simulation of laminar reactive mixing in micro-flows
Multi-scale and/or multi-disciplinary approach to process-product innovation
CFD & Chemical Engineering- II (T3-4b)
Keywords: laminar mixing, numerical methods, Monte Carlo
In the present investigation we discuss reliable and computationally non-expensive numerical methods for simulation of laminar reactive mixing in micro-flows. The numerical solution of advection-diffusion-reaction equations with high Péclet numbers is almost as time-consuming as a direct numerical simulation of turbulent flows with high Reynolds numbers. We discuss two main approaches which provide a solution to the above-mentioned difficulty, namely, coarse-grained modelling and Monte Carlo stochastic simulations, which can be combined with conditional moment closure (CMC) method.
Note that the advection-diffusion is a linear equation (while the Navier-Stokes equations are nonlinear) and we can use the similarity between the advection-diffusion equation and Fokker-Plank equation of a diffusive process. Then linear functionals of the solution of the advection-diffusion equation can be estimated by a Monte Carlo method and the required computational resources do not depend on Péclet number.
In the coarse-grained simulations the large scales of the concentration field are resolved by a finite-volume method. A closure assumption is used to account for the sub-grid scales. The proposed model captures the two main features of the chaotic mixing, namely, lamellar structure of the concentration field and exponential decay of the variations of the scalar.
We implement CMC for simulation of chemical reactions in laminar chaotic flows. The CMC approach predicts the expected concentration of reactive species, conditional upon the concentration of a corresponding non-reactive scalar. We first use a Monte Carlo method to calculate the evolution of the moments of a conserved scalar; we then reconstruct the corresponding probability density function and dissipation rate. Finally, the concentrations of the reactive scalars are determined. The results are compared (and show excellent agreement) with full numerical simulations of the reaction processes in a chaotic laminar flow.
Presented Tuesday 18, 16:20 to 16:40, in session CFD & Chemical Engineering- II (T3-4b).
