Effect of Gas Introduction on Temperature Distribution for Tube Flow with Internal Heat Sources

An experimental study has been conducted to investigate the effect of gas introduction on the heat transfer characteristics for turbulent flow of a heat generating liquid in an adiabatic tube 20 mm in inside diameter. Heat generation within the fluid was brought about by passing an alternating current through the working fluid, which was an aqueous solution of sodium chloride mixed with air bubbles. The superficial liquid Reynolds number ranged 3,700–11,000. The quality was varied from 2.6×10^?5 to 3.3×l0^?3. Measurements were made of the temperature distributions in the fluid as well as on the tube wall. The experimental results were compared with theoretical analyses.

In bubbly flow; the introduction of air into liquid brought forth a flat temperature distribution due to a considerable increase of turbulence and a saddle-shaped void distribution, which had a maximum near the tube wall. In slug flow, however, the void distribution changed to a dome-shaped profile with a maximum at the tube center and the rate of heat generation was higher near the wall than in the center region, resulting in a steep temperature distribution.     

几何参数对含空气蒸汽冷凝影响的数值分析

含空气蒸汽冷凝是反应堆失水事故时安全壳内重要的热工水力现象。已有研究多关注气体压力、温度等热工参数对传热特性的影响,而对几何参数的影响及其作用原理分析较少。采用三维CFD数值模拟方法,基于扩散边界层冷凝机理模型研究了管径(4~60 mm)、管长(0.1~7 m)及倾角(0°~90°)对含空气蒸汽冷凝传热特性的影响。结果表明,管径、管长及倾角均对含空气蒸汽冷凝传热特性有显著影响。平均冷凝传热系数随管径的增大而减小;随管长的增长先减小后增大,3 m左右达到最小值;随倾角的增大而增大。局部冷凝传热系数沿管长方向先迅速减小后缓慢增大。倾斜布置时,迎流面产生明显传热强化,向两侧逐渐减弱,背流面存在一定的传热抑制。     

An investigation on heat transfer characteristics of different pressure steam-water in vertical upward tube

Within the range of pressure from 9 to 30 MPa, mass velocity from 600 to 1200 kg/(m² s), and heat flux at inner wall from 200 to 600 kW/m², experiments have been performed to investigate the heat transfer characteristics of steam-water two-phase flow in vertical upward tube. The outer diameter of the tube is 32 mm, and the wall thickness is 3 mm. Based on results, it was found that Dryout is the main mechanism of the heat transfer deterioration in the sub-critical pressure region. Near the critical pressure, when the heat transfer deterioration occurs, the steam quality of water is lower than that in the sub-critical pressure region, so that DNB is the main mechanism in this pressure region. At supercritical pressure, the heat transfer performance in circular channel is improved and enhanced. Heat transfer deterioration phenomenon is observed when the fluid bulk temperature approaches to the pseudo-critical value. Nusselt correlation of the forced-convection heat transfer in supercritical pressure region has been provided, which can be used to predict heat transfer coefficient of the vertical upward flow in tube.     

Investigation of forced convection heat transfer of supercritical pressure water in a vertically upward internally ribbed tube

