Pseudo-critical Region Research Articles

A comparative analysis of ammonia and supercritical carbon dioxide in horizontal microchannels

Supercritical carbon dioxide (sCO2) and ammonia (NH3) can be used as coolants in high power-density microelectronics. sCO2 at the micro scale provides enhanced heat transfer solutions for a range of microelectronics cooling applications·NH3 can also potentially provide appropriate cooling solutions as it has favorable thermophysical properties at high pressure, and it can be used as an energy carrier as it contains Hydrogen atoms. Near its critical and pseudocritical condition sCO2 exhibits abrupt changes in its thermophysical properties and at similar pressures liquid NH3 too has adequate properties that make it a good coolant. While sCO2 is non-toxic, NH3 is a toxic substance and should only be used in closed loop micro heat exchangers.The current study compares the convective heat transfer performance of supercritical carbon dioxide (sCO2) and ammonia for microchannel cooling. A total of 144 numerical cases inside a square microchannel of hydraulic diameter of 200 µm with a total length of 52 mm and a heated length of 50 mm at constant surface temperatures in laminar flow conditions were examined. Two scenarios were investigated, in one the inlet mass flux was kept constant at 100, 150, and 200 kg/m2s, and in the second the pressure drop across the microchannel was maintained at 200, 400, and 600 Pa. Both scenarios were investigated at pressures of 8 and 10 MPa and at surface temperatures of 32, 40, 50, 60, 70, and 80 °C. In all cases the inlet temperature of both fluids was kept at 21 °C. At the same mass flux, NH3 yielded a higher average heat transfer coefficient (havg) but at the same pressure drop, sCO2 resulted in higher havg at certain surface temperatures. The havg for NH3 didn’t show significant variation but for sCO2 it showed significant change with surface temperature, and this was due to the significant change in the thermophysical properties of sCO2. The havg showed a mixed behavior with respect to the pumping power. The coefficient of performance (COP) was as high as 600,000 for sCO2 and it was significantly higher than that for NH3. Near the pseudocritical region, the COP for sCO2 witnessed a significant improvement, more than double, for 8 MPa compared to 10 MPa.

Assessment of Look-up tables for the prediction of heat transfer coefficient distribution in rod bundles cooled by supercritical water

The evaluation of available Look-Up Tables for prediction of heat transfer coefficient distribution in rod bundles cooled by supercritical water with the aim of their further use in computational analyses of various Fuel Assembles of Supercritical Water-Cooled Reactors is made. The comparison between the calculations based on Look-Up Tables with the values from empirical correlations and experimental data for smooth and wire-wrapped rod bundles was presented. The obtained results showed that Look-Up Table of the University of Ottawa, which was created to describe improved and deteriorated heat transfer regimes in round tubes, allows describing available data points with 30 % of the mean square deviation. It is noted that the presence of wire intensifies heat transfer exchange near pseudocritical temperature region but existing versions of Look-Up Tables cannot take into account this effect. Nevertheless, there is potential for further improvement in predicting the heat transfer coefficient using Look-Up Table by introducing additional correction factors.

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.

Effect of operating regimes on the heat transfer and buoyancy characteristics of supercritical CO2 natural circulation loop - A numerical study

At present, 82% of global energy is generated by fossil fuels which produce substantial emissions and have a significant impact on the environment. Heat transfer devices play a vital role in enhancing the efficiency of power generation systems and mitigating environmental impact. Among various heat transfer devices, natural circulation loops (NCLs) assume significance due to their simplicity and safety. In the present study, numerical investigations were conducted on three-dimensional rectangular circular cross-section supercritical CO2-based NCL across three distinct operating regimes. These regions include the average temperature of NCL maintained near the widom line (near pseudo-critical region), away from the widom line (higher buoyancy region) and very far away from the widom line (deeply supercritical region). The results indicate that in all regions, there is an increase in both the mass flow rate and heat transfer rate as pressure increases. At a pressure of 14 MPa, the maximum heat transfer rate across all regions is observed. Although the higher buoyancy region exhibits a superior heat transfer rate, the near pseudo-critical region demonstrates efficient heat transfer capabilities. For example, at 11 MPa, the temperature difference in the higher buoyancy region exceeds that in the near pseudo-critical region by 73%. However, the reduction in heat transfer rate in the near pseudo-critical region is only 37% compared to the higher buoyancy regions. For low-temperature applications, the near pseudo-critical region effectively transfers heat. However, in high-temperature applications, the sink temperature should be kept in the liquid-like region to maximize system buoyancy.

