Experimental and numerical investigation of convection heat transfer of CO2 at supercritical pressures in a vertical mini-tube

Convection heat transfer of CO₂ at supercritical pressures in a 0.27 mm diameter vertical mini-tube was investigated experimentally and numerically for inlet Reynolds numbers exceeding 4.0 × 10³. The tests investigated the effects of heat flux, flow direction, buoyancy and flow acceleration on the convection heat transfer. The experimental results indicate that the flow direction, buoyancy and flow acceleration have little influence on the local wall temperature, with no deterioration of the convection heat transfer observed in either flow direction for the studied conditions. The heat transfer coefficient initially increases with increasing heat flux and then decreases with further increases in the heat flux for both upward and downward flows. These phenomena are due to the variation of the thermophysical properties, especially c_p. The numerical results correspond well with the experimental data using several turbulence models, especially the Realizable k–ε turbulence model.     

Development of a new forced convection heat transfer correlation for CO2 in both heating and cooling modes at supercritical pressures

Experimental and numerical investigations on forced convection heat transfer of carbon dioxide at supercritical pressures in a prototypic printed circuit heat exchanger under both cooling and heating conditions have been performed in this present study. The experiment test section has nine semi-circular channels with a hydraulic diameter of 1.16 mm and a length of 0.5 m. Primary operational parameters include inlet pressure of 7.5–10 MPa, mass fluxes of 326 kg/m² s and 762 kg/m² s, inlet temperatures from 10 °C to 90 °C and the average heat flux was 30 kW/m². Beyond reproducing the regular experimental cases, numerical modeling also implemented higher heat fluxes of 60 kW/m² and 90 kW/m² in order to investigate the effect of heat flux. Good agreement was found between the experiments and FLUENT simulations using an SST k–w model with the near-wall region being completely resolved. The distinctive behavior of convection heat transfer at supercritical pressures between heating and cooling modes was systematically analyzed. A more physically reasonable property-averaging technique, Probability Density Function (PDF)-based time-averaged property, was developed to account for the effect of nonlinear dependency of properties on instantaneous local temperature. Furthermore, experimental and computational data were compared to empirical predictions by the Dittus–Boelter and Jackson correlations. The results showed that Dittus–Boelter correlation has better precision for the average value of the predicted heat transfer coefficient but cannot take account of the effect of heat flux. In contrast, the Jackson correlation, with property ratio correction terms to account for the distribution of the properties in the radial direction, could predict the distinction of heat transfer characteristics under heating and cooling conditions. However, it overestimates the average value of heat transfer coefficient in the whole range of the experiment conditions. Finally, a new correlation evaluated by PDF-based time-averaged properties for forced convection heat transfer of CO₂ in both heating and cooling mode at supercritical pressures was developed. Comparison of experimental and computational data with the prediction results by the new developed correlation reveals that it works quite well; i.e., more than 90% data in either heating or cooling mode with various heat fluxes are predicted within an accuracy of ±25%.     

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.     

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.     

Convective boiling heat transfer characteristics of CO2 in microchannels

Convective boiling heat transfer coefficients and dryout phenomena of CO₂ are investigated in rectangular microchannels whose hydraulic diameters range from 1.08 to 1.54 mm. The tests are conducted by varying the mass flux of CO₂ from 200 to 400 kg/m² s, heat flux from 10 to 20 kW/m², while maintaining saturation temperature at 0, 5 and 10 °C. Test results show that the average heat transfer coefficient of CO₂ is 53% higher than that of R134a. The effects of heat flux on the heat transfer coefficient are much significant than those of mass flux. As the mass flux increases, dryout becomes more pronounced. As the hydraulic diameter decreases from 1.54 to 1.27 mm and from 1.27 to 1.08 mm at a heat flux of 15 kW/m² and a mass flux of 300 kg/m² s, the heat transfer coefficients increase by 5% and 31%, respectively. Based on the comparison of the data from the existing models with the present data, the Cooper model and the Gorenflo model yield relatively good predictions of the measured data with mean deviations between predicted and measured data of 21.7% and 21.2%, respectively.     

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。     

Experimental study on the heat transfer characteristics during the pressure transients under supercritical pressures

Main objective of this study is to investigate an applicability of a steady-state heat transfer correlation to pressure transient sequences and an effect of the pressure transient rates on the overall heat transfer rates under the supercritical pressures. Heat transfer rates are brought in line for both the pressure increasing and the pressure decreasing transients. And effects of pressure transient rates on heat transfer rates are trivial. As for an applicability of steady-state heat transfer correlation to the pressure transient sequences, the heat transfer correlation always overestimates the Nusselt number measured in the pressure transient heat transfer experiments by average 30%.     

