Superheat Limit Research Articles

The Parallel between Boiling Point Elevation and Limit of Superheat for Polymer Solutions

The derivation for boiling point elevation (BPE) for polymer solutions goes back to mathematics of the Clausius-Clapeyron equation combined with Raoult's Law or the Gibbs-Helmholtz equation combined with Raoult's Law. BPE can be used to measure polymer molecular weight and is effective when the concentration of polymer approaches zero. The limit of superheat for polymer solutions formula (LSPS) was derived by (Jennings, 2012) [1], a complicated derivation involving the surface tension in particular. (Jennings and Middleman, 1985) [2] Published data that agrees with Jennings' formula. BPE and LSPS have various uses that will be discussed as will the parallel between the two equations.

Nucleation Process in Explosive Boiling Phenomena of Water on Micro-Platinum Wire.

The maximum temperature limit at which liquid boils explosively is referred to as the superheat limit of liquid. Through various experimental studies on the superheating limit of liquids, rapid evaporation of liquids has been observed at the superheating limit. This study explored the water nucleation process at the superheat limit achieved in micro-platinum wires using a molecular interaction model. According to the molecular interaction model, the nucleation rate and time delay at 576.2 K are approximately 2.1 × 1011/(μm3μs) and 5.7 ns, respectively. With an evaporation rate (116.0 m/s) much faster than that of hydrocarbons (14.0 m/s), these readings show that explosive boiling or rapid phase transition from liquid to vapor can occur at the superheat limit of water. Subsequent bubble growth after bubble nucleation was also considered.

A four-parameter generalized van der Waals equation of state: theoretical determination of thermodynamic stability boundary and vapor–liquid equilibrium of vanadium, niobium and tantalum

ABSTRACT A new four-parameter generalized van der Waals equation of state is proposed. The criteria for the applicability of the proposed equation of state in describing the thermodynamic properties of substances have been formulated. The generalized van der Waals equation of state is found to be applicable to vanadium, niobium and tantalum. To validate the generalized van der Waals equation of state, the spinodal, ideal tensile strength, thermodynamic limit of superheat and binodal of vanadium, niobium and tantalum have been determined. The obtained results agree with that of Filippov correlation and other equations of state. Using the obtained spinodal, the binodal of vanadium, niobium and tantalum has been determined.

A Study on the Dynamic Collision Behaviors of a Hydrous Ethanol Droplet on a Heated Surface

This study uses high-speed imaging to investigate the dynamic collision behavior of a single hydrous ethanol droplet in different water/ethanol ratios on a heated horizontal glass surface. The initial droplet diameter varied from 3.3 to 4.1 mm, and the impact velocity was 0.57 m/s. The study covers a range of surface temperatures (373 K to 553 K) and ethanol mass fractions (0% to 100%) to reveal four regimes of droplet-impinging behaviors, including quiescent surface evaporation, puffing or partial boiling, explosive nuclear boiling, and the Leidenfrost effect. The addition of volatile ethanol to less volatile water shifts the droplet collision behavior toward explosive boiling and the Leidenfrost phenomenon. As the ethanol mass fraction increased from 0% to 100%, the superheat limit temperature decreased by approximately 80 K, while the Leidenfrost temperature decreased by at least 100 K. The dimensionless droplet diameter in the regime of droplet spreading with quiescent surface evaporation is influenced by surface temperature, surface tension, and viscosity. Meanwhile, the dimensionless diameter and height of a droplet in the regime of the Leidenfrost phenomenon are mainly influenced by its surface tension. The study concludes that a single parameter, such as the superheat level, Weber number, or Reynolds number, is difficult to describe droplet collision behavior, and multiple factors would be required to best describe droplet collision behavior and establish empirical correlations. However, it is feasible to predict partial collision behaviors by using one of the single parameters under certain conditions.

Melting Behaviour under Pressure of Kaolinite Clay: A Nanoscale Study

In this study, the curves of variation of melting temperature as a function of pressure were determined for pressures up to 20 GPa using molecular dynamics (MD) calculations. The CLAYFF force field is used for the simulated PT curve of the clay kaolinite structure. For this purpose, we have adopted the Z-method to determine the melting point (Tm) and superheat limit temperature (TLS) for different densities in kaolinite clay. In addition, various quantities, such as the radial distribution function (RDF), the mean square displacement (MSD), and the diffusion coefficient were evaluated in order to ensure the solid behaviour at the superheat limit temperature and the liquid behaviour at the melting point for the equilibrated structure of kaolinite.

