Heat Transfer Of Supercritical Fluids Research Articles

Experimental investigation of the heat transfer characteristics of CO2 at supercritical pressures flowing in heated vertical pipes

Supercritical CO2 shows great potential as a working fluid in power plant cycles due to its moderate critical pressure of 7.38 MPa and critical temperature of 30.98 °C, closely matching typical heat sink temperatures. Understanding the heat transfer characteristics of sCO2 is crucial for designing cycle components. This publication presents a systematic analysis of sCO2 heat transfer in two heated vertical pipes with 4 and 8 mm inner diameters, with both upward and downward flow at pressures of approximately 7.75, 8.00, and 9.50 MPa, and flow inlet temperatures between 5 and 40 °C, based on 196 experiments. The study investigates a range of mass fluxes from 400 to 2000 kg/m2s and heat fluxes from 10 to 195 kW/m2, resulting in a heat to mass flux ratio of 6 to 275 J/kg. The findings reveal enhanced, normal, and deteriorated heat transfer within the experimental dataset. Buoyancy effects are identified as the main cause of deteriorated heat transfer in the investigated parameter range, with flow acceleration showing no significant influence on heat transfer. A new proposed dimensional criterion categorises 36 out of 119 experiments with upward flow in the deteriorated heat transfer regime, accompanied by temperature peaks rising to 47 K. Thermal inflow lengths range from 0 to 480 inner pipe diameters, with some experiments not achieving a thermally fully developed flow over the entire pipe length. Based on a comparison with approximately 8950 experimental data points, two Nusselt correlations are found, capable of reproducing the experimental results with a mean absolute deviation of around 30 %. This publication provides valuable data for validating numerical models and developing correlations to predict the heat transfer of supercritical fluids.

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.

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.

Study of the hydraulic roughness impact on turbulent heat transfer at supercritical pressure based on a fast direct numerical simulation method

A numerical experiment on turbulent heat transfer of supercritical fluids (SCFs) in hydraulically rough heating tubes is performed using a fast direct numerical simulation method for characterizing hydraulic roughness. The objective is to assess the impact of hydraulic roughness on SCF turbulent flow and heat transfer and delve into the underlying mechanism. Four cases are simulated, including one case of smooth flow and three cases with varying roughness parameters. The simulations are conducted at a bulk inlet Reynolds number of Rein=2700 based on the tube radius and inlet parameters. The results demonstrate that hydraulic roughness effectively enhances heat transfer, leading to reduced wall temperatures and increased Nusselt numbers at the heated wall. As the roughness height increases, the heat transfer deterioration typically observed in SCF flows is significantly mitigated. This enhancement in heat transfer primarily arises from increased turbulent shear stress and turbulent heat flux induced by hydraulic roughness. Additionally, hydraulic roughness fosters more turbulent structures and intensifies vortex motion during transient flow, thereby further enhancing turbulent heat transfer. The insights gained from this research offer valuable guidance for addressing heat transfer deterioration in supercritical fluids.

Experimental study of buoyancy and centrifugal effects on supercritical heat transfer in U-bend and contiguous straight tubes

The buoyancy-induced thermal non-uniformity in heat transfer of supercritical fluids is a major issue that must be addressed in transcritical systems like organic Rankine cycle. In cases where U-bends are involved in heat exchangers, the introduction of centrifugal effect and its decaying nature makes the heat transfer process even more complex. In this work the buoyancy and centrifugal effects on local heat transfer to supercritical R410A were experimentally studied in a U-bend and its contiguous horizontal straight tubes (tube diameter d = 4.35 mm, bend diameter D = 43.5 mm). Measurements were performed at four circumferential positions along the heated length. Results show that bend-induced enhancement reached the maximum at the bend center, where heat transfer coefficients at the outside, top, bottom, and inside increase by 88%, 49%, 28% and 19% respectively. U-bend also caused a significant enhancement on contiguous horizontal straight tubes. In the upstream straight section, the affected distance can reach 11.5d, and the downstream affected range is more than 23d. The enhancement and the affected distance generally increased with heat flux, mass flux, and inlet temperature, but barely affected by pressure. Further analysis indicates that the centrifugal force dominated heat transfer in the bend section. Moving away from the bend, it gradually decayed, buoyancy force recovered and eventually played the major role. Existing dimensionless numbers failed to represent this transition, and a new parameter ψ* was proposed to evaluate the competition between the buoyancy effect and the decaying centrifugal effect. With a threshold value of 1, ψ* can quantitatively characterize the local heat transfer.

