Triple Point Pressure Research Articles

The effect of solid nitrogen on nucleate boiling heat transfer in a slush nitrogen pool

The nucleate boiling heat transfer in a slush nitrogen pool has been studied across a heat-flux range from 5 to 400 kW/m2 and a system pressure range from 12.5 kPa (triple point pressure) to 101 kPa (atmospheric pressure). The effect of solid nitrogen on the heat transfer process was found to vary with the heat flux and the pressure. Experimental results reveal that the nucleate boiling heat transfer coefficient (HTC) of slush nitrogen is higher than that of subcooled liquid nitrogen at the low heat flux, which can be attributed to the fact that the solid nitrogen particles (with their latent heat of melting) absorb heat in the thermal boundary layer and form a sharper temperature gradient near the boiling surface. However, at the high heat flux, the HTC of slush nitrogen is lower than that of subcooled liquid nitrogen, which can be attributed to the invasion and inhibition occurring between the solid nitrogen particles and the bubbles during boiling, leading to the accumulation of vapor phase with low thermal conductivity on the boiling surface, thereby the heat transfer will be suppressed. As a result, a dual effect for the nucleate boiling heat transfer in slush nitrogen can be observed. Furthermore, the critical heat flux (CHF) of slush nitrogen is obtained and compared with the CHF of subcooled liquid nitrogen. According to the CHF model, the bubble period is the dominant parameter in determining the CHF. A calibrated CHF correlation for slush nitrogen is developed based on the hypothesis that the bubble period is prolonged as the effective viscosity of slush nitrogen increases with the solid volume fraction. The CHF values of slush nitrogen with the solid volume fraction of 10%, 20% and 30% are 0.96, 0.91 and 0.84 times those of subcooled liquid nitrogen, respectively, at the pressures higher than 50 kPa. Consequently, the solid volume fraction of slush nitrogen and the degree of subcooling of subcooled liquid nitrogen are found to have opposite effects on CHF.

The Nanoscale Wetting Parameter and Its Role in Interfacial Phenomena: Phase Transitions in Nanopores.

Through analysis of the statistical mechanical equations for a thin adsorbed film (gas, liquid, or solid) on a solid substrate or confined within a pore, it is possible to express the equilibrium thermodynamic properties of the film as a function of just two dimensionless parameters: a nanoscale wetting parameter, αw, and pore width, H*. The wetting parameter, αw, is defined in terms of molecular parameters for the adsorbed film and substrate and so is applicable at the nanoscale and for films of any phase. The main assumptions in the treatment are that (a) the substrate structure is not significantly affected by the adsorbed layer and (b) the diameter of the adsorbate molecules is not very small compared to the spacing of atoms in the solid substrate. We show that different surface geometries of the substrate (e.g., slit, cylindrical, and spherical pores) and various models of wall heterogeneity can be accounted for through a well-defined correction to the wetting parameter; no new dimensionless variables are introduced. Experimental measurements are reported for contact angles for various liquids on several planar substrates and are shown to be closely correlated with the nanoscale wetting parameter. We apply this approach to phase separation in nanopores of various geometries. Molecular simulation results for the phase diagram in confinement, obtained by the flat histogram Monte Carlo method, are reported and are shown to be closely similar to experimental results for capillary condensation, melting, and the triple point. The value of the wetting parameter, αw, is shown to determine the qualitative behavior (e.g., increase vs decrease in the melting temperature, capillary condensation vs evaporation), whereas the pore width determines the magnitude of the confinement effect. The triple point temperature and pressure for the confined phase are always lower than those for the bulk phase for all cases studied.