Criticality points on the phase diagram of substances as scaling parameters in the law of corresponding states: alkali metals

The law of corresponding states (LCS), based on a generalized van der Waals equation of state (gvdWEoS) has been formulated by rescaling its thermodynamic variables with liquid- vapour critical—point parameters, the spinodal, the thermodynamic limit of superheat (TLS) and the supercritical (SC) point. This gvdWEoS differs from the known van der Waals equation of state (vdWEoS) by the modified attractive term. The scaling properties have been derived on the basis of the gvdWEoS. The expressions for the isothermal compressibility, a derivate of Gibbs free energy, have been derived. In all the cases of rescaling, the gvdWEoS has the similar functional form and the expression for isothermal compressibility has a similar functional form. This shows that the parameters of any spinodal-point on the phase diagram, including the TLS as a particular case, and the SC point, characteristic point on the quasispinodal, provide the alternate scales of parameterizing the thermodynamic properties of substances other than the liquid-vapour critical point. Moreover, an isothermal compressibility regularity is formulated on the basis of the gvdWEoS and it is found to satisfactorily trace the literature data for saturated liquid alkali metals.

Experiments and modelling of choked flow of CO2 in orifices and nozzles

In order to accelerate the deployment of CO2 capture and storage (CCS), engineers need experimentally validated models, among other things, to predict the mass flow rate in process equipment and flow restrictions like valves, nozzles and orifices. There are few available, relevant data for choked CO2 flow in such geometries. To amend the situation, in this work, we report on six pipe-depressurization experiments from a pressure of 12 MPa and a temperature of 25 °C through three sizes (4.5, 9.0 and 12.7 mm) of orifices and nozzles. The results indicate that for the present cases, the choke point is at a non-equilibrium state. In order to predict quasi-steady choked flow in restrictions, the homogeneous equilibrium model (HEM) and the Henry–Fauske (HF) model are commonly used. The HEM often underpredicts the mass flow rate because it does not account for delayed phase transition. Here we develop a delayed HEM (D-HEM) where evaporation starts at the superheat limit described using classical nucleation theory. We then employ the HEM, D-HEM, and HF model in 1D CFD pipe simulations to describe the outflow of depressurization experiments and we also compare with experimental data for converging–diverging nozzles. In the CFD simulations, HF gave the best results, while HEM consistently underpredicted the mass flux. For the nozzle calculations, we found D-HEM to be the best model with a relative absolute error of 2.5 % for the predicted mass flux.

Comprehensive analysis of spherical bubble oscillations and shock wave emission in laser-induced cavitation

The dynamics of spherical laser-induced cavitation bubbles in water is investigated by plasma photography, time-resolved shadowgraphs and sensitive single-shot probe beam scattering that portrays the transition from initial nonlinear to late linear oscillations. The frequency of late oscillations yields the bubble's gas content. Numerical simulations with an extended Gilmore model using plasma size as input and oscillation times as fit parameter provide insights into experimentally not accessible bubble parameters and shock wave emission. Model extensions include a term covering the initial shock-driven acceleration of the bubble wall, an automated method determining shock front position and pressure decay and a complete energy balance for the partitioning of absorbed laser energy into vaporization, bubble and shock wave energy and dissipation through viscosity and condensation. These tools are used for analysing a scattering signal covering 102 oscillation cycles from a bubble with 36 μm maximum radius produced by a plasma with 1550 K average temperature. Predicted bubble wall velocities during expansion agree well with experimental data. Upon first collapse, most energy was stored in the compressed liquid around the bubble and radiated away acoustically. The collapsed bubble contained more vapour than gas and had a pressure of 13.5 GPa. The decay of the rebound shock wave pressure with radius r was initially $\mathrm{\ \propto }{r^{ - 1.8}}$ , and energy dissipation at the shock front heated the liquid near the bubble wall to temperatures above the superheat limit. The shock-induced temperature rise reduces damping during late bubble oscillations. Damping in first collapse increases significantly for small bubbles with less than 10 μm radius.