In the present paper, the forced convection heat transfer characteristics of water in a vertically upward internally ribbed tube at supercritical pressures were investigated experimentally. The six-head internally ribbed tube is made of SA-213T12 steel with an outer diameter of 31.8 mm and a wall thickness of 6 mm and the mean inside diameter of the tube is measured to be 17.6 mm. The experimental parameters were as follows. The pressure at the inlet of the test section varied from 25.0 to 29.0 MPa, and the mass flux was from 800 to 1200 kg/(m² s), and the inside wall heat flux ranged from 260 to 660 kW/m². According to experimental data, the effects of heat flux and pressure on heat transfer of supercritical pressure water in the vertically upward internally ribbed tube were analyzed, and the characteristics and mechanisms of heat transfer enhancement, and also that of heat transfer deterioration, were also discussed in the so-called large specific heat region. The drastic changes in thermophysical properties near the pseudocritical points, especially the sudden rise in the specific heat of water at supercritical pressures, may result in the occurrence of the heat transfer enhancement, while the covering of the heat transfer surface by fluids lighter and hotter than the bulk fluid makes the heat transfer deteriorated eventually and explains how this lighter fluid layer forms. It was found that the heat transfer characteristics of water at supercritical pressures were greatly different from the single-phase convection heat transfer at subcritical pressures. There are three heat transfer modes of water at supercritical pressures: (1) normal heat transfer, (2) deteriorated heat transfer with low HTC but high wall temperatures in comparison to the normal heat transfer, and (3) enhanced heat transfer with high HTC and low wall temperatures in comparison to the normal heat transfer. It was also found that the heat transfer deterioration at supercritical pressures was similar to the DNB at subcritical pressures.     

Two-phase flow and boiling heat transfer in two vertical narrow annuli

Experimental study associated with two-phase flow and heat transfer during flow boiling in two vertical narrow annuli has been conducted. The parameters examined were: mass flux from 38.8 to 163.1 kg/m² s; heat flux from 4.9 to 50.7 kW/m² for inside tube and from 4.2 to 78.8 kW/m² for outside tube; equilibrium mass quality from 0.02 to 0.88; system pressure from 1.5 to 6.0 MPa. It was found that the boiling heat transfer was strongly influenced by heat flux, while the effect of mass velocity and mass quality were not very significant. This suggested that the boiling heat transfer was mainly via nucleate boiling. The data were used to develop a new correlation for boiling heat transfer in the narrow annuli. In the two-phase flow study, the comparison with the correlation of Chisholm [Chisholm, D., 1967. A theoretical basis for the Lockhart–Martinelli correlation for two-phase flow. Int. J. Heat Mass Transfer 10, 1767–1778] and Mishima and Hibiki [Mishima, K., Hibiki, T., 1996. Some characteristics of air–water two-phase flow in small diameter vertical tubes. Int. J. Multiphase Flow 22, 703–712] indicated that the existing correlations could not predict the two-phase multiplier in the narrow annuli well. Based on the experimental data, a new correlation was developed.     

Post-CHF two-phase flow with low wall-superheat

Heat transfer was measured to a two-phase flow in the post-CHF region under liquid-heated conditions and low wall-superheat. The boiling fluid was water at high pressure, 7.0–15.3 MPa, and mass fluxes in the range of 720–3200 kg/m²s. Experiments were performed in a vertical tube with a 10 mm inside diameter and a 13.1 m heated length. In considering the effects of thermodynamic non-equilibrium and direct drop-wall heat transfer at the low wall-superheats of this investigation (25–100°C), 13 correlations, models and analysis were compared to the data. A review of these formulations is presented including development bases and approaches. The effects of both non-equilibrium and drop-wall heat transfer were evaluated, and recommendations are presented for post-CHF heat transfer predictions at low wall-superheat.     

竖直圆管内跨临界压力区水对流传热数值模拟研究

应用CFD方法对跨临界压力区竖直圆管内水的对流传热进行了数值模拟研究。通过与实验结果比较,分析了浮升力因素的影响机理。研究结果表明,采用浮升力修正的k-ε两方程湍流模型可准确预测跨临界压力区正常对流传热现象。当流体温度达到拟临界点,尽管该模型可预测传热恶化现象,但与实验数据偏差较大,在水热物性及数值模型等方面有待进行更深入研究。     

An investigation of transient heat transfer in the region of flow boiling dryout with freon-12 in a heated tube

