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The heat transfer characteristic of supercritical water is one of the crucial issues in SuperCritical Water-Cooled Reactors (SCWRs). The efficiency and safety of the SCWR system are largely dependent on the local heat transfer performance. This paper establishes the numerical model for supercritical water in a long vertical circular loop (inside diameter = 10 mm) and analyzes the flow and heat transfer mechanism during the transition process from subcritical to supercritical states under various heat fluxes (uniform and nonuniform). The results reveal that the difference in thermophysical properties between the boundary layer and the core region is the main reason for the heat transfer behavior, especially during the transition from subcritical to supercritical and liquidlike to gaslike. The flow structure on the buffer layer is a dominating factor for heat transfer deterioration. The cases under variable nonuniform heat fluxes have a higher heat transfer coefficient compared with uniform heat fluxes. But, this will cause large changes of the parameter locally. The dominating factors of heat transfer deterioration under these conditions are also identified. [ABSTRACT FROM AUTHOR]

Summary: Supercritical heat transfer loops are widely used in large‐scale thermal equipment, which development is restricted by the thermal‐hydraulic characteristics, especially the safety and thermal efficiency under high‐heat fluxes. This study is focused on numerical simulation for a 4‐m test section of the loop and further analyzes the flow transitions and heat transfer mechanisms from subcritical to supercritical. The heat transfer characteristics of supercritical water in the vertical loop were simulated for conditions: P = 24 MPa, Tin = 320°C, 340°C, mass flux (G) = 1000 kg/m2s, 1500 kg/m2s, and heat fluxes varied from 100 to 1200 kW/m2. The heat transfer transitions are analyzed from the perspective of local parameters that affect the status of both core flow and boundary layers. The empirical correlation and the error backpropagation (BP) neural network prediction model are proposed and compared with experimental and numerical results. The results show that transitions of both boundary layer and core flow from subcritical to supercritical contribute to the heat transfer behaviors: normal heat transfer, heat transfer deterioration, and heat transfer enhancement. The zero‐velocity gradient (∂u/∂r = 0) on the M‐shaped velocity curve causes the turbulent shear stress near the wall to be close to zero, which leads to the suppression of the turbulence. At the same time, the thickness of the thermal boundary layer reaches the maximum, resulting in a large thermal resistance, which affects the heat transfer from the wall to the core area. [ABSTRACT FROM AUTHOR]

The virtual boundary meshfree Galerkin method (VBMGM) is given to calculate the multi-domain transient heat conduction with heat source problem. The radial basis function interpolation is used to obtain the virtual source function on the virtual boundary, the heat source, the particular solutions of the temperature, and the heat flux in the computational domain. The formula of the proposed method is gotten by the Galerkin method and the control equations of the multi-domain transient heat conduction with heat source. Therefore, there are the advantages of the Galerkin method, the boundary element method, and the meshfree method for the multi-domain transient heat conduction with heat source problem by VBMGM. The numerical meaning of the weighted values are definite for the multi-domain transient heat conduction with heat source problem through VBMGM, such as the partial derivatives of the temperature, the heat flux, the heat source, and the continuity conditions on the public boundary at time. The detailed calculation scheme of VBMGM is deducted for the multi-domain transient heat conduction with heat source problem. Two numerical examples, four subdomains with the time-dependent heat source problem and two subdomains with the constant heat source and mixed boundary condition problem, are computed. The accuracy and the stability of VBMGM for the multi-domain transient heat conduction with heat source problem are verified. [ABSTRACT FROM AUTHOR]

