Heat transfer characteristics of water under supercritical conditions

doi:10.1016/j.ijthermalsci.2021.107238

International Journal of Thermal Sciences

Volume 171, January 2022, 107238

https://doi.org/10.1016/j.ijthermalsci.2021.107238 Get rights and content

Highlights

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Experiments on the study of deteriorated heat transfer regimes in small round pipes are analyzed.
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Maps of heat exchange modes in supercritical pressure water are proposed.
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The limiting heat flux in normal modes is obtained.

Abstract

The paper deals with the problems of describing heat transfer modes in a turbulent flow of supercritical water based on generalization of known experimental data for vertical round tubes. Due to the danger of overheating of heat transfer surfaces, special attention is paid to modes with deteriorated heat transfer. Later, the authors developed a universal model that includes the well-known Dittus–Boelter correlation with corrections for changes in the thermophysical properties of water with temperature and the effect of thermal acceleration occurring in the flow. It is shown that the variation of the coefficients in the correction functions allows us to take into account individual features of changes in characteristics of the process in modes with deteriorated heat transfer. Three forms of displaying the modes of heat transfer to water of supercritical parameters with conditional boundaries of the modes of normal, improved and deteriorated heat transfer are proposed. The estimates of the limiting heat flux obtained in this paper for normal modes are compared with the data of other authors.

Introduction

The use of supercritical water as a coolant in fourth-generation nuclear reactors would significantly (up to 45%) increase the efficiency of the energy cycle, as well as significantly reduce the cost of construction and operation of nuclear power plants with SCWRs [1]. The desire to achieve this goal has prompted researchers around the world to start a new stage in the study of heat and mass transfer processes in media at supercritical pressures. The main outcomes of these investigations, conducted during the last ten years, have been summarized in the IAEA reports [2,3].

The peculiarity of states of a substance at pressures above the critical point is the absence of phase transitions. Therefore, the formation of a vapor film on the cladding surfaces is excluded. At subcritical pressures, when the critical heat flux is exceeded, the transition to film boiling of water usually ends with burnout of fuel elements due to a sharp jump in temperature. However, in the region of states close to the critical or pseudo-critical temperature, strong variations of the thermophysical properties of the coolant occur with a small change of temperature. This, firstly, significantly complicates the processes of energy exchange between the heated wall of the channel and the medium moving in it, and, secondly, leads to additional effects (thermal acceleration and Archimedean forces). As a result of the influence of them on the flow under certain conditions (with large heat loads and low velocities of the heat transfer medium in the channel), deteriorated heat transfer modes occur. In such modes, the temperature of the heated wall usually rises gradually and not as much as in the case of a critical heat flux in a two-phase flow at a pressure below the critical one. However, due to the increased values of the coolant temperature, the heat transfer in the core of the SCWR reactor should be carefully studied, and special attention should be paid to modes with deteriorated heat transfer, taking into account the design margin from excess heat up of the fuel rod cladding material operating in the conditions of corrosion at elevated temperatures.

Section snippets

Normal heat transfer modes

The concept of normal heat transfer modes appeared in the second half of the last century when studying the processes of turbulent flow of supercritical pressure fluids in round tubes [4]. “Normal” then began to be called modes, when the observed in experiments dependences of the convective heat transfer coefficient on the Reynolds and Prandtl numbers for a medium with variable thermal properties had approximately the same form as for constant properties. In these modes, the temperature of the

Identification of modes with the deterioration of heat transfer

Modes of deteriorated heat transfer at supercritical pressure usually occur in the sections of heated tubes where the bulk temperature of water has not yet reached the pseudo-critical value t_m, and the wall temperature already exceeds this value.

In reviews [13,14] devoted to the analysis of data on heat transfer in supercritical fluids, several methods are described, which had been used in experiments in order to recognize the onset of heat transfer deterioration (by means of the observation of

Universal model and its main characteristics

The authors [6,21] developed a universal model of heat transfer in fluids of supercritical parameters. This model is intended for calculating various heat transfer modes in the conditions of forced turbulent movement of supercritical pressure media in channels of relatively small hydraulic diameter (d_h ≤ 10 mm), which is typical for fuel assemblies of nuclear reactors. The model is based on the equation of normal heat transfer with corrections for the variability of the thermophysical

Map of heat transfer modes and the onset of heat transfer deterioration

The equations of the universal model considered above allow us to construct a map of heat transfer modes in supercritical pressure water on a plane ${\tilde{K}}_{A m}$ – ${\tilde{K}}_{h}$ . Taking into account the principle of identification of normal modes 0.8 < Nu/Nu_n < 1.2 adopted in this work, three forms of the map were implemented, shown in Fig. 6. The boundaries of the regions of existence of individual modes in the case A were determined by equations (3), (5) with the coefficients indicated in Table 3 for the function

Conclusion

To date, a lot of experimental data has been accumulated on heat transfer during the turbulent flow of supercritical pressure water in vertical round pipes. The main regularities of changes in the heat transfer coefficient in a wide range of operating parameters, including those in the region with variable thermal properties of the coolant near the pseudocritical temperature, are investigated.

