Phase Change Flow Research Articles

Understanding the impact of flow mechanisms in unsaturated layer on heat transfer near a partially submerged geothermal heat exchanger

Heat transfer near geothermal heat exchangers in the presence of groundwater flow has been extensively studied over the past years. However, previous studies often overlooked the presence of an unsaturated layer in the shallow subsurface soil, or disregarded phase change and fluid flow within this layer. In this study, a comprehensive hydro-thermal model is developed to evaluate heat transfer near a partially submerged geothermal borehole in groundwater flow while incorporating phase change and liquid and vapor flow in the unsaturated layer. The effect of unsaturated soil hydraulic analysis on heat transfer and energy efficiency of the geothermal piles is explored under varying soil permeabilities, air-entry suctions, solid thermal conductivities, and soil types. Consideration of water content variation and unsaturated fluid flow in the model enhances heat injection rate by up to 11.23 % in highly permeable soils. However, in scenarios with higher solid thermal conductivity, or lower air-entry suction values, the heat injection rate reduces by as much as 16.13 % due to unsaturated soil hydraulic analysis. Furthermore, it is found that consideration of unsaturated soil hydraulic analysis is of greater importance in Bonny silt than sandy soil, lowering the heat injection rate by 8.53 % and 2.53 %, respectively.

Study on the influence factors of rock breaking by supercritical CO2 thermal fracturing

At present, there is a growing demand for safe and low-pollution rock-breaking technology. The rock breaking technology of supercritical CO2 thermal fracturing has many advantages, such as no dust noise, no explosion, high efficiency, controllable shock wave and so on. Fully considering the combustion rate of energetic materials, heat and mass transfer, CO2 phase change and transient nonlinear flow process, a multi-field coupled numerical model of rock breaking by supercritical CO2 thermal fracturing was established based on the existing experiments. The influence factors of CO2 thermal fracturing process were studied to provide theoretical guidance for site construction parameters optimization. The numerical simulation results were in good agreement with the experimental observation results. The results showed that the maximum temperature of CO2 and the growth rate of CO2 pressure during the fracturing process would decrease accordingly with the increase of CO2 initial pressure. But the change in CO2 peak pressure wasn't significant. Appropriately increasing the heat source power could improve the heating and pressurization rate of CO2 and accelerate the damage rate of rock. The relevant results were of great importance for promoting the application of rock breaking by supercritical CO2 thermal fracturing technology.

Entropy transfer efficiency-effectiveness method for heat exchangers, part 1: Local entropy generation number and operation performance limits

Here, to resolve the open problem of the second-law efficiency evaluation for heat exchangers, an efficiency-effectiveness method is developed from pure convection theory, where the entropy transfer efficiency defined as the outlet temperature ratio of cold and hot fluids exchanging entropy and local entropy generation number can measure the global and local irreversibilities of heat transfer. The efficiency and effectiveness are related by the inlet temperature ratio τ and capacity rate ratio φ, and their maxima subject to the local entropy generation number are determined for different flow arrangements. When τ = φ2, the effectiveness maxima are 0.5/(1 + φ) and 1/(1 + φ) while the highest efficiencies are φ and unity for parallelflow and counterflow arrangements, respectively. The optimum operating points of counterflow exchangers, at which the equal outlet temperature τT1∞ (T1∞ represents the hot inlet temperature) of two fluids with a critical capacity rate ratio τ induces uniform irreversibility, the effectiveness limit of 1/(1+τ), and the efficiency limit of unity, are obtained. A linear temperature difference method is also developed based on the redefined convective and overall heat transfer coefficients, invariably yielding an effectiveness equal to the number of heat transfer units. This method has potentials to be extended to wet heat exchangers with phase-change flows.

