The composition probability density function moment variables are based on a new type of filter.
Liquid sprays are commonly used to inject fuels into combustion devices, making it important to study multicomponent (MC) two-phase flows in order to reveal their physics. “Multicomponent” is the terminology describing all fuels that are combinations of a myriad of species. Single-component simulations lack a detailed representation of the complex composition and reaction mechanisms of realistic fuels, which can contain hundreds to thousands of species. Some species may be responsible for fuel ignition, other species may be the initiators of soot formation, and yet others may be involved in surface corrosion, all of which demonstrates the importance of being able to track the multitude of species.
A new formulation has previously been developed that mitigates this problem: the fluid equations are deterministic whereas the composition equations are statistic and the composition is described statistically in terms of the molar densities. Thus, instead of tracking individual pseudo-components, this previous study used a statistical model, based on continuous thermodynamics (CT), to represent the composition by means of a probability density function (pdf) having an assumed shape. This approach considerably reduced the computational effort, since to obtain information of the type needed to predict mixing and combustion, it turns out that transport equations for only a small number of the lower moments of the pdf must be solved.
That previous formulation was valid when solving all scales of the flow, in a type of computation called direct numerical simulation (DNS). However, DNS requires very fine grids and is not practical in engineering applications where coarser grids are necessary for computational efficiency. For these engineering applications, the formulation called large eddy simulation (LES) is used instead of DNS. In LES, the larger scales are computationally resolved and the small scales, called subgrid-scales (SGSs), are modeled. A previous study deriving the LES equations showed that the SGS terms identified from the conventional methodology to derive the LES composition equations dominated the activity of all other terms, in contrast to the general assumptions of LES. Therefore, it was clear that a more adept formulation for the composition equations must be found.
In this study, a new set of equations was developed that leads to a formulation respecting the LES assumptions. To derive these LES composition equations, instead of the Favre mass density weighted filtering typically used to filter the equations, vapor partial molar density filtering is used. In this new LES formulation, the composition pdf moment variables are based on a new type of filter akin to, but different from, Favre filtering. For the SGS terms in the pdf composition equations that originate from the advective terms, the predictive capabilities of the dynamic Smagorinsky and the approximate-deconvolution-model-issued SGS models have been evaluated in an a priori analysis, and it was found that the latter showed superior capabilities compared to the former LES model for the composition equations.