Due to the peculiarities of the heat transfer process established in experiments at supercritical

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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This study is focused on measuring the transient boundary heat transfer in supercritical CO₂ mini-channel flows under local heat application. A pixelated-array masked phase-shifting interferometer system and quantitative data procedures have been established for sCO₂ boundary flow. The experiments have been conducted at a Reynolds number level of 10⁴, spanning across both subcritical and supercritical regions (5.0 ∼ 7.9 MPa). High resolution local density and temperature have been extracted from the raw interferograms by developing a digital phase-shifting algorithm. The temporal and spatial evolutions of Nu show good agreement with classic correlations. The effects of differential pressures (10.87 ∼ 52.59 Pa) and heat fluxes (2014, 5500, 14,057 W/m²), along with their associated heat transfer behaviors, have been quantitatively examined under transient scenarios using the current method. The results show: (1) although the Re number is high, such small thermal perturbations can be clearly visualized in the entire window, which shows the capability of field extraction of the current method proposed for complicated supercritical boundary flows; (2) rapid density decrease (1.0 kg/m³) occurs locally, while small temperature differences (0.01 K) are observed, which also lead to local Nu variations under different operation conditions; (3) detailed convective patterns and time evolution of Nu curve groups identified for subcritical, near-critical and supercritical states.
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Citation Excerpt :
Many researches point out that supercritical fluids have special heat transfer and flow characteristics, such as heat transfer deterioration, buoyancy effect and flow acceleration. Lots of them are about supercritical CO2 [1,2], supercritical water [3,4], and other working fluids [5,6]. The following focuses on the literatures about supercritical methane/LNG.
The main component of liquefied natural gas (LNG) is methane. The regasification process of LNG is usually under a supercritical condition. In this paper, a three-dimensional model is established to study the heat transfer and flow mechanism of supercritical methane in a heating process. The special physical properties of supercritical methane are compiled and imported through user-defined database. The standard k–ε model with the standard wall function is selected for simulation. The results show that deterioration of heat transfer occurs on the upper surface of the channel, which is most evident when the bulk temperature approaches the pseudocritical temperature. And the heat transfer coefficient increases first and then decreases along the channel with the bulk temperature rising. The peak value appears near the pseudocritical temperature. The pressure also has a great influence on heat transfer and flow. Besides, the buoyancy effect is strong near the pseudocritical point, leading to nonuniform distribution of temperature and density on the cross section, and causing significant radial circulation. The heat transfer deterioration can be effectively reduced by using special structures such as fins to hinder the buoyancy.
Research Progress on Convective Heat Transfer Characteristics of Supercritical Fluids in Curved Tube
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View full text

Heat transfer characteristics of water under supercritical conditions

Highlights

Abstract

Introduction

Section snippets

Normal heat transfer modes

Identification of modes with the deterioration of heat transfer

Universal model and its main characteristics

Map of heat transfer modes and the onset of heat transfer deterioration

Conclusion

Declaration of competing interest

J. Supercrit. Fluids

Therm. Sci. Eng. Progr.

Int. J. Heat Mass Tran.

Ann. Nucl. Energy

Appl. Therm. Eng.

Int. J. Heat Mass Tran.

Int. J. Heat Mass Tran.

Int. J. Heat Mass Tran.

Int. J. Heat Mass Tran.

Int. J. Heat Mass Tran.

Int. J. Heat Mass Tran.

Ann. Nucl. Energy

Int. J. Heat Mass Tran.

Super Light Water Reactors and Super Fast Reactors

Understanding and Prediction of Thermohydraulic Phenomena Relevant to Supercritical Water Cooled Reactors (SCWRs), Final Report of a Coordinated Research Project

Heat Transfer Behaviour and Thermohydraulics Code Testing for Supercritical Water Cooled Reactors (SCWRs)

Heat transfer in a single-phase medium under supercritical conditions (survey)

High Temp.

Analysis of relations for calculating normal heat transfer to supercritical pressure water flow in vertical tubes

Atom. Energy