Heat transfer investigation of nano – Encapsulated phase change materials (NEPCMs) in a thermal energy storage device

Phase change natural convection heat transport and flow features of a variety and new types of hybrid nanoliquids, suspension of Nano – encapsulated phase change materials (NEPCMs), within a square cavity is inspected theoretically in this analysis. The capsules are arranged with a shell and a PCM as a core. The shell of this NEPCM prevents the phase change material from the direct interaction of hot fluid and from the leakage. The heat capacity of the suspension contains latent heat generated at the time of phase change. The modeled equations are numerically scrutinized with Finite element method. Variable thermal conductivity parameter 1≤Nc≤5, variable viscosity parameter 1≤Nv≤5, radiation number 0.5≥R≥0.1, Rayleigh parameter 102≤Ra≤103, volume fraction of NEPCMs1%≤ϕ≤5% and fusion temperature (0.2≤θf≤1.0) impact on the patterns of heat capacity ratio, isotherms and velocity lines are examined in detail. The results indicates that, as the volume fraction values of NEPCMs amplifies from 1% to 5% the rates of heat transfer of the nanoliquid magnifies 42% compared to the host fluid. Non – dimensional rates of heat transport magnifies with growing (Ste) values.

New Friction Factor Correlation for Phase-Change Flow in Plate Heat Exchangers

This article reports a new two-phase friction factor correlation for condensing and evaporating flows in plate heat exchangers. Over a thousand condensation pressure drop data compiled from seventeen articles were reduced to a two-phase friction factor correlation and successfully evaluated with data not used for correlation development. Similarly, over two thousand evaporation pressure drop data were collected from twenty-four articles and were empirically modeled to yield a two-phase friction factor, which was also successfully validated with independent data. The condensation friction factor correlation fit 72% of the data within ±50% and modeled 92% of the evaluation data within ±50%. Similarly, the evaporation friction factor correlation fit 64.9% of the data within ±50 and 89.8% of the evaluation data within ±50%. Pressure drop in condensers was predominantly due to convective condensation and buoyancy forces. Inertial forces and convective boiling were mainly responsible for the pressure drop in evaporators. As the Weber number was much <1, drop condensation and nucleate boiling were insignificant. Meta-analysis strongly recommended deploying plate heat exchangers as condensers for lowering the pressure drop and was inconclusive for evaporators.

Three-dimensional CFD simulation of geyser boiling in high-temperature sodium heat pipe

A deep understanding of the characteristics and mechanism of geyser boiling and capillary pumping is necessary to optimize a high-temperature sodium heat pipe. In this work, the Volume of Fluid (VOF) two-phase model and the capillary force model in the mesh wick were used to model the complex phase change and fluid flow in the heat pipe. Computational Fluid Dynamics (CFD) simulations successfully predicted the process of bubble nucleation, growth, aggregation, and detachment from the wall in the liquid pool of the evaporation section of the heat pipe in horizontal and tilted states, as well as the reflux phenomenon of capillary suction within the wick. The accuracy and stability of the capillary force model within the wick were verified. In addition, the causes of geyser boiling in heat pipes were analyzed by extracting the oscillation distribution of heat pipe wall temperature. The results show that adding the capillary force model within the wick structure can reasonably simulate the liquid backflow phenomenon at the condensation; Under the horizontal and inclined operating conditions of the heat pipe, the phenomenon of local dry-out will occur, resulting in a sharp increase in local temperature. The speed of bubble detachment and the timely reflux of liquid sodium (condensate) replenishment in the wick play a vital role in the geyser temperature oscillation of the tube wall. The numerical simulation method and the results of this study are anticipated to provide a good reference for the investigation of geyser boiling in high-temperature heat pipes.

The influence of aspect ratios of two elliptical cylinders on the solid-liquid phase change flow

Nowadays, phase change materials are widespread in different engineering applications including cooling of electronics, thermal performance in building elements, heat exchangers, and many more. It is critical to gain thorough comprehension on phase change material behavior. The present research aims to numerically simulate phase change material in a heat storage unit having two isothermal elliptical elements. The formulated partial differential equations have been solved by the finite element technique taking into account the enthalpy-porosity approach and adaptive mesh refinement technique. The developed computational code has been validated using numerical and experimental data from the literature. The influence of the aspect ratios of the two elliptical cylinders on the melting phenomenon has been scrutinized, and the most efficient shapes have been identified. It has been found that more intensive melting occurs when the aspect ratios of the upper and lower cylinders are ARu = 0.25 and ARl = 4.0, with a reduction of 18.45 % in the melting time compared to the case with ARu = ARl = 1.0. Furthermore, the case with ARu = 1.0 and ARl = 0.5 shows the longest melting time, with an increase of 0.6 % in the melting time compared to the case with ARu = ARl = 1.0.

