Computational fluid dynamics (CFD) modeling of turbulent reacting flows has a variety of applications, including minimizing the amount of pollutants from internal combustion engines and maximizing the selectivity of a desired product in a chemical reactor. One goal of modeling these flows is to better understand how fluid mixing affects selectivity. A transport equation for the joint composition probability density function (PDF) can be used to model for this purpose (Fox, 2003). Here, the interaction-by-exchange-with-the-mean (IEM) model is used to close the micromixing term in the joint composition PDF transport equation. Both the Conditional Quadrature Method of Moments (CQMOM) (Yuan and Fox, 2011) and the Direct Quadrature Method of Moments (DQMOM) (Fox, 2003) are used in this study to solve the joint PDF transport equation. Compared to direct numerical simulations (DNS), these two methods reduce the computational cost significantly and are applicable to simulate large-scale systems by forcing lower-order moments of a presumed PDF to be exactly preserved (Fox, 2003). Despite reducing the computational cost, statistical methods like these introduce errors that deviate from exact solutions obtained from DNS. In the past, DQMOM has been studied and found comparable results to previous methods (Zucca et al., 2007), but DQMOM introduces correction terms to the transport equations. CQMOM does not introduce these correction terms, and the optimal moments (Fox, 2008) are transported directly rather than as weights and weighted abscissas. Here, a competitive-consecutive reaction system is modeled by the PDF transport equation and solved using DQMOM-IEM and CQMOM-IEM to compare the statistical errors and computational costs of each method. The CQMOM formulation results in a robust solution algorithm for the PDF transport equation with a similar computational cost by avoiding the potentially singular correction terms arising in DQMOM-IEM (Akroyd et al., 2010).
Akroyd, J., Smith, A.J., McGlashan, L.R., Kraft, M., 2010. Numerical investigation of DQMOM-IEM as a turbulent reaction closure. Chemical Engineering Science 65, 1915–1924.
Fox, R.O., 2003. Computational Models for Turbulent Reacting Flows. Cambridge University Press.
Fox, R.O., 2008. Optimal moment sets for multivariate direct quadrature method of moments. Industrial & Engineering Chemistry Research 48, 9686–9696.
Yuan, C., Fox, R.O., 2011. Conditional quadrature method of moments for kinetic equations. Journal of Computational Physics 230, 8216–8246.
Zucca, A., Marchisio, D.L., Vanni, M., Barresi, A.A., 2007. Validation of bivariate DQMOM for nanoparticle processes simulation. AIChE Journal 53, 918–931.