On the fulfillment of the energy conservation law in mathematical models of evolution of single spherical bubble

The problem of the evolution of a single spherical bubble in an infinite liquid is considered, as the result of a variation of the pressure in the liquid at an infinite distance from the bubble. It has been assumed the bubble is filled with vapor from the surrounding liquid or insoluble gas. The question of the fulfillment of the integral energy conservation law is investigated using different ways of describing the hydrodynamic and heat and mass exchange processes in both the bubble and surrounding liquid and at the bubble interface. Kinetic and internal energy of vapor (gas) in the bubble, kinetic and internal energy of the liquid, and energy of surface tension are taken into account in the energy balance. The liquid is assumed to be incompressible, viscous and heat-conducting, the vapor (gas) to be nonviscous, heat-conducting and obeying the Clapeyron equation. Thermal–physical properties, exclusive of specific heats, are allowed to be temperature-dependent. For the above suppositions and assumptions, a mathematical model ensuring exact fulfillment of the integral energy conservation law has been developed. It has been shown that the conservation integral can be fulfilled by the given model. As simplified variants of the principal model, models of the uniform bubble and pressure uniform bubble, have been proposed which ensure the exact fulfillment of the integral energy balance disregarding the relatively small vapor kinetic energy. A relation defining the imbalance in the integral energy conservation law for some often-used extra simplifications has been derived.     

Simulation of heat transfer with the growth and collapse of a cavitation bubble near the heated wall

The growth and collapse behaviors of a single cavitation bubble near a heated wall and its effect on the heat transfer are numerically investigated. The present study is designed to reveal the mechanism of cavitation enhanced heat transfer from a microscopic perspective. In the simulation, the time-dependent Navier-Stokes equations are solved in an axisymmetric two-dimensional domain. The volume of fluid (VOF) method is employed to track the liquid-gas interface. It is assumed that the gas inside the bubble is compressible vapor, and the surrounding liquid is incompressible water. Mass transfer between two phases is ignored. The calculated bubble profiles were compared to the available experimental data, and a good agreement was obtained. Then, the relationship among bubble motion, flow field and surface heat transfer coefficient was analyzed. On this basis, the effects of such factors as the initial distance between the bubble and the wall, the initial vapor pressure and the initial bubble nucleus size on the heat transfer enhancement are discussed. The present study is helpful to understand the heat transfer phenomenon in presence of cavitation bubble in liquid.     

On the rise paths of single vapor bubbles after the departure from nucleation sites in subcooled upflow boiling

A photographic study was carried out for the subcooled flow boiling of water to elucidate the rise characteristics of single vapor bubbles after the departure from nucleation sites. The test section was a transparent glass tube of 20 mm in inside diameter and the flow direction was vertical upward; liquid subcooling was parametrically changed within 0–16 K keeping system pressure and liquid velocity at 120 kPa and 1 m/s, respectively. The bubble rise paths were analyzed from the video images that were obtained at the heat flux slightly higher than the minimum heat flux for the onset of nucleate boiling. In the present experiments, all the bubbles departed from their nucleation sites immediately after the inception. In low subcooling experiments, bubbles slid upward and consequently were not detached from the vertical heated wall; the bubble size was increased monotonously with time in this case. In moderate and high subcooling experiments, bubbles were detached from the wall after sliding for several millimeters and migrated towards the subcooled bulk liquid. The bubbles then reversed the direction of lateral migration and were reattached to the wall at moderate subcooling while they collapsed due to the condensation at high subcooling. It was hence considered that the mechanisms of the heat transfer from heated wall and the axial growth of vapor volume were influenced by the difference in bubble rise path. It was observed after the inception that bubbles were varied from flattened to more rounded shape. This observation suggested that the bubble detachment is mainly caused by the change in bubble shape due to the surface tension force.     

A unified model for multi-turn closed-loop pulsating heat pipe

Numerical modeling of  the multi-turn closed-loop pulsating heat pipe (CLPHP) in the bottom, horizontal, and top heat mode is presented in this paper, with water as working fluid. Modeling is carried out for 2-mm ID CLPHP having 5, 16, and 32 turns at different orientations for 10 different cases. Momentum and heat transfer variations with time are investigated by numerically solving the one-dimensional governing equations for vapor bubble and liquid plugs. Instead of considering all the vapor bubble at saturation temperature, vapor bubbles are allowed to remain in super-heated condition. Film thickness is found using a correlation. Two-phase heat transfer coefficient is calculated by considering conduction through the thin film at liquid–vapor interface. Liquid plug merging and splitting result in continuous variation in the number of liquid plugs and vapor bubble with time, which is also considered in the code. During the merging of liquid plugs, a time step-adaptive scheme is implemented and this minimum time step was found to be 10⁻⁷ s. Model results are compared with the experimental results from literature for heat transfer and the maximum variation in heat transfer for all these cases is below ±39%.     

