Supercritical Transition Research Articles

A molecular dynamics study on the supercritical evaporation of liquid ammonia under forced convection conditions

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 supercritical 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 supercritical 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.

One-dimensional models for supercritical and subcritical transitions in rotating convection

One-dimensional models for supercritical and subcritical transitions in rotating convection

Response of Hydrodynamic Characteristics to Tillage-Induced Microtopography of Rill Erosion Processes under Heavy Rainfalls

Response of Hydrodynamic Characteristics to Tillage-Induced Microtopography of Rill Erosion Processes under Heavy Rainfalls

Mild-Temperature Supercritical Water Confined in Hydrophobic Metal-Organic Frameworks.

Fluids under extreme confinement show characteristics significantly different from those of their bulk counterpart. This work focuses on water confined within the complex cavities of highly hydrophobic metal-organic frameworks (MOFs) at high pressures. A combination of high-pressure intrusion-extrusion experiments with molecular dynamic simulations and synchrotron data reveals that supercritical transition for MOF-confined water takes place at a much lower temperature than in bulk water, ∼250 K below the reference values. This large shifting of the critical temperature (Tc) is attributed to the very large density of confined water vapor in the peculiar geometry and chemistry of the cavities of Cu2tebpz (tebpz = 3,3',5,5'-tetraethyl-4,4'-bipyrazolate) hydrophobic MOF. This is the first time the shift of Tc is investigated for water confined within highly hydrophobic nanoporous materials, which explains why such a large reduction of the critical temperature was never reported before, neither experimentally nor computationally.

Microscopic investigation and local standard deviation analysis of liquid propane jets in supercritical environment

To improve the thermal efficiency of engines, the temperature and pressure in the combustion chamber are continually increased, potentially reaching the critical points of the fuels. Additionally, light fuels such as liquid ammonia and propane are utilized to reduce carbon emissions. The relatively low critical temperature of light fuels facilitates their transition into a supercritical state, which greatly change the jet characteristics. To gain a deeper understanding of the supercritical transition of fuels, jets of liquid propane are investigated through high-speed microscopic imaging technology, covering subcritical to supercritical environmental conditions. Liquid propane is injected through a transparent flat nozzle to observe the internal flow states within the nozzle. For image and data processing, local standard deviation (LSD) analysis and a Residual Network (ResNet-50) model are employed to identify the structures within the mixing region. Droplets counting and frequency domain analysis are also performed to reveal the features of supercritical transition. The findings highlight the importance of mask size in the jet feature extraction. Large mask highlights large scale structures including jet surface and mixing region structures, while small mask brings about full-scale feature including droplets and all other features. A criterion for mixing regime classification based on reduced temperature (Tr) and reduced pressure (Pr) is established directly from image data using the ResNet-50 model, where a condition of Tr1.6Pr0.4 ≥ 1.067 indicates a transcritical mixing regime. Both droplet counting and frequency domain analysis corroborate this mixing regime criterion. These insights enhance our understanding of supercritical transitions and are useful for simulation verifications.

Characterization and modeling of supercritical CO2 pulse pressures: Effects of activator mass and discharge plate thickness

Utilizing a bespoke CO2 phase transition pulse pressure experimental system, we conducted pulse pressure characterization tests across various activator masses, CO2 filling pressures, and energy discharge plate thicknesses. This approach enabled us to ascertain the pulse pressure's response characteristics and variation patterns under diverse conditions. The formula for calculating the peak supercritical CO2 pulse pressure was deduced by modeling the ultimate load calculation of the clamped circular plate, and then the time-course expression of the supercritical CO2 phase transition pulse pressure and energy was carried out by introducing the time factor and taking into account the parameters of the activator mass and the thickness of the energy discharging plate. Our findings reveal a four-stage pressure evolution in the cracking tube during initiation: a gradual increase, a rapid spike, swift attenuation, and eventual negative pressure formation. The activator mass and discharge plate thickness critically influence the peak pressure's timing and magnitude. Specifically, increased activator mass hastens peak pressure onset, while a thicker discharge plate amplifies it. The errors between calculated and experimental values for peak supercritical CO2 phase transition pressure fall within −5%–5%. Furthermore, the pressure peak and arrival time model demonstrates less than 10% error compared to experimental data, affirming its strong applicability. These insights offer theoretical guidance for controlling phase transition pressure and optimizing energy in supercritical CO2 systems.

