Heat losses in applied smouldering systems: Sensitivity analysis via analytical modelling

Abstract

As applied smouldering systems gain popularity for a variety of energy conversion purposes, there is a strong interest in optimizing the reactor design to support robust smouldering. Heat losses play a critical role in the energy balance of smouldering systems, and therefore have strong implications toward understanding propagation limits and reactor design. Heat losses in an applied smouldering system were approximated by adapting the analytical model from Kuznetsov (1996), originally developed for unsteady local thermal non-equilibrium heat transfer in a porous cylinder, to simulate the cooling zone trailing the smouldering front. The analytical model was adapted to a smouldering system by solving on a domain that lengthens as the cooling zone expands at the rate of the smouldering velocity. The results are incorporated into a global energy balance on the smouldering system, thereby providing an inexpensive and rapid method to estimate the system energy efficiency. Confidence in the analytical model was provided by demonstrating its predictions compare well with existing experimental and numerical estimates of heat losses from similar smouldering systems. The model was then used to quantify the sensitivity of the heat losses to two key reactor design parameters: radius and insulation quality. The system energy efficiency was shown to be highly sensitive to improved insulation and increased radius up to ~0.1 m (i.e., laboratory-sized reactors). However, this sensitivity diminished with size. Beyond 0.4 m radius, the predicted system energy efficiency was high (~85-95%) and relatively insensitive to reactor radius and insulation quality. Therefore, commercial, batch treatment smouldering reactors do not need to be larger than 0.4 m in radius to protect against heat losses and maximize their energy efficiency. This threshold design radius is considerably less than used in current reactors and therefore can provide valuable cost savings.