Supercritical Heat Research Articles

Blow-up of the critical norm for a supercritical semilinear heat equation

We consider the scaling critical Lebesgue norm of blow-up solutions to the semilinear heat equation u_{t}=\Delta u+|u|^{p-1}u in an arbitrary C^{2+\alpha} domain of \mathbf{R}^{n} . In the range p>p_{S}:=(n+2)/(n-2) , we show that the critical norm must be unbounded near the blow-up time, where the type I blow-up condition is not imposed. The range p>p_{S} is optimal in view of the existence of type II blow-up solutions with bounded critical norm for p=p_{S} .

Microscale heat transfer and phase change mechanisms of carbon dioxide at near-critical conditions

Recent studies highlight the potential benefits of two-phase carbon dioxide (CO2) systems operating near their thermodynamic critical point. Significant heat transfer coefficients and resistance to critical heat flux from improved vapor phase properties can enable heat transfer and reliability enhancements. However, the physical mechanisms of phase change that govern heat transfer behavior in the near-critical regime of reduced pressures (0.85<PR<1, where PR=P/Pcrit) are not well understood. In the present study, subcooled microscale (hydraulic diameter, Dh=500μm) flow boiling experiments are conducted to elucidate the heat transfer behavior near the critical point and the underlying mechanisms that influence it. Experimental data reveals a deviation from the trends predicted by the Cheng correlation (Cheng, L et al., 2008, “New prediction methods for CO2 evaporation inside tubes: Part II—An updated general flow boiling heat transfer model based on flow patterns.” Int. J. Heat Mass Transfer), in particular, displaying a decreasing peak heat transfer coefficient as pressure increases. Heat transfer in the near-critical regime can be further partitioned into two regions: near-critical boiling (0.85<PR<0.96) that exhibits heat transfer highly dependent on surface temperature, and supercritical-like behavior (0.96<PR<1) exhibiting a strong heat transfer dependence on mass flux. High-speed side-view flow visualization reveals the dominant nucleation mechanism (heterogeneous or homogeneous) governs the heat transfer behavior and is adequately predicted using flow inlet conditions. The present study provides a method for predicting nucleation behavior, which, in turn, facilitates the prediction of heat transfer near the critical point. The continuous alteration of heat transfer in the near-critical regime as a function of PR is underscored by this mechanistic insight, bridging the gap between typical flow boiling (PR<0.85) and supercritical heat transfer (PR>1).

Investigation on heat transfer of supercritical CO2/Xe mixture crossing pseudo-critical temperature cooled in a horizontal circular tube

Supercritical CO2/Xe mixture has a potential application prospect in the Brayton cycle system from the perspective of thermodynamic. Supercritical cooler is one of the key components there. However, the cooling heat transfer characteristics and mechanism of supercritical CO2/Xe mixture is still unclear, which restricts the development and design of supercritical cooler. The heat transfer of supercritical CO2/Xe mixture crossing Tpc cooled in a horizontal tube with inner diameter 8 mm is numerically explored in this study. The influences of operating parameters on supercritical mixture heat transfer are thoroughly examined. Buoyancy effect is evaluated through the buoyancy criterion Gr/Re2. Further, the mechanism of supercritical CO2/Xe mixture cooling heat transfer is revealed. It is found that heat transfer enhancement may occur during supercritical CO2/Xe cooled process, and heat transfer is weakened when mass fraction of Xe increases. Considering the bulk specific heat and buoyancy dominating jointly the behavior of supercritical cooling heat transfer, a modified Dittus-Boelter correlation is newly developed to predict heat transfer coefficient of supercritical CO2 and its mixture with Xe. The correlation matches well with the experimental and numerical data, and the average relative deviations of the new correlation are 18.27 % and 14.14 %, respectively. The investigation provides insight into the characteristics and mechanism of supercritical CO2/Xe mixture cooling heat transfer. The correlation can provide significant theoretical guidance for accurate design and optimization of supercritical cooler.