Power transient experiments using vertical round tube test sections have provided information on the heat transfer characteristics associated with a change from pre-dryout to post-dryout flow boiling conditions. The test sections were heated by passing electric current along the tube wall, and cooled internally by Freon-12 flowing upwards through the tube.Seven steel tubes of various sizes were used (internal diameters in the range 7.1–26.6 mm, wall thicknesses 0.9–2.0 mm, and lengths of 0.9–3.9 m). Data were obtained for coolant mass fluxes in the range 150–3270 kg m⁻² s⁻¹, at a nominal pressure of 1.0 MPa, with exit qualities in the range 0.3–1.0. The transients were initiated by small increases in power input to the test section. Heat transfer characteristics were determined by calculating wall temperature responses as functions of time and comparing these with the corresponding temperature traces recorded in the experiments.In relation to the temperature responses of the tube wall under these transient conditions, the results show that transition boiling has only a slight effect and that film boiling has very significant effects.     

Mixed convection heat transfer to carbon dioxide flowing upward and downward in a vertical tube and an annular channel

This paper addresses three main subjects in supercritical heat transfer: (1) difference in thermal characteristics between upward and downward flows; (2) effect of simulating flow channel shape; (3) evaluation of the existing supercritical heat transfer correlations. To achieve the objectives, a series of experiments was carried out with CO₂ flowing upward and downward in a circular tube with an inner diameter of 4.57 mm and an annular channel created between a tube with an inner diameter of 10 mm and a heater rod with an outer diameter of 8 mm. The working fluid, CO₂, has been regarded as an appropriate modeling fluid for water, primarily because of their similarity in property variations against reduced temperatures. The mass flux ranged from 400 to 1200 kg/m² s. The heat flux was varied between 30 and 140 kW/m² so that the pseudo-critical point was located in the middle of the heated section at a given mass flux. The measurements were made at a pressure of 8.12 MPa, which corresponds to 110% of the critical pressure of CO₂. The difference between the upward and downward flows was observed clearly. The heat transfer deterioration was observed in the downward flow through an annular subchannel over the region beyond the critical point. Several well-known correlations were evaluated against the experimental data, and new correlations were suggested for both a tube and an annular channel.     

Twisted-tape-induced swirl flow heat transfer and pressure drop in a short circular tube under velocities controlled

The twisted-tape-induced swirl flow heat transfer due to exponentially increasing heat inputs with various exponential periods (Q = Q₀ exp(t/τ), τ = 7, 14 and 23 s) and the twisted-tape-induced pressure drop were systematically measured with mass velocities, G, ranging from 4022 to 15,140 kg/m² s by an experimental water loop flow. Measurements were made on a 59.2 mm effective length which was spot-welded two potential taps on the outer surface of a 6 mm inner diameter, a 69.6 mm heated length and a 0.4 mm thickness of platinum circular test tube. The twisted tapes with twist ratios, y [=H/d = (pitch of 180° rotation)/d], of 2.39, 3.39 and 4.45 were used in this work. The relation between the swirl velocity and the pump input frequency and that between the fanning friction factor and Reynolds number (Re_d = 2.04 × 10⁴ to 9.96 × 10⁴) were clarified. The twisted-tape-induced swirl flow heat transfers with y = 2.39, 3.39 and 4.45 were compared with the values calculated by our correlation of the turbulent heat transfer for the empty tube and other worker's one for the circular tube with the twisted-tape insert. The influence of y and Reynolds numbers based on swirl velocity, Re_sw, on the twisted-tape-induced swirl flow heat transfer was investigated into details and the widely and precisely predictable correlation of the twisted-tape-induced swirl flow heat transfer was derived based on the experimental data. The correlation can describe for the twisted-tape-induced swirl flow heat transfer for the wide ranges of twist ratios (y = 2.39-4.45), mass velocities (G = 4022-15140 kg/m² s) and Reynolds numbers based on swirl velocity (Re_sw = 2.88 × 10⁴ to 1.22 × 10⁵) within −10 to +30% difference.     