Investigation of thermodynamic state evolution, phase transition and mixing of the hydrocarbon droplet in convective supercritical environments

Liquid alkane droplets transit to supercritical fluids under supercritical conditions. However, the subsequent thermodynamic state evolution, phase transition, and mixing in this case, which directly influences combustion in actual diesel engines, need further investigation. We studied the thermodynamic state evolution, phase transition, and mixing of n-heptane droplets in supercritical laminar nitrogen streams through a set of conservation equations. Non-ideal thermodynamic and transport properties were calculated to incorporate the dramatic variation of physical properties in the supercritical regime. We focus on the effects of Reynolds number, ambient pressure, and droplet size on the thermodynamic state evolution, phase transition and mixing of droplets. Results showed that increasing the Reynolds number can accelerate the evolution of thermodynamic states, which leads to the faster transition of droplets from the liquid phase and supercritical fluids to gas-phase mixtures. With the increased Reynolds number, the phase transition rate is increased and the mixing homogeneity is improved due to the enhanced mass transfer. Caused by the negative correlation between mass transfer and ambient pressure, in higher pressure, droplets after the supercritical transition require more time to transition from supercritical fluids to vapor-phase mixtures. Increasing ambient pressure inhibited the droplet phase transition process and deteriorated the mixing homogeneity, but no significant influence was shown on the droplet dynamic evolution process. Smaller droplets transition faster from liquid phase and supercritical fluids to vapor-phase mixtures. The faster thermodynamic state evolution and faster dynamic evolution process of the smaller droplet leads to its more rapid homogeneous mixing with ambient gasses, but the mode of dynamics is independent of the droplet size.

Recognition of supercritical CO2 liquid-like and gas-like molecules based on deep neural network

So far, it is still controversial about how to divide the liquid-like and gas-like states boundary and Widom delta, since the deviation of boundaries determined by different thermodynamic criteria increases significantly when away from the critical point. For this reason, a superior method that does not rely on thermodynamic criteria to define the boundary line between liquid-like and gas-like states needs to be proposed urgently and the recent extensive use of deep neural networks in molecular dynamics simulation provides a feasible choice. The present work attempts to determine a novel phase state boundary and Widom delta of supercritical CO2 from extracting the microstructure features of subcritical vapor and liquid states in equilibrium by deep neural network coupled with molecular dynamics simulation. In addition, visualization of simulated systems containing distinct liquid-like molecule ratio πLL of supercritical CO2 is also presented as well as the radial distribution function at different states. The results show that the novel boundary is located in the middle of the Widom lines constructed by multiple thermodynamic criteria. The lower boundary T- of the novel Widom delta agrees well with the theoretical boundary constructed by pseudo-boiling theory when it is close to the critical point but starts to deviate when it is far away from the critical point, while the upper boundary T+ of that is opposite. More importantly, the novel boundary and Widom delta constructed have no pressure upper limit compared to those constructed by thermodynamic criteria, only depending on πLL, which means that the novel boundary and Widom delta can extend to the supercritical deep region. Further, the visualization and radial distribution function of simulated systems of supercritical CO2 at different states provide the persistence of a liquid-like and a gas-like transition. The work conducted here can present novel microscopic insight into supercritical phase transition and provide another available alternative to define the Widom line.

A molecular dynamics study on supercritical evaporation of ammonia droplets in multi-component environments

The evaporation characteristics of ammonia fuel droplets in single and multi-component supercritical environments were studied using molecular dynamics simulations. A new approach for determining the supercritical transition of droplet evaporation modes was proposed from the perspective of atomic pair entropy fingerprints. Some improvements of the previous pair entropy fingerprint formulas were conducted to better analyze the variations in the disorder of fuel molecules during evaporation. The transition moment of droplet evaporation under supercritical conditions was based on the degree of fuel molecular disorder within the vapor–liquid mixing layer. Then, the effects of ambient conditions on the mode transition of droplet evaporation were studied. The findings indicated that the supercritical transition would not be obvious if ambient pressure was high enough. The existence of polar molecules in the environment can accelerate the mode transition. In addition, the diffusion tendency of the ambient gas components into the droplets was investigated. It was found that polar molecules diffused more strongly into the ammonia droplet than non-polar molecules.