Buoyancy influences on local heat transfer characteristic of supercritical LNG across the pseudo-phase transition in variable cross-section horizontal channels

The regasification process within the printed circuit heat exchanger (PCHE) channel for supercritical liquefied natural gas (S-LNG) will produce a large temperature difference. This process is considered a pseudo-phase transition process, and the resulting density difference driving buoyancy has a crucial action in influencing the heat transfer and flow of S-LNG. Three horizontal variable cross-section channels are established to examine the buoyancy impact on the local heat transfer and flow of S-LNG within the pseudo-phase transition process in the PCHE channel. It comprehensively analyzes the buoyancy impact on local heat transfer and flow under different channel shapes and mass flow rates. The findings demonstrated that the eddy blockage caused by buoyancy mainly acts on the top of the channel and mainly occurs in the liquid-like and pseudo-critical regions, resulting in the deterioration of local heat transfer on the upper and lower walls of the channel. The hybrid channel achieves the intended design goal, and the diverging channel is almost unaffected by buoyancy. The overall performance evaluation criterion (PEC) is used to evaluate the thermal and hydraulic performance of each channel under different mass flow rates. The data show that the diverging channel has the best thermal and hydraulic performance, and its PEC can reach 1.28. The hybrid channel also achieves the expected effect, and its PEC can reach 1.09.

Investigation of local flow and heat transfer of supercritical LNG in airfoil channels with different vortex generators using field synergy principle

Vortex generators（VGs） have gained significant attention as a potential technology for enhancing heat transfer. This study introduces a novel delta airfoil VG with the objective of improving the heat transfer efficiency of heat exchangers. The overall heat transfer performance of four types of printed circuit heat exchanger (PCHE) channels is evaluated using three-dimensional numerical analysis in this paper. These channels comprise of two VGs with different shapes and installations, along with NACA0024 airfoil fins. The delta winglet VG (DWVG), the delta airfoil VG (DAVG), and the delta airfoil staggered VG (DASVG) are the VGs used in the three PCHE channel configurations. The performance of the four PCHE flow channels is assessed using the dimensionless thermal enhancement factor (TEF). To investigate and explain the interaction between VGs and flow structure distribution as well as heat transfer, the secondary flow number Se and the field synergy principle are employed. The results show that the local field synergy angle of the channel with VGs is smaller than that of the non-VG baseline case, indicating the best enhanced heat transfer in the pseudo-critical region. Among the four cases, the DAVG exhibits the best hydrothermal performance, and the local heat transfer coefficient can be increased up to 120%, which aligns with the interpretation of the field synergy principle.

Research on the flow and heat transfer characteristics of RP-3 and structural optimization in parallel bending cooling channels

