A wall heat transfer model for subcooled boiling flow

High compactness, low weight and little space requirement are gaining attention as prominent design criteria in the development of modern cooling systems in many applications. The resulting demand for highest possible heat transfer rates has lead to the very promising concept of providing for a controlled transition from pure single-phase convection to subcooled boiling flow in thermally highly loaded regions. For its application in modern engineering design this approach requires a realistic modeling of the complex phenomena associated with the two-phase flow heat transfer. The present work proposes for the computation of the specific wall heat transfer rate a modified superposition model, where the total heat flux is assumed to be additively composed of a forced convective and a nucleate boiling component. Since the present model requires only local input quantities, it is well suited to CFD of geometrically very complex coolant flows, where the definition of global length or velocity scales would be impractical. The wall heat fluxes predicted by the present model were compared against experimental data which were obtained by in-house measurements with water being the working fluid. The overall agreement is very good, particularly, in the partially nucleate boiling regime, where the effect of the bulk flow rate on the heat transfer is significant. Deviations are primarily observed at higher wall superheats, where a strong two-way coupling between the motion of the liquid and the motion of the bubbles as well as considerable bubble–bubble interactions typically occur.     

Interfacial heat transfer during subcooled flow boiling

In order to develop a mechanistic model for the subcooled flow boiling process, the key issues which must be addressed are wall heat flux partitioning and interfacial (condensation) heat transfer. The sink term in the two-fluid models for void fraction prediction is provided by the condensation rate at the vapor-liquid interface. Low pressure subcooled flow boiling experiments, using water, were performed using a vertical flat plate heater to investigate the bubble collapse process. A high-speed CCD camera was used to record the bubble collapse in the bulk subcooled liquid. Based on the analyses of these digitized images, bubble collapse rates and the associated heat transfer rate were determined. The experimental data were in turn used to correlate the bubble collapse rate and the interfacial heat transfer rate. These correlations are functions of bubble Reynolds number, liquid Prandtl number, Jacob number, and Fourier number. The correlations account for both the effect of forced convection heat transfer and thickening of the thermal boundary layer as the vapor bubble condenses which in turn makes the condensation heat transfer time dependent. Comparison of the measured experimental data with those predicted from the correlations show that predictions are well within ±25% of the experimentally measured values. These correlations have also been compared with those available in the literature.     

狭缝中流动沸腾传热过冷沸腾起始点的实验研究

以间隙为1．0mm和1．5mm的环形狭缝通道中流动沸腾传热的实验数据为基础，分析了影响过冷沸腾起始点热负荷的主要因素，给出了计算环形狭缝通道中流动沸腾传热过冷沸腾起始点的经验关联式，并将计算结果与实验值进行了比较。该关联式可以用来预测实验范围内的过冷沸腾起始点的热负荷。     

Marangoni heat transfer in subcooled nucleate pool boiling

The liquid motion induced by surface tension variation, termed the Marangoni effect, and its contribution to boiling heat transfer has been an issue of much controversy. Boiling heat transfer theory, although acknowledging its existence, considers its contribution to heat transfer to be insignificant in comparison with buoyancy induced convection. However, recent microgravity experiments have shown that although the boiling mechanism in a reduced gravity environment is different, the corresponding heat transfer rates are similar to those obtained under normal gravity conditions, raising questions about the validity of the assumption. An experimental investigation was performed in which distilled water was gradually heated to boiling conditions on a copper heater surface at four different levels of subcooling. Photographic investigation of the bubbles appearing on the surface was carried out in support of the measurements. The results obtained indicate that Marangoni convection associated with the bubbles formed by the air dissolved in the water which emerged from solution when the water was heated sufficiently, significantly influenced the heat transfer rate in subcooled nucleate pool boiling. A heat transfer model was developed in order to explain the phenomena observed.     

High Heat Flux Burnout in Subcooled Flow Boiling

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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.     