Interpretable machine learning-based prediction and analysis of supercritical fluid heat transfer characteristics at different boundary conditions

The study of the heat transfer characteristics of supercritical fluids is crucial for the safe and economical operation of supercritical energy systems. This study presents a new method to study the heat transfer characteristics of supercritical fluids, employing interpretable machine learning. Two back propagation neural network models are proposed for the prediction of heat transfer to supercritical fluid for the cases with given heat flux and given wall temperature, respectively. The particle swarm optimization algorithm was employed to search for the optimal hyperparameters, and the resulting accuracy was evaluated in comparison with that of the traditional empirical correlation and a number of machine learning models. Combining the SHAP interpretable algorithm with prediction models, the supercritical heat transfer mechanism is explored from the perspective of global and local prediction behaviors based on explainable models. The results demonstrate that the average error of two established neural network models on the test set is 0.47 % and 0.69 %. Furthermore, for vertical upward flow, the buoyancy and acceleration effects are of greater feature importance in heat transfer deterioration. They are the primary factors contributing to heat transfer deterioration behavior. The research method proposed in this study has certain reference significance for further study of the heat transfer characteristics of supercritical fluids.

Numerical Investigation on Characteristics of Supercritical CO2 Heat Transfer in Vertical Circular Tubes with Circumferentially Half-Side Heating

Numerical Investigation on Characteristics of Supercritical CO2 Heat Transfer in Vertical Circular Tubes with Circumferentially Half-Side Heating

Effect of Channel Shape on Heat Transfer and Mechanical Properties of Supercritical CO2 Microchannel Heat Exchanger

The heat exchanger plays a key role in the S-CO2 power cycle of power generation systems based on waste heat and has a large impact on their cost control and compactness. In this paper, we take the channel shape of a microchannel heat exchanger as the research object and combine orthogonal tests and numerical simulation, taking the microchannel cross-section length/short-axis ratio, volume ratio and filling rate as independent variables, to numerically study multi-channel thermal–fluid–solid coupling and explore the effects of different microchannel cross-section length/short-axis ratios, volume ratios and filling rates on the thermal hydraulic and mechanical properties of the heat exchanger. The results show that a change in the channel volume ratio has a greater impact on the thermal hydraulic performance of the heat exchanger and that its heat transfer performance is only marginally affected by a change in the channel filling rate. Additionally, when other geometric parameters are kept to a certain level, the closer the shape of the channel is to a circle, the better its mechanical properties are. Within the range of permissible designs, a change in the channel volume ratio does not have an obvious impact on the mechanical properties of the microchannels, while the channel filling rate has the most significant impact. The most significant effect of the channel filling rate on the mechanical properties occurs through the channel volume ratio.

Effect of bend orientation on the heat transfer performance of U-bend vapor generator in transcritical ORC

Adequate recognition of supercritical heat transfer characteristics in U-bends is important to guide the optimization of the design and practical application of heat exchanges containing U-bends. Past studies have focused on the heat transfer performance under different operating conditions and geometric parameters, however, the influence of bend orientation on the local heat transfer and overall performance of U-bends is still unclear and rarely reported. This work fills this gap with numerical simulation to quantitatively analyze and explain the heat transfer performance of U-bend vapor generators with three different bend orientations (horizontal, horizontally downward, and horizontally upward). The results show that as the ratio of heat flux to mass flux increases, bend orientation effects start to appear only when the buoyancy parameter Grq/Grth at the bend inlet is above 80 ∼ 95. In all three orientations, horizontally downward flow U-bend has the best average heat transfer performance within the bend, followed by horizontal and horizontal upwardly. However, there is no significant difference in the average performance of the three orientations over the entire bend-affecting region, with a maximum difference of only 5%. Therefore, when the downstream length is much greater than the bend, there is no need to consider the influence of flow orientation. Increasing the bend curvature considerably improves the heat transfer within the bend, and the downstream bend-affecting distance becomes larger as well. However, larger curvature also causes greater fluctuation in the heat transfer coefficient. Finally, heat transfer correlations were recommended and developed for all three orientations. Correlations predict over 93% of the entire dataset with a maximum error of 20%.

