Operational characteristics of oscillating heat pipes under micro-gravity condition

A mathematical model to investigate the oscillating motion characteristics of liquid slugs and vapor plugs/bubbles in oscillating heat pipes (OHPs) was developed considering the contact angle hysteresis (CAH) and interconnected-tube induced pressure fluctuations. Results show that a short period less than 1 s is available to attain the steady state after startup and then the oscillation amplitudes and frequencies for both of slug/bubble displacement and velocity are kept fixed. The slug/bubble displacement and velocity display quasi-sine oscillating waves with small pressure fluctuations induced by the interconnected-tube. However, small oscillation waves are superimposed on a main quasi-sine oscillation wave and cause a chaotic oscillating behavior of slug/bubble inside the OHP if the induced pressure fluctuation is large enough. Besides, the effects of filling ratio, tube length, inner diameter, temperature difference between the evaporator and condenser sections, and working fluid on the oscillating motion were numerically analyzed and discussed. The numerical model provides a physical insight to understand the operational mechanism of OHPs under the microgravity condition.     

High speed flow visualization of a closed loop pulsating heat pipe

We provide the high speed flow visualization results for the closed loop pulsating heat pipes (PHPs). It is identified that there exists the bulk circulation flow which lasts longer and the local flow direction switch flow. The bubble displacements and velocities do display the sine oscillation waves but the local oscillation waves were superimposed with short periods and small oscillation amplitudes. Distinct with the methanol PHP, the water PHP has quasi-rectangular shape for the bubble displacements, behaving the periodic stationary-fast movement characteristics. Dispersed bubbles, vapor plugs and the transition flow patterns from the dispersed bubbles to the vapor plugs are the major flow patterns in PHP. Long vapor plugs are only observed for the methanol PHP, not observed in the water PHP, due to the vapor plug deformation and breakup mechanism, which was analyzed in the present paper. Bubble sizes have quasi-fixed distributions versus time over the entire PHP, but have unsymmetry distributions among various tubes. The complicated combined effects of bubble nucleation, coalescence and condensation are responsible for the oscillation flow in PHP.     

Advances and Unsolved Issues in Pulsating Heat Pipes

Pulsating (or oscillating) heat pipes (PHP or OHP) are new two-phase heat transfer devices that rely on the oscillatory flow of liquid slug and vapor plug in a long miniature tube bent into many turns. The unique feature of PHPs, compared with conventional heat pipes, is that there is no wick structure to return the condensate to the heating section; thus, there is no countercurrent flow between the liquid and vapor. Significant experimental and theoretical efforts have been made related to PHPs in the last decade. While experimental studies have focused on either visualizing the flow pattern in PHPs or characterizing the heat transfer capability of PHPs, theoretical examinations attempt to analytically and numerically model the fluid dynamics and/or heat transfer associated with the oscillating two-phase flow. The existing experimental and theoretical research, including important features and parameters, is summarized in tabular form. Progresses in flow visualization, heat transfer characteristics, and theoretical modeling are thoroughly reviewed. Finally, unresolved issues on the mechanism of PHP operation, modeling, and application are discussed.     

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.     

Analysis of pulsating heat pipe with capillary wick and varying channel diameter

Variation in channel diameter is investigated as a means of enhancing heat transfer in a pulsating heat pipe with capillary wick using the model presented here. The model is one-dimensional with slug flow where the momentum equation is solved for each liquid slug. The number and mass of liquid slugs are allowed to vary throughout a simulation. The energy equation is solved both in the wall and wick and in the working fluid. The effects of diameter profile, gravity, fill ratio, and heating and cooling schemes can be studied with the model. Results yield similar trends to what has been experimentally observed. Results also indicate that heat transfer can be enhanced when the diameter of the channel is varied along the channel length, thereby providing increased range of heat load capability, less sensitivity to gravity, and in some cases smaller temperature differentials.     

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%.     

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.     

Numerical study of the hydrodynamics and heat transfer characteristics of liquid–liquid Taylor flow in microchannel

A numerical study of an oil–water Taylor flow is presented in this paper to explore its flow and heat transfer characteristics. Due to the large surface area to volume ratio in narrow channels, using slug flows, high heat and mass transfer rates could be achieved. Sound knowledge of the underlying physics of slug flow is required for the practical design of microfluidic devices. In this study, hydrodynamics and heat transfer characteristics of dispersed oil droplets flowing inside a vertically upward circular microchannel (D = 0.1 mm) with water being the carrier phase have been explored numerically. ANSYS Fluent was employed to capture the liquid–liquid interface using volume of fluid method. Two different boundary conditions were considered in the present study. First, an isothermal wall of 373 K and later a constant wall heat flux (420 kW/m²) were, respectively, prescribed over the wall of the microchannel. The numerical code was validated against the results available in the literature, and the significant results in the form of pressure drop and heat transfer rates have been discussed. A considerable increase in Nusselt number, up to 180% and 210%, was observed with the oil–water slug flow in contrast to the liquid‐only single‐phase flow inside the microchannel for isothermal and constant wall heat flux conditions, respectively.     

