Experimental and theoretical study of critical heat flux in vertical upflow with inlet vapor void

This study explores the mechanism of flow boiling critical heat flux (CHF) for FC-72 in a 2.5 mm × 5 mm vertical upflow channel that is heated along its 2.5 mm sidewall downstream of an adiabatic development section. Unlike most prior CHF studies, where the working fluid enters the channel in liquid state, the present study concerns saturated inlet conditions with finite vapor void. Temperature measurements and high-speed video imaging techniques are used to investigate the influence of the inlet vapor void on interfacial behavior at heat fluxes up to CHF as well during the CHF transient. The flow entering the heated portion of the channel consists of a thin liquid layer covering the entire perimeter surrounding a large central vapor core. Just prior to CHF, a fairly continuous wavy vapor layer begins to develop between the liquid layer covering the heated wall and the heated wall itself, resulting in a complex four-layer flow consisting of the liquid layer covering the insulated walls, the central vapor core, the now separated liquid layer adjacent to the heated wall, and the newly formed wavy vapor layer along the heated wall. This behavior in captured in a new separated control-volume-based model that facilities the determination of axial variations of thicknesses and mean velocities of the four layers. Incorporating the results of this model in a modified form of the Interfacial Lift-off CHF Model is shown to provide fairly good predictions of CHF data for mass velocities between 185 and 1600 kg/m² s, evidenced by a mean absolute error of 24.52%.     

The effect of the top and bottom wall temperatures on the laminar natural convection in an air-filled square cavity

The effect of the top and bottom wall temperatures on the natural convection heat transfer characteristics in an air-filled square cavity driven by a difference in the vertical wall temperatures was investigated by measuring the temperature distributions along the heated vertical wall and visualizing the flow patterns in the cavity. The experiments were performed at a horizontal Grashof number of 1.9 × 10⁸. Increasing the top wall temperature resulted in a separated flow region on the top wall, which caused a secondary flow between the separated flow and the boundary layer on the heated vertical wall. This secondary flow had a significant effect on the heat transfer in this region. Changes in the top and bottom wall temperatures changed the temperature gradient and the average temperature of the air outside the thermal boundary layers in the cavity. The local heat transfer along much of the heated vertical wall could be correlated by Nu = C · Ra^0.32, but the constant C increased when the average of the top and bottom wall temperatures increased.     

Theoretical model for annular flow condensation in rectangular micro-channels

This study examines the pressure drop and heat transfer characteristics of annular condensation in rectangular micro-channels with three-sided cooling walls. A theoretical control-volume-based model is proposed based on the assumptions of smooth interface between the annular liquid film and vapor core, and uniform film thickness around the channel’s circumference. Mass and momentum conservation are applied to control volumes encompassing the liquid film and the vapor core separately. The model accounts for interfacial suppression of turbulent eddies due to surface tension with the aid of a new eddy diffusivity model specifically tailored to shear-driven turbulent films. The model predictions are compared with experimental pressure drop and heat transfer data for annular condensation of FC-72 along 1 × 1 mm² parallel channels. The condensation is achieved by rejecting heat to a counterflow of water. The data span FC-72 mass velocities of 248–367 kg/m² s, saturation temperatures of 57.8–62.3 °C, qualities of 0.23–1.0, and water mass flow rates of 3–6 g/s. The data are also compared to predictions of previous separated flow mini/micro-channel and macro-channel correlations. While some of the previous correlations do provide good predictions of the average heat transfer coefficient, they fail to capture axial variation of the local heat transfer coefficient along the channel. The new model accurately captures the pressure drop and heat transfer coefficient data in both magnitude and trend, evidenced by mean absolute error values of 3.6% and 9.3%, respectively.     

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.     

Studies on critical heat flux in flow boiling at near critical pressures

Experimental studies on critical heat flux (CHF) have been conducted in a uniformly heated vertical tube of 12.7 mm internal diameter and 3 m length at different reduced pressures ranging from 0.24 to 0.99 with R-134a as the working fluid. The onset of CHF was determined by the sudden rise in the wall temperature of the electrically heated tube. Experiments were performed over a wide range of parameters: mass flux values from 200 to 2000 kg/m² s, pressure from 10 to 39.7 bars and heat flux from 2 to 80 kW/m² and exit quality from 0.17 to 0.94. The results show considerably lower critical heat flux at high pressures. Well known CHF prediction methods, such as the look-up table and correlations of earlier workers show poor agreement at high pressures. A new correlation has been proposed to estimate the CHF in uniformly heated vertical tubes up to the critical pressure and over a wide range of parameters.     

