Correlation of critical heat flux for flow boiling of water in mini-channels

In view of practical significance of a correlation of critical heat flux (CHF) in the aspects of engineering design and prediction, this study is aiming at evaluation of existing CHF correlations for flow boiling of water with available databases taken from small-diameter tubes, and then development of a new, simple CHF correlation. Available CHF databases in the literature for flow boiling of water in small-diameter tubes (0.33 < D_h < 6.22 mm) are collected, covering wide parametric ranges. Three correlations by Bowring, Katto and Shah are evaluated with the CHF data for saturated flow boiling, and three correlations by Inasaka–Nariai, Celata et al. and Hall–Mudawar evaluated with the CHF data for subcooled flow boiling. The Hall–Mudawar correlation and the Shah correlation seem to be the most reliable tools for CHF prediction in the subcooled and saturated flow boiling regions, respectively. In order to avoid the defect of predictive discontinuities often encountered when applying previous correlations, a simple, nondimensional, inlet conditions dependent CHF correlation for saturated flow boiling has been formulated. Its functional form is determined by the application of the artificial neural network and parametric trend analyses to the collected database. Superiority of this correlation has been verified by the database. The new correlation has a mean deviation of 16.8% for this collected databank, smallest among all tested correlations. Compared to many inordinately complex correlations, this new correlation consists only of a single equation.     

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.     

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.     

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.     

Flow structure of subcooled boiling flow in an internally heated annulus

Local measurements of flow parameters were performed for vertical upward subcooled boiling flows in an internally heated annulus. The annulus channel consisted of an inner heater rod with a diameter of 19.1 mm and an outer round pipe with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. The double-sensor conductivity probe method was used for measuring local void fraction, interfacial area concentration, and interfacial velocity. A total of 11 data were acquired consisting of four inlet liquid velocities, 0.500, 0.664, 0.987 and 1.22 m/s and two inlet liquid temperatures, 95.0 and 98.0 °C. The constitutive equations for distribution parameter and drift velocity in the drift-flux model, and the semi-theoretical correlation for Sauter mean diameter, namely, interfacial area concentration, which were proposed previously, were validated by local flow parameters obtained in the experiment.     

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.     

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.     

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.     

Measurements of jet flows impinging into a channel containing a rod bundle using dynamic PIV

In this investigation, full-field velocity profiles of jet flows impinging into a rod bundle were measured using Particle Image Velocimetry (PIV) technique in a facility with Matched-Index of Refraction. The test section consisted of a 1 m long rectangular channel with a cross-sectional area of 76.2 × 76.2 mm². Water was pumped through either single or double jets located on the top wall of the channel. The Reynolds numbers of the inlet jets were varied from 4470 to 13,400. Inside the channel adjacent to the inlet jets, a rod bundle was configured with 29 staggered tubes of 10.67 mm outside diameter (O.D.). The time-resolved velocity fields were obtained for regions within the rod bundle from which the vorticity fields and the turbulent characteristics of those regions were calculated. The results are useful for developing new models to help predict the flow patterns in the lower plenum of Gas Cooled Reactors.     

Modeling capability of R134a for a critical heat flux of water in a vertical 5 × 5 rod bundle geometry

Critical heat flux (CHF) tests have been performed for a vertically upward R134a flow in a 5 × 5 rod bundle in the following parameter ranges: outlet pressure 1.5–3.0 MPa, mass flux 50–2500 kg m⁻² s⁻¹, inlet quality −0.08 to −0.75 and critical quality −0.17 to 1.58. Parametric trends of the CHF data agree well with the general understanding. Water equivalent CHF data is generated using a set of well-established modeling parameters, then compared with (a) the EPRI/Colombia University’s water CHF database for similar geometry and experimental conditions and (b) commonly used CHF prediction methods. The water equivalent CHF data generated from the present tests shows a good agreement with the actual water CHF data for both Katto’s and Ahmad’s modeling methods when considering the differences in the detailed geometric and flow conditions. They are also predicted well by the 1995 CHF look-up table. These results indicate that R134a can be a good modeling fluid for the CHF of water in rod bundles at least in the investigated parameter ranges.     

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.     

