normal parameter values, although highly damped oscillations were still able to exist. This is compatible with the initial experimental observations in microgravity. Only when the values of the mass and thermal diffusive fluxes were doubled could sustained oscillatory reaction be recovered numerically. Experiments performed in mixtures diluted with helium could be compatible with this. The dependence of oscillations on the magnitude of mass and thermal diffusion coefficients is explored. The spatial development of temperature and intermediate species concentration reveals that, although the Sal'nikov model is driven kinetically through thermal feedback, there is an effect of diffusive flux which support the high reaction rate at the (hot) centre of the spherical system by transport of the intermediate species from the cooler, lower reactivity region at the periphery. The oscillatory reaction no longer occurs when this mass transport is suppressed.