Study on Phase Change Flow and Heat Transfer Characteristics of Microalgae Slurry in the Absorber Tube of a Parabolic trough Solar Collector

The study of gas–liquid two-phase flow and heat transfer in non-Newtonian fluids is of great significance for the research and development of refrigeration and energy storage. In this paper, the characteristics and influencing factors of the phase change reaction in microalgae slurry were studied by numerical simulation and experimental verification. In order to further study the rheological and heat transfer characteristics of gas–liquid two-phase flow in the collector, the effects of wall heat flux, inlet velocity and microalgae slurry concentration on the phase change reaction in microalgae slurry were studied. The results show that when the boundary conditions of microalgae slurry with the same concentration change, the phase transition of microalgae slurry is different. The higher the wall heat flux, the more forward the phase transition occurs, and the smaller the flow rate, the more forward the phase transition occurs. When the boundary conditions remain unchanged, the phase transition point of microalgae slurry with different concentrations is the same, and the concentration of microalgae slurry will not be affected. However, the deviation between the fluid temperature and the thermal conductivity of high-concentration fluid after phase change is larger than that of low-concentration fluids. The deviation in the fluid temperature reaches approximately 10 K, and the deviation in thermal conductivity reaches approximately 0.025 W/(m·K). Therefore, the change in the fluid temperature and heat transfer intensity after phase change in microalgae slurry is more intense than that of Newtonian fluids.

Numerical Study of Coupled Water and Vapor Flow, Heat Transfer, and Solute Transport in Variably‐Saturated Deformable Soil During Freeze‐Thaw Cycles

AbstractAs climate change intensifies, soil water flow, heat transfer, and solute transport in the active, unfrozen zones within permafrost and seasonally frozen ground exhibit progressively more complex interactions that are difficult to elucidate with measurements alone. For example, frozen conditions impede water flow and solute transport in soil, while heat and mass transfer are significantly affected by high thermal inertia generated from water‐ice phase change during the freeze‐thaw cycle. To assist in understanding these subsurface processes, the current study presents a coupled two‐dimensional model, which examines heat conduction‐convection with water‐ice phase change, soil water (liquid water and vapor) and groundwater flow, advective‐dispersive solute transport with sorption, and soil deformation (frost heave and thaw settlement) in variably saturated soils subjected to freeze‐thaw actions. This coupled multiphysics problem is numerically solved using the finite element method. The model's performance is first verified by comparison to a well‐documented freezing test on unsaturated soil in a laboratory environment obtained from the literature. Then based on the proposed model, we quantify the impacts of freeze‐thaw cycles on the distribution of temperature, water content, displacement history, and solute concentration in three distinct soil types, including sand, silt and clay textures. The influence of fluctuations in the air temperature, groundwater level, hydraulic conductivity, and solute transport parameters was also comparatively studied. The results show that (a) there is a significant bidirectional exchange between groundwater in the saturated zone and soil water in the vadose zone during freeze‐thaw periods, and its magnitude increases with the combined influence of higher hydraulic conductivity and higher capillarity; (b) the rapid dewatering ahead of the freezing front causes local volume shrinkage within the non‐frozen region when the freezing front propagates downward during the freezing stage and this volume shrinkage reduces the impact of frost heave due to ice formation. This gradually recovers when the thawed water replenishes the water loss zone during the thawing stage; and (c) the profiles of soil moisture, temperature, displacement, and solute concentration during freeze‐thaw cycles are sensitive to the changes in amplitude and freeze‐thaw period of the sinusoidal varying air temperature near the ground surface, hydraulic conductivity of soil texture, and the initial groundwater levels. Our modeling framework and simulation results highlight the need to account for coupled thermal‐hydraulic‐mechanical‐chemical behaviors to better understand soil water and groundwater dynamics during freeze‐thaw cycles and further help explain the observed changes in water cycles and landscape evolution in cold regions.