Heat transfer to supercritical water were investigated both experimentally and numerically. A 2-m long vertical upward smooth tube with a diameter of 19 mm was tested at pressures ranged from 11 to 32 MPa, values of mass flux from 170 to 800 kg·m −2 ·s −1 and heat fluxes up to 600 kW·m −2 . Various dimensionless parameters representing effects of property variations, buoyancy and thermal induced acceleration were estimated. Some of them show unique and strong relations to heat transfer coefficient, while no single behavior of independence is obtained with the majority of them. This result indicates additional parameters are required in case these dimensionless parameters are applied to predict supercritical heat transfer. Based on the experimental data, six typical correlations were evaluated. It turns out that the Mokry et al. correlation and Bishop et al. correlation show the best performance in predicting heat transfer. The shear stress transport k-ω model was employed to numerical analysis. Results of numerical prediction show a good agreement with experimental data, which proves the suitability of the present model. According to the result, physical mechanisms of both enhanced and deteriorated heat transfer at supercritical pressure are revealed. The integral effect of specific heat and buoyancy effect are the main reasons resulting in the abnormal heat transfer. [ABSTRACT FROM AUTHOR]

This article presents a virtual boundary meshless with Trefftz method for calculation of the two-dimensional steady-state heat conduction crack problem, which is based on the idea of multidomain combination. The virtual source function is constructed by the radial basis functions approximation in the subdomain not containing the crack. The temperature or heat flux is calculated by crack special solution of Trefftz function in the crack subdomain. Thus, the proposed method has the advantages of both the boundary-type meshless method and the Trefftz method. No nodes or elements are distributed on the crack, because the boundary condition of the crack is automatically satisfied by employing the crack special solution of the Trefftz function. The heat stress intensity factor is simply and directly calculated. [ABSTRACT FROM PUBLISHER]

Abstract: In the range of pressure from 11.5 to 28MPa, mass flow rate from 450 to 1550kgm−2 s−1, and heat flux at inner wall from 50 to 585kWm−2, an experiment was conducted to investigate the heat transfer characteristics of water in a vertical downward tube. The temperature distribution in the tube wall was obtained. The effects of heat flux on heat transfer coefficient and wall temperature were analyzed and the corresponding empirical correlations were presented. The heat transfer coefficients of vertical downward flow were compared with that of vertical upward flow. The experimental results show that at subcritical and near critical pressure, dryout and departure from nucleate boiling (DNB) can occur in vertical downward tube. With the increase of heat flux, heat transfer deterioration occurs ahead and the peak wall temperature after heat transfer deterioration increases obviously. At supercritical pressure, the wall temperature increases slowly with fluid enthalpy when the bulk temperature is lower than the pseudo-critical temperature and increases considerably when the bulk temperature is higher than the pseudo-critical temperature. In the pseudo-critical enthalpy region, the heat transfer is enhanced. [Copyright &y& Elsevier]

• Experimental platform established for sCO 2 mini-channel flow local visualization. • Quantitative procedures established for sCO 2 boundary in field info extraction. • Rapid density decreases and small t differences (0.01 K) under sCO 2 local heating. • Grouped nu trends found for the first time during local boundary visualization. This study is focused on measuring the transient boundary heat transfer in supercritical CO 2 mini-channel flows under local heat application. A pixelated-array masked phase-shifting interferometer system and quantitative data procedures have been established for sCO 2 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. [ABSTRACT FROM AUTHOR]

Abstract: An experiment for heat transfer of water flowing in a vertical rifled tube was conducted at subcritical and supercritical pressure. The main purpose is to explore the heat transfer characteristics of the new-type rifled tube at low mass flux. Operating conditions included pressures of 12–30MPa, mass flux of 232–1200kg/(m2 s), and wall heat fluxes of 133–719kW/m2. The heat transfer performance and wall temperature distribution at various operating conditions were captured in the experiment. In the present paper, the heat transfer mechanism of the rifled tube was analyzed, the effects of pressure, wall heat flux and mass flux on heat transfer were discussed, and corresponding empirical correlations were also presented. The experimental results exhibit that the rifled tube has an obvious enhancement in heat transfer, even at low mass flux. In comparison with a smooth tube, the rifled tube efficiently prevents Departure from Nucleate Boiling (DNB) and delays dryout at subcritical pressure, and also improves the heat transfer of supercritical water remarkably, especially near pseudo-critical point. An increase in pressure or wall heat flux impairs the heat transfer at both subcritical and supercritical pressure, whereas the increasing mass flux has a contrary effect. [Copyright &y& Elsevier]