Dynamic Behavior of Bubble Interface During Boiling

A brief review with discussions is conducted for some pertinent works, done and ongoing in the Laboratory of Phase-Change and Interfacial Phenomena at Tsinghua University, on interfacial behavior of vapor bubbles and interfacial transport phenomena during liquid nucleation boiling. From a sequence of experimental investigations, some new phenomena, particularly, the visually observed interfacial transport phenomena or processes including jet-like flows, bubble interaction and spatial scale effect, were described in this article. The interfacial effects and transport phenomena associated with surface tension gradients caused by temperature and concentration variations were theoretically analyzed to reveal the marked influence on bubble interfacial shape and dynamic behavior, the bubble dynamics including nucleation, bubble motion and coalescence. Several theoretical models and methods were proposed to describe the dynamic characteristics and explain the physics of interfacial phenomena/processes. The spe     

High-Speed Visualization of Bubble Behaviors for Pool Boiling of R-141b

A visualization study on the behavior of bubbles has been carried out for pool boiling of R141b on a horizontal transparent heater at pressure 0.1 MPa. The behaviors of bubbles were recorded by a high-speed camera placed beneath the heater surface. The departure diameter, departure time of bubbles and nucleation site density at different heat flux were obtained. The visualization results show that bubble departure diameter and departure time decrease , while the nucleation site density increases as the heat flux increases. It is also observed that there is no liquid recruited into the microlayer in the experiment. Based on the experimental results, boiling curve for R141b was predicted by using the dynamic microlayer model. As a result, the agreement between the predictive result based on the dynamic microlayer model and the experiment data for boiling curve of R141b is good at high heat flux.     

黏性液体中锐孔处气泡的形成

考察一定流量气体,通过锐孔在静止黏性液体中连续溢出气泡的过程。应用动力学平衡半经验关系式,综合考虑气泡受力,分析气泡形成过程,给出合理假设,预测气泡直径。分析表面张力、气体流速、锐孔直径及液相物性对气泡脱离尺寸的影响,找到影响气泡脱离尺寸的主要因素。计算预报值与实验结果符合良好。     

Holographic interferometric study of heat transfer to a sliding vapor bubble

Heat transfer associated with a vapor bubble sliding along a downward-facing inclined heater surface was studied experimentally using holographic interferometry. Volume growth rate of the bubbles as well as the rate of heat transfer along the bubble interface were measured to understand the mechanisms contributing to the enhancement of heat transfer during sliding motion. The heater surface was made of polished silicon wafer (length 185 mm and width 49.5 mm). Experiments were conducted with PF-5060 as test liquid, for liquid subcoolings ranging from 0.2 to 1.2 °C and wall superheats from 0.2 to 0.8 °C. The heater surface had an inclination of 75° to the vertical. Individual vapor bubbles were generated in an artificial cavity at the lower end of the heater surface. High-speed digital photography was used to measure the bubble growth rate. The temperature field around the sliding bubble was measured using holographic interferometry. Heat transfer at the bubble interface was calculated from the measured temperature field. Results show that for the range of parameters considered the bubbles continued to grow, with bubble growth rates decreasing with increasing liquid subcooling. Heat transfer measurements show that condensation occurs on most of the bubble interface away from the wall. For the parameters considered condensation accounted for less than 12% of the rate heat transfer from the bubble base. In this study the heater surface showed no drop in temperature as a result of heat transfer enhancement during bubbles sliding.     

Optimization of gas hydrate reactors with slug flow

A model of heat transfer during gas hydrate formation at a gas-liquid interface in gas-liquid slug flow with liquid plugs containing small bubbles is suggested. Under the assumption of perfect mixing of liquid in liquid plugs, recurrent relations for temperature in the n-th liquid plug and heat and mass fluxes from the n-th unit cell in a gas-liquid slug flow are derived. The ratio of the total mass flux during gas hydrate formation in a cluster with N unit cells to the mass flux in a cluster with an infinite number of unit cells is determined. The number of unit cells that yield 95% of the total amount of gas hydrates in an infinite cluster of unit cells is calculated and formula for an optimal length of a gas hydrate slug flow reactor is derived.     