The regenerative cooling channel is curved due to the unique structural form of the combined nozzle of the turbine-based combined cycle engine for hypersonic flight. Research on the flow and heat transfer characteristics of fuel in the parallel bending cooling channels is insufficient, which causes difficulties in properly designing the thermal protection structure of the combined nozzle. This paper numerically investigated of the flow and heat transfer characteristics of hydrocarbon fuel RP-3 under non-uniform heating conditions in parallel bending cooling channels. The basic heat flux is 0.50 MW/m2, and the heat flux ratio of the upper and lower channels is 1.2, 1.5, and 2.4 respectively. The heat transfer and flow distribution mechanisms of RP-3 in parallel bending channels are revealed. The bending structure is beneficial to reduce thermal stratification and prevent heat transfer deterioration caused by buoyancy. In the pseudo-critical region of the channel, a “thermal insulation zone” is formed due to the low thermal conductivity of RP-3, which hinders the transfer of heat to the mainstream and causes heat transfer deterioration. When the fluid temperature is below 455 K, viscosity is the primary factor affecting the flow resistance difference between parallel channels. As the temperature further increases, the density difference and velocity difference between the parallel channels dominate in the flow resistance differences. Additionally, a connected hole structure in the middle of the bending section has been applied to optimize the flow deviation of parallel bending channels, which promotes the secondary distribution of flow. Finally, the influence mechanism of the connected hole on flow distribution has been studied under different heat flux ratios and connected hole widths.

The role of buoyancy and thermal acceleration in heat transfer deterioration and thermal oscillation for the CO2 around pseudo-critical region

Trans-critical CO2 Rankine cycle has great potential in converting low-grade heat into electricity, because of its good temperature glide matching between working medium and heat source. However, the drastic variation in thermo-physical properties of CO2 around the pseudo-critical region causes the abnormal flow and heat transfer behaviors. In this paper, the heat transfer deterioration and thermal oscillation in the heat addition of trans-critical CO2 cycle are investigated by experiments. The test section is heated uniformly by a DC power (0∼6 kW) and the minimum Reynolds number in the test section inlet is about 8000 (it is much larger than 2300) for the all cases. A shear stress reconstruction model is corrected by introducing the velocity profile of turbulence in the boundary layer to attempt to provide a quantitative criterion for deterioration and oscillation. The role of buoyancy and thermal acceleration in heat transfer deterioration and thermal oscillation is elucidated by connecting the shearing-stress reconstruction model and experimental results. It is found that, the thermal acceleration in the near-wall zone provides the key motivation to drive the heat transfer deterioration. The thermal oscillation is driven by the transition between partial and full re-laminarization flows in the local zone of heat transfer deterioration. When (Δτa/τw)<1&(Δτ/τw)tot>1 or 0.1<(Δτ/τw)tot<1, the turbulence is partially re-laminarized. When(Δτa/τw)>1&(Δτa/τw)>>(Δτbo/τw), the intense thermal acceleration causes the turbulence to be fully re-laminarized in the near-wall zone and it maintains the new laminar boundary . The turbulence is partially re-laminarized in the lower boundary and it is almost full re-laminarization in the upper boundary of the oscillation wall temperatures. The results confirm that the emergence of heat transfer deterioration and oscillation instability in mixed turbulent convective relate with the change of flow states caused by acceleration and buoyancy effects.

Study on the dynamic characteristics of thermal oxidation deposition of aviation kerosene under supercritical pressure

Thermal oxidation deposition of aviation kerosene has a significant impact on the long-term operation of aircraft. In this study, a two-dimensional axisymmetric numerical model incorporating a pseudo-detailed chemical kinetic model of thermal oxidation deposition was developed based on dynamic mesh technology, and a 30-hour transient simulation of the thermal oxidation deposition process of supercritical aviation kerosene was conducted. The dynamic characteristics of the thermal oxidation deposition are examined and the effect of dissolved oxygen concentration is analyzed. According to the results, the large temperature gradient at the inlet and the higher temperatures in the second half of the channel encourage the thermal oxidation and surface deposition reactions to proceed rapidly. And it is found that the surface deposition rate decreases with increasing heating time. Both temperature and concentration determine the rate of dissolved oxygen consumption. The surface deposition rate increased by 195.33 % as the dissolved oxygen concentration increased from 10 to 40 ppm. In addition, the entry of aviation kerosene into the pseudo-critical region can indirectly reduce the rate of thermal oxidation surface deposition. This study is a guide to predict and inhibit the thermal oxidation deposition of aviation kerosene, improving the structural design of the regenerative cooling channel, and ensuring aircraft safety.

