Analysis of forced convection heat transfer to supercritical carbon dioxide inside tubes using neural networks

The modeling of forced convection heat transfer for carbon dioxide flowing inside a heated tube at supercritical conditions was studied. The conventional models in the literature tend to modify a constant property correlation by including thermodynamic property terms that follow the heat flux trends. An innovative heuristic method is assumed here for the first time to draw the case-specific heat transfer coefficient correlation from the experimental data on said quantity alone.Neural networks were used since they constitute a general, powerful function-approximator tool proving able to represent a conventional heat transfer surface precisely in the present case. Four different correlation architectures were considered for the neural network function, alternatively based on dimensionless groups and on directly accessible physical quantities as independent variables. In all these architectures, the optimal functional form of the correlation was obtained using a completely heuristic procedure based exclusively on experimental data, reaching an accuracy comparable with the experimental uncertainties declared.An improved performance of the present model was found with respect to conventional correlations. On all the data sets, the third architecture reaches an AAD of 3.98% against 4.09% for the conventional equation and the fourth architecture an AAD of 2.67% against 4.30% for the conventional equation. Besides both these NN architectures present Bias values very close to 0, whereas the conventional equation has a Bias considerably greater.     

Predictions of heat transfer coefficients of supercritical carbon dioxide using the overlapped type of local neural network

An overlapped type of local neural network is proposed to improve accuracy of the heat transfer coefficient estimation of the supercritical carbon dioxide. The idea of this work is to use the network to estimate the heat transfer coefficient for which there is no accurate correlation model due to the complexity of the thermo-physical properties involved around the critical region. Unlike the global approximation network (e.g. backpropagation network) and the local approximation network (e.g. the radial basis function network), the proposed network allows us to match the quick changes in the near-critical local region where the rate of heat transfer is significantly increased and to construct the global smooth perspective far away from that local region. Based on the experimental data for carbon dioxide flowing inside a heated tube at the supercritical condition, the proposed network significantly outperformed some the conventional correlation method and the traditional network models.     

Numerical prediction of turbulent convective heat transfer in mini/micro channels for carbon dioxide at supercritical pressure

A new approach to take into account the effects of variable physical properties on turbulence is suggested. It allows to choose freely the turbulent closure model for conventional terms due to velocity fluctuations and to describe coherently the additional terms due to density fluctuations. Numerical calculations based on the suggested approach have been performed for carbon dioxide flowing within mini/micro channels under cooling conditions. The numerical predictions show that the effects due to density fluctuations are smaller than it could have been initially supposed and that the heat transfer impairment for mini/micro channels, which some experiments seem to highlight, is not completely explained by the considered model.     

An experimental investigation of convection heat transfer to supercritical carbon dioxide in miniature tubes

Experimental results of convection heat transfer to supercritical carbon dioxide in heated horizontal and vertical miniature tubes are reported in this paper. Stainless steel circular tubes having diameters of 0.70, 1.40, and 2.16 mm were investigated for pressures ranging from 74 to 120 bar, temperatures from 20 to 110 °C, and mass flow rates from 0.02 to 0.2 kg/min. The corresponding Reynolds numbers and Prandtl numbers ranged from 10⁴ to 2×10⁵ and from 0.9 to 10, respectively. It is found that the buoyancy effects were significant for all the flow orientations, although Reynolds numbers were as high as 10⁵. The experimental results reveal that in downward flow, a significant impairment of heat transfer was discerned in the pseudocritical region, although heat transfer for both horizontal and upward flow was enhanced. The experimental results further indicate that in all the flow orientations, the Nusselt numbers decreased substantially as the tube diameter shrunk to <1.0 mm. Based on the experimental data, correlations were developed for the axially-averaged Nusselt number of convection heat transfer to supercritical carbon dioxide in both horizontal and vertical miniature heated tubes.     

超临界CO2水平细微管内层流流动与换热的数值模拟

对超临界CO2在水平细微管内层流流动与换热进行了数值模拟.给出了冷却和加热条件下,细微管(d＜1.0 mm)内有代表性的速度、温度剖面,以及Nusselt数随流体温度的变化.研究表明超临界CO2在水平细微管内层流流动时,由于流体热物性随温度剧烈变化,浮升力的影响非常显著,加强了管内换热;且由于流体强变物性特点,只要流体和壁面存在温差,速度及无量纲温度分布就不断变化,充分发展流不可能达到.研究结果对超临界CO2高效紧凑式换热器的设计与优化有重要的意义.     

超临界二氧化碳水平管内传热的数值模拟及与实验对比

以二氧化碳为研究对象,应用k-ε方法对其在水平管内与管外水成垂直交叉冷却的换热进行了分析.用FLUENT软件模拟了超临界二氧化碳在8、10 Mpa,流量为3.4、6.8 g/s,管径6 mm,壁厚1.1 mm,长400 mm的管中流动的状况;计算了平均换热系数h、Nu和Re的变化;并将10 Mpa、3.4 g/s时数值模拟得出的换热系数与实验进行了比较和分析.得出等热流密度下壁面温度的变化情况,数值模拟的换热曲线和实验测量的结果具有相同的趋势,在准临界点处都达到最大值.     