Interaction of two cavitation bubbles in a tube and its effects on heat transfer

When two cavitation bubbles exist in a confined space, the interaction between the bubbles significantly affects the characteristics of bubble dynamic behaviors. In this paper, a three-dimensional (3D) model is established to study the growth and collapse of two cavitation bubbles in a heated tube and its effects on heat transfer. The liquid and gas phases throughout the calculation domain are solved by a set of Navier-Stokes equations. It is assumed that the gas inside the bubble is compressible vapor, and the surrounding liquid is incompressible water. The mass transfer between two phases is ignored. The calculated bubble profiles were compared to the available experimental data, and a good agreement has been achieved. Then, the relationship among the bubble motion, flow field and pressure distributions was analyzed. On this basis, the effects of bubble interaction on the heat transfer between the wall surface and sounding liquid were discussed. It is found that heat transfer in the centre wall region is enhanced owing to the vortex flow and micro-jet induced by the bubble contraction and collapse. In contrast, the highest surface temperature appears in the surrounding region, which is mainly attributed to the thermal resistance induced by the bubble. The present study is helpful to understand the heat transfer phenomenon with cavitation in the liquid.     

The effect of liquid film evaporation on flow boiling heat transfer in a micro tube

Flow boiling in micro channels is attracting large attention since it leads to large heat transfer area per unit volume. Generated vapor bubbles in micro channels are elongated due to the restriction of channel wall, and thus slug flow becomes one of the main flow regimes. In slug flow, sequential bubbles are confined by the liquid slugs, and thin liquid film is formed between tube wall and bubble. Liquid film evaporation is one of the main heat transfer mechanisms in micro channels and liquid film thickness is a very important parameter which determines heat transfer coefficient. In the present study, liquid film thickness is measured by laser focus displacement meter under flow boiling condition and compared with the correlation proposed for an adiabatic flow. The relationship between liquid film thickness and heat transfer coefficient is also investigated. Initial liquid film thickness under flow boiling condition can be predicted well by the correlation proposed under adiabatic condition. Under flow boiling condition, liquid film surface fluctuates due to high vapor velocity and shows periodic pattern against time. Frequency of periodic pattern increases with heat flux. At low quality, heat transfer coefficients calculated from measured liquid film thickness show good accordance with heat transfer coefficients obtained directly from wall temperature measurements.     

Understanding of Interactions for Bubbles Generated at Neighboring Nucleation Sites

Bubble dynamics and site interaction are studied numerically by solving conservation of mass, momentum, and energy equations for the liquid and vapor phases. The liquid-vapor interface is tracked by a volume of fluid method. The effects of applied mean heat flux, site-site interactions, orientation of the boiling surface, inclination of nucleating tunnels, and reentrant cavity shape on the bubble dynamics are investigated. With the increase of mean heat flux three separate regimes namely surface tension driven interaction, no interaction and instability driven interaction between the bubbles were shown. Closer nucleation sites fascilitates bubble merging whereas sites away from each other behaves like individual bubble release. Critical spacing between the sites are predicted bifurcating interaction and no interaction zones separately. Site-site interaction patterns are also tested on inclined planes and critical inclination angle has been reported beyond which columnar bubble formation is observed as a result of merging. Using numerical simulation efforts have been also made to check suitability of site inclination and base pocket at the end of the tunnel to generate high heat transfer coefficient. Proposal of reentrant cavity base geometry matches well with literature.     

Interface Shape and Marangoni Effect Around aBubble Within the Thermal Boundary Layer

INTRoDUCTIoNDuetohighheattransferperformancecharacter-izedbysmalltemPeraturedifferencesandhighheatfluxes,transportprocesseswithphasechange,espe-ciallyboilingandcondensationprocessesarewidelyemployedinnumerousenergyconversionandtrans-portsystems,heatingand/orcoolingdevices,andaerospaceaPplications.Priortotheutilizationofboil-ingprocessesinspaceapplications,suchasspacecraftthermalcontrol,additionalunderstandingofboilingheattransferbehaviorisneeded.Becauselargedmer-encesekistinthefiuiddensiti…     

Molecular dynamics simulation on bubble formation in a nanochannel

Molecular dynamics simulations are carried out to examine the bubble behavior confined in a nanochannel with particular emphasis on the nucleation phenomenon. Simple Lennard-Jones fluids are under consideration and nano-sized bubbles are observed under different conditions of solid–liquid interfacial wettability. It is found that the bubble nucleation behavior shows a marked dependence on the solid–liquid interfacial interaction. In particular, it is found that bubbles appear in the bulk liquid homogenously for a hydrophilic surface, but grow directly on a hydrophobic solid surface. Also, a bubble will not form on a non-wetting surface. A nanobubble exists stably under the equilibrium state and the number density distribution of the curved liquid–vapor interface is examined. It is also found that there are few vapor atoms in the nano-sized bubble and the internal vapor pressure of the nanobubble is much lower than that required from the Young–Laplace equation. The disagreement with the prediction of the Young–Laplace equation can be attributed to the fact that the liquid–vapor interface region plays an important role on the force balance at the curved liquid–vapor interface of a nanobubble.     

