Heat Transfer Of Supercritical CO2 Research Articles

Cooling heat transfer attributions of supercritical CO2 in a spiral groove tube casing heat exchanger: A numerical investigation

Abstract To improve the performance of the CO2 heat pump water heater, the spiral groove tube casing heat exchanger is used as a gas cooler. At present, the flow mode of supercritical CO2 (SCO2) flows between inner and outer tube channels is mainly adopted. However, the efficiency of the gas cooler was studied rarely when the SCO2 flows in the inner tube channel (ITC). So, the heat transfer of SCO2 in the two flow channels are studied and compared in this paper. A physical model of the cooling heat transfer of SCO2 is established for the spiral groove tube casing. The impact of SCO2 pressure, the mass flow ratios of SCO2 and water on the heat transfer attributions of SCO2 in the tube are analyzed using numerical simulation. The outcomes designate that the flow channel in the exchanger can affect the heat transfer attributions of SCO2. When the mass flow ratio of SCO2 becomes lower, the average heat transfer coefficient (h) of SCO2 flowing between inner and outer tube channels is higher, with about 2.09%. As the mass flow ratio of SCO2 rises, the average h of SCO2 flowing in an ITC is higher, with about 3.90%. Moreover, both the safety of the system operation and the heat transfer attributions of the functioning medium should be considered, the flow mode of SCO2 flows in the ITC is recommended.

Study on Flow and Heat Transfer in Supercritical CO2 in Micro-channel Heat Exchanger

In order to investigate the flow and heat transfer performances of supercritical CO2 in the PCHE, a two-dimensional micro-channel heat transfer model was established. The impacts of the airfoil fin arrangement on flow and heat transfer of supercritical CO2 in a PCHE were studied using Computational Fluid Dynamics software. The results show that the transfer efficiency of PCHE can be effectively improved by reducing the abeam and vertical distances between airfoil fins. However, the pressure drop of supercritical CO2 flow in the microchannel reduces with an increase in abeam and vertical spacing distances.

Experimental and numerical investigation on the mechanisms of novel heat transfer deterioration of supercritical CO2 in vertical tubes

Understanding the mechanisms of supercritical CO2 heat transfer deterioration (HTD) has significant importance for ensuring the safety and reliability of supercritical Brayton cycles. Therefore, the effects of mass flux, wall heat flux, and tube diameters on the heat transfer characteristics of supercritical CO2 inside vertical tubes are studied using experimental and numerical methods. Results indicate that the heat transfer performance is positively influenced by an increase in mass flux and heat flux, as well as a decrease in tube diameter. When HTD occurs, the overall heat transfer performance is indeed significantly compromised. When the bulk fluid temperature exceeds Tpc, the thermal acceleration effect amplifies the mainstream velocity, stabilizing the Kelvin-Helmholtz instability between the pseudo-two-phases, thereby causing a new type of HTD that is named Type II HTD in this paper. The so-called post-dryout HTD occurs when the bulk temperature surpasses T+, causing a complete transition from pseudo-liquid to pseudo-gas state and resulting in a pseudo-single-phase flow. The heat transfer capability of the low-density and low-thermal-conductivity pseudo-gas diminishes as the temperature rises, leading to post-dryout HTD. The present work explains the mechanisms of two types of HTD and highlights the similarities between subcritical boiling and supercritical pseudo-boiling flow structures. This study also establishes a theoretical foundation for understanding pseudo-two-phase flow patterns during pseudo-boiling.