Convective Heat Transfer Analysis of Supercritical CO2 in Artificial Rock Fractures

Geothermal energy has emerged as a promising renewable and sustainable resource. This research article explores the utilization of supercritical CO2 and convective heat transfer in porous rock to enhance geothermal extraction. Artificial cement rock with a smooth and manmade slotted surface fracture was used as a working sample for heat transfer source in the test. Heat transfer characteristics under various flow rates, fluid inlet temperature and pressure, rock initial temperature are analyzed. The results indicate that the geometry characteristics of fracture surface impact the overall heat transfer intensity to a certain extent, whereas lithology has little influence on the heat transfer intensity. In addition, it is found that increasing injection pressure affects the operating temperature and density of the injected fluid, which helps to improve the production effect, to obtain more heat. However, limited by the heat transfer area, low injection flow is required. The maximum error of the heat transfer coefficient model is 7.05% compared with the empirical value and less than 10% compared with the experimental results. By examining the interaction between fluid and porous fractures, we aim to provide insights into the potential of these techniques for maximizing energy efficiency and tapping into deep geothermal resources.

Characterization of supercritical CO2 heat transfer in microporous media under (T/p)-mutability and integrated random function

The thermophysical properties of supercritical carbon dioxide (sCO2) undergo drastic changes under reservoir conditions, which significantly affects transfer characteristics and the storage efficiency. The present work seeks to identity of the heat transfer response of a mutable sCO2 in porous micromodels with integrated Boolean stochastic models. An upgraded variant of Lattice Boltzmann model is used after a thorough validation with literature experiments. The injection conditions of sCO2 are ranged from 295 to 333 K and 8–10 MPa, with a mass flow rate of 0.05–0.20 kg/min. The thermodynamic instabilities are discussed through the joint bonds between temperature and density, local and overall heat transfer, and pressure drop coefficient, under a series of pore-throats dimension from 7.5 to 401.3 μm. The results showed: (i) the remarkable (T/p)-nature of heat transfer capacity of sCO2 to lead the transfer coefficients with a subordinate impact of thermal conductivity near the Widom line, as long as the convective mode primes with increased temperature and pressure; (ii) The heterogeneity of the microporous media promoted the decrease of the transfer capacity while adjusting the spatiotemporal density and the heat transfer orientations inside the pore bodies; (iii) the growth of the pressure drop under increasing temperature has revealed an equilibrium stage where, neither the mutability of sCO2 properties nor the injection intensity can significantly affect the heat transfer of the integrated microporous.

Multi-objective optimization study of airfoil fin printed circuit heat exchanger with tip gap based on machine learning

The printed circuit heat exchanger (PCHE), a compact and highly efficient device, is capable of operating effectively under demanding conditions, which makes it ideal for supercritical CO2 Brayton cycles. In this study, we present a novel airfoil fin PCHE with tip gap, and conduct multi-objective optimization on the tip gap and arrangement of airfoil fins based on the analysis of the supercritical CO2 flow and heat transfer characteristics. We conduct a parameter design using Design of Experiment to examine the impact of the dimensionless design parameters, including the horizontal number (ζh), staggered number (ζs), vertical number (ζv), and gap number (ζg). To forecast the flow and heat transfer performance, we utilize a neural network model called Particle Swarm Optimization-Back Propagation (PSO-BP). We employ the non-dominated sorting genetic algorithm II to obtain the Pareto optimal front by utilizing ζh, ζs, ζv, and ζg as variables for optimization, and the volumetric heat transfer coefficient (hv) and Fanning friction factor (f) as objectives for optimization. The results find that the utilization of tip gap can enhance heat transfer while reducing flow resistance. The PSO-BPNN model exhibits higher prediction accuracy and excellent generalization ability compared with traditional BPNN model. The VIKOR and TOPSIS methods identify compromise schemes with excellent thermal-hydraulic performance. The mechanism of heat transfer enhancement can be elucidated using the principle of field synergy.

Numerical study on natural convection heat transfer of supercritical CO2 in an infinite space

