Heat Transfer Of Supercritical Fluids Research Articles

Numerical investigation on heat transfer of supercritical fluid in a vertical 7-rod bundle

Thermal–hydraulic behaviors in fuel assemblies of supercritical water-cooled reactor (SCWR) have been investigated worldwide since the SCWR was selected as a candidate of the Generation IV nuclear reactors for further development. However, the understanding of thermal–hydraulic behavior of supercritical fluids is still insufficient and a well prediction model has not been established, especially in rod bundles. In this paper, four turbulence models are assessed for simulating the Freon R12 flowing through a 7-rod bundle vertically and the simulated results are validated with experimental data. It is shown that the predicted results by all the turbulence models match the experimental data well in the region far from the pseudo-critical temperature. The ω type turbulence models predict the heat transfer deterioration qualitatively in the near-critical region. Strong non-uniform circumferential temperature distribution is observed in the vicinity of pseudo-critical temperature. The anisotropic turbulence models show that secondary flow structure has little impact on rod wall temperature while the mass flux distribution is non-uniform greatly among different sub-channels. It is interesting that the flow direction exhibits crucial impact on the mass flux distribution as well as the wall temperature distribution which is valuable for future experimental study and fuel assembly design.

Experimental analysis of heat transfer of supercritical fluids in plate heat exchangers

Heat transfer of a supercritical refrigerant with highly variable properties close to pseudo-critical temperature was experimentally investigated in plate heat exchangers. Two different plate corrugation angles (30° and 60°) were examined while the Reynolds and the Prandtl number range from 800 to 4200 and 3.2 to 4.2, respectively. The results are found to be different from those obtained using classical Dittus–Boelter type correlations. Two possible effects were investigated: effect of wall-to-bulk property ratio and that of buoyancy. The former was found to be important and was accounted for in the correlation using the correction factor proposed by Jackson and Hall. The latter was found not to be significant for corrugation angle of 60°. For corrugation angle of 30°, however, buoyancy effects were found to have some influence, yet majority of the data points are found to be within 15% of those predicted using the correlation.

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.

Numerical study of turbulent convection in inclined pipes with significant buoyancy influence

Convection heat transfer in inclined pipes with significant influence of buoyancy is investigated numerically. V2F eddy viscosity turbulence model is used and, to isolate the effect of buoyancy, constant values are used for thermo-physical properties with Boussinesq approximation for the density variation with temperature in the momentum equations. This problem is particularly significant for better understanding of flow and heat transfer in supercritical fluids. It is found that the same mechanism that leads to impairment of turbulence production, and thus heat transfer, in a vertical pipe (α=90°) is present in inclined pipes; however it is less pronounced when α<60°. Secondary flows are observed as a result of buoyancy force leading to non-uniformity of local heat transfer coefficient along the pipe periphery.

Review of the Wall Temperature Prediction Capability of Available Correlations for Heat Transfer at Supercritical Conditions of Water

The validity of the wall temperature predictions by 18 correlations available in the literature for supercritical heat-transfer regimes of water was verified for 12 experimental datasets consisting of 355 data points available in the literature. The correlations were ranked based on criteria like % data with &lt;5% error, % data with &lt;10°C error and minimum error band in temperature prediction. Details of the best fitting correlations were tabulated. The analysis indicated that for normal heat-transfer conditions, most of the correlations give close predictions. However, at deteriorated heat transfer regimes, only very few prediction points are closer to experimental value. Also, in the ranking process, the first position keeps varying, and no one correlation shall be said as the best for all experiments. Evaluation of the applicability of heat flux to mass-flux-ratio-based prediction of heat-transfer deterioration indicated 75% agreement. The empirical formulae linking mass flux for the prediction of the starting heat flux for heat-transfer deterioration indicated 58.33% of agreement. This review indicated that continued precise experimentation covering wide range of parameter conditions near pseudocritical regime and development of correlations is felt necessary for the accurate prediction of supercritical fluid heat transfer.

Heat transfer in supercritical fluids under pulse heating regime

The peculiarities of the heat transfer in supercritical fluids under short characteristic times scale has been studied experimentally. The constant heating power mode for the technique of controlled pulse heating of a wire probe was used for isobaric penetrating into the region of supercritical temperatures. The pressure range was (1–6)p/pс and the temperature range was (0.6–1.6)Тс, where subscript “c” corresponds to the critical point of a substance. The characteristic pulse length was 10ms; the heat flux density through the probe surface was from 1MW/m2 to 10MW/m2. A sharp decrease in the heat transfer intensity for supercritical fluids with respect to that of subcritical liquids has been obtained. A high sensitivity of the heat transfer pattern to the reduced pressure values was revealed as well.