Investigations on post-dryout heat transfer in bilaterally heated annular channels

Post-dryout heat transfer in bilaterally heated vertical narrow annular channels with 1.0, 1.5 and 2.0 mm gap size has been experimentally investigated with deionized water under the condition of pressure ranging from 1.38 to 5.9 MPa and low mass flow rate from 42.9 to 150.2 kg/m²s. The experimental data was compared with well known empirical correlations including Groeneveld, Mattson, etc., and none of them gave an ideal prediction. Theoretical investigations were also carried out on post-dryout heat transfer in annular channels. Based on analysis of heat exchange processes arising among the droplets, the vapor and two tube walls of annular channel, a non-equilibrium mechanistic heat transfer model was developed. Comparison indicated that the present model prediction showed a good agreement with our experimental data. Theoretical calculation result showed that the forced convective heat transfer between the heated wall and vapor dominate the overall heat transfer. The heat transfer caused by the droplets direct contact to the wall and the interfacial convection/evaporation of droplets in superheated vapors also had an indispensable contribution. The radiation heat transfer would be neglected because of its small contribution (less than 0.11%) to the total heat transfer.     

Experimental investigations on single-phase heat transfer enhancement with longitudinal vortices in narrow rectangular channel

Four pairs of rectangular block as longitudinal vortex generators (LVG) were mounted periodically in a narrow rectangular channel to investigate fluid flow and convective heat transfer respectively in the narrow rectangular channel with LVG and without LVG. Both the channels have the same narrow gap (d) = 3 mm, the same hydraulic diameter (D_h) = 5.58 mm and the same length to diameter ratio (L/D_h) = 80.65. The experiments were performed with the channels oriented uprightly and uniform heat fluxes applied at the one side of the heating plate and single-phase water was used as test fluid. The parameters that were varied during the experiments included the mass flow rate, inlet liquid temperature, system pressure, and heat flux.In each of the experiments conducted, the temperature of both the liquid and the wall was measured at various locations along the flow direction. Based on the measured temperatures and the overall energy balance across the test section, the heat transfer coefficients for single-phase forced convection have been calculated. At the same time, in these experiments, the single-phase pressure drop across the channels was also measured. The correlations have been developed for mean Nusselt numbers and friction factors. Additionally, the visual experiments of infrared thermo-image recording the temperature on the outer wall of the heating plate have been conducted for validating the effects of LV.In these experimental investigations, both laminar regime and turbulent regime were under the thermo-hydraulic developing conditions, laminar-to-turbulent transition occurred in advance with the help of LV when Reynolds numbers vary between 310 and 4220. In laminar regime, LV causes heat transfer enhancement of about 100.9% and flow resistance increase of only 11.4%. And in turbulent regime, LV causes heat transfer enhancement of above 87.1% and flow resistance increase of 100.3%. As a result, LV can obviously enhance heat transfer of single-phase water, and increase flow resistance mildly.     

An experimental investigation of a passive cooling unit for nuclear plant containment

A set of condensation experiments in the presence of noncondensables (e.g. air, helium) was conducted to evaluate the heat removal capacity of a passive cooling unit in a post-accident containment. Condensation heat transfer coefficients on a vertically mounted smooth tube have been obtained for total pressure ranging from 2.48×10⁵ Pa(abs) to 4.55×10⁵ Pa(abs) and air mass fraction ranging from 0.30 to 0.65. An empirical correlation for heat transfer coefficient (h), has been developed in terms of a parameter group made up of steam mole fraction (Xs), total pressure (P_t), temperature difference between bulk gas and wall surface (dT). This correlation covers all data points within 20%. All data points are also in good agreement with the prediction of the diffusion layer model (DLM) with suction and are approximately 2.2 times the Uchida heat transfer correlation. Experiments with an axial shroud around the test tube to model the restriction on radial flow experienced within a tube bundle demonstrated a reduction of the heat transfer coefficient by a factor of about 0.6. The effect of helium (simulating hydrogen) on the heat transfer coefficient was investigated for helium mole fraction in noncondensable gases (X_He/X_nc) at 15, 30 and 60%. It was found that the condensation heat transfer coefficients are generally lower when introducing helium into noncondensable gas. The difference is within 20% of air-only cases when X_He/X_nc is less than 30% and total pressure is less than 4.55×10⁵ Pa(abs). A gas stratification phenomenon was clearly observed for helium mole fraction in excess of 60%.     

