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Investigation of thermodynamic state evolution, phase transition and mixing of the hydrocarbon droplet in convective supercritical environments
... 204 Considering that the system in this study is a binary ammonia-nitrogen system, it is suitable to determine 205 the mode transition time using the criterion based on the temperature-fuel mole fraction (T-x) line versus the 206 vapor-liquid equilibrium (VLE) line proposed by Mo et al [5]. The Peng-Robinson cubic equation of state 207 (PR-EoS) was used to calculate the VLE of the binary system and the critical parameters for ammonia and 208 nitrogen were shown in Table 3. PR-EoS was widely used to calculate the thermodynamic properties of 209 mixture and phase equilibria at high pressures with good reliability [30,35,36]. Recently, Vrabec et al. [37] 210 studied the VLE of ammonia with supercritical gases (Ar, CH4, H2, N2, O2). ...
... The finding indicated that forced convection may have a greater effect on the 275 diffusion mixing process than the classical evaporation process. In the previous studies [27,30], it was found 276 that the high-pressure environment has an inhibitory effect on the supercritical diffusion of fuels. Combined 277 with the above analyses, it was suggested that the negative effect of high pressure on the diffusion and mixing 278 of fuels can be improved by creating a forced convection environment in the actual high-pressure combustion 279 chamber to accelerate the mixing process of fuels. ...
... It meant that forced convection promoted the movement of ammonia molecules in the x-direction. However, 336 there was almost no difference in the trend of the average z-direction velocity component in all cases with 337 temperature, as shown in Fig. 15 364 [30] as shown in Table 5. The supercritical evaporation of n-heptane droplets in forced convective nitrogen 365 environments was simulated by Ai et al [30]. ...
Although the behavior of the supercritical transition during the evaporation of liquid fuels in engine combustion chambers has been studied by many researchers, the effects of convection on the phase transition of liquid fuel in supercritical environments have been little studied. Previous studies mainly focused on hydrocarbon fuels for supercritical evaporation, with fewer on the zero-carbon liquid ammonia fuel. Aiming at the above deficiencies, this study used molecular dynamics simulations (MD) to explore the phase transition of liquid ammonia in a nitrogen supercritical environment under forced convection conditions. The Peng-Robinson equation of state (PR-EoS) was used to calculate the vapor–liquid equilibrium of the ammonia–nitrogen system to determine the transcritical transition time of liquid ammonia under forced convection conditions. The effects of forced convection on the heat and mass transfer process and the evolution of the liquid-phase region and the vapor–liquid interface region were analyzed. It was found that forced convection can promote the mass and heat transfer process and accelerate the phase transition of liquid ammonia to some extent. Forced convection may have a greater effect on the single-phase diffusive mixing process compared to the two-phase evaporation process. The increase in the interfacial thickness under forced convection conditions is mainly attributed to the temperature increase promoted by convection. The interfacial temperature dominates the development of its thickness and the thickness is approximately linear with temperature during the diffusive mixing stage. The shear effect induced by convection has an inhibitory effect on the diffusion of ammonia molecules within the interface region along the vertical convection direction. The cases in this study indicate that forced convection may promote the transcritical transition of liquid ammonia. In addition, a dimensionless number κ was proposed to explore the possibility of scaling up the MD results to the engineering scale.
Molecular dynamics (MD) simulation is a powerful tool to reveal the microscopic characteristics of supercritical transitions. However, the accuracy of MD depends strongly on the potential model that describes the interaction forces between atoms. In this study, four commonly used potential models for long-chain n-alkanes in MD simulations are evaluated, and a hybrid model is introduced. The vaporization and phase-transition characteristics of n-alkane blended fuels with different mole fractions are then explored under a wide variety of ambient conditions by using the hybrid model. Compared to the commonly used potentials, the hybrid model shows higher accuracy for predicting the thermodynamic and transport properties. In subcritical environments, vaporization belongs to typical two-phase evaporation with a sharp gas–liquid interface. The preferential evaporation of the light-end component is obvious, and the evaporation rate of the heavy-end component is maximized after the light-end component is consumed. Under supercritical conditions, the interface dissolves rapidly, the evaporation rates for both the light- and heavy-end components increase simultaneously, and both components coexist throughout the evaporation process. Based on the maximum potential energy and evaporation rate, a new criterion for the supercritical transition is proposed. The dimensionless transition time, which reflects the proportion of the sub/supercritical stage within the lifetime, is nearly independent of the ambient temperature and fuel composition; instead, it mainly depends on the ambient pressure. Finally, an empirical formula is obtained by curve-fitting to describe the variation in the dimensionless transition time with ambient pressure.
