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.     

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.     

A General Predictive Technique for Heat Transfer during Saturated Film Boiling in Tubes

Abstract

A simple predictive technique for heat transfer during film boiling in tubes is presented. This technique is based on the two-step model and consists of a graphic correlation for nonequilibrium quality and an equation for liquid droplet cooling at high pressures. It has been developed from and verified with data for water, nitrogen, para-hydrogen, R-113, methane, and propane. The range of data includes equilibrium qualities from 0.1 to 2.9, pressures from 1.4 to 215 bar, reduced pressures from 0.01 to 0.97, mass flux from 30 to 3442 kg/m² s, tube diameters from 2.5 to 14.9 mm, heat flux from 0.012 to 2.1 [Macute]W/m², and wall temperatures from 81 to 1112 K. For all 722 data points analyzed, heat transfer coefficients based on actual vapor temperatures are correlated with a root-mean-square error of 15%.     

Nucleate pool boiling heat transfer measurements of HFC23/CFC13 system

Nucleate pool boiling heat transfer data of the HFC23/CFC13 system have been systematically measured in awide range of pressures and heat fluxes.The experimental results are also compared with the measured data ofR508A and R508B.It is found that the heat transfer coefficient of R503(HFC23/CFC13=0.511/0.489)is higherthan that of R508A and R508B.Furthermore,the measured data were compared with the predicted results withthree well-known correlations.Correlation by Fujita and Tsutsui can provide acceptable results.Most of the datafall within±20% of this correlation.     

Saturated flow boiling heat transfer and critical heat flux in small horizontal flattened tubes

This paper presents experimental results for flow boiling heat transfer coefficient and critical heat flux (CHF) in small flattened tubes. The tested flattened tubes have the same equivalent internal diameter of 2.2 mm, but different aspect height/width ratios (H/W) of ¼, ½, 2 and 4. The experimental data were compared against results for circular tubes using R134a and R245fa as working fluids at a nominal saturation temperature of 31 °C. For mass velocities higher than 200 kg/m²s, the flattened and circular tubes presented similar heat transfer coefficients. Such a behavior is related to the fact that stratification effects are negligible under conditions of higher mass velocities. Heat transfer correlations from the literature, usually developed using only circular-channel experimental data, predicted the flattened tube results for mass velocities higher than 200 kg/m²s with mean absolute error lower than 20% using the equivalent diameter to account for the geometry effect. Similarly, the critical heat flux results were found to be independent of the tube aspect ratio when the same equivalent length was kept. Equivalent length is a new parameter which takes into account the channel heat transfer area. The CHF correlations for round tubes predicted the flattened tube data relatively well when using the equivalent diameter and length. Furthermore, a new proposed CHF correlation predicted the present flattened tube data with a mean absolute error of 5%.     

Condensation in horizontal tubes, part 2: new heat transfer model based on flow regimes

A new general flow pattern/flow structure based heat transfer model for condensation inside horizontal, plain tubes is proposed based on simplified flow structures of the flow regimes, and also includes the effect of liquid-vapor interfacial roughness on heat transfer. The model predicts local condensation heat transfer coefficients for the following flow regimes: annular, intermittent, stratified-wavy, fully stratified and mist flow. The new model has been compared to test data for 15 fluids (R-11, R-12, R-22, R-32, R-113, R-125, R-134a, R-236ea, a R-32/R-125 near-azeotrope, R-404A, R-410A, propane, n-butane, iso-butane and propylene) obtained in nine independent research laboratories. The new model has been tested over the following range of conditions: mass velocities from 24 to 1022 kg/(m² s), vapor qualities from 0.03 to 0.97, reduced pressures from 0.02 to 0.80 and tube internal diameters from 3.1 to 21.4 mm. Overall, the model predicts 85% of the heat transfer coefficients in the non-hydrocarbon database (1850 points) to within ±20% with nearly uniform accuracy for each flow regime and predicts 75% of the entire database to within ±20% when including the hydrocarbons (2771 points), the latter all from a single laboratory whose data had some unusual experimental trends over part of their test range.     

