Critical heat flux in non‐uniformly heated tube under low‐pressure and low‐mass‐flux condition

In an actual boiling channel, e.g., a boiler water‐tube, the circumferential heat flux is not uniform. Thus, the critical heat flux (CHF) of a non‐uniformly heated tube becomes an important design factor for conventional boilers, especially for a compact water‐tube boiler with a tube‐nested combustor. A small compact boiler is operated under low‐pressure and low‐mass‐flux conditions compared with a large‐scale boiler, thus the redistribution of liquid film strongly affects the characteristics of CHF. In this investigation, non‐uniform heat flux distribution along the circumferential direction was generated by using the Joule heating of SUS304 tubes with the wall thickness distribution. The heated length of test‐section was 900 mm with an inner diameter of 20 mm and an outer diameter of 24 mm. The center of the inner tube surface was shifted by ε=0, 0.5, 1.0, 1.5 mm from the center of the outer tube surface. The heat flux ratio between maximum and minimum heat flux of these tubes corresponded to 1.0, 1.7, 3.0, and 7.0, respectively. The experimental conditions were as follows: system pressure at 0.3 and 0.4 MPa, mass flux of 10–100kg/(m²s), inlet temperatures at 30° and 80°. The experimental results showed an increase in the critical heat flux substantiated by the existence of the redistribution of the flow. These characteristics are explained by using a concept similar to that of Butterworth's spreading model. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(1): 47–60, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20095     

CHF in a circumferentially non‐uniformly heated tube under low‐pressure and low‐mass‐flux condition (inclined upward flow)

Most investigations on forced convective boiling have been conducted by using uniformly heated round tubes under a vertical upward flow condition, although the actual system has a non‐uniformly heated condition with several tube orientations. The non‐uniformity of the heat flux and tube inclination causes the liquid film distribution, which in turn affects the critical heat flux. In this investigation, the flow and heat‐transfer characteristics were experimentally investigated under non‐uniformly heated conditions along the circumferential direction with a 45° tube inclination. In the experiment, CHF was measured by using two different heated lengths, i.e., 900 and 1800 mm. The experimental results showed a unique tendency of CHF caused by the interrelationship of the non‐uniform heat flux distribution, the tube inclination, and liquid film redistribution. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20333     

Effect of channel length on critical heat flux under conditions of high subcooling and high velocity in short heated channels

The characteristics of critical heat flux (CHF) in existing experiments under high subcooling and high velocity in short heated channels have, for the first time, been systematically and quantitatively investigated to provide a CHF correlation that can properly predict the effect of channel length, especially when the channel length-to-channel diameter ratio L/D is less than about 20. The major test conditions of existing CHF experiments investigated in this study were channel diameter 1 to 4 mm, L/D 1 to 25, 0.1 to 1.2 MPa pressure, 34 to 117°C inlet water subcooling and 500 to 40 700 kg/(m² · s) mass flux in circular channels, and 3 to 20 mm gap size, 6 to 40 L/D_e, 0.1 to 3.1 MPa pressure, 4 to 166°C inlet water subcooling, and 940 to 27,000 kg/(m² · s) mass flux in rectangular channels. The effect of L/D on CHF was evaluated referring to the analytical solution of CHF, which was previously derived by the author for the channel flow at high subcooling and high velocity. As a result, the effect of L/D was quantitatively clarified as an effect of magnitude in heat transfer of single-phase forced-convection flow, giving a larger CHF with a smaller L/D in the case of L/D less than about 20. The proposed correlation predicts CHF to within a ±35 percent error margin. ©1998 Scripta Technica, Heat Trans Jpn Res, 27(7): 509–521, 1998     

Characteristics of heat transfer inside a tube during sodium‐water reaction in a FBR steam generator