Review on Supercritical Fluids Heat Transfer Correlations, Part I: Variants of Fundamental Dimensionless Variables

When supercritical fluids absorb heat energy through channels, their thermophysical properties rapidly change, resulting in an enhanced, deteriorated, or normal heat transfer phenomenon. Understanding the phenomena of heat transfer is essential for applications involving supercritical fluids, particularly nuclear power generation. As a result, the Nusselt number correlation is developed and used to characterize the heat transfer performance under a variety of operating conditions, geometries, and flow directions. Unfortunately, for supercritical fluid heat transfer, there are now over 50 Nusselt number correlations, which create difficulties to comprehend all of the Nusselt number correlations due to their complex structures and distinctive formulations of the modifying factors. Therefore, this review article is devoted to providing a comprehensive yet succinct overview of the key components of the majority of supercritical Nusselt number correlations. The supercritical properties of water, carbon dioxide, and helium are briefly introduced, taking supercritical carbon dioxide as an example. The potential use of supercritical fluid in engineering applications, such as Generation IV nuclear reactors, waste heat recovery, and concentrated solar power, is presented. The origin and properties of the variants of the Reynolds number, the Prandtl number, and the reference temperature modified for the Nusselt number correlation are categorized and examined.

Determination of the position and characteristics of supercritical heat transfer deterioration

Supercritical fluids (SFs) are widely used in power generation systems using nuclear, solar, geothermal, and fossil energies. The heat transfer deterioration (HTD) phenomenon during heat transfer of SFs is of great importance to the design and operation of the components in supercritical power cycles. The criteria for determining the onset of HTD has been reported in the literature, but the quantitative model to obtain the position of the wall temperature peak during HTD occurrence, and the correlation to accurately predict the heat transfer characteristics at the wall temperature peak, are both missing. In this work, to determine the position and to predict the characteristics of HTD at the wall temperature peak, we developed two correlations based on experimental results for supercritical CO2 (sCO2) in vertical upward tubes with wide range of experimental parameters. The first correlation to predict the location of the peak is developed using experimental data for sCO2, which can accurately determine the dimensionless bulk fluid temperature corresponding to the wall temperature peak. Moreover, a new heat transfer correlation is developed for the Nusselt number at the wall temperature peak, which has a simple form of NuHTD=0.00796Reb0.7215Prb−0.1568K−0.115, where Reb, Prb, and K are Reynolds number, Prandtl number, and supercritical K number, respectively. This correlation shows smaller prediction error compared with five existing correlations in the literature for not only sCO2, but also various other working fluids. It also outperforms the recently proposed K number correlation in predicting characteristics at the wall temperature peak during HTD conditions. The two correlations developed in this work provides the quantitative models for the HTD phenomenon, and can benefit the engineering application of supercritical power cycles.