A numerical study of natural convection heat transfer from horizontal heating wire to supercritical carbon dioxide (sCO2) in an infinite space was performed. The qw ∼ ∆T curves of sCO2 natural convection heat transfer were calculated in a wide range of parameters, where initial bulk temperature (Tib) and operating pressure (P) varied in the range: 275 K < Tib < 345 K and 7.5 MPa < P < 11 MPa, respectively. Then, we reported from the viewpoint of pseudo-phase transition for supercritical fluids, the characteristics and mechanism of sCO2 natural convection heat transfer were revealed through comparing with qw ∼ ∆T curve of subcritical pool boiling. The similarity between film-like heat transfer at Tw > Tpc for supercritical pressure and film boiling at Tw > Tsat for subcritical pressure was demonstrated. The influence of operating parameters such as Tw, Tib, and P on sCO2 heat transfer was also discussed. For supercritical film-like heat transfer, thermal resistance of film-like which reflects the effect of gas-like film thickness and its thermal conductivity on heat transfer was proposed. Expectedly, the variation of thermal resistance explained successfully the difference of sCO2 heat transfer under different operating parameters. The investigation is of paramount importance in comprehension of sCO2 heat transfer mechanism for designing heat exchanger component in the advanced sCO2 application.

Enhanced flow and heat transfer of aviation kerosene in porous media microchannels

The increasing turbine inlet temperature of the aero-engine requires higher heat transfer capability of the thermal management system. To improve the compactness of the air–fuel heat exchanger in the aero-engine, the heat transfer capability of kerosene can be enhanced by using porous media with a larger surface area per unit. Enhancement of supercritical RP-3 aviation kerosene heat transfer in microchannels by a porous structure and optimization of the structure to reduce pressure loss were investigated through experiments and numerical simulations. It is found that porous structures increase the heat transfer area by more than double, change the flow state, destroy the boundary layer structure, and produce more vortex and secondary flow. At the same time, the kerosene reaches the supercritical state earlier. These factors collaborate to enhance heat transfer with a local Nusselt number approximately six times. Filling the porous structure in the part where the flow has not been sufficiently developed is the main factor of heat transfer enhancement. The flow of the hexagonal shape is more uniform, and its heat transfer capability is better. Using alternating rotating porous microchannels can increase the local convective heat transfer coefficient by 18.6 %. And the optimized design of a partially filled porous microchannel can reduce the pressure loss by 40.7 %.

Optimal design of supercritical He–H2 PCHE in SABER system by multi-objective genetic algorithm

A double-circle straight-channel printed circuit heat exchanger (PCHE) was first employed in a synergistic air-breathing rocket engine (SABER) system for supercritical He and H2 heat transfer. The heat transfer mechanism of the supercritical flow in the PCHE channel was numerically analyzed. For considered the pressure drop, heat transfer efficiency, and ratio of heat flux to weight, simultaneously, the design of the PCHE is multi-objective genetic optimized. The results shown that the supercritical H2 flow is chaotic near the pseudo-critical point, which is a coupled effect of buoyancy and gravity. Chaotic flow leads to an asymmetrical temperature distribution, which deteriorates the heat transfer performance. For 27 numerical experimental cases designed using the center composite surface method, the determine factors of the regression models of the three objectives for both cold and hot sides were all above 92 %. The Pareto optimal solutions for the supercritical He - H2 PCHE design and performance were obtained based on the nondominated sorting genetic algorithm II. From a comprehensive view of the three targets, the optimal designs were the A-4 and B-4 solutions for the cold and hot sides, respectively.

Local solvability and dilation-critical singularities of supercritical fractional heat equations

We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for local-in-time solvability. We introduce the notion of a dilation-critical singularity (DCS) of the initial data and show that such singularities always exist for a large class of supercritical nonlinearities. Moreover, we provide exact formulae for such singularities.

Numerical investigations on heat transfer of supercritical RP-3 flowing in circular tube

This study aims to develop a reliable numerical model for predicting the supercritical heat transfer of aviation kerosene RP-3 in a tube under heating conditions, thereby providing a reference for revealing the mechanism behind the experimental phenomena. Based on validation studies between seven turbulence models and experiments, a numerical method using the Yang-Shih turbulence model is proposed. A detailed prediction of the turbulent flow process is obtained, and the heat transfer characteristics of RP-3 are analyzed. The evolution of parameters and properties in axial and radial directions is demonstrated, followed by investigations of the effects of system pressure, fuel inlet temperature, and mass flow rate. The drastic change in the specific heat of the fuel when its temperature is close to the pseudocritical value and the temperature difference between the area near the wall and the center of the tube are the main causes of the enhancement and deterioration of the heat exchange. A higher inlet temperature increases the heat transfer coefficient, but due to its different effects on decreasing the density and the viscosity, it increases the pressure drop. In addition, larger mass flow rates can promote turbulence intensity and heat transfer, but cause a higher pressure drop across the tube.

