Metastable Liquid Region Research Articles

Numerical simulation and validation of a stepped capillary tube using as throttling device in residential heat pump systems

A stepped capillary tube is a new design proposed by Zhao et al. that consist of two serial-connected capillary tubes with different diameter as an alternative in order to reduce the manufacturing cost of the typical assembly of two capillary tubes and a by-pass check valve widely used to achieve different mass flow rates in residential heat pump systems.In previous works, one-dimensional numerical modeling of fluid-flow inside capillary tubes and short tube orifices were performed, and successfully validated against a wide range of mass flow rate measurements reported for different refrigerant and mixtures. In this article, the model is applied to stepped capillary tubes (expansion devices). Governing equations (continuity, momentum, energy, and entropy) for describing the fluid flow have been solved by using a fully implicit step-by-step method. A numerical treatment has been codified for considering thermodynamic and flow transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). Sudden contraction and enlargement were also considered. A comparison and validation analyses of the simulation results were carried out by using mass flow rate experimental data (No = 30), which have been recently reported in the literature for R-22. Linear relationships between mass flow rate (predicted) and experimental mass flow rate data were statistically demonstrated. Average deviation error of ±3.2% was consistently computed between numerical model and experimental data, which demonstrates the good capability of the model developed for predicting the fluid flow processes.These results demonstrate a new and robust application of the model developed to predict reliably the mass flow rate through stepped capillary tubes, which enable this tool to be reliably used for the design of this kind of systems.

Modelling of fluid flow through short tube orifices under metastable conditions: A new numerical validation approach for evaluating the mass flow rate with refrigerant mixtures (HFC-407C and HFC-410A)

In a previous work, one-dimensional numerical modelling of fluid-flow inside short tube orifices was performed, and successfully validated against a wide range of mass flow rate measurements reported for the refrigerant HFC-134a. Governing equations of continuity, momentum, energy and entropy were solved for describing the fluid flow under a wide variety of thermodynamic transitions (e.g., subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region), including sudden contraction and enlargement. In this new study, a comprehensive comparison analysis between numerical simulation data and experimental measurements obtained for HFC-407C and HFC-410A refrigerants (No = 241) to extend the applicability of the same mathematical model was carried out. Using a widespread statistical analysis, based on weighted linear regressions with an outlier detection/rejection module at 95% of confidence level, the prediction performance of the mathematical model was again assessed. Linear regressions between predicted mass flow rate data and experimental measurements were computed, and used them as a statistical comparison criterion. A statistical comparison between predicted simulation results and mass flow rate experimental data are reported. Average deviation errors of ±11.1% (for the refrigerant HFC-407C) and ±7.3% (for refrigerant HFC-410A) were found between numerical model and experimental data. These results demonstrate a new and robust application of the model to predict reliably the mass flow rate through short tube orifices under metastable conditions, which enable this tool to be reliably used for the design of short tube orifices.

Slow Molecular Dynamics in Three Organic Salts of Active Pharmaceutical Ingredients

The slow molecular mobility in three ionic liquids (ILs) that are active pharmaceutical ingredients (APIs) was studied by thermally stimulated depolarization currents (TSDC). One liquid readily crystallizes on cooling and its thermal behavior was analyzed. The other two liquids were studied in the temperature regions of the glassy state, the glass transition, and the metastable liquid. The kinetic parameters associated with the different modes of motion in these APIs were determined from the output of the TSDC experiments. Differential scanning calorimetry (DSC) was used to characterize the glass transition and analyze the thermal behavior in the metastable liquid region. The analysis of the glass transition relaxation showed that these APIs are strong glass-formers. TSDC also showed the presence in both glass-forming APIs of a relaxation in the metastable liquid, which has some features of a liquid–liquid transition and was characterized by a high intensity and a moderate cooperativity. No secondary relaxations were detected.

Estimation of the Thermodynamic Limit of Overheating for Bulk Water from Interfacial Properties

The limit of overheating or expanding is an important property of liquids, which is relevant for the design and safety assessment of processes involving pressurized liquids. In this work, the thermodynamic stability limit—the so-called spinodal—of water is calculated by molecular dynamics computer simulation, using the molecular potential model of Baranyai and Kiss. The spinodal pressure is obtained from the maximal tangential pressure within a liquid–vapor interface layer. The results are compared to predictions of various equations of state. Based on these comparisons, a set of equations of state is identified which gives reliable results in the metastable (overheated or expanded) liquid region of water down to $$-55$$ MPa.

