Correlation of high critical heat flux during flow boiling for water in a small tube at various subcooled conditions

High critical heat fluxes (CHFs) for subcooled boiling of water in a small tube were investigated experimentally. A platinum tube with an inner diameter of 1.0 mm and a length of 40.9 mm was used in the experiment. The upward flow velocity, the subcooling of water, and the outlet pressure of the experimental tube were varied to enable a parametric study of the CHFs. The flow velocity ranged from 9 to 13 m/s and the inlet subcooling ranged from 69 to 148 K. The boiling number decreased with increasing Weber number. The boiling number is also dependent on a non-dimensional parameter and the density ratio of liquid to vapor. A correlation for the high CHF of the small tube was obtained based on the experimental data. Finally, the high CHF correlation was evaluated using the CHF data obtained by other researchers.     

Study of the critical heat flux condition with water and R-123 during flow boiling in microtubes. Part I: Experimental results and discussion of parametric effects

Extensive experimentation was performed to obtain flow boiling critical heat flux data in single stainless steel microtubes with diameters from 0.286 to 0.700 mm over a wide range of mass fluxes, inlet subcoolings, and exit pressures for two different working fluids (water and R-123). The effect of different operating parameters – mass flux, inlet subcooling, exit quality, heated length and diameter – were assessed in detail (Part I of the paper). The conventional DNB-type behavior is observed in the high subcooled region, and the typical dryout type behavior is seen in the high-quality saturated region when the flow is completely annular. The flow in transitional flow patterns (churn–annular or slug–annular) causes a peculiar increase of CHF with exit quality. Also, the increased void fraction near the saturated region in subcooled boiling results in increased subcooled CHF values. Part II of the paper deals with comparison of data with existing correlations and development of a new correlation to predict the CHF condition in the subcooled liquid region.     

Subcooled and saturated boiling of ammonia–lithium nitrate solution in a plate-type generator for absorption machines

This paper presents the experimental heat transfer evaluation during subcooled and saturated boiling of ammonia–lithium nitrate solution in a fusion plate heat exchanger, acting as a vapor generator under operating conditions representative of single-effect absorption machines. The solution flow rate and outlet temperature were modified in the ranges of 0.041–0.083 kg/s and 78–97 °C, respectively. The region where vapor bubbles begin to arise is estimated using a correlation for the wall superheat required for the onset of nucleate boiling. Results show that subcooled boiling is present in the generator. The initial boiling temperature is about 3.1 °C lower than the saturation temperature. The influence of the heat and mass fluxes on the boiling heat transfer coefficient is analyzed. The paper offers a correlation for the Nusselt number, including the subcooled and saturated boiling regions.     

Correlation of critical heat flux and two-phase friction factor for subcooled convective boiling in structured surface microchannels

Critical heat flux (CHF) and pressure drop of subcooled flow boiling are measured for a microchannel heat sink containing 75 parallel 100 μm × 200 μm structured surface channels. The heated surface is made of a Cu metal sheet with/without 2 μm thickness diamond film. Tests and measurements are conducted with de-ionized water, de-ionized water +1 vol.% MCNT additive solution, and FC-72 fluids over a mass velocity range of 820–1600 kg/m² s, with inlet temperatures of 15(8.6)°C, 25(13.6)°C, 44(24.6)°C, and 64(36.6)°C for DI water (FC-72), and heat fluxes up to 600 W/cm². The CHF of subcooled flow boiling of the test fluids in the microchannels is measured parametrically. The two-phase pressure drop is also measured. Both CHF and the two-phase friction factor correlation for one-side heating with two other side-structured surface microchannels are proposed and developed in terms of the relevant parameters.     

Drift-flux model in a sub-channel of rod bundle geometry

In view of the practical interest of the drift-flux model for two-phase flow analysis, the distribution parameter and drift velocity constitutive equations have been obtained for subcooled boiling flow in a sub-channel of rod bundle geometry. The constitutive equation of the distribution parameter for subcooled boiling flow in a sub-channel is obtained from the bubble-layer thickness model. In this derivation an existing constitutive equation for subcooled boiling flow in a round pipe is modified by taking account of the difference in the flow channel geometry between the sub-channel and round pipe. The constitutive equation of the drift velocity is proposed based on an existing correlation and considering the rod wall and sub-channel geometry effects. The prediction accuracy of the newly developed correlations has been checked against experimental data in a 3 × 3 rod bundle sub-channel, obtaining better predicting errors than the existing correlations most used in literature.     

