Evaluation of the Heat Transfer Correlations for Supercritical Pressure Water in Vertical Tubes

A large number of studies have been carried out on the flow and heat transfer of supercritical pressure fluids in the past decades. However, there are still some uncertainties and deficiencies in the accurate prediction for supercritical fluid heat transfer coefficient due to the large and fast variations of fluids properties in the so-called pseudo-critical region. In this paper, 15 correlations were selected from the literature and were compared with each other to verify their capability in predicting heat transfer coefficient of supercritical pressure water in vertical tubes. Based on the comparison between the calculation results of the existing heat transfer correlations and the experimental data obtained from the open literature, it was found that the Swenson et al. correlation and the Hu correlation can reasonably predict the heat transfer coefficient of supercritical water in the pseudo-critical region. After evaluating these correlations, the authors conducted polynomial fitting for the collected experimental data and got a new correlation for heat transfer coefficient of water at supercritical pressures. The new correlation can fit well with the experimental data even in the neighborhood of pseudo-critical temperature.     

Effect of the Chevron Angle on Cooling Heat Transfer Characteristics of Supercritical Pressure Fluids in Plate Heat Exchangers

ABSTRACT

For the development of industrial heat pump systems supplying a high-temperature heat source over 130°C, the authors have studied on cooling heat transfer of supercritical pressure fluids flowing in chevron-type plate heat exchangers (PHEs). In this study, to examine the effect of chevron angle on cooling heat transfer of supercritical pressure refrigerants, experiments were conducted for HFC134a and HFO1234ze(E) flowing in the PHEs with the chevron angles from 30° to 65°. In the experiments, cooling heat transfer coefficients were obtained in the wide range of bulk fluid enthalpy from vapor-like high temperature to liquid-like low temperature, changing the pressure in the reduced pressure range from 1.01 to 1.2 at the mass flow rates of 7 and 11 kg/min. Especially for the enthalpy region of the pseudo critical point and its vicinity in which good heat transfer appeared, the effect of chevron angle on heat transfer of supercritical pressure fluids was clarified based on the measurements. Furthermore, the effect of chevron angle was examined for the wide angle range from 0° to 90° with estimating the heat transfer coefficient for the angles 0° and 90° from appropriate correlations. Besides, the present data were compared with some conventional heat transfer correlations.     

Effect of Serpentine Grooves on Heat Transfer Characteristics of Microchannel Heat Sink with Different Nanofluids

An experimental and numerical investigation of the thermal performance of three different nanofluids ethylene glycol‐based CuO, water‐based CuO, and Al₂O₃ is done in a serpentine‐shaped micorchannel heat sink. The microchannels considered ranged from 810 μm to 890 μm in hydraulic diameter and were made of copper material. The experiments were conducted with the Reynolds number ranging from approximately 100 to 1300. The forced convective heat transfer coefficient of nanofluids shows that there is an improved heat transfer rate compared to base fluids water and ethylene glycol. The experimental results also confirm that there is an earlier transition from laminar to turbulent flow in microchannels. The results prove that as the hydraulic diameter decreases there is increased pressure drop and the heat transfer coefficient increases for both the base fluids and nanofluids. The flow characteristics are discussed based on the pressure drop. While investigating the heat transfer coefficient of the three different nanofluids the nanofluid CuO/EG has the highest heat transfer coefficient as a result of the material's property. This research also will encourage young researchers to work on nanofluids of varying nanoparticle size and concentration to discover new results.     

超临界碳氢燃料流动换热的仿真研究

建立了适用于温度、压力大范围变化的超临界碳氢燃料换热特性研究的一维模型,试验验证了模型的可靠性,基于该模型分析了质量流率、换热状态转换和压力等因素对超临界碳氢燃料的换热特性的影响。结果表明:4.0 MPa的低压力工况下,在超临界碳氢燃料的拟临界温度附近存在传热强化现象,而7.0 MPa的高压力工况下,该传热强化现象消失;不论质量流率的大小,4.0 MPa工况下的传热系数始终高于7.0 MPa工况下的传热系数,压力的高低在超临界碳氢燃料的汽相换热区对传热性能的影响更为显著;40kg/(m2.s)的低质量流率条件下,由液相换热区向汽相换热区的换热状态转换将导致转换区附近的传热恶化,而增大质量流率则可避免该问题的发生。     

A Novel Model of Turbulent Convective Heat Transfer in Round Tubes at Supercritical Pressures