Experimental investigation of the supercritical heat transfer of the low GWP refrigerant R1234ze(E): calibration and validation of test rig

Heat transfer of supercritical refrigerants is applied in practical systems such as the transcritical organic Rankine cycle or supercritical heat pump. The concept of supercritical heat transfer is not new and has already been studied and applied for decades in several applications. However, results on one fluid cannot be directly translated to another one. This is because the thermohydraulic behavior of fluids is heavily influenced in the near-supercritical region due to sudden variations in the thermophysical properties when the fluid is heated or cooled close to its critical point. For refrigerants under horizontal flow, the research is limited. Most studies in literature are on small diameter tubes and on R134a, which has a high global warming potential. Therefore, an experimental test rig has been built to measure the supercritical heat transfer of low global warming potential refrigerants over a large temperature and pressure range in the supercritical region. In this work, the calibration and validation of this test rig is presented using the refrigerant R1234ze(E). The test section consists of a 4 m long horizontal tube with an inner diameter of 22.9 mm, equipped with thermocouples at both the tube wall and in the bulk of the flow, and is heated by resistance wires wrapped around the tube. For the calibration, the temperature profiles under both non-heating and heating conditions are evaluated. For the validation, the average Nusselt numbers obtained through experiments under subcritical conditions are compared to the average Nusselt numbers calculated based on the Dittus-Boelter and Gnielinski correlation.

Enhancing supercritical carbon dioxide heat transfer in helical tube heat exchangers with twisted tape inserts: A computational investigation

Supercritical carbon dioxide (sCO2) has recently gained considerable attention due to its unique thermal properties that make it favorable as working fluid in various thermal system. It is particularly promising in cooling application of powerplant in combination with helical tube heat exchanger. One way to further enhance its heat transfer performance is by introducing twisted tape insert to the helical tube heat exchanger working with sCO2. Nonetheless, no study evaluating this idea has been reported, withholding further implementation of this innovative idea. Hence, this study aims to investigate the heat transfer performance of sCO2 in helical tubes with twisted tape inserts. A three-dimensional computational model, considering mass, momentum, and energy conservation, is developed and validated against experimental data. The heat transfer characteristics are evaluated in terms of wall and bulk fluid temperature as well as heat transfer coefficient. The impact of twisted tape width, twisting turns, and operating parameters (heat and mass fluxes) are evaluated to gain understanding on the contribution of these parameters on the heat transfer mechanism of the flow. The results reveal that introduction of twisted tape inserts enhanced heat exchange performance because of the intensified secondary flow within the helical tube. The most notable enhancement takes place when the temperature remains within the pseudo-critical region, driven by the higher thermal conductivity that dominates heat transfer near the wall and the higher specific heat capacity, enabling efficient heat absorption while restraining temperature rise. However, increasing the number of turns and tape width does not necessarily result in a greater heat transfer enhancement. Performance evaluation criterion (PEC) is utilized to evaluate overall performance. Further exploration using the Taguchi method underscores the dominance of operating parameters including mass flux and heat flux, over geometric factors like the number of turns and tape width. Moreover, strong interactions are only observed between geometric parameters (number of turns and tape width) and the temperature difference between the inlet and pseudo-critical points. Results from this study are expected to augment critical information required in developing high performance cooling mechanisms for various thermal systems, especially power plants.

Numerical study on heat transfer deterioration of supercritical CO2 in lattice structure array channel

This study numerically explores the fluid flow and heat transfer features of supercritical carbon dioxide (CO2) in lattice structure array channel. The mitigation mechanism of the miniature cylindrical lattice structure array on heat transfer deterioration (HTD) of supercritical CO2 in vertically upward heated channel is studied. This paper evaluates the effect of several key influential parameters (length, diameter, pitch and number) of cylindrical lattice structure array on fluid flow field involving vortex structures, heat transfer coefficient, buoyancy effect and accelerated effect. The results indicate that the lattice structure can effectively suppress the HTD by generating the vortex structure which promoting the turbulent mixing effect and enhancing the turbulent kinetic energy (TKE) of the fluid. Compared with the smooth channel, the peak wall temperature of the lattice structure channel is reduced by about 50 °C, with a corresponding increase in the heat transfer coefficient of about 140 %. The average heat transfer coefficient of the channel is increased by more than 1/3. Furthermore, by increasing lattice length can reduce flow layer stratification and by increasing lattice diameter can creating a composite vortex, which enhance flow mixing strength. The larger the lattice pitch, the worse the overall suppression effect. A denser lattice arrangement produces more temperature valleys, thereby increasing the heat transfer coefficient. The conclusions in this study could provide the main theory support for security and stability of supercritical CO2 heat exchangers in power system.

