Liquid-vapor Mixture Research Articles

Slip velocity and field information of two-phase cavitating flows

In this work, laser-induced florescent particle image velocimetry was performed to measure simultaneously the liquid and vapor velocity fields at the mid-span of a small-scale Venturi type section to determine the presence of a slip velocity between the phases. Various dynamic behavior and Kelvin–Helmholtz (K-H) instability involved in the cloud cavity shedding regime are discussed at four different cavitation numbers. The velocity, vorticity, and turbulence field information of the two phases are analyzed. The liquid–vapor mixture in a cavitating flow is usually considered a homogeneous medium in currently used computational models, but it is shown in this study that the two phases have very different dynamics. The measurements of the time-averaged velocities highlight the existence of a noteworthy slippage between the liquid and the vapor phases, especially in the upstream part of the cavitation region, where the slippage between the two phases can reach about 50% of the liquid velocity. Using phase-locked average, it is shown that the slip velocity in the upstream region is mainly located at the upper liquid–vapor interface, while the slip velocity in the closure area is near the bottom wall, due to the reentrant jet. These results contradict a primary assumption of the current models, where the medium is usually considered as a homogeneous mixture with a unique velocity field, thus providing a reference for future computational model improvement.

A Comprehensive Approach to Modeling Air Injection-Based Enhanced Oil Recovery Processes

Summary Modeling of air-injection-based processes for enhanced oil recovery (EOR) is a challenging task, mostly due to the complexity of the chemical reactions taking place. Also, the applicability of currently available kinetic models is limited to the reservoir systems they were originally developed for. The objective of this study is to derive a general chemical reaction framework that could be used to develop a kinetic model for a variety of crude oils (i.e., light or heavy oils). The work is based on the modeling of high-pressure ramped temperature oxidation (HPRTO) experiments, and combustion tube (CT) tests, performed on two different oil systems: a volatile oil that is near critical at reservoir conditions (44 °API), and a bitumen sample (10 °API). The HPRTO test is a kinetic experiment that intends to mimic the flow conditions within the reservoir and allows the determination of kinetic parameters of the different reactions. On the other hand, the CT test is meant to provide quantitative information on the combustion performance that can be expected in the field. Therefore, a kinetic model was derived for each of the cases based on the history match of an HPRTO experiment. The resulting model was validated by history matching a CT test for each of the oils. An important feature of these experiments is that they were performed at representative reservoir pressure conditions. The modeling approach chosen is an extension of the methodology originally proposed by Belgrave et al. in 1993, which is arguably the most comprehensive kinetic model available in the air injection literature. However, their model was developed from experiments performed on Athabasca bitumen, and it fails to represent the high-pressure air injection process as it occurs in light oil reservoirs, which are typically encountered at higher pressure conditions. For example, Belgrave’s model is based on the deposition and combustion of semisolid residue commonly known as “coke,” which is rarely present during the combustion of light oils at high pressure. As in Belgrave’s model, this study also describes the original composition of the oil in terms of maltenes and asphaltenes. The main difference lies in the presence and importance of oxygen-induced cracking reactions, as well as the combustion of a liquid-vapor flammable hydrocarbon mixture that is generated by cracking and oxidation reactions, which take place in the gas phase. Also, a unique feature of these simulations is that, apart from history-matching traditional variables such as thermocouple temperatures, fluid recovery, and produced gas composition, they also capture changes in the physical properties of the produced oil, such as viscosity and density, as well as the amount of the residual phases in the post-test core. This enhancement to Belgrave’s reactions allows modeling the air injection process in cases where coke is not the main source of fuel, such as in high-pressure light oil reservoirs. This work changes a paradigm deeply rooted in the original in-situ combustion (ISC) theory, by deriving a general chemical reaction framework that is used to develop a kinetic model for two crude oils, which are at opposite ends of the density spectrum. This allows the consolidation of a new and comprehensive general theory for the description of the ISC process as applied to oil reservoirs. Moreover, as the pseudocomponents representing the fuel are not present in the original oil, the method is not limited to a fluid characterization in terms of maltenes and asphaltenes but could potentially be applied along with any type of characterization of the original oil.