Numerical simulation and validation of HFC-134a fluid flow through short-tube orifices considering metastable conditions

One-dimensional numerical modelling of the fluid-flow behaviour inside short-tube orifices (expansion devices) has been carried out. Governing equations (continuity, momentum, energy, and entropy) for describing the fluid flow have been solved by using a fully implicit step-by-step method. A numerical treatment has been codified for considering thermodynamic and flow transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). Sudden contraction and enlargement at inlet and outlet sections were also considered. Fluid-flow variables (e.g., enthalpies, temperatures, pressures, mass fractions, and heat fluxes) and thermophysical and transport properties of fluid were numerically evaluated at each grid point in a discretized domain. The physical model used for solving the fluid-flow problem enabled an analysis of geometry, fluid type, critical and non-critical flow conditions, metastable regions, and transient effects to be performed. A comparison and validation analyses of the simulation results were carried out by using a wide range of mass flow rate experimental data (No = 634), which have been reported in the literature for the refrigerant 134a. Using a comprehensive statistical analysis, based on weighted linear regressions with an outlier detection/rejection algorithm at 95% of confidence level, the prediction performance of the numerical model was evaluated. Linear relationships between mass flow rate (predicted) and experimental mass flow rate data were statistically demonstrated. A global statistical evaluation of deviation errors between mass flow rate experimental data and predicted simulation results was also calculated. Average deviation error of ±8.9% was consistently computed between numerical model and experimental data, which demonstrates the good capability of the model developed for predicting the fluid-flow processes.

Numerical simulation of refrigerants flowing through short-tube orifices during flashing process

A numerical simulation for calculating the flashing flow characteristics of refrigerants inside short-tube orifices is presented. The refrigerant flow behaviors along short-tube orifices are separated into three sections: subcooled liquid region, metastable liquid region, and two-phase region. Annular two-phase flow pattern is developed from the mass, energy, and momentum equation. The present simulation is corroborated by comparison with the experimental data. The selection charts are also presented to estimate the refrigerant mass flow rate along short-tube orifices in practical applications.

NUMERICAL AND EXPERIMENTAL INVESTIGATION OF THE FLOW CHARACTERISTICS OF R134a FLOWING THROUGH ADIABATIC HELICAL CAPILLARY TUBES

This paper presents numerical and experimental results of the flow characteristics of R134a flowing through adiabatic helical capillary tubes. The local pressure distribution along the length of the capillary tubes is measured at inlet pressures ranging from 10 to 14 bar, mass flow rates from 8 to 20 kg h-1, and degrees of subcooling from 0.5°C to 15°C. The theoretical model is based on conservation of mass, energy and the momentum of the fluids in the capillary tube. The model is divided into three regions: subcooled liquid region, metastable liquid region and equilibrium two-phase region and can be applied for various tube geometries, new alternative refrigerants and critical or noncritical flow conditions. The model is validated by comparing results from the present experimental data with that of the available literature. Based on the comparison results, the model used in the present study provides reasonable agreement with the experimental data.

Small-angle scattering and the structure of ambient liquid water

Structural polyamorphism has been promoted as a means for understanding the anomalous thermodynamics and dynamics of water in the experimentally inaccessible supercooled region. In the metastable liquid region, theory has hypothesized the existence of a liquid-liquid critical point from which a dividing line separates two water species of high and low density. A recent small-angle X-ray scattering study has claimed that the two structural species postulated in the supercooled state are seen to exist in bulk water at ambient conditions. We analyze new small-angle X-ray scattering data on ambient liquid water taken at third generation synchrotron sources, and large 32,000 water molecule simulations using the TIP4P-Ew model of water, to show that the small-angle region measures standard number density fluctuations consistent with water's isothermal compressibility temperature trends. Our study shows that there is no support or need for heterogeneities in water structure at room temperature to explain the small-angle scattering data, as it is consistent with a unimodal density of the tetrahedral liquid at ambient conditions.

