Simulation of transcritical fluid jets using the PC-SAFT EoS

The present paper describes a numerical framework to simulate transcritical and supercritical flows utilising the compressible form of the Navier–Stokes equations coupled with the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS); both conservative and quasi-conservative formulations have been tested. This molecular model is an alternative to cubic EoS which show low accuracy computing the thermodynamic properties of hydrocarbons at temperatures typical for high pressure injection systems. Liquid density, compressibility, speed of sound, vapour pressures and density derivatives are calculated with more precision when compared to cubic EoS. Advection test cases and shock tube problems are included to show the overall performance of the developed framework employing both formulations. Additionally, two-dimensional simulations of nitrogen and dodecane jets are presented to demonstrate the multidimensional capability of the developed model

CFD simulation of pseudo-diesel injections at high-load conditions employing the PC-SAFT EoS and VLE calculations

The molecular-based Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS) iscoupled with Vapor-Liquid Equilibrium (VLE) calculations in a density-based solver of the Navier-Stokes equations to perform multicomponent two-phase simulations of Diesel injections at high-pressure conditions. The PC-SAFTEoS requires three parameters, which can be fitted to experimental data or calculated using group contribution methods,to model the properties of a specific component. Therefore, there is no need for extensive model calibration, as is typically the case when the NIST library is utilised. PC-SAFT can flexibly handle the thermodynamic propertiesof multi-component mixtures for which the NIST (REFPROP) library supports only limited component combinations. Moreover, complex hydrocarbon mixtures can be modelled as a single pseudo-component knowing its number averaged molecular weight and the hydrogen-to-carbon ratio. One and two-dimensional simulations areincluded to demonstrate the multidimensional, multispecies and multiphase capability of the numerical framework

Thermodynamic modeling for numerical simulations based on the generalized cubic equation of state

We further elaborate on the generalized formulation for cubic equation of state proposed by Cismondi and Mollerup [Fluid Phase Equilib. 232 (2005)]. With this formulation all well-known cubic equations of state can be described with a certain pair of values, which allows for a generic implementation of different equations of state. Based on this generalized formulation, we derive a complete thermodynamic model for computational fluid dynamics (CFD) simulations by providing the resulting correlations for all required thermodynamic properties. For the transport properties, we employ the Chung correlations. Our generic implementation includes the often used equations of state Soave-Redlich-Kwong and Peng-Robinson and the Redlich-Kwong-Peng-Robinson (RKPR) equation of state. The first two assume a universal compressibility factor and are therefore only suitable for fluids with a matching critical compressibility. The Redlich-Kwong-Peng-Robinson overcomes this limitation by considering the equation of state parameter as function of the critical compressibility. We compare the resulting thermodynamic modeling for the three equations of state for selected fluids with each other and CoolProp reference data. As supplementary material to this paper, we provide a Python tool called real gas thermodynamic python library (realtpl). This tool can be used to evaluate and compare the results for a wide range of different fluids. Additionally, we also provide the implementation of the generalized form in OpenFOAM

Entropy scaling based viscosity predictions for hydrocarbon mixtures and diesel fuels up to extreme conditions

An entropy scaling based technique using the Perturbed-Chain Statistical Associating Fluid Theory is described for predicting the viscosity of hydrocarbon mixtures and diesel fuels up to high temperatures and high pressures. The compounds found in diesel fuels or hydrocarbon mixtures are represented as a single pseudo-component. The model is not fit to viscosity data but is predictive up to high temperatures and pressures with input of only two calculated or measured mixture properties: the number averaged molecular weight and hydrogen to carbon ratio. Viscosity is predicted less accurately when the mixture contains high concentrations of iso-alkanes and cyclohexanes. However, it is shown that predictions for these mixtures are improved by fitting a third parameter to a single viscosity data point at a chosen reference state. For hydrocarbon mixtures, viscosity is predicted with average mean absolute percent deviations (MAPDs) of 12.2% using the two-parameter model and 7.3% using the three-parameter model from 293 to 353 K and up to 1000 bar. For two different diesel fuels, viscosity is predicted with an average MAPD of 21.4% using the two-parameter model and 9.4% using the three-parameter model from 323 to 423 K and up to 3500 bar

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

Simulation of supercritical Diesel jets using the PC-SAFT EoS

A numerical framework has been developed to simulate supercritical Diesel injection using a compressible density-based solver of the Navier-Stokes equations along with the conservative formulation of the energy equation. Multi-component fuel-air mixing is simulated by considering a diffused interface approximation. The thermodynamic properties are predicted using the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) real-fluid equation of state (EoS). This molecular-based EoS requires three empirically determined but well-known parameters to model the properties of a specific component, and thus, there is no need for extensive model calibration, as is typically the case when the NIST library is utilised. Moreover, PC-SAFT can handle flexibly the thermodynamic properties of multi-component mixtures, which is an advantage compared to the NIST library, where only limited component combinations are supported. This has allowed for the properties of Diesel fuel to be modelled as surrogates comprising four, five, eight and nine components. The proposed numerical approach improves the overall computational time and overcomes the previously observed spurious pressure oscillations associated with the utilization of conservative schemes. In the absence of experimental data, advection test cases and shock tube problems are included to validate the developed framework. Finally, two-dimensional simulations of planar jets of n-dodecane and a four component Diesel surrogate are included to demonstrate the capability of the developed methodology to predict supercritical Diesel fuel mixing into air