Demonstration of a multi-channel fluidized bed particle–supercritical carbon dioxide heat exchanger for concentrating solar applications

High-temperature thermal energy storage in oxide particles at temperatures above 600°C can couple concentrated solar energy with high-efficiency thermal power cycles to provide dispatchable solar-driven electricity. Challenges remain in developing cost-effective primary heat exchangers, which require expensive alloys, to extract the high-temperature thermal energy from the particles to power cycle fluids, such as supercritical CO2 (sCO2) in recuperated Brayton cycles. To explore one pathway for cost-effective, high-temperature particle heat exchangers, the current study demonstrates a shell-and-plate, particle–sCO2 heat exchanger with narrow-channel fluidized beds coupled with micro-channel sCO2 flows in the heat exchanger walls. This study evaluates the feasibility of multiple parallel, narrow-channel fluidized beds in shell-and-plate particle–sCO2 HXs, to achieve high bed-wall heat fluxes at elevated temperatures. A reduced-order model simulates the narrow-channel, fluidized-bed particle–sCO2 heat exchanger to design the fluidized bed geometry, in terms of depth, height, and number of channels,for a nominal 40-kWth heat exchanger at particle and sCO2 inlet temperatures up to 600°C and 400°C respectively. The resulting shell-and-plate heat exchanger design operates with bubbling fluidization of the downward-flowing oxide particles to enhance bed-wall heat transfer. The heat exchanger core is fabricated with etched sCO2 micro-channels in thin wall plates that are diffusion bonded to spacer frames to form the shell-and-plate structure with 12 parallel, fluidized bed channels, 10.4 mm deep. The heat exchanger is tested at the National Solar Thermal Test Facility at Sandia National Laboratories with CARBOBEAD HSP particles at design particle flow rates of 0.20 kg s−1 and inlet temperatures up to 525°C. Results show that fluidization across multiple parallel channel beds can maintain uniform particle inventory with a common freeboard zone above the heat exchanger core. Bubbling fluidization improves particle–wall heat transfer coefficients but also increases axial dispersion of particle thermal energy, which lowers the log-mean temperature difference such that total heat transfer remains relatively constant to within ±10% over a broad range of fluidization gas velocities. The axial dispersion required particle and sCO2 flow rates to be increased by 25% over model-designed conditions to achieve the targeted 40 kWth, which indicates the importance of incorporating axial dispersion into heat exchanger design models and of deploying bed structures to suppress it. This study demonstrates the feasibility and preferred fluidizing gas conditions for particle heat exchangers for releasing high-temperature thermal energy storage systems.

Study on the criterion of the onset of heat transfer deterioration for supercritical CO2 in upward flow

Supercritical fluid heat transfer deterioration (HTD) tends to lower the heat transfer capacity and should be avoided in designing and optimizing heat transfer equipment. It is essential to establish accurate criteria for predicting the onset of HTD. In this study, an experimental investigation of supercritical CO2 in a heated tube with diameters of 8 and 14.5 mm was conducted. By integrating the data obtained from this experiment with experimental data from the published literature, a large dataset covering a wide range of parameters was constructed. Eleven HTD criteria that are only applicable to other fluids and ten HTD criteria that can be applied to supercritical CO2 were compared and evaluated with the experimental dataset. Results show that most of the correlations established for other fluids cannot be directly adapted to CO2. The criteria that only consider mass flux are not accurate for predicting the onset of HTD. With a detailed analysis of the influence pattern of each system parameter on HTD, a new criterion incorporating multiple influencing factors was established. Excellent prediction accuracy of the new criterion was observed from the validation with the experimental dataset.