Sodium reacts chemically with water in the case of an unexpected tube failure of a steam generator (SG) in a fast breeder reactor (FBR). In order to predict the event with high accuracy, it is very important to understand the characteristics of heat transfer inside the tube in detail during the tube failure due to the sodium–water reaction. Experiments were performed by using purified water under the following conditions: initial pressure of 11.2–13.4 MPa, initial water temperature of 200 °C, and water mass flux of 45.7 to 3630 kg/(m²s). The test tube was heated rapidly by high‐frequency induction current. The time averaged heat flux was estimated by using an inverse solution from the measured temperatures at two points on three different locations along the tube. It was confirmed that the derived values agreed with the measured heat fluxes on the outer surface within 20% accuracy. It was found that the characteristics of the heat transfer strongly depend on the flow rate. The heat transfer on the wall changed from nucleate boiling to transient‐film boiling during increasing the heat flux and returned to the nucleate boiling during decreasing the heat flux. A counterclockwise cycle always appeared in the transition boiling region, where the nucleate and film boiling coexisted and the area ratio of these varied with time. The adequacy of heat transfer correlations to evaluate tube overheating was confirmed. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20320     

Heat transfer and flow characteristics of flow boiling of CO2‐oil mixtures in horizontal smooth and micro‐fin tubes

Experiments were carried out on the flow pattern, heat transfer, and pressure drop of flow boiling of pure CO₂ and CO₂‐oil mixtures in horizontal smooth and micro‐fin tubes. The smooth tube is a stainless steel tube with an inner diameter of 3.76 mm. The micro‐fin tube is a copper tube with a mean inner diameter of 3.75 mm. The experiments were carried out at mass velocities from 100 to 500 kg/(m²·s), saturation temperature of 10 °C, and the circulation ratio of lubricating oil (PAG) was from 0 to 1.0 mass%. Flow pattern observations mainly showed slug and wavy flow for the smooth tube, but annular flow for the micro‐fin tube. Compared with the flow patterns in the case of pure CO₂, an increase in frequency of slug occurrence in the slug flow region, and a decrease in the quantity of liquid at the top of the tube in the annular flow region were observed in the case of CO₂‐oil mixtures. With pure CO₂, the flow boiling heat transfer was dominated by nucleate boiling in the low vapor quality region, and the heat transfer coefficients for the micro‐fin tube were higher than those of the smooth tube. With CO₂‐oil mixtures, the flow boiling heat transfer was dominated by convective evaporation, especially in the high vapor quality region. In addition, the heat transfer coefficient decreased significantly when the oil circulation ratio was larger than 0.1 mass%. For the pressure drop characteristics, in the case of pure CO₂, the homogeneous flow model agreed with the experimental results within ±30% for the smooth tube. The pressure drops of the micro‐fin tube were 0–70% higher than those predicted with the homogeneous flow model, and the pressure drops increased for the high oil circulation ratio and high vapor quality conditions. The increases in the pressure drops were considered to be due to the increase in the thickness of the oil film and the decrease in the effective flow cross‐sectional area. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20287     

Micro‐bubble emission boiling from horizontal and vertical surfaces to subcooled parallel flow water

Heat removal of more than 10 MW/m² in heat flux has been required in high‐heat‐generation equipment in nuclear fusion reactors. In some conditions of water subcooling and velocity, there appears an extraordinary high heat flux boiling in the transition boiling region. This boiling regime is called micro‐bubble emission boiling (MEB) because many micro‐bubbles are spouted from the heat transfer surface accompanying a huge sound. The study intent is to obtain heat transfer performance of MEB in horizontal and vertical heated surfaces to parallel flow of subcooled water, comparing with CHF of this system. Three types of MEB with different heat transfer performance and bubble behavior are observed according to the flow velocity and liquid subcooling. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(2): 130–140, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10077     

Study of thermal characteristics of bubble‐driven heat‐transport device

In the present paper, we report on heat transport rates and fluid flow patterns of a bubble‐driven heat‐transport device (BD‐HTD) made of glass, obtained with the working fluids water, soapsuds, ethanol, and R141b. In this type of HTD, the cooling and heating sections are connected to each other by a closed loop of tube meandering between them, and the loop is filled to a certain volume fraction with a working fluid. The present BD‐HTD was set vertically and was heated at the bottom by warm water and cooled at the top by cold water. Experimental parameters were the inner diameter of the tube (D = 1.8, 2.4, 5.0 mm), the total temperature difference of heating and cooling water (ΔT = 20 to 60 K), and liquid volume fraction (α = 18 to 98%). The main results are summarized as follows. Heat transfer coefficient of the working fluid at the heating and cooling sections, h_fi, is not strongly dependent on α and ΔT. Among the present test liquids, the effective thermal conductivity k_ef is the highest for R141b, but the heat transfer coefficient h_fi is the highest for water. As k_ef is sufficiently high even for water, the heat transport rate Q is the highest for water. Q of the present BD‐HTD using water can exceed the maximum heat transport rate of conventional heat pipes of the same geometry. For R141b, the BD‐HTD operated for D/λ₀ = 1.5 to 4.2 (λ₀: the capillary length) and Q is not strongly dependent on the tube diameter. This result indicates that BD‐HTDs are suitable for micro‐HTDs, but the BD‐HTD did not operate with water at D/λ₀ = 0.65. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(2): 167–177, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10082     