Liquid–vapor structure near heating surface at high heat flux in subcooled pool boiling

Liquid–vapor behavior close to a heating surface was measured using two conductance probes with tip diameters smaller than 5 μm. Measurements were carried out for water boiling on an upward-facing copper surface under subcooling from 0 to 30 K. The probe signals and the void fraction distributions showed that there is little difference in the liquid–vapor structure beneath large vapor masses in saturated and subcooled boiling, that a macrolayer remains on the heating surface, and that in subcooled boiling it does not dry out even at heat fluxes far higher than CHF for saturated boiling. The thickness of the macrolayer forming beneath large vapor masses was determined from the location where the probe signals corresponding to the large vapor masses disappear. It was found that the thicknesses of the macrolayer formed in subcooled boiling are comparable to or thicker than those near the CHF in saturated boiling, and it is considered that this is most likely to be one of the causes why the CHF increases with the increasing subcooling.     

Measurement of surface dryout near heating surface at high heat fluxes in subcooled pool boiling

The authors have conducted measurements of liquid–vapor behavior in the vicinity of a heating surface for saturated and subcooled pool boiling on an upward-facing copper surface by using a conductance probe method. A previous paper [A. Ono, H. Sakashita, Liquid–vapor structure near heating surface at high heat flux in subcooled pool boiling, Int. J. Heat Mass Transfer 50 (2007) 3481–3489] reported that thicknesses of a liquid rich layer (a so-called macrolayer) forming in subcooled boiling are comparable to or thicker than those formed near the critical heat flux (CHF) in saturated boiling. This paper examines the dryout behavior of the heating surface by utilizing the feature that a thin conductance probe placed very close to the heating surface can detect the formation and dryout of the macrolayer. It was found that the dryout of the macrolayer formed beneath a vapor mass occurs in the latter half of the hovering period of the vapor mass. Two-dimensional measurements conducted at 121 grid points in a 1-mm × 1-mm area at the center of the heating surface showed that the dryout commences at specific areas and spreads over the heating surface as the heat flux approaches the CHF. Furthermore, transient measurements of wall void fractions from nucleate boiling to transition boiling were conducted under the transient heating mode, showing that the wall void fraction has small values (<10%) in the nucleate boiling region, and then steeply increases in the transition boiling region. These findings strongly suggest that the macrolayer dryout model is the most appropriate model of the CHF for saturated and subcooled pool boiling of water on upward facing copper surfaces.     

Wall heat flux partitioning during subcooled forced flow film boiling of water on a vertical surface

Subcooled flow film boiling experiments were conducted on a vertical flat plate, 30.5 cm in height, and 3.175 cm wide with forced convective upflow of subcooled water at atmospheric pressure. Data have been obtained for mass fluxes ranging from 0 to 700 kg/m²s, inlet subcoolings ranging from 0 to 25 °C and wall superheats ranging from 200 to 400 °C. Correlations for wall heat transfer coefficient and wall heat flux partitioning were developed as part of this work. These correlations derive their support from simultaneous measurements of the wall heat flux, fluid temperature profiles, liquid side heat flux and interfacial wave behavior during steady state flow film boiling. A new correlation for the film collapse temperature was also deduced by considering the limiting case of heat flux to the subcooled liquid being equal to the wall heat flux. The premise of this deduction is that film collapse under subcooled conditions occurs when there is no net vapor generation. These correlations have also been compared with the data and correlations available in the literature.     

Enhanced boiling of HFE-7100 dielectric liquid on porous graphite

Enhanced boiling of HFE-7100 dielectric liquid on porous graphite measuring 10 mm × 10 mm is investigated, and results are compared with those for smooth copper (Cu) of the same dimensions. Although liquid is out-gassed for hours before performing the pool boiling experiments, air entrapped in re-entrant type cavities, ranging in size from tens to hundreds of microns, not only enhanced the nucleate boiling heat transfer and the critical heat flux (CHF), but also, the mixing by the released tiny air bubbles from the porous graphite prior to boiling incipience enhanced the natural convection heat transfer by ∼19%. No temperature excursion is associated with the nucleate boiling on porous graphite, which ensues at very low surface superheat of 0.5–0.8 K. Conversely, the temperature overshoot at incipient boiling on Cu is as much as 39.2, 36.6, 34.1 and 32.8 K in 0 (saturation), 10, 20 and 30 K subcooled boiling, respectively. Nucleate boiling ensues on Cu at a surface superheat of 11.9, 10.9, 9.5 and 7.5 K in 0 (saturation), 10, 20 and 30 K subcooled boiling, respectively. The saturation nucleate boiling heat flux on porous graphite is 1700% higher than that on Cu at a surface superheat of ∼10 K and decreases exponentially with increased superheat to ∼60% higher near CHF. The CHF values of HFE-7100 on porous graphite of 31.8, 45.1, 55.9 and 66.4 W/cm² in 0 (saturation), 10, 20 and 30 K subcooled boiling, are 60% higher and the corresponding superheats are 25% lower than those on Cu. In addition, the rate of increase in CHF with increased liquid subcooling is 50% higher than that on Cu.     