Abstract: Water wall design is a key issue for supercritical Circulating Fluidized Bed (CFB) boiler. On account of the good heat transfer performance, rifled tube is applied in the water wall design of a 600MW supercritical CFB boiler in China. In order to investigate the heat transfer and frictional characteristics of the rifled tube with vertical upward flow, an in-depth experiment was conducted in the range of pressure from 12 to 30MPa, mass flux from 230 to 1200kg/(m2 s), and inner wall heat flux from 130 to 720kW/m2. The wall temperature distribution and pressure drop in the rifled tube were obtained in the experiment. The normal, enhanced and deteriorated heat transfer characteristics were also captured. In this paper, the effects of pressure, inner wall heat flux and mass flux on heat transfer characteristics are analyzed, the heat transfer mechanism and the frictional resistance performance are discussed, and the corresponding empirical correlations are presented. The experimental results show that the rifled tube can effectively prevent the occurrence of Departure from Nucleate Boiling (DNB) and keep the tube wall temperature in a permissible range under the operating condition of supercritical CFB boiler. [Copyright &y& Elsevier]

The boiler equipment should be able to adapt to the load requirements and overcome the interference of various external conditions. By establishing a one-dimensional single-channel general numerical calculation model suitable for flow instability analysis of ultra-supercritical boilers at 700 °C, the rules of flow in the tubes are calculated. The 7th loop and the 22nd loop of the boiler water wall are selected as typical loops, and the dynamic characteristics of the two loops are calculated. The results show that after applying different multiples of heat flux disturbance, regardless of whether metal heat storage is considered, the inlet and outlet mass flow rates of the two circuits show inverse dynamic responses and eventually return to a steady state. When considering heat storage, it takes about 63 s for the 7th loop to return to stability. The recovery and stabilization time of the 22nd loop is about 60 s. Metal thermal storage has a positive effect on the settling time of the pipe section after heat flux disturbance. And when the maximum heat flux disturbance is applied, the maximum wall temperatures of the two loops are 443.9 °C and 446.5 °C, and the boiler can operate safely and stably. [ABSTRACT FROM AUTHOR]

Experiments were conducted to investigate the heat transfer and flow characteristics of the vertical upward smooth and rifled tubes from subcritical to supercritical pressure. The distributions of wall temperature and heat transfer coefficient (HTC) were obtained, and the HTC correlations and friction resistance coefficient correlations were fitted with experimental data. In addition, the influences of heat flux and type of tube on heat transfer performance were analyzed. The research shows that heat flux has different influences on the heat transfer characteristics under different pressures. The increase in heat flux improves the heat transfer characteristics in the nucleate boiling region, yet it leads to the advance in heat transfer deterioration. However, for supercritical water, the increase in heat flux reduces the heat transfer ability. In addition, using the rifled tube not only improves the heat transfer performance, but also inhibits the occurrence of heat transfer deterioration. The fitted correlations have great predictive ability for the heat transfer coefficient and friction resistance coefficient, and the average relative fitting errors are limited to 20%. [ABSTRACT FROM AUTHOR]

A numerical study is conducted to investigate heat transfer characteristics of supercritical water flowing upward in an inclined smooth tube under uniform heating conditions. In this study, model verification was performed under the conditions of low heat flux and high heat flux to ensure the accuracy of experimental data. Inner wall temperature and heat flux distribute non-uniformly on the circumference due to the influence of natural convection. The increase of heat flux enhances the non-uniform circumferential distribution, while the increase of mass flux reduces the non-uniform circumferential distribution. Heat transfer of upward vertical and inclined flows is compared under low and high heat flux conditions. Radial distributions of fluid temperature, density, specific heat capacity, velocity, and turbulent kinetic energy are presented and analyzed. The analysis shows that the increase of heat flux reduces radial turbulence and heat-absorbing capacity of the boundary fluid, while increases radial temperature and density gradient. Three dimensionless buoyancy parameters are used to evaluate the buoyancy effect of inclined flow. [ABSTRACT FROM AUTHOR]