This article describes an experimental investigation into the flame dynamics of a subscale rocket combustor operating with five shear-coaxial injectors fed with methane and oxygen. We describe three cases labeled after the thermodynamic state at which oxygen is injected into the combustor: gaseous, subcritical or transcritical, whereas methane is continuously injected at a gaseous state. We employ the backlit and OH* chemiluminescence imaging techniques to describe the oxygen atomization and flame dynamics. We provide, with high time-resolution, visualizations of the transitional dynamics of the oxygen injection across the saturation line and through the critical pressure. The Gaseous Case presents a Low-Frequency instability which manifests by an apparent flapping of the flame. The instability is analyzed by means of the Spectral Proper Orthogonal Decomposition technique to reveal the space/time coherence of the instability. It appears that the instability could lock itself inside the combustor as a result of a coupling mechanism between the 1L acoustic resonance of the oxygen feed line and a confinement-induced hydrodynamic instability of the combustion chamber. We observe another flapping instability when the oxygen is in the liquid state (Subcritical and Transcritical cases). This apparent self-induced instability seems to occur at a constant Strouhal number of St=0.051. Finally, we provide quantitative descriptions of the atomization process in terms of (i) the dynamic evolution of the liquid core length and (ii) a probabilistic characterization of the oxygen spray.
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.
Diesel spray experiments at controlled high-temperature and high-pressure conditions offer the potential for an improved understanding of diesel combustion, and for the development of more accurate CFD models that will ultimately be used to improve engine design. Several spray chamber facilities capable of high-temperature, high-pressure conditions typical of engine combustion have been developed, but uncertainties about their operation exist because of the uniqueness of each facility. For the IMEM meeting, we describe results from comparative studies using constant-volume vessels at Sandia National Laboratories and IFP. Targeting the same ambient gas conditions (900 K, 60 bar, 22.8 kg/m³, 15% oxygen) and sharing the same injector (common rail, 1500 bar, KS1.5/86 nozzle, 0.090 mm orifice diameter, n-dodecane, 363 K), we describe detailed measurements of the temperature and pressure boundary conditions at each facility, followed by observations of spray penetration, ignition, and combustion using high-speed imaging. Performing experiments at the same high-temperature, high-pressure operating conditions is an objective of the Engine Combustion Network (http://www.ca.sandia.gov/ECN/), which seeks to leverage the research capabilities and advanced diagnostics of all participants in the ECN. We expect that this effort will generate a high-quality dataset to be used for advanced computational model development at engine conditions.
The development of a new two-constant equation of state in which the attractive pressure term of the semiempirical van der Waals equation has been modified is outlined. Examples of the use of the equation for predicting the vapor pressure and volumetric behavior of single-component systems, and the phase behavior and volumetric behavior of binary, ternary, and multicomponent systems are given. The proposed equation combines simplicity and accuracy. It performs as well as or better than the Soave-Redlich-Kwong equation in all cases tested and shows its greatest advantages in the prediction of liquid phase densities.
The dynamical characteristics of the shear-driven mixing layer can be inhibited due to the variations of fluid density. In this work we expect to address this issue by increasing shear rate. Direct numerical simulations of mixing layer between two streams with different temperatures at supercritical pressure are conducted. We confirm that the turbulent characteristics of mixing layer are inhibited with increasing density ratio between the lower and upper streams, resulting in the destruction of large-scale vortex, especially at the high-density side. By increasing the velocity ratio between the two streams, however, the mixing performance is enhanced with regeneration of the hairpin vortex due to increase in mean shear. The enstrophy production thus increases due to enhancement of vortex stretching and the thermal mixing efficiency is enhanced due to the entrainment of vortical structures. Further, the streamwise spectra of the temperature fluctuations follow a slope of -3 in the viscous-diffusive range.
