Modelling of turbulent reacting flows with polydispersed particle formation

Abstract

The formation of particles in a turbulent carrier flow is central to many environmental processes and engineering applications. Specific examples include the precipitation of crystals from aqueous solutions, the condensation of droplets in the context of cloud formation, flame synthesis of metal oxide particles or the formation of soot in hydrocarbon combustion devices. Frequently, the particles can be characterized by intrinsic properties such as the particle size, shape or charge and the distribution of values for these properties amongst a particle population is taken as an indicator for the quality, toxicity or environmental impact of the particulate product.

In the present work, we consider particle size as a representative property and develop a comprehensive model and numerical solution scheme for predicting the evolution of the size distribution associated with a particulate phase forming in a turbulent carrier flow. Physically, the evolution of the particle size distribution can be described by the population balance equation (PBE) which we incorporate into a large eddy simulation (LES) framework for turbulent reacting flows. In order to resolve the influence of turbulence on chemical reactions and particle formation, a formulation based on an evolution equation for the LES-filtered one-point, one-time probability density function (PDF) associated with the instantaneous fluid composition and particle number density distribution is developed. This forms the basis of our LES-PBE-PDF approach; its main advantage is that the LES-filtered particle size distribution can be predicted at each spatial location in the flow domain and every time instant without any restriction on the chemical or particle formation kinetics.

In view of a numerical solution scheme, we present a formulation in terms of Eulerian stochastic fields whose evolution statistically reproduces that of the joint scalar-number density PDF. For the discretization of the particle number density stochastic field equation, we develop a novel explicit adaptive grid technique which is able to accurately resolve sharp and moving features of the LES-filtered particle size distribution. This scheme is based on a space and time dependent coordinate transformation on particle size space which is explicitly marched in time. One innovative feature is an adjustment scheme for the distribution of grid points in particle size space which allows us to accommodate nucleation source terms and control the grid stretching. Our analysis demonstrates that the explicit adaptive grid method requires over an order of magnitude fewer grid points in particle size space to obtain a similar accuracy as a comparable fixed grid discretization scheme.

In a final investigation, we explore accelerating the time consuming chemical kinetics integration by implementing a high order implicit integration scheme for execution on a graphics card (GPU). This GPU implementation can be operated in conjunction with conventional solver implementations on central processing units (CPUs), yielding a notable performance benefit on desktop computer systems.

The combined LES-PBE-PDF approach is applied to model the precipitation of BaSO4 particles in a coaxial pipe mixer, the condensation of an aerosol in a developed turbulent mixing layer and the formation of soot in a turbulent, non-premixed methane-air flame. Here, predictions of the particle size distribution or its moments are compared with experimental measurements and solutions from direct numerical simulations (DNS). Our analyses and findings not only indicate the predictive capabilities of the LES-PBE-PDF approach, but also demonstrate the computational efficiency and accuracy of the numerical solution scheme.