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In this paper, a fully compressible real-fluid and homogeneous equilibrium model (HEM) has been developed, in which the two-phase characteristics are obtained using a tabulated multicomponent vapor-liquid equilibrium approach. This classical HEM model consists of four balance equations posed in terms of mass density, partial species density, momentum, and internal energy (e). The thermodynamic properties of the mixture are calculated as a function of temperature, pressure and species composition (z_i) based on the Peng-Robinson equation of state. Most importantly, a bijective look-up table linking (ρ, e) and (T, P) is constructed using a computationally efficient isothermal isobaric (TPn) flash. This look-up table also includes various thermodynamic derivatives such as sound speed, heat capacity as well as the transport properties. During the simulation, all thermal and transport properties are linearly interpolated using (T, P, z_i). This tabulation approach has been successfully applied to the investigation of subcritical evaporation and transcritical mixing characteristics of spherical n-dodecane droplets in a nitrogen ambient. Primarily, an isolated droplet with uniform initial temperature is put into a moderate ambient condition (P_(amb.)=62 bar,T_(amb.)=700 K), in which it undergoes a classical evaporation process with the continuous diameter reduction. Then, the droplet is injected into a high temperature and pressure condition (P_(amb.) = 102 bar,T_(amb.) = 1200 K), in which the droplet firstly remains spherical for a while, and then deforms to an olive shape. The predicted results are shown to be in good agreement with the recent experimental findings. The thermodynamic analysis also demonstrates that the droplet has entered the two-phase regime with a diffused interface in which vapor and liquid coexist. This proves that the experimentally observed clouds around the droplet at (P_(amb.)=102 bar,T_(amb.)=1200 K) is still mainly generated by evaporation, and not due to diffusive mixing, even though the initial ambient gas is significantly above the n-dodecane critical point (P_c== 18.1 bar). The transition from the subcritical classical evaporation to the supercritical mixing regimes is also discussed in this work based on thermodynamic arguments.

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Content uploaded by Chaouki Habchi

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All content in this area was uploaded by Chaouki Habchi on Sep 12, 2019

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... Several contributions based on pre-tabulated thermodynamic closures have been presented in the literature for two-phase flow simulations. Yi et al. [59] investigated n-dodecane droplets evaporation in transcritical conditions using a three-dimensional (3D) uniform tabulation approach based on the (VLE) solver developed by [60,57]. Besides, Koukouvinis et al. [32] employed a tabulated thermodynamic approach based on (log 10 P −T ) tables to investigate the high pressure/temperature injection of n-dodecane in ECN spray A condition [1]. ...

... However, these approaches are still under investigation and their efficiency for multi-component problems is not evaluated. Therefore, the current work adopts an efficient pre-tabulation approach as initially proposed by Yi et al. [59], for binary systems. In this work, the tabulation approach is further developed to handle ternary mixtures as those encountered in dual-fuel engines, in contrast to the previous research limited to binary mixtures tabulation. ...

... This behavior is due to the multi-component mixture critical point variation compared to that of the pure component. For instance, Yi et al. [59] have demonstrated that the transition from subcritical evaporation to diffusive mixing regime, is based on the mixture's critical point for the multi-species problem, not the pure-fuel critical point. It also implies that considering the vapor-liquid equilibrium theory is essential for the correctness of the modeling as subcritical and supercritical states may exist simultaneously based on the local temperature, pressure, and species composition [24,57,35]. ...