A new turbulent viscosity modification method based on multiphase compressibility for cavitating flows

The alteration of physical properties in cavitating flows due to phase transition presents challenges for accurately expressing turbulent viscosity in Reynolds-Averaged Navier–Stokes models. Addressing this issue is crucial for capturing cavitating flow characteristics effectively. This study introduces a modification to turbulent viscosity by considering the compressibility of the vapor–liquid mixture, applied within the k-omega Shear-Stress Transport (SST k−ω) model framework. Simulations of cavitating flow around the Clark-Y hydrofoil, National Advisory Committee for Aeronautics 66 hydrofoil, and wedge are conducted to validate the proposed method. Results indicate that the modified model can reproduce the cavity inception, development, cutoff, and shedding processes observed in the experiment. Notably, the modification model accurately reproduces distinct cavitating flow features such as U-shaped cavities, secondary shedding, and high-pressure phenomena resulting from collapse. Moreover, the predicted time-averaged velocity, time-averaged Reynolds stress component, and dominant frequencies of pressure and phase volume fraction surpass those of the original SST k−ω model, demonstrating improved performance. These findings highlight the enhanced accuracy and reliability of the proposed SST-multiphase compressibility modification k−ω model for simulating cavitating flows, thus contributing to improved understanding and prediction capabilities in relevant engineering applications.

Short-period flow oscillation during eruptions of Onikobe geyser, NE Japan: Insights from thermal infrared observation and acoustic measurements

Geysers are episodic features with variable eruption intervals that range from minutes to years. Although many previous studies on geysers have focused on subsurface properties and processes such as plumbing geometry and recharge process, it is known that erupting fluid column exhibits short-term behaviors such as individual water jets from the vent. In the present study, we conducted observations at Onikobe geyser, NE Japan, a relatively small geyser (geysering well) erupting water up to ∼6–8 m every ∼10 min and observed the erupting fluid column using a thermal infrared camera and an acoustic sensor. We succeed in tracking the water jets by analyzing spatio-temporal temperature map obtained from the thermal infrared observation, which clearly shows the eruptions at Onikobe geyser are not completely stationary but rather a series of intermittent jets with a short period interval of <1 s. We estimate the exit velocity by fitting a ballistic model under the air drag condition of inertial resistance to the jet trajectory. The exit velocity and the averaged gas volume fraction of the erupting fluid are estimated to be ∼4–79 m/s and ∼0.93–0.96, respectively. The exit velocity is ∼30 m/s during the first bursts, then it rapidly increases to ∼50–80 m/s for ∼15 s, and then decreases to ∼20–30 m/s until ∼10 s before the eruption ends. Time series analyses of the thermal infrared and acoustic signals during an eruption indicate harmonic spectra with integer multiple peaks. The fundamental frequency showing ∼4 Hz at the beginning gradually decreases to ∼2 Hz for ∼15 s, keeps almost constant in the following 30 s, and then slightly increases near the end of the eruption. These harmonic spectra may be caused by a resonance mechanism, non-linear fluid motion, and/or subsurface two-phase flow. We discuss the case of a closed organ-pipe resonance in a subsurface crack and attribute the frequency decrease to a decrease in the water level in the crack (an increase in the length of the resonating liquid-vapor column) and/or a decrease in the gas volume fraction of the liquid-vapor mixture in the crack. Since such harmonic characteristics are observed at other geysers, further simultaneous observation of the short-period oscillations on the erupting column proposed in this study with seismic observations of harmonic tremor may provide an improved understanding of geyser subsurface phenomena.

Flow boiling of R32 and R410A inside brazed plate heat exchangers with different geometries

A proposed midterm substitute of R410A, mixture with 1924 GWP100 (Global Warming Potential over 100 years), is R32 (GWP100 = 677), which, although mildly flammable, is pure, relatively cheap, already available on the market, with different suppliers due to the absence of patents. Moreover, its thermo-physical properties are already well known. Increasingly stringent energy saving regulations are boosting the residential heat pump market, which typically requires reversible brazed plate heat exchangers to be used both as evaporators and condensers. This work reports an experimental analysis of the two refrigerants during flow boiling in brazed plate heat exchangers, varying the channel volumes. The number of plates of the heat exchangers ranges from 4 (1 refrigerant channel) to 120 (59 refrigerant channels in parallel). The heat transfer coefficient and the pressure drop have been measured for R410A and R32 at saturation temperature between 1.5 °C and 5.5 °C, outlet vapour superheating of 5 K, heat flux from 4 to 31 kW m−2, mass velocity from 8 to 87 kg m−2 s−1 and inlet channels vapour quality from 0.2 to 0.3. The number of plates affects the distribution of the liquid-vapour mixture in the channels and its effect is discussed by comparing the heat transfer coefficients. It is shown that the differences in performance between the two fluids increase with the mass velocity, suggesting the influence of a convective component on the heat transfer coefficient. This is further confirmed by comparing the data with the results of two different models from literature.