Critical heat flux for subcooled flow boiling in micro-channel heat sinks

Critical heat flux (CHF) was measured and examined with high-speed video for subcooled flow boiling in micro-channel heat sinks using HFE 7100 as working fluid. High subcooling was achieved by pre-cooling the working fluid using a secondary low-temperature refrigeration system. The high subcooling greatly reduced both bubble departure diameter and void fraction, and precluded flow pattern transitions beyond the bubbly regime. CHF was triggered by vapor blanket formation along the micro-channel walls despite the presence of abundant core liquid, which is consistent with the mechanism of Departure from Nucleate Boiling (DNB). CHF increased with increasing mass velocity and/or subcooling and decreasing hydraulic diameter for a given total mass flow rate. A pre-mature type of CHF was caused by vapor backflow into the heat sink’s inlet plenum at low mass velocities and small inlet subcoolings, and was associated with significant fluctuations in inlet and outlet pressure, as well as wall temperature. A systematic technique is developed to modify existing CHF correlations to more accurately account for features unique to micro-channel heat sinks, including rectangular cross-section, three-sided heating, and flow interaction between micro-channels. This technique is shown to be successful at correlating micro-channel heat sink data corresponding to different hydraulic diameters, mass velocities and inlet temperatures.     

Heat transfer in subcooled jet impingement boiling at high wall temperatures

An analytical approach for heat transfer modelling of jet impingement boiling is presented. High heat fluxes with values larger than 10 MW/m² can be observed in the stagnation region of an impinging jet on a red hot steel plate with wall temperatures normally being associated with film boiling. However, sufficiently high degrees of subcooling and jet velocity prevent the formation of a vapor film, even if the wall superheat is large. Heat transfer is governed by turbulent diffusion caused by the rapid growth and condensation of vapor bubbles. Due to the high population of bubbles at high heat fluxes it has to be assumed that a laminar sublayer cannot exist in the immediate vicinity of a red hot heating surface. A mechanistic model is proposed which is based on the assumption that due to bubble growth and collapse the maximum turbulence intensity is located at the wall/liquid interface and that eddy diffusivity decreases with increasing wall distance.     

Fundamental consideration of wall heat partition of vertical subcooled boiling flows

Improved wall heat flux partitioning accounting sliding bubbles and a mechanistic model that incorporates the fundamental consideration of bubble frequency during low-pressure subcooled flow boiling is presented. A model considering the forces acting on departing bubbles at the heated surface is employed. Coupled with a three-dimensional two-fluid and population balance equations based on the modified MUSIG (MUltiple-SIze-Group) model, the behavior of an upward forced convective subcooled boiling flows in a vertical annular channel is simulated. Comparison of model predictions against local and axial measurements (heat fluxes ranged from 152.9 to 705.0 kW/m²) is made for the void fraction, Sauter mean bubble diameter and interfacial area concentration covering a range of different mass and heat fluxes and inlet subcoolings. Good agreement is achieved between the predicted and measured profiles. Reasonable agreement with recent experimental measurements is also attained for the predicted growth and waiting times of bubble frequency at particular local wall superheat and subcooling temperatures.     

Critical heat flux correlation for subcooled boiling flow in narrow channels

The purpose of this study is to conduct the critical heat flux (CHF) correlation for narrow channels. The CHF of subcooled flow boiling of water in narrow rectangular channels under atmospheric pressure was measured parametrically. Experimental test channels were rectangular and heated from one side with the channel gap of 0.2-3.0 mm, channel width of 7-22 mm, and heated length of 50-200 mm. First, the CHF correlation for the one-side heated rectangular channels was proposed with investigating the various system parameter effects on CHF. Next, applicability of the correlation to both-side heated rectangular channel, half-circumferentially heated tube, and full-circumferentially heated tubes was examined. New CHF correlation for narrow rectangular channels and small-diameter tubes was proposed using the critical quality, dimensionless CHF parameter and heated perimeter ratio. Calculation accuracy of the correlation is ±45% (maximum 10 times better in comparison with the existing CHF calculation methods which were proposed for the full-circumferentially heated tubes).     

Consolidated method to predicting pressure drop and heat transfer coefficient for both subcooled and saturated flow boiling in micro-channel heat sinks

Published studies concerning transport phenomena in micro-channel heat sinks can be divided into those concerning saturated boiling versus those focused on subcooled boiling, with the vast majority related to the former. What has been lacking is a single generalized method to tackle both boiling regimes. The primary objective of the present paper is to construct a consolidated method to predicting transport behavior of micro-channel heat sinks incurring all possible heat transfer regimes. First, a new correlation is developed for subcooled flow boiling pressure drop that accounts for inlet subcooling, micro-channel aspect ratio, and length-to-diameter ratio. This correlation shows excellent predictive capability against subcooled HFE 7100 pressure drop data corresponding to four different micro-channel geometries. Next, a consolidated method is developed for pressure drop that is capable of tackling inlet single-phase liquid, subcooled boiling, saturated boiling, and single-phase vapor regimes as well as inlet contraction and outlet expansion. A similar consolidated method is developed to predict the heat transfer coefficient that is capable of tackling all possible combinations of heat transfer regimes. The new consolidated method is shown to be highly effective at reproducing both data and trends for HFE 7100, water and R134a.     