Experimental and theoretical investigation of the dry ice sublimation temperature for varying far-field pressure and CO2 concentration

Solid carbon dioxide, also known as dry ice, is extensively used in various applications, such as cleaning large telescopes, refrigeration, spray cooling, and biological processes like cryopreservation. In standard atmospheric conditions, dry ice sublimates continuously because the triple point pressure of carbon dioxide is higher than the atmospheric pressure. While the sublimation temperature of dry ice at atmospheric pressure is widely reported in the literature to be approximately −78.5∘C, this value is only conditionally true as it refers to dry ice exposed to an ambient saturated with its vapor. In reality, dry ice is mainly utilized in an unsaturated atmosphere. This study investigates the effect of the atmosphere on the sublimation temperature of a dry ice sphere, both experimentally and theoretically. Specifically, the far-field pressure is varied from 0.6 bar to 1.3 bar in steps of 0.1 bar, and the far-field CO2 concentration is varied from 100%vol to 0%vol in steps of 20%vol. The results show that the sublimation temperature reduces and reaches a lower thermodynamic wet-bulb temperature when the far-field CO2 concentration is lowered from the previously set value at a given ambient pressure. The lowest value of the sublimation temperature, for the ambient pressure of 1 atm and 0%vol CO2 concentration, is measured to be −97.3∘C, which deviates from the commonly quoted value in the literature by approximately 19∘C. Finally, the results are presented in the form of an extended phase diagram showing the solid-vapor coexistence line for various far-field CO2 concentrations in comparison to the standard coexistence line present on the phase diagram. A mathematical model that considers heat and mass transport phenomena in the surroundings of a dry ice sphere is developed, and its predictions are found to be in encouraging agreement with the experimental results. This study provides important insights into the behavior of dry ice under different atmospheric conditions and can be useful in various industrial and scientific applications.

Performance improvement of ORC by breaking the barrier of ambient pressure

Decreasing the condensation pressure of organic Rankine cycle (ORC), which is usually limited by ambient pressure, can greatly increase the system efficiency. In this paper, the condensation pressure is extended from traditional ambient condensation to vacuum condensation. Liquefied natural gas (LNG) is used as the cold sink to generate vacuum condensation pressures between 0.001 MPa and 0.1 MPa. Nine substances with no or low flammability are chosen as the working fluids. The system main parameters are optimized with the objective of maximum exergy efficiency. The results show that the exergy efficiency of R227ea increases from 18.87% to 26.03% as the condensation pressure decreases from 0.1 MPa to 0.001 MPa. For some substances, however, their efficiencies turn to decrease as the condensation pressure is approaching 0.001 MPa and their optimal condensation pressures are different. The working fluids share the same optimal condensation temperature of around −90 °C under the studied conditions. R227ea is a generally good substance because of its higher critical temperature to match with heat source and lower triple point pressure (temperature) to reach lower condensation pressure (temperature). The condensation pressure always has opposite effect on exergy destructions of condenser and steam generator, as well as on direct expansion turbine and ORC turbine.

CO2 Liquefaction Close to the Triple Point Pressure

For vessel-based transport of liquid CO2 in carbon capture and storage chains, transport at 8 bar(a) enable significant cost reductions compared to transport at higher pressures for most transport distances and volumes. Transport at even lower pressures could further reduce the costs. There are, however, concerns related to dry ice formation and potential clogging in parts of the chain that could lead to operational issues when operating close to the triple point pressure of CO2. In this paper, results from an experimental campaign to de-risk and gain operational experience from the low-pressure CO2 liquefaction process are described. Six experiments using pure CO2 or CO2/N2 mixtures are presented. In four of the experiments, the liquid product pressure was continuously lowered until dry ice was detected and eventually clogged the system. In the final two experiments, the liquefaction process was run in steady-state at low liquefaction pressures for five hours to ensure that there is no undetected dry ice in the process that could lead to accumulation and operational issues over time. These experiments demonstrate that pure CO2 can be safely liquefied at 5.8 bar(a) and a CO2/N2 mixture can be liquefied at 6.5 bar(a) without issues related to dry ice formation.