Experimental study on microscopic characteristics of transcritical spray for high density environment

As the power density of diesel engines increases, the in-cylinder spray process appears supercritical phase transition, but the transition boundary and judgment criteria are unclear. This study explores the supercritical phase transition of spray using a constant volume combustion chamber and a high-speed optical system, considering ambient temperatures of 700 K to 1600 K and densities of 12 kg/m3 to 22.8 kg/m3. The results show that under subcritical conditions, the droplets at the end of the spray remain spherical during the evaporation process due to the existence of surface tension, and eventually evaporate. Under supercritical conditions, the droplets begin to be spherical during the evaporation process. As time goes on, the wake appears and falls off, oscillates and deforms, and finally diffuses and disappears, which is regarded as the occurrence of supercritical phase transition. The temperature limit of supercritical phase transition decreases with the increase of ambient density, and the density limit decreases with the increase of ambient temperature. This is because as the ambient density or temperature increases, the heat absorption required to destroy the gas–liquid interface (reducing the surface tension, thickening the interface, and reducing the average free molecular path) decreases. The supercritical phase transition time is shortened with the increase of ambient temperature or ambient density. The reason is that the ambient density and temperature increase under supercritical conditions, the heat and mass transfer is accelerated, and the temperature rise of the droplet surface is accelerated. As the droplet size increases, the supercritical phase transition boundary remains unchanged, and the supercritical transition time is prolonged, which is due to the decrease of the surface volume ratio and the slow heating of the droplet.

Flow regimes and heat transfer mechanisms affecting supercritical transition in microchannels

Supercritical carbon dioxide (sCO2) exhibits unique thermophysical and transport properties, which have the potential to enhance a wide range of thermal systems. Significant property variations accompanying the pseudocritical transition preclude accurate and generalized predictions of heat transfer, particularly at the microscale. A novel method for investigating fundamental fluid flow and heat transfer mechanisms through heat transfer coefficient measurements and side-view high-speed (8000 fps) schlieren imaging was developed. Experiments are conducted in a square microchannel (Dh=500μm) at reduced pressure near unity (PR=1.05) over a range of heat and mass fluxes (qc″=1.3−82.6 Wcm−2; G=280−1380 kgm−2s−1). Non-uniform density profiles within the boundary layer and distinct, freely mixed liquid-like and gas-like packets at various stages of pseudocritical transition were observed. Three flow regimes were identified as a function of heat flux with unique convection boundary layer characteristics. Transport of liquid-like and the production of gas-like sCO2 at the wall were found to be the primary mechanisms affecting heat transfer and were quantified using a modified form of the Richardson number. The experimental approach and mechanistic insight developed herein provide a basis for high-fidelity heat transfer models for the design of supercritical fluid systems.

Decay Law of Supercritical CO2 Phase Transition-Induced Shock Waves in Rocky Media

Supercritical CO2 phase change fracturing technology has been widely used in rock engineering, with the advantages of low disturbance and no pollution. However, the phase change shock wave inevitably affects the surrounding environment, and the influence range is still unclear. In this paper, we present a computational model for the symmetric generation, propagation, and attenuation of supercritical CO2 phase transition shock waves, with the center of the borehole as the origin, based on the C–J theory. The attenuation of the shock wave in the rock medium under the influence of the type of fracturing tube, the thickness of the shear sheet, and the rock performance parameters are further analyzed. The results show that the rock stress under the action of the phase change shock wave attenuates logarithmically with the propagation distance, which correlates with the magnitude of the incident rock stress at the borehole wall. The incident rock stress decreases with the increase in the initial density of CO2 in the fracturing tube, increases linearly with the thickness of the shear sheet, and correlates with the rock wave impedance.