Boiling heat transfer and dryout phenomenon of CO2 in a horizontal smooth tube

Evaporation heat transfer characteristics of carbon dioxide (CO₂) in a horizontal tube are experimentally investigated. The test tube has an inner diameter of 6.0 mm, a wall thickness of 1.0 mm, and a length of 1.4 m. Experiments are conducted at saturation temperatures of 5 and 10 °C, mass fluxes from 170 to 320 kg/m² s and heat fluxes from 10 to 20 kW/m². Partial dryout of CO₂ occurs at a lower quality as compared to the conventional refrigerants due to a higher bubble growth within the liquid film and a higher liquid droplet entrainment, resulting a rapid decrease of heat transfer coefficients. The effects of mass flux, heat flux, and evaporating temperature are explained by introducing unique properties of CO₂, flow patterns, and dryout phenomenon. In addition, the heat transfer coefficient of CO₂ is on average 47% higher than that of R134a at the same operating conditions. The Gungor and Winterton correlation shows poor prediction of the boiling heat transfer coefficient of CO₂ at low mass flux, while it yields good estimation at high mass flux.     

Investigation of turbulent convective heat transfer and pressure drop of TiO2/water nanofluid in circular tube

Turbulent heat transfer behavior of titanium dioxide/water nanofluid in a circular pipe was investigated experimentally where the volume fraction of nanoparticles in the base fluid was less than 0.25%. The experimental measurements have been carried out in the fully-developed turbulent regime for various volumetric concentrations. The results indicated that addition of small amounts of nanoparticles to the base fluid augmented heat transfer remarkably. There was no much effect on heat transfer enhancement with increasing the volume fraction of nanoparticles. The measurements also showed that the pressure drop of nanofluid was slightly higher than that of the base fluid and increased with increasing the volume concentration. In this paper, experimental results have been compared with the existing correlations for nanofluid convective heat transfer coefficient in turbulent regime. Finally, a new correlation of the Nusselt number will be presented using the results of the experiments with titanium dioxide nanoparticles dispersed in water.     

表面强化管外池沸腾传热特性研究

为实现节能降耗,开发了多种强化沸腾传热的高效换热管。以水为工质,在0.1MPa下对垂直光管、烧结多孔管和T槽管进行了池沸腾传热实验研究,并分析了沿管子轴向的温度分布。实验结果表明,烧结多孔管与T槽管能显著降低起始沸腾过热度、强化沸腾传热:烧结多孔管和T槽管的起始沸腾过热度比光管的低1.5K左右;烧结多孔管和T槽管的核态沸腾传热系数分别为光管的2.4～3.2倍和1.6～2.0倍。此外,烧结多孔管和T槽管能降低相同热流密度下的壁面温度,且有利于降低管子轴向的温差。     

CFD based evaluation of polymer particles heat transfer coefficient in gas phase polymerization reactors

In this work, computational fluid dynamics (CFD) has been employed to compute convection heat transfer coefficient (h) that is the key parameter in calculation of heat transfer rate between particles and fluids in an ethylene polymerization fluidized bed reactor. In addition, the effects of various parameters such as free stream fluid velocity, particles size, and particles interactions with different configurations on heat transfer coefficient were studied. Simulation results are in agreement with common engineering knowledge of the process. The results also indicate that particle interactions, particle size and fluid velocity have more significant impacts on h.     

Comparative study on heat transfer enhancement of nanofluids flow in ribs tube using CFD simulation

This study presents, a numerical investigation of two‐dimensional turbulent nanofluids flow in different ribs tube configurations on heat transfer, friction, and thermal performance coefficients using ANSYS‐FLUENT software version‐16. Governing equations of mass, momentum, and energy have been solved by means of a finite volume method (FVM). Four types of nanoparticles namely; Al₂O₃, CuO, SiO₂, and ZnO with volume fraction range (1%‐4%) and different size of nanoparticles (dp = 30 nm, 40 nm, 50 nm, and 60 nm) with various Reynolds number (10 000‐30 000) in a constant heat flux tube with rectangular, triangular, and trapezoidal ribs were conducted for simulation. The results exhibit that Nusselt number for all cases enhanced with Reynolds number and nanofluid volume fraction increases. Likewise, the results also reveal that SiO₂ with volume fractions of 4% and diameters of nanoparticles of 30 nm in triangular ribs offered the highest Nusselt number at Reynolds number of Re = 30 000. In addition, the higher value of thermal performance factor was obtained at Reynolds number of Re = 10 000.     