High heat flux flow boiling in silicon multi-microchannels – Part III: Saturated critical heat flux of R236fa and two-phase pressure drops

New experimental critical heat flux results for saturated boiling conditions have been obtained for R236fa flowing in a silicon multi-microchannel heat sink composed of 67 parallel channels, 223 μm wide, 680 μm high and with 80 μm thick fins separating the channels. The microchannel length was 20 mm. The footprint critical heat fluxes measured varied from 112 to 250 W/cm² and the wall critical heat fluxes from 21.9 to 52.2 W/cm² for mass velocities from 276 to 992 kg/m²s. When increasing the mass velocity, the wall critical heat flux was observed to increase. The inlet saturation temperatures (20.31 ? T_sat,in ? 34.27 °C) and the inlet subcoolings (0.4 ? Δ T_sub ? 15.3 K) were found to have a negligible influence on the saturated CHF. The best methods for predicting the data were those of Wojtan et al. [L. Wojtan, R. Revellin, J. R. Thome, Investigation of critical heat flux in single, uniformly heated microchannels, Exp. Therm. Fluid Sci. 30 (2006) 765–774] and Revellin and Thome [R. Revellin, J. R. Thome, A theoretical model for the prediction of the critical heat flux in heated microchannels, Int. J. Heat Mass Transfer 50 (in press)]. They both predict the experimental CHF results with a mean absolute error of around 9%. Using the critical vapour quality, an annular-to-dryout transition is also proposed as a limit in a diabatic microscale flow pattern map. Pressure drop measurements were measured and analysed, showing that the homogeneous model could correctly predict the observed trends.     

Interfacial heat transfer during microdroplet evaporation on a laser heated surface

A comprehensive experimental and numerical investigation on water microdroplet impingement and evaporation is presented from the standpoint of phase-change cooling technologies. The study investigates microdroplet impact and evaporation on a laser heated surface, outlining the experimental and numerical conditions necessary to quantify the interfacial thermal conductance (G) of liquid-metal interfaces during two-phase flow. To do this, continuum-level numerical simulations are conducted in parallel with experimental measurements facilitating high-speed photography and in-situ time-domain thermoreflectance (TDTR). During microdroplet evaporation on laser heated Al thin-films at room temperature, an effective interfacial thermal conductance of G_eff = 6.4 ± 0.4 MW/m² is measured with TDTR. This effective interfacial thermal conductance (G_eff) is interpreted as the high-frequency (ac) interfacial heat transfer coefficient measured at the microdroplet/Al interface. Also on a laser heated surface, fractal-like condensation patterns form on the Al surface surrounding the evaporating microdroplet. This is due to the temperature gradient in the Al surface layer and cyclic vapor/air convection patterns outside the contact line. Laser heating, however, does not significantly increase the evaporation rate beyond that expected for microdroplet evaporation on isothermal Al thin-film surfaces.     

Flow condensation in parallel micro-channels – Part 1: Experimental results and assessment of pressure drop correlations

In this first part of a two-part study, experiments were performed to investigate condensation of FC-72 along parallel, square micro-channels with a hydraulic diameter of 1 mm and a length of 29.9 cm, which were formed in the top surface of a solid copper plate. The condensation was achieved by rejecting heat to a counter flow of water through channels brazed to the underside of the copper plate. The FC-72 entered the micro-channels slightly superheated, and operating conditions included FC-72 mass velocities of 68–367 kg/m² s, FC-72 saturation temperatures of 57.2–62.3 °C, and water mass flow rates of 3–6 g/s. Using high-speed video imaging and photomicrographic techniques, five distinct flow regimes were identified: smooth-annular, wavy-annular, transition, slug, and bubbly, with the smooth-annular and wavy-annular regimes being most prevalent. A detailed pressure model is presented which includes all components of pressure drop across the micro-channel. Different sub-models for the frictional and accelerational pressure gradients are examined using the homogenous equilibrium model (with different two-phase friction factor relations) as well as previous macro-channel and mini/micro-channel separated flow correlations. Unexpectedly, the homogenous flow model provided far more accurate predictions of pressure drop than the separated flow models. Among the separated flow models, better predictions were achieved with those for adiabatic and mini/micro-channels than those for flow boiling and macro-channels.     

CHF determination for high-heat flux phase change cooling system incorporating both micro-channel flow and jet impingement

This paper explores the subcooled nucleate boiling and critical heat flux (CHF) characteristics of a hybrid cooling module that combines the cooling attributes of micro-channel flow and jet impingement. A test module was constructed and tested using HFE-7100 as working fluid. Increasing the coolant’s flow rate and/or subcooling shifted both the onset of boiling (ONB) and CHF to higher heat fluxes and higher wall temperatures. The hybrid module yielded heat fluxes as high as 1127 W/cm², which is the highest value ever achieved for a dielectric coolant at near atmospheric pressure. It is shown the hybrid cooling configuration involves complex interactions between circular jets and micro-channel flow, and unusual spatial variations of void fraction and liquid velocity. These variations are ascertained using the Developing Homogeneous Layer Model (DHLM) in which the micro-channel flow is described as consisting of a homogeneous two-phase layer along the heated wall and a bulk liquid layer. CHF is determined by a superpositioning technique that consists of dividing the heated wall into two portions, one dominated by jet impingement and the other micro-channel flow. This technique is shown to be highly effective at predicting the CHF data for the hybrid cooling configuration.     

