Presumed Beta-PDF Model for the Prediction of the NOx and CO Emissions in Combustion Chambers
Optimization by means of computational tools has been stunningly useful for different industrial furnaces. However, the complexity of the equations, the wide range of characteristic times in the process, and the difficulty to extract precise enough data to model a combustion chamber hinders the development of a strategy for the reduction of NOx and CO. The computational time required to solve all the physics that describes the system is another obstacle for the implementation of computational optimization in this field.
Therefore, a simple, computationally cheap, but highly flexible combustion model is desired. All these characteristics can be found in a presumed beta-PDF model. The main advantage of beta-PDF combustion model is that the mass fraction of the number of chemical species can be calculated by solving transport equations of mixture fraction and its variance, instead of solving transport equation for all individual chemical species. Moreover, the convergence of transport equations for mixture fraction and its variance is easier due to the absence of non-linear source term.
A simple squared-2D section with two air inlets and one fuel inlet is built as a test case. COMSOL Multiphysics® software is used for solving the system of equations. The combustion modeling in COMSOL Multiphysics® software is limited to a simple eddy dissipation model. In this study, a presumed beta-PDF combustion model is introduced in the software by means of equation-based modelling with module of COMSOL Multiphysics® and external MATLAB® functions. The balance equations for mixture fraction and its variance are derived and the results are compared with the results by the ANSYS® Fluent® software. The flow is modeled by RANS equation and standard k-ε model for closing the Reynolds stress term using a Turbulent Flow interface in COMSOL Multiphysics®. The transport equations for mixture fraction and its variance are solved using stabilized convection-diffusion equation from mathematics module. The flow computations are used as an input for the convection part of these transport equations. The presumed beta-PDF function is calculated based on the mixture fraction and its variance.
Finally, the calculations of the mass fraction of various chemical species are carried out by defining correlation functions using certain assumptions at the post-processing stage. The assumption of ‘mixed is burnt’ is considered. The NOx source term is computed based on the Zeldovich mechanism. The equilibrium values obtained from ASPEN database are used for the formation of CO. The dependency of all the variables with respect to the mixture fraction is described by a system of non-linear algebraic equations. This system was solved in MATLAB® and introduced as an interpolation function in COMSOL Multiphysics®. The computed variables are then compared with the ANSYS® Fluent®.
Gaining a proper understanding of the formation of NOx and CO and producing a reliable and flexible model are the expected results of this work. Further implementation and validation of the model with industrial furnaces will allow to use it as an optimization tool.
