Combustion simulation technique for reducing chemical mechanisms using look-up table of chemical equilibrium calculations: Application to CO–H2–air turbulent non-premixed flame
Introduction
A turbulent non-premixed flame is often encountered in combustion equipment such as incinerators and gasification furnaces. A combustion model is required for the turbulent non-premixed flame to estimate the chemical reaction rates in order to design equipment using computational fluid dynamics (CFD).
Many combustion models have been developed to simulate turbulent non-premixed flames, such as the eddy dissipation (ED) model [1], eddy dissipation concept (EDC) model [2], [3], laminar flamelet model [4], probability density function (PDF) model [5], linear eddy model [6] (LEM), and conditional moment closure (CMC) model [7]. The ED model can take into account the overall chemical reaction rate of one or two steps, and is sometimes used for modeling combustion equipment having a turbulent non-premixed flame [8]. The EDC, laminar flamelet, PDF, LEM, and CMC models take into consideration the detailed chemical mechanisms to predict the mass fractions of chemical species, including intermediate species such as H, O, and OH. Therefore, these models can be used to estimate the mass fraction of NOx or CO by using the detailed chemical mechanism including the intermediate species.
In recent years, simulations of complex combustion phenomena have been performed using these combustion models. For example, the simulation of a lifted CH4 flame was conducted using the large eddy simulation (LES) model and CMC model [9]; these approaches can predict the characteristics of the flow and concentration of the reactive species appearing in the lifted CH4 flame. Thermal stratification upon auto-ignition was investigated using the LEM model [10], and the simulation showed reasonable qualitative and quantitative agreement with the direct numerical simulation (DNS) data over the whole range of investigated temperature fluctuations.
However, combustion models considering detailed chemical mechanisms require considerable computational time, because the reaction calculations involve n-dimension ordinary differential equations (ODEs) that are solved according to the number of chemical species. If the computational time could be easily reduced according to the required prediction accuracy, we would be able to obtain the results more quickly. For example O is the significant species whose the mass fraction is necessary to compute the amount of NO; therefore, the accuracy of the mass fraction of O cannot be neglected. To determine the mass fraction of O with sufficient accuracy, a reduced mechanism including O must be built. Generally, a quasi-steady state or partial equilibrium is assumed when building the reduced mechanism [11].
The chemical equilibrium method [12] did not use the reaction equations; instead, the equilibrium composition of a chemical system was determined by minimizing the Gibbs free energy, which is subject to the conservation of the chemical elements involved in the combustion. The composition was obtained by solving a system of simultaneous nonlinear equations with five unknowns (one for each of the elemental species involved in that study, namely, C, H, O, and N, plus one). In another study, a partial non-premixed flame of CH4 was modeled using the vortex method in combination with the chemical equilibrium method [13]. Although this method did not use any chemical equations, the calculated temperature and main products were in good agreement with experimental results. In some cases, the data obtained from the simulation concerning the minor products disagreed with experimental results.
A combustion simulation technique based on a combination of the chemical equilibrium method with the EDC model was developed in a previous study, and was validated by simulating a H2-air turbulent non-premixed flame [14] and a CO–H2–air turbulent non-premixed flame [15]. An advantage of the technique is the ease with which a reduced chemical mechanism can be built according to the accuracy requirement for the chemical species. Thus, the technique can predict intermediate species with high accuracy when a reduced mechanism for the minor species is built. The key to this proposed technique is the incorporation of the concept of equilibrium into the chemical kinetics, which decreases the dimensionality of the chemical reaction calculation and reduces the computational time for a combustion simulation.
In this study, the technique proposed in [14], [15] was applied to the CO–H2–air turbulent non-premixed flame; the results were compared with experimental data reported by Correa and Gulati [16], as well as computational data obtained by using the EDC model. Moreover, a look-up table approach was used to obtain the chemical equilibrium values to decrease the computational time; the relation between the prediction accuracy and the computational time of the technique was also investigated. As an example of the application of the proposed technique, prediction of NO was conducted and the results are presented herein.
Section snippets
Overview of numerical procedure
FLUENT version 6.3.26 [17] was used in this study. The temperature, enthalpy, and reaction rate of chemical species were calculated by a user-defined function (UDF) in FLUENT. The UDF is a function that can be programmed to load dynamically with the FLUENT solver in order to enhance the standard features of FLUENT. Moreover, the momentum equation, turbulence model, and mass fraction equation were computed using FLUENT.
To solve the momentum equation, the velocity and pressure were coupled by
Influence of number of cells
First, we verified the influence of the number of cells in the computational grids on the numerical error, as this error needed to be decreased as much as possible to increase the prediction accuracy of the proposed technique. However, although increasing the number of cells led to a decrease in the numerical error, the computational time increased with an increase in the number of cells. Three different grids were prepared to examine the influence of the number of cells. The total number of
Conclusions
We have developed a dimension reduction technique for non-premixed flames based on a chemical equilibrium method combined with the EDC model. An advantage of the technique is the ease with which a reduced chemical mechanism can be built according to the accuracy requirement for the chemical species. To validate the model accuracy, a non-premixed CO–H2–air turbulent flame was simulated; the results obtained by the proposed technique were compared with that obtained from Correa’s experiment and
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