Experimental and theoretical study of orientation effects on flow boiling CHF

The effects of orientation on flow boiling critical heat flux (CHF) were investigated using high-speed video and microphotographic techniques. Interfacial features were measured just prior to CHF and statistically analyzed. A dominant wavy vapor layer regime was observed for all relatively high-velocities and most orientations, while several other regimes were encountered at low velocities, in downflow and/or downward-facing heated wall orientations. The interfacial lift-off model was modified and used to predict the orientation effects on CHF for the dominant wavy vapor layer regime. The photographic study revealed a fairly continuous wavy vapor layer travelling along the heated wall while permitting liquid contact only in wetting fronts, located in the troughs of the interfacial waves. The waves, which were generated at an upstream location, had a tendency to preserve a curvature ratio as they propagated along the heated wall. CHF commenced when wetting fronts near the outlet were lifted off the wall. This occurred when the momentum of vapor normal to the wall exceeded the pressure force associated with interfacial curvature. The interfacial lift-off model is shown to be very effective at capturing the overall dependence of CHF on orientation.     

Measurements of critical heat flux and liquid–vapor structure near the heating surface in pool boiling of 2-propanol/water mixtures

Saturated pool boiling of 2-propanol/water mixtures on a 12 mm diameter horizontal disk under atmospheric pressure was investigated. The CHF of the mixtures increased up to 1.7 times the CHF of water at 3.0–4.7 mol% concentrations of 2-propanol. To examine the mechanism of the CHF enhancement in the mixtures, liquid–vapor structures close to the heating surface were measured using a conductance probe. It was found that in the boiling of the mixtures, liquid–vapor structures show strong non-uniformity in the radial direction of the heating surface. The void fractions at 0.1–1 mm above the heating surface are small at the central region and large near the periphery of the heating surface. The liquid layer between the vapor mass and the heating surface is considerably thicker than that of water at the central region and becomes thinner near the periphery of the heating surface. This thicker liquid layer is likely to be the cause of the CHF enhancement in the 2-propanol/water mixtures.     

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.     

Refrigerant flow boiling heat transfer in parallel microchannels as a function of local vapor quality

Flow boiling of refrigerant HFC-134a in a multi-microchannel copper cold plate evaporator is investigated. The heat transfer coefficient is measured locally for the entire range of vapor qualities starting from subcooled liquid to superheated vapor. The test piece contains 17 parallel, rectangular microchannels (0.762 mm wide) of hydraulic diameter 1.09 mm and aspect ratio 2.5. The design of the test facility is validated by a robust energy balance as well as a comparison of single-phase heat transfer coefficients with results from the literature. Results are presented for four different mass fluxes of 20.3, 40.5, 60.8, and 81.0 kg m^?2 s^?1, which correspond to refrigerant mass flow rates of 0.5–2.0 g s^?1, and at three different pressures 400, 550 and 750 kPa corresponding to saturation temperatures of 8.9, 18.7, and 29 °C. The wall heat flux varies from 0 to 20 W/cm² in the experiments. The heat transfer coefficient is found to vary significantly with refrigerant inlet quality and mass flow rate, but only slightly with saturation pressure for the range of values investigated. The peak heat transfer coefficient is observed for a vapor quality of approximately 20%.     

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.     

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.     

Saturated flow boiling heat transfer and critical heat flux in small horizontal flattened tubes

This paper presents experimental results for flow boiling heat transfer coefficient and critical heat flux (CHF) in small flattened tubes. The tested flattened tubes have the same equivalent internal diameter of 2.2 mm, but different aspect height/width ratios (H/W) of ¼, ½, 2 and 4. The experimental data were compared against results for circular tubes using R134a and R245fa as working fluids at a nominal saturation temperature of 31 °C. For mass velocities higher than 200 kg/m²s, the flattened and circular tubes presented similar heat transfer coefficients. Such a behavior is related to the fact that stratification effects are negligible under conditions of higher mass velocities. Heat transfer correlations from the literature, usually developed using only circular-channel experimental data, predicted the flattened tube results for mass velocities higher than 200 kg/m²s with mean absolute error lower than 20% using the equivalent diameter to account for the geometry effect. Similarly, the critical heat flux results were found to be independent of the tube aspect ratio when the same equivalent length was kept. Equivalent length is a new parameter which takes into account the channel heat transfer area. The CHF correlations for round tubes predicted the flattened tube data relatively well when using the equivalent diameter and length. Furthermore, a new proposed CHF correlation predicted the present flattened tube data with a mean absolute error of 5%.     