含内热源可燃性多孔介质中的传热研究

煤粉、弹药等含内热源的可燃性多孔介质传热过程在自然界和工程中广泛存在。文中分析了可燃多孔介质的热传递机理，建立了相应的导热计算模型，给出了典型物种在内热源作用下的内部温度场。     

Boiling heat transfer from mechanically fabricated porous tubes at atmospheric and superatmospheric pressures

Experiments on pool boiling heat transfer from a circumference-interrupted T-finned (CIT) tube and a Thermoexcel-E tube are conducted at system pressures ranging from 1 to 6 bars, with ethyl alcohol and R-113 as the working media. The strong effects of system pressure on the excellent boiling heat transfer performance of the two enhanced boiling tubes are presented. Based on the analyses of boiling vapor-liquid two-phase flow and heat transfer within the microchannels of the two mechanically fabricated porous layers, and by synthesizing experimental data, semiempirical correlations are established for predicting the boiling heat transfer performance of CIT and Thermoexcel-E tubes separately at atmospheric and superatmospheric pressures.© 1999 Scripta Technica, Heat Trans Asian Res, 28(8): 640-648, 1999     

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.     

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.     

Heat transfer with water flowing upward in a tube for pressures up to supercritical region

A heat transfer experiment was conducted in a tube of 6.07mm in diameter with water flowing upward, covering the ranges of pressure of 10―23MPa, mass flux of 288―1298kg/(m²·s), local water temperature of 78°C―270°C, heat flux of 0.23―1.18MW/m² and Reynolds number of 5.5×10³―3.9×10⁴. The experimental results were compared with the predictions of the Dittus-Boelter correlation, Jackson correlation, Bishop correlation, Swenson correlation and Yamagata correlation. Significant deterioration in heat transfer was observed in both subcritical and supercritical region due to the effect of buoyancy force, but it was not predicted reasonably by the existing correlations.     

Numerical investigation of heat transfer and pressure drop in enhanced tubes

This study investigates passive heat transfer enhancement techniques to determine the distribution of temperature and static pressure in test tubes, the friction factor, the heat flux, the temperature difference between the inlet and outlet fluid temperatures, the pressure drop penalty and the numerical convective heat transfer coefficient, and then compares the results to the experimental data of Zdaniuk et al. It predicts the single-phase friction factors for the smooth and enhanced tubes by means of the empirical correlations of Blasius and Zdaniuk et al. This study performed calculations on a smooth tube and two helically finned tubes with different geometric parameters also used in the analyses of Zdaniuk et al. It also performed calculations on two corrugated tubes in the simulation study. In Zdaniuk et al.'s experimental setup, the horizontal test section was a 2.74 m long countercurrent flow double tube heat exchanger with the fluid of water flowing in the inner copper tube (15.57–15.64 mm i.d.) and cooling water flowing in the annulus (31.75 mm i.d.). Their test runs were performed at a temperature around 20 °C for cold water flowing in the annulus while Reynolds numbers ranged from 12,000 to 57,000 for the water flowing in the inner tube. A single-phase numerical model having three-dimensional equations is employed with either constant or temperature dependent properties to study the hydrodynamics and thermal behaviors of the flow. The temperature contours are presented for inlet, outlet and fully developed regions of the tube. The variations of the fluid temperature and static pressure along tube length are shown in the paper. The results obtained from a numerical analysis for the helically tubes were validated by various friction factor correlations, such as those found by Blasius and Zdaniuk et al. Then, numerical results were obtained for the two corrugated tubes as a simulation study. The present study found that the average deviation is less than 5% for the friction factors obtained by the Fluent CFD program while Blasius's correlation has the average deviation of less than 10%. The corrugated tubes have a higher heat transfer coefficient than smooth tubes but a lower coefficient than helically finned tubes. The paper also investigates the pressure drop penalty for the heat transfer enhancement.     

Experimental investigation of turbulent heat transfer and flow characteristics of SiO2/water nanofluid within helically corrugated tubes

Experiments were conducted to investigate the effect of nanofluid on turbulent heat transfer and pressure drop inside concentric tubes. Water and SiO₂ with mean diameter of 30 nm were chosen as base fluid and nano-particles, respectively. Experiments were performed for plain tube and five roughened tube with various heights and pitches of corrugations. Results show that adding the nano-particles in tube with high height and small pitch of corrugations augments the heat transfer significantly with negligible pressure drop penalty. It is discussed on relative Nusselt number and thermal performance of heat exchanger.     

Modeling of turbulent forced convective heat transfer and friction factor in a tube for Fe3o4 magnetic nanofluid with computational fluid dynamics

A numerical study based on the computational fluid dynamics (CFD) method, with a single phase approach, has been presented to determine the effects of nanoparticle concentration and flow rate on the convective heat transfer and friction factor of nanofluid flowing through a plain copper tube in turbulent regime with different Reynolds numbers (3000 < Re < 22000). The nanofluid consists of Fe₃o₄ magnetic nanoparticles, with the average diameter of 36 nm, suspended in water as a base fluid with four particle concentrations of 0.02, 0.1, 0.6 vol.%. Applying the modeling results, two relations were developed to estimate the Nusselt number and friction factor, based on the dimensionless numbers. The results showed that the modeling data were in very good agreement with experimental data. The maximum error was around 10%.