Explosive boiling of liquid nitrogen in a long thin tube and its application to the detection of a local temperature rise

To promote the commercial use of high-temperature superconducting devices, the ability to detect temperature anomalies easily and reliably and thereby protect the devices is important. In particular, a sudden local temperature increase due to a superconducting-to-normal transition can damage a device. In the present study, we propose a method to detect explosive boiling of superheated liquid nitrogen sealed in a long thin tube using a pressure gauge connected to the end of the tube. Experiments using a stainless-steel tube with an inner diameter of 1 mm and a maximum length of 50 m under various conditions showed that the local temperature rise caused explosive boiling at a temperature slightly below the superheat limit of 110 K for liquid nitrogen; the results also showed that the rapid pressure increase was transmitted to the end of the tube at approximately the speed of sound (∼830 m/s). The proposed method of placing a thin tube along high-temperature superconducting conductors or cryogenic structures can be used to easily detect a local temperature rise.

Fluidics of an immiscible drop impact onto a hot oil film

Droplet rapid phase transition during its impact over a hot immiscible oil film is studied experimentally, which is of paramount importance in fire extinguishing, forensics, internal combustion engines, and various accident scenarios in the industries. The impact of a cold methanol droplet on a hot mustard oil film and its repercussions are analyzed from high-speed images for a temperature range relevant from the thermodynamic and heat transfer perspective. The interfacial temperature of the hot oil film has been varied through the saturation temperature, Leidenfrost point, superheat limit, and critical temperature, for methanol. A regime map has been proposed to characterize fluidic observations on Weber number and non-dimensional average temperature plane. Violent cavity crater explosions have been observed above a critical Weber number ranging 70–80 for average interfacial temperature higher than the critical point of methanol due to direct contact between the droplet and base of the petridish.

Choked liquid flow in nozzles: Crossover from heterogeneous to homogeneous cavitation and insensitivity to depressurization rate

The critical mass flow rate is the maximum flow rate that can pass through a constrained geometry such as a nozzle. For liquid CO2, it has been shown that homogeneous relaxation models systematically underpredict the critical mass flow rate. In this work, we demonstrate that a delay of the phase transition is necessary to reproduce experiments. To analyze this in further detail, two methodologies are presented: (1) the delayed homogeneous relaxation model (Delayed HRM), and (2) the metastable isentrope model (MIM). Delayed HRM is a relaxation model that can readily be incorporated into a spatially distributed description of the fluid flow, e.g. in ejectors. MIM assumes isentropic flow and instantaneous equilibrium up to the limit of metastability, and yields a geometry-independent critical mass flux as the solution of a set of algebraic equations. We compare the two methodologies to available experimental data on the critical mass flow rates of CO2 and H2O through nozzles, finding that they give nearly identical predictions. This suggests that the critical mass flow rate is mostly determined by the achievable degree of metastability before onset of phase change, and is rather insensitive to dynamic variables such as the depressurization rate or the rate of relaxation towards equilibrium. Using the limit of metastability predicted by homogeneous nucleation theory works well at high temperatures, rendering the methodologies completely predictive. They deviate on average 11% from experimental data on CO2, and thus outperform homogeneous relaxation models by a large margin, even when the latter employs several fitted parameters. Especially good agreement was found with experiments that employ a lubrication oil, which is hypothesized to suppress heterogeneous nucleation. The limit of superheat at lower temperatures must be described by heterogeneous nucleation theory. For water and CO2 we find a crossover between homogeneous and heterogeneous nucleation at T≈590 K and T≈285 K respectively. Moreover, the predicted limit of superheat falls on a single curve in the temperature–pressure space of water, and we present an empirical correlation of this curve. By combining this expression with the above methodologies, we obtained an average deviation of 3% with available experimental data on H2O mass flow rates.

Ultrasound-assisted investigation of photon triggered vaporization of poly(vinylalcohol) phase-change nanodroplets: A preliminary concept study with dosimetry perspective.