Molecular dynamics simulation and thermodynamic model of triple point of Lennard-Jones fluid in cylindrical nanopores

Triple points of a Lennard-Jones (LJ) fluid in cylindrical nanopores were examined using molecular dynamics simulations. At higher temperatures, the LJ fluid was capillary-condensed and was in equilibrium with the vapour phase in the pore space. The freezing of capillary condensates in cylindrical nanopores upon cooling represented phase transitions from vapour–liquid coexistence to vapour–solid coexistence, which occurred at the triple point in the cylindrical nanopores. The triple-point pressures in the cylindrical nanopores were approximately one order of magnitude lower than those in the bulk. The triple-point temperatures in the cylindrical nanopores were not inversely proportional to the pore size. The intersection of the thermodynamic models of vapour–liquid and solid–liquid coexistence previously derived by the authors can represent the state of vapour–liquid–solid coexistence. The thermodynamic triple-point model in cylindrical nanopores was successfully used to predict the molecular dynamics in nanopores.

Development of a Multiphase Beryllium Equation of State and Physics-based Variations.

We construct a family of beryllium (Be) multiphase equation of state (EOS) models that consists of a baseline ("optimal") EOS and variations on the baseline to account for physics-based uncertainties. The Be baseline EOS is constructed to reproduce a set of self-consistent data and theory including known phase boundaries, the principal Hugoniot, isobars, and isotherms from diamond-anvil cell experiments. Three phases are considered, including the known hexagonal closed-packed (hcp) phase, the liquid, and the theoretically predicted high-pressure body-centered cubic (bcc) phase. Since both the high-temperature liquid and high-pressure bcc phases lack any experimental data, we carry out ab initio density functional theory (DFT) calculations to obtain new information about the EOS properties for these two regions. At extremely high temperature conditions (>87 eV), DFT-based quantum molecular dynamics simulations are performed for multiple liquid densities using the state-of-the-art Spectral Quadrature methodology in order to validate our selected models for the ion- and electron-thermal free energies of the liquid. We have also performed DFT simulations of hcp and bcc with different exchange-correlation functionals to examine their impact on bcc compressibility, which bound the hcp-bcc transition pressure to within 4 ± 0.5 Mbar. Our baseline EOS predicts the first density maximum along the Hugoniot to be 4.4-fold in compression, while the hcp-bcc-liquid triple-point pressure is predicted to be at 2.25 Mbar. In addition to the baseline EOS, we have generated eight variations to accommodate multiple sources of potential uncertainties such as (1) the choice of free-energy models, (2) differences in theoretical treatments, (3) experimental uncertainties, and (4) lack of information. These variations are designed to provide a reasonable representation of nonstatistical uncertainties for the Be EOS and may be used to assess its sensitivity to different inertial-confinement fusion capsule designs.

Mars: Quantitative Evaluation of Crocus Melting behind Boulders

Abstract The possibility of liquid water on present-day Mars has been debated for half a century. Melting is physically difficult under Martian environmental conditions, because with the total pressure of the atmosphere near the triple point pressure of water, evaporative cooling of ice is high near the melting point. Here, a suite of quantitative models is used to investigate whether melting of seasonal water frost can occur on present-day Mars. An updated and generalized parameterization is derived for the turbulent convective heat flux that results from the buoyancy of water vapor. A three-dimensional surface energy balance model is used to calculate surface temperatures; it includes terrain shadowing, self heating, and subsurface conduction. Protruding topography creates locations that experience a rapid transition from conditions where water frost accumulates to high solar energy input. Beyond the pole-facing side of a boulder, CO2 and frost can accumulate seasonally, and once the Sun reemerges and the CO2 frost disappears, the water frost is heated to near melting temperature within one or two sols. Dust contained in the CO2 frost facilitates the formation of a protective sublimation lag. Temperatures within about 10 K of the melting point are reached within one or two sols after the end of water frost accumulation. For expected sublimation lag thicknesses, evaporative cooling is not significantly reduced. Overall, melting of pure water ice is not expected under present-day Mars conditions. However, at temperatures that are readily reached, seasonal water frost can melt on a salt-rich substrate. Hence, crocus melting behind boulders can lead to the formation of brines under present-day Mars conditions.