Restricted Phase Space Thermodynamics of Einstein-Power-Yang–Mills AdS Black Hole

We consider the thermodynamics of the Einstein-power-Yang-Mills AdS black holes in the context of the gauge-gravity duality. Under this framework, Newton's gravitational constant and the cosmological constant are varied in the system. We rewrite the thermodynamic first law in a more extended form containing both the pressure and the central charge of the dual conformal field theory, i.e., the restricted phase transition formula. A novel phenomena arises: the dual quantity of pressure is the effective volume, not the geometric one. That leads to a new behavior of the Van de Waals-like phase transition for this system with the fixed central charge: the supercritical phase transition. From the Ehrenfest's scheme perspective, we check out the second-order phase transition of the EPYM AdS black hole. Furthermore the effect of the non-linear Yang-Mills parameter on these thermodynamic properties is also investigated.

A complementarity‐based vapor‐liquid equilibrium formulation for equation‐oriented simulation and optimization

AbstractVapor‐liquid equilibrium (VLE) is a cornerstone of computer‐aided process engineering (CAPE). Embedded within process system models, VLE calculations are inherently procedural with non‐smooth behavior that frequently requires discrete decisions. Traditionally, these features resist the incorporation of VLE within efficient, large‐scale equation‐oriented (EO) process simulation and optimization strategies. On the other hand, recent reformulation of VLE models through the incorporation of complementarity constraints has broadened its scope to deal seamlessly with phase transitions and even supercritical excursions in process simulation and optimization. In this study, we extend these VLE complementarity models to EO frameworks where procedural thermodynamic property libraries are still required. Here we develop an efficient, non‐intrusive, and intuitive “square‐flash” equation system that has been implemented within the IDAES Integrated Platform (IDAES‐IP). The effectiveness of this modular approach is demonstrated on case studies for non‐ideal flash calculations and distillation optimization, with disappearing phases and supercritical transitions.

Phase behavior investigation of the vinyl toluene and poly (vinyl toluene) + co-solvents in supercritical CO2

This study's purpose is to probe the binary and ternary systems phase behavior including vinyl toluene and poly(vinyl toluene) + co-solvents in supercritical solvent i.e. supercritical CO2 respectively. The vapor + liquid phase behavior of a binary supercritical CO2 + vinyl toluene solution was investigated at five different temperatures from 313.2 K to 393.2 K, up to 20.55 MPa of pressure, and vinyl toluene liquid phase mole fractions ranging from 0.070 to 0.67. Experimental data were compared to computed values using the Peng-Robinson, and Patel-Teja cubic equations of state. At each temperature, the results demonstrated good agreement with experimental readings.The phase separation behavior of poly(vinyl toluene) [P(VT)] + monomers (vinyl toluene, dimethyl ether, toluene, xylene) solutions under supercritical CO2 was presented from 304.55 K to 434.75 K at a pressure range of 14.66–192.59 MPa with different monomer concentration ranges. P(VT) + monomers (vinyl toluene, xylene) + supercritical CO2 ternary mixture phase transition shows phase gradient region from upper critical solution temperature (UCST) to upper-lower critical solution temperature (U-LCST) region in (pressure vs temperature) diagram. Furthermore, P(VT) + monomers (dimethyl ether, toluene) + supercritical CO2 demonstrates UCST to LCST phase separation curves.

Investigation of supercritical transition and evaporation process of a hydrocarbon droplet under diesel engine-relevant conditions