The emphasis of this paper is to explore the gas-liquid interface characteristics of binary-component n-alkane fuels composed of n-heptane and n-dodecane at sub/supercritical nitrogen environments, and examine the vapor-liquid equilibrium (VLE) assumption adopted in the continuum-based vaporization models using the molecular dynamics simulation. In addition, the phase transition characteristics are also revealed. The results indicate that the vaporization of the binary-component fuel follows the classical multi-component vaporization theory in subcritical environment, in which the preferential vaporization of the light-end component is obvious with distinguishing gas-liquid interface. On the contrary, in supercritical environment, the vaporization rates of light-/heavy-end components are simultaneously enhanced even in the early stage. When approaching the critical point of the heavy-end component, the solubility of the ambient gas of nitrogen in the liquid phase is greatly enhanced with the indistinguishable gas-liquid interface. The transition mechanism from VLE to non-VLE for single-component fuels is caused by the remarkable ambient gas solubility in the liquid phase and the non-ideal gas effect at high pressures. However, for binary-component fuels, it is related to the complicated interaction between the light- and heavy-end components with significant differences in the physical properties and critical points. It is also found that ambient temperature and pressure play more dominant roles in controlling the phase transition process compared to the light-end component blended ratio for the binary-component fuels.
Direct numerical simulations are performed to quantify the mixing performance of reactors commonly used for crystallization assisted by supercritical fluid above the mixture critical point. Two different reactors are tested: the semi-continuous reactor of milliliter volume range and the continuous microfluidic chip of nanoliter volume range. The current work shows that high performance computing (HPC) is a modern tool useful to analyze various designs and to quantify performances in chemical engineering. In-depth discussions on the numerical methods chosen to strike a good compromise between accuracy and CPU time are presented. Physical analysis is also conducted with an emphasis on the turbulent mixing performance of the reactors. The results show a good mixing for the supercritical technologies considered and underline the increased mixing performance of the microfluidic chip.
The mixing of fuels with oxidizer has been an increasingly interesting area of research with new engine technologiesand the need to reduce emissions, while leveraging efficiency. High-efficiency combustion systems such as diesel engines rely on elevated chamber pressures to maximize power density, producing higher output. In such systems, the fuel is injected under liquid state in a chamber filled with pressurized air at high temperatures. Theoretical calculations on the thermodynamics of fuel mixing processes under these conditions suggest that the injected liquid can undergo a transcritical change of state. Our previous experimental efforts in that regard showed through high- speed imaging that spray droplets transition to fluid parcels mixing without notable surface tension forces, supporting a transcritical process. Only mono-component fuels were used in these studies to provide full control over boundary conditions, which prevented extrapolation of the findings to real systems in which multi-component fuels are injected. Multi-component fuels add another layer of complexity, especially when detailed experiments serve model development, requiring the fuels to be well characterized. In this work, we performed high-speed microscopy in the near-field of high-pressure sprays injected into elevated temperature and pressure environments. A reference diesel fuel and several multi-component surrogates were studied and compared to single component fuels. The results support that a transition occurs under certain thermodynamic conditions for all fuels. As anticipated, the transition from classical evaporation to diffusive mixing is affected by ambient conditions, fuel properties, droplet size and velocity, as well as time scales. Analogous to previous observations made with the normal alkane sprays, the behavior of the multi-component fuels correlate well with their bulk critical properties.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.5065
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.
Mixing under supercritical conditions plays an important role in a number of industrial processes including the selective separation or fractionation of certain species from oils or hydrocarbons and determining the final particle size distribution and product quality in supercritical nanoparticle synthesis routes. This paper presents a computational study of mixing in supercritical antisolvent systems in which the enthalpy of mixing is finite. In particular we focus on the mixing of an ethanol droplet immersed in a carbon dioxide stream near and far above the critical point using computational fluid dynamics (CFD) code coupled to the Peng–Robinson equation of state and appropriate mixing rules. The result of mixing is investigated under different process conditions: immediately above, above and far above the mixture critical point, all under laminar flow conditions. We show how mixing is far from being isothermal due to the large enthalpy of mixing and that significant spatially distributed temperature deviations can result. In particular, the mass and heat transfer in the droplet boundary layer exhibit large temperature gradients. Besides, this local heating/cooling may be responsible for the onset of a two-phase flow under the conditions studied; a phenomenon revealed experimentally in recent studies. Two different modes of mixing between the droplet and free stream, called “deformation” and “stripping”, are observed for the cases under study. The mixing pattern depends on the Reynolds number and significant droplet deformation is observed as the convective velocity is increased and the vorticity forming in the boundary layer between the droplet and the flow accumulates in the wake region. Our results confirm previous observations, highlighting the fact that mixing is a crucial step in nanoparticle precipitation under supercritical conditions (supercritical particle synthesis, rapid expansion of supercritical solutions, supercritical antisolvent processes, etc.) due to its effect on particle size and morphology.