An improved frequency-domain model for the supercritical flow instability analysis in vertical tubes

In a supercritical water reactor, the density wave oscillation (DWO) may occur due to the dramatic changes in the density of the working fluid in the pseudo-critical region. Based on the frequency-domain method, this study proposes an improved model to study DWO. First, the latest partition method is used in this study. Second, in the derivation of the transfer function in the light fluid region, the density change of the fluid is considered. Moreover, the different states of the outlet fluid are handled differently. We use the Nyquist criterion to determine the flow stability and obtain the boundary heat flux (BHF) of different working conditions. After model verification, it is proved that the model accuracy is improved. We analyze the influence of pressure, inlet enthalpy, mass flow rate, inlet throttling coefficient, and tube parameter on the instability boundary. At a certain inlet enthalpy, a minimum BHF of flow instability exists.

Investigation of flow and heat transfer characteristics of supercritical argon in conical Hampson heat exchangers for a J-T cryocooler

The Hampson-type heat exchanger is critical for the rapid cooling of a conical J-T cryocooler, and its internal flow and heat transfer characteristics directly affect the performance of the conical cryocooler. The flow and heat transfer characteristics of supercritical argon are studied using a numerical model of a conical helical tube in this work. The simulated results show that supercritical argon flow in the conical helical tube is mainly influenced by the combined effect of variable thermophysical properties and the secondary flow produced by centrifugal force. The buoyancy has little impact on heat transfer. The heat transfer coefficient reaches its maximum at the pseudo-critical region. A more significant heat transfer coefficient and faster heat exchanger cooling rate can be achieved by increasing the mass flow rate and maintaining the fluid in the tube close to the pseudo-critical region. At a cone angle of 50°, the maximum total heat exchange quantity is observed. With a greater temperature drop per unit length, a stronger heat transfer effect can be achieved close to the outlet of the tube. Based on the numerical analyses, a new correlation for heat transfer is proposed.

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.

Coupling heat transfer study of liquid sodium and supercritical carbon dioxide in a PCHE straight channel based on a four-equation model

The Brayton cycle using supercritical carbon dioxide (S-CO2) as the working fluid is expected to be a thermo-power conversion technology for sodium-cooled fast reactors. Printed Circuit Heat Exchanger (PCHE) is the key heat transport structure to realize the above technology. The study of conjugate heat transfer characteristics of sodium (Na) with low Prandtl number turbulent heat transfer characteristics and S-CO2 with supercritical convective heat transfer behaviors in a PCHE channel are of great significance. However, the constant turbulent Prandtl number (Prt) model obtained by the general Reynolds analogy hypothesis may affect the conjugate heat transfer assessment between Na and S-CO2. Compared with the constant Prt model, the fluid’s Prt distribution can be obtained by four-equation models, introducing the transport of turbulent kinetic energy k, dissipation rate ε of k, temperature fluctuation kθ, and dissipation rate εθ of kθ. The four-equation model is expected to obtain more effective conjugate heat transfer characteristics between Na andS-CO2, while there are no available commercial codes. Therefore, in this paper, two kinds of four-equation model, which can effectively evaluate the heat transport performance of Na with low-Prandtl number and S-CO2 away from the pseudo-critical region, respectively, are first introduced into the conjugate heat transfer solver of OpenFOAM. Then the conjugate heat transfer experiment data of Na in a pipe and the simulation data of S-CO2 in a PCHE straight channel are used to verify the validity of the numerical model in this paper. The results show that the present calculation method can effectively reproduce the numerical conjugate heat transfer process of Na and S-CO2. Finally, based on four-equation models, the coupling heat exchange performance of Na/S-CO2 are studied to obtain the effects of mass rate and temperature on the conjugate heat transfer process between Na and S-CO2 in a PCHE straight channel.

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%.

