A comparison of measured temperatures with those calculated numerically and analytically for an exothermic chemical reaction inside a spherical batch reactor with natural convection

Abstract

When any exothermic chemical reaction occurs inside e.g., an unstirred spherical vessel, the heating effect of the reaction often induces temperature gradients and consequently natural convection. This work sets out to compare previously measured temperatures at different positions inside such a batch reactor with values computed numerically and analytically. It is the first such study for a reaction with an order greater than zero, occurring in a spherical reactor. The main reaction considered is the thermal decomposition of the gas, azomethane, which has often been used in experimental studies of thermal explosion. Other experimental results for the reaction between nitric oxide and oxygen, as well as between hydrogen and chlorine are also considered here. The measured temperatures at the centre of the vessel are first compared with analytical scales, derived by inspecting the governing equations. It is found that the temperature rise when diffusion is the dominant transport mechanism (i.e., at small values of the Rayleigh number) is directly proportional to the ratio of the characteristic timescales for diffusion and for the reaction. Similarly, when natural convection is the dominant transport mechanism, the temperature rise is proportional to the ratio of the timescales for convection and reaction. A numerical scheme was developed to simulate the thermal decomposition of azomethane vapour under the influence of natural convection, as well as the diffusion of both matter and heat ( via thermal conduction). The results of these simulations are compared with the temperature profiles measured along the vertical axis of the reactor. There is excellent agreement between experimental and numerical results. This confirms the computational procedures. The simulations indicate that the hottest point in the reactor moves upwards above the centre of the vessel when Ra is increased. In fact, three distinct types of temperature profile occur, depending on the value of Ra. For low Ra, the temperature profile is approximately spherically symmetric, as expected. When Ra is increased, the symmetry in the temperature profile is disrupted by the flow produced by natural convection. In that case, the temperature profile becomes skewed, with the maximum occurring on the axis in the top half of the reactor. Thirdly, under some circumstances at high Ra, a large, sharp peak in the temperature profile near the top of the reactor is produced. This resembles a stabilised flame front, but could be an explosion. These three types of temperature distribution have also been observed experimentally. Finally, the ratio of the notional temperature rise in a purely diffusive system to that measured experimentally is compared over a wide range of Ra. The experimental results for the three reactions considered all follow the same trend; the numerical and analytical solutions are in excellent agreement with the experimental results, confirming that the onset of natural convection inside a spherical vessel occurs at Ra ∼ 500 . This result seems to be true, regardless of the order of the reaction, and only depends on the shape of the reactor.