Effects of natural convection on thermal explosion in a closed vessel

Abstract

A new way of ascertaining whether or not a reacting mixture will explode uses just three timescales: that for chemical reaction to heat up the fluid containing the reactants and products, the timescale for heat conduction out of the reactor, and the timescale for natural convection in the fluid. This approach is developed for an n-th order chemical reaction, A → B occurring exothermically in a spherical, batch reactor. The three timescales are expressed in terms of the physical and chemical parameters of the system. Numerical simulations are performed for laminar natural convection occurring; also, a theoretical relation is developed for turbulent flow. These theoretical and numerical results agree well with previous experimental measurements for the decomposition of azomethane in the gas phase. The new theory developed here is compared with Frank-Kamenetskii's classical criterion for explosion. This new treatment has the advantage of separating the two effects inhibiting explosion, viz. heat removal by thermal conduction and by natural convection. Also, the approach is easily generalised to more complex reactions and flow systems.

On the occurrence of thermal explosion in a reacting gas: The effects of natural convection and consumption of reactant

“…However, in most reacting systems heat loss occurs due to the combined effects of natural convection and heat conduction. Recently, Liu et al [3] proposed that in such systems the occurrence or not of an explosion depends on the relative magnitudes of three timescales: that for chemical reaction to heat up the fluid to ignition, the timescale for thermal conduction and that for natural convection. They summarized their results in a new two-dimensional regime diagram, in which Frank-Kamenetskii's purely conductive system and Semenov's well-mixed system appear as two limiting cases, represented by the two axes.…”

When do chemical reactions promote mixing?

“…The straight lines for Ra = 500 and Ra = 10 6 are shown; they separate the space into three regions, where natural convection is either very weak, strong but laminar and, for Ra > 10 6 , turbulent. From Liu et al [18]. (24) - (26) and (b) after replacing X by X/(1 + X) for  = 10, r = 28 and  = 8/3.…”

“…Thus, at or above this temperature, there is likely to be an explosion of some kind. In this language, Ze is also the ratio,  reac / H , of the characteristic ) to its ignition temperature [18]. That Ze =  reac / H is important and this conclusion will be used again below.…”

“…Turbulence occurs in a fluid, when the Rayleigh number Ra ( = gL 3 T/κ) exceeds a value varying from ~ 10 5 [13] to ~ 10 6 [16], depending on the geometry of the system. Another consequence of natural convection in a reactor is that ignition and explosion can be suppressed [17,18] by enhancing heat and mass transfer in a reactor. Natural convection, which is strongest in large vessels (because Ra  L 3 , where L is the characteristic dimension of the reactor), is thus an important way whereby chemical reaction promotes mixing.…”

“…15 [18,25]. Again the walls of the reactor are held at a constant temperature, which might require an unusually efficient system of external cooling and also Bi >> 1.…”