Compressible Scalar Filtered Mass Density Function Model for High-Speed Turbulent Flows

Abstract

The scalar filtered mass density function model is further extended and employed for large-eddy simulations of high-speed turbulent mixing and reacting flows. The model is implemented through a hybrid mathematical/ computational methodology. In this methodology, the filtered compressible Navier-Stokes equations in a curvilinear coordinate system are solved with a generalized, high-order, multiblock, finite difference scheme for the turbulent velocity and pressure. However, the scalar mixing and combustion are computed with the compressible scalar filtered mass density function. The pressure effect in the energy equation, as needed in high-speed flows, is included in the filtered mass density function formulation. The new compressible large-eddy simulation/filtered mass density function model is used for the simulations of flows in a rapid compression machine, in a shock tube and in a supersonic coaxial jet. The numerical results indicate that the model is able to correctly capture the scalar mixing in compressible subsonic and supersonic turbulent flows.

Large eddy simulation of turbulent spray combustion

“…The gas phase is treated by a hybrid methodology. The compressible LES equations for velocity and pressure are solved by high-order compact finite difference methods via a grid-based Eulerian multiblock flow solver [16,51,52]. The scalar field (i.e.…”

“…Li et al [22] extended the original FMDF to two-phase flows. Banaeizadeh et al [52] included the compressibility effects in the scalar FMDF methodology.…”

Turbulent mixing in non-isothermal jet in crossflow

“…Three-dimensional filtered Navier-Stokes equations for compressible flows in a generalized curvilinear coordinates system (n; g; f) is represented in the following compact form [37,38] @JU @t…”

“…Earlier applications of the FMDF/FDF model (FDF or filtered density function is the constant-density version of the FMDF) were for fundamental problems and were focused on the development and testing of various formulations of the model. The scalar FDF was considered in Colucci et al [29], the scalar FMDF in Jaberi et al [30]; Jaberi [31]; James and Jaberi [32]; Sheikhi et al [33]; Yaldizli et al [34]; Nik et al [35]; Yilmaz et al [36]; Banaeizadeh and Jaberi [37]; Afshari et al [38]; Afshari and Jaberi [39], the velocity FDF in Gicquel et al [40], the velocity-scalar FDF in Sheikhi et al [41] and the velocity-scalar FMDF in Sheikhi et al [42]; a review of these works is provided in Givi [43] and Madnia et al [44]. The LES/FMDF used in this study is implemented via a hybrid Eulerian-Lagrangian numerical scheme.…”

Methods for Prediction of High-Speed Reacting Flows in Aerospace Propulsion

“…A number of additional cases have been simulated with LES/FDF methods including high-speed mixing [167], flows with shocks [168], and combusting flows [169][170][171][172]. One of these interesting cases considered the LES of turbulent nonreacting and reacting flow in an axisymmetric dump combustor [172].…”