Development of Heat Transfer Correlation for Supercritical Water in Vertical Upward Tubes

Supercritical water is widely used in many advanced single-phase thermosiphons due to its favorable heat and mass transfer characteristics and potentially high thermal efficiency. However, the heat transfer characteristics of supercritical water in the deterioration regime cannot be accurately predicted due to the absence of exact evaluation of the effect on steep variation in thermophysical properties near the pseudocritical point. The present paper focuses on the deterioration mode by analyzing the physical mechanism and constructing a new correlation. About 3,000 experimental data on supercritical water, including 40 deteriorated heat transfer cases from open literature, were collected. Quantitative assessment of heat transfer behavior was conducted based on existing test data and previous criteria gathered from extant literature. Based on experimental data evaluation and phenomenological analysis, an improved dimensionless correlation is proposed by introducing multi-dimensionless parameters, which can correct the deviation of heat transfer from its conventional behavior in the Dittus-Boelter equation. Comparisons of various heat transfer correlations with the selected test data show that the new correlation agrees better with the test data versus other correlations selected from the open literature.     

Development of Empirical Correlation for Heat Transfer to Nanofluids

Nanofluids are emerging as alternative fluids for heat transfer applications due to enhanced thermal properties. Several correlations are available in open literature for heat transfer coefficient (HTC) and thermophysical properties of nanofluids. Reliability of correlations that use effective properties for estimation of HTC needs to be checked. Comparison of experimental HTC and that estimated from existing correlations is the main objective of the present study. An empirical correlation is developed with experimental data of the HTC for zinc–water and zinc oxide–water nanofluids. Experimental HTC is compared with that estimated from developed correlation and existing correlations. The range of Re considered for the study is 4000 to 18,000. Comparison indicated large deviation in experimental values and the values estimated from existing correlations. Based on comparison results, it can be concluded that the single‐phase models of forced convective heat transfer cannot be extended to nanofluids.     

A new heat transfer correlation for supercritical fluids

A new method of heat transfer prediction in supercritical fluids is presented. Emphasis is put on the simplicity of the correlation structure and its explicit coupling with physical phenomena. Assessment of qualitative behaviour of heat transfer is conducted based on existing test data and experience gathered from open literature. Based on phenomenological analysis and test data evaluation, a single dimensionless number, the acceleration number, is introduced to correct the deviation of heat transfer from its conventional behaviour, which is predicted by the Dittus-Boelter equation. The new correlation structure excludes direct dependence of heat transfer coefficient on wall surface temperature and eliminates possible numerical convergence. The uncertainty analysis of test data provides information about the sources and the levels of uncertainties of various parameters and is highly required for the selection of both the dimensionless parameters implemented into the heat transfer correlation and the test data for the development and validation of new correlations. Comparison of various heat transfer correlations with the selected test data shows that the new correlation agrees better with the test data than other correlations selected from the open literature.     

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.     

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.     

A Study on Characteristics of Cooling Heat Transfer of Supercritical Pressure Fluids in a Plate Heat Exchanger

For the development of industrial heat pump systems supplying a high-temperature heat source over 130°C, experiments were carried out on cooling heat transfer of supercritical pressure fluids flowing in a plate heat exchanger (PHE). Using two refrigerants of HFC134a and HCFC22 as the test fluids, heat transfer coefficient data were obtained at different pressure, flow rate, and heat load conditions. The heat transfer coefficient generally had a maximum in the vicinity of the pseudocritical point and showed seven- to ninefold values compared with tube flow. Based on the measurements, characteristics of cooling heat transfer of supercritical pressure fluids in the PHE were clarified and a correlation of heat transfer coefficient was developed.     

Experimental study on heat transfer characteristics of supercritical carbon dioxide in horizontal tube

The heat transfer characteristics of supercritical carbon dioxide in a horizontal tube with water in the vertical cross flow form were experimentally investigated. The results indicate that the changes of inlet pressure, mass flow rate, and cooling water flow rate have major effects on heat transfer performance. The variations of Reynolds number and Prandtl number were obtained in counter flow and vertical cross flow. The four conventional correlations for convection heat transfer of supercritical carbon dioxide were verified by the experimental data in this study and the correlation agree with this experimental condition was determined.     