Atomization and mixing of sprays are key parameters to successfully describe and predict combustion in direct-injection engines. Understanding these processes at the conditions most relevant to engines (high pressures and temperatures) is of primary interest. The present work investigates the atomization and mixing processes of sprays injected into environments with progressively higher pressure and temperature. An Engine Combustion Network Spray A single-hole injector is used to inject n-dodecane fuel into an optically accessible combustion chamber. High-speed imaging is performed using long-distance microscopy and diffused back-illumination to resolve ligament structures and droplets in the near-nozzle region. A unique aspect of this study is the application of high-speed imaging of sprays in the near-field under realistic diesel conditions, particularly those near top-dead-center. Imaging showed droplet and ligament dynamics at low pressure and temperature, but not at high pressure and temperature typical of engine operation, indicating diminished effects of surface tension. Relating the ambient conditions to the fuel critical pressure and temperature showed that when the ambient conditions are slightly above the critical point of the fuel, surface tension remains in effect at gas-liquid interfaces. However, for higher pressure and temperature conditions, the surface tension appears to diminish significantly as expected for supercritical fuel-air mixtures. Published by Elsevier Ltd.
Direct numerical simulations (DNS) of a supercritical temporal mixing layer are conducted for the purpose of exploring the characteristics of high-pressure transitional mixing behaviour. The conservation equations are formulated according to fluctuation-dissipation (FD) theory, which is consistent with non-equilibrium thermodynamics and converges to kinetic theory in the low-pressure limit. According to FD theory, complementing the low-pressure typical transport properties (viscosity, diffusivity and thermal conductivity), the thermal diffusion factor is an additional transport property which may play an increasingly important role with increasing pressure. The Pengspecies PDFs are well correlated, meaning that their joint PDF is not properly approximated by the product of their marginal PDFs; this indicates that the traditional reactive flow modelling based on replacing the joint PDF representing the reaction rate by the product of the marginal PDFs is not appropriate. Finally, the subgrid-scale temperature–species PDFs are also well correlated, and the species PDF exhibits important departures from the Gaussian. These results suggest that classic PDFs used in atmospheric pressure flows would not capture the physics of this supercritical mixing layer, either in an assumed PDF model at the larger scale, or at the subgrid scale.
Prior work on an engine combustion network Diesel fuel injector led to the conclusion that under Diesel engine conditions (combustion chamber pressure and temperature) the jet was transitionally supercritical; meaning that the core of the jet would be condensed liquid while the edge of the jet would be supercritical. We report initial experiments aimed at observing the thickened turbulent mixing layer that would result if the jet were transitionally supercritical. We have applied ballistic imaging to the same Diesel fuel injector, under similar conditions, and we find that the images do indicate a structural change when going from subcritical to supercritical conditions. Under subcritical conditions we observe a well-defined liquid/gas interface, surface wave structure, and formation of ligaments and voids. Under supercritical conditions the interface transitions into a continuous, turbulent mixing layer. Images of this layer include the cellular structure characteristic of gas jets. These changes are consistent with experimental literature on cryogenic supercritical jets and with DNS modeling of supercritical mixing layers.
A theory that explains the operating pressures where liquid injection
processes transition from exhibiting classical two-phase spray
atomization phenomena to single-phase diffusion-dominated mixing is
presented. Imaging from a variety of experiments have long shown that
under certain conditions, typically when the pressure of the working
fluid exceeds the thermodynamic critical pressure of the liquid phase,
the presence of discrete two-phase flow processes become diminished.
Instead, the classical gas-liquid interface is replaced by
diffusion-dominated mixing. When and how this transition occurs,
however, is not well understood. Modern theory still lacks a physically
based model to quantify this transition and the precise mechanisms that
lead to it. In this paper, we derive a new model that explains how the
transition occurs in multicomponent fluids and present a detailed
analysis to quantify it. The model applies a detailed property
evaluation scheme based on a modified 32-term Benedict-Webb-Rubin
equation of state that accounts for the relevant real-fluid
thermodynamic and transport properties of the multicomponent system.
This framework is combined with Linear Gradient Theory, which describes
the detailed molecular structure of the vapor-liquid interface region.
Our analysis reveals that the two-phase interface breaks down not
necessarily due to vanishing surface tension forces, but due to
thickened interfaces at high subcritical temperatures coupled with an
inherent reduction of the mean free molecular path. At a certain point,
the combination of reduced surface tension, the thicker interface, and
reduced mean free molecular path enter the continuum length scale
regime. When this occurs, inter-molecular forces approach that of the
multicomponent continuum where transport processes dominate across the
interfacial region. This leads to a continuous phase transition from
compressed liquid to supercritical mixture states. Based on this theory,
a regime diagram for liquid injection is developed that quantifies the
conditions under which classical sprays transition to dense-fluid jets.
