(130c) Direct Numerical Simulation of Reactive Particulate Flows

For prediction of particulate flows in engineering scale equipment, accurate closures for fluid-solid interaction are of utmost importance. Among various simulation strategies, direct numerical simulation (DNS) models are a powerful tool to resolve all the details at the smallest relevant length scales and obtain improved correlations for interface transfer which could be applied in coarser scale models. An efficient ghost-cell based immersed boundary method is introduced to perform DNS of particulate flows. The fluid-solid coupling is achieved by implicit incorporation of the boundary conditions into the discretized momentum, species and thermal energy conservation equations of the fluid phase. Taking the advantage of a second order quadratic interpolation scheme utilized in the reconstruction procedures, the unique feature of this ghost-cell based immersed boundary method is its capability to handle mixed boundary conditions at the exact position of the particle surface.

Two important factors need to be considered in reactive particulate flows: reaction rate and heat liberation. With our ghost-cell based immersed boundary method, a surface reaction rate can be incorporated into the general mixed boundary condition to study the interplay between chemical reaction and mass transfer processes in fluid-solid systems. This is characterized by the Damköhler number changing from zero to infinity, indicating a process limited by reaction and mass transfer respectively. Since most chemical reactions have a significant heat effect, the thermal energy equation needs to be solved to determine local temperatures. The heat and mass transport is coupled through the solid temperature. Considering an exothermal chemical reaction proceeding at the exterior surface of the particles, the thermal conservation equation of individual particle is solved to offer a dynamic boundary condition for the fluid phase thermal energy equation.

Although DNS has been widely applied for studies of momentum transfer in fluid-solid flows, very few computational results are available in the field of mass and heat transfer especially in integrated reactive systems. In our work, a fixed Eulerian grid is used to solve the conservation equations for the entire computational domain, and the strength of our DNS model is demonstrated by several simulation cases of different fluid-solid systems. The first case is the unsteady mass and heat transport in a large pool of quiescent fluid, with variable reaction rates imposed at the spherical particle’s surface. The solution of solid temperature development obtained from DNS is compared with the “exact solution” obtained from a standard second-order finite difference technique. Following that, we consider a stationary spherical particle under forced convection over a range of Damköhler numbers. Using the Frössling and Ranz-Marshall empirical correlations for mass and heat transfer, respectively, the steady state temperature of the particle can be estimated. The computed temperature rise from DNS agrees well with this estimated value. The third test case is an in-line array of three spheres, the so-called three-bead reactor. A single Damköhler number , which owns the equivalent reaction and diffusion rate, is specified at the sphere surface, and the influence of Reynolds number is investigated. The adiabatic temperature rise obtained from DNS is compared with the value calculated from the overall species conversion ratio of the reactor. In the last simulation case, our DNS model is applied to a dense particle array which consists of hundreds of particles distributed in a random fashion. Taking the advantages of DNS, detailed information such as cup-average temperature/concentration profile, local heat/mass transfer rate and individual particle temperature are obtained and analyzed.