A correlation to evaluate critical heat flux in small diameter tubes under subcooled conditions of the coolant

A correlation is generated by applying regression analysis to the data under subcooled conditions from the literature to determine the critical heat flux in small diameter tubes less than 3 mm at different pressures for a wide range of system parameters. The correlation is accomplished for the model of slug flow in the tube considering the determining criteria for the formation of the slugs as vapor locks in the tubes leading to departure from nucleate boiling [DNB] conditions. It is observed that the correlation satisfies a wide range of system parameters. Application of the correlation to the data of larger diameter tubes revealed satisfactory agreement. Besides for saturated flow conditions of the coolant (x > 0), another generalized correlation is also proposed with reasonably good accuracy. Comparison of the present correlations with some of the recent correlations indicated satisfactory agreement supporting the validity of the criteria employed in the regression.     

Dry-out CHF correlation for R134a flow boiling in a horizontal helically-coiled tube

An experimental study was carried out to investigate the R134a dry-out critical heat flux (CHF) characteristics in a horizontal helically-coiled tube. The test section was heated uniformly by DC high-power source, and its geometrical parameters are the outer diameter of 10 mm, inner diameter of 8.4 mm, coil diameter of 300 mm, helical pitch of 75 mm and valid heated length of 1.89 m. The experimental parameters are the outlet pressures of 0.30–0.95 MPa, mass fluxes of 60–500 kg m^?2 s^?1, inlet qualities of ?0.36–0.35 and heat fluxes of 7.0 × 10³–5.0 × 10⁴ W m^?2. A method based on Agilent BenchLink Data Logger Pro was developed to determine the occurrence of CHF with a total of 68 T-type thermocouples (0.2 mm) set along the tube for accurate temperature measurement. The characteristics of wall temperatures and the parametric effect on dry-out CHF showed that temperature would jump abruptly at the point of CHF, which usually started to form at the front and offside (270° and 90°) of the outlet cross-section. The CHF values decrease nearly linearly with increasing inlet qualities, while they decrease more acutely with increasing critical qualities, especially under larger mass flux conditions. The mass flux has a positive effect on CHF enhancement, but the pressure has negative one. A new dimensionless correlation was developed to estimate dry-out CHF of R134a flow boiling in horizontal helically-coiled tubes under current experimental conditions and compared to calculated results from Bowring and Shah correlations.     

Experimental investigation and modelling of heat transfer during convective boiling in a minichannel

Flow boiling heat transfer characteristics of water are experimentally studied in a circular minichannel with an inner diameter of 1500 μm. The fluid flows upwards and the test section, made of the nickel alloy Inconel 600, is directly electrically heated. Thus, the evaporation takes place under the defined boundary condition of constant heat flux. Mass fluxes between 50 and 100 kg/(m² s) and heat fluxes from 10 to 115 kW/m² at an inlet pressure of 3 bar are examined.Infrared thermography is applied to measure the outer wall temperatures of the minichannel. This experimental method permits the identification of different boiling regions, boiling mechanisms and the determination of local heat transfer coefficients. Measurements are carried out in single-phase flow, subcooled and saturated boiling regions. The experimental heat transfer coefficients in the region of saturated boiling are compared with correlations available in literature and with a physically founded model developed for convective boiling.     