Experimental investigation of condensation heat transfer and pressure drop of R22, R410A and R407C in mini-tubes

Condensation heat transfer and pressure drop of R22, R410A and R407C were investigated experimentally in two single round stainless steel tubes with inner diameter of 1.088 mm and 1.289 mm. Condensation heat transfer coefficients and two phase pressure drop were measured at the saturation temperatures of 30 °C and 40 °C. The mass flux varies from 300 to 600 kg/m² s and the vapor quality 0.1–0.9. The effects of mass flux and vapor quality were investigated and the results indicate that condensation heat transfer coefficients increase with mass flux and vapor quality, increasing faster in the high vapor quality region. The experimental data was compared with the correlations based on experimental data from large diameter tubes (d_h > 3 mm), such as the Shah and Akers correlations et al. Almost all the correlations overestimated the present experimental data, but Wang correlation and Yan and Lin correlation which were developed based on the experimental data from mini-tubes predicted present data reasonably well. Condensation heat transfer coefficients and two phase pressure drop of R22 and R407C are equivalent but both higher than those of R410A. As a substitute for R22, R410A has more advantages than R407C in view of the characteristics of condensation heat transfer and pressure drop.     

Modified Wilson Plots for Enhanced Heat Transfer Experiments: Current Status and Future Perspectives

Heat transfer coefficients for enhanced tubes are typically measured indirectly using the “Wilson plot” method to first characterize the thermal performance of the one side (heating or cooling supply) and then to obtain the heat transfer data for the enhanced side based on the Wilson plot results. A brief history of the Wilson plot evolution and alternative methods to the Wilson plot, including the advantages and disadvantages, are discussed as applied for enhanced heat transfer. A slight modification to the Briggs and Young (1969) method is proposed so that the experimental errors can be propagated through the method, allowing us to estimate the error in the generated correlations. Furthermore, a new method based on unconstrained minimization is proposed as an alternative to the least-squares regression. As an example, both methods have been applied to two enhanced boiling tubes (the most recent generation) and heat transfer coefficients were compared against direct wall temperature based heat transfer coefficient measurements made on the same tubes for water flow with high-performance internal helical ribs. Both the unconstrained minimization method and the modified Briggs and Young (1969) method performed well and predicted the same heat transfer performance within experimental uncertainty for two databases taken on two different experimental facilities. Furthermore, if the presently modified Wilson plot method is utilized, and the form of the correlating equation is chosen judiciously and is only applied within the range of experimental conditions tested, the results garnered from the analysis can very adequately predict the local heat transfer performance.     

Laminar film condensation heat transfer of hydrogen and nitrogen inside a vertical tube

There have been a number of experimental investigations on condensing heat transfer to cryogenic fluids. The investigations with nitrogen and oxygen have shown reasonable agreement between experimental data and those predicted by Nusselt's theory. On the other hand, in the previous investigations with much colder fluids, such as hydrogen, deuterium, and helium, the experimental condensing heat transfer coefficients are smaller than those predicted by Nusselt's theory, and these differences become much larger when the film Reynolds number or decreasing temperature difference across the condensate film is decreased. In the present investigation, hydrogen and nitrogen were condensed inside a vertical tube (d = 15 mm, L = 30 mm) under steady‐state conditions, respectively, and condensing heat transfer coefficients were precisely measured. From the experimental results, the condensing heat transfer coefficients for saturated hydrogen and nitrogen vapors agree with those predicted by Nusselt's theory within ±20%. The results of the present study suggest that deuterium and helium might also behave as predicted by Nusselt's theory. © 2001 Scripta Technica, Heat Trans Asian Res 30(7): 542–560, 2001     

Flow boiling in horizontal flattened tubes: Part II – Flow boiling heat transfer results and model