Investigation on forced convective heat transfer of molten salts in circular tubes

In this paper, experiments are carried out to obtain convective heat transfer coefficients of turbulent flow and transition flow of molten Hitec salts in a circular tube. The present experimental data together with experimental data of four kinds of molten salts from the existing literature are correlated for transitional and turbulent convective flow respectively. In addition, the Prandtl number dependence of convective heat transfer with different working fluids is examined. It is shown that the present experimental data are in good agreement with existing correlations.     

Hydrogen production from solar energy powered supercritical cycle using carbon dioxide

A hydrogen production method is proposed, which utilizes solar energy powered thermodynamic cycle using supercritical carbon dioxide (CO₂) as working fluid for the combined production of hydrogen and thermal energy. The proposed system consists of evacuated solar collectors, power generating turbine, water electrolysis, heat recovery system, and feed pump. In the present study, an experimental prototype has been designed and constructed. The performance of the cycle is tested experimentally under different weather conditions. CO₂ is efficiently converted into supercritical state in the collector, the CO₂ temperature reaches about 190 °C in summer days, and even in winter days it can reach about 80 °C. Such a high-temperature realizes the combined production of electricity and thermal energy. Different from the electrochemical hydrogen production via solar battery-based water splitting on hand, which requires the use of solar batteries with high energy requirements, the generated electricity in the supercritical cycle can be directly used to produce hydrogen gas from water. The amount of hydrogen gas produced by using the electricity generated in the supercritical cycle is about 1035 g per day using an evacuated solar collector of 100.0 m² for per family house in summer conditions, and it is about 568.0 g even in winter days. Additionally, the estimated heat recovery efficiency is about 0.62. Such a high efficiency is sufficient to illustrate the cycle performance.     

Modeling of convection heat transfer of supercritical carbon dioxide in a vertical tube at low Reynolds numbers using artificial neural network

Today, many researches have been directed on heat transfer of supercritical fluids; however, since the analysis of heat transfer in these fluids founded by a mathematical model based on the effective parameters is complicated, so in this paper, a group method of data handling (GMDH) type artificial neural network are used for calculating local heat transfer coefficient h_x of supercritical carbon dioxide in a vertical tube with 2 mm diameter at low Reynolds numbers (Re < 2500) by empirical results obtained by Jiang et al. [1].At first, we considered h_x as target parameter and G, Re, Bo^?, x⁺ and q_w as input parameters. Then, we divided empirical data into train and test sections in order to accomplish modeling. We instructed GMDH type neural network by 80% of the empirical data. 20% of primary data which had been considered for testing the appropriateness of the modeling were entered into the GMDH network. Results were compared by two statistical criterions (R² and RMSE) with empirical ones. The results obtained by using GMDH type neural network are in excellent agreement with the experimental results.     

Adaptive neuro-fuzzy modeling of convection heat transfer of turbulent supercritical carbon dioxide flow in a vertical circular tube

Heat transfer of supercritical fluids has been the subject of many investigations; however, since the analysis of heat transfer in these fluids established by a mathematical model based on the planning parameters is complicated, this study attempts to provide a model for convection heat transfer of turbulent supercritical carbon dioxide flow in a vertical circular tube with a hydraulic diameter of 7.8 mm in inlet bulk temperature of 15 °C and a 8 MPa constant pressure by empirical results obtained by Kim et al.[1] and adaptive neuro-fuzzy inference system (ANFIS). At first, we considered Nu_x as a target parameter and q_w, G, Bo* and x⁺ as input parameters. Then, we randomly divided 123 empirical data into train and test sections in order to accomplish modeling. We instructed ANFIS network by 75% of the empirical data. Twenty-five percent of primary data which had been considered for testing the appropriateness of the modeling were entered into the ANFIS model. Results were compared by two statistical criterions (R² and RMSE) with empirical ones. Considering the results, it is obvious that our proposed modeling by ANFIS is efficient and valid and it can be expanded for more general states.     

Overall heat transfer coefficient in the presence of the axial dispersion coefficient for a forced draught cooling tower

An overall heat transfer coefficient was calculated for a forced draught counterflow cooling tower by using the pulse response technique. The presence of an axial dispersion coefficient for both gas and liquid was considered. Results indicate that, on neglecting the axial mixing and assuming a plug flow, the overall heat transfer coefficient is overestimated and can lead to errors in design applications.     