The substitution of diesel by cleaner renewable fuels such as short-chain alcohols in dual-fuel internal combustion engines is considered an attractive solution to reduce the pollutant emissions from internal combustion engines. In this context, two-phase flow models for multi-component mixtures considering the real-fluid thermodynamics are required for further understanding the evaporation and mixing processes in transcritical conditions. The present study proposes an efficient real-fluid model (RFM) based on a two-phase, fully compressible four-equation model under mechanical and thermal equilibrium assumptions with a diffused interface and closed by a thermodynamic equilibrium tabulation approach. Compared to previous research limited to binary mixtures tabulation, the proposed pre-tabulation approach can further handle ternary mixtures using a thermodynamic table that has been coupled to the CONVERGE CFD solver. The newly developed RFM model has been applied to investigate the evaporation of an n-dodecane droplet in a mixed ambient (methanol and nitrogen) relevant to dual-fuel configuration compared to pure nitrogen ambient. The four equation model is closed by a tabulated Cubic Plus Association (CPA) and Peng-Robinson (PR) equations of state for the droplet evaporation in a mixed and single component ambient, respectively. Numerical predictions show that the n-dodecane droplet lifetime decreases monotonically with increasing the methanol ambient concentration under the considered transcritical conditions. The performed thermodynamic analysis demonstrates that the droplet follows a different thermodynamic path as a function of the methanol ambient concentration. The different mechanisms contributing to the droplet lifetime behavior under varying ambient conditions are discussed.

... Indeed, there are previous studies that have proposed various methods for tabulation, interpolation, and look-up of data [46][47][48][49][50][51][52]. Azimian et al. [48] introduced an artificial neural network model for generating the water/steam thermodynamic tables to reduce the computational expenses of solving flash calculations. ...

... In this study, a fully compressible multi-component two-phase real fluid model (RFM) [8,9,46] considering vapor liquid equilibrium (VLE) is proposed using a generalized three-dimensional (3D) tabulation method. In this method, an in-house thermodynamic library IFPEN-Carnot is used to generate the 3-D table (with T-P-Y as the axis for a binary mixture) based on various real fluid EoS. ...

... The uniform look-up table is generated based on an isothermal-isobaric flash (TPn flash) [53]. This tabulation method also improves the efficiency of the tabulation approach previously developed by Yi et al. [46] based only on the PR-EoS [8,9]. The RFM model along with the generalized 3D tabulation method was implemented in the CONVERGE solver [54]. ...

A fundamental understanding and simulation of fuel atomization, phase transition, and mixing are among the topics researchers have struggled with for decades. One of the reasons for this is that the accurate, robust, and efficient simulation of fuel jets remains a challenge. In this paper, a tabulated multi-component real-fluid model (RFM) is proposed to overcome most of the limitations and to make real-fluid simulations affordable. Essentially, a fully compressible two-phase flow and a diffuse interface approach are used for the RFM model, which were implemented in the CONVERGE solver. PISO and SIMPLE numerical schemes were modified to account for a highly coupled real-fluid tabulation approach. These new RFM model and numerical schemes were applied to the simulation of different fundamental 1-D, 2-D, and 3-D test cases to better understand the structure of subcritical and transcritical liquid–gas interfaces and to reveal the hydro-thermodynamic
characteristics of multicomponent jet mixing. The simulation of a classical cryogenic injection of liquid nitrogen coaxially with a hot hydrogen jet is performed using thermodynamic tables generated by two different equations of state: Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK). The numerical results are finally compared with available experimental data and published numerical studies with satisfactory agreement.

... To reduce the computational effort, different researchers have proposed to calculate the fluid properties before the simulation[78,[87][88][89][90][91][92]. Then, these properties are stored inside a table,and an interpolation of the updated values is carried out during the simulation. ...