CO2 based natural circulation loops: New correlations for friction and heat transfer

Results obtained from CFD analysis of 3-dimensional natural circulation loops (NCL) that employ carbon dioxide and water as loop fluids are presented for various isothermal wall temperatures of source and sink in the range of 278–341 K. Such a temperature range would be useful in various heat transfer applications of NCL, e.g. air conditioning, solar collectors, extraction of geothermal energy, etc. For the same wall temperature and geometrical parameters, comparison is made between CO₂ and water in terms of heat transfer rate. Water is considered at atmospheric pressure whereas CO₂ is either in subcritical (liquid) or supercritical state. Liquid CO₂ exhibits very high heat transfer rate, approximately seven times higher than water, whereas performance of supercritical CO₂ depends on the operating pressure and temperature. Effect of loop operating pressure on the system performance is also investigated. Results show that near pseudo-critical region, CO₂ yields very high heat transfer rate, approximately seven times higher than water. Results also show that, due to the presence of bends and local buoyancy effects, fluid parameters such as local velocity and temperature vary in all three dimensions. Validation of simulation results against experimental results reported in the literature with respect to modified Grashof number (Gr_m) and Reynolds number (Re) exhibit good agreement. Additionally, new correlations are proposed for Re in terms of Gr_m, friction factor (f) in terms of Re, and Nusselt number (Nu) in terms of Re and Prandtl number (Pr).     

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。     

Experimental investigation on heat transfer characteristics of low mass flux rifled tube with upward flow

An experiment for heat transfer of water flowing in a vertical rifled tube was conducted at subcritical and supercritical pressure. The main purpose is to explore the heat transfer characteristics of the new-type rifled tube at low mass flux. Operating conditions included pressures of 12–30 MPa, mass flux of 232–1200 kg/(m² s), and wall heat fluxes of 133–719 kW/m². The heat transfer performance and wall temperature distribution at various operating conditions were captured in the experiment. In the present paper, the heat transfer mechanism of the rifled tube was analyzed, the effects of pressure, wall heat flux and mass flux on heat transfer were discussed, and corresponding empirical correlations were also presented. The experimental results exhibit that the rifled tube has an obvious enhancement in heat transfer, even at low mass flux. In comparison with a smooth tube, the rifled tube efficiently prevents Departure from Nucleate Boiling (DNB) and delays dryout at subcritical pressure, and also improves the heat transfer of supercritical water remarkably, especially near pseudo-critical point. An increase in pressure or wall heat flux impairs the heat transfer at both subcritical and supercritical pressure, whereas the increasing mass flux has a contrary effect.     

Flow and Heat Transfer Characteristics of Liquid–Solid Circulating Fluidized Beds

A series of experiments was conducted to investigate the flow and heat transfer characteristics of liquid–solid circulating fluidized beds. The experimental apparatus consisted of a single riser and a downcomer. Water at ambient conditions was used as the fluidizing fluid. Six kinds of particles were tested. First, particle holdup was measured, and a set of systematic data was acquired. By analyzing the experimental data, a simple predicting correlation was derived for the particle holdup. Next, pressure drop measurement was performed, and a predicting correlation was derived. Then heat transfer coefficient was measured, where two regions were identified, i.e., the “heat transfer enhanced region” and the “liquid single-phase heat transfer region.” On the basis of the experimental data, a predicting correlation was derived for each region, and a correlation was proposed for the entire region. Lastly, making use of the already-derived correlations, an analogy was investigated between the frictional pressure drop and the heat transfer coefficient.     

Boiling Heat Transfer Characteristics for Methane,Ethane and Their Binary Mixtures

Abstract

Methane (R50) and ethane (R170) are the dominated components of natural gas and the important components in mixture refrigerants for the mixture Joule–Thomson refrigeration cycle. In this article, experimental investigations on nucleate pool boiling and flow boiling heat transfer characteristics of R50, R170, and their binary mixtures are presented. The effects of saturation pressure, heat flux, mass flux, concentration, and vapor quality on heat transfer coefficients are analyzed and discussed. Firstly, the pool boiling heat transfer data were compared with six well-known correlations. Labuntsov correlation shows the best agreement with a mean absolute relative deviation (MARD) of 11.3%. Secondly, a new flow boiling heat transfer correlation for pure fluids was proposed based on the asymptotic addition of forced convection and pool boiling. The modified enhancement factor and suppression factor were developed to account for their relative contribution. In addition, in order to consider the mass transfer resistance of mixtures, a new mixture factor was deduced. The new flow boiling heat transfer correlations can well predict the experimental data with the MARD of 9.5% for pure fluids and 8.3% for mixtures.     