Well Test Analysis for a Well in Gas Storage Reservoirs With the Formation Containing High Salinity Water

Abstract The production capacity of the gas wells is seriously affected by salt deposition during the injection and production process for underground gas storage with high salt content, so it is necessary to predict the production performance through well test technology. However, the existing well test analysis methods cannot be reliably used to interpret the well test data affected by salt deposition phase change and high-speed non-Darcy flow during the injection and production process. Therefore, this paper first determines the relationship between salt deposition and temperature and pressure through flash calculation of phase equilibrium of saltwater and hydrocarbon system, then establishes a porosity and permeability model considering the effect of salt deposition, and further establishes a high-speed injection-production well test analysis model considering the effect of salt deposition in combination with Forchheimer’s percolation law. Finally, the model is solved by numerical method, and the dynamic changes of reservoir pressure and salt deposition are simulated and calculated. The results show that the higher the salinity of formation water is, the greater the risk of salt deposition in the reservoir is, and the permeability of the reservoir will significantly decrease after salt deposition occurs; the non-Darcy flow effect will aggravate the risk of salt deposition in the reservoir. The research results provide a theoretical method for the evaluation of reservoir parameters and production performance prediction of salt gas storage reservoirs.

Two-Phase Flow Visualization and Heat Transfer Characteristics Analysis in Ultra-Long Gravity Heat Pipe

The ultra-long gravity heat pipe has a long heat transfer distance and narrow working fluid flow channel within its tube. Due to these unique design features, the vapor–liquid counter-flow and heat transfer characteristics of these heat pipes are more complex than those found in conventional-size heat pipes. This paper innovatively proposes the design of a segmented visualization window structure of an ultra-long gravity heat pipe, which successfully overcomes the challenge of visualizing the internal flow during operations. A visualization experimental platform, measuring 40 m in height with an inner diameter of 7 mm and the aspect ratio up to 5714, was built to investigate the evolving characteristics of two-phase flows with an increasing heat input and the impact of the phase change flow characteristics on the thermal performance of ultra-long gravity heat pipes. The results obtained can provide guidance for the development of the internal structure of ultra-long gravity heat pipes that are being applied in exploiting geothermal energy. The results show that, at low heat input (200 W, 250 W), there are separate flow paths between the condensate return and the steam, but the high hydrostatic pressure due to the height of the liquid injection results in the presence of an unsaturated working fluid with a higher temperature in the liquid pool area, which has a lower evaporation rate, limiting the heat transfer through the heat pipe. It is found that if increasing the heat input up to 300 W, the evaporative phase change in the heating section becomes intense and stable. At the same time, despite the intermittent formation of liquid columns in the adiabatic section due to the vapor–liquid rolls, which increases the resistance to the vapor–liquid counter-flow, the liquid columns are blocked for a short period of time, and the path of steam rises and the condensate return is smooth, which does not seriously affect the steam condensation and liquid return evaporation. At this point, the overall temperature of the heat pipe is evenly distributed along the tube and the heat transfer performance is optimal. When the heat input further increases (350 W, 400 W), a large amount of condensate is trapped in the upper part of the adiabatic section and the condensing section by long liquid plugs for a long time. At this point, the condensate flow back to the heating section is significantly reduced, and the steam is seriously prevented from entering the condensation section, resulting in a significant increase in the temperature gradient between the lower part of the evaporating section and the upper part of the adiabatic section and deterioration of the heat transfer performance.