Film boiling heat transfer from a vertical cylinder in forced flow of liquids under saturated and subcooled conditions at pressures

Forced convection film boiling heat transfer on a vertical 3-mm diameter and 180-mm length platinum test cylinder located in the center of the 40-mm inner diameter test channel was measured. Saturated water, and saturated and subcooled R113 were used as the test liquids that flowed upward along the cylinder in the test channel. Flow velocities ranged from 0 to 3 m s⁻¹, pressures from 102 to 490 kPa, and liquid subcoolings for R113 from 0 to 60 K. The heat transfer coefficients for a certain pressure and liquid subcooling are almost independent of flow velocity and of a vertical position on the cylinder for the flow velocities lower than ≈1 m s⁻¹ (the first range), and they become higher for the velocities higher than ≈1 m s⁻¹ (the second range). Slight dependence on a vertical position being nearly proportional to z^−1/4, where z is the height from the leading edge of the test cylinder, exists for the flow velocities in the second range. The heat transfer coefficients at each velocity in the first and second ranges are higher for higher pressure and liquid subcooling. Correlation for the forced convection film boiling heat transfer with radiation contribution on a vertical cylinder was derived by modifying an approximate analytical solution for a two-phase laminar boundary layer model to agree better with the experimental data. It was confirmed that the experimental data of film boiling heat transfer coefficients in water and R113 were described by the correlation within ±20% difference.     

Experimental Study on Heat Removal Characteristics for Water Wall Type Passive Containment Cooling System

To evaluate the heat removal capability of a water wall type cooling system, which is one passive containment cooling system (PCCS), the thermal hydraulic behavior in the suppression pool (S/P) and the outer pool (O/P, flat plate water wall) have been investigated experimentally. The following results were obtained. (1) A thermal stratification boundary, which separates the pools into the upper high temperature and lower low temperature regions, was formed just below the vent tube outlet. (2) Convection heat transfer characteristics in the S/P and O/P along the primary containment vessel (PCV) wall had no significant differences and were those of natural convection. Correlation of the natural convection heat transfer up to the Ra number of 2×10¹⁴ was obtained. (3) Vertical variations of local condensation heat transfer coefficients under a noncondensable gas presence were within ±10% of the average value for the 4.7 m heat transfer length. An experimental correlation for the average condensation heat transfer coefficients was obtained as a function of steam and noncondensable gas mass ratio. (4) An analytical model to evaluate the system performance of the water wall type PCCS was verified. (5) A baffle plate concept to mitigate thermal stratification at the vent outlet and to enlarge the high temperature region in the S/P was considered as a means to improve heat release capability. Thermal hydraulics with a baffle plate were examined, and effectiveness of the baffle plate to improve the heat release capability was confirmed.     

Heat Transfer in a Fluid with Internal Heat Generation Flowing through a Vertical Tube

This paper deals with heat transfer in a fluid, with uniformly distributed internal heat source, flowing upwards through a vertical tube. Measurements were made of the temperature distribution in both laminar and turbulent flow, and both with and without heat transfer at wall. Heat generation within the fluid was brought about by passing an electrical current through the working fluid, which was an aqueous solution of sodium chloride. The experimental results were compared with analytical calculations.

Free convection, which occurs and is superimposed on the movement by forced convection, flattens the fluid temperature distribution in laminar flow through thermally insulated vertical tube. In turbulent flow with heat transfer to wall, the temperature distribution near the wall is affected considerably by the outgoing heat flux.     