Molecular dynamics studies of CaAl 2Si 2O 8 liquid. Part II: Equation of state and a thermodynamic model

A thermodynamic model and equation of state (EOS) is developed from the molecular dynamics simulation experiments of Spera et al. (2009) for CaAl 2Si 2O 8 liquid over the temperature range 3500–6000 K and pressure interval 0–125 GPa. The model is constructed utilizing the isothermal Universal EOS of Vinet et al. (1986) combined with an expression for the temperature-dependence of the internal energy derived from density functional theory ( Rosenfeld and Tarazona, 1998). It is demonstrated that this model is more successful at reproducing the data than the temperature-dependent Universal EOS ( Vinet et al., 1987) or the volume-explicit EOS of Ghiorso (2004a). Distinct parameterizations are required to model low (<20 GPa) and high (>20 GPa) pressure regimes. This result is ascribed to the affect of liquid structure on macroscopic thermodynamic properties, specifically the interdependence of average cation-oxygen coordination number on the bulk modulus. The thermodynamic transition between the high- and low-pressure parameterizations is modeled as second order, although the nature of the transition is open to question and may well be first order or lambda-like in character. Analysis of the thermodynamic model reveals a predicted region of liquid–liquid un-mixing at low-temperatures (<1624 K) and pressures (<1.257 GPa). These pressure–temperature conditions are above the glass transition temperature but within the metastable liquid region. They represent the highest temperatures yet suggested for liquid–liquid un-mixing in a silicate bulk composition. A shock wave Hugoniot curve is calculated for comparison with the experimental data of Rigden et al. (1989) and of Asimow and Ahrens (2008). The comparison suggests that the model developed in this paper underestimates the density of the liquid by roughly 10% at pressures greater than ∼20 GPa.

Numerical analysis of adiabatic flow of refrigerant through a spiral capillary tube

In the present work, a homogenous model including the metastable liquid region has been developed for the adiabatic flow of refrigerant through the spiral capillary tube. In order to develop the model, both liquid region and two phase region have been discretized into infinitesimal segments to take into account the effect of varying radius of curvature of spiral tube on the friction factor. The effect of the pitch of spiral on the mass flow rate of refrigerant and capillary tube length has been investigated. A comparison of flow characteristics of refrigerant R22 and its alternatives, i.e., R407C and R410A has been made at different operating conditions at the inlet of the capillary tube and it has been found that the flow characteristics of R22 and R407C are almost similar for a given condenser pressure and degree of subcooling at the inlet of capillary tube.

Simulation of shock-induced fragmentation and vaporization in metals

Simulations of experiments on shock-induced melting, fragmentation and vaporization in aluminum and zinc targets are presented. A titanium impactor moves at a velocity of 10.4 km/s and causes melting of these materials in a shock wave. Under rarefaction the thermodynamic path crosses the liquid–vapor coexistence boundary and enters into a metastable liquid region. Liquid in a metastable state may undergo either liquid–vapor phase separation or mechanical fragmentation. Homogeneous nucleation theory and the mechanical fragmentation criterion of Grady are taken into account to control the kinetics of these processes in our model. The first effect dominates in the vicinity of the critical point, the second one – at lower temperatures. Analysis of phase transitions and kinetics of phase separations is performed using a thermodynamically complete equation of state with stable and metastable states for all materials under consideration.

Simulation of melting and vaporization of metals at hypervelocity impact

Simulations of experiments on shock-induced melting, fragmentation and vaporization in aluminum and zinc targets are presented. A titanium impactor moves at a velocity of 10.4 km/s and causes melting of these materials in a shock wave. Under rarefaction thermodynamic path crosses the liquid–vapor coexistence boundary and enters into metastable liquid region. Liquid in a metastable state may undergo either liquid–vapor phase separation or mechanical fragmentation. Homogeneous nucleation theory and mechanical fragmentation criterion of Grady are taken into account to control the kinetics of these processes in our model. The first effect dominates in the vicinity of the critical point, the second one — at lower temperatures. Analysis of phase transitions and kinetics of phase separation is performed using thermodynamically complete equation of state with allowance for stable and metastable regions for all materials under consideration.

Material decomposition mechanisms in femtosecond laser interactions with metals

A numerical hydrodynamic study of femtosecond laser ablation is presented. A detailed analysis of material decomposition is performed using a thermodynamically complete equation of state with separate stable and metastable phase states and phase boundaries. The lifetime of the metastable liquid state is estimated based on the classical theory of homogeneous nucleation. In addition, mechanical fragmentation of the target material is controlled based on available criteria. As a result, several ablation mechanisms are observed. A major fraction of the ablated material, however, is found to originate from the metastable liquid region, which is decomposed either thermally in the vicinity of the critical point into a liquid-gas-mixture or mechanically at high strain rate and negative pressure into liquid droplets and chunks. The calculation results explain available experimental findings.