Effect of two-phase flow lubrication on sealing performance of spiral groove mechanical seal under high speed and low temperature conditions

The function of the turbo-pump shaft within the liquid rocket engine is rendered exceedingly complex due to the operation in an environment characterized by drastically low temperatures, elevated velocities, and high pressures. Given these operational conditions, it is highly plausible that a two-phase flow might form within the liquid film located on the terminal face of the mechanical seal. This liquid-vapor mixture significantly modifies the fluid lubrication pattern across the end faces and poses consequential implications on the overall sealing stability. In this study, the phase change characteristics of the fluid in the seal clearance were investigated based on the Laminar and Mixture multi-phase flow models in a spiral groove mechanical seal. The behaviors of two-phase flow characteristics and phase transition under extreme temperature, rotational speed and pressure with liquid nitrogen media were studied. The sealing performance was quantified through metrics including the leakage rate, opening force, and internal gas phase volume ratio. The findings offered valuable insights into the role of operational conditions in influencing the phase change of the liquid film. Moreover, we discerned and explicated the intricate interconnections between the leakage rate, the opening force, and the phase change behavior of the liquid film.

Transient ablation topography of a thin chromium film after ultrashort pulsed laser irradiation in the spallation and phase explosion regime

Time-resolved imaging pump–probe reflectometry is an established technique to characterize the dynamic processes occurring during the material ablation upon ultrashort pulsed laser irradiation. In the phase explosion regime, however, the presence of an expanding liquid–vapor mixture on top of the ablated material makes an unambiguous determination of the transient ablation topography almost impossible, especially when only front-side pump–probe reflectometry is used. To circumvent this limitation, the front-side reflectometry was complemented by rear-side reflectometry, where the probe radiation does not interact with the liquid–vapor mixture, and the underneath ablation kinetics of the material becomes observable. To interpret the measured front- and rear-side reflectances, an optical multilayer model of the ablation process was developed. Its applicability is demonstrated on a thin chromium film that was ablated by a single pump pulse. The optical model replicates the Newton rings measured during spallation and phase explosion very well, which allows the reconstruction of the transient ablation topography. The combination of the front- and rear-side reflectometry with modeling offers a valuable tool for studying the ablation processes in thin metal films, because it overcomes the challenges of the phase explosion regime, and thus enhances the understanding of material dynamics upon laser irradiation.

Subcritical and supercritical Rankine steam cycles, under elevated temperatures up to 900°C and absolute pressures up to 400 bara

The Rankine cycle is a conceptual arrangement of four processes as a closed vapor power thermodynamic cycle, where a working fluid (especially water as a liquid, as a vapor, and as a liquid-vapor mixture) can be used to convert heat into mechanical energy (shaft rotation). This cycle and its variants are widely used in electric power generation through utility-scale thermal power plants, such as coal-fired power plants and nuclear power plants. In the steam-based Rankine cycle, water should be pressurized and heated to be in the form of very hot high-pressure water vapor called “superheated steam,” before the useful process of expansion inside a steam turbine section occurs. If the absolute pressure and temperature of the superheated steam are both above the critical values for water (220.6 bara and 374.0°C), the cycle is classified as “supercritical.” Otherwise, the cycle is classified as “subcritical.” This study considers the impact of the temperature and pressure, independently, on the performance of a steam Rankine cycle. Starting from a representative condition for a subcritical cycle (600°C peak temperature and 50 bara peak absolute pressure), either the peak temperature or the peak absolute pressure of the cycle is increased with regular steps (up to 900°C, with a temperature step of 50°C, and up to 400 bara, with a pressure step of 50 bar). The variation of five scale-independent performance metrics is investigated in response to the elevated temperature and the elevated pressure. Thus, a total of 10 response curves are presented. When the temperature increased, all the five response variables were improved in a nearly linear profile. On the other hand, increasing the pressure did not give a monotonic linear improvement for each response variable. In particular, the cycle efficiency seemed to approach a limiting maximum value of 45% approximately, where further increases in the pressure cause diminishing improvements in the efficiency. When varying the peak pressure, an optimum minimum ratio of (water-mass-to-output-power) is found at 203 bara, although the cycle efficiency still increases beyond this value. In the present research work, the web-based tool for calculating steam properties by the British company Spirax Sarco Limited, and the software program mini-REFPROP by NIST (United States National Institute of Standards and Technology) were used for finding the necessary specific enthalpies (energy content) of water at different stages within the steam cycle. Both tools were found consistent with each other, as well as with the Python-based software package Cantera for simulating thermo-chemical-transport processes. The results showed that if the peak temperature reaches 900°C, a gain of about 5 percentage points (pp) in the thermal cycle efficiency becomes possible (compared to the case of having a base peak temperature of 600°C), as the predicted efficiency was found to increase from 38.60% (base case) to 43.67%. For the influence of the steam peak pressure, operating in the subcritical regime but close to the critical point appears to be a good choice given the gradual decline in efficiency gains at higher pressures. About 4.7 percentage point increase was found at the high subcritical peak pressure of 200 bara (compared to a base subcritical peak pressure of 50 bara). The results of this study also showed that the liquid water droplet mass fraction at the steam turbine exit diminishes from 11.00% at 600°C to only 1.48% at 900°C, which is favorable. This mass fraction grows from 11.00% at 50 bara to 27.89% at 400 bara, which is not acceptable. Every 100°C increase in the superheating temperature between 600°C and 900°C was found to cause aa increase in the cycle thermal efficiency by about 1.69 percentage points, and simultaneous a beneficial increase in the steam quality at the turbine exit by about 3.17 percentage points.