Analysis of heat transfer mechanism in supercritical fluids from the aspect of pool heating

For the special phenomena of heat transfer deterioration or enhancement in supercritical fluid heat transfer, existing research still presents inconsistent opinions. In this study, we perform an analysis of the property changes, and present new understandings for pseudo-boiling theory. More importantly, essential differences between subcritical boiling and supercritical pseudo-boiling are highlighted; the critical factors being thermodynamic instability and stability. For isothermal heating cases, pseudo film boiling can be regarded as an extension of near-critical boiling. Moreover, pseudo nucleate boiling only appears in non-isothermal heating cases and is strongly dependent on the heater geometry, materials, etc. A coupled level-set and volume-of-fluid method is used to simulate the near-critical film boiling of carbon dioxide at pressures of 7.0 and 7.37 MPa. In comparison, supercritical cases at a pressure of 7.5 MPa are the natural convections of single-phase fluid with variable physical properties. The numerical results indicate the similar motions of low-density fluids in subcritical and supercritical cases. All results are consistent with prior experiments, providing a better understanding of the special features of supercritical fluid heat transfer.

A Critical Review on Heat Transfer of Supercritical Fluids

Supercritical fluids have been widely used in a variety of applications, in which heat transfer under supercritical pressure is of great importance. This paper presents a critical review on supercritical heat transfer, including a summary on the past work focusing on in-tube heat transfer and the pseudo-boiling concept, the understanding of the mechanisms of supercritical heat transfer, and suggestions for future work. For supercritical fluids heated in tubes, the typical characteristics, the effects of various parameters, the buoyancy and flow acceleration effects, and the heat transfer deterioration phenomenon are all discussed, and the heat transfer correlations and numerical methodologies are summarized. For supercritical fluids cooled in tubes, the experimental observations and explanations, the proposed heat transfer correlations, and the numerical results are summarized and discussed. More importantly, this review provides a comprehensive review of the supercritical pseudo-boiling concept, including the experimentally observed pseudo-boiling phenomenon, the theoretical studies for supercritical fluids to reveal their heterogenous two-phase features, and the progress in the application of the pseudo-boiling concept on supercritical heat transfer. Finally, suggestions for future research are provided to further advance the understanding and enable accurate prediction of supercritical heat transfer.

Modeling of deteriorated heat transfer in supercritical fluids using a two-phase method

In heat transfer processes of supercritical fluids, heat transfer deterioration (HTD) is normally manifested by unusual rise of wall temperature with one or multiple peaks. Despite being dangerous for the heat exchanger equipment, there is a lack of accurate predictions and reasonable explanations of such HTD phenomena. In this work, a two-phase numerical method is validated and optimized in terms of the two-phase model and interval temperature ΔT. The results showed that the Mixture model outperformed the volume of fluid model, where the modeling results were more consistent with the experimental values when ΔT was set as 1 K. In addition, considering the pseudo-boiling theory and the two-phase numerical method, three cases with different forms of HTD were selected for further investigation. The selection of the saturation temperature Tsat and condensation frequency fe was found to also have a significant impact on calculation results. The best predicted results were obtained at a saturation temperature equal to the termination of pseudo-boiling temperature with a fe of around 200. Overall, the two-phase numerical method was found to yield more accurate predictions compared to the single-phase numerical method in this work. Through the analysis of the average gas volume fraction along the flow direction, a link between this fraction and HTD was developed. Moreover, HTD in the case of supercritical fluids could also be divided into two types of pseudo-film boiling, similar to that under subcritical pressure. The first type of HTD is similar to stable pseudo-film boiling where the gas volume fraction is very high at the deterioration point. By dividing the supercritical fluid into three regimes, a good agreement was reported between the wall temperature and the vapor-like regime. Also, the wall temperature and the vapor-like regime were found to peak at the same position. On the other hand, the second type of HTD is similar to the departure from nuclear boiling, which can occur at the inlet or in the low gas volume fraction zone.

