2D chaotic flow in competitive exothermic-endothermic reactions

• Main Authors: Huang, Zhe Jun, Watt, Simon, Sidhu, Harvi, McIntosh, Andy, Brindley, John, Jovanoski, Zlatko, Towers, Isaac
• Format: Conference Proceeding
• Language: English
• Published: Modelling and Simulation Society of Australia and New Zealand 01.12.2019

We study the effects of chaotic advection in a two-dimensional competitive reaction with an exother-mic reaction and an endothermic reaction and investigate the formation of the filament structure. In a chemical reaction, there are many processes and steps, even in the simplest reactions. By "lumping" these reactions together, a chemical reaction can be modelled using a fewer number of steps. As with any modelling exercise, the more steps that are included, the more complex the model is in terms of the number of system parameters, but this also allows a rich array of behaviour. The model considered here has two reactions, competing for the same fuel source, an exothermic reaction, which generates energy, and an endothermic reaction, which absorbs energy. An example of this type of reaction is the burning of ammonium nitrate in the context of emulsion explosives [Sinditskii et al., 2005]. In one dimension, these exothermic-endothermic reaction models can display complex behaviour. With a suitable initial temperature profile, a t ravelling r eaction wave q uickly d evelops, with t hree r egions: Ahead of the reaction where the fuel is unburnt and is at an ambient temperature, behind the reaction where the fuel has been consumed and is at a final burnt temperature and at the reaction front where the fuel is being consumed. Tracking the location of the reaction front, the system can exhibit a range of behaviour. Depending on the system parameters, the speed of the travelling wave can become constant, become oscillatory, with the possibility of period doubling behaviour, or the reaction does not propagate, leading to quenching. This was studied in detail by Sharples et al. [2012]. In two dimensions, similar behaviour can be found [Watt et al., 2019a]. By adding a mixing process to the combustion process, the system behaviour changes. The mixing added to the system was a blinking vortex flow. This flow models the outflow from a large bathtub with with two sinks that are opened in an alternating manner. This alternating flow has been shown to induce chaotic mixing [Károlyi and Tél, 1997]. Kiss et al. [2004] studied this flow as applied to a single step combustion process. It was shown that there is a critical mixing rate, above which the flame is quenched and the reaction s tops. We extend this work by replacing the single step reaction with a two-step competitive reaction. As before, there is a critical mixing rate, above which the flame is quenched. In addition, we explore the sensitivity of the system parameters on the performance of the reaction, as measured by the average steady state temperature.