We investigate the vaporization of phase-change ultrasound contrast agents using photon radiation for dosimetry perspectives in radiotherapy. We studied superheated perfluorobutane nanodroplets with a crosslinked poly(vinylalcohol) shell. The nanodroplets' physico-chemical properties, and their acoustic transition have been assessed firstly. Then, poly(vinylalcohol)-perfluorobutane nanodroplets were dispersed in poly(acrylamide) hydrogel phantoms and exposed to a photon beam. We addressed the effect of several parameters influencing the nanodroplets radiation sensitivity (energy/delivered dose/dose rate/temperature). The nanodroplets-vaporization post-photon exposure was evaluated using ultrasound imaging at a low mechanical index. Poly(vinylalcohol)-perfluorobutane nanodroplets show a good colloidal stability over four weeks and remain highly stable at temperatures up to 78°C. Nanodroplets acoustically-triggered phase transition leads to microbubbles with diameters <10μm and an activation threshold of mechanical index=0.4, at 7.5MHz. A small number of vaporization events occur post-photon exposure (6MV/15MV), at doses between 2 and 10Gy, leading to ultrasound contrast increase up to 60% at RT. The nanodroplets become efficiently sensitive to photons when heated to a temperature of 65°C (while remaining below the superheat limit temperature) during irradiation. Nanodroplets' core is linked to the degree of superheat in the metastable state and plays a critical role in determining nanodroplet' stability and sensitivity to ionizing radiation, requiring higher or lower linear energy transfer vaporization thresholds. While poly(vinylalcohol)-perfluorobutane nanodroplets could be slightly activated by photons at ambient conditions, a good balance between the degree of superheat and stability will aim at optimizing the design of nanodroplets to reach high sensitivity to photons at physiological conditions.

Explosion of metastable droplets in immiscible liquids

Evaporation of metastable droplets in an immiscible liquid can occur in a wide range of practical applications and in particular in cryogenic systems due to the low saturation temperature of the cryogenic liquid. In this article, we show experimentally that the incomplete explosion of a metastable droplet can lead to a ‘film evaporation’ configuration, where a remaining droplet is eventually separated from the host immiscible liquid by an established vapour layer. Based on a transient heat diffusion model, we identified that the necessary but not sufficient condition for the complete explosion of a metastable droplet is that the droplet must absorb, before explosion, an amount of heat larger than the latent heat required for a full evaporation, i.e. the global Jacob number Ja≥1. In addition, the measured superheat limits of pentane and isohexane are 420.65 K and 444.95 K respectively, which are very close to the theoretical Spinodal points (≤ 1.5 K) and other reported values in existing literature. Therefore, the experimental setup reported here can be used as an alternative way to quantify the superheat limit. The Droplet relaxation time was also found scaled to the square root of the diffusion characteristic time.

Critical heat flux and Leidenfrost temperature on Electrical Discharge Machining (EDM) - constructed hemispherical surface

This paper reports a Leidenfrost temperature on hemispherical surface constructed by Electrical discharge machining or known as EDM. We focus our study on the droplet evaporation lifetime to investigate and identify the Leidenfrost temperature. Three (3) different types of materials were selected i. e such as Brass (Br), Aluminum (Al) and Copper (Cu). Meanwhile, ethanol liquid has been chosen as the test liquid. Ethanol liquid was elected due to its low boiling point of approximately 78 °C. The droplet impact velocity and droplet diameter was approximately 1.129 m/s and 3.476 mm, respectively. As a result, we finally succeeded in determining the Leidenfrost temperature for all materials mentioned above. On top of that, all the Leidenfrost temperature results, TL were close to the superheat limit temperature of ethanol liquid, TSL which is about 197.8 °C.

Experiments and modeling on cryogenic quenching enhancement by the structured capillary-porous coatings of surface

In the present study, the influence of structured capillary-porous coatings of surface on cryogenic quenching by the falling liquid nitrogen film is investigated. The coating was produced by the directional plasma spraying technique. The cryogenic quenching experiments were performed on high-temperature vertical copper slab with bare surface and on the surfaces with different orientation of coating protrusions. Thermocouples and a high-speed digital video camera were employed to obtain a synchronized data on the temperature-time history of the transient process and the pattern of quench front propagation. The peculiarities of quench front dynamics and heat transfer in the transient process are studied. The created numerical model determines the quench front velocity and the temperature fields in the heater, varying in space and time. The dynamic pattern of quench front propagation obtained numerically satisfactorily correlates with the observed in the experiments one. The heat transfer curves during quenching were determined for different surfaces based on the experimental cooling thermograms and visualization data. The results show that the cooling rate is influenced by the thermal properties of the coating as well as the geometry of the protrusions on the solid surface. The presence of capillary-porous coating significantly affects the dynamics of quenching, which results in the decrease more then threefold of the total quench time. In this way, the structured capillary-porous coating is a method for reducing the time and the total mass of cryogenic fluid required for a quenching process. The effect is due to the fact that the initialization of a quench front on a specimen with the coating occurs at a temperature significantly higher than the thermodynamic limit of a liquid superheat, when a stable solid-liquid contact is thermodynamically impossible. This phenomenon appears as a result of local contacts of the crests of wavy liquid flow at the liquid-vapor interface with the protrusions on the modified surface. The results indicated also the minimum film boiling temperature increase on heat transfer surface coated with capillary-porous layer. This increased temperature caused earlier transition to nucleate boiling, which results in the decrease in the quenching time. The results reliability is confirmed by direct comparison with experimental data on the quench front dynamics, velocity and geometry.

