Convective heat transfer to water near the critical region in a horizontal square duct

Numerical analysis has been carried out to investigate forced convective heat transfer to water near the critical region in a horizontal square duct. Near the critical point convective heat transfer in the duct is strongly coupled with large variation of thermophysical properties such as density and specific heat. Buoyancy force parameter has also severe variation with fluid temperature and pressure in the duct. There is flow acceleration along the horizontal duct resulted from fluid density decrease due to the heat transfer from the wall. Local heat transfer coefficient has large variation along the inner surface of the duct section and it depends on pressure. Nusselt number on the center of the bottom surface also has a peak where bulk fluid temperature is higher than the pseudocritical temperature and the peak decreases with the increase of pressure. Flow characteristics of velocity, temperature, and local heat transfer coefficient with water properties are presented and analyzed. Nusselt number distributions are also compared with other correlations for various pressures in the duct.     

Numerical study of convective heat transfer to supercritical water in rectangular ducts

Numerical investigation has been performed to analyze forced convective heat transfer to supercritical water in horizontal rectangular ducts. Convective heat transfer near the critical region in the rectangular ducts is strongly influenced by large variations of thermodynamic and transport properties of supercritical fluid with gravity force, especially close to pseudocritical temperature. Fluid flow and heat transfer characteristics such as velocity, temperature, and local heat transfer coefficient with water properties distribution in the ducts are presented. Flow accelerates along the horizontal ducts because of decreased water density from heat transfer at the duct walls. Center of large flow recirculation in the duct section locates near the middle of vertical surface and additional secondary recirculation in clockwise direction appears with the increase of duct height. Local wall temperature severely varies along the inner surface of the duct section and its variation depends on aspect ratio of the duct. The heat transfer coefficient distributions along the ducts for various aspect ratios are compared with the proximity effect to the critical pressure.     

Investigation on the characteristics and mechanisms of unusual heat transfer of supercritical pressure water in vertically-upward tubes

The heat transfer characteristics of supercritical pressure water in a vertically-upward optimized internally-ribbed tube was investigated experimentally to study the mechanisms of unusual heat transfer of supercritical pressure water in the so-called large specific heat region. The experimental parameters were as follows. The pressure at the inlet of the test section ranged from 22.5 to 29.0 MPa, and the mass flux of the fluid was from 650 to 1200 kg/m² s, and the heat flux on the inside wall of the tube varied from 200 to 660 kW/m². According to experimental data, the characteristics of heat transfer enhancement and also the heat transfer deterioration of supercritical pressure water in the large specific heat region was analyzed and based on the comparison and analysis of the current major theories that were used to explain the reasons for unusual heat transfer to occur, the mechanisms of heat transfer enhancement and deterioration were discussed, respectively. The enhanced heat transfer was characterized by the gently changing wall temperature, the small temperature difference between the inside-tube-wall and the bulk fluid and the high heat transfer coefficient in comparison to the normal heat transfer. The deteriorated heat transfer could be characterized by the sharply increasing wall temperature, the large temperature difference and a sudden decrease in heat transfer coefficient in comparison to the normal heat transfer. The heat transfer enhancement of the supercritical pressure water in the large specific heat region was suggested to be a result of combined effect caused by the rapid variations of thermophysical properties of the supercritical pressure water in the large specific heat region, and the same was true of the heat transfer deterioration. The drastic changes in thermophysical properties near the pseudocritical points, especially the sudden rise in the specific heat of water at supercritical pressures, might 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 made the heat transfer deteriorated eventually and explained how this lighter fluid layer formed.     

An Investigation on Heat Transfer to Supercritical Water in Inclined Upward Smooth Tubes

Within the range of pressures from 23 to 30 MPa, mass velocities from 600 to 1200 kg/(m²s), and heat fluxes from 200 to 600 kW/m², experiments have been performed for an investigation on heat transfer to supercritical water in inclined upward smooth tubes with an inner diameter of 26 mm and an inclined angle of 20° from the horizon. The results indicated that heat transfer characteristics of supercritical water are not uniform along the circumference of the inclined tube. An increase in the mass velocity of the working fluid can decrease and even eliminate the non-uniformity. Properties of supercritical fluid acutely vary with the temperature near the pseudocritical point. While the ratio of the mass velocity to the heat flux exceeded 2.16 kg/(kWs), heat transfer enhancement occurred near the pseudocritical point; conversely, heat transfer deterioration occurred while the ratio of the mass velocity to the heat flux was lower than 2.16 kg/(kWs). As the pressure increased far from the critical pressure, the amount of deterioration decreased. Correlations of heat transfer coefficients of the forced-convection heat transfer on the top and bottom of the tube have been provided, and can be used to predict heat transfer coefficient of spirally water wall in supercritical boilers.     