In the present study, a novel model was established to investigate the enhanced heat transfer to turbulent pipe flow of supercritical pressure fluids. The governing equations for the steady turbulent compressible pipe flow were simplified into the one-dimensional nondimensionalized forms based on the boundary layer theory. A conventional mixing length turbulence model for constant-property pipe flows was modified by introducing the effect of density fluctuations into the equations of turbulent transport, and the modified turbulence model was applicable to both constant-property and variable-property pipe flows. With the suggested model, which was a combination of the nondimensional governing equations and the modified turbulence model, the numerical calculations were carried out for the turbulent convective heat transfer of water in round tubes at supercritical pressures. The results showed that the present model can provide a relatively precise prediction about the effect of pressure, mass flux, and wall heat flux on heat transfer for supercritical fluid flows and greatly reduce the calculation workload. The modified turbulence model showed a much better agreement with the experimental results than the original turbulence model.     

Condensation heat transfer and pressure drop of refrigerant R-410A flow in a vertical plate heat exchanger

Heat transfer and associated frictional pressure drop in the condensing flow of the ozone friendly refrigerant R-410A in a vertical plate heat exchanger (PHE) are investigated experimentally in the present study. In the experiment two vertical counter flow channels are formed in the exchanger by three plates of commercial geometry with a corrugated sinusoidal shape of a chevron angle of 60°. Downflow of the condensing refrigerant R-410A in one channel releases heat to the upflow of cold water in the other channel. The effects of the refrigerant mass flux, imposed heat flux, system pressure (saturated temperature) and mean vapor quality of R-410A on the measured data are explored in detail. The results indicate that the R-410A condensation heat transfer coefficient and associated frictional pressure drop in the PHE increase almost linearly with the mean vapor quality, but the system pressure only exhibits rather slight effects. Furthermore, increases in the refrigerant mass flux and imposed heat flux result in better condensation heat transfer accompanying with a larger frictional pressure drop. Besides, the imposed heat flux exhibits stronger effects on the heat transfer coefficient and pressure drop than the refrigerant mass flux especially at low refrigerant vapor quality. The friction factor is found to be strongly influenced by the refrigerant mass flux and vapor quality, but is almost independent of the imposed heat flux and saturated pressure. Finally, an empirical correlation for the R-410A condensation heat transfer coefficient in the PHE is proposed. In addition, results for the friction factor are correlated against the Boiling number and equivalent Reynolds number of the two-phase condensing flow.     

Predictions of In-Tube Cooling Heat Transfer Coefficients and Pressure Drops of CO2 and Lubricating Oil Mixture at Supercritical Pressures

The in-tube cooling heat transfer and flow characteristics of supercritical pressure CO₂ mixed with small amounts of lubricating oil differ from those for pure CO₂ due to the entrainment of the lubricating oil as well as the sharp property variations of the supercritical CO₂ working fluid. In-tube gas cooling flow and heat transfer models were developed in this study for CO₂ with entrained polyol ester type lubricating oil in a CO₂ gas cooler at supercritical pressures. A “thermodynamic approach,” which treats the CO₂–oil mixture as a homogenous mixture was used with the heat transfer coefficients and frictional pressure drops evaluated based on the thermophysical properties of the CO₂–oil mixture. Thermophysical property variation correction terms as a function of the wall temperature and the oil concentration were included in the models. The frictional pressure drop correlation predicts more than 90% of the experimentally measured data within ±10%, while the heat transfer coefficient correlation predicts more than 90% of the experimentally measured data within ±20%.     

矩形冷却通道内超临界RP-3航空煤油对流传热数值研究

对超临界压力下RP-3航空煤油在内截面宽为4mm、高为4mm、固体壁面厚为1mm、加热段长度为500mm的水平矩形冷却通道内的对流传热特性进行了数值模拟研究。分析了通道内速度场的分布规律,讨论了热流密度、压力、进口温度对传热的影响。计算结果表明:当主流温度处于拟临界温度附近时,流体物性参数变化剧烈,导致传热系数降低,传热出现恶化。在超临界压力下,较低的热流密度、增大压力、降低进口流体温度或提高质量流速均有利于改善冷却通道内的传热性能。     

Effect of Flow Distribution to the Channels on the Thermal Performance of the Multipass Plate Heat Exchangers