It is shown that the chamber pressure required to support
diffusion-dominated mixing dynamics depends on the composition and
temperature of the injected liquid and ambient gas. To illustrate the
method and analysis, we use conditions typical of diesel engine
injection. We also present a companion set of high-speed images to
provide experimental validation of the presented theory. The basic
theory is quite general and applies to a wide range of modern propulsion
and power systems such as liquid rockets, gas turbines, and
reciprocating engines. Interestingly, the regime diagram associated with
diesel engine injection suggests that classical spray phenomena at
typical injection conditions do not occur.
Evaporation of stagnant (zero relative velocity) as well as moving spherical droplets of n-dodecane in a zero-gravity and high pressure nitrogen environment is modeled. The non-ideal effects, solubility of ambient gas into the liquid-phase, variable thermo-physical properties, and gas- and liquid-phase transients are included in the model. The model is quantitatively validated using published experimental data. Numerical predictions show that, for stagnant droplets at sub-critical ambient temperatures, the droplet lifetime continuously increases with pressure, while at critical temperature, the lifetime initially increases and thereafter remains almost constant. At super-critical temperatures, the lifetime decreases continuously with increasing ambient pressure and the average evaporation constant shows a local maximum at a particular ambient pressure. In the case of moving droplets, at super-critical ambient temperature, the rate of increase of average evaporation constant with ambient pressure becomes significant as the initial droplet relative velocity increases. For low initial velocities (
a b s t r a c t A droplet-in-bubble approach has been incorporated into a previously developed high-pressure droplet vaporization model to study the clustering effects on a liquid oxygen (LOX) droplet evaporating in hydrogen environments under both sub-and supercritical conditions. A broad range of ambient pressures and temperatures are considered. Results indicate that pressure exerts strong influence on droplet vaporization behaviors in a dense cluster environment. Increasing ambient pressure reduces droplet interactions and significantly decreases the droplet vaporization time. The effect of ambient temperature on droplet interactions is found to be very weak. The present study is intended to illuminate the underlying physics of droplet clustering phenomena in combustion devices.
This paper presents a model of the dispersion of a vapor fuel droplet that is suddenly set in motion in a still-gaseous environment. A time series expansion solution is developed for small times, and the solution is extended to longer times using a numerical procedure. Results were obtained for Reynolds numbers 50 and 200, showing that the initially spherical gaseous fuel droplet is extensively distorted, adopting a mushroomlike shape. It is shown that the distortion is caused by the evolution of the vorticity distribution that tends to form a ring vortex, and that the vapor mixing process is greatly enhanced around the vortex ring.
A validated comprehensive axisymmetric numerical model, which includes the high pressure transient effects, variable thermo-physical properties and inert species solubility in the liquid phase, has been employed to study the evaporation of moving n-heptane droplets within a zero-gravity nitrogen environment, for a wide range of ambient pressures and initial freestream velocities. At the high ambient temperature considered (1000 K), the evaporation constant increases with the ambient pressure. At low ambient pressure, the evaporation constant becomes almost a constant during the end of the lifetime. At high ambient pressures, the transient behavior is present throughout the droplet lifetime. The final penetration distance of a moving droplet decreases exponentially with increasing ambient pressure. The average evaporation constant increases with ambient pressure. The variation is almost linear for reduced ambient pressures smaller than approximately 2. For higher values, depending on the initial freestream velocity, the average evaporation constant either becomes a constant (at low initial freestream velocities) or it non-linearly increases (at high initial freestream velocities) with the ambient pressure. Droplet lifetime decreases with increasing ambient pressure and/or increasing initial freestream velocity.