Boiling heat transfer and critical heat flux of ethanol–water mixtures flowing through a diverging microchannel with artificial cavities

This paper presents an experimental study on the convective boiling heat transfer and the critical heat flux (CHF) of ethanol–water mixtures in a diverging microchannel with artificial cavities. The results show that the boiling heat transfer and the CHF are significantly influenced by the molar fraction (x_m) as well as the mass flux. For the single-phase convection region except for the region near the onset of nucleate boiling with temperature overshoot, the single-phase heat transfer coefficient is independent of the wall superheat and increases with a decrease in the molar fraction. After boiling incipience, the two-phase heat transfer coefficient is much higher than that of single-phase convection. The two-phase heat transfer coefficient shows a maximum in the region of bubbly-elongated slug flow and deceases with a further increase in the wall superheat until approaching a condition of CHF, indicating that the heat transfer is mainly dominated by convective boiling. A flow-pattern-based empirical correlation for the two-phase heat transfer coefficient of the flow boiling of ethanol–water mixtures is developed. The overall mean absolute error of the proposed correlation is 15.5%, and more than 82.5% of the experimental data were predicted within a ±25% error band. The CHF increases from x_m = 0–0.1, and then decreases rapidly from x_m = 0.1–1 at a given mass flux of 175 kg/m² s. The maximum CHF is reached at x_m = 0.1 due to the Marangoni effect, indicating that small additions of ethanol into water could significantly increase the CHF. On the other hand, the CHF increases with increasing the mass flux at a given molar fraction of 0.1. Moreover, the experimental CHF results are compared with existing CHF correlations of flow boiling of the mixtures in a microchannel.     

Critical heat flux of steady boiling for saturated liquids jet impinging on the stagnation zone

An experimental investigation was carried out for predicting the critical heat flux (CHF) of convective boiling of saturated liquids for a round jet impinging on the horizontal jet stagnation zone. The model of maximum liquid subfilm thickness based on the Helmholtz instability was used to derive a semi-theoretical equation. The experimental data of four liquids: water, ethanol, R-113 and R-11 were employed to determine the correlation factor. The impact velocity ranged from 0.5 m/s to 10 m/s and the diameters of the jet nozzle ranged from 3 mm to 10 mm. A semi-theoretical correlation was proposed for predicting CHF of convective boiling for saturated liquids jet impinging on the stagnation zone in a wide range.     

A new mechanistic model for pool boiling CHF on horizontal surfaces

This work proposes a new mechanistic model for predicting the critical heat flux (CHF) in horizontal pool boiling systems. It is postulated that when the vapor momentum flux is sufficient to lift the liquid macrolayer from the heating surface, wetting is no longer feasible, and a transition from nucleate to film boiling occurs. This is the same mechanism that has found success in predicting CHF in flow boiling systems. An experimental investigation of CHF with pentane, hexane, and FC-72 in saturated horizontal pool boiling with chamber pressures of 150, 300, and 450 kPa provides evidence that the new model captures the variation of CHF with pressure reasonably well compared with other well known models. The new model is also compared with existing data from the literature over a reduced pressure range of 2 × 10^?5–2 × 10^?1. The mean deviation between the predicted and measured CHF is typically within 20% over the parameter space covered.     

Subcooled flow boiling and microbubble emission boiling phenomena in a partially heated microchannel

A simultaneous visualization and measurement study has been carried out to investigate subcooled flow boiling and microbubble emission boiling (MEB) phenomena of deionized water in a partially heated Pyrex glass microchannel, having a hydraulic diameter of 155 μm, which was integrated with a Platinum microheater. Effects of mass flux, inlet water subcooling and surface condition of the microheater on subcooled flow boiling in microchannels are investigated. It is found that MEB occurred at high inlet subcoolings and at high heat fluxes, where vapor bubbles collapsed into microbubbles after contacting with the surrounding highly subcooled liquid. In the fully-developed MEB regime where the entire microheater was covered by MEB, the mass flux, the inlet water subcooling and the heater surface condition have only small effects on the boiling curves. The occurrence of MEB in microchannel can remove a large amount of heat flux, as high as 14.41 MW/m² at a mass flux of 883.8 kg/m² s, with only a moderate rise in wall temperature. Therefore, MEB is a very promising method for cooling of microelectronic chips. Heat transfer in the fully-developed MEB in the microchannel is presented, which is compared with existing subcooled flow boiling heat transfer correlations for macrochannels.     