Over last two decades, plate heat exchangers (PHEs) have presented themselves as a viable alternative to the conventional shell and tube heat exchangers in the process and power industries. The thermal theory available for plate heat exchangers in the literature largely works on the assumption of equal flow in each channel. However, it is well known that the distribution of fluid from port to channel in PHE is far from being uniform. The present study brings about this port to channel flow distribution effect on the thermal behavior of multipass plate heat exchangers. The variation of the heat transfer coefficient due to flow variation from channel to channel has also been taken into consideration. Heat exchangers with both equal and unequal passes of the fluids have been studied. The results indicate that the flow maldistribution severely affects the performance of plate heat exchangers, and multipassing can act as an important tool to reduce the deterioration in performance due to maldistribution. The results show that with a low number of passes, the increase of velocity of fluid may be counterproductive in terms of heat transfer enhancement. Also, adding plates in order to increase the heat transfer surface may not be effective due to an increase in flow maldistribution. The correlations for 1-1, 1-2, 2-2, and 2-3 pass plate heat exchangers with the maldistribution index as a parameter are also presented.     

Heat Transfer Characteristics of Printed Circuit Heat Exchanger with Supercritical Carbon Dioxide and Molten Salt

Molten salt and supercritical carbon dioxide (S-CO_2) are important high temperature heat transfer media,but molten salt/S-CO_2 heat exchanger has been seldom reported.In present paper,heat transfer in printed circuit heat exchanger (PCHE) with molten salt and S-CO_2 is simulated and analyzed.Since S-CO_2 can be drove along passage wall by strong buoyancy force with large density difference,its heat transfer is enhanced by natural convection.In inlet region,natural convection weakens along flow direction with decreasing Richardson number,and the thermal boundary layer becomes thicker,so local heat transfer coefficient of S-CO_2 significantly decreases.In outlet region,turbulent kinetic energy gradually increases,and then heat transfer coefficient increases for turbulent heat transfer enhancement.Compared with transcritical CO_2 with lower inlet temperature,local heat transfer coefficient of S-CO_2 near inlet is lower for smaller Richardson number,while it will be higher for larger turbulent kinetic energy near outlet.Performance of PCHE is mainly determined by the pressure drop in molten salt passage and the heat transfer resistance in S-CO_2 passage.When molten salt passage width increases,molten salt pressure drop significantly decreases,and overall heat transfer coefficient slightly changes,so the comprehensive performance of PCHE is improved.As a result,PCHE unit with three semicircular passages and one semi-elliptic passage has better performance.     

Pressure Drop Analysis of Steam Condensation in a Plate Heat Exchanger

In cooperation with Alfa Laval Thermal AB Company in Sweden, a steam condensation test rig of a plate heat exchanger (PHE) was set up. The heat transfer and pressure drop characteristics of two kinds of typical operation condition in a PHE were obtained: complete condensation and partial condensation. This article introduces the test rig, various sensors, and the data acquisition system used in the measurements. The process of steam condensation in a PHE is analyzed in detail. The two-phase frictional pressure drop along this wavy channel was obtained from the measured steam condensation pressure drop. The Lockhart-Martinelli model was extended to predict the pressure drop of steam condensation in a PHE and was verified by the experimental results. Based on the data processing of 109 experimental points, a correlation of frictional pressure drop of steam condensation in a PHE is suggested. This correlation is recommended for calculation of the steam condensation pressure drop in a PHE.     

超临界和超超临界汽轮机汽缸传热系数的研究

提出了汽轮机汽缸传热系数的计算方法。介绍了超，临界和超超临界压力汽轮机汽缸光滑内表面和安装镶片式汽封表面的对流换热表面传热系数的计算公式，安装整体车制式汽封的汽缸内表面、安装静叶的汽缸内表面和安装隔板的汽缸内表面的传热过程总传热系数的计算方法。采用圆筒壁与肋片传热等简化模型来计算汽封块、静叶和隔板的传热过程总传热系数。给出了某型号超，临界600MW汽轮机高压内缸内表面传热系数的计算结果。该方法考虑了不同运行工况下汽缸不同部位的传热过程，在超临界和超超临界压力汽轮机汽缸的温度场与热应力场的有限元法数值计算和寿命评定中，为确定传热边界条件提供了依据。     

Study of Variable Turbulent Prandtl Number Model for Heat Transfer to Supercritical Fluids in Vertical Tubes

In order to improve the prediction performance of the numerical simulations for heat transfer of supercritical pressure fluids, a variable turbulent Prandtl number (Pr_t) model for vertical upward flow at supercritical pressures was developed in this study. The effects of Pr_t on the numerical simulation were analyzed, especially for the heat transfer deterioration conditions. Based on the analyses, the turbulent Prandtl number was modeled as a function of the turbulent viscosity ratio and molecular Prandtl number. The model was evaluated using experimental heat transfer data of CO₂, water and Freon. The wall temperatures, including the heat transfer deterioration cases, were more accurately predicted by this model than by traditional numerical calculations with a constant Pr_t. By analyzing the predicted results with and without the variable Pr_t model, it was found that the predicted velocity distribution and turbulent mixing characteristics with the variable Pr_t model are quite different from that predicted by a constant Pr_t. When heat transfer deterioration occurs, the radial velocity profile deviates from the log-law profile and the restrained turbulent mixing then leads to the deteriorated heat transfer.     