In this thesis, a fully compressible real-fluid model has been developed, in which the two-phase characteristics are obtained using a tabulated vapor-
liquid equilibrium (VLE) approach. This tabulated multicomponent real-fluid model (RFM) is proposed to overcome most limitations and make real-fluid
simulations affordable. Basically, the RFM model consists of four balance equations: mass density, partial species density, momentum, and energy. The thermodynamic properties of the mixture are calculated as a function of temperature (T), pressure (P), and compositions (Y) based on different equations of state (EoS). This is carried out using the IFPEN-Carnot thermodynamic library which generates a 3D-table with (T,P,Y) as inputs. This look-up table is generated using a computationally efficient isothermal-isobaric (TPn)-flash, thereby avoiding the costlier iterative isochoric-isoenergetic (UVn)-flash employed in previous works. It specifically includes different thermodynamic outputs such as sound speed, heat capacity, and
transport properties. The RFM model, along with the 3D tabulation method, has been implemented in the CONVERGE CFD solver. All thermal and transport properties are linearly interpolated using the updated (T,P,Y) during the simulation. First, various studies have been done for the refinement, and grid in-dependency of the thermodynamic tables, especially near the
thermodynamic phase boundary using uniform and nonuniform grids. These studies have demonstrated that nonuniform grids, like octree and quadtree, is costly compared to the uniform approach. Therefore, uniform tabulation coupled with IFPEN's shared memory technique proved to be the most
appropriate approach for tabulation, for the targeted industrial studies. Next, the present work has also investigated the robustness and accuracy of the
proposed RFM model and the tabulation methodologies in conjunction with two different modified numerical schemes, a modified PISO and modified SIMPLE algorithms, adapted for the current real fluid modeling approach.
Then, the proposed RFM model has been successfully applied to different academic and industrial applications to investigate subcritical classical evaporation/condensation and transcritical mixing characteristics. Among them, two industrially important test cases for which recent experimental results are available have been simulated and analyzed to validate the RFM model.
1- Simulation of a conventional cryogenic injection of liquid nitrogen coaxially with a hot hydrogen jet was performed using thermodynamic tables generated by two different equations of state: Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK).
2- Simulation of the interaction between phase transition and turbulent fluid
dynamics for subcritical and supercritical multi-species jets using different
turbulence models including large-eddy simulations (LES Sigma and Smagorinsky) models as well as a Reynolds Averaged Navier-Stokes (RANS K-ε).
The numerical results were found to be in good agreement with the available experimental data and published numerical studies, which also showed the relevance of the LES approach associated with the Sigma model for these very complex two-phase flows. Finally, numerical results showed that the tabulation method improves the liquid-vapor equilibrium (VLE) efficiency for real fluid modeling and provides a means to study and understand the structure of subcritical and transcritical liquid-gas interfaces revealing the hydro-thermodynamic characteristics of the multicomponent jet mixture.

... We found that more than 70% of the CPU time is consumed in the thermodynamic equilibrium computation. A possible solution to address this issue is using tabulation method [70], [71]. Indeed, all the thermal properties including phase composition, speed of sound, internal energy…etc, from phase equilibrium calculation could be stored in a table prepared before the simulation starts. ...

In this article, a fully compressible two-phase flow model combined with a multi-component real-fluid phase equilibrium solver is proposed for the cavitation modelling. The model is able to simulate the dissolving process of non-condensable gas through resolving the real-fluid phase change equations. A three-dimensional cavitating nozzle test is considered to validate the suggested model. The achieved numerical results have been compared to available X-ray experiments. The results have confirmed that the model can tackle the phase transition phenomena including gas dissolving and homogeneous nucleation processes. Thus, the cavitation inception has been modelled dynamically when the fluid crosses the phase boundary from single-phase state to two-phase state and vice-versa. The effects of non-condensable gas on the cavitation inception, development and unsteadiness have been particularly analysed, based on the Large-Eddy simulations and X-ray experiments. Finally, the encountered challenges are mentioned, aiming at providing recommendations for similar researches.

Today, injection of liquid fuels at supercritical pressures is a frequently used technique to improve the efficiency of energy systems and address environmental constraints. This paper focuses on the analysis of the coupling between the hydrodynamics and thermodynamics of multi-species supercritical jets. Various phase transition phenomena, such as droplet formation process by condensation, which have been shown experimentally to significantly affect the flow and mixing dynamics of the jet, are studied. For this purpose, a tabulated multicomponent real fluid model assuming vapor-liquid equilibrium is proposed for the simulation of turbulent n-hexane jets injected with different inflow temperatures (480 K, 560 K, 600 K) into supercritical nitrogen at 5 MPa and 293 K. Numerical results are compared with available experimental data but also with published numerical studies, showing a good agreement. In addition, comparisons between different turbulence models, including the LES Sigma, Smagorinsky and RANS K − ϵ models have been performed, showing the relevance of the LES Sigma model for these very complex two-phase flows.