The van der Waals equation of state is used to determine phase diagrams
for a wide variety of binary fluid mixtures. The locus of the critical
line in pressure-temperature-composition space is determined exactly by
solving a set of equations with the aid of a computer. The van der Waals
constants am and bm for the mixture depend
quadratically and linearly upon the mole fractions xi:
am = sumisumj xi
xjaij and bm =
sumixibii. Mixtures are characterized
by three non-dimensional parameters: ξ =
(b22-b11)/(b11+b22), zeta =
(a22b22-2-
a11b11-
2)/(a11b11-
2+a22b22-2) and Λ =
(a11b11-2-
2a12/b11b22+a22b22-2)/(a11b11-
2+a22b22-2). The parameter
Λ can be related to the low-temperature enthalpy of mixing and
the parameter zeta to the difference between the gas-liquid critical
pressures of the pure fluids. Most of the calculations are for molecules
of equal size (ξ = 0), but calculations for a size ratio of two (ξ
= 1/3) are also reported. Nine characteristic types of critical lines
are distinguished and these correspond to nine separate regions on a
Λ , zeta -diagram. Isobaric temperature-composition diagrams and
pressure-temperature projections are given for one example from each
region to illustrate the possible types of phase equilibrium. Special
attention is given to the details of lower critical solution temperature
behaviour (type IV) such as is found in the system methane + n-hexane,
to tricritical points (symmetrical and unsymmetrical), to azeotropy, and
to the possibility of double azeotropy. The phase diagrams calculated
from the van der Waals equation seem to account, at least qualitatively,
for all but one of the varieties of phase equilibria found in binary
fluid mixtures: the low-temperature lower critical solution points in
some highly structured aqueous solutions of alcohols and amines.
The present paper is concerned with combustion of an initially spherical kernel of cold fuel, which in a hot oxidizing atmosphere is suddenly put into motion. The investigations are within the framework of an axisymmetric geometry and the flame-sheet model. After a brief description of the aerodynamics of the burning process, including deformation and breakup of the fuel kernel, attention is focused on the study of the combustion time t′comb, which by definition is the time required to consume practically all the fuel. First, the case of zero heat release is addressed. It is found that—due to deformation and straining of isoscalar surfaces—the direct dependence of the combustion time on the magnitude of the diffusivity of heat and matter decreases rapidly as the Reynolds number, Re, is increased. In particular, the combustion time t′comb becomes independent of the magnitude of the diffusivity as soon as the Reynolds number exceeds a few hundred. In this high-Re regime, t′comb is found to be proportional to the convective time t′conv multiplied by the square root of the density ratio, Eq. (17). Next, the influence of heat release on the combustion time is studied. It is found that at high Reynolds numbers the combustion time increases with increasing heat release. This increase is found to be essentially due to the decrease of the scalar gradients, which in turn is caused by the gas expansion due to heat release. Furthermore, the effect of heat release on the vorticity distribution is studied, and the relative importance of baroclinicity and gas expansion on the vorticity production is assessed. Finally, the influence of the stoichiometry of the reaction on the combustion time is briefly discussed.
Results of a numerical investigation of droplet vaporization in a
high-pressure and temperature stagnant environment are presented.
Findings are presented for an n-hexane droplet evaporating into nitrogen
and for ambient pressures of 1-100 atm and temperatures of 500-1250 K.
The droplet lifetime dependence on ambient pressure and temperature is
predicted. At the lowest ambient temperature considered (500 K), the
droplet lifetime increases monotonically with ambient pressure. At a
higher ambient temperature of 600 K, it exhibits a maximum with ambient
pressure. At an ambient temperature of 1000 K, the droplet lifetime is
less sensitive to pressure. At even higher ambient temperatures (1250
K), it decreases monotonically with pressure. The steady-state
vaporization assumption underpredicts droplet lifetimes substantially
with increasing ambient pressure.
A comprehensive theoretical analysis has been developed to study vaporization of liquid oxygen (LOX) droplets in hydrogen over a wide range of pressure. The formulation accommodates complete sets of conservation equations for both gas and liquid phases, and accounts for variable properties, thermodynamic non-idealities, and vapor-liquid phase equilibria. The model is capable of treating the entire history of a vaporizing LOX droplet, including the thermodynamic phase transition through the critical mixing point. Various distinct high-pressure effects on the droplet behavior were investigated in depth. In particular, a parametric study of the droplet lifetime as a function of the ambient pressure, temperature, and initial droplet diameter has been conducted. The droplet lifetime exhibits a strong pressure dependence and can be correlated well with the square of the initial diameter.
The transport and dynamics of an isolated liquid oxygen (LOX) droplet in a supercritical hydrogen stream has been numerically studied based on the complete conservation equations in axisymmetric coordinates. The approach employs a unified treatment of general fluid thermodynamics and transport, and accommodates rapid variations of fluid properties in the transcritical regime. Surface tension of the droplet is ignored in consistency with the supercritical thermodynamic condition. The analysis allows for a systematic investigation into droplet behaviour over broad ranges of fluid thermodynamic states and ambient flow conditions. Detailed flow structures and transport phenomena are examined to reveal various key mechanisms underlying droplet vaporization in a supercritical forced convective environment. In addition, correlations of droplet lifetime and drag coefficient are established in terms of fluid properties, pressure, and free-stream Reynolds number.
