Numerical Modeling of the Heterogeneous Combustion in a Micro Scale Chemical Reactor

Abstract

The concentration slip model to describe the rarefied gas effect on species diffusion in microscale chemical reactors and nanoscale structures is developed and numerically examined. First, the model is applied to a pure diffusion test case and the results are compared with the DSMC results at different Knudsen numbers. Then, the coupling between the surface catalytic reactions and the homogeneous gas phase reactions with and without flow coupling in a microscale chemical reactor is investigated using the one-step overall reaction model and the slip boundary conditions. The results show that present analytical model for concentration slip boundary condition can reasonably predict the rarefied gas effect within the slip regime; the rarefied gas effect significantly reduces the momentum, heat, and mass transfer near the wall, and thus decreases the surface reaction rate. Furthermore, it is shown that the slip effects can dramatically change the near wall temperature field and transport properties, which will yield a strong coupling between the gas phase reaction and catalytic surface reaction in microscale reactors. INTRODUCTION Modeling of reactive flows in microand nanoscale structures is gaining increasing attention due to the rapid development of micro-electro-mechanical systems (MEMS) [1-4] for power generation, hydrogen synthesis, and chemical sensors. Conventionally, investigators have been using continuum based NavierStokes equations and energy and species conservation equations to simulate gas and surface reactions. However, when the length scale of the flow approaches the mean free path of the operating fluid such as the catalytic reaction in fuel cell, there are no longer sufficient collisions between gas molecules to achieve thermodynamic equilibrium. As such, non-continuum and non-equilibrium transport processes cannot be accurately predicted without considering the rarefied gas effect. Slip models accounting for velocity and temperature have been developed to correct the numerically efficient continuum methods for nonequilibrium processes near solid boundaries [2]. The basic idea is to relax the traditional no-slip boundary to allow for the presence of slip on surface while the equations applicable to the continuum regime are retained. It is well known that slip conditions can greatly affect the energy exchange between gas and the wall [3]. It can also affect the catalytic surface reaction due to the temperature dependent Arrhenius law and transport properties. A recent study has shown that slip flow significantly affects the conversion efficiency of catalytic micro-channels [4]. Similar to the velocity, there is possibility that the species concentration near the boundary may also be very different from that at the boundary, which significantly influences the surface reaction. The rarefied gas surface reaction is also an important issue in chemical vapor deposition because many depositions are conducted at very low pressure environments. In spite of its great practical importance, to date although there are increasing studies emphasizing velocity and temperature slips in microfluidics, the concentration slip and its impact on catalytic reaction in micro and nanoscale have not been well investigated. This study is motivated by the above discussions and is aimed to develop a slip condition of species concentration for the purpose of numerical modeling of micro and nanoscale chemical structures. First, a concentration slip model is developed from the approximate solutions of the Boltzmann equation. Second, a pure diffusion problem is solved using the newly developed slip model and the results are compared with those obtained by the DSMC [5] method. Third, the impact of slip boundary conditions on the catalytic reaction is investigated using the catalytic reaction in a low pressure, two-dimensional micro channel. Finally, discussions and conclusions are made. A SLIP MODEL FOR SPECIES CONCENTRATION Slip model For a rarified gaseous flow, collision frequency between molecule and surface are comparable with that between molecules. As a result, flow cannot be considered as local thermodynamic equilibrium (LTE) any more. The degree that a gas deviates from LTE can be measured by the Knudsen number (Kn), which is defined as Kn=λ/L, where λ is the mean free path of the gas and L is the characteristic length of the physical problem. A flow with a higher Knudsen number is said 42nd AIAA Aerospace Sciences Meeting and Exhibit 5 8 January 2004, Reno, Nevada AIAA 2004-304 Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.