Whilst the physics of both classical evaporation and supercritical fluid mixing are reasonably well characterized and understood in isolation, little is known about the transition from one to the other in the context of liquid fuel systems. The lack of experimental data for microscopic droplets at realistic operating conditions impedes the development of phenomenological and numerical models. To address this issue we performed systematic measurements using high-speed long-distance microscopy, for three single-component fuels (n-heptane, n-dodecane, n-hexadecane), into gas at elevated temperatures (700–1200 K) and pressures (2–11 MPa). We describe these high-speed visualizations and the time evolution of the transition from liquid droplet to fuel vapour at the microscopic level. The measurements show that the classical atomization and vaporisation processes do shift to one where surface tension forces diminish with increasing pressure and temperature, but the transition to diffusive mixing does not occur instantaneously when the fuel enters the chamber. Rather, subcritical liquid structures exhibit surface tension in the near-nozzle region and then, after time surrounded by the hot ambient gas and fuel vapour, undergo a transition to a dense miscible fluid. Although there was clear evidence of surface tension and primary atomization for n-dodecane and n-hexadecane for a period of time at all the above conditions, n-heptane appeared to produce a supercritical fluid from the nozzle outlet when injected at the most elevated conditions (1200 K, 10 MPa). This demonstrates that the time taken by a droplet to transition to diffusive mixing depends on the pressure and temperature of the gas surrounding the droplet as well as the fuel properties. We summarise our observations into a phenomenological model which describes the morphological evolution and transition of microscopic droplets from classical evaporation through a transitional mixing regime and towards diffusive mixing, as a function of operating conditions. We provide criteria for these regime transitions as reduced pressure–temperature correlations, revealing the conditions where transcritical mixing is important to diesel fuel spray mixing.

The present paper aims at building a fast and accurate phase transition solver dedicated to unsteady multiphase flow computations. In a previous contribution (Chiapolino et al. 2017), such a solver was successfully developed to compute thermodynamic equilibrium between a liquid phase and its corresponding vapor phase. The present work extends the solver’s range of application by considering a multicomponent gas phase instead of pure vapor, a necessary improvement in most practical applications. The solver proves easy to implement compared to common iterative procedures, and allows systematic CPU savings over 50%, at no cost in terms of accuracy. It is validated against solutions based on an accurate but expensive iterative solver. Its capability to deal with cavitating, evaporating and condensing two-phase flows is highlighted on severe test problems both 1D and 2D.

A numerical parametric study was carried out for a conventional gasoline direct injection (GDI) fuel injector. The Homogeneous Relaxation Model (HRM) which is used in predicting cavitation and flash boiling point is shown to be able to predict non-flashing yet vaporizing moderately flashing and intensely flashing setups in accordance with the measurements of the pressure ration and the degree of superheat. Despite the HRM constants originally obtained for water under circumstances varying from GDI systems HRM is a desirable option for internal combustion engines whether diesel or gasoline fuel is used.

The injection, evaporation and mixing processes of hydrocarbon fuels into a supercritical environment are not yet well understood. The present paper investigated evaporation of three n-alkane fuels into nitrogen under various temperatures and pressures by molecular dynamics simulations. The emphasis was to understand at what conditions, when and how the transition from classical two-phase evaporation to one-phase diffusion-controlled mixing takes place. The reduced ambient temperature and pressure range from 0.8 to 2.4 and 0.55 to 14.3, respectively. Scaling law was explored with hopes to extend the conclusions to macroscopic systems. The dimensionless transition time from subcritical to supercritical (with respect to the liquid lifetime) was found to be independent of liquid film thickness, but it has strong dependence on ambient temperature and pressure. With higher ambient temperature and pressure, the transition occurs earlier in the liquid's lifetime. Correlations for dimensionless transition time were proposed to describe such dependence. Additionally, a threshold dimensionless transition time of 0.35 may be used to separate the subcritical-dominated regime and the supercritical-dominated regime on the P-T diagram. Lastly, the normalized liquid lifetime (by a reference lifetime and the film thickness) depends only on the ambient temperature and pressure. As pressure increases, it decreases for subcritical-dominated cases mainly because the enthalpy of vaporization reduces with increasing pressure. The trend, however, is reversed for supercritical-dominated cases where the liquid lifetime increases slightly with increasing pressure.