Multiphase phenomena in Diesel fuel injection systems

Fuel Injection Equipment (FIE) are an integral component of modern Internal Combustion Engines (ICE), since they play a crucial role in the fuel atomization process and in the formation of a fuel/air combustible mixture, consequently affecting efficiency and pollutant formation. Advancements and improvements of FIE systems are determined by the complexity of the physical mechanisms taking place; the spatial scales are in the order of millimetres, flow may become locally highly supersonic, leading to very small temporal scales of microseconds or less. The operation of these devices is highly unsteady, involving moving geometries such as needle valves. Additionally, extreme pressure changes imply that many assumptions of traditional fluid mechanics, such as incompressibility, are no longer valid. Furthermore, the description of the fuel properties becomes an issue, since fuel databases are scarce or limited to pure components, whereas actual fuels are commonly hydrocarbon mixtures. Last but not least, complicated phenomena such as phase change or transition from subcritical to transcritical/supercritical state of matter further pose complications in the understanding of the operation of these devices

Numerical modelling of multiphase diesel fuel properties using the PC-SAFT equation of state and its effect on nozzle flow and cavtation under extreme pressurisation

The present work investigates the influence of properties variation of Diesel fuel in the range of injection pressures from 60MPa to 450MPa on nozzle flow and cavitation. The PC-SAFT equation of state is utilised to derive physical property predictions of a grade no.2 Diesel emissions certification fuel. Four candidate multicomponent Diesel surrogates are modelled. Density, viscosity and volatility predictions are compared to experimental data from several other Diesel fuels and against Peng Robinson. PC-SAFT calculations are performed using different sources for the pure component parameters, namely LC and GC methods. An eight-component surrogate yields the best match for Diesel properties with a combined mean absolute deviation of 7.1% from experimental data found in the literature for conditions up to 373 K and 500 MPa. The vapour-liquid equilibrium of this surrogate is then calculated with a novel algorithm, which uses as independent variables the mixture composition, density and temperature. This algorithm is based on unconstrained minimisation of the Helmholtz Free energy via a combination of the successive substitution iteration and Newton-Raphson minimisation. The reliability of two different methods presented in the existing literature is assessed for 7 different cases. The properties of the eight component surrogate are derived and put onto tables to be used in simulations. These simulations are performed on a tapered heavy-duty Diesel engine injector at a nominal fully open needle valve lift of 350μm. Two approaches have been followed: (i) a barotropic evolution and (ii) the inclusion of wall friction-induced thermal effects. Results indicate a significant increase in the mean vapour pressure of the fuel and an unprecedented decrease of cavitation volume inside the fuel injector with increasing injection pressure. This has been attributed to the shift of the pressure drop from the feed to the back pressure inside the injection hole orifice as fuel discharges. The study links friction-induced thermal effects to the preferential cavitation of the fuel components. Lighter fuel components are found to cavitate to a greater extent than heavier ones, independently of the initial fuel composition. Moreover, the final vapour cloud composition was found to differ with injection pressure, as the components within vaporise at their respective rhythm according to their molecular structure and global pressure/temperature conditions

Numerical simulations of real-gas flows with phase-equilibrium thermodynamics

Motivated by the complex physics of multi-component mixtures in strongly non-ideal, real-gas (RG) conditions reported in the field of chemical engineering, this work aims to address the behavior of multi-phase thermodynamics from a broader point of view. The focus is to evaluate the differences, as well as the possible sources of errors that would arise in a computational fluid-dynamics (CFD) simulation when conventional single-phase and multi-phase equilibrium RG thermodynamics are employed: an area of research that despite the active interest in many communities (especially CFD), has not been completely understood. Knowledge of the effects that multi-phase RG thermodynamics with the assumption of vapor-liquid equilibrium (VLE) can have on a flow dynamics is important because it establishes the relevance of the fully coupled CFD-VLE solver. In fact, this relevance may go beyond the stand-alone calculation of a multi-phase state, providing important insights about the physics that may not be captured if the single-phase assumption is invoked. This work provides an extensive study of RG mixtures from a physical and numerical point of view. The difficulties associated with their modeling are discussed in detail and solutions are provided accordingly. Emphasis is given to the occurrence and suppression of numerical noise in form of pressure oscillations that can pollute the simulation to the point that it cannot be performed. Extension of existing models to eliminate such problem is achieved by incorporating the effects of VLE thermodynamics in a consistent manner, ultimately forming a new and robust tool to investigate the physics further. The resulting model is applied to non-reacting and reacting flows in canonical setups where emphasis is devoted to the discussion of the differences and sources of errors that would occur if this multi-phase behavior is not taken into account. Results show that the different thermodynamic states reached by this advanced model can have an impact on the flow physics, especially in a non-reacting (or more in general cold) regime. In particular, the strong non-linear coupling between the VLE thermodynamics and the transport properties is identified as a key element of difference with respect to the single-phase model counterpart. These differences manifest into the occurrence of localized changes in the fluid properties (such as density) that affect the flow-field in their vicinity, causing visible discrepancies even when time-averaging is performed. Concurrently, results obtained on the reacting side and carried out (for the first time) with finite-rate kinetics suggest that any VLE formation between the products and the reactants may be considered of minor importance. The latter conclusion is supported by the analysis conducted on the multi-phase field which appears to be largely composed of the vapor solution, as expected, hence limiting the analogous effect observed the non-reacting system where a broader range of phase-separation appears instead.Ph.D