Machine learning and prediction study on heat transfer of supercritical CO2 in pseudo-critical zone

The utilization of supercritical carbon dioxide(S-CO2) as a working fluid in energy conversion systems has gained widespread recognition as an efficient and environmentally friendly option. However, accurately predicting the heat transfer process is still challenging due to the significant variation of thermophysical properties within the pseudo-critical zone. The accurate prediction of the S-CO2 heat transfer process is of utmost importance for the design of heat exchangers and the safe operation of the system. Aiming at the current problems of high experimental cost and long numerical simulation time, machine learning is adopted in this paper to predict the heat transfer characteristics of S-CO2 in this temperature region. In this paper, the heat transfer process of S-CO2 flowing upward in a circular tube under heating conditions is taken as the research object, and a total of 11,032 sets of experimental data samples in the open literature are collected. Four machine learning models, namely, Random Forest (RF), Extreme Gradient Boosting (XGBoost), Support Vector Machines (SVR), and Artificial Neural Networks (ANN) are trained by taking mass flow rate, wall heat flux, pressure, fluid enthalpy, and tube diameter as the input parameters, and wall temperature as the output parameter. The prediction performance of the four machine learning models and the heat transfer correlations were compared. The results show that all four machine learning models have excellent prediction performance, and the ANN model provides the best prediction performance, with an R2 of 0.995 on new data. XGboost and ANN can accurately predict the heat transfer deterioration when the fluid temperature (Tb) approaches the pseudo-critical temperature (Tpc) or over Tpc, yet the accuracy decreases in the region of Tb < Tpc, suggesting that the prediction error is mainly originated in this region. Compared with the existing heat transfer correlations, the prediction accuracy of the ANN model obtained from the training in this paper is higher. The present study further elucidated the feasibility and accuracy of utilizing an ANN model for predicting the S-CO2 heat transfer process. A trained ANN model is a useful tool that can be directly applied to system design and heat exchanger design.

Analysis of heat and mass transfer characteristics of supercritical CO2 in vertical U-tube

The heat and mass exchange of CO2 in a vertical U-tube under supercritical pressure was simulated. The effects of the geometry of the bend area, The center arc radius of the bend area and the different bend orientations on the flow heat transfer of supercritical CO2 in the U-tube were analyzed. The results show that in the bend area, the flow is affected by the combined action of centrifugal force and gravity, as well as the pipe structure, so the flow mixing is intense, and the heat transfer capacity is significantly enhanced. When the direction of the bend changes, the interaction between centrifugal force and gravity will affect the heat transfer at pipe bending. When the central arc radius r of the bend area increases from 0.5D to 3D, the heat transfer at the bend can be strengthened, but will weaken the heat transfer at the bend outlet area.

Rapid 2-Dimensional prediction of supercritical CO2 heat transfer behaviors in inclined tubes based on deep learning

At present, there is a dearth of empirical correlations for the prediction of the inclined supercritical heat transfer. Considering the shortage of the rapid prediction method in the initial design stages for the supercritical fluid heat exchanger with inclined tubes or under inclined conditions, a 2-Dimensional rapid prediction method based on the numerical method combining deep learning method was proposed to reconcile the accuracy and the efficiency of the inclined supercritical heat transfer behaviors prediction. In order to train the deep learning model, 200 numerical cases with 520,000 data were conducted. After that, 7 new cases were chosen to analyze the inclined heat transfer behaviors and validate the current model. The results were indicative of a significant circumferential inner wall temperature difference in the inclined supercritical heat transfer. The temperature difference was larger when the inclined angle was closer to 90°, even though the circumferentially averaged temperature is smooth and acceptable. This potential temperature difference would not only cause large thermal stress which may accelerate fatigue failure, but also increase the risk of over-temperature. Fortunately, the current deep learning model could predict the 2D temperature distribution of these new cases with the max absolute relative error of 16.60%. Therefore, the circumferential inner wall temperature distribution of the inclined supercritical CO2 heat transfer could be evaluated during the initial heat exchanger design. Moreover, the trained model and the relative files are available at Supplementary materials.