Droplet dynamics and emission of a supercritical droplet in crossing gas stream are numerically investigated. Effects of ambient pressure and velocity of nitrogen gas on the dynamics of the supercritical oxygen droplet are parametrically examined. Unsteady conservative axisymmetric Navier-Stokes equations. in curvilinear coordinates are preconditioned and solved by dual-time stepping method. A unified property evaluation scheme based on a fundamental equation of state and extended corresponding-state principle is established to deal with thermodynamic non-idealities and transport anomalies.
At lower pressures and velocities of nitrogen cross flows, both the diffusion and the convection are important in determining the droplet dynamics. Relative flow motion causes a secondary breakup and cascading vortices, and the droplet lifetime is reduced with increasing in ambient pressure. At higher ambient pressures and velocities, however, the droplet dynamics become convection-controlled while the secondary breakup is hindered by reduced diffusivity of the oxygen. Gas-phase mixing depends on the convection and diffusion velocities in conjunction with corresponding droplet deformation and flow interaction. Supercritical droplet dynamics and emission is not similar with respect to the pressure and velocity of the ambient gas and thus provides no scale.
A comprehensive numerical model is developed to study a vaporizing n-heptane droplet in a forced convective environment under different temperature conditions, which includes high-pressure effects, liquid phase internal circulation, variable thermophysical properties, solubility of inert species into the liquid phase, and gas and liquid phase transients. Numerical predications of time histories of the dimensionless diameter square of a vaporizing fuel droplet within a zero gravity environment are in very good agreement with the micro-gravity experimental data.The numerical results show that at higher ambient pressure (such as 4 MPa) the droplet swells initially due to the heat-up of the cold droplet and its subsequent regression rate is far from following the d2-law during the early stages of droplet evaporation. However, at the ambient pressure of 0.1 MPa, the droplet swells are not obvious. The droplet presents an almost d2-law behavior in later stages of droplet evaporation for all considered pressures (up to 4 MPa). The numerical results also show that the droplet lifetime decreases with increasing ambient temperature. For example, the droplet lifetime at the ambient temperature 1200 K can be only 50–60% of the droplet lifetime at the ambient temperature 600 K. The final penetration distance of the vaporizing droplet decreases almost linearly with the ambient temperatures considered.
The ‘extended’ and ‘effective-conductivity’ droplet vaporization models developed by Abramzon and Sirignano [Abramzon B, Sirignano WA. Droplet vaporization model for spray combustion calculations. Int J Heat Mass Transfer 1989;32(9):1605–18] are generalized to take into account the contribution of thermal radiation and the temperature dependence of liquid fuel properties. The thermal radiation effect is simulated using the simplified model for thermal radiation absorption suggested by Dombrovsky and Sazhin [Dombrovsky LA, Sazhin SS. Absorption of thermal radiation in a semi-transparent spherical droplet: a simplified model. Int J Heat Fluid Flow 2003;24: 919–27]. Physical properties of liquid fuel, including density, are evaluated at the average liquid temperature and updated at each time-step. These generalized models are applied to the analysis of the vaporization process of n-decane and diesel fuel droplets injected into hot air. It is pointed out that the radiation absorption in diesel fuel is generally stronger than in n-decane, and it needs to be taken into account in modelling the combustion processes in diesel engines. Calculations of the droplet vaporization rate performed using the simplified ‘effective-conductivity’ model with the internal radiation heat source uniformly distributed show exceptionally good agreement with results obtained based on the more accurate ‘extended’ vaporization model with the non-uniform distribution of radiation absorption. This allows us to recommend using the ‘effective-conductivity’ model with uniform radiation absorption for spray combustion calculations, including applications in internal combustion engines.