Critical heat flux under conditions of high subcooling and high velocity at atmospheric pressure

A quantitative analysis of critical heat flux (CHF) under high mass flux with high subcooling at atmospheric pressure was successfully carried out by applying a new transition region model for a macro-water sublayer on heated walls to the existing model of a vapor blanket over the macro-water sublayer. The CHF correlation proposed in this study could predict well the experimental data obtained for water mass flux of 940 to 20,300 kg/m²s using circulate tubes 2 to 4 mm in diameter and 30 to 100 mm in length with inlet subcooling of 30 to 90 °C and rectangular channels heated from one side with gaps of 3 to 20 mm, length of 50 to 305 mm, and inlet subcooling of 30 to 77 °C and revealed a unique feature of CHF, namely, that the effects of wall friction of subcooled boiling flow and the velocity of the steam blanket above the macro-water sublayer at atmospheric pressure become the dominant factors while they were not dominant at higher pressures. © 1997 Scripta Technica, Inc Heat Trans Jpn Res, 26 (1): 16–29, 1997     

High Heat Flux Burnout in Subcooled Flow Boiling

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Fluid flow and heat transfer of opposing mixed convection adjacent to downward‐facing,inclined heated plates

Experimental investigations were carried out for opposing mixed convective flows of air adjacent to downward‐facing, inclined heated plates. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers from Re_L=400 to 4600 and Ra_L^*=1.0×10⁷ to 5.4×10⁸, and the inclination angles from θ=15 to 75^° from horizontal. The flow fields over the plates were visualized with smoke. The results showed that a separation of forced boundary layer flow occurs first at the bottom edge of the plate, and then the separation point shifts toward upstream with increasing wall heat flux, and finally, reaches the top edge of the plates. It was found that the separations at the bottom and top edges are predicted with a non‐dimensional parameter (Gr_Lθ^*/Re_L^2.5)=0.35 and 1.0, respectively. The local heat transfer coefficients of the inclined plates were also measured and the results showed that the minimum coefficients appear in the separation region. Moreover, it was revealed that forced, natural, and combined convective flows can be classified by the non‐dimensional parameter (Gr_Lθ^*/Re_L^2.5). © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Pub‐ lished online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20233     

Heat transfer research on vapor‐gas mixture with condensation in a vertical tube

The convection‐condensation heat transfer of vapor‐gas mixtures in a vertical tube was studied theoretically and experimentally. The effects of the condensation of a small amount of water vapor (8 to 20%) on heat transfer in a vertical tube were discussed. Comparisons show that theoretical solutions obtained through modified film model and experimental results are in good agreement. The results show that the condensation heat transfer of a small amount of water vapor and single‐phase convection heat transfer in the vapor‐gas mixtures are of the same order of magnitude, and these two modes of heat transfer could not be neglected. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 531–539, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10055     

Heat transfer enhancement by crossflow‐induced vibration

A new method of heat transfer enhancement by water crossflow‐induced vibration is presented. A heat transfer element which involves elastic tube bundles has been designed. This system has excellent response characteristics of vibration to the crossflow. A triangular pole device for producing pulsating flow was adopted. This device can induce vibration in a fixed range of frequencies and has a profound influence on heat transfer augmentation. For the constant heat flux boundary condition, experiments are carried out on the heat transfer characteristics of elastic tube bundles augmented by flow‐induced vibration in a water crossflow. Compared with static tube bundles, the out‐tube average convective heat transfer coefficients of the elastic tube bundles are increased by 100–150% under the condition of crossflow‐induced vibration. Dimensionless equations describing the outside heat transfer coefficient for the elastic tube bundles were acquired. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(4): 211–218, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20012     