Numerical Simulation of Fluid Flow and Heat Transfer of Supercritical Fluids in Fuel Bundles

A supercritical water-cooled reactor (SCWR) was proposed as a kind of generation IV reactor in order to improve the efficiency of nuclear reactors. Although investigations on the thermal-hydraulic behavior in SCWR have attracted much attention, there is still a lack of CFD study on the heat transfer of supercritical water in fuel channels. In order to understand the thermal-hydraulic behavior of supercritical fluids in nuclear reactors, the local fluid flow and heat transfer of supercritical water in a 37-element fuel bundle has been studied numerically in this work. Results show that secondary flow appears and the cladding surface temperature (CST) is very nonuniform in the fuel bundle. The maximum cladding surface temperature (MaxCST), which is an important design parameter for SCWR, can be predicted and analyzed using the CFD method. Due to a very large circumferential temperature gradient in cladding surfaces of the fuel bundle, the precise cladding temperature distributions using the CFD method is highly recommended.

Numerical Simulation of Heat Transfer of Supercritical Fluids in Circular Tubes Using Different Turbulence Models

In this study, the heat transfer of supercritical fluids in vertical and horizontal circular tubes has been investigated numerically to understand the thermal-hydraulic behavior of supercritical fluids. The simulations are carried out using different turbulence models and the numerical results are compared with the experimental data to evaluate the accuracy and applicability of those turbulence models. Six turbulence models are used in this study, the LB low-Re k-ϵ model, the LS low-Re k-ϵ model, the RNG k-ϵ model, the realizable k-ϵ model, the standard k-ϵ model, and the Reynolds stress model. The comparison shows that the Reynolds stress model gives better agreement with the experimental data than other turbulence models studied in this work.

Numerical Simulation of Heat Transfer of Supercritical Fluids in Circular Tubes Using Different Turbulence Models

In this study, the heat transfer of supercritical fluids in vertical and horizontal circular tubes has been investigated numerically to understand the thermal-hydraulic behavior of supercritical fluids. The simulations are carried out using different turbulence models and the numerical results are compared with the experimental data to evaluate the accuracy and applicability of those turbulence models. Six turbulence models are used in this study, the LB low-Re k-ϵ model, the LS low-Re k-ϵ model, the RNG k-ϵ model, the realizable k-ϵ model, the standard k-ϵ model, and the Reynolds stress model. The comparison shows that the Reynolds stress model gives better agreement with the experimental data than other turbulence models studied in this work.

Numerical Simulation of Fluid Flow and Heat Transfer of Supercritical Fluids in Fuel Bundles

Numerical Simulation of Fluid Flow and Heat Transfer of Supercritical Fluids in Fuel Bundles

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 (R 2 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.

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 ( R 2 and RMSE) with empirical ones. The results obtained by using GMDH type neural network are in excellent agreement with the experimental results.

Numerical study on in-tube laminar heat transfer of supercritical fluids

Abstract Numerical calculations were carried out for supercritical carbon dioxide flowing in miniature tubes with Re less than 1000. The heat transfer coefficient α and friction factor f were numerically studied for different values of the tube diameter, pressure, mass flux, and heat flux. When compared with the constant property flow, where Nu = 4.364 and f = 64/Re for a circular tube under a constant heat flux condition, a large divergence from the constant value was obtained for both Nu and f·Re in the vicinity of the pseudocritical temperature Tm. When cooled under a constant heat flux, Nu attained its peak value when Tb > Tm and its minimum value when Tb

A simplified method for heat transfer prediction of supercritical fluids in circular tubes

This paper presents a new method for heat transfer prediction in supercritical fluids. Emphasis is put on the simplicity of the correlation structure, its explicit coupling with physical phenomena and the selection criteria of the test data. Assessment of qualitative behaviour of heat transfer is carried out based on existing test data and the experience gathered in the open literature. A single dimensionless number, the acceleration number, is introduced to correct the deviation of heat transfer of supercritical fluids from that of conventional fluids. The new correlation structure excludes any direct dependence of the heat transfer coefficient on the wall surface temperature, and eliminates possible numerical instability. The uncertainty analysis of the test data provides information about the sources and the levels of uncertainties of various parameters, and is strongly required for the selection of both the dimensionless parameters implemented into the heat transfer correlation and the test data for the derivation of correlations. Detailed assessment shows that the new correlation gives reasonable prediction accuracy over a wide parameter range and is also capable of predicting heat transfer behaviour in the heat transfer deterioration region.

Modeling heat transfer in supercritical fluid using the lattice Boltzmann method

A lattice Boltzmann model has been developed to simulate heat transfer in supercritical fluids. A supercritical viscous fluid layer between two plates heated from the bottom has been studied. It is demonstrated that the model can be used to study heat transfer near the critical point where the so-called piston effect speeds up the transfer of heat and results in homogeneous heating in the bulk of the layer. We have also studied the onset of convection in a Rayleigh-Bénard configuration. It is shown that our model can well predict qualitatively the onset of convection near the critical point, where there is a crossover between the Rayleigh and Schwarzschild criteria.