An OpenFOAM framework to model thermal bubble-driven micro-pumps

Thermal bubble-driven micro-pumps (also known as inertial pumps) are an upcoming micro-pump technology that can be integrated directly into micro/mesofluidic channels to displace fluid without moving parts. These micro-pumps are high-power resistors that locally vaporize a thin layer of fluid above the resistor surface to form a high-pressure vapor bubble which performs mechanical work. Despite their geometric simplicity, thermal bubble-driven micro-pumps are complex to model due to the multiphysics couplings of Joule heating, thermal bubble nucleation, phase change, and multiphase flow. As such, most simulation approaches simplify the physics by neglecting Joule heating, nucleation, and phase change effects as done in this study. To date, there are no readily available, reduced physics open-source modeling tools that can resolve both pre-collapse (defined as when the bubble is expanding and collapsing) and post-collapse (defined as when the bubble has re-dissolved back into the subcooled fluid) bubble and flow dynamics. In this study, an OpenFOAM framework for modeling thermal bubble-driven micro-pumps is presented, validated, and applied. The developed OpenFOAM model agrees with both experimental data and commercial computational fluid dynamics (CFD) software, FLOW-3D. Additionally, we assess the shape of the transient velocity profile during a pump cycle for the first time and find that it varies substantially from theoretical Poiseuille flow during pre-collapse but is within 25% of the theoretical flow profile during post-collapse. We find that this deviation is due to flow never becoming fully developed during each pump cycle. We envision the developed OpenFOAM framework as an open-source CFD toolkit for microfluidic designers to simulate devices with thermal bubble-driven micro-pumps.

Thermal analysis and optimization of metal foam PCM-based heat sink for thermal management of electronic devices

Efficient thermal management in electric devices is highly essential for ensuring the reliability and durability of electronics. This study aims to investigate the thermal performance and optimization of metal foam PCM-based heat sink for thermal management units. Different design parameters, such as PCM types (RT31, RT42, and RT55), metal foam porosities (85%, 90%, and 95%), and metal foam materials, are studied to determine heat sink optimal parameters, considering various critical temperatures: 40 °C, 50 °C, 60 °C and 70 °C. The volume-averaged method is used to simulate the heat transfer, phase change, and fluid flow within the heat sink unit. Heat transfer between PCM and metal foam is established using a thermal non-equilibrium model. The results show that the usage of metal foam is conducive to the thermal performance enhancement of heat sinks. Among the three parameters, PCM types show a considerable effect on thermal performance of heat sinks, e.g., the maximum operation time of heat sinks with RT31 is about 5 times that of heat sinks with RT55 for the critical temperature of 40 °C. Among all the cases, heat sinks using RT31 and aluminum foam perform optimally, which can achieve the optimal design of heat sinks.

Numerical method for gas-liquid two-phase flow with phase change heat transfer considering compressibility using OpenFOAM

The numerical simulation of phase change heat transfer is important for predicting the gas-liquid two-phase flow and heat transfer characteristics and optimizing the phase change heat dissipation system. For the isovolumetric phase change heat transfer process, the compressibility of the gas phase has a significant impact on the simulation accuracy. A numerical simulation method of flow and phase change heat transfer considering gas-liquid two-phase compressibility is established based on VOF method using OpenFOAM in this paper. This method introduces a generalized phase change source term and a compressible source term to improve the isoAdvector geometric reconstruction algorithm and establishes a method for capturing the phase interface of a compressible two-phase flow. The phase change flux based on the phase interface is converted into a phase change source term based on the unit volume by calculating the phase interface density. The compressible term of the governing equation is constructed and its implicit discrete method is proposed. The coupling between velocity and pressure is realized based on the PISO algorithm. A numerical calculation method for phase change heat transfer of compressible two-phase flow is established. The effectiveness and accuracy of the proposed numerical method for predicting the heat transfer characteristics of phase change flows are verified by the simulation of vertical flat film condensation and film boiling. The numerical simulation results are in good agreement with the experiment. Compared with the other numerical simulation methods, the proposed method considering the influence of the compressibility of the gas phase on the flow and heat transfer characteristics in the heat pipe has high accuracy in predicting the gas-liquid two-phase flow, capturing the evolution characteristics of the phase interface and predicting the phase change heat transfer. The numerical simulation method can provide algorithm support for the numerical simulation of compressible two-phase flow phase change heat transfer and the design of a phase change heat dissipation system.

