Numerical Simulation of Multicomponent Diesel Fuel Spray Surrogates Using Real-Fluid Thermodynamic Modelling

Abstract

Computational models widely employed for predicting the dispersion of fuel sprays in combustion engines suffer from well-known drawbacks associated with the utilization of case-dependent empirical phase-change models, describing the conversion of liquid into vapour during fuel injection. The present work couples the compressible Navier-Stokes and energy conservation equations with a thermodynamic closure approximation covering pressures from 0 to 2000bar and temperatures that expand from compressed liquid, vapor-liquid equilibrium to trans/supercritical mixing, and thus, cover the whole range of P-T values that diesel fuel undergoes during its injection into combustion engines. The model assumes mechanical and thermal equilibrium between the liquid, vapour and surrounding air phases and thus, it avoids utilization of case-dependent empirical phase-change models for predicting in-nozzle cavitation and vaporization of fuels. Model development is based on the recent works reported for one mono-component (n-dodecane) and extended here to consider the influence of two multicomponent diesel surrogates. Fuel properties are predicted via the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS). The tabulated thermodynamic approach proposed is based on P-T tables, providing very high accuracy across the range of conditions with only a small number of interpolation points. The developed model is validated against experimental data for the liquid and vapour penetration for the Spray A conditions reported in the Engine Combustion Network (ECN) database. Results show good agreement for three non-reacting target conditions. Then, from simulations obtained using the two multi-component fuel surrogates their effect can be quantified on spray development.

A General Predictive Methodology for Fuel-Mixture Properties Up to Supercritical Conditions

“…Alternatively, a tabulated approach can be used to mitigate the increase in computational time by calculating all thermodynamic properties and storing them inside a table in advance. This has been demonstrated in the work of Koukouvinis et al [48] and Justino et al [27] with pressure-temperature-composition (P-T-x) tables, as well as in the work of Vidal et al [16] and Kolovos et al [51] using two-dimensional density-internal energy (ρ-e) tables. However, in these publications mainly a single component fuel is used, while for the cases of multi-component fuels very limited experimental data for validation are available.…”

“…The weakness of cubic EoS like the PR [46] and the Soave-Redlich-Kwong (SRK) [47], related to calculations at HPHT conditions, are also highlighted in [32,[48][49][50]. A series of previous publications by the authors' group [16,27,43,48,51] show that the PC-SAFT can offer sufficient precision when used as thermodynamic closure in a CFD model. The use of the PC-SAFT EoS does come with a substantial computational cost, especially when the EoS is directly implemented in the CFD solver, like in the work of Rodriguez et al [24].…”

“…In [25], the proposed diesel surrogates are split into high and low compositional-accuracy surrogates, based on the number of components and the level of correlation with the target properties that they exhibit. These types of surrogates, both for diesel and gasoline, have been used in computational [16,27] as well as experimental studies [28], allowing a straightforward calculation of fuel properties and reproducibility of the study. Among the various methods available for calculating fuel properties over the wide range of pressure-temperature variation, the PC-SAFT is part of the larger Statistical Associating Fluid Theory (SAFT) EoS family and has been proven to be capable of calculating thermodynamic properties of pure substances and mixtures [29][30][31][32][33].…”