Phase Change and Space Travel

Here we discuss the implications of phase change equations and what bearing they might have on interstellar space travel. The phase change equations are derived from either thermodynamics or statistical mechanics and have a similarity. Then, the main equation for limit of superheat is posited to be a solution to the problem of propulsion in space travel. There are two matter-antimatter systems considered: electron – positron and hydrogen – antihydrogen. What is involved in the space travel problem is harvesting of antimatter in magnetic bottles and keeping it separate.

Spinodal and thermodynamic limit of superheat of gold

A four-parameter generalized Berthelot equation of state has been employed to determine the spinodal and the thermodynamic limit of superheat of liquid gold. It is established that gold obeys the two-parameter law of corresponding states. It is also established that the new parameters introduced in the attractive term of the equation of state are thermodynamic similarity parameters. It is shown that liquid gold can be superheated to a temperature 6719K. That is, liquid gold, under rapid heating, can be superheated to temperature 3476K above the boiling temperature without undergoing liquid-vapour phase transition. Above this temperature, liquid gold will undergo explosive boiling owing to homogeneous nucleation.

API standard 521 guidance on mixing of hot/cold liquids and prevention of superheat limit explosions

American Petroleum Institute (API) standards and recommended practices have identified inadvertent mixing of hot and cold liquids as a potential cause for equipment overpressure since 1955. The limited guidance has been informative but provides minimal if any details on conditions that could cause an overpressure and its potential severity. Therefore, the user must interpret how and when to prevent and/or mitigate the scenario. This guidance has changed little over the years. In June 2020, API published the 7th Edition of API Standard 521 which now provides specific guidance as to conditions whereby pressure relief devices can be considered for protection and conditions where prevention remains as the only recourse. This paper discusses the basis for the revised guidance in API Standard 521 and includes supplemental guidance.

Ability of the generalized van der Waals and Berthelot equations of state to determine the thermodynamic stability of liquid lead

The known van der Waals and Berthelot equations of state do-not precisely describe the thermodynamic properties of fluids. To improve its accuracy, the attractive term of the van der Waals equation of state has been modified in six different ways. These generalized equations of state have been employed to determine the spinodal (thermodynamic stability boundary) and the thermodynamic limit of superheat of liquid lead. The equations of state are rewritten in reduced form, from which follows the law of corresponding states. The appropriate modification of the attractive term of the equation of state yielding the value of thermodynamic limit of superheat agreeing with the experimental value for lead has been established. It has been established that liquid lead can be superheated, under rapid heating, up to a temperature 4565 K. That is, liquid lead can be superheated to 2544 K above the normal boiling temperature. At the thermodynamic limit of superheat, the volume of the liquid lead is 4.0095 × 10-5 m3 mol-1. This fact is to be taken into account when liquid lead is subjected to rapid heating.

Peculiarities of the initialization and dynamics of the quench front on an extremely overheated plate cooled by a falling film of a cryogenic fluid

Quenching is a generally accepted term for the process of rapid cooling of a solid body that is superheated above the temperature of the thermodynamic limit of a liquid superheat. The paper presents the results of computational experiments simulating the quenching of a high-temperature vertical copper plate by a gravitationally flowing film of liquid nitrogen. The peculiarities of the initialization and dynamics of the quench front in the transition process are investigated. The initial temperature of the test sample was higher than the Leidenfrost temperature and even higher than the critical temperature, which excluded the possibility of long-term stable liquid-solid contact. An improved numerical model of quenching is implemented, which assumes at the time of the quench front initialization an unsteady local contact of the liquid with the extremely overheated surface in the vicinity of the upper boundary of the heater. A dynamic pattern of the running quench front was obtained numerically, which satisfactorily correlates with that observed in cryogenic experiments by the high-speed digital video camera. The reliability of the results obtained numerically is confirmed by direct comparison with experimental data on the velocity and the shape of the quench front.