Coupling the fictitious domain and sharp interface methods for the simulation of convective mass transfer around reactive particles: Towards a reactive Sherwood number correlation for dilute systems

Abstract

We suggest a reactive Sherwood number model for convective mass transfer around reactive particles in a dilute regime. The model is constructed with a simple external-internal coupling and is validated with Particle-Resolved Simulation (PRS). The PRS of reactive particle-fluid systems requires numerical methods able to handle efficiently sharp gradients of concentration and potential discontinuities of gradient concentrations at the fluid-particle interface. To simulate mass transfer from reactive catalyst beads immersed in a fluid flow, we coupled the Sharp Interface Method (SIM) to a Distributed Lagrange Multiplier/Fictious Domain (DLM/FD) two-phase flow solver. We evaluate the accuracy of our numerical method by comparison to analytic solutions and to generic test cases fully resolved by boundary fitted simulations. A previous theoretical model that couples the internal diffusion-reaction problem with the external advection-diffusion mass transfer in the fluid phase is extended to the configuration of three aligned spherical particles representative of a dilute particle-laden flow. Predictions of surface concentration, mass transfer coefficient and chemical effectiveness factor of catalyst particles are validated by DLM-FD/SIM simulations. We show that the model captures properly the effect of an internal first order chemical reaction on the overall respective reactive Sherwood number of each sphere depending on their relative positions. The proposed correlation for the reactive Sherwood number is based on an existing non-reactive Sherwood number correlation. The model can be later used in Euler/Lagrange or Euler/Euler modelling of dilute reactive particle-laden flows.