Convective transport characteristics of condensing droplets in moist air flow

Condensation of convective moist air flow is a crucial physical process and is directly related to various industries. It is essential to understand the underlying growth mechanism of condensing droplets, while past studies have commonly considered convective transport with a negligible/simplified approach. In this work, a three-dimensional transient multiphysics coupling model was developed to investigate the transport characteristics of condensing droplets in convective moist air flow. This model typically interconnects heat transfer with vapor–liquid phase change, mass transport, and fluid flow. The results reveal that convective flow significantly dominates heat and mass transport during condensation. On the gas side, the incoming flow thins the diffusion layer at the windward part with a large concentration gradient. However, a low vapor-concentration zone behind the droplet is formed due to the resulting rear-side vortex, which presents an increased influence as the contact angle increases. By forcing molecular diffusion with convection transport, vapor transport from surroundings to the condensing interface is enhanced several times depending on the Reynolds number. Within the droplet, the flow shearing at the interface is principally responsible for the strong internal convection, while the Marangoni effect is negligible. The internal flow greatly affects the droplet temperature profile with a large gradient close to the base. Finally, convective flow contributes to over 3.3 times higher overall heat transfer coefficient than the quiescent environment. In addition, in interaction-governed growth, transport characteristics depend on not only the size and space distributions of droplets but also the interaction between droplets and convective flow.

Integrity of Newton’s cooling law based on thermal convection theory of heat transfer and entropy transfer

Although thermal convection is omnipresent in nature and technology and serves important purposes in various energy transport systems, whether convection can be viewed as an independent heat transfer means has long been argued The constant coefficient in the original version or convective heat transfer coefficient defined in the modern version of Newton’s cooling law quantifies the ratio of the surface heat flux to the temperature difference between a body surface and an adjacent fluid. However, none of the consistent analytical expressions for these two coefficients are present in Newton’s cooling law. The inherently complex relationship between these pending coefficients and convective heat flux vectors makes revealing the convective mechanism extremely difficult. Theoretical determination of these coefficients would bring new insights to thermal convection and direct applications to thermal management. Here we theoretically show consistent analytical expressions for the constant and convective heat transfer coefficients for various flows to make Newton’s cooling law a complete scientific law. For this purpose, a three-dimensional (3D) energy transfer theory of thermal convection is developed, and the convective heat flux vector, entropy flux vector and entropy generation rate inside the system are derived for both single-phase and phase-change flows. By recasting a control volume system into an equivalent control mass system and employing the first and second laws of thermodynamics, the fundamental advective heat transfer mode characterized by temperature differences and entropy changes is demonstrated. The physical implications underlying the 3D convective formulae are elucidated. Comparisons of the analytical results with laminar experiments and turbulent flow measurement benchmark data validate our theoretical findings. Our 3D heat and entropy transfer theory will broaden the research area of thermal convection processes and open up a new arena for the design and thermal management of convective heat transfer in single-phase and phase-change flows.

Characteristics of phase-change flow and heat transfer in loop thermosyphon: Three-dimension CFD modeling and experimentation

Two-phase loop thermosyphon (TPLT) shows an oscillation phenomenon since the complex phase-change heat transfer and flow behaviors, decreases the system reliability in practice. A combined three-dimension CFD simulating/experimental investigation was carried out to investigate the phase-change flow inside TPLT. Results of the 3D-CFD model show good agreement with the experiments, with a maximum deviation of 2.86% and 3.98% for temperature distribution and pressure, respectively. In the vertical evaporator heating mode, the filling ratio of 23.3% produced the lowest total thermal resistance of 0.28–0.22K/W since the dominant heat transfer mechanism of phase-change in the loop. With the increasing FR, from 48.0 to 84.1%, the dominant heat transfer mechanism might be transformed to single-phase convection. Thermal performance with the horizontal evaporator heating mode is better than that with the vertical evaporator heating mode since the good flowability at high FR = 84.1%. In the horizontal evaporator heating mode, a bidirectional flow was observed in the loop with the horizontal evaporator even at low FR = 23.3%, which caused pressure fluctuation and reduced thermal performance. But the flow stability could increase by 90% with the auxiliary of a porous media in the horizontal evaporator, indicating that the porous media had a positive effect on avoiding bidirectional flow.