Numerical analysis of heat transfer in supercritical water cooled flow channels

Research activities are ongoing worldwide to develop nuclear power plants with a supercritical water cooled reactor (SCWR) with the purpose to achieve a high thermal efficiency and to improve their economical competitiveness. However, there is still a big deficiency in understanding and prediction of heat transfer in supercritical fluids. In this paper, heat transfer of supercritical water has been investigated in various flow channels using the computational fluid dynamics (CFD) code CFX-5.6 to provide basic knowledge of the heat transfer behaviour and to gather the first experience in the application of CFD codes to heat transfer in supercritical fluids. Three different flow channels are selected, i.e. circular tubes, the sub-channel of a square-array rod bundle and the sub-channel of a triangular-array rod bundle. The effect of mesh structures, turbulence models, as well as flow channel configurations is analysed. Based on the present results, recommendations are made on the application of turbulence models to the heat transfer of supercritical fluids in various flow channels. A new definition for the onset of heat transfer deterioration is proposed. A strong non-uniformity of heat transfer is observed in sub-channel geometries. This non-uniformity has to be taken into account in the design of fuel assemblies of SCWR.

Heat Transfer in a Supercritical Fluid: Classification of Heat Transfer Regimes

Because of the dramatic variation of physical properties with a modest change of temperature, no existing engineering correlation or models can accurately predict heat transfer of supercritical fluids. This paper seeks to classify the conditions where the existing models are applicable and to better understand these local heat transfer mechanisms. The first objective is the focus of this paper. FLUENT was employed to compute the wall temperatures for various heat flux and mass flux conditions and to be compared with experimental data. Because the model was developed for a wide range of flow conditions, it was necessary to make certain assumptions. The simulations showed a good agreement with high mass flux conditions, where buoyancy effects could be neglected. The FLUENT model, however, had difficulty predicting the localized low heat transfer rates seen in the combined condition of high heat flux and low mass flux. A new generalized parameter, dependent on the heat and mass flux, was developed to classify under which conditions this FLUENT standard model was applicable. This global Froude number can be used as the parameter to predict under which conditions the buoyancy effect will be dominant and lower heat transfer rates will occur.

Design analysis of core assemblies for supercritical pressure conditions

The increase of steam parameters to supercritical conditions could reduce the power generating costs of light water reactors significantly [Proceedings of SCR-2000 (2000) 1]. Core assemblies, however, will differ from current BWR or PWR design. In this context, this paper summarizes the main results related to a thermal-hydraulic design analysis of applicable fuel assemblies. Starting from a thorough literature survey on heat transfer of supercritical fluids, the current status indicates a large deficiency in the prediction of the heat transfer coefficient under reactor prototypical conditions. For the thermal-hydraulic design of such fuel assemblies the sub-channel analysis code Sub-channel Thermal-hydraulic Analysis in Fuel Assemblies under Supercritical conditions (STAFAS) has been developed, which will have a higher numerical efficiency compared to the conventional sub-channel analysis codes. The effect of several design parameters on the thermal-hydraulic behaviour in sub-channels has been investigated. Based on the results achieved so far, two fuel assembly configurations are recommended for further design analysis, i.e. a tight square lattice and a semi-tight hexagonal lattice.

Tetragonal phase in ZrO 2Y 2O 3 ceramic system

U-bend is widely used as a pipe fitting in heat exchangers, but the flow and heat transfer of supercritical fluid in and following a U-bend have not been well understood yet. This work numerically investigates a heated flow of supercritical R134a in horizontal U-bend tubes. After validating the model against experimental data from U-tube and straight tubes, numerical runs were performed at a constant pressure (1.05 times the critical pressure) with varying mass flux, heat flux, tube diameters, and bend curvatures. Results show that U-bend barely affects heat transfer in the preceding straight section, while significantly affecting flow and heat transfer in and downstream of the U-bend under mixed convection. Local wall temperatures vary sharply in the U-bend and fluctuate after the bend. Remarkable influence can extend to a far distance of 90d downstream. Compared to the straight tube, average heat transfer coefficients increases by 6% to 53% within the U-bend and up to 23% after the U-bend, respectively. The flow field gradually evolves due to the competition between buoyancy and centrifugal forces. The introduction of U-bend disrupts the original development of buoyancy-driven mixed convection. Secondary flows developed in and after the bend is so strong that they have almost an identical effect as the thermal development at the tube entrance. This is the underlying mechanism of better heat transfer performance in U-bend pipes.

Flow and Heat Transfer of Supercritical Fluid

General feature of supercritical fluid is discussed putting stress on its flow and heat transfer characteristics.In section 1 history of investigation and technological background are described briefly. Then the definition of supercritical fluid and descriptions on its thermodynamic and transport properties are made in section 2. The singularity and peculiarity of fluid near the critical point are discussed also. General nature of convective process, natural convection and forced convection of supercritical fluid are explained in section 3, 4 and 5 respectively.