Numerical simulation of non-adiabatic capillary tubes considering metastable region. Part I: Mathematical formulation and numerical model

A detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behavior of capillary tube–suction line heat exchangers has been carried out. The governing equations (continuity, momentum, energy and entropy) for fluid flows, together with the energy equation in solids, are solved iteratively in a segregated manner. The discretized governing equations in the zones with fluid flow are coupled using a fully implicit step-by-step method. An implicit central difference numerical scheme and a line-by-line solver were used in solids. A special treatment has been implemented in order to consider transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). All the flow variables (enthalpies, temperatures, pressures, mass fractions, heat fluxes, etc.) together with the thermophysical and transport properties are evaluated at each point of the grid in which the domain is discretized. The numerical model allows analysis of aspects such as geometry, type of fluid, critical or non-critical flow conditions, metastable regions and transient cases. Comparison of the numerical simulation with experimental data presented in the technical literature will be shown in Part II of the present paper.

Numerical simulation and experimental validation of coiled adiabatic capillary tubes

The objective of this study is to extend and validate the model developed and presented in previous works [O. García-Valladares, C.D. Pérez-Segarra, A. Oliva, Numerical simulation of capillary tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part I: mathematical formulation and numerical model, Applied Thermal Engineering 22 (2) (2002) 173–182; O. García-Valladares, C.D. Pérez-Segarra, A. Oliva, Numerical simulation of capillary tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part II: experimental validation and parametric studies, Applied Thermal Engineering 22 (4) (2002) 379–391] to coiled adiabatic capillary tube expansion devices working with pure and mixed refrigerants. The discretized governing equations are coupled using an implicit step by step method. A special treatment has been implemented in order to consider transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). All the flow variables (enthalpies, temperatures, pressures, vapor qualities, velocities, heat fluxes, etc.) together with the thermophysical properties are evaluated at each point of the grid in which the domain is discretized. The numerical model allows analysis of aspects such as geometry, type of fluid (pure substances and mixtures), critical or non-critical flow conditions, metastable regions, and transient aspects. Comparison of the numerical simulation with a wide range of experimental data presented in the technical literature will be shown in the present article in order to validate the model developed.

Thermophysical and Thermodynamic Properties of 1-Butyl-3-methylimidazolium Tetrafluoroborate and 1-Butyl-3-methylimidazolium Hexafluorophosphate over an Extended Pressure Range

The current study focuses on 1-butyl-3-methylimidazolium tetrafluoroborate, [bmim][BF4], and 1-butyl-3-methylimidazolium hexafluorophosphate, [bmim][PF6]. The objective is to study the influence of pressure as well as that of the anion on several properties of this type of ionic liquid. The speed of sound and densities in pure ionic liquids (ILs) as a function of temperature and pressure have been determined. Several other thermodynamic properties such as compressibilities, expansivities, and heat capacities have been obtained. To the best of our knowledge, this research comprises both the first speed of sound data and the first evaluation of heat capacities at high pressures for ILs. Speed of sound measurements have been carried out in broad ranges of temperature (283 < T/K < 323) and pressure (0.1 < p/MPa < 150), sometimes inside the metastable liquid region using a nonintrusive microcell. The T−P melting line of [bmim][PF6] has also been determined by an acoustic method. Density measurements have been ...

An assessment of friction factor and viscosity correlations for model prediction of refrigerant flow in capillary tubes

In this paper, a homogeneous model including the metastable liquid and metastable two-phase region is presented to assess the effects of various friction factor equations and two-phase viscosity correlations on simulating the behaviour of capillary tubes. Both straight and coiled capillary tubes are considered and R-22 is used for comparison. The predicted pressure distribution, tube lengths or mass flow rates are compared with experimental data reported in literature. It is confirmed that the predicting accuracy with homogeneous model can be improved by employing the suitable correlations of friction factor and two-phase viscosity. For straight capillaries, the Churchill and Colebrook friction factor correlations give almost the same simulating results. However, the numerical results show that the optimum combination of correlations of friction factor and two-phase viscosity may be different when compared with different experimental data. For coiled capillaries, the Mori and Nakayama friction factor correlation agrees well with Ito's formula for single liquid-phase flow. Together with Giri's friction factor equation for two-phase flow, Cicchitti viscosity model best predicts the measured mass flow rate with an average error of 4.88%. Copyright © 2004 John Wiley & Sons, Ltd.