Approximate Solution for the Heat-Transfer-Controlled Growth of a Steadily Translating Vapor Bubble

The existing analytical solution for the problem of the heat-transfer-controlled growth of a spherical vapor bubble moving with a constant velocity under the assumptions of a thin thermal boundary layer and potential flow results in a complicated integral equation for the bubble radius and is too unwieldy to be used in multiphase flow models. The goal of this work is to suggest for this problem an approximate solution that gives correct asymptotic behavior and yields a simpler expression for the bubble growth rate. Comparison with the exact solution showed that this way a good approximation can be obtained.     

Dynamics of discrete bubble in nucleate pool boiling on thin wires in microgravity

A space experiment on bubble behavior and heat transfer in subcooled pool boiling phenomenon has been performed utilizing the temperature-controlled pool boiling (TCPB) device both in normal gravity in the laboratory and in microgravity aboard the 22^nd Chinese recoverable satellite. The fluid is degassed R113 at 0.1 MPa and subcooled by 26°C nominally. A thin platinum wire of 60 μm in diameter and 30 mm in length is simultaneously used as heater and thermometer. Only the dynamics of the vapor bubbles, particularly the lateral motion and the departure of discrete vapor bubbles in nucleate pool boiling are reported and analyzed in the present paper. It’s found that these distinct behaviors can be explained by the Marangoni convection in the liquid surrounding vapor bubbles. The origin of the Marangoni effect is also discussed.     

On the dynamics and heat transfer of bubble train in micro-channel flow boiling

The dynamics and heat transfer characteristics of flow boiling bubble train moving in a micro channel is studied numerically. The coupled level set and volume of fluid (CLSVOF) is utilized to track interface and a non-equilibrium phase change model is applied to calculate the interface temperature as well as heat flux jump. The working fluid is R134a and the wall material is aluminum. The fluid enters the channel with a constant mass flux (335 kg/m² 1 s), and the boundary wall is heated with constant heat flux (14 kW/m²). The growth of bubbles and the transition of flow regime are compared to an experimental visualization. Moreover, the bubble evaporation rate and wall heat transfer coefficient have been examined, respectively. Local heat transfer is significantly enhanced by evaporation occurring vicinity of interface of the bubbles. The local wall temperature is found to be dependent on the thickness of the liquid film between the bubble train and the wall.     

Bubble characteristics in time periodic evaporation flow of R-134a in a narrow annular pipe due to heat flux oscillation

In this work, bubble characteristics of periodic evaporation flow with refrigerant R-134a in a horizontal narrow annular pipe were examined experimentally in details. Attention is focused on the time periodic evaporation flow characteristics affected by the mean levels, amplitudes, and periods of the heat flux oscillation. The photos of the R-134a time periodic evaporating flow taken from the duct side are presented to show the change of the dominant two-phase flow pattern in the duct with the experimental parameters. The results show that at the low vapor quality, the bubbles get smaller with time and become less crowded in the duct in the first half of the cycle in which the R-134a heat flux decreases. The changes of the bubble characteristics with the instantaneous heat flux become more pronounced for an increase in the amplitude of the heat flux oscillation. At the very high mean vapor quality the bubble nucleation can be barely seen in the entire periodic cycle since the liquid film covering the heating surface is very thin. In addition, the duct flow is dominated by the annular two-phase flow at all time.     

重力热管传热波动特性研究及抑制方法探讨

重力热管在启动、稳定操作、工况条件变化时的脉冲沸腾和温度波动现象，对热管的传热效果和使用寿命有不利影响。采用简单的弹簧抑泡装置，可以抑制热管内工质产生气泡，吸收气泡中的热能，使工质温度分布趋于均匀，同时，可以强化工质和管壁间的对流换热。实验表明，采用弹簧式抑泡装置的重力热管强化传热效果十分明显。     

Interfacial heat transfer of condensing bubble in subcooled boiling flow at low pressure

The interfacial heat transfer coefficient is an important parameter for the analysis of multi-phase flow. In subcooled boiling flow, bubbles condense through the interface of phases and the interfacial heat transfer determines the condensation rate which affects the two-phase parameters such as void fraction and local liquid temperature. Thus, the present experiments are conducted to correlate the interfacial heat transfer coefficient at low pressure in the subcooled boiling flow. The local liquid temperature is measured by microthermocouple and the bubble condensation rate is estimated by orthogonal, two-image processing. The condensate Nusselt number, which is a function of bubble Reynolds number, local liquid Prandtl number, and local Jacob number, is obtained from the experimental results. The bubble history is derived from the newly proposed correlation and the condensate Nusselt number is compared with the previous models.