A theoretical model for the prediction of the critical heat flux in heated microchannels

A theoretical model for the prediction of the critical heat flux of refrigerants flowing in heated, round microchannels has been developed and presented here. The model is based on the two-phase conservation equations and includes the effect of the height of the interfacial waves of the annular film. Validation has been carried out by comparing the model, a numerical solution of a non-linear system of five differential equations, with a critical heat flux (CHF) database including three different refrigerants from two different laboratories. More than 96% of the data are predicted within a ±20% error band and a mean absolute error of 8%. Furthermore, it is also possible to predict CHF data from a third laboratory for water and R-113 flowing in rectangular (using the width of the channel as the characteristic dimension) and circular microchannel heat sinks with multiple channels. All together, 90% of the entire database, including four different fluids and different geometries, are predicted by the model within a ±20% error band and a mean absolute error of 9.3% for channels from 0.215 to 3.15 mm in size, mass fluxes from 29 to 1600 kg/m² s, heated lengths from 10 to 126 mm and subcoolings from 2 to 77 °C.     

Study on flow characteristics and pressure distribution along a heated channel in subcooled flow boiling

In the present work, an experimental investigation is presented which is focused on the pressure drop along the heated as well as the unheated zone of a flow channel. The experiments were performed by using a 16 mm stainless steel ID tube with a 350 mm heated length followed by a 500 mm unheated extension downstream. Pressure drops and pressure distribution were measured along the flow channel, with water, at mass flow velocities of 6342–9513 kg/m² s and at heat fluxes of 3.37–4.1 MW/m². The whole experiments were conducted near atmospheric pressure by keeping the outlet of the flow channel open to the atmospheric pressure. The experimental results show a reduction of the pressure at the outlet of the heated zone at the onset of significant void (OSV) conditions, caused by the increasing of the average velocity at that zone. That reduction of the pressure, at the outlet of the heated zone, decreases as the inlet (and also the outlet) temperature increases, due to the increasing of the length of the two phase flow at the unheated zone. That phenomenon is backed by photographing the flow in the unheated zone.     

Experimental study of evaporation heat transfer of R-134a inside a corrugated tube with different tube inclinations

Experimental heat transfer studies during evaporation of R-134a inside a corrugated tube have been carried out. The corrugated tube has been provided with different tube inclination angles of the direction of fluid flow from horizontal, α. The experiments were performed for seven different tube inclinations, α, in a range of − 90° to + 90° and four mass velocities of 46, 81, 110 and 136 kg m^− 2 s^− 1 for each tube inclination angle during evaporation of R-134a. Data analysis demonstrate that the tube inclination angle, α, affects the boiling heat transfer coefficient in a significant manner. The effect of tube inclination angle, α, on heat transfer coefficient, h, is more prominent at low vapor quality and mass velocity. In the low vapor quality region, the heat transfer coefficient, h, for the + 90° inclined tube is about 62% more than that of the − 90° inclined tube. The results also showed that at all mass velocities, the highest average heat transfer coefficient were achieved for α = + 90°. An empirical correlation has also been developed to predict the heat transfer coefficient during flow boiling inside a corrugated tube with different tube inclinations.     

Experimental assessment of the effects of body force, surface tension force, and inertia on flow boiling CHF

The interfacial instabilities important to the modeling of critical heat flux (CHF) in reduced-gravity systems are sensitive to even minute body forces, especially for small coolant velocities. Understanding these effects is of paramount importance to both the reliability and safety of two-phase thermal management loops proposed for future space and planetary-based thermal systems. Unfortunately, reduced gravity systems cannot be accurately simulated in 1g ground-based experiments. However, ground-based experiments can help isolate the effects of the various forces (body force, surface tension force and inertia) which influence flow boiling CHF. In this project, the effects of the component of body force perpendicular to a heated wall were examined by conducting 1g flow boiling experiments at different orientations. Boiling experiments were performed using FC-72 in vertical and inclined upflow and downflow, as well as horizontal flow, and with the heated surface facing upward or downward relative to gravity. CHF was very sensitive to orientation for flow velocities below 0.2 m/s and near-saturated flow; CHF values for downflow and downward-facing heated surface were much smaller than for upflow and upward-facing surface orientations. Increasing velocity and subcooling dampened the effects of flow orientation on CHF. For saturated flow, the vapor layer characteristics fell into six different regimes: wavy vapor layer, pool-boiling, stratification, vapor stagnation, vapor counterflow, and vapor concurrent flow. The wavy vapor layer regime encompassed all subcooled and high-velocity saturated conditions at all orientations, as well as low-velocity upflow orientations. Prior CHF correlations and models were compared, and shown to predict the CHF data with varying degrees of success.