The vapor pressure of Se and SeO2 measurement using thermogravimetric analysis

The vapor pressure data of Se and SeO2 in low temperature range are essential for the study of emission and migration of selenium from stationary sources. The vapor pressure of SeO2 at 353.2–473.2 K was measured by thermogravimetric analysis, and the corresponding pressure was 0.026–319.2 Pa. The vapor pressure of Se at 423.2–573.2 K was measured, and the corresponding pressure was 0.007–80.9 Pa. The triple point temperature and pressure of Se determined in this experiment were 491.2 ± 1 K and 2.16 ± 0.27 Pa. The extended uncertainty of temperature measurement (k = 2) was 1.86 K, and the extended relative uncertainty of pressure measurement (k = 2) was 0.128p. The vapor pressures of Se and SeO2 were fitted to Antonie equation, respectively, and compared with the available literature data.

Direct numerical simulation of sublimating ice particles

A thermodynamically consistent numerical framework for the simulation of three-dimensional sublimation processes of ice at temperatures below the triple point and low pressure is presented. To this end, a novel description of the local thermodynamic equilibrium of frozen water (ice) and a mixture of water vapour and an inert gas is derived, where anisotropic surface energy densities can be considered. A new correlation for the diffusion coefficient of water vapour in nitrogen is proposed based on equilibrium molecular dynamics simulations. The simulation results are in excellent agreement with experimentally obtained sublimation rates.

Melting probe experiments under Mars surface conditions – the influence of dust layers, CO2-ice and porosity

This paper reports about recent melting probe experiments under a pressure that is within the pressure regime at the surface of Mars. As compared to the results given in Kömle et al. (2018), the experiments were extended in several aspects: (i) A deeper ice sample was used in order to study the performance of the probe in the subsurface, (ii) dust layers were embedded inside the samples in order to study their influence on probe penetration, (iii) a surface cover of granular CO2-ice was added, in order to study the performance of the probe in the presence of dry ice, and (iv) the performance of the melting probe in a highly porous ice layer (fresh bonded snow) was studied. In addition, the case of several heating cycles, interrupted by cooling periods, was considered. The experiments demonstrated that the melting probe concept remains successful also in the presence of embedded sand and dust layers, as long as such non-volatile layers are thin, say in the order of centimetres. Under Mars pressure there is always liquid water present in the melt hole, except for the fresh bonded snow case, where the melt water is absorbed by the surrounding snow. However, because the Mars surface pressure is typically just slightly above the water triple point pressure, this water is permanently boiling and there are strong convective motions which whirl up dust particles and remove them at least partially from the hot nose region. The presence of a porous CO2-ice cover on the surface does not seriously hamper melting probe penetration, because CO2-ice is much more volatile than water ice and the probe passes such a layer very fast when heated with the same power. In fresh bonded snow, which has very high porosity, the probe penetrates correspondingly faster than in compact ice. Finally, in the last experiment, it was demonstrated explicitly that the melting probe concept works also, when heating is applied in several cycles, interrupted by periods of no active heating.

Pressure effect on magnetic phase transitions in slowly cooled NiMn1-xCrxGe

For a slowly cooled series of NiMn1-xCrxGe half-Heusler alloys (x = 0.04, 0.11, 0.18 and 0.25) the magnetostructural (P,T) phase diagrams, under hydrostatic pressure up to 13.5 kbar, were determined. At ambient pressure a magnetic (second order) transition and a structural (first order, martensitic) phase transition are observed. The temperature of the magnetic phase transition increases while the one of the structural phase transition decreases with increasing pressure. The lines of these dependences intersect at so-called triple point (PTRI, TTRI) and a magneto-structural (first order) phase transition develops with further pressure increase. The magneto-structural transition temperature decreases with increasing pressure. The value of the triple point pressure PTRI decreases with increasing Cr content, from about 8 kbar (for x = 0.04) to about 1 kbar (for x = 0.25) on heating.