Numerical simulation of capillary tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part I: mathematical formulation and numerical model

A detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behaviour of capillary tube expansion devices working with pure and mixed refrigerants has been developed. The discretised governing equations are coupled using an implicit step by step method. A special treatment has been implemented in order to consider transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). All the flow variables (enthalpy, temperatures, pressures, vapour quality, velocities, heat fluxes, etc.) together with the thermophysical properties are evaluated at each point of the grid in which the domain is discretised. The numerical model allows analysis of aspects such as geometry, type of fluid (pure substances and mixtures), critical or non-critical flow conditions, metastable regions, adiabatic or non-adiabatic capillary tubes and transient aspects. Comparison of the numerical simulation with experimental data presented in the technical literature will be shown in part II of the present article.

Extended Insight into the Metastable Liquid Region Behavior in an Adiabatic Capillary Tube

Over the past decade, the development of theoretical models used to simulate capillary tube performance has steadily progressed. Currently, the major obstacle to improving performance model accuracy is the inability to accurately predict the onset of vaporization (flash point) and thereby the metastable liquid region length. It has been demonstrated that neglecting this region's effect on the overall flow resistance can lead to an underprediction by 5 to 25% of the actual mass flow rate through a capillary tube. Before an accurate metastable liquid region model can be developed, however, a more thorough understanding of the region behavior is necessary. In response, an experimental study has been completed with R-134a using a single adiabatic capillary tube. Testing was undertaken to determine if the metastable liquid region effect on steady-state mass flow rate measurements was repeatable and dependent on controllable test parameters, as had been suggested in a recent study. The experimental parameters were: steady-state inlet subcool level (three levels), the direction of approach to the steady-state inlet temperature (increasing or decreasing temperature), and the forced inlet temperature response rate used in attaining the steady-state flow condition. The resulting general data trend demonstrated increasing scatter in repeated flow rate measurements as the inlet subcool level decreased. Further, there appeared to be some dependence of the flow rate data on the experimental procedure used in setting the inlet condition. However, even under controlled test conditions the dependence was not always repeatable. Using a theoretical flow model, it was shown that most of the data scatter among repeated measurements was caused by variation in the flash point location and thereby the metastable liquid region length. These results precipitated a second experimental phase designed to determine if the flash point location could be controlled. If so, the scatter in measured mass flow rate data for a common inlet condition would be reduced. Two modifications were made to the capillary tube. First, a thin wire was run through its entire length and the original test matrix repeated. The overall measured flow rate levels were lower due to the decrease in flow area caused by the wire. But in comparison to the measurements without the wire, the proportional range of data scatter was cut in half. The second modification was made by drilling five 0.020 in. (0.51 mm) diameter holes through the tube wall, which were spaced at 5 in. (127 mm) toward the end of the tube. Each hole was sealed along the outer tube surface, thus creating a series of wall cavities acting as potential nucleation sites. The overall measured flow rate levels were reduced by roughly 13% in comparison to the original unmodified tube. But more interestingly, the range of data scatter was reduced by nearly an order of magnitude. In conclusion, it was proven that the data scatter in repeated measurements of mass flow rate was caused by variation in the flash point location. It was then demonstrated that the variation in the flash point location could be controlled. Once controlled, an accurate prediction of the metastable liquid region length is potentially possible, which will in turn improve the accuracy of theoretical flow models used to simulate capillary tube performance.

Pressure and temperature variation of the depolarized light scattering spectra of the fragile glass-former liquid salol

The pressure and temperature dependences of the depolarized light scattering spectra of salol have been measured at isobaric condition P = 1 bar for T between 328 and 393 K, and at isothermal condition T = 343 K for P between 1 and 625 bar, i.e. outside the metastable liquid region. The experimental results for both the α- and β-relaxations can be well described by the Mode Coupling Theory. The independence of the power-law parameters a, and consequently b and γ, from the thermodynamic variables T and P is demonstrated.The critical temperature Tc at 1 bar and the critical pressure Pc at T = 343 K have been determined from the normal liquid state.