Numerical analysis on the hot spot in reactive chemical storage

In an exothermic reactive chemical storage tank, a thermal explosion can occur when the heat generation within the storage tank is greater than the heat removal from the storage tank. In a solid system, the existence of an inflection point in the temperature versus time curve is often used as a criterion for thermal explosion. In this study the applicability of this criterion to fluid storage is examined by investigating the hot spot in the system. Transient natural convection of an exothermically reactive fluid in a vertical, cylindrical storage tank with isothermal walls is investigated numerically. The axisymmetric 2-D Navier–Stokes equations governing the flow fields are reduced by introducing the stream function–vorticity formulation and solved by the alternating-direction-implicit (ADI) technique. The reactive heat sources are represented by a zeroth-order rate expression with an Arrhenius-type rate constant. It is found that the hot spot is no longer located in the center of the tank due to the buoyancy effect. In a particular range of Rayleigh number and Frank-Kamenetskii number, the hot spot is found to move periodically. A stable steady regime, stable oscillatory regime and thermal explosion regime can be specified based on the dependence of the critical Frank-Kamenetskii number on the Rayleigh number. In the stable oscillatory regime multiple inflections in temperature versus time are found. Therefore, the existing criterion, which defines thermal explosion by the appearance of an inflection in the temperature versus time curve, is no longer applicable in reactive fluid systems. The results of nonconvective systems do, however, provide a preliminary and conservative estimate for thermal explosion of a reactive storage tank.