Numerical modelling of particulate matter deposition in exhaust gas after-treatment systems

As urban air quality declines, the corresponding levels of particulate matter (PM), that include pollutants such as sulfates, nitrates and black carbon, rise posing the greatest risks to human health. Hence, the control of these particulate emissions constitutes a major global challenge that commands serious attention. In order to design strategies to mitigate PM emissions, it is necessary to establish the physical laws that govern their motion and deposition at these nano-scales. These systems are challenging to understand particularly as both the decreased momentum exchange with the gas (rarefaction due to the small sizes) and the meandering Brownian particle trajectories need to be studied simultaneously. For such an effort, numerical methods offer an attractive alternative to experiments, as the costs of setting up complicated experiments can be offset by insilico-methods that can provide a more exhaustive description of the particulate flow physics.In this work, we propose a suite of numerical tools that can be used for understanding PM deposition (including its transformation) in traditional after-treatment devices. First we undertake a system level modelling of PM deposition in exhaust after-treatment devices, such as diesel particulate filters (DPF\u27s), using a computational fluid dynamics driven approach. We show that the results from a fully Eulerian simulation of the the PM deposition process (based on the assumption of inertia less inert particles) shows a lesser capture of PM than the actual experimental data. The noted disagreement can be attributed to the assumption of \u27inert\u27 particles while modelling the deposition. Consequently, a multiphase direct numerical simulation (DNS) technique, that can completely resolve the fluid scales as well as the inherent particle-fluid coupling, is identified as an alternative to model these reactive particulate flows. We formulate such a framework by coupling the extended Langevin description of the particle with a mirroring Immersed boundary method. Further, to get an accurate resolution of the particle dynamics, we solve for it using a finite element based rigid body solver. This entire method (referred to as the IB-FSI framework) is implemented in the in-house immersed boundary code IPS IBOFlow. We analyse the consequences of resolving Brownian motion in an unbounded domain using this framework and evaluate the diffusion dynamics (mean squared displacements, velocity auto-correlation functions and diffusivities) of a spherical transported particle, in relation to the conventional Langevin treatment. Moreover, we demonstrate the applicability of such a method to resolve the Brownian dynamics of PM aerosols with particle densities comparable to a real soot-particle. We finally extend this framework to describe fractal like soot PM in unbounded domains