Numerical study on flow structure and heat transfer of supercritical CO2 in tubes with different inclination angles

To reveal how buoyancy affects heat transfer of supercritical carbon dioxide (sCO2), the flow and heat transfer characteristics of sCO2 in circular tubes with an inner diameter of 19 mm at different inclination angles were numerically investigated. The calculation results of RNG k−ϵ, RKE k−ϵ, SST k−ω and SST k−ω using a variable turbulent Prandtl number model (TWL model) have been compared with experimental data. The TWL model is chosen for numerical calculations because of its significant advantage in predicting wall temperature. Both forced convection (Richardson number Ri < 0.1, weak buoyancy) and mixed convection (Ri > 0.1, strong buoyancy) of sCO2 are calculated. Result shows that the position of the velocity peak moves upward, then downward as the flow changes from vertical upward (inclination angle α = 0°) to horizontal flow (α = 90°) due to the secondary flow caused by radial buoyancy and the increase in velocity magnitude in the near top wall region caused by axial buoyancy. Under strong buoyancy effects, as α increases from 0° to 90°, the heat transfer deterioration (HTD) becomes severe when α < 15°, then alleviated and finally severe again when α approaches 90° due to the change of the heat transfer mechanism. This work deepens our understanding of sCO2 heat transfer and may provide reference for the design of heat exchangers in nuclear reactors.

Impact of adiabatic entrance length on numerical simulations of supercritical CO2 heat transfer in horizontal circular tubes

Horizontal supercritical carbon dioxide (sCO2) pipe-flow studies in the heat transfer literature commonly use a fixed-length adiabatic hydraulic development section prior to the heat transfer region. It is expected that the length of the adiabatic entrance region is long enough to generate hydrodynamically fully developed flow, such that the influence of the entrance is eliminated. However, despite the criteria for subcritical flows being well established, the criteria defining the adiabatic entrance length for sCO2 flows are not as clear. In this paper, 6-mm-diameter round tubes with heat-flux-to-mass-flux ratios (q/G) equal to 60 J/kg are considered. The tubes have adiabatic entrance lengths between 0 and 1000 mm (0 and 167D), followed by a 500 mm (83D) heat transfer cooling section. An assessment of the effect of adiabatic entrance lengths on flow development and heat transfer behavior is given. An analysis of several flow features such as centerline pressure, centerline velocity, axial velocity profile, wall shear stress, and local heat transfer coefficient are presented. Based on findings for a 6-mm-diameter tube with cooling heat flux boundary conditions and a q/G ratio equal to 60 J/kg, it has been determined that a critical adiabatic length, which is the minimum entrance length necessary to achieve hydrodynamically fully developed flow, of greater than 60D is required.

Progress and Prospects for Research and Technology Development of Supercritical CO2 Thermal Conversion Systems for Power, Energy Storage, and Waste Heat Recovery

CO2 is an environmentally friendly heat transfer fluid and has many advantages in thermal energy and power systems due to its peculiar thermal transport and physical properties. Supercritical CO2 (S-CO2) thermal energy conversion systems are promising for innovative technology in domestic and industrial applications including heat pump, air-conditioning, power generation, renewable energy systems, energy storage, thermal management, waste heat recovery and others. Both S-CO2 and transcritical CO2 thermodynamic cycles have been extensively investigated in order to improve the efficiencies of thermal and power systems and achieve net zero carbon emissions. This paper focuses on the progress and prospects for current research and technology development of S-CO2 thermal energy conversion systems and their applications including power generation, energy storage and waste heat recovery. First, the CO2 thermal transport and physical properties and benefits using CO2 as a heat transfer fluid in thermal energy and power systems are discussed. Then, classification of CO2 thermodynamic systems is presented. Next, S-CO2 for power generation, energy storage and waste heat recovery systems are presented. Finally, research needs of subcritical and supercritical CO2 heat transfer, fluid flow and heat exchangers for the development of various thermal energy and power systems are discussed.

Prediction of supercritical CO2 heat transfer behaviors by combining transfer learning and deep learning based on multi-fidelity data