Experiments of flow boiling heat transfer were conducted in four horizontal flattened smooth copper tubes of two different heights of 2 and 3 mm. The equivalent diameters of the flattened tubes are 8.6, 7.17, 6.25, and 5.3 mm. The working fluids were R22 and R410A. The test conditions were: mass velocities from 150 to 500 kg/m² s, heat fluxes from 6 to 40 kW/m² and saturation temperature of 5 °C. The experimental heat transfer results are presented and the effects of mass flux, heat flux, and tube diameter on heat transfer are analyzed. Furthermore, the flow pattern based flow boiling heat transfer model of Wojtan et al. [L. Wojtan, T. Ursenbacher, J.R. Thome, Investigation of flow boiling in horizontal tubes: Part I – A new diabatic two-phase flow pattern map, Int. J. Heat Mass Transfer 48 (2005) 2955–2969; L. Wojtan, T. Ursenbacker, J.R. Thome, Investigation of flow boiling in horizontal tubes: Part II – Development of a new heat transfer model for stratified-wavy, dryout and mist flow regimes, Int. J. Heat Mass Transfer 48 (2005) 2970–2985], using the equivalent diameters, were compared to the experimental data. The model predicts 71% of the entire database of R22 and R410A ±30% overall. The model predicts well the flattened tube heat transfer coefficients for R22 while it does not predicts well those for R410A. Based on several physical considerations, a modified flow boiling heat transfer model was proposed for the flattened tubes on the basis of the Wojtan et al. model and it predicts the flattened tube heat transfer database of R22 and R410A by 85.8% within ±30%. The modified model is applied to the reduced pressures up to 0.19.     

Condensation in horizontal tubes, part 1: two-phase flow pattern map

A new flow pattern map and flow pattern based heat transfer model for condensation inside horizontal plain tubes are proposed in this two-part paper. In Part I, a new version of a two-phase flow pattern map, originally developed by Kattan et al. [J. Heat Transfer 120 (1998) 140] for flow boiling, is presented for condensation inside horizontal tubes while a new heat transfer model is presented in Part II. The new flow pattern map incorporates a newly defined logarithmic mean void fraction (LMε) method for calculation of vapor void fractions spanning from low pressures up to pressures near the critical point. Several other modifications are also made that are appropriate for condensation as opposed to evaporation. In the absence of void fraction data at high reduced pressures for these conditions, the new LMε method has been indirectly validated using the convective condensation model for annular flow and corresponding heat transfer test data at reduced pressures up to 0.8. The new map has also been successfully compared to some recent flow pattern observations for condensation and other existing flow transition criteria and maps.     

Experimental and theoretical studies of thermal conductivity,viscosity and heat transfer coefficient of titania and alumina nanofluids

Thermal conductivity, viscosity and heat transfer coefficient of water-based alumina and titania nanofluids have been investigated. The thermal conductivity of alumina nanofluids follow the prediction of Maxwell model, whilst that of titania nanofluids is slightly lower than model prediction because of high concentration of stabilisers. None of investigated nanofluids show anomalously high thermal conductivity enhancement frequently reported in literature. The viscosity of alumina and titania nanofluids was higher than the prediction of Einstein–Batchelor model due to aggregation. Heat transfer coefficients measured in nanofluids flowing through the straight pipes are in a very good agreement with heat transfer coefficients predicted from classical correlation developed for simple fluids. Experimental heat transfer coefficients in both nanofluids as well as corresponding wall temperatures agree within ±10% with the values obtained from numerical simulations employing homogeneous flow model with effective thermo-physical properties of nanofluids. These results clearly shows that titania and alumina nano-fluids do not show unusual enhancement of thermal conductivity nor heat transfer coefficients in pipe flow frequently reported in literature.     

Characteristics of heat transfer coefficients during nucleate pool boiling of binary mixtures

Experimental studies were made on heat transfer on a horizontal platinum wire during nucleate pool boiling in nonazeotropic refrigerant binary mixtures at pressures of 0.25 to 0.7 MPa and at heat fluxes up to CHF. The boiling features of the mixtures and the single-component substances were observed by photography. The relationship between the boiling behavior and the reduction of heat transfer coefficients in binary mixtures is discussed in order to propose a correlation useful for predicting the present experimental data over a wide range of low to high heat fluxes. It is shown that the correlation is applicable to alcoholic mixtures. The physical meaning of k, which was introduced to evaluate the effect of heat flux on the reduction of a heat transfer coefficient, is clarified based on measured nucleate pool boiling heat transfer data and visual observations of the boiling features. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(7): 535–549, 1998     

New prediction methods for CO2 evaporation inside tubes: Part II—An updated general flow boiling heat transfer model based on flow patterns

