ABSTRACT

The objective of this paper is twofold: first, to extend the direct quadrature-based sectional method of moments (DQbSMOM), a new hybrid approach for the numerical modeling of polydisperse sprays in an Eulerian framework, recently proposed by the authors (Gumprich and Sadiki, Proceedings of ICLASS, Heidelberg, 2012), by accounting for droplet heat and mass transfer along with the evaporation process while including a joint NDF of droplet size, velocity and temperature; and second, to assess the extended approach in predicting turbulent evaporating polydisperse sprays. The DQb- SMOM combines the direct quadrature method of moments (DQMOM) with a sectional method (SM) in order to allow an increase in the total amount of DQMOM quadrature points without jeopardizing the well conditioning of the solver matrices. An increase in the total amount of quadrature points as well as an optimal discretization of the droplet size domain into sections results in a considerably higher accuracy regarding convective transport and drag. A higher accuracy is also achieved in comparison to the standard DQMOM regarding the prediction of the evaporative flux as provided by the Eulerian multisize moment model (EMSM) following Massot et al. (SIAM J. Appl. Math., vol. 70, pp. 3203−3234, 2010). The EMSM model not only accurately describes the evaporating droplet polydispersity but also allows DQMOM to be coupled with a SM, since the moment flux between two sections can be calculated. A realistic evaporation model, namely the Abramzon- Sirignano model (Abramzon and Sirignano, Int. J. Heat Mass Transfer, vol. 32, no. 9, pp. 1605-1618, 1989), is coupled to the DQbSMOM and used for the simulation of dilute evaporating spray systems, the nonreacting acetone spray jets experimentally investigated by Gounder (PhD thesis, University of Sydney, 2009). The evaluation of the complete model is successfully achieved in terms of droplet mean diameters, droplet number concentration and volume flux as well as droplet velocity components in a Reynolds-averaged Navier-Stokes (RANS) based framework.