An experimental study of heat transfer in an open thermosyphon

An experimental study was performed on heat transfer of an open thermosyphon with constant wall heat flux. Water and aqueous glycerin were used as working fluids. The experimental range of modified Rayleigh number was 1 × 10³ < Ra_m < 3 × 10⁵. The average and local heat transfer coefficients, vertical temperature distributions of the tube wall and fluid at the centerline of the tube, and temperature fluctuations of the fluid were measured. Flow patterns were observed by adding tracer powder to the fluid. Fluid velocities were measured by laser Doppler velocimeter. Experimental results indicate that, for a water thermosyphon, there are three regimes where different heat transfer characteristics and flow patterns occur. For 1 × 10³ < Ra_m < 3 × 10³, the flow was laminar and the thermal boundary layer reached the center of the tube. Heat was exchanged between the wall and descending flow. Wall temperature increased in the downward direction. For 4 × 10³ < Ra_m < 3 × 10⁴, no turbulence was observed in the flow and the thermal boundary layer was localized in the vicinity of the wall. The wall temperature increased upward. For 3 × 10⁴ < Ra_m < 3 × 10⁵, flow was considerably disturbed by the mixing of upward and downward flow in the upper part of the tube. However, the flow was laminar in the lower part of the tube. Reduction of the flow rate induced by the flow mixing at high Ra_m can be one of the major causes of the deterioration of heat transfer from Lighthill's theory. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 301–312, 2001     

An investigation into the heat transfer characteristics of spiral wall with internal rib in a supercritical sliding-pressure operation once-through boiler

Within the pressure range of 9–28 MPa, mass velocity range of 600–1 200 kg/(m²·s), and heat flux range of 200–500 kW/m², experiments were performed to investigate the heat transfer to water in the inclned upward internally ribbed tube with an inclined angle of 19.5 degrees, a maximum outer diameter of 38.1 mm, and a thickness of 7.5 mm. Based on the experiments, it was found that heat transfer enhancement of the internally ribbed tube could postpone departure from nucleate boiling at the sub-critical pressure. However, the heat transfer enhancement decreased near the critical pressure. At supercritical pressure, the temperature difference between the wall and the fluid increased near the pseudo-critical temperature, but the increase of wall temperature was less than that of departure from nucleate boiling at sub-critical pressure. When pressure is closer to the critical pressure, the temperature difference between the wall and the fluid increased greatly near the pseudo-critical temperature. Heat transfer to supercritical water in the inclined upward internally ribbed tube was enhanced or deteriorated near the pseudo-critical temperature with the variety of ratio between the mass velocity and the heat flux. Because the rotational flow of the internal groove reduced the effect of natural convection, the internal wall temperature of internally ribbed tube uniformly distributed along the circumference. The maximum internal wall temperature difference of the tube along the circumference was only 10 degrees when the fluid enthalpy exceeded 2 000 J/g. Considering the effect of acute variety of the fluid property on heat transfer, the coreelation of heat transfer coefficient on the top of the internally ribbed tube was provided. Translated from Proceedings of CSEE, 2005, 25(16): 90–95 [译自: 中国电机工程学报]     

Experimental study of critical heat flux in a two-phase open concentric-tube thermosyphon

An experimental study was made to elucidate critical heat flux (CHF) characteristics in a two-phase concentric-tube thermosyphon. The experiment was performed by using saturated water, ethanol, and R113 over the experimental range of configuration: inner diameter of heated outer tube D_i = 17 mm, outer diameter of unheated inner tube d_o = 3 to 15 mm and heated tube length L = 500 and 1000 mm. The experiment shows that the CHF is enhanced by an increase in the inner tube diameter, and that the CHF decreases beyond a certain diameter of the inner tube. There is an optimum diameter for the inner tube that maximizes the CHF, for each tube length and test liquid. The CHF maximum is about four or six times as large as that without an inner tube. For a large inner tube, the CHF characteristic is similar to that for natural convective boiling in a vertical annular tube. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(5): 319–331, 1997     