Smectic phases in ionic liquid crystals

Ionic liquid crystals (ILCs) are anisotropic mesogenic molecules which carry charges and therefore combine properties of liquid crystals, e.g. the formation of mesophases, and of ionic liquids, such as low melting temperatures and tiny triple-point pressures. Previous density functional calculations have revealed that the phase behavior of ILCs is strongly affected by their molecular properties, i.e. their aspect ratio, the loci of the charges, and their interaction strengths. Here, we report new findings concerning the phase behavior of ILCs as obtained by density functional theory and Monte Carlo simulations. The most important result is the occurrence of a novel, wide smectic-A phase , at low temperature, the layer spacing of which is larger than that of the ordinary high-temperature smectic-A phase . Unlike the ordinary smectic SA phase, the structure of the phase consists of alternating layers of particles oriented parallel to the layer normal and oriented perpendicular to it.

Modelling of source term from accidental release of pressurised CO2

Abstract Storage and transportation in carbon capture and sequestration (CCS) technology involve dealing with CO2 at high pressures, which can lead to accidental releases. To assess and control risks and to calculate the minimum safe distance from tanks and pipelines to populated areas, the source term model of the leakage is extremely important, as it serves as input to model the dispersion of CO2 into the atmosphere. The modelling of high pressurised CO2 releases is relatively complex due to its thermofluidynamics particularities. Its triple point pressure is higher than the atmospheric pressure and it has a relatively high Joule–Thomson coefficient depending on the temperature and pressure conditions. Hence, it might lead to a two-phase flow and to solid formation when the depressurisation to atmospheric pressure occurs. Also, the molecular vibration of CO2 might be important in some leakage scenarios. There are several approaches in the literature which address differently the aspects of the flow, specially regarding thermal and mechanical equilibrium or non-equilibrium. The present work provides an innovative approach for the discharge calculation in accidental high pressure releases. The Homogeneous Non-Equilibrium Model (HNM) is proposed, which accounts for non-equilibrium effects regarding not only metastability but also vibrational relaxation of the molecule. It considers the possible phase transitions and dry ice formation and it is applicable to steady-flow conditions. The model was tested with experimental data from CO2PIPETRANS project, HSE experiments and Cooltrans research programme. It was found that the model works well leading to results which agree with available experimental data. The proposed source model is relatively simple to implement and it does not demand numerical effort. The discussed discharge approach for CO2 releases emerges as a good alternative to existing models.

Melting probes revisited – Ice penetration experiments under Mars surface pressure conditions

Melting probes as vehicles to explore terrestrial ice sheets have been designed and applied successfully since the early 1960’s. Later on, in the 1990’s, various proposals were made to apply such probes also as a means to explore ice sheets on other bodies of the solar system, e.g. Jupiter’s icy satellite Europa or the ice caps of Mars. For this type of subsurface probes the name cryobot has become common. We review both early developments and more recent efforts to develop probes for application in planetary environments, i.e. under low pressures and low temperatures. The current state of art as well as the pros and cons of the different concepts hitherto considered are described. While many tests with various probes have been done in terrestrial environments, experiments under low surface pressure conditions are rare. Therefore, we report here on lab tests with a simple melting probe under the range of pressure and temperature conditions that would be encountered on the surface of Mars and compare them with corresponding tests under a much lower gas pressure, possibly representative for icy satellites. The contribution of evaporation during the melting and its variation with surface pressure is also considered.All surface pressure measurements that have been performed on Mars up to now indicate a surface pressure above the water triple point pressure (612 Pa). This means that water ice always transforms into the liquid phase when warmed up to 0°C, before it evaporates into the ambient atmosphere. The temporary existence of the liquid phase around the heated tip of the cryobot allows good thermal conductance between probe and surrounding ice, which is an important pre-requisite for efficient melt penetration. Our experiments indicate that under all possible Mars surface pressures the liquid phase is present when the probe is heated up. This finding confirms experimentally that a probe as it was proposed by Paige (1992) for in situ exploration of the Mars north polar layers would work in the expected way, although the penetration velocity must be expected be lower than under Earth pressure conditions. A test with the same probe, but under an almost two orders of magnitude lower gas pressure than on Mars, still indicates the temporary existence of the liquid phase in the contact region between the probe and the surrounding ice.