Effects of high subcooling on two-phase spray cooling and critical heat flux

Experiments were performed with FC-77 using three full-cone spray nozzles to assess the influence of subcooling on spray performance and critical heat flux (CHF) from a 1.0 × 1.0 cm² test surface. The relatively high boiling point of FC-77 (97 °C at one atmosphere) enabled testing at relatively high levels of subcooling. Increasing the subcooling delayed the onset of boiling but decreased the slope of the nucleate boiling region of the spray boiling curve. The enhancement in CHF was relatively mild at low subcooling and more appreciable at high subcooling. CHF was enhanced by about a 100% when subcooling was increased from 22 to 70 °C, reaching values as high as 349 W/cm². The FC-77 data were combined with prior spray CHF data from several studies into a broad CHF database encompassing different nozzles, fluids, flow rates, spray orientations, and subcoolings. The entire CHF database was used to modify the effect of subcooling in a previous CHF correlation that was developed for relatively low subcoolings. The modified correlation shows excellent predictive capability.     

Subcooled flow boiling heat transfer and associated bubble characteristics of FC-72 on a heated micro-pin-finned silicon chip

Experiments are conducted here to investigate subcooled flow boiling heat transfer and associated bubble characteristics of FC-72 on a heated micro-pin-finned silicon chip flush-mounted on the bottom of a horizontal rectangular channel. In the experiments the mass flux is varied from 287 to 431 kg/m² s, coolant inlet subcooling from 2.3 to 4.3 °C, and imposed heat flux from 1 to 10 W/cm². Besides, the silicon chips contain three different geometries of micro-structures, namely, the smooth, pin-finned 200 and pin-finned 100 surfaces. The pin-finned 200 and 100 surfaces, respectively, contain micro-pin-fins of size 200 μm × 200 μm × 70 μm (width × length × height) and 100 μm × 100 μm × 70 μm. The measured data show that the subcooled flow boiling heat transfer coefficient is reduced at increasing inlet liquid subcooling but is little affected by the coolant mass flux. Besides, adding the micro-pin-fin structures to the chip surface can effectively raise the single-phase convection and flow boiling heat transfer coefficients. Moreover, the mean bubble departure diameter and active nucleation site density are reduced for rises in the FC-72 mass flux and inlet liquid subcooling. Increasing coolant mass flux or reducing inlet liquid subcooling results in a higher mean bubble departure frequency. Furthermore, larger bubble departure diameter, higher bubble departure frequency, and higher active nucleation site density are observed as the imposed heat flux is increased. Finally, empirical correlations for the present data for the heat transfer and bubble characteristics in the FC-72 subcooled flow boiling are proposed.     

Assessment of dimensionless CHF correlations for subcooled flow boiling in microgravity and Earth gravity

A comprehensive review and analysis of prior subcooled flow boiling CHF correlations was conducted to identify those correlations that provide the most accurate predictions for dielectric working fluids and small rectangular flow passages found in electronics cooling applications in both microgravity and Earth gravity. Since most prior correlations were derived from water databases, only those with dimensionless form were deemed potentially suitable for other working fluids. Only a small fraction of these dimensionless correlations were found to tackle other fluids and more complicated flow and heating configurations with acceptable accuracy. These correlations were ranked relative to mean error, mean absolute error, and root mean square error. Better predictions where achieved when correlations were based on the heated diameter rather than the hydraulic diameter because of the ability of the former to better describe vapor development in subcooled flow. Two previous correlations by Hall and Mudawar provided the best overall CHF predictions for both microgravity and Earth gravity.     

Critical heat flux on flow boiling of methanol–water mixtures in a diverging microchannel with artificial cavities

This study constitutes an experimental investigation into the convective boiling heat transfer and critical heat flux (CHF) of methanol–water mixtures in a diverging microchannel with artificial cavities. Flow visualization shows that bubbles are generally nucleated at both the artificial cavities and side walls of the channel. This confirms the proper functioning of such artificial cavities. Consequently, the wall superheat of the onset nucleate boiling is significantly reduced. Experimental results show that the boiling heat transfer and CHF are significantly influenced by the molar fraction (x_m) as well as the mass flux. The CHF increases with an increase in mass flux at the same molar fraction. On the other hand, the CHF increases slightly from x_m = 0 to 0.3, and then decreases rapidly from x_m = 0.3 to 1 at the same mass flux. The maximum CHF is reached at x_m = 0.3, particularly for a mass flux of 175 kg/m² s, due to the Marangoni effect. Flow visualization confirms that the Marangoni effect helps a region with a liquid film breakup persist to a higher heat flux, and therefore a higher CHF. Moreover, a new empirical correlation involving the Marangoni effect for the CHF on the flow boiling of methanol–water mixtures is developed. The present correlation prediction shows excellent agreement with the experimental data, and further confirms that the present correlation may predict the Marangoni effect on the CHF for the convective boiling heat transfer of binary mixtures.