Corresponding to the updated flow pattern map presented in Part I of this study, an updated general flow pattern based flow boiling heat transfer model was developed for CO₂ using the Cheng–Ribatski–Wojtan–Thome [L. Cheng, G. Ribatski, L. Wojtan, J.R. Thome, New flow boiling heat transfer model and flow pattern map for carbon dioxide evaporating inside horizontal tubes, Int. J. Heat Mass Transfer 49 (2006) 4082–4094; L. Cheng, G. Ribatski, L. Wojtan, J.R. Thome, Erratum to: “New flow boiling heat transfer model and flow pattern map for carbon dioxide evaporating inside tubes” [Heat Mass Transfer 49 (21–22) (2006) 4082–4094], Int. J. Heat Mass Transfer 50 (2007) 391] flow boiling heat transfer model as the starting basis. The flow boiling heat transfer correlation in the dryout region was updated. In addition, a new mist flow heat transfer correlation for CO₂ was developed based on the CO₂ data and a heat transfer method for bubbly flow was proposed for completeness sake. The updated general flow boiling heat transfer model for CO₂ covers all flow regimes and is applicable to a wider range of conditions for horizontal tubes: tube diameters from 0.6 to 10 mm, mass velocities from 50 to 1500 kg/m² s, heat fluxes from 1.8 to 46 kW/m² and saturation temperatures from ?28 to 25 °C (reduced pressures from 0.21 to 0.87). The updated general flow boiling heat transfer model was compared to a new experimental database which contains 1124 data points (790 more than that in the previous model [Cheng et al., 2006, 2007]) in this study. Good agreement between the predicted and experimental data was found in general with 71.4% of the entire database and 83.2% of the database without the dryout and mist flow data predicted within ±30%. However, the predictions for the dryout and mist flow regions were less satisfactory due to the limited number of data points, the higher inaccuracy in such data, scatter in some data sets ranging up to 40%, significant discrepancies from one experimental study to another and the difficulties associated with predicting the inception and completion of dryout around the perimeter of the horizontal tubes.     

椭圆管内对流换热与流动阻力特性研究

通过CFD技术,分别对5种长短轴之比的椭圆管管内湍流和层流状态时的换热与流动进行数值研究,分析了流体流动状态和椭圆管长短轴之比对换热系数与流动阻力的影响,并根据数值计算结果拟合出湍流区椭圆管管内换热系数的准则关系式,最后绘制每种类型椭圆管的局部换热系数曲线。研究结果表明:数值计算结果与实验值吻合良好;采用当量直径的方法计算椭圆管内换热系数误差较大;随着雷诺数的增加,每种类型的椭圆管管内阻力系数逐渐减小;而在相同的雷诺数下,随着长短轴之比K的增大,管内阻力系数逐渐增加;每种类型的椭圆管具有类似的局部换热特性,即长半轴两端点处局部换热系数最低,而短半轴两端点处具有最大局部换热系数。     

Falling Films on Arrays of Horizontal Tubes with R-134a,Part I: Boiling Heat Transfer Results for Four Types of Tubes

A new falling film heat transfer test facility has been built for the measurement of local heat transfer coefficients on a vertical array of horizontal tubes, including flow visualization capabilities, for use with refrigerants. Presently, the facility has been used for evaporation tests on four types of tubes at three tube pitches and three nominal heat flux levels for R-134a at 5°C. A new method for determining local heat transfer coefficients using hot water heating has been applied, and test results for a wide range of liquid film Reynolds numbers have been measured for arrays made of plain, Turbo-BII HP, Gewa-B, and High-Flux tubes. The results show that there is a transition to partial dryout as the film Reynolds number is reduced, marked by a sharp falloff in heat transfer. Above this transition, the heat transfer coefficients are nearly insensitive to the film Reynolds number, apparently because vigorous nucleate boiling is always seen in the liquid film. The corresponding nucleate pool boiling data for the four types of tubes were also measured for direct comparison purposes. Overall, about 15,000 local heat transfer data points were obtained in this study as a function of heat flux, film Reynolds number, tube spacing, and type.     

Experimental study on saturated flow boiling heat transfer of R290/R152a binary mixtures in a horizontal tube

An experimental study on the saturated flow boiling heat transfer for a binary mixture of R290/R152a at various compositions is conducted at pressures ranging from 0.2 to 0.4 MPa. The heat transfer coefficients are experimentally measured over mass fluxes ranging from 74.1 to 146.5 kg/(m²·s) and heat fluxes ranging from 13.1 to 65.5 kW/m². The influences of different parameters such as quality, saturation pressure, heat flux, and mass flux on the local heat transfer coefficient are discussed. Existing correlations are analyzed. The Gungor-Winterton correlation shows the best fit among experimental data for the two pure refrigerants. A modified correlation for the binary mixture is proposed based on the authors’ previous work on pool boiling heat transfer and the database obtained from this study. The result shows that the total mean deviation is 10.41% for R290/R152a mixtures, with 97.6% of the predictions falling within ±30%.     