Effects of n-decane pyrolytic products on heat transfer in regenerative channels under supercritical pressure

The study of the heat transfer process in the regenerative cooling channel of the scramjet engine is always one of the main focuses on highlighting the heat transfer characteristics caused by the pyrolysis of n-decane under supercritical pressure. The heat transfer is simulated in detail using the standard k-ε two-equation turbulent model and pseudo-detailed chemical kinetics mechanism. The results indicate that the dramatic changes in density and dynamic viscosity could lead to heat transfer deterioration at the beginning of the heated channel. The change rate of density and dynamic viscosity can reach up to 75 % and 97.4 %, separately. At the same time, the physical heat sink takes the lead because of the changes in the mixture’s specific heat capacity near the pseudo-critical region which are mainly contributed by C5 (pentane and pentene), and the proportion in total heat sink can reach up to 17.4 % when the conversion is below 15.0 %. The advantage of the endothermic cracking reaction is not reflected in the heat transfer process when the conversion of the fuel is lower than 25.0 % in this work. For practical applications, the effects of the pyrolytic products’ types and properties on the pyrolytic mechanism and heat sink should be performed to maximize the cooling capacity of n-decane in the cooling channel.

The mechanism of abnormal corrosive behavior of metallic materials in the pseudocritical region of supercritical water

To study the corrosive behavior of metal materials in the pseudocritical region of supercritical fluid and explain the abnormal mechanism in corrosive within the pseudocritical region, a corrosive experimental platform for supercritical fluids was built. Three different candidate materials for Supercritical Water Reactor (i.e. Q235 low carbon steel, 316 L austenite stainless steel and 3Cr13 martensitic steel) were selected and reacted for 200 h in the pseudocritical region (375.6 ℃, 22.5 MPa) and gas-like region (405.6 ℃, 22.5 MPa) respectively. The results show that 316 L exhibits abnormal corrosive exacerbation in the pseudocritical region with a corrosive rate 1.67 times that of the gas-like region. Considering the special variation of physical properties in pseudocritical region, the enhanced kinetic effect is further analyzed. It is found that the migration of corrosive media such as oxygen to the material matrix is accelerated, which aggravates the corrosive products shedding and freeing. The present study can provide a basis for improving the anti-corrosive performance of materials under supercritical fluid environments and providing a safe operation of the Supercritical Water Reactor.

Numerical study on conjugate heat transfer characteristics of liquid lead-bismuth eutectic and supercritical carbon dioxide in a PCHE straight channel

The Printed Circuit Heat Exchanger (PCHE) is the optimal heat transfer structure of the fourth-generation advanced Lead–Bismuth Eutectic (LBE) cooled fast reactor coupling with the supercritical carbon dioxide (S-CO2) Brayton cycle system. It is of great significance to study the conjugate heat transfer characteristics between LBE with low Prandtl number turbulent heat transfer characteristics and S-CO2 with supercritical convective heat transfer characteristics. However, the conventional Reynolds analogy assumption will affect the numerical heat transfer precision of LBE and, thus, the accuracy of the coupled heat transfer of LBE and S-CO2. In the present work, an advanced two-equation turbulent heat transfer model, which can effectively correct the numerical heat transfer process of LBE, is introduced into the conjugate heat transfer solver of the open-source Computational Fluid Dynamics (CFD) program OpenFOAM, where the Reynolds analogy assumption is retained to reproduced the heat transfer of S-CO2 flow away from the pseudo-critical region. The currently developed model and numerical method are compared with the experimental data of an LBE-cooled pipe and the simulation data of conjugated heat transfer of S-CO2 and S-CO2 in a PCHE straight channel. The results show that the calculation method in this study can improve the numerical conjugate heat transfer accuracy of LBE compared with the Reynolds analogy assumption model and can reproduce the flow and heat transfer process of S-CO2 in a PCHE straight channel. Then, the conjugate heat transfer characteristics between LBE and S-CO2 in a PCHE straight channel are studied. The effects of inlet Reynolds number and inlet temperature are focused on to study the conjugate heat transfer law of LBE coupling S-CO2.