A lattice Boltzmann method for simulation of liquid–vapor phase-change heat transfer

A lattice Boltzmann model for the liquid–vapor phase change heat transfer is proposed in this paper. Two particle distribution functions, namely the density distribution function and the temperature distribution function, are used in this model. A new form of the source term in the energy equation is derived and the modified pseudo-potential model is used in the proposed model to improve its numerical stability. The commonly used Peng–Robinson equation of state is incorporated into the proposed model. The problem of bubble growth and departure from a horizontal surface is solved numerically based on the proposed model.     

Macroscopic continuum analysis of simultaneous heat and mass transfer in unsaturated porous materials containing a heat source

The paper briefly outlines a development of the transport equations which describes simultaneous heat and mass transfer in unsaturated porous materials when a heat source is embedded in the medium. A macroscopic continuum mechanics approach is adopted to derive the coupled continuity, momentum and energy equations. Hydrodynamic laws such as Darcy's law and the Darcy-Buckingham theorem are utilized to simplify the continuity and momentum equations of fluid flow. Migration of liquid due to surface tension effects is modeled in the analysis. The effects of phase change on the heat transfer are also included in the energy equation. The resulting equations reported in this paper are found to agree with equations obtained by other researchers who used volume averaging techniques to study similar phenomena in unsaturated porous materials.     

Evaporation heat transfer of steady thin film in micro capillary tubes of micron scale

This paper reports that the heat transfer mechanism of phase change in a capillary tube belongs to liquid film conduction and surface evaporation. The surface evaporation is influenced by vapor temperature, vapor‐liquid interfacial temperature, and vapor‐liquid pressure difference. In the vapor‐liquid flow mechanism, flow is effected by both the gradient of disjoining pressure, and the gradient of capillary pressure. The mechanism of vapor‐liquid interaction consists of the shear stress caused by momentum transfer owing to evaporation, and frictional shear stress due to the velocity difference between vapor and liquid. In the model presented for a capillary tube, the heat transfer, vapor‐liquid flow, and their interaction are more comprehensively considered. The thin film profile and heat transfer characteristics have close relations with a capillary radius and heat transfer power. The results of calculation indicate that the length of the evaporating interfacial region decreases to some extent with decreasing capillary radius and increasing heat transfer power. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 513–523, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ).DOI 10.1002/htj.10050     

Numerical simulation of the pressure drop and heat transfer of two phase slug flows in microtubes using moving frame of reference technique

Enhancement in heat transfer using two phase slug flow in microtubes and microchannels has encouraged researchers to focus on this topic as one of the potential methods for miniaturizing heat sinks and exchangers. Numerical simulation of two phase slug flow is time consuming, so some researchers conduct their numerical studies using the moving frame of reference technique for a unit cell consisting of only one slug, i.e. a single phase study, in order to accelerate the simulation process. Both single phase and two phase simulation methods have been performed in the present study and results have been compared. This shows to what extent the moving frame of reference assumption is valid in the case of two phase flow in hydrophilic microtubes when a thin liquid film exists around moving gas bubbles. The present comparison has been conducted for pressure drop and heat transfer for two thermal boundary conditions i.e. constant wall temperature and constant wall heat flux. It has been shown that the moving frame of reference method overpredicts pressure drop and heat transfer and possible reasons have been discussed. This also shows that in a slug flow with no film around bubbles more heat transfer could be achieved.     

Thermo-hydrodynamics analysis of vapor–liquid two-phase flow in the flat-plate pulsating heat pipe

A three-dimensional unsteady model of vapor–liquid two-phase flow and heat transfer in a flat-plate pulsating heat pipe (FP-PHP) is developed and numerically analyzed to study the thermal-hydrodynamic characteristics in two different configurations of FP-PHPs. The thermo-hydrodynamics characteristics under steady unidirectional circulation condition of the studied FP-PHPs are numerically investigated and discussed. The results indicate that the bubbly flow, slug flow and semi-annular/annular flow occur in the FP-PHP under the condition of steady unidirectional circulation, when the adjacent tubes of the FP-PHP become ‘upheaders’ and ‘downcomers’ of working fluid. The periodical oscillations of fluid temperature and vapor volume fraction are observed to be synchronous, while the temperature oscillation amplitude at adiabatic section is larger than that at condenser section but less than that at evaporator section. The increases in the heat load lead to the high temperature level and small integral equivalent thermal resistance of the FP-PHP. Additionally, compared with the traditional FP-PHP with uniform channels, the FP-PHP with micro grooves incorporated in the evaporator section is effective for the heat transfer enhancement and possesses a smaller thermal resistance at high heat loads.     

Three-dimensional simulation of saturated film boiling on a horizontal cylinder

Three-dimensional simulations of film boiling on a horizontal cylinder have been performed. A finite difference method is used to solve the equations governing the conservation of mass, momentum and energy in vapor and liquid phases. A level set formulation for tracking the liquid–vapor interface is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip condition at the fluid–solid interface. From the numerical simulations, the effects of cylinder diameter and gravity on the interfacial motion and heat transfer in film boiling are quantified. The heat transfer coefficients obtained from numerical analysis are found to compare well with those predicted from empirical correlations reported in the literature.     

