Supercritical, transcritical and subcritical real-fluid mixing at high-pressure conditions using the PC-SAFT EoS

The goal of this work is to develop a new numerical framework to simulate supercritical, transcritical and subcritical injections at Diesel engine relevant conditions using a compressible density-based solver of the Navier Stokes equations, along with the conservative formulation of the energy equation. This new algorithm allows one to perform practical CFD simulations using complex EoS at affordable CPU times, and smooths-out the previously observed spurious pressure oscillations associated with fully conservative schemes when used along with real-fluid EoS. For the first time, the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS) has been coupled with the Navier-Stokes equations, energy conservation equation and vapor liquid equilibrium (VLE) calculations in a numerical algorithm. This molecular based EoS is an alternative to cubic EoS, which show low accuracy when computing the thermodynamic properties of hydrocarbons at temperatures that are typical for today’s high-pressure fuel injection systems. It only requires three empirically determined but well-known parameters (when the association term is neglected) to model the properties of a specific component without the need for extensive model calibration, as is typically the case when the NIST (REFPROP) library is utilised. Moreover, PC-SAFT can flexibly handle the thermodynamic properties of multi component mixtures for which the NIST (REFPROP) library supports only limited component combinations. One dimensional simulations (shock tube problems and advection test cases) were performed to validate the numerical framework against analytical /exact solutions. Nitrogen, n dodecane and Diesel were used as working fluids. The properties of Diesel fuel have been modelled as: multicomponent surrogates comprising of four, five, eight and nine components divided into accuracy types, depending on how closely they match the composition of real Diesel; or as a pseudo-component obtained by applying a purely predictive method based on the PC-SAFT model. Published molecular dynamic simulations have been employed to demonstrate that the algorithm properly captures the multicomponent VLE interface at high-pressure conditions. Additionally, planar two-dimensional simulations of jets of nitrogen, n-dodecane, a four component Diesel surrogate and a Diesel pseudo-component are included to demonstrate the multidimensional, multispecies and multiphase capability of the developed numerical framework