Numerical Investigation of Jet Impingement Cooling of a Flat Plate with Carbon Dioxide at Supercritical Pressures

Confined round jet impingement cooling of a flat plate at constant heat flux with carbon dioxide at supercritical pressures was investigated numerically. The pressure ranged from 7.8 to 10.0 MPa, which is greater than the critical pressure of carbon dioxide, 7.38 MPa. The inlet temperature varied from 270 to 320 K and the heat flux ranged from 0.6 to 1.6 MW/m². The shear-stress transport turbulence model was used and the numerical model was validated by comparison with experimental results for jet impingement heating with hot water at supercritical pressures. Radial conduction in the jet impingement plate was also considered. The sharp variations of the thermal-physical properties of the fluid near the pseudocritical point significantly influence heat transfer on the target wall. For a given heat flux, the high specific heat near the wall for the proper inlet temperature and pressure maximizes the average heat transfer coefficient. For a given inlet temperature, the heat transfer coefficient remains almost unchanged with increasing surface heat flux at first and then decreases rapidly as the heat flux becomes higher due to the combined effects of the thinner high specific heat layer and the smaller thermal conductivity at higher temperature.     

Forced convective heat transfer to supercritical water flowing in tubes

Experimental investigations were made of heat transfer to supercritical water flowing in a horizontal tube and vertical tubes. A comprehensive set of data was obtained for pressures from 226 to 294 bar, bulk temperatures from 230 to 540°C, heat fluxes from 116 to 930 kW/m² and mass velocities from 310 to 1830 kg/m²s. Because the physical properties of supercritical fluids change rapidly with temperature in the pseudocritical region, the heat transfer coefficients show unusual behavior depending upon the heat flux. At low or modetate heat fluxes relatively to the flow rate, a satisfactory correlation was obtained, which predicts reasonably well the enhanced heat transfer coefficients near the pseudocritical point. The several characteristics of the deterioration in heat transfer which occurs at high heat fluxes were clarified, and the limit heat flux for the occurrence of the deterioration was determined in connection with the flow rate.     

Heat Transfer Analysis of a Microspherical Particle in the Slip Flow Regime by Considering Variable Properties

In order to investigate how far the temperature-dependent fluid properties and characteristic length influence the drag coefficient and the heat flux, a three-dimensional simulation study for a slip flow around an unconfined microspherical particle has been performed. Gas properties such as density, viscosity, conductivity, and mean free path were assumed to vary with temperature. Slip velocity and temperature jump at the gas particle interface were both treated numerically by imposition of the slip boundary conditions. The effects of variable gas properties and Knudsen number on momentum and heat transfer were also taken into account. It was concluded that for microflows with high heat transfer rates, the constant fluid properties approximation is very crude. In addition, the slip velocity and temperature jump affect the heat transfer in opposite ways: a large slip on the wall increases the convection along the surface, whereas a large temperature jump decreases the heat transfer by reducing the temperature gradient at the wall. Therefore, neglecting temperature jump will result in the overestimation of the heat transfer coefficient.     

物性参数对环形空间流动和传热影响的模拟研究

利用有限容积法,建立了环形空间内单相流体竖直向上流动过程中流动和传热的稳态模型。模型将环形空间内管设置为具有固定生热速率的发热体;流体与内管壁之间设置流动和传热边界层,以更精确的描述壁面位置流体与固体之间动量和热量的耦合传递过程。通过与常物性模型的对比,流体密度、导热系数和黏度随温度变化的变物性模型,在传热能力上具有一定的减少,流体与固体传热面之间的界面剪切力稍有下降。通过比较常物性模型和变物性模型的Re和Ri,结果表明,随着流体强制循环速度的加大,流体物性变化对流动和传热过程的影响逐渐减小。     

ENCLOSED BUOYANT CONVECTION OF A VARIABLE-VISCOSITY FLUID UNDER TIME-PERIODIC THERMAL FORCING

Finite-volume numerical solutions are obtained for buoyant convection of a fluid with temperature-dependent viscosity in an enclosed space. At one vertical wall the temperature is constant, and at the other vertical wall the temperature is time-periodic. Solutions to the governing Navier-Stokes equations are acquired for a fixed Rayleigh number and over wide ranges of viscosity contrast, which measures the ratio of viscosities at the cold side wall and hot side wall. The effects of variable viscosity on the time-mean value as well as the amplitude of fluctuation of instantaneous heat transfer rate are delineated. The extensive results reveal the existence of resonance and show that resonance becomes more distinctive for large viscosity contrast in the case of the hot-wall temperature oscillation. As the viscosity contrast increases, the upward convective motion is invigorated during the relative heating phase due to the lowered viscosity in the thermal boundary layer near the hot vertical side wall. This is also reflected in the augmentation of the cycle-averaged heat transfer rate. When the temperature oscillation is imposed on the cold wall, the flow is less sensitive to the viscosity variation. Physical interpretations of the overall flow and heat transfer are offered.     