Based on the viewpoint of bubble crowding in near-wall bubble layer, a critical heat flux (CHF) prediction model was developed for low quality flow boiling of water in uniformly heated vertical circular tube under high pressure and low flow rate conditions. In this model, a CHF formula was derived from the conservation equations of mass, momentum and energy, where the transverse mass transport between the near-wall bubble layer and core is assumed to be limited. Taking account of the convective shear effect caused by the frictional drag on the wall-attached bubbles, the limiting transverse interchange of mass flux crossing the bubble layer–core interface was determined from the momentum balance equations. A new formula of bubble departure diameter considering the effect of buoyancy was put forward and used to solve the model with numerous other empirical correlations (e.g. bubble departure point, turbulence velocity profile, void fraction and so on). The model shows good agreements with the experimental data of uniformly heated circular tube. Based on this, the effects of flow variables such as pressure, mass flux and inlet subcooling on CHF prediction results were also discussed. [ABSTRACT FROM AUTHOR]

Heat transfer to supercritical water in a smooth tube with an inclined angle of 25° was investigated experimentally and numerically. Experimental results show that the increase of mass flux improves the heat transfer. As the pressure increases, influence of physical property variation to the heat transfer becomes gentle. Thereby, the increase of pressure reduces the heat transfer under an enhanced condition. Dimensionless buoyancy parameters Gr q */ Gr qth and G r ‾ / R e 2.7 are compared on the basis of experimental results. The evaluated result shows that Gr q */ Gr qth is applicable to the inclined tube flow. Base on the supercritical data, a new heat transfer correlation is proposed. Numerical analysis was completed with the shear stress transport k - ω model. Corresponding results show that the influence of variable mass flux and pressure on supercritical heat transfer is realized by changing radial distributing characteristics of turbulence and physical property. The increase of mass flux improves the radial turbulence and heat-absorbing capacity of the boundary fluid, so the supercritical heat transfer is enhanced. At a low mass flux condition where heat transfer reduction occurs, the increase of pressure improves the heat transfer. At a high mass flux condition where heat transfer enhancement occurs, the increase of pressure reduces the heat transfer. Influence of natural convection caused by the buoyancy leads to the occurrence of heat transfer disparity between top and bottom sides of the inclined tube. The increase of mass flux weakens the influence of natural convection and improves local heat transfer at the top side. At the low mass flux condition, the increase of pressure conducts the same effect with the increase of mass flux. At the high mass flux condition, the increase of pressure reduces the local heat transfer at the top side. • Buoyancy parameter Gr q */ Gr qth is applicable to the inclined tube flow. • The increase of pressure improves heat transfer reduction at low mass flux. • The increase of pressure reduces heat transfer enhancement at high mass flux. [ABSTRACT FROM AUTHOR]

• An improved model is made to study the flow instabilities of supercritical water. • The different states of the outlet working fluid are handled differently. • The error of this model is smaller than that of the previous models. • The relationship between the minimum CHF point and the pressure is analyzed. 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. [ABSTRACT FROM AUTHOR]