Heat flux capabilities of first-wall tube arrays for an experimental fusion reactor

A preliminary design study has been made of some of the thermomechanical problems of water and helium cooling for the first wall of a near-term experimental fusion reactor. The first wall is envisioned as an array of 316 stainless steel tubes between the plasma and the blanket modules to intercept a heat flux from the plasma estimated to be between 0.25 and 1.0 MW/m². Evaluations have been made of the maximum allowable heat fluxes for constraints imposed on the tube wall temperature, the cyclic stresses, the quasi-steady stresses and energy recovery from the coolant. For tubes with 2 meter long heated sections, 10 mm inside diameter and 1 mm wall thickness, water cooling was found to be more than adequate for plasma heat fluxes over 1 MW/m² with a fatigue life of 10⁶ cycles; for a 2 mm wall thickness, at least 0.7 MW/m² can be handled for the same fatigue life. Helium-cooled tubes can also handle heat fluxes up to about 1 MW/m² with a 1 mm tube wall thickness and over 0.5 MW/m² with a 2 mm tube wall thickness, but the required pumping powers tend to be high. The problems of plasma disruptions and erosion by energetic plasma ions are also discussed briefly.     

Prediction of Liquid Film Dryout in Two-Phase Annular-Mist Flow in a Uniformly Heated Narrow Tube Development of Analytical Method under BWR Conditions

A method was developed based on the conservation lows to predict critical heat flux (CHF) causing liquid film dryout in two-phase annular-mist flow in a uniformly heated narrow tube under BWR conditions. The applicable range of the method is within the pressure of 3–9 MPa, mass flux of 500–2,000 kg/m²·s, heat flux of 0.33–2.0 MW/m² and boiling length-to-tube diameter ratio of 200–800.

The two-phase annular-mist flow was modeled with the three-fluid streams with liquid film, entrained droplets and gas flow. Governing equations of the method are mass continuity and energy conservation on the three-fluid streams. Constitutive equations on the mass transfer which consist of the entrainment fraction at equilibrium and the mass transfer coefficient were newly proposed in this study.

Confirmation of the present method were performed in comparison with the available film flow measurements and various CHF data from experiments in uniformly heated narrow tubes under high pressure steam- water conditions. In the heat flux range (q“<2MW/m²) practical for a BWR, agreement of the present method with CHF data was obtained as, (Averaged ratio)±(Standard deviation)=0.984±0.077, which was shown to be the same or better agreement than the widely-used CHF correlations.     

Experimental investigation of heat transfer for supercritical pressure water flowing in vertical annular channels

An experiment has recently been completed at Xi’an Jiaotong University (XJTU) to obtain wall-temperature measurements at supercritical pressures with upward flow of water inside vertical annuli. Two annular test sections were constructed with annular gaps of 4 and 6 mm, respectively, and an internal heater of 8 mm outer diameter. Experimental-parameter ranges covered pressures of 23-28 MPa, mass fluxes of 350-1000 kg/m²/s, heat fluxes of 200-1000 kW/m², and bulk inlet temperatures up to 400 °C. Depending on the flow conditions and heat fluxes, two distinctive heat transfer regimes, referring to as the normal heat transfer and deteriorated heat transfer, have been observed. At similar flow conditions, the heat transfer coefficients for the 6 mm gap annular channel are larger than those for the 4 mm gap annular channel. A strong effect of spiral spacer on heat transfer has been observed with a drastic reduction in wall temperature at locations downstream of the device in the annuli. Two tube-data-based correlations have been assessed against the experimental heat transfer results. The Jackson correlation agrees with the experimental trends and overpredicts slightly the heat transfer coefficients. The Dittus-Boelter correlation is applicable only for the normal heat transfer region but not for the deteriorated heat transfer region.     

传热管异径布管方式传热系数的数值分析

针对管壳式换热器,提出一种新的异径管布管方式.运用CFD软件分析了该结构在流量降低时对管侧传热系数的数值影响;得出随着流量的变化,大小管道内流量速度分配变化率有明显不同,且变化率并与管长有关,并在一定的流速范围内,小管抵抗传热系数降低的趋势较为显著.