The flow and heat transfer characteristics of supercritical CO2 are important for heat exchanger design and the safe operation of supercritical CO2 power cycles. However, it is difficult to predict the supercritical heat transfer behaviors due to the non-monotonic temperature distribution in the case of the heat transfer deterioration (HTD) phenomenon. For low-cost, fast and accurate prediction of the supercritical heat transfer behavior, this study proposed a transfer learning model based on multi-fidelity data to achieve fast prediction with acceptable accuracy over a wide range of working conditions. This method fully utilized the low fidelity data (empirical correlations) and the medium fidelity data (numerical results) to generate a large amount of data for pretraining, in which the Latin Hypercube Sampling (LHS) method combined with the HTD correlation was used for sampling. For fine-tuning, high fidelity data from experiments was employed. Compared to the deep learning model trained directly with high fidelity dataset, the transfer learning model demonstrated vastly improved predictive performance on both the test and validation datasets. Additionally, the coefficient of determination R2 was discussed to preventing from “physical overfitting”. Instead of excessively pursuing the high R2 (close to 1), the validity of the prediction should be concerned, especially when using the non-smooth experimental data as the dataset for model training. Moreover, the trained models and the relative files are available at Supplementary materials.

Numerical investigation on flow and heat transfer of supercritical CO2 in variable cross-section tubes under precooler working conditions

The performance of the precooler in the supercritical CO2 (S-CO2) Brayton cycle may be greatly affected by the interactions between the structure and the thermophysical properties. Variable cross-section tubes, which can effectively enhance heat transfer and reduce pressure drop, can be adopted in the precooler. In this paper, the flow and heat transfer performance of S-CO2 in a circular tube and variable cross-section tubes with different unit length divergent ratio (DR) and convergent ratio (CR) is firstly investigated when the heat transfer area is kept constant. The results show that the converging tubes can effectively enhance the heat transfer compared with the circular tube, and a greater CR is more beneficial for heat transfer. The heat transfer coefficient (htotal) is increased by 84.77% at the maximum. The diverging tubes are found to have a strong advantage in reducing the pressure drop, and a larger DR is more helpful to reduce pressure drop, with a maximum decrease of 84.4%. The heat transfer mechanism is analyzed from the aspects of flow field distribution, thermophysical property changes and buoyancy effect. Furthermore, combined with the performance of different variable cross-section tubes, two new hybrid tubes are proposed based on the idea of partitioned heat transfer enhancement matching the thermophysical property changes under the constant heat transfer area condition. The comprehensive thermal–hydraulic performance of the two hybrid tubes is significantly improved compared with that of the converging tube. A 34.81% higher htotal and a 6.25% lower pressure drop can be obtained when using the hybrid tube A under high heat flux conditions. The hybrid tube B is found to enhance heat transfer by 54.98% and reduced pressure drop by 55.14% under low heat flux conditions. Finally, the flow and heat transfer characteristics of different types of tubes are also further studied under the constant inlet Reynolds number condition. This study can provide some guidance for the design and optimization of precoolers where the thermophysical properties of the working fluid are highly variable.

Computational investigation on turbulent heat transfer of supercritical CO2 in the half-roughen horizontal pipe

To address the heat transfer degradation that occurs in the top section of horizontal pipes when sCO2 fluid flows are heated, the upper half wall with higher temperatures is particularly roughened using uniform sand-grain roughness. The SST k−ω model is validated and used to simulate the horizontal sCO2 heat transfer involving a variety of operating parameters and roughness heights. Results indicate that the half-roughen scheme is effective in significantly reducing higher temperatures of the entire upper wall and improving heat transfer homogeneity. The roughness height plays a crucial role, and an optimal value exists, which is largely influenced by the buoyancy strength and its local variations of horizontal sCO2 flows under different conditions.

Experimental study on cooling heat transfer performance of supercritical CO2 in zigzag printed circuit heat exchanger