In this paper, the evaporation heat transfer coefficient of carbon dioxide at low temperature of −30 to −20 °C in a horizontal smooth tube was investigated experimentally. The test devices consist of mass flowmeter, pre-heater, magnetic gear pump, test section (evaporator), condenser and liquid receiver. Test section is made of cooper tube. Inner and outer diameter of the test section is 8 and 9.52 mm, respectively. The experiment is conducted at mass fluxes from 100 to 300 kg/m s, saturation temperature from −30 to −20 °C. The main results are summarized as follows: In case that the mass flux of carbon dioxide is 100 kg/m s, the evaporation heat transfer coefficient is almost constant regardless of vapor quality. In case of 200 and 300 kg/m s, the evaporation heat transfer coefficient increases steadily with increasing vapor quality. For the same mass flux, the evaporation heat transfer coefficient increases as the evaporation temperature of the refrigerant decreases. In comparison of heat transfer correlations with the experimental result, the evaporation heat transfer correlations do not predict them exactly. Therefore, more accurate heat transfer correlation than the previous one is required. [ABSTRACT FROM AUTHOR]

• The flow instability and oscillatory heat transfer of ultra-supercritical water in parallel channels was investigated. • The effects of parameters on flow instabilities were analyzed. • The effects of amplitude and frequency of oscillatory flow on heat transfer was discussed. • The heat transfer correlations were evaluated and proposed. The flow instability and oscillatory heat transfer characteristics of ultra-supercritical water in vertical upward parallel channels were experimentally investigated under the condition range of pressure within 26–30 MPa, inlet pressure drop coefficient from 0 to 5, time-averaged mass flux of 420 kg•m−2•s−1, and heat flux in the range of 0–130 kW•m−2. Two types of oscillations, called low-frequency oscillation and high-frequency oscillation, were observed during the experiment. The effects of mass flux, pressure, and inlet pressure drop coefficient on flow instability were discussed. The influences of mass flux oscillation on wall temperature and oscillatory amplitude ratio and oscillation frequency number on time-averaged Nusselt (Nu) number were analyzed. The time-averaged Nu number of oscillatory flow was compared with the supercritical heat-transfer correlation equations. Results showed that the increase in pressure, inlet pressure drop coefficient, and inlet mass flux were beneficial to system stability when low-frequency oscillation occurred. Pressure and inlet pressure drop coefficient had a slight effect on flow stability, but inlet mass flux could still improve flow stability for the high-frequency oscillation. The heat transfer was restrained in the quasi-critical enthalpy region when the oscillation occurred. The wall temperature fluctuated with mass flux oscillation with the same period and opposite phase, and the larger amplitude of mass flux oscillation led to the stronger fluctuation of the wall temperature. Upon the occurrence of low-frequency oscillation, the time-averaged Nu number decreased with the increase of oscillatory amplitude ratio, and initially decreased with the increase of oscillatory frequency number and then remained constant. Upon the occurrence of high-frequency oscillation, the time-averaged Nu number increased slowly with the increase of oscillatory amplitude ratio and decreased with the increase of oscillatory frequency number. The values of Nu number predicted by correlations were generally higher than those obtained by experiments. [ABSTRACT FROM AUTHOR]

In this study, a numerical code that applies a time-domain method is established to analyze the flow instability of a uniformly heated parallel-channel system. Nonlinear dynamics of the ultra-supercritical flow in the water wall are discussed. Results show that the inlet and outlet mass flow rates demonstrate antiphase. The mass flow rates with heat flux perturbations imposed on either single channel decline gradually with time, suggesting that flow stability can be maintained at normal operation. In addition, the effects of heat flux perturbation on transient responses of the typical parallel channels are studied. Results illustrate that the maximum of the inlet mass flow rate in both channels are high when perturbation is imposed on a strong heated channel. Moreover, flow in the stronger heated channel reveals more remarkable dynamic characteristics than in the weaker one. Approximately 141.6 and 139.8 s are needed for perturbation.1 and perturbation.2 to restore to steady state, respectively. Furthermore, data under different inlet temperatures and mass flow rates are calculated to generate the dimensionless instability boundary. When the inlet temperature is low, the inlet mass flow rate should be increased to stabilize the system. Otherwise, the effect of the mass flow rate on the instability boundary is almost negligible. [ABSTRACT FROM AUTHOR]