Modeling and numerical investigation of hydrogen nucleate flow boiling heat transfer

Liquid hydrogen flow boiling heat transfer in tubes is of great importance in the hydrogen applications such as superconductor cooling, hydrogen fueling. In the present study, a numerical model for hydrogen nucleate flow boiling based on the wall partition heat flux model is established. The key parameters in the model such as active nucleation site density, bubble departure diameter and frequency are carefully discussed and determined to facilitate the modeling and simulation of hydrogen flow boiling. Simulation results of the numerical model show reasonably well agreement with experimental data from different research groups in a wide operation condition range with the means absolute error (MAE) of 10.6% for saturated and 5.3% for subcooled flow boiling. Based on the model, wall heat flux components and void fraction distribution of hydrogen flow boiling are studied. Effects of mass flow rate and wall heat flux on the flow boiling heat transfer performance are investigated. It is found that in the hydrogen nucleate flow boiling, the predominated factor is the Boiling number, rather than the vapor quality. A new simple correlation is proposed for predicting hydrogen saturated nucleate flow boiling Nusselt number. The MAE between the correlation predicted and experimentally measured Nusselt number is 13.6% for circular tubes and 12.5% for rectangular tubes. The new correlation is applicable in the range of channel diameter 4–6.35 mm, Reynolds number 64000–660,000, saturation temperature 22–29 K, Boiling number 8.37 × 10^?5–2.33 × 10^?3.     

Transient boiling heat transfer performances of subcooled water during quenching process

Transient boiling of subcooled water on a vertical flat surface during quenching process was visually observed using high-speed photography technology and analyzed by special boiling heat transfer models. After the quenching process began, the nucleation was initiated within a short time, and then followed by the outbreak transition boiling with extremely unstable bubbles and sharp heat flux increment which lasted only for about 1 s. According to the boiling curves, the nucleate boiling should be divided into two stages including the stable nucleate boiling and transition nucleate boiling with the effects of initial conditions. The outbreak transition boiling was first studied by special boiling curve corresponding to the temperature decrement, and was further analyzed using a theoretical model based on the combination of the boiling heat flux evolution and lumped parameter assumption. The results showed that the boiling curve of outbreak transition boiling predicted by the theoretical model had a good agreement with experimental data and the heat flux almost had linear relation with the square root of temperature decrement.     

Photographic study of high-flux subcooled flow boiling and critical heat flux

This study examines both high-flux flow boiling and critical heat flux (CHF) under highly subcooled conditions using FC-72 as working fluid. Experiments were performed in a horizontal flow channel that was heated along its bottom wall. High-speed video imaging and photomicrographic techniques were used to capture interfacial features and reveal the sequence of events leading to CHF. At about 80% of CHF, bubbles coalesced into oblong vapor patches while sliding along the heated wall. These patches grew in size with increasing heat flux, eventually evolving into a fairly continuous vapor layer that permitted liquid contact with the wall only in the wave troughs between vapor patches. CHF was triggered when this liquid contact was finally halted. These findings prove that the CHF mechanism for subcooled flow boiling is consistent with the interfacial lift-off mechanism proposed previously for saturated flow boiling.     

Numerical and experimental investigation of heat transfer on heating surface during subcooled boiling flow of liquid nitrogen

Closure correlations describing bubble nucleation and departure on the heating surface is indispensable when modeling subcooled boiling flow using a two-fluid model. Due to the small contact angle and surface tension, nucleation and departure of nitrogen vapor bubble has different characteristics to those of high-boiling liquids. For the purpose of accurate two-fluid model formulation, these factors have to be taken into consideration. In this study, some closure correlations of the bubble departure diameter, active site density and bubble waiting time were tested in the frame of the two-fluid model and the CFX code. Benchmark experiments were then performed to evaluate the correlations. Comparison of the numerical results against the experimental data demonstrates that the surface tension is crucial to modeling the bubble departure diameter and the active site density. The bubble waiting time correlation formulated according to bubble growth is expected to be used as a criterion of judging the transition from subcooled to saturated boiling.     