Experimental and numerical study of convection heat transfer of CO2 at super-critical pressures during cooling in small vertical tube

Convection heat transfer of CO₂ at super-critical pressures during cooling in a vertical small tube with inner diameter of 2.00 mm was investigated experimentally and numerically. The local heat transfer coefficients were determined through a combination of experimental measurements and numerical simulations. This study investigated the effects of pressure, cooling water mass flow rate, CO₂ mass flow rate, CO₂ inlet temperature, flow direction, properties variation and buoyancy on convection heat transfer in small tube. The results show that the local heat transfer coefficients vary significantly along the tube when the CO₂ bulk temperatures are in the near-critical region. The increase of specific heat and turbulence kinetic energy due to the density variation leads to the increase of the local heat transfer coefficients for upward flow. The buoyancy effect induced by density variation leads to a different variation trend of the local heat transfer coefficients along the tube for upward and downward flows. The numerical simulations were conducted using several k–ε turbulence models including the RNG k–ε model with a two-layer near wall treatment and three low-Reynolds number eddy viscosity turbulence models. The simulations using the low-Reynolds number k–ε model due to Yang–Shih has been found to be able to reproduce the general features exhibited in the experiments, although with a relatively large overestimation of measured wall temperatures. A better understanding of the mechanism of properties variation and buoyancy effects on convection heat transfer of CO₂ at super-critical pressures in a vertical small tube during cooling has been developed based on the information generated by the simulation on the detailed flow and turbulence fields.     

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]     

Thermodynamic and thermophysical effects enabling high-forced convection heat transfer coefficients in supercritical fluids

Abstract

The strong variation of thermophysical properties of working fluids operating in the vicinity of the critical point makes this thermodynamic domain attractive to several energy applications. Therefore, herein a two-dimensional numerical method is used to investigate the effect of local thermophysical property variations on the local and overall thermal performance of internal convective heat transfer in a pipe in 324 operational conditions. Focusing on carbon dioxide and water as heat transfer fluids, an association of the variation of key thermophysical properties with thermohydraulic performance metrics is proposed, namely: (a) the local and (b) mean convective heat transfer coefficient and (c) the maximal temperature obtained at the tube wall. It is shown that there is an optimal combination of parameters such as mass flow rate, operating pressure, wall heat flux, and inlet temperature that, when properly selected, allow for a minimal maximal wall temperature. As expected, optimality is strongly associated with the Widom—or pseudo critical—line that extends from the critical point. Interestingly, however, contrary to what is observed in constant-property fluids, high heat transfer coefficient or minimal maximum temperature lead to different sets of optimal operating conditions. This difference is explained by how thermophysical properties vary locally along heat exchangers, which significantly affects overall heat transfer.     

Numerical investigation on conjugate heat transfer to supercritical CO2 in membrane helical coiled tube heat exchangers

ABSTRACT

Conjugate heat transfer to supercritical CO₂ in membrane helical coiled tube heat exchangers has been numerically investigated in the present study. The purpose is to provide detailed information on the conjugate heat transfer behavior for a better understanding of the abnormal heat transfer mechanism of supercritical fluid. It could be concluded that the supercritical fluid mass flux and vertical/horizontal placement would significantly affect the abnormal heat transfer phenomenon in the tube side. The flow field of supercritical fluid is affected by both the buoyancy and centrifugal force in the conjugate heat transfer process. The local wall temperature and heat transfer coefficient in the tube side would rise and fall periodically for the horizontal heat exchanger, but this phenomenon will gradually disappear with the increase of the mass flow rate or fluid temperature in the tube side. The dual effects of buoyancy force and centrifugal force lead to the deflection of the second flow direction for the vertical placement, which further results in the heat transfer deterioration region on the top-generatrix wall for the downward flow being larger than that for the upward flow.     

垂直内螺纹管内超临界水的二次流特性

运用计算流体力学方法,采用SSG雷诺应力模型对高温条件下垂直内螺纹管中超临界水的二次流特性进行了研究。研究发现:内螺纹的导流作用在垂直于主流的方向产生了很强的二次流场,主流焓的变化对二次流场的基本结构影响很小。内螺纹管周向和径向上的传热系数分布不均,超临界水在螺纹顶部区域的传热效果远好于螺纹底部。在螺纹顶部表面形成的单个旋涡产生一个压力相对较低的区域,传热增强。在大比热区,由于流体热物性急剧变化,传热的不均性更加显著。螺纹底部壁面是内螺纹管周向传热的薄弱位置,其内部结构的优化应重点集中在该区域。     