The flow characteristics of an upward gas‐liquid two‐phase flow in a vertical tube with a wire coil: Part 1. Experimental results of flow pattern,void fraction,and pressure drop

Experiments were carried out to investigate the flow pattern, average void fraction, and pressure drop of an upward air‐water two‐phase flow in vertical tubes of 25‐mm inside diameter with wire coils of varying wire diameter, pitch, and number of coils in cross section. Five kinds of flow patterns—bubble, slug, churn, semiannular, and annular flow—were defined based on the observation of flow behavior in the experiments. At higher water flowrates, the bubble‐to‐slug transition occurred at lower air flowrates in tubes with wire coils than in smooth tubes. The average void fraction was found by using the drift flux model. Further, the experimental results of the friction pressure drop were compared with the Lockhart‐Martinelli correlation. As a result, a correlation with the constant C in Chisholm's equation was obtained as a function of the wire coil pitch‐to‐diameter ratio. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(8): 639–651, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10066     

Prediction of critical heat flux on natural convective boiling in vertical short‐thick tube submerged in saturated liquid

An experimental and semitheoretical study was carried out for the critical heat flux (CHF) on natural convective boiling in uniformly heated vertical short‐thick tubes and vertical short‐thick annular tubes submerged in saturated liquids. By adapting a mathematical dealing method based on the theoretical formulas of CHF of both the natural convective boiling in vertical narrow‐long tubes and the pool boiling, a simple semitheoretical formula was derived. The new formula expands the prediction range of CHF from pool boiling of vertical plates to very long vertical tubes and agrees well with the data of the tubes, annular tubes submerged in water or other liquids under various pressure conditions. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(5): 402–410, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10103     

Equation of state for fluid mixtures based on the principle of corresponding states with a two‐fluid model: Application to fluid mixtures of water + ammonia

We propose an equation of state for fluid mixtures of water + ammonia which is expressed in Helmholtz free energy as a function of temperature, molar volume, and mole fraction. IAPWS Formulation 1995 for water and the equation of state by Tillner‐Roth and colleagues for ammonia should be used for each pure component with the present equation. We applied the principle of corresponding states with a two‐fluid model to the present equation for fluid mixtures. On comparison with experimental data, the uncertainty in property calculations by the present equation was evaluated: within ±0.03 · x for bubble point curve, within ±0.04 · x for dew point curve, within ±0.02 · ρ^L for saturated liquid density, and within ±0.02 · ρ for PVTX properties. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 131(4): 320–330, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10023     

A theoretical study of evaporative heat transfer in high‐velocity two‐phase flow of air–water in a small vertical tube

A theoretical study was performed to investigate the evaporative heat transfer of high‐velocity two‐phase flow of air–water in a small vertical tube under both heating conditions of constant wall temperature and constant heat flux. A simplified two‐phase flow boundary layer model was used to evaluate the evaporative heat transfer characteristics of the annular two‐phase flow. The analytical results show that the gravitational force, the gas–liquid surface tension force, and the inertial force are much smaller than the frictional force and hence can be neglected for a small tube. The evaporative heat transfer characteristics of the small tube with constant wall temperature are quite close to those of the small tube with constant heat flux. The mechanism of the heat transfer enhancement is the forced convective evaporation on the surface of the thin liquid film. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(5): 430–444, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10110     

Critical heat flux of R22 and R142b mixtures flowing in a vertical tube

An experimental study on the critical heat flux (CHF) in forced convective boiling of R142b/R22 mixtures was conducted with an electrically heated vertical test tube with 17 mm inner diameter, in which the inner surface temperature was controlled and the heated length varied from 0.058 to 0.661 m. Experiments were carried out under the following conditions: constant pressures of 1.3 and 2.0 MPa, constant mass fluxes of 1000 and 2000 kg/(m²s), and constant outlet qualities of −0.2, 0.0, and 0.1. Whole boiling curves were obtained and the effects of heated length, local quality, and mole fraction on the CHF were investigated. The CHF of mixtures was higher than that of pure fluids and showed a maximum in a CHF versus mole fraction plot at a certain mole fraction. However, the maximum was less significant for the longer test section and the higher outlet quality condition. © 1998 Scripta Technica. Heat Trans Jpn. Res., 26(5): 292–305, 1997