Condensation from superheated vapor flow of R744 and R410A at subcritical pressures in a horizontal smooth tube

This paper presents experimentally determined heat transfer coefficients for condensation from a superheated vapor of CO₂ and R410A. The superheated vapor was flowed through a smooth horizontal tube with 6.1 mm ID under almost uniform temperature cooling at reduced pressures from 0.55 to 0.95, heat fluxes from 3 to 20 kW m^?2, and superheats from 0 to 40 K. When the tube wall temperature reaches the saturation point, the measured results show that the heat transfer coefficient gradually starts deviating from the values predicted by a correlation valid for single-phase gas cooling. This point identifies the start of condensation from the superheated vapor. The condensation starts earlier at higher heat fluxes because the tube wall temperature reaches the saturation point earlier. The heat transfer coefficient reaches a value predicted by correlations for condensation at a thermodynamic vapor quality of 1. The measured heat transfer coefficient of CO₂ is roughly 20–70% higher than that of R410A at the same reduced pressures. This is mainly because the larger latent heat and liquid thermal conductivity of CO₂, compared to that of R410A, increase the heat transfer coefficient.     

Flow Patterns and Heat Transfer for Flow Boiling in Small to Micro Diameter Tubes

An overview of the recent developments in the study of flow patterns and boiling heat transfer in small to micro diameter tubes is presented. The latest results of a long-term study of flow boiling of R134a in five vertical stainless-steel tubes of internal diameter 4.26, 2.88, 2.01, 1.1, and 0.52 mm are then discussed. During these experiments, the mass flux was varied from 100 to 700 kg/m²s and the heat flux from as low as 1.6 to 135 kW/m². Five different pressures were studied, namely, 6, 8, 10, 12, and 14 bar. The flow regimes were observed at a glass section located directly at the exit of the heated test section. The range of diameters was chosen to investigate thresholds for macro, small, or micro tube characteristics. The heat transfer coefficients in tubes ranging from 4.26 mm down to 1.1 mm increased with heat flux and system pressure, but did not change with vapor quality for low quality values. At higher quality, the heat transfer coefficients decreased with increasing quality, indicating local transient dry-out, instead of increasing as expected in macro tubes. There was no significant difference between the characteristics and magnitude of the heat transfer coefficients in the 4.26 mm and 2.88 mm tubes but the coefficients in the 2.01 and 1.1 mm tubes were higher. Confined bubble flow was first observed in the 2.01 mm tube, which suggests that this size might be considered as a critical diameter to distinguish small from macro tubes. Further differences have now been observed in the 0.52 mm tube: A transitional wavy flow appeared over a significant range of quality/heat flux and dispersed flow was not observed. The heat transfer characteristics were also different from those in the larger tubes. The data fell into two groups that exhibited different influences of heat flux below and above a heat flux threshold. These differences, in both flow patterns and heat transfer, indicate a possible second change from small to micro behavior at diameters less than 1 mm for R134a.     

Pool boiling heat transfer of propane, isobutane and their mixtures on enhanced tubes with reentrant channels

Pool boiling heat transfer experiments were carried out on a conventional smooth tube and four enhanced tubes with reentrant surfaces using propane, isobutane and their mixtures as working fluids for six saturation temperatures. The heat transfer performance is very different for different surface-fluid combinations. Compared to the smooth tube, the mixture boiling heat transfer degradation is more significant for the enhanced tubes. The current data are compared with available literature data for the same fluids and also with data for R12 and R134a. Experimental results of boiling hysteresis and for twin-tube bundles are also provided. Further explanations for the different heat transfer performances is provided by means of visualization in an accompanying paper [Y. Chen, M. Groll, R. Mertz, R. Kulenovic, Visualization and mechanisms of pool boiling of propane, isobutane and their mixtures on enhanced tubes with reentrant channels, submitted to Int. J. Heat Mass Transfer (H/S 04016)].