Heat Transfer Of Supercritical Water Research Articles

Direct numerical simulation of flow and heat transfer of supercritical water with different heat fluxes

The flow and heat transfer characteristics of supercritical water (SCW) are important considerations in the thermal-hydraulic design of the Supercritical Water-Cooled Reactor (SCWR). In the present study, the direct numerical simulation (DNS), developed with OpenFOAM, was utilized to investigate the effect of heat flux on the flow and heat transfer of SCW in a vertical circular pipe. The investigation involves detailed analyses of the wall temperature, velocity distribution, and turbulent statistics at various heat fluxes. It was found that buoyancy first impairs heat transfer, and then recovers heat transfer. This is attributed to the variation of buoyancy production and turbulence production, which are resulted from the buoyancy direct effect and indirect effect, respectively. As the heat flux increases, the recovery occurs earlier with higher magnitude. The vortex structures based on Q-criterion clearly illustrate the same process as well. Several heat-transfer correlations were assessed based on the DNS results. It indicates that Dittus and Boelter correlation (1930) cannot accurately predict the heat-transfer characteristics of SCW, while Chen and Fang correlation (2014) exhibits a higher level of predictive accuracy for Nusselt number. In addition, several turbulence models were evaluated against the DNS data. The results show significant deviations in predicting the heat transfer of SCW. The large discrepancy may be due to the inappropriate model coefficients, the failed predication of turbulence kinetic energy, as well as the constant turbulent Prandtl number commonly applied.

Research on prediction and analysis of supercritical water heat transfer coefficient based on support vector machine

In order to better perform thermal hydraulic calculation and analysis of supercritical water reactor, based on the experimental data of supercritical water, the model training and predictive analysis of the heat transfer coefficient of supercritical water were carried out by using the support vector machine (SVM) algorithm. The changes in the prediction accuracy of the supercritical water heat transfer coefficient are analyzed by the changes of the regularization penalty parameter C, the slack variable epsilon and the Gaussian kernel function parameter gamma. The predicted value of the SVM model obtained after parameter optimization and the actual experimental test data are analyzed for data verification. The research results show that: the normalization of the data has a great influence on the prediction results. The slack variable has a relatively small influence on the accuracy change range of the predicted heat transfer coefficient. The change of gamma has the greatest impact on the accuracy of the heat transfer coefficient. Compared with the calculation results of traditional empirical formula methods, the trained algorithm model using SVM has smaller average error and standard deviations. Using the SVM trained algorithm model, the heat transfer coefficient of supercritical water can be effectively predicted and analyzed.

Experimental and numerical investigations on the influence of buoyancy on supercritical water heat transfer characteristics in inclined smooth tubes

The influence of the varying buoyancy effects on heat transfer characteristics was experimentally and numerically investigated. Different pressures, heat fluxes, and inclination angles were selected to alter the buoyancy effect. Operating parameters were varied (Pressure varied from 25 MPa to 29 MPa, mass flux varied from 800 kg/(m2·s) to 2294 kg/(m2·s), heat flux varied from 500 kW/m2 to 714 kW/m2, and the inclination angle varied from 0° to 90°). The comparison of heat transfer characteristics between 2000 kg/(m2·s) and 2294 kg/(m2·s) was conducted by experiments, showing that the average heat transfer coefficients at G = 2000 kg/(m2·s) are better than those at G = 2294 kg/(m2·s) due to the different buoyancy effects. The comparison between 650 kW/m2 and 714 kW/m2 showed that the heat transfer characteristics improve with the increase in heat flux under a high mass flux condition. Moreover, a 3-D numerical model was built for predicting the heat transfer characteristics in inclined tubes. The influence of buoyancy effects induced by the different inclination angles on the heat transfer characteristics was investigated numerically. The numerical results showed that the buoyancy effect is evident at G = 800 kg/(m2·s). The buoyancy effects reflect in the velocity of secondary flow, fluid temperature, and temperature gradient of boundary layers. The influence of pressure on the heat transfer characteristics reflects in the radial distributions of properties. The temperature and temperature gradient are higher at the bottom of the 75° inclined tube and the top of the 15° inclined tube, resulting in a decline in the heat transfer coefficients. Finally, the ratio of vorticity and Reynold’s numbers (Se/Re) was adopted as a criterion to predict the buoyancy effects in the inclined tubes, and the results showed that Se/Re is suitable for evaluating buoyancy effect.

Experimental investigation on heat transfer of supercritical water flowing in a horizontal tube with axially non-uniform heating

For a heat exchanger, the heat flux is usually non-uniform in the axial direction, and the knowledge about heat transfer of supercritical water with axially non-uniform heating is scarce. To fill the gap, experiments were conducted in a horizontal tube to study the heat transfer characteristics of supercritical water with axially sinusoidal heating. The pressures varied from 23.5 to 26.5 MPa, mass fluxes 200 to 400 kg·m−2·s−1 and average heat fluxes 50 to 150 kW·m−2. Compared with uniform heat flux, the temperature difference between the top and bottom wall is larger than that of the axially sinusoidal heat flux. The inner-wall heat flux is non-uniform along the circumference due to the temperature difference, being higher at the side wall and lower at the top wall. A relative heat flux parameter is defined to describe the relative magnitude of the local heat flux. The relative heat flux parameter of the top generatrix, which is inversely proportional to the average heat flux, decreases linearly with the increase of the temperature difference between the top and side generatrix. The non-uniform degree of heat flux along the circumference is positively correlated with the average heat flux. Additionally, the local heat transfer characteristics should be considered in horizontal tubes. On the one hand, the heat transfer deterioration may occur when the fluid temperature near the top wall is higher than the pseudo-critical temperature and it can be suppressed with increasing Reynolds number. On the other hand, the local heat transfer can be enhanced if the side and bottom wall temperatures exceed the pseudo-critical temperature.

Numerical investigation of upward supercritical water flow with Joule heating effect

By using Joule's Law, resistivity equation, Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) functions, and resistivity-temperature correlation established based on the available experimental data, Joule heating heat flux profiles of upward supercritical water heat transfer in the annular tube are modelled and applied as the boundary condition. The calculated wall temperature result is compared to the Razumovskiy et al. experiment dataset. It is discovered that by using the PCHIP-modelled Joule heating profiles, the estimated wall temperature for both the Normal Heat Transfer (NHT) and Deteriorated Heat Transfer (DHT) regimes is comparable to the experiment in terms of trend and magnitude. However, by using the conventional constant heat flux profiles, the upstream and downstream wall temperatures are overestimated and underestimated respectively. This study demonstrated that CFD can adequately replicate experimental heat flux conditions, hence improving CFD estimates of supercritical heat transfer, particularly for the DHT, which has a substantial heat flux variation. With this fine imitation of the Joule heating heat flux, the critical DHT regime can be more accurately predicted.

Heat transfer of supercritical pressure water in helical tubes

Subcritical steam generators in the current high-temperature gas-cooled reactor pebble-bed module in China can be replaced by supercritical steam generators to better coordinate the reactors and supercritical steam turbine unit to improve the thermal efficiency with no fluid phase change at supercritical pressures. The heat transfer of supercritical-pressure water flow in helical tubes with various helix diameters was simulated using the re-normalization group k–ε model to investigate the effects of finite-