Experimental Investigation of Supercritical Fluid Heat Transfer Properties in a Miniature Heat Sink

Currently, efficient heat transmission for compact electronic elements is an essential matter. The objective of this project is to build a test rig to study the heat transfer effect of SCF-CO2 on the miniature heat sink, which is used in cooling in much small electronic equipment. It needs a heat sink with a liquid cooling scheme that meets these demands as much as feasible. The dimensions of 20 mm x 20 mm and a width of 3 mm were adopted for features of heat transfer as well as the fluid flow of supercritical CO2 in heat sink copper 360 alloys in this study. A heat sink has 20 homogeneous arrays of fins and 19 tubes, each having a rectangular cross-section and a 1mm hydraulic diameter. Moreover, the adopted pressures, temperatures, and mass velocity ranges were 7.5 to 12 MPa, 35 to 50 oC, and 100 to 500 Kg m-2 s-1, respectively, wherein the CO2 cooled under these conditions. The results of the experiment found that there is a substantial impact on the properties of liquid inflow and temperature motion by the system pressure, the temperature of CO2 as well as cluster velocity. Additionally, as the medium temperature of CO2 in the adjacent significant point area increased, the pressure decreased and the medium temperature movement factor augmented dramatically. It was also noted that the medium temperature movement factor peaked at the pseudo-critical temperature. Using the obtained data, a novel correlation mechanism for limited convection of super-critical CO2 in regular multi-port micro tubes based on chilling conditions was constructed using the obtained coefficients in this study.

Heat transfer in a U-bend pipe flow at supercritical pressure

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

Experimental and numerical investigation of the effects of buoyancy and flow acceleration on the heat transfer of hexamethyldisiloxane (MM) at supercritical pressures

The hexamethyldisiloxane (MM) has relatively higher thermostability and lower critical parameters than other organic working fluids, making it suitable for the medium/high temperature supercritical ORC system. However, the fluid at supercritical pressures experiences sharp variation of thermophysical properties near the pseudo-critical temperature which results in the abnormal heat transfer phenomenon, so the heat transfer design becomes one of the challenges for supercritical ORC system. Most of the extant researches believe that the abnormal heat transfer of supercritical fluid is caused by the effects of buoyancy and flow acceleration induced by the dramatic change of fluid density, but it is still necessary to further improve the understanding of its physical mechanism and prediction of heat transfer characteristics. Based on experimental and numerical data, the present work analyses the distributions of key parameters to reveal the main causes of abnormal heat transfer. Then, the dimensionless parameters of the buoyancy and flow acceleration and their thresholds are obtained in combination of the in-tube turbulent flow theory. The results show that the effects of buoyancy and flow acceleration can reduce the local turbulence intensity. The affected positions are respectively the near-wall area after the wall temperature reaching the pseudo-critical point and the mainstream area where the fluid temperature reaches the pseudo-critical point. For this reason, the thermophysical reference temperature in the dimensionless boundary layer thickness for the buoyancy parameter (Bu) and flow acceleration parameter (Ac) are set as the wall temperature and bulk temperature respectively. The corresponding thresholds where the buoyancy and flow acceleration have large influence on the heat transfer are 3.9 × 10−6 and 9.8 × 10−7, which can well predict the initial position of heat transfer deterioration (HTD).

The three-regime-model for pseudo-boiling in supercritical pressure

Supercritical pseudo-boiling (SPPB) refers to the phenomena that when heat is applied to supercritical fluid, bubble-like and vapor-film-like features appear and wall temperature peaks occur, similar to subcritical boiling (SBB). Even though SPPB was reported in 1960s∼1970s, it has not been paid attention and supercritical heat transfer (SHT) is still treated with single-phase fluid assumption, introducing difficulties in accurately describing the flow and heat transfer characteristics. Here, by analogy between SPPB and SBB, a three-regime-model is proposed for SPPB, including liquid-like (LL), two-phase-like (TPL) and vapor-like (VL) regimes. The three regimes are interfaced at an onset of pseudo-boiling temperature T− and a termination of pseudo-boiling temperature T+, determined by thermodynamics. Thermophysical properties of LL and VL phases are evaluated using the two pseudo-boiling temperatures. Pseudo-boiling enthalpy is defined as the enthalpy difference across the temperature span from T− to T+, which is analogous to latent heat of evaporation in subcritical pressure. Pseudo-vapor mass quality x is calculated using bulk fluid enthalpy and fluid enthalpies at T− and T+. Non-dimensional parameters are proposed to reflect interactions of mass, momentum and energy between LL and VL phases. Based on the three-regime-model, SHT is re-analyzed in a different perspective from literature. We show that SHT deviates from that of single-phase convection significantly for 0 < x < 1 corresponding to the TPL regime, indicating that SHT cannot be treated with single-phase fluid assumption under this condition. Reynolds number for LL phase (ReLL) explains the non-monotonic variation of SHT versus heat fluxes. Froude number Fr explains the difference of SHT between top generatrix and bottom generatrix in horizontal tubes. Supercritical boiling number SBO and K number successfully correlate heat transfer and pressure drop for SHT in tubes, and the K number correlation has much smaller error than DB correlation. Our work establishes a new theoretical framework for SPPB and provides a new research direction for heat transfer of supercritical fluids.

