(131d) Simulation of Turbulent Mixing and Chemical Reaction in a Partially Stirred Reactor Using the Direct Quadrature Method of Moments

The prediction of mixing and chemical reactions in the presence of a turbulent flow field is of great importance in the chemical process industries and has been the subject of intense research. In a turbulent flow chemical reactor there are fluctuations in the flow field over a very wide range of scales while chemical reactions usually occur in the smallest time and length scales. Traditionally, stochastic methods have been used for turbulent mixing and reaction coupled with a simplified model of the turbulent flow. The stochastic model involves the solution of a pdf transport equation and particle based Monte Carlo methods have been used for its solution. In recent years Large Eddy Simulation (LES) has been widely used to simulate complex turbulent flows. A method that combines LES and the pdf transport method called the LES-Filtered Mass Density Function (LES-FMDF) appears to be a promising tool for studying the complex interactions between the turbulence and the chemical reactions in industrial reactors. However, due to the computational complexity of the method, LES-FMDF is only at the research level. For instance a very large number of computational grid cells are required for any realistic simulation of the turbulent flow and in each grid cell a number of particles have to be used to represent the pdf leading to intensive CPU and memory requirements. Recently, an efficient method for solution of the pdf transport equation called the Direct Quadrarture Method of Moments (DQMOM) has been developed. In DQMOM only a few selected moments of the pdf are evolved. An advantage of DQMOM is that it is an Eulerian method and hence is compatible with commercial CFD codes. In this study we investigate the use of Direct Quadrature Method of Moments for simulating turbulent mixing and chemical reaction in a partially stirred reactor (PaSR). A partially stirred reactor is characterized by perfect macromixing but imperfect micromixing. PaSRs are the building blocks of zone models for industrial scale chemical reactors but they can also be considered to be a single computational grid in a more detailed CFD simulation such as the LES-FMDF. We consider a two stream mixing problem of a hydrocarbon fuel and air with an Arrhenius type chemical reaction rate that is commonly used for combustion processes. We consider a single step, a two step competitive-consecutive, and a more detailed chemical reaction mechanism. For the mixing, we use two common turbulent mixing models called the Interaction by Exchange with Mean (IEM) and the Coalescence Dispersion model. We then compare the solutions obtained using DQMOM with solutions obtained using Monte Carlo simulations. Due to the exponential dependence of the chemical reaction rate, the equations for the moments are unclosed and there is some error in the DQMOM solutions. Further as the dimension of the pdf increases (for example by considering more complicated reaction mechanisms involving larger number of species), moment methods become less efficient and difficult to solve. However for simplified chemical schemes and in use with CFD models, DQMOM appears to be a very promising tool. The objective of the comparison of the Monte Carlo and DQMOM solutions is to investigate the tradeoffs inherent in both methods and attempt to provide guidelines as to when one method may be preferred over the other.