Isobaric, isenthalpic (PH) flash is challenging for multiphase non-isothermal flow simulation using an equation of state (EOS). This is because the number of equilibrium phases is unknown in temperature and composition space, and because the system of equations in PH flash becomes nearly degenerate for narrow-boiling fluids. The term “narrow-boiling” is used in the literature to refer to enthalpy that is sensitive to temperature.
The primary objective of this research is to develop the multiphase PH-flash algorithm integrated with stability analysis that resolves the two technical challenges mentioned above. The secondary objective is to present a new analysis of narrow-boiling behavior by coupling energy and phase behavior equations through the temperature dependency of K values. The thermodynamic model used is the Peng-Robinson EOS with the van der Waals mixing rules.
PH flash in this research is formulated by use of the tangent-plane-distance function, in which phase-split computation is integrated with phase-stability analysis. The formulated PH flash is solved by the direct-substitution algorithm with an arbitrary number of sampling compositions (NS), at which phase stability is measured during the iteration. The number of equilibrium phases is not required to be fixed in the new algorithm.
Results in case studies show that the new algorithm can robustly handle phase appearance/disappearance with narrow-boiling behavior, including the case of one degree of freedom. The algorithm becomes more robust with increasing NS because the possibility of finding all stationary points of the tangent-plane-distance function increases. However, the number of iterations required tends to increase with increasing NS because the algorithm with more sampling compositions may take more iterations for merging and adding some of the sampling compositions.
The general condition presented for narrow-boiling behavior is that the interplay between energy balance and phase behavior is significant. Two subsets of the condition are derived by analyzing the convex function whose gradient vectors consist of the Rachford-Rice equations; (i) the overall composition is near an edge of composition space, and (ii) the solution conditions (temperature, pressure, and overall composition) are near a critical point, including a critical endpoint. A special case of the first specific condition is the fluids with one degree of freedom. These conditions for narrow-boiling behavior are demonstrated in case studies.

A new quasi-dimensional multi-component vaporization model considering the finite thermal conductivity and mass diffusivity within the droplet was constructed. First, the heat flux of conduction, enthalpy diffusion, and radiation absorption in the gas phase were calculated based on the Fourier’s law, a multi-diffusion sub-model, and a simplified analytical solution, respectively. The phase equilibrium at the gas–liquid interface was calculated by the ideal and real gas approaches according to the ambient pressure. For the liquid phase, the assumption of the quadratic polynomial distributions of the temperature and component concentration within the droplet was proposed in the quasi-dimensional model. Then, the proposed vaporization model was extensively validated by the experimental measurements, and good agreements were observed. Based on the computational results, the vaporization and movement behaviors of fuel droplets under forced convection conditions were further understood. Finally, by comparing with the zero-dimensional vaporization model with uniform temperature and component concentration distributions within the droplet and the one-dimensional vaporization model with finite thermal conductivity and mass diffusivity in the radical direction of the droplet, it is found that the quasi-dimensional model agrees better with the one-dimensional model than the zero-dimensional model, especially for the conditions with high ambient temperature and velocity. Sensitivity analysis indicates that the temperature gradient within the droplet plays a significantly important role in the droplet vaporization process.