Influence of geometric factors on the heat transfer characteristics of two-phase thermosyphons

Thermosyphons are two-phase closed heat exchange systems that contain a certain amount of liquid and utilize the latent heat of vaporization and condensation to transfer heat between the heat source and the heat sink without any external devices. They are a type of heat pipe that lacks a capillary structure, so the return of the condensed coolant from the condensation zone to the heating zone is driven by gravitational forces. Due to the absence of a capillary structure, thermosyphons exhibit lower resistance to the movement of the vapor-liquid mixture from the heating zone to the condensation zone, as well as to the return flow of the condensate. A distinctive feature of such systems is their high equivalent thermal conductivity, which is several orders of magnitude greater than that of natural metals (such as copper or silver). Because of their superior heat transfer characteristics, thermosyphons are widely used in various technical fields, including the chemical and petroleum industries, electronics, telecommunications devices, energy storage systems, and geothermal heating systems, among others. This paper presents experimental data on the heat transfer characteristics of two-phase thermosyphons with an internal diameter of 9 mm and lengths of 500, 700, and 1000 mm, using water as the coolant. The filling ratio (Fr) varied from 0.3 to 1.2. The length of the condensation zone was the same for all thermosyphons. The study was conducted with the thermosyphons oriented vertically at an angle of 90° relative to the horizontal. The influence of the filling ratio and the effective length of the thermosyphons on the minimum thermal resistance, the maximum heat flux, and the equivalent thermal conductivity is analyzed.

A novel relaxation drift model for simulating liquid-vapor momentum non-equilibrium in two-phase ejectors

A novel relaxation drift model (RDM) was proposed to simulate the interphase momentum non-equilibrium (slip) inside two-phase work-recovery CO2 ejectors. The RDM was validated using the experimental data of 5 different ejectors under 15 trans-critical conditions in total. The proposed model was compared with the existing homogeneous model (HM) and algebraic slip model (ASM) through case studies. The effects of ejector mixer design and nozzle expansion state were also disclosed. The results showed that the prediction errors of ejector performance by the RDM were within 17 %, which was smaller than the maximum error of 23 % predicted by the HM and the ASM. The numerical results demonstrated that the liquid droplets had lower velocities than the vapor when the liquid-vapor mixture accelerated, but the droplets travelled faster than the vapor during deceleration of the mixture. It was also revealed that the velocity slip would affect the shock pattern at the diffuser inlet if the mixer was choked. The effects of slip, however, became insignificant when the mixer was designed too large. In addition, the RDM might overestimate the ejector performance if the motive nozzle was strongly under-expanded. This study facilitates understanding of interphase velocity slip in two-phase CO2 ejector flow.

Experimental and Numerical Investigation of the Behavior of a Vapor–Liquid Mixture in a Venturi Tube

Experimental and Numerical Investigation of the Behavior of a Vapor–Liquid Mixture in a Venturi Tube

Thermodynamic Study of the Electric Field Effect on Liquid-Vapor Mixture at Equilibrium: An Analysis on a Water-Ethanol Mixture.