A novel strategy of thermal management system for battery energy storage system based on supercritical CO[formula omitted

Supercritical CO2 (sCO2) is examined as a working fluid for the first time in a unique thermal management strategy that aims to control undesirable thermal behavior in battery cooling applications. In the pseudocritical region, sCO2 has a high volumetric thermal capacity with low critical pressure and temperature, which not only reduces system complexity and costs but also eliminates the possibility of two-phase critical heat flux and flow instabilities. A pack of 20×5 Li-ion batteries for battery energy storage system (BESS) applications was designed and employed in a structurally optimized thermal management system. Further, the effects of different dielectric fluid media on the number of flow inlets, flow rates, and discharge rates were numerically investigated. Compared with conventional coolants, sCO2 exhibited superior temperature suppression and temperature differences. The rise in both mass flow rate and the number of flow inlets significantly suppressed the maximum temperature and temperature difference. Besides, the pressure drop was slightly increased with the increased mass flow rate. Moreover, sCO2 controls the thermal behavior of a large battery pack at high discharge rates within an optimal range. The finding offers various attributes for cooling large battery packs, particularly for high-power grid stations and BESS. In the future, the practicality of high working pressures and power requirements for the pump should be carefully studied.

Contrasting pseudocriticality in the classical two-dimensional Heisenberg and RP^{2} models: Zero-temperature phase transition versus finite-temperature crossover.

Tensor-network methods are used to perform a comparative study of the two-dimensional classical Heisenberg and RP^{2} models. We demonstrate that uniform matrix product states (MPSs) with explicit SO(3) symmetry can probe correlation lengths up to O(10^{3}) sites accurately, and we study the scaling of entanglement entropy and universal features of MPS entanglement spectra. For the Heisenberg model, we find no signs of a finite-temperature phase transition, supporting the scenario of asymptotic freedom. For the RP^{2} model we observe an abrupt onset of scaling behavior, consistent with hints of a finite-temperature phase transition reported in previous studies. A careful analysis of the softening of the correlation length divergence, the scaling of the entanglement entropy, and the MPS entanglement spectra shows that our results are inconsistent with true criticality, but are rather in agreement with the scenario of a crossover to a pseudocritical region which exhibits strong signatures of nematic quasi-long-range order at length scales below the true correlation length. Our results reveal a fundamental difference in scaling behavior between the Heisenberg and RP^{2} models: Whereas the emergence of scaling in the former shifts to zero temperature if the bond dimension is increased, it occurs at a finite bond-dimension independent crossover temperature in the latter.

A limitation to determine heat transfer of water at supercritical pressure: The repeatability issue

• Published data indicates non-reproducibility of the heat transfer in the pseudo-critical region. • Non-reproducibility appears at conditions for which DHT is possible. • Experimental results at the Technical University of Munich confirm this hypothesis. • Origin of the non-reproducibility may be linked to variations of the properties close to the pseudo-critical points. As the heat transfer is based on physical processes which are expected to be deterministic, a major anticipation is that the experimental data should show good repeatability, if not reproducibility. In other words, it is expected that repetition of experiments with very similar inputs (bulk pressure and enthalpy, mass flow rate, heat flux …), should result in consistent and very similar outputs (heat transfer coefficient or inside wall temperature). However, comparable experiments with supercritical water in the literature, although rather scarce, as well as the experimental work conducted at the Chair of Energy Systems at the Technical University of Munich tend to show that repeatable or reproducible data are difficult to obtain. This is the case particularly within the pseudo-critical region where DHT is likely to occur. This may impair the ability to assess accurately the overheating of the piping in critical cases, and therefore the safety of the concerned plants. This paper aims to focus on this problem from an experimental perspective, trying to identify both the magnitude of the phenomenon as well as at which parameters non-reproducibility occurs. Ultimately, the authors try to answer the following question: Is it possible to reach reproducibility?