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 Investigation of the Effect of Baffle Orientation on Heat Transfer and Pressure Drop in a Shell and Tube Heat Exchanger With Leakage Flows

The commercial CFD code FLUENT is used to investigate the effect of baffle orientation and of viscosity of the working fluid on the heat transfer and pressure drop in a shell-and-tube heat exchanger in the domain of turbulent flow. The shell-and-tube heat exchanger considered follows the TEMA standards and consists of 76 plane tubes with fixed outside diameter, which are arranged in a triangular pitch. Two baffle orientations as well as leakage flows are considered. In order to determine the effect of viscosity on heat transfer and pressure drop, simulations are performed for the working fluids air, water, and engine oil with Prandtl numbers in the range of 0.7 to 206. For each baffle orientation and working fluid, simulations are performed using different flow velocities at the inlet nozzle. Heat transfer and pressure drop are reported in order to describe the performance of vertically and horizontally baffled shell-and-tube heat exchangers. The heat transfer coefficient is described as modified shell-side Nusselt number, which is defined similar to the VDI method.     

微细圆管内CO2两相沸腾换热实验研究

本文对CO_2在水平微细管内流动沸腾特性进行实验研究。实验结果表明:热流密度增加对强化核态沸腾换热和高干度区域流型转变具有显著影响,随着热流密度的增加换热系数增加,对摩擦压降影响很小;质量流率对于换热系数的影响较小,但随着质量流率的增加摩擦压降大幅增加,质量流率的大小直接决定了换热过程所经历流态;饱和温度升高换热系数相应升高,摩擦压降减小,且对流态转变特性有重要影响。在同样工况下摩擦压降最大值先于换热系数最大值出现,理论分析采用的流态形式与实际CO_2管内流动流动沸腾换热流态基本一致。     

Numerical Analysis Of Heat Transfer Parameters Using Ferrofluid

Heat transfer, thermal management, and acoustics are the important parameters that determine the effectiveness of any miniaturized electronic circuit. As the density of electronic components is increasing, the reliability of such systems is of great concern. The proposed work discusses a novel technique of a magnetic pumping fluid system without conventional cooling components. Here the integrated effect of the conjugate heat transfer and magnetic field is taken into account to study flow phenomena. Two different fluids—water and kerosene—as a base fluid for ferrofluid are evaluated for physical quantities such as pressure, temperature, and heat transfer coefficient to measure the performance of a magnetic cooling system. Flow in the cooling setup is optimized by using numerical analysis and number of experiments on the given setup. It was found that flow depends on the magnetic field gradient, temperature gradient, fluid properties, and material combination. In addition, flow characteristics depend on the influence of magnetic field and temperature of the fluid. Analysis results show that the heat transfer and pressure head in the kerosene-based ferrofluid are more stable compared to the water-based ferrofluid. A better magnetic fluid with both high magnetization and a high pyromagnetic coefficient can enhance the flowability of the ferrofluid to a large extent.     

圆形换热板片传热及流动性能对比计算研究

整理了几种与研究结构相关的换热器的传热系数与压降计算公式,如:螺旋板式、伞板式、弯管式,并针对新型圆形换热板片进行了传热和压降的计算研究及其对比分析,得出了板片的主要设计参数对流动与传热的影响规律,所做工作对新型圆形板片式换热器的优化设计有重要的参考价值。     

Heat flux distribution on circulating fluidized bed boiler water wall

The future of circulating fluidized bed (CFB) combustion technology is in raising the steam parameters to supercritical levels. Understanding the heat flux distribution on the water wall is one of the most important issues in the design and operation of supercritical pressure CFB boilers. In the present paper, the finite element analysis (FEA) method is adopted to predict the heat transfer coefficient as well as the heat flux of the membrane wall and the results are validated by direct measurement of the temperature around the tube. Studies on the horizontal heat flux distribution were conducted in three CFB boilers with different furnace size, tube dimension and water temperature. The results are useful in supercritical pressure CFB boiler design.