Heat Transfer Analysis of Supercritical Methane on a Cooling Channel of Electromechanical Actuator Under Various Flight Acceleration Overloads

Abstract The crucial distinction of heat transfer between the earth environment and the high acceleration overloads of flight vehicle is the secondary flow resulting from the gravitational buoyancy force and centrifugal one, which influences the heat transfer of supercritical fluid significantly. Hence, in this work, the effect of various flight acceleration overloads on turbulent convection heat transfer in the cooling channel of flight vehicle electromechanical actuator (EMA) is investigated numerically. The cooling channel is constructed from a helically coiled tube with an inner diameter of 8 mm, coil diameter of 74 mm, and screw pitch of 10 mm, the operation pressure covers the range of 5–9 MPa, and the gravity ranges from 1 g to 50 g. Based on this model, the heat transfer characteristics of supercritical methane in the cooling channel of flight vehicle EMA under various acceleration overloads are studied, aiming to obtain a deep understanding of flow and heat transfer mechanism and thermal performance of supercritical methane in the cooling channel under the conditions of actual flight. The simulation result indicates that with the high-g overload, the heat transfer enhancement becomes obvious and the effect of secondary flow caused by the flight acceleration exhibits the non-negligible influence. The secondary flow caused by flight acceleration overloads disturbs the flow acceleration of the main stream that weakens the suppression of heat transfer. However, the effect of gravitational buoyancy does not dominate on forced convection heat transfer even under the high acceleration overload.

Investigation of flow and heat transfer of supercritical water in double-pipe heat exchanger

Objective The flow and heat transfer of supercritical fluid is complex, and most of the existing research is based on the conditions of constant wall temperature and constant heat flux. However, in practical engineering, heat transfer often occurs under the conditions of variable heat flux. In order to better understand the relevant performance, this paper studies the coupled flow and heat transfer of supercritical fluid in a double-pipe heat exchanger. Method The experimental section of this paper focuses on a double-pipe heat exchanger. The flow and heat transfer characteristics of supercritical water in the double-pipe heat exchanger are analyzed by collecting temperature and pressure data from the temperature and pressure measuring points arranged on the inside and outside of the double pipe. Results The experimental results show that great changes in physical parameters near pseudo-critical points are the main reasons for the phenomenon of supercritical water heat transfer, and they differ from those of ordinary heat transfer. There is a difference between the peak heat transfer coefficient temperature and pseudo-critical temperature which increases with the increase of pressure. This phenomenon is caused by the temperature gradient and variations in thermal-physical properties in the heat transfer section. The heat transfer coefficient of the outer pipe increases with the increase in water temperature at the inlet of the inner pipe when the mean bulk temperature is lower than the pseudo-critical temperature due to the buoyancy effect decreasing at the same time, while the buoyancy effect is almost independent of the water temperature at the inlet of the inner pipe when the mean bulk temperature is higher than the pseudo-critical temperature and the buoyancy effect is non-significant. Conclusion The results can provide valuable references for the design of double-pipe heat exchangers and research and mechanism analysis of the coupled flow and heat transfer of supercritical fluid in double-pipe heat exchangers.