In this paper, the effect of electric fields on phase equilibria through polarization is investigated. A relation is derived for the chemical potential of a system, where the electric field is localized over a liquid phase mixture in equilibrium with a vapor phase mixture. This relation is then applied to a water-ethanol mixture to explore the effect of polarization-based electric fields on the liquid phase composition. It is observed that the quadratic dependence on electric field strength produces little effect below field strengths of approx. 10 MV/m. However, above this field strength, the mole fraction of water in the liquid phase grows rapidly, increasing by a factor of 8 for a water vapor phase fraction of 0.2 and a field strength of 500 MV/m, which approaches the dielectric breakdown strength of water. Nonetheless, this field strength could be achievable with microfluidic experimental setups.

On the pressure drop calculation during the flow of two-phase non-azeotropic mixtures

• The effect of changes in the properties of the liquid and vapor phase during the flow of zeotropic mixture on the pressure drop. • The use of the equations of state of the liquid and vapor phases of a zeotropic mixture in the calculation of flow acceleration. • The approach has been developed for calculating the pressure gradient distribution and phase composition during the flow of a vapor-liquid zeotropic mixture. This article discusses the distinctive features of non-azeotropic vapor-liquid flows. It is shown that for the correct calculation of the pressure drop, the change in the thermophysical properties of the liquid and vapor phase along the flow must be taken into consideration. A calculation method that allows one to take the effect of a change in the composition of phases on the pressure drop and reasonably select a friction model for a two-phase flow has been proposed. In this method, the change in flow acceleration is calculated using the equations of state of the mixture for the liquid and vapor phases under phase equilibrium conditions. The method was verified. The calculation results are compared with experimental data from open sources for a non-azeotropic mixture of methane-ethane.

Heat transfer characteristics and operational visualization of two-phase loop thermosyphon

The advantages of high-efficiency and pumpless long-distance heat transport make the two-phase loop thermosyphon (TPLT) a promising candidate for various energy- and thermal-related applications. In this work, the simultaneous temperature/pressure measurement and high-speed visualization observation were conducted to compare and evaluate the heat transfer performance and two-phase flow characteristics of a vertical-positioned TPLT having an inner diameter of 10 mm. R141b was used as the working fluid at volumetric filling ratios of 35–50 %. The TPLT functioned well and had high heat transfer capacity at relatively high filling ratios (⩾ 40 %), while it failed to operate at a low filling ratio of 35 % under the power inputs greater than 250 W due to the local dry-out. A maximum effective thermal conductivity of 2.0 × 105 W/(m·K) was achieved at the optimal filling ratio of 40 %. Further, a flow regime map was developed to identify the combination effect of filling ratio and heat power on the flow pattern evaluation and two-phase flow instability. The geyser boiling usually manifests itself as an alternation of two or even three flow patterns, and tends to occur at the combination conditions of relatively low filling ratios (35 % and 40 %) and low heat powers or a moderate filling ratio (50 %) and relatively high heat powers. Additionally, the white mist phenomena caused by the flash vaporization was observed in the riser at relatively higher power inputs. The liquid-vapor mixture flow in the riser would partially degrade the TPLT performance due to the inhibition of vapor condensation in the condenser region. This study provides new insight into the operation characteristics of TPLT and gives guidelines for proper design and applications.

Refrigerant overheating in the compression circuit air heat pump

The authors considered the processes of phase transformation of the working fluid in the compression unit of the freon circuit in the section “thermal expansion valve (TEV) - evaporator - compressor”. By adjusting the expansion valve under the conditions of the bubble mode of boiling of the refrigerant, the evaporation process takes place, accompanied by the achievement of a certain excess of steam temperature. Determination of rheological parameters (droplet size, vapor viscosity, refrigerant droplet vaporization rate) is necessary so that when moving from the throttle valve (TEV) to the compressor inlet, they have time to go into the vapor phase or return to the mass of boiling liquid. The article presents the results of an analytical calculation of the parameters of the kinetics of evaporation of Freon droplets as they move in a steam flow. The results of such an analysis make it possible to formulate requirements for the optimal droplet size in the created vapor-liquid mixture in order to ensure their maximum evaporation and the required thermal efficiency of the AHP as a whole. The established patterns of evaporation of refrigerant droplets can be used to select the design and operation of the AHP.