圆管内对流换热过程中潜热型功能流体流动阻力特性的实验研究

实验研究了由正十四烷和尿素甲醛树脂制成的相变微胶囊和水混合制成的潜热型功能流体在流过恒热流圆管进行对流换热时的流动阻力特性,获得了压降随流速的变化关系、摩擦阻力系数和表观黏度随R e的变化关系。并在同样条件下用单相水进行了对比实验。相变微胶囊的加入导致流体流动阻力较单相流体有显著增大。管路中扰动件导致单相流体的流动阻力特性在低R e条件下呈湍流特征;功能流体则呈不同规律,扰动仅导致流动阻力进一步增大,而流动阻力特性仍呈层流特征。     

Entropy generation and pumping power in a turbulent fluid flow through a smooth pipe subjected to constant heat flux

In a heat exchange process, heat transfer and pumping power requirements are the two main considerations. Efforts made to increase heat transfer in a fluid flow usually cause increase in the pumping power requirement. In an effort to avoid inefficient utilization of energy through excessive entropy generation, a thermodynamic analysis of turbulent fluid flow through a smooth duct subjected to constant heat flux has been made in this study. The temperature dependence of the viscosity was taken into consideration in determining the heat transfer coefficient and friction factor. It was shown that the viscosity variation has a considerable effect on both the entropy generation and the pumping power. Pumping power to heat transfer ratio and the entropy generation per unit heat transfer can become very large especially for low heat flux conditions.     

循环流化床锅炉膜式水冷壁管与鳍片上的温度分布

研究了循环流化床锅炉膜式水冷壁管的传热，并通过采用二维传热分析方法，讨论了带有竖直鳍片和横向鳍片的水冷壁管上温度与热流分布。探讨了炉膛侧传热系数、水冷壁管水侧传热系数、水温、床温、水冷壁管材的导热率以及竖直鳍片部最高，然后逐渐下降，但在横向鳍处理的根部又会上升。为了验证传热分析的真实性，在1台6MWth循环流化床锅炉膜式水冷壁管的横裁面内安置了0.8mm的热电偶，测量子水管横截面上的一些点的温度。实际测量值符合得相当好。     

Effect of dynamic load on heat transfer characteristic of a two‐phase pipe boiling flow

An experimental investigation was performed to obtain the flow and heat transfer characteristics of a single‐phase water flow and a two‐phase pipe boiling water flow under dynamic load in the present work. By analyzing the fluid resistance, effective heat, flow pattern, and heat transfer coefficient of the experimental data, the effects of dynamic load on the flow and heat transfer characteristics of single‐phase water and two‐phase boiling water flow were investigated. The results show that the dynamic load significantly influences the flow characteristic and boiling heat transfer of the two‐phase pipe flow. It will enhance the fluid resistance and heat dissipation toward the ambient environment, and reduce the heat transferred to the two‐phase fluid. The impact mixing flow caused by the dynamic load breaks the uniform and varying principle of the wall temperatures. As a result of that, the greater the dynamic load, the lower the wall inner bottom temperature and the higher the wall inner top temperature in a certain extent. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20378     

超临界压力下航空煤油在竖直管内的传热研究

对竖直上升管内超临界压力下航空煤油的传热特性进行了实验研究。分析了不同质量流量、热流密度、压力和进口温度对超临界压力下航空煤油传热特性的影响。实验结果表明,提高质量流量或进口温度均使煤油传热效果变好。而热流密度对流体传热的影响主要在于改变了流体和壁面温度,热流密度越大,传热系数越高。压力对煤油传热影响不大,一般情况下,提高压力会恶化传热。超临界状态下,煤油物性变化很大,因此对煤油的传输和热力学性质的准确计算是研究超临界压力下传热现象的关键。利用拓展的对比态法来计算煤油的密度和传输特性,如黏度、热导率等。给出了煤油在超临界压力下的传热关联式,其计算值和实验值吻合良好。     

Numerical simulation and experimental validation of a helical double-pipe vertical condenser

A predictive model is developed to describe heat transfer and fluid dynamic behavior of a helical double-pipe vertical condenser used in an absorption heat transformer integrated to a water purification process. The condenser uses water as working fluid connected in countercurrent. Heat transfer by conduction in the internal tube wall is considered; in addition the change of phase is carried out into the internal tube. The dynamic model considers equations of continuity, momentum and energy in each flow. The discretized governing equations are coupled using an implicit step by step method. Comparison of the numerical simulation over range of experimental data presented in the heat device is applied to validate the model developed. The model is also evaluated of form dynamic to determine the principal operation variables that affect the condenser with the main objective to optimize and control the system. A variation of mass flow rate in the internal pipe induces important changes on the heat flux that the pressure and temperature.