The differences between subcritical liquid drop and supercritical fluid drop behavior are shown to be a direct consequence of the length scales near the fluid drop boundary. Under subcritical, evaporative high emission rate conditions, a film layer is present in the inner part of the drop surface which contributes to the unique determination of the boundary conditions; it is this film layer in conjunction with evaporation which gives to the solution its convective–diffusive character. In contrast, under supercritical conditions the boundary conditions contain a degree of arbitrariness due to the absence of a physical surface, and the solution has then a purely diffusive character. Results from simulations of a free fluid drop under no-gravity conditions are compared to microgravity experimental data from suspended, large drop experiments at high, low and intermediary temperatures and in a range of pressures encompassing the sub- and supercritical regime. Despite the difference between the conditions of the simulations and the experiments, the time rate of variation of the drop diameter square is remarkably well predicted in the linear curve regime. Consistent with the optical measurements, in the simulations the drop diameter is determined from the location of the maximum density gradient. Detailed time-wise comparisons between simulations and data show that this location is very well predicted at 0.1 MPa. As the pressure increases, the data and simulations agreement becomes good to fair, and the possible reasons for this discrepancy are discussed. Simulations are further conducted for a small drop, such as that encountered in practical applications, over a wide range of specified, constant far field pressures. Additionally, a transient pressure simulation crossing the critical point is also conducted. Results from these simulations are analyzed and major differences between the sub- and supercritical behavior are explained. In particular, it is shown that the classical calculation of the Lewis number gives erroneous results at supercritical conditions, and that an effective Lewis number previously defined gives correct estimates of the length scales for heat and mass transfer at all pressures.
This paper addresses the physiochemical mechanisms involved in transcritical and supercritical vaporization, mixing, and combustion processes in contemporary liquid-fueled propulsion and power-generation systems. Fundamental investigation into these phenomena poses an array of challenges due to the obstacles in conducting experimental measurements and numerical simulations at scales sufficient to resolve the underlying processes. In addition to all of the classical problems for multiphase chemically reacting flows, a unique set of problems arises from the introduction of thermodynamic nonidealities and transport anomalies. The situation becomes even more complex with increasing pressure because of an inherent increase in the flow Reynolds number and difficulties that arise when fluid states approach the critical mixing condition. The paper attempts to provide an overview of recent advances in theoretical modeling and numerical simulation of this subject. A variety of liquid propellants, including hydrocarbon and cryogenic fluids, under both steady and oscillatory conditions, are treated systematically. Emphasis is placed on the development of a hierarchical approach and its associated difficulties. Results from representative studies are presented to lend insight into the intricate nature of the problem.
Evaporation of an individual fuel droplet at high pressures and high temperatures has been studied experimentally under microgravity conditions. A suspended n-heptane droplet was used in the experiments at pressures in the range of 0.1–5.0 MPa and temperatures varying from 400 to 800 K. Temporal variations of the droplet diameter were measured with a computer-aided image analysis system. Microgravity conditions, which were produced by using 5-m and 110-m drop towers and parabolic flights, were employed to prevent natural convection that complicates the phenomena.It was observed that dense fuel vapor surrounded a droplet and the droplet surface became obscure at high pressures and high temperatures. The slope of the temporal variations of the squared droplet diameter initially increases but later becomes approximately constant at ambient pressures below the critical pressure of the fuel. At a pressure of 5.0 MPa and temperatures below the critical temperature, the slope becomes less in the latter half of the evaporation lifetime. The ratio of the initial heat-up time to the evaporation lifetime was used as a measure of unsteadiness of droplet evaporation. The ratio is almost independent of ambient temperature at an ambient pressure of 0.1 MPa, but, as ambient pressure is increased, its tendency to rise with ambient temperature becomes noticeable. Corrected evaporation lifetime tc decreases monotonically as ambient temperature is increased. The slope of its curve becomes steeper as ambient pressure increases. Dependence of tc on ambient pressure changes according to ambient temperature. Above 550 K, tc decreases as ambient pressure is increased. Below 450 K, tc tends to increase as ambient pressure is increased. It is suggested that there exists a certain ambient temperature at which ambient pressure has little effect on tc.
The objective of this research is to improve understanding of the combustion of binary fuel mixtures in the vicinity of the critical point. Fiber-supported droplets of mixtures of n-heptane and n-hexadecane, initially 1 mm in diameter, were burned in room-temperature air at pressures from 1 MPa to 6 MPa under free-fall microgravity conditions. For most mixtures the total burning time was observed to achieve a minimum value at pressures well above the critical pressure of either of the pure fuels. This behavior is explained in terms of critical mixing conditions of a ternary system consisting of the two fuels and nitrogen. The importance of inert-gas dissolution in the liquid fuel near the critical point is thereby re-emphasized, and nonmonotonic dependence of dissolution on initial fuel composition is demonstrated. The results provide information that can be used to estimate high-pressure burning rates of fuel mixtures.