Fuel spray supercritical transition in the diesel engine has been concerned widely, especially supercharged ones, however, whether the transition can significantly affect the fuel–air mixing under diesel engine-relevant conditions is an issue that still needs evaluating carefully. Thus, the transition and evaporation of individual n-heptane droplets in a nitrogen environment under various ambient conditions were investigated through a high-pressure evaporation model. The influence of ambient pressures on droplet lifetime (τlife) and evaporation rate constant (K) varies with ambient temperature. When Tr < 0.98, with increasing pressure, τlife first increases and then decreases, and K decreases. When 0.98 < Tr < 1.28, as pressure increases, τlife would increase even if K increases, because the increment of initial heat-up periods exceeds the decrease in quasi-steady evaporation periods. When Tr > 1.28, with increasing pressure, τlife decreases, and K increases. As the droplet heats up, the droplet interface is where the binary mixture would reach the critical mixing state if ambient conditions are high enough. Increasing ambient density decreases the minimum ambient temperature (Tm) required for the transition to occur. Above the Tm, transitions occur earlier with the increasing energy density of ambient gas. Increasing ambient density decreases the minimum ambient temperature required for diffusive fuel-gas mixing modes to dominate the mixing process. For droplets large enough to ignore gas–liquid interfacial thickness, the Tm required for the attainment of critical mixing states is almost independent of droplet diameter.

Supercritical transition mechanism of immiscible ethanol/hexadecane droplets

Although the properties of supercritical fluids have been significantly focused on, few studies have focused on the transition process of multicomponent fluids from the subcritical to supercritical state. Herein, the trans-critical behavior of an immiscible binary ethanol/hexadecane (EtOH/C16) droplet under supercritical nitrogen environments is analyzed for the first time using molecular dynamics. The ambient pressure (p) and ambient temperature (T) of the droplets exceed the critical conditions for both EtOH and C16. Moreover, trans-critical EtOH/C16 droplets undergo a two-stage bulging-to-shrinking process. Liquid fraction λ is introduced to quantify the structural characteristics of trans-critical fluids. Fluids inside the droplet are shown to transform from the vapor to liquid phase, signified by the increase in λ with p. Three droplet evolution types are classified based on p: micro-explosion, puffing, and mixing types. The occurrence of each trans-critical droplet evolution type is determined by the competition between the subcritical gasification of EtOH and the supercritical pseudo-boiling of C16. The supercritical transition of C16 can be detected under each condition, while that of EtOH only occurs for the mixing-type droplet evolution. Furthermore, a p–T diagram is provided to analyze the combined effect of T and p on the trans-critical droplet evolution types.

Study on mechanism of abnormal variation of n-dodecane film thickness under supercritical condition by molecular dynamic simulations

Though extensive studies have been carried out to study the supercritical transition behaviors, some key issues in the supercritical fluids have not been well understood. Recently, some researchers proposed that there is an abnormal increase of droplet diameter during the supercritical transition. However, it is unclear whether the occurrence of this abnormal increase would be affected by different definitions of vapor–liquid interface, and the underlying physics has not been unraveled. Besides, the relationship between the occurrence of supercritical transition and abnormal variation has not been clearly demonstated. In this study, the evolutions of n-dodecane film thickness are predicted by three vapor–liquid interface definitions. Although the values of film thickness are different among definitions, the evolution trends are similar, confirming the negligible effect of interface definition on the occurrence of abnormal variation. Based on the microscopic structure and thermodynamic analyses, the abnormal thickness variation is observed to occur after the supercritical transition rather than the transition instant. This is attributed to the sparse molecular distribution due to the abrupt variations of film temperature and supercritical diffusion rate.

Molecular dynamics investigation of the vaporization characteristics of n-alkane blended fuels under different ambient conditions

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.

Modified Landau model for fluids: A rethink of pseudoboiling theory for supercritical fluids

A new model based on Landau theory is proposed that can quantitatively predict the density, isobaric specific heat capacity distortions of supercritical fluids. Unifying supercritical fluids into classical Landau gas-liquid transition theory, this model gives reasonable explanations for subcritical gas-liquid transition and critical/pseudo-critical phenomena. The results indicate that as inner fluctuations diminish away from the critical point, macroscale mean field approximations are valid, although microscale inhomogeneity exists. Based on the model, disputable pseudoboiling theory is reanalyzed. The thermodynamic stabilities of the supercritical and subcritical transitions are essentially different. Although transitions between the gas-like regime and liquid-like regimes exist, the separation and coexistence of these two regimes on a macroscopic scale never occur in supercritical fluids. For most applications, supercritical fluids can be regarded as single-phase fluids with anomalous properties. In the vicinity of the critical point, the classical description is invalid as the correlation length is on the macroscopic scale.