脉动热管流型的电容层析成像识别及热管换热特性

结合高速摄像和电容层析成像技术,对脉动热管进行了可视化测量研究.从流型和流向两方面分析了脉动热管的运行机理和传热特性.根据受力分析对脉动热管的结构进行了改进.结果表明:脉动热管存在3种不同流型,即塞状流、环状流以及两者共存的混合流,其对应的影响因素、运行特性与传热强度也不同;从流动方向来看,脉动热管内工质的流动可分为脉动流和循环流;对脉动热管的改进说明改变脉动热管流道的对称性和均衡性有利于循环流的形成和维持.     

Study on flow and heat transfer characteristics of heat pipe with axial “Ω”-shaped microgrooves

A theoretical model of fluid flow and heat transfer in a heat pipe with axial “Ω”-shaped grooves has been conducted to study the maximum heat transport capability of these types of heat pipes. The influence of variations in the capillary radius, liquid–vapor interfacial shear stress and the contact angle are all considered and analyzed. The effect of vapor core and wick structure on the fluid flow characteristics and the effect of the heat load on the capillary radius at the evaporator end cap, as well as the effect of the wick structure on the heat transfer performance are all analyzed numerically and discussed. The axial distribution of the capillary radius, fluid pressure and mean velocity are obtained. In addition, the calculated maximum heat transport capability of the heat pipe at different working temperatures is compared with that obtained from a traditional capillary pressure balance model, in which the interfacial shear stress is neglected. The accuracy of the present model is verified by experimental data obtained in this paper.     

Two-Phase Flow and Boiling Heat Transfer in Small-Diameter Tubes

For the development of a high-performance heat exchanger using small channels or minichannels for air-conditioning systems, it is necessary to clarify the characteristics of vapor‐liquid two-phase flow and heat transfer of refrigerants in small-diameter tubes. In this keynote paper, the related research works that have already been performed by the author and coworkers are introduced. Based on the observations and experiments of R410A flowing in small-diameter circular and noncircular tubes with hydraulic diameter of about 1 mm, the characteristics of vapor‐liquid two-phase flow pattern and boiling heat transfer were clarified. In low quality or mass flux and low heat flux condition, in which the flow was mainly slug, the “liquid film conduction evaporation” heat transfer peculiar to small-diameter tubes prevailed and exhibited considerably good heat transfer compared to nucleate boiling and forced convection evaporation heat transfer. The effects of the tube cross-sectional shape and flow direction on the heat transfer primarily appeared in the region of the “liquid film conduction evaporation” heat transfer. A new heat transfer correlation considering all of three contributions has been developed for small circular tubes.     

A Mathematical Model of an Oscillating Heat Pipe

A mathematical model predicting the oscillating motion in an oscillating heat pipe is developed. The model considers the system multidegree oscillation of vapor bubbles and liquid plugs, including the effects of filling ratio, operating temperature, gravitational force, and temperature difference between the evaporator and condenser. The model shows that the average velocity of liquid slugs is determined by the temperature difference between the evaporator and condenser. As the turn number increases, the temperature difference for the system to start the oscillating motion decreases. Increasing the bubble number will make the system more unstable and the system can be easily started up. The existence of gravity at the bottom heating mode will make the system easily produce the oscillating motion and decrease the temperature difference as well. Results presented here will assist in optimizing the heat transfer performance and provide a better understanding of heat transfer mechanisms occurring in the oscillating heat pipe.     

Direct simulation of spray cooling: Effect of vapor bubble growth and liquid droplet impact on heat transfer

Numerical modeling of multiphase flow using level set method is discussed. The 2-D model considers the effect of surface tension between liquid and vapor, gravity, phase change and viscosity. The level set method is used to capture the movement of the free surface. The detail of incorporating the mechanism of phase change in the incompressible Navier–Stokes equations using the level set method is described. The governing equations are solved using the finite difference method. The computer model is used to study the spray cooling phenomenon in the micro environment of about 40 μm thick liquid layer with vapor bubble growing due to nucleation. The importance of studying the heat transfer mechanism in thin liquid film for spray cooling is identified. The flow and heat transfer details are presented for two cases: (1) when the vapor bubble grows due to nucleation and (2) merges with the vapor layer above the liquid layer and when a liquid droplet impacts the thin liquid layer with vapor bubble growing.     

Closed-loop pulsating heat pipe

Flow visualization was conducted for the closed-loop pulsating heat pipe (PHP) using a charge coupled device (CCD). It was observed that during the start-up period, the working fluid oscillates with large amplitude, however, at steady operating state, the working fluid circulates. The direction of circulation for the working fluid is consistent once circulation is attained, but the direction of circulation can be different for the same experimental run. Phenomena such as nucleation boiling, coalescence of bubbles, formation of slug and propagation of inertia wave were observed in the closed-loop PHP. The findings showed that the meandering bends, uneven slug and plug distribution and non-concurrent boiling at the evaporator contributed to the driving and restoring forces for fluid circulation and oscillations.