The zigzag printed circuit heat exchanger (PCHE) is promising as the precooler in the application of supercritical CO2 (S-CO2) Brayton cycle. In this study, the experimental investigation is conducted to explore the heat transfer performance of supercritical CO2 in the mini channels of zigzag PCHE. The experimental range of pressure, temperature and mass flux is 7.5–9.0MPa, 50–90°C and 300–600kg/(m2·s), respectively. The structural parameters of diameter, pitch, and bend angle are D=2.0mm, Lp = 7.24mm and θ = 40°, respectively. The effects of system pressure, inlet temperature, and mass flux on the heat transfer performance of supercritical CO2 are investigated by measuring multiple temperature points along the zigzag channel. The results show that the heat transfer coefficient exhibits a higher level near the pseudocritical region due to the dramatic thermophysical properties variation of supercritical CO2. Meanwhile, both the change of mass flux and pressure have a significant influence on the S-CO2 heat transfer coefficient, while the effect of inlet temperature is relatively small. Furthermore, the comparison is conducted between the existing heat transfer correlations and the experimental results. Four new cooling heat transfer correlations are proposed and compared by considering the effect of velocity change and cross-sectional thermophysical property variation on heat transfer performance. It is found that adding variates to the correlation can improve the prediction accuracy of the results while iterative calculation becomes more difficult. In order to improve the robustness and prediction accuracy, it is determined to choose the correlation without the density form, which predict 91.5% of the experimental data within ±25% error band.

Experimental investigation of the effects of transverse vibration on the supercritical CO2 heat transfer characteristics in horizontal tubes

It is inevitable for mechanical motion to generate vibration, which may affect fluid heat transfer. Although some developments on heat transfer in supercritical carbon dioxide (S-CO2) have been established, there is none research on the impact of vibration on S-CO2 heat transfer currently. The effect of transverse vibration on heat transfer characteristics of S-CO2 in 1200 mm tube is investigated experimentally in this study. The results demonstrate that the vibration enhances the heat transfer of S-CO2 clearly. With the increase of the vibration amplitude, frequency, mass flux, or pressure, the heat transfer enhancement efficiency (HTE) tended to rise, and the HTE of the upper vertex is better than the lower vertex. Within the test range, the highest average HTE is 10.2%. Along the tube, the local HTE in the pseudo critical region is much more noteworthy than in other regions. Finally, the heat transfer correlation is proposed in accordance with the experimental findings, and 95.6% of the data error is within ±15%.

CFD investigation of flow and heat transfer of supercritical CO2 in wire wrapped rod bundle

Computational fluid dynamics is increasingly applied to reactor safety analysis, and the applicability evaluation of turbulence model can effectively improve the calculation accuracy. In this paper, the applicability of six turbulence models and two near wall models is compared for simulation of flow and heat transfer of supercritical carbon dioxide in wire wrapped rod bundle. According to experimental data under various conditions, the applicability of turbulence models and near wall models is respectively evaluated from wall temperature and surface heat transfer coefficient. The results show that SST k–ω model combined with low-Re model can simulate the change of wall temperature and surface heat transfer coefficient in critical state best, and the average relative error (Tw and h) is 6.88% and 13.17%. When CO2 is heated into supercritical state in the latter 900 mm of wire wrapped rod bundle, the relative error (Tw and h) calculated by RNG k–ω model is 5.94% and 18.02%. The grids number of low Re method is nearly double of the grids number of wall function method. Therefore, the simulation results computed by wall function method at supercritical region are also acceptable due to the low computational consumption. This paper researches the applicability of turbulence model and near wall model to enhance the accuracy of simulation of flow and heat transfer in supercritical CO2 reactor rod bundle.

Investigation of field synergy principle for convective heat transfer with temperature-dependent fluid properties

The field synergy principle is widely used in the analyses and optimizations of convective heat transfer, but its original derivations are based on fluids with constant thermal properties. The applicability of the principle for fluids with temperature-dependent properties needs clarification. A theoretical analysis of the problem is conducted. It is found that a synergy principle of mass flux vector and specific enthalpy gradient is more fundamental. Because temperature gradients are parallel to specific enthalpy gradients, the original field synergy principle of velocity and temperature fields is still valid. Heat transfer of supercritical CO2 and molten salt in different finned channels is numerically studied, and different mean synergy angles are compared. It is found that the domain integration mean synergy angles calculated with specific enthalpy gradient or temperature gradient have the same trends. For the volume-weighted mean angles, the absolute value of dot product of velocity and temperature gradient should be used in calculating the local synergy angles. Otherwise, the trend of the volume-weighted mean angles can be contrary to the field synergy principle. Meanwhile, the accuracy of the mesh and the temperature gradient near the heat transfer surfaces is important for the numerical applications of the field synergy principle.