The Riedel vapor pressure correlation and multi-property optimization

The Riedel vapor pressure correlation is a useful model that has been employed for decades. The shape of the temperature dependent correlation is a strong function of the value of the final coefficient (denoted as E), particularly at the low temperature end. Vapor pressure data can be accurately correlated with different values of E, but properties derived from vapor pressure are more sensitive to the value of E. Such properties include enthalpy of vaporization and liquid heat capacity. Because these three properties are linked through rigorous thermodynamic relationships (including the Clapeyron equation and the derivative of enthalpy of vaporization), a multi-property optimization is possible to obtain the value of E that will give the best thermodynamic picture for the compound. To determine the effects of the final coefficient on subsequent properties, E was varied from 1 to 6 in integer steps and for E = 0.5, and vapor pressure data were fit for several well-known compounds. These correlations were then tested to see how well they predict enthalpy of vaporization and liquid heat capacity data. The results indicate that the traditional practice of setting E = 6 rarely produces the best thermodynamic consistency, and that E = 2 is superior for many compounds. The improved vapor pressure correlations were then used to predict triple point pressures with favorable results that compare well with the literature.

Reply to “Comments on ‘MSE minus CAPE is the True Conserved Variable for an Adiabatically Lifted Parcel’”

Abstract A standard convention in moist thermodynamics, adopted by D. M. Romps and others, is to set the specific energy and entropy of dry air and liquid water to zero at the triple-point temperature and pressure. P. Marquet claims that this convention leads to physically incorrect results. To support this claim, Marquet presents numerical calculations of a lifted parcel. It is shown here that the claim is false and that the numerical calculations of Marquet are in error. In the context of a simple two-phase thermodynamic system, an analysis is presented here of the freedoms one has to choose additive constants in the definitions of energy and entropy. Many other misconceptions are corrected as well.

Nanoparticle Solvation in Polymer–CO2 Mixtures

We study the solvation of a single nanoparticle in poly(methyl methacrylate)-CO2 mixture at coexistence by using statistical classical density-functional theory. In the temperature range where there is triple-phase coexistence, the lowest solvation free energy occurs at the triple point pressure. Beyond the end point temperature of the triple line, and for particle radii less than a critical value, there is an optimal pressure in the solvation free energy, as a result of the competition between the creation of nanoparticle-fluid interface and the formation of cavity volume. The optimal pressure decreases with increasing nanoparticle radius or the strength of nanoparticle attraction with the fluid components. The critical radius can be estimated from the pressure dependence of the interfacial tension between the fluid and the particle in the limit of infinitely large particle size (i.e., planar wall).

Phase Equilibria for CO<sub>2</sub>-Ethanol Mixtures by Perturbed-Chain Statistical Associating Fluid Theory

The perturbed-chain statistical associating fluid theory (PC-SAFT) is used to correlate and predict the phase equilibria and the triple point pressure of CO2 and ethanol binary mixtures. The binary interaction parameters (kij) are regressed by fitting to the experimental data of mixtures. The vapor-liquid equilibria and liquid-liquid equilibria of the mixtures are investigated and the influence of temperature and pressure on the phase equilibria and the triple point pressures is demonstrated. Our results show that the pressure dependent kij can describe the phase equilibria of CO2- ethanol mixtures quantitatively well.

Communication: Direct determination of triple-point coexistence through cell model simulation

In simulations of fluid-solid coexistence, the solid phase is modeled as a constrained system of Wigner-Seitz cells with one particle per cell. This model, commonly referred to as the constrained cell model, is a limiting case of a more general cell model, which is formed by considering a homogeneous external field that controls the number of particles per cell and, hence, the relative stability of the solid against the fluid phase. The generalized cell model provides a link that connects the disordered, fluid phase with the ordered, solid phase. In the present work, the phase diagram of this model is investigated through multicanonical simulations at constant pressure and histogram reweighting techniques for a system of 256 Lennard-Jones particles. The simulation data are used to obtain an estimate of the triple point of the Lennard-Jones system. The triple-point pressure is found to be higher compared to previous work. The likely explanation for this discrepancy is the highly compressible nature of the gas phase.