Gravity-controlled condensation heat transfer of carbon dioxide (relationship between condensation condition and heat transfer)

This paper concerns the condensation of carbon dioxide and its heat transfer on a vertical surface in the subcritical region. In this region, the physical properties of carbon dioxide show significant temperature and pressure dependence. In particular, as the pressure increases and approaches the critical pressure, the difference in the properties of liquid and vapor, and surface tension approach zero. Therefore, condensate flow from natural convection decreases and the configuration of condensation may differ from that at lower pressures. In this study, the configuration of condensation is observed and at the same time, condensation heat transfer is obtained by measuring the volume of condensate. Heat transfer is discussed in connection with the configuration. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res 25(4): 214–225, 1996     

Numerical simulation of supercritical carbon dioxide flows across critical point

Numerical study of supercritical carbon-dioxide flows across the critical point is presented. The present numerical method is based on the preconditioning method developed by Yamamoto and mathematical models of thermophysical properties for carbon dioxide programmed in the program package for thermophysical properties of fluids, developed by Kyushu University. First, the two-dimensional natural convection of carbon dioxide between two parallel plates is calculated while changing the bulk pressure. The calculated thermophysical properties of the carbon-dioxide flow under supercritical pressure are compared with those in a gas condition. Next, the natural convection of carbon dioxide in an O-shaped cyclic channel is calculated, and the effect of the density difference induced by the phase change to the flow is investigated. For application to high-speed flows, supercritical carbon dioxide flows through a nozzle with free-jet expansion (known as the process of rapid expansion of supercritical solutions) process are calculated. The calculated shock distance to the Mach disk generated in the free jet is compared with experiments and the density variations in the nozzle while changing the inlet temperature are numerically predicted.     

Three dimensional numerical and experimental study of forced convection heat transfer on solar collector surface

In this study, experimental and three dimensional numerical work was carried out to determine the average heat transfer coefficients for forced convection air flow over a rectangular flat plate. Three dimensional numerical simulations were obtained using a commercial finite volume based fluid dynamics code called Fluent 6.3. The experiments were performed for mass transfer using the naphthalene sublimation technique. The results were presented in terms of heat transfer parameters using the analogy between heat and mass transfer. All the experimental results are correlated within an accuracy of ± 12%.     

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]     

Study on carbon dioxide gas cooler heat transfer process under supercritical pressures

In carbon dioxide transcritical air‐conditioning and heat pump systems, the high‐pressure‐side heat exchanger operating at supercritical pressures is usually called as gas cooler. The carbon dioxide gas cooler displays much difference from the traditional heat exchangers employing constant property fluids. The commonly used logarithmic mean temperature difference (LMTD) and effectiveness—heat transfer unit (ε‐NTU) fail for the gas cooler design calculation as the carbon dioxide properties change sharply near the critical or pseudo‐critical point in the heat transfer processes. The new effective heat transfer temperature difference expression for variable fluid property derived by the authors is verified by numeric simulation of the carbon dioxide gas cooler. Moreover, the available correlated models for the cooled carbon dioxide supercritical heat transfer are used to simulate the gas cooler. Detail analysis is made for the deviations among the different models, and for the distributions of local convective coefficient, heat flux, and local temperature of carbon dioxide along the flow path in the gas cooler. Copyright © 2002 John Wiley & Sons, Ltd.     

管式PV/T水冷装置的对流传热性能分析与效能实验

针对PV/T的研究主要以实验方法为主缺乏理论依据的问题,利用管道液体对流传热理论,对PV/T水冷装置的热吸收能力和传热时延进行了初步分析,研究了流速对装置性能的影响。通过设计U型管水冷PV/T进行模型实验,表明了在功能方面,PV/T既可以实现太阳能的热利用,也可以降低组件温度,从而提高光伏发电效率。在性能方面,PV/T的热吸收能力受流速的影响很大,需要平衡热吸收能力与水泵驱动功率之间的矛盾。     

Neural network analysis of boiling heat transfer enhancement using additives

A model was developed to evaluate and predict boiling heat transfer enhancement using additives. The model is based on the molecular structures of the additives and uses artificial neural network technology. The effects of 30 additives tested by the authors and other researchers on the augmentation of boiling heat transfer were analyzed with the model. The results show that the evaluation of all 30 additives is consistent with the experimental data, which means that the training accuracy of the model is 100%. In addition, the boiling heat transfer enhancement with sodium oleate and 11 other additives was also predicted, with a prediction accuracy of over 90% since the calculated results for 10 of the 11 additives were in agreement with the experimental results.     

Prediction of heat transfer and flow characteristics in helically coiled tubes using artificial neural networks

In this study, Artificial Neural Network (ANN) models were developed to predict the heat transfer and friction factor in helically coiled tubes. The experiments were carried out with hot fluid in coiled tubes which placed in a cold bath. Coiled tubes with various curvature ratios and coil pitches (nine Layouts) were used. The output data of the ANNs were Nusselt number and friction factor. The validity of the method was evaluated through a test data set, which were not employed in the training stage of the network. Moreover, the performance of the ANN model for estimating the Nusselt number and friction factor in the coiled tubes was compared with the existing empirical correlations. The results of this comparison show that the ANN models have a superior performance in predicting Nusselt number and friction factor in the coiled tubes.     

Convective Heat and Mass Transfer in Water at Super—Critical Pressures under Heating or Cooling Conditions in Vertical Tubes

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