Experimental study on heat transfer characteristics of supercritical carbon dioxide in horizontal tube

The heat transfer characteristics of supercritical carbon dioxide in a horizontal tube with water in the vertical cross flow form were experimentally investigated. The results indicate that the changes of inlet pressure, mass flow rate, and cooling water flow rate have major effects on heat transfer performance. The variations of Reynolds number and Prandtl number were obtained in counter flow and vertical cross flow. The four conventional correlations for convection heat transfer of supercritical carbon dioxide were verified by the experimental data in this study and the correlation agree with this experimental condition was determined. __________ Translated from Journal of Refrigeration, 2007, 28(1): 8–11 [译自:制 冷学报]     

Heat Transfer Coefficients for Turbulent Flow in Concentric Annular Ducts

On the basis of a large number of experimental data from the literature, correlations were developed for the heat transfer coefficient for turbulent flow in concentric annular ducts. A proven correlation for heat transfer in circular tubes was extended by factors that take into consideration the effect of the diameter ratio of the annulus and the different boundary conditions for heating or cooling.     

New correlations for heat transfer coefficients during direct cooling of products

An analytical method for determining the heat transfer coefficients of food products being cooled in water and in air flows is presented. Food products are idealized as geometrical solid objects of regular shapes. New correlations between heat transfer coefficients and cooling coefficients are developed in simple forms for practical use in the refrigeration industry. These correlations are then used to determine the heat transfer coefficient for a cylindrical carrot cooled in air flow as an illustrative example. In addition, evaluating the heat transfer coefficients for several products using the available experimental cooling coefficient values from the literature, two new correlations between the heat transfer coefficient and the cooling coefficient are also obtained for water and air cooling applications. The results show that the correlations presented in this article can determine the heat transfer coefficients of food products forced-convection cooling in a simple and accurate manner.     

Convective heat transfer in helical coils for constant-property and variable-property flows with high Reynolds numbers

Forced convection heat transfer of single-phase water in helical coils was experimentally studied. The testing section was constructed from a stainless steel round tube with an inner diameter of 10 mm, coil diameter of 300 mm, and pitch of 50 mm. The experiments were conducted over a wide Reynolds number range of 40000 to 500000. Both constant-property flows at normal pressure and variable-property flows at supercritical pressure were investigated. The contribution of secondary flow in the helical coil to heat transfer was gradually suppressed with increasing Reynolds number. Hence, heat transfer coefficients of the helical tube were close to those of the straight tube under the same flow conditions when the Reynolds number is large enough. Based on the experimental data, heat transfer correlations for both incompressible flows and supercritical fluid flows through helical coils were proposed.     

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。     

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]     

Fluid‐to‐fluid scaling of heat transfer to mixed convection flow of supercritical pressure fluids

Fluid‐to‐fluid scaling for supercritical heat transfer can effectively reduce the difficulty and cost of heat transfer experiments in supercritical boilers and supercritical water reactors and can reduce the number of experiments by converting experimental data of the model fluid to the prototype fluid in organic Rankine cycles. Currently, most existing scaling methods are only suitable for forced convection, while few are developed for mixed convection where buoyancy significantly affects the heat transfer. This paper attempts to extend the applicability of scaling method to mixed convection with the aid of computational fluid dynamic simulations. The scaling parameters were analyzed first and then the shear‐stress transport k‐ω model was used to analyze the supercritical heat transfer characteristics of water and R134a to provide further information for developing a dimensionless number. The results show that significant variations of properties and flow parameters occur in the layer of y⁺ = 5 to 100 and the axial velocity gradient in this layer changes in quite a similar manner to the wall temperature. Based on numerical results, the axial velocity gradient was used with a thermal resistance analogy to derive a new dimensionless number, Re^?0.9π_A , to scale the mass flux. Then, a set of fluid‐to‐fluid scaling laws were developed to predict the heat transfer to supercritical fluids. To validate the newly proposed scaling laws, well‐developed correlations were used for forced convection flow and a direct validation method was developed for buoyancy‐influenced flow. Results show that this new scaling method exhibits reasonable accuracy for both forced and mixed convection heat transfer with supercritical fluids.     

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.