Bubble dynamics at boiling incipience in subcooled upward flow boiling

Bubble dynamics in water subcooled flow boiling was investigated through visualization using a high-speed camera. The test section was a vertical rectangular channel, and a copper surface of low contact angle was used as a heated surface. Main experimental parameters were the pressure, mass flux and liquid subcooling. Although all the experiments were conducted under low void fraction conditions close to the onset of nucleate boiling, no bubbles stayed at the nucleation sites at which they were formed. Depending on the experimental conditions, the following two types of bubble behavior were observed after nucleation: (1) lift-off from the heated surface followed by collapsing rapidly in subcooled bulk liquid due to condensation, and (2) sliding along the vertical heated surface for a long distance. Since the bubble lift-off was observed only when the wall superheat was high, the boundary between the lift-off and the sliding could be determined in terms of the Jakob number. Based on the present experimental results, discussion was made for the possible mechanisms governing the bubble dynamics.     

Correlation for flow boiling heat transfer in mini-channels

In view of practical significance of a correlation of heat transfer coefficient in the aspects of such applications as engineering design and prediction, some efforts towards correlating flow boiling heat transfer coefficients for mini-channels have been made in this study. Based on analyses of existing experimental investigations of flow boiling, it was found that liquid-laminar and gas-turbulent flow is a common feature in many applications of mini-channels. Traditional heat transfer correlations for saturated flow boiling were developed for liquid-turbulent and gas-turbulent flow conditions and thus may not be suitable in principle to be used to predict heat transfer coefficients in mini-channels when flow conditions are liquid-laminar and gas-turbulent. By considering flow conditions (laminar or turbulent) in the Reynolds number factor F and single-phase heat transfer coefficient h_sp, the Chen correlation has been modified to be used for four flow conditions such as liquid-laminar and gas-turbulent one often occurring in mini-channels. A comparison of the newly developed correlation with various existing data for mini-channels shows a satisfactory agreement. In addition, an extensive comparison of existing general correlations with databases for mini-channels has also been made.     

Subcooled flow boiling heat transfer in narrow passages

Subcooled flow boiling heat transfer coefficients for refrigerants R11 and HCFC123 in smooth copper tubes of small diameter have been investigated experimentally. The parameter ranges examined are: tube diameters of 0.92 and 1.95 mm; heat fluxes 11-170 kW m⁻²; mass fluxes 110-1840 kg m⁻² s⁻¹. The range of liquid Reynolds numbers encompassed by the data set is 450 to 12,000.The data in the subcooled and saturated regions are well represented by the simple addition of convective and nucleate boiling heat transfer contributions

     

A novel interphase mass transfer model toward the VOF simulation of subcooled flow boiling

In this study, a novel interphase mass transfer model has been developed to predict mass and energy exchange in the vicinity of the phase interface. The proposed model involves the new time relaxation parameter which takes into account the effect of the subcooling, the wall superheat, and Reynolds number, and is obtained from simulation results by the method of trial and error. Transient simulations of subcooled flow boiling in Hua’s experimental horizontal rectangular channel are performed. The Volume of Fluid (VOF) method is used to track the vapor–liquid interface using OpenFOAM software package. The constant coefficients of new time relaxation parameter are determined using fitted method. The predicted results show that the deviation between the predicted and experimental wall superheats using the proposed model, which is within 20%, is smaller than that of Lee model. As a further step, the novel interphase mass transfer model has been validated in other experimental data under similar condition. These results indicate that the novel interphase mass transfer model is quite accurate and robust.     

Numerical study of bubble growth and wall heat transfer during flow boiling in a microchannel

A numerical study has been performed to analyze the wall heat transfer mechanisms during growth of a vapor bubble inside a microchannel. The microchannel is of 200 μm square cross section and a vapor bubble begins to grow at one of the walls, with liquid coming in through the channel inlet. The complete Navier–Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid vapor interface is captured using the level set technique. Experiments have been conducted to validate the numerical model. The bubble growth rate and shapes show good agreement between numerical and experimental results. The numerical results show that the wall heat transfer increases with wall superheat but stays almost unaffected by the liquid flow rate. The liquid vapor surface tension value has little influence on bubble growth and wall heat transfer. However, the bubble with the lowest contact angle resulted in the highest wall heat transfer.