IFP-C3D: an Unstructured Parallel Solver for Reactive Compressible Gas Flow with Spray - IFP-C3D, a hexahedral unstructured parallel solver dedicated to multiphysics calculation, is being developed at IFP to compute the compressible combustion in internal engines. IFP-C3D uses an unstructured formalism, the finite volume method on staggered grids, time splitting, SIMPLE loop, sub-cycled advection, turbulent and Lagrangian spray and a liquid film model. Original algorithms and models such as the conditional temporal interpolation methodology for moving grids, the remapping algorithm,for transferring quantities on different meshes during the computation enable IFP-C3D to deal with complex moving geometries with large volume deformation induced by all moving geometrical parts (intake/exhaust valve, piston). The Van Leer and Superbee slop limiters are used for advective fluxes and the wall law for the heat transfer model. Physical models developed at IFP for combustion (ECFM gasoline combustion model and ECFM3Z for Diesel combustion model), for ignition (TKI forauto-ignition and AKTIM for spark plug ignition) and for spray modelling enable the simulation of a large variety of innovative engine configurations from non-conventional Diesel engines using for instance HCCI combustion mode, to direct injection hydrogen internal combustion engines. Large super-scalar machines up to 1000 processors are being widely used and IFP-C3D has been optimized for running on these Cluster machines. IFP-C3D is parallelized using the Message Passing Interface (MPI) library to distribute calculation over a large number of processors. Moreover, IFP-C3D uses an optimi7 d linear algebraic library to solve linear matrix systems and the METIS partitionner library to distribute the computational load equally for all meshes used during the calculation and in particular during the remap stage when new meshes are loaded. Numerical results and timing are presented to demonstrate the computational efficiency of the code.

A comprehensive analysis of multicomponent droplet vaporization at near critical conditions has been carried out. The model is based on complete time-dependent conservation equations, with a full account of variable properties and vapor-liquid interfacial thermodynamics. The influences of various high-pressure phenomena (including ambient gas solubility, property variation, thermodynamic non-ideality, and transient diffusion) on the vaporization mechanism are examined systematically. As a specific example, problems involving n-paraffin fuel droplets in nitrogen gas are studied, Results indicate that the ambient gas pressure has a profound impact on the vaporization process, especially for the conditions under which the droplet reaches its critical stale. Owing to its inability to accurately describe droplet behavior, the conventional low-pressure model may erroneously overpredict the evaporation rate significantly.

Stability analysis is suggested as a preliminary step in isothermal flash calculations, and a number of numerical methods for stability analysis based on Gibbs' tangent plane criterion are described. These methods, which are applicable for both single phase and multiphase systems, are developed mainly for Equation of State calculations using a single model for all fluid phases. Special adaptions ensuring convergence in critical regions are discussed.

A critical review of recent investigations in the realm of supercritical (and subcritical) fluid behavior is presented with the goal of obtaining a perspective on the peculiarities of high pressure observations. Experiments with drops, isolated or in groups, streams, shear and mixing layers, jets and sprays are tabulated and discussed as a precursor to forming a conceptual picture of fluid comportment. The physics of fluid behavior in the supercritical and subcritical regimes is discussed, and major differences between the observations in these two regimes are identified and explained. A variety of supercritical fluid models is then examined in the context of drop studies, and salient aspects of fluid behavior are identified. In particular, a model that has been validated with microgravity drop experiments is described and summarized; in this validated model, the differences in subcritical/supercritical comportment are interpreted in terms of lengths scales and it is this difference that is responsible for the traditional Lewis number expression no longer portraying the ratio of heat to mass transfer in supercritical fluids; instead, an effective Lewis number is recommended that gives a realistic estimate of the ratio of these length scales. Furthermore, the application of various fluid models to the description of supercritical fluid in various geometric configurations is discussed for conditions relevant to liquid rocket, Diesel and gas turbine engines. Such preliminary simulations performed with the validated fluid model have already reproduced some specific experimental features of supercritical fluid jet disintegration. Finally, comments are offered regarding future areas of research.