Analysis of Heat Transfer Oscillation and Buoyancy Effects of Supercritical R1234ze(E) Cooled in Horizontal Helically Coiled Tubes

Abstract The helically coiled tubes (HCTs) have been attracting huge attention for enhancing the heat transfer of supercritical fluids and improving energy efficiency. Moreover, the new refrigerant R1234ze(E) has excellent environmental properties and system performance, but few researches have been concentrated on the supercritical R1234ze(E) heat transfer. In this work, the shear stress transport (SST) turbulence model is adopted for the numerical simulation of the cooling heat transfer performance of s-R1234ze(E) in horizontal HCT. The influences of heat flux, mass flux, coil pitch, and tube radius on the heat transfer coefficient, gravitational buoyancy effect, and centrifugal buoyancy effect are, respectively, investigated. Furthermore, the results reveal heat transfer oscillation occurs when Rig*|cosβ|max&amp;gt;0.17, and the oscillation mechanism is analyzed. Different from that in the vertical HCT, the angle between the radial component of gravitational buoyancy and centrifugal force varies continuously in the horizontal helical tube, resulting in the fluid with lower temperature may locate in the inner-left region or the inner-right region. Subsequently, the heat transfer piecewise correlation for supercritical R1234ze(E) in horizontal HCT is developed. The average absolute deviation of the predicted results is 5.88%.

Heat Transfer in Supercritical Fluids: Reconciling the Results of Pulse and Stationary Experiments

Heat Transfer in Supercritical Fluids: Reconciling the Results of Pulse and Stationary Experiments

Heat Transfer in Supercritical Fluids: A Review

Abstract Supercritical fluids (SCF) find potential applications in the upcoming energy systems due to various advantages associated with them. One of such applications is nuclear reactor where supercritical water and carbon-dioxide, both are proposed as the coolants in advanced reactor designs. Higher efficiency, simplified systems, lower operational costs are some of the advantages which propels the research fraternity to employ these fluids in application. However, there are also some challenges associated with the use of these fluids. Heat transfer behavior of these fluids is one among them. As SCF undergo tremendous changes in thermophysical properties across pseudo-critical temperature, heat transfer may get affected. It may get enhanced, deteriorated or remain unaltered. Various studies, experimental and analytical, have been carried out in the past using SCF to evaluate their heat transfer behavior. Various heat transfer correlations have been proposed by researchers catering to different operating range of parameters. Also, studies have been dedicated by researchers to investigate fluid-to-fluid scaling of SCF based on which scaling laws were proposed by them. This way prototypic fluid behavior can be predicted if the model fluid conditions are known. This paper presents a latest review of the scaling laws and heat transfer correlations applicable to SC fluids. Illustrations have also been presented considering reference experimental data from literature to get a feel about how these scaling laws fare among themselves. Various heat transfer correlations have been compared and important observations have also been discussed in this article.

The staged development of a horizontal pipe flow at supercritical pressure

The axial development of heat transfer to supercritical fluids in horizontal pipe has been studied both experimentally and numerically. It has been demonstrated that the flow and heat transfer exhibit a distinct three-stage development, including two entrance effect stages and an asymptotic development stage. Stage I is characterized by a rapid heat transfer coefficient reduction and is largely caused by the thermal boundary layer development. When the inlet temperature is close to the pseudo-critical value however, flow laminarisation also plays a role. Stage II is a special entrance effect, which has not been observed in flow and heat transfer at subcritical pressure condition. This is caused by the strong buoyancy effect, leading to stratification and secondary flow. Most interestingly the heat transfer of supercritical fluids in a horizontal flow can reach a pseudo-developed state stage III, where the flow and heat transfer is free from the influence of the entrance condition. This contrasts the common belief that the heat transfer of supercritical fluids can never reach an axially asymptotic condition because of the significant property variations. The existence of such a condition can be of great value for fluid-to-fluid similarity analyses.