A phase-change model for diffusion-driven mass transfer problems in incompressible two-phase flows

We present a VOF-based numerical method for incompressible Direct Navier–Stokes (DNS) equations for diffusion-driven phase-change flows. A special emphasis is placed on the treatment of velocity discontinuities across the interface. A novel algorithm is presented to smoothly extend the liquid velocity field across the interface in a way that the interface can be transported by a divergence-free velocity field. The transport of species is treated with a two-scalar approach and special attention is paid to the advection and diffusion steps in order to prevent artificial mass transfer. The methodology is implemented in the open-source code Basilisk and is validated against analytical and semi-analytical models. The relative errors on the relevant quantities are generally below 1% for the finest grids. The method is finally applied to study the growth of electrochemically generated bubbles on planar electrodes and the effect of contact angles and number of nucleation sites is investigated.

Modeling of multiphase flow during underbalanced drilling considering velocity, temperature and pressure

A clear understanding of multiphase flow with phase change is of great significance in productivity evaluation, process optimization, and production analysis, which is one of the focus issues of underbalanced drilling. In the process of underbalanced drilling, the annular flow is very complex. To drill safely and protect the reservoir, the dynamic separation process of dissolved natural gas and the characteristics of downhole multiphase flow are studied in this paper. Focusing on the characteristics of live crude oil and physical parameters in the wellbore, the authors creatively consider the influence of the velocity on the solubility and establish a mathematical model of multi-physical field non-equilibrium phase change and multiphase flow considering velocity, temperature and pressure. According to the established mathematical model, the solubility diagram of natural gas is drawn, and the evolution law of flow parameters is analyzed. The results show that the influence of the three factors on solubility is that the influence of pressure is greater than that of temperature, and the influence of temperature is greater than that of flow velocity. The effect of flow velocity on annular pressure, temperature and phase content does not seem to be very great in the natural gas solubility model. However, the dissolved gas in the wellbore separates earlier when considering the velocity than when the velocity is not considered. It is concluded that the research presented here confirms that the influence of flow velocity cannot be ignored. The innovative mathematical model in this paper takes into account the effect of flow velocity on non-equilibrium multiphase flow with phase change. By using the model developed, a better understanding can be obtained of what the phase change characteristics of downhole fluid are and how the multiphase flow laws will change, which is of great significance to reservoir protection and drilling safety.

Fluid dynamics of frozen precipitation at the air–water interface

Precipitation in the forms of snow, hail, and rain plays a critical role in the exchange of mass, momentum and heat at the surfaces of lakes and seas. However, the microphysics of these interactions are not well understood. Motivated by recent observations, we study the physics of the impact of a single frozen canonical particle, such as snow and hail, onto the surface of a liquid bath using a numerical model. The descent, melting, bubble formation and thermal transport characteristics of this system are examined. Three distinct response regimes, namely particle impact, ice melting and vortex ring descent, have been identified and characterized. The melting rate and air content of the snow particle are found to be leading factors affecting the formation of a coherent vortex ring, the vertical descent of melted liquid and the vortex-induced transportation of the released gas bubble to lower depths. It is found that the water temperature can substantially alter the rate of phase change and subsequent flow and thermal transport, while the particle temperature has minimal effect on the process. Finally, the effects of the Reynolds, Weber and Stefan numbers are examined and it is shown that the Reynolds number modifies the strength of the vortex ring and induces the most significant effect on the flow dynamics of the snow particle. Also, the change of Weber number primarily alters the initial phases of snow–bath interaction while modifying the Stefan number of the snow particle essentially determines the system response in its later stages.