Heat Transfer Characteristics of CO2 in a Horizontal Tube under Subcritical and Supercritical Pressures

Supercritical CO2 heat transfer in vertical tubes has been widely studied, but limited work exists for that in horizontal tubes. In this work, experiments were conducted for CO2 in a horizontal tube with inner diameter of 8 mm under wide range of pressures (5.51–20.41 MPa), covering both subcritical and supercritical conditions. The ranges of heat flux and mass flux were 97.5–404.0 kW/m2 and 510.2–1314.2 kg/m2s, respectively. The heat transfer for subcritical pressure far below critical pressure showed typical flow boiling characteristics, with a wall temperature peak along the tube corresponding to departure from nucleate boiling. For near-critical pressure, it showed characteristics similar to supercritical heat transfer, with continuous increase of wall temperature along the tube. The effects of different parameters including pressure, mass flux, and heat flux on the heat transfer behavior were analyzed and discussed. Moreover, using the pseudo-vapor quality concept of the supercritical three-regime-model introduced in a previous work, the heat transfer coefficient was found to behave very similarly between subcritical and supercritical conditions. The experimental results showed significant deviation from single-phase convection within the two-phase/two-phase-like region compared with the single-phase regions, and which validates the similarity between subcritical boiling and supercritical pseudo-boiling.

Experimental study on turbulent convection heat transfer of supercritical CO2 in cooled inclined miniature tubes

This study explores experimentally turbulent convection heat transfer characteristics of supercritical carbon dioxide (CO2) in cooled miniature tubes (Dh = 1 mm) with various inclined angles (θ = 0, 30, 60 and 90°). The influence of tube inclined angles, CO2 mass flow rates and wall heat fluxes on wall temperature and heat transfer coefficient were analyzed. Results related to buoyancy effect and thereby affected heat transfer were discussed. It was found that the wall temperature and the heat transfer coefficient markedly increase with the increased inclined angle, indicating the gradual weakness of mixed convection flow with the increased inclined angle. This effect was strengthened as mass flow rate decreased. In addition, the liquid-like region witnesses more significant influence of buoyancy effect on the heat transfer coefficient. Increasing mass flow rate could promote the heat transfer intensification, accompanied by the flow shifting from mixed convention flow to forced convection flow. The heat transfer coefficient is independent of the wall heat flux in liquid-like region, and slightly increased with the augment of wall heat flux in gas-like region. Given that the previously existing heat transfer correlations showed large deviations in predicting the present experimental data, a set of new correlations were proposed for cooling heat transfer prediction of supercritical CO2 in inclined miniature tubes and yield excellent predictive capability, evidenced by overall mean obsolete error of 11.13%, 7.72%, 12.30% and 14.24% for the inclined angle θ = 0°, 30°, 60° and 90° respectively.

Enhancement analysis of turbulent flow and heat transfer of supercritical CO2 in a static mixer with three helical blades

Enhancement analysis of turbulent flow and heat transfer of supercritical CO2 in a static mixer with three helical blades

Experimental investigation on natural circulation heat transfer of supercritical CO2 in a closed loop

The natural circulation system based on supercritical CO2 has attracted attention due to its simple structure and safety compared with the forced circulation system. This work presented an experimental investigation of the heat transfer characteristics of CO2 based on natural circulation. Two heat transfer modes can also be observed in supercritical CO2 natural circulation, normal heat transfer and heat transfer deterioration. The development of heat transfer deterioration criterion and heat transfer correlation is significant for the application of supercritical CO2 natural circulation, but there are few related studies. Direct adoption of the supercritical CO2 forced convective criteria and heat transfer correlations to natural circulation introduces large deviations. By analyzing the existing research results of forced convection in supercritical CO2 and introducing new dimensionless parameters SBO and K, a deterioration criterion and a heat transfer correlation suitable for natural circulation of supercritical CO2 are developed based on experimental data. The new criterion can well distinguish the two heat transfer modes, and the new correlation improves markedly. The results can benefit engineering applications in advanced power cycles.