Heat transfer characteristics during subcooled flow boiling of a kerosene kind hydrocarbon fuel in a 1 mm diameter channel

The subcooled flow boiling heat transfer characteristics of a kerosene kind hydrocarbon fuel were investigated in an electrically heated horizontal tube with an inner diameter of 1.0 mm, in the range of heat flux: 20–1500 kW/m², fluid temperature: 25–400 °C, mass flux: 1260–2160 kg/m² s, and pressure: 0.25–2.5 MPa. It was proposed that nucleate boiling heat transfer mechanism is dominant, as the heat transfer performance is dependent on heat flux imposed on the channel, rather than the fuel flow rate. It was found that the wall temperatures along the test section kept constant during the fully developed subcooled boiling (FDSB) of the non-azeotropic hydrocarbon fuel. After the onset of nucleate boiling, the temperature differences between inner wall and bulk fluid begin to decrease with the increase of heat flux. Experimental results show that the complicated boiling heat transfer behavior of hydrocarbon fuel is profoundly affected by the pressure and heat flux, especially by fuel subcooling. A correlation of heat transfer coefficients varying with heat fluxes and fuel subcooling was curve fitted. Excellent agreement is obtained between the predicted values and the experimental data.     

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.     

Heat transportation by oscillatory flow in a new type of heat transportation pipe

The present paper deals with experimental and numerical study on the longitudinal heat transportation by an oscillatory water flow in a double tube type heat transportation pipe. Experiments were performed to measure the heat transportation rate in the ranges of 2.3 ? Wo ? 7.2 and 400 ? Re_max ? 6600. The heat transportation rate was approximately 10–490 times the heat transportation rate of a straight round pipe, and it was around 1–40 times the heat conduction rate through a copper rod. Analytical heat transportation rates agreed well with the experimental ones.     

Experimental investigation of flow boiling heat transfer of jet impingement on smooth and micro structured surfaces

Flow boiling heat transfer experiments using R134a were carried out for jet impingement on smooth and enhanced surfaces. The enhanced surfaces were circular micro pin fins, hydrofoil micro pin fins, and square micro pin fins. The effects of saturation pressure, heat flux, Reynolds number, pin fin geometry, pin fin array configuration, and surface aging on flow boiling heat transfer characteristics were investigated. Flow boiling experiments were carried out for two different saturation pressures, 820 kPa and 1090 kPa. Four jet exit velocities ranging from 1.1–4.05 m/s were investigated. Flow boiling jet impingement on smooth surfaces was characterized by large temperature overshoots, exhibiting boiling hysteresis. Flow boiling jet impingement on micro pin fins displayed large heat transfer coefficients. Heat transfer coefficients as high as 150,000 W/m² K were observed at a relatively low velocity of 2.2 m/s with the large (D = 125 μm) circular micro pin fins. Jet velocity, surface aging, and saturation pressure were found to have significant effects on the two-phase heat transfer characteristics. Subcooled nucleate boiling was found to be the dominant heat transfer mechanism.     

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.     

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 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.     

Unstable and stable flow boiling in parallel microchannels and in a single microchannel

A simultaneous visualization and measurement study have been carried out to investigate flow boiling instabilities of water in microchannels at various heat fluxes and mass fluxes. Two separate flow boiling experiments were conducted in eight parallel silicon microchannels (with flow interaction from neighboring channels at headers) and in a single microchannel (without flow interaction), respectively. These microchannels, at a length of 30 mm, had an identical trapezoidal cross-section with a hydraulic diameter of 186 μm. At a given heat flux and inlet water temperature, it was found that stable and unstable flow boiling regimes existed, depending on the mass flux. A flow boiling map, in terms of heat flux vs mass flux, showing stable flow boiling regime and unstable flow boiling regime is presented for parallel microchannels as well as for a single microchannel, respectively, at an inlet water temperature of 35 °C. In the stable flow boiling regime, isolated bubbles were generated and were pushed away by the incoming subcooled liquid. Two unstable flow boiling regimes, with long-period oscillation (more than 1 s) and short-period oscillation (less than 0.1 s) in temperature and pressure, were identified. The former was due to the expansion of vapor bubble from downstream while the latter was owing to the flow pattern transition from annular to mist flow. A comparison of results of flow boiling in parallel microchannels and in a single microchannel shows that flow interaction effects from neighboring channels at the headers are significant.     

Turbulent flow in the near field of a round impinging jet

This paper reports on detailed measurements of the turbulent flow in the stagnation region of a single impinging jet issuing from a round pipe with diameter D and a length of 76D. The distance between the pipe exit and the flat impingement plate is 2D, and the Reynolds number (based on the bulk velocity and pipe diameter) is 2.3 × 10⁴. Mean velocity components and Reynolds stresses were determined by using a two-component LDA. A modified one-component LDA was used to perform near-wall measurements with minimum wall distances of approximately 40 μm. PIV measurements were taken in a small field of view (approximately 4 × 5 mm²) to study instantaneous reversals in the near wall region.