Influence of a nonlinear degenerate diffusion on an advection-diffusion equation in a diffuse interface framework

This work is motivated by the modelling a liquid-vapour flows with phase transition describing the evolution of the coolant within an heat exchanger (e.g. the core of a Pressurized Water Reactor). We investigate an advection-diffusion equation with a degenerate and nonlinear diffusion coefficient. The degeneracy corresponds to a liquid-vapor mixture in the original model whereas the diffusion coefficient is non-degenerate in the pure phase cases. We focus on the influence of the diffusion coefficient on a simple 1D configuration for which some analytical computations can be done, leading to a surprising behavior of the phase transition with respect to the diffusion.

Analysis of direct steam generation in parabolic trough solar collectors under hot climate

• We present in the following, all the main contributions of this article. • Modeling and simulation of parabolic trough collectors for direct steam generation. • Numerical investigation of the direct steam generation thermohydraulic behavior. • A parametric analysis using various operating conditions is performed. • The optimal working conditions are proposed for the adopted installation. • Direct steam generation feasibility under climatic condition of Ouarzazate region. Direct steam generation in parabolic trough solar collectors is a promising technology for improving the performance of solar power plants. However, it remains a challenge because it induces liquid-vapor flows in the solar field. This process requires adequate control to avoid the deterioration risk of the receiver tube walls. In the present paper, a detailed numerical model of the system has been presented and validated. The proposed model is based on the conservation laws of the liquid-vapor mixture coupled with the energy balances of the receiver tube and the cover. An accurate parametric analysis is carried out to predict the appropriate operating conditions of the adopted installation. Indeed, the effects of the inlet conditions (mass flow, pressure, and fluid temperature) on the thermohydraulic behavior are investigated. From the obtained results, it emerges that for a good operation of the system, it is suitable to choose a mass flow rate higher than 0.4 kg/s to avoid the stratification phenomenon. Moderate pressure is appropriate to have a compromise between pressure drops and stratification of the mixture flow. The numerical simulation of the system operating under the meteorological conditions of the Ouarzazate region (Morocco) shows that regulation of the inlet flow rate according to the solar flux (0.5-0.75 kg/s for December 17 and 0.5-1.2 kg/s during June 20) and the combination of once-through and recirculation operating mode can ensure a steam production with sufficiently high qualities and durations.

PIGGY BACK SEPARATOR DESIGN

A PIGGY BACK separator is a device used in industrial oil and gas applications to separate a vapor-liquid mixture into its constituent phases. The aim of this study is to size the Piggy Back, a separator placed upstream of an electrostatic dehydrator to perform gas-liquid separation. In the course of this study, we sized the Piggy Back using manual calculations in accordance with the guidelines of the main standards and codes in force today, such as API 12J. To validate the manual assessment of the separator's dimensions, a static simulation was carried out using ASPEN HYSYS® software. Using the finally approved manual sizing methodology, and taking into account the Piggy Back separator's operational data, an economic evaluation was carried out to conclude that the design was cost-effective.

Global Dynamics of the Compressible Fluid Model of the Korteweg Type in Hybrid Besov Spaces

We are concerned with a system of equations governing the evolution of isothermal, viscous, and compressible fluids of the Korteweg type, which is used to describe a two-phase liquid–vapor mixture. It is found that there is a “regularity-gain" dissipative structure of linearized systems in case of zero sound speed P′(ρ*)=0, in comparison with the classical compressible Navier–Stokes equations. First, we establish the global-in-time existence of strong solutions in hybrid Besov spaces by using Banach’s fixed point theorem. Furthermore, we prove that the global solutions with critical regularity are Gevrey analytic in fact. Secondly, based on Gevrey’s estimates, we obtain uniform bounds on the growth of the analyticity radius of solutions in negative Besov spaces, which lead to the optimal time-decay estimates of solutions and their derivatives of arbitrary order.

Molecular dynamics study of liquid–vapor transition in underwater electrical wire explosion

During underwater electrical wire explosion, liquid–vapor transitions are crucial to the energy deposition and the generation of shock waves. To explore the characteristics of liquid–vapor transition during electrical explosions in water, a large-scale molecular simulation method was designed. The modeling scales experimental exploding wires to nano-size and then tracks the motion of each atom. The surrounding water medium was simplified as an expanding wall, whose velocity was determined by experimental steak images. Using this model, the phase transition processes at different energy deposition rates were compared. The results show that high energy deposition rates can make the discontinuous liquid–vapor phase transition disappear, forming an axially uniform vapor column, while slow energy injection will change the exploding wire into a foamlike liquid–vapor mixture at a subcritical temperature. The different shapes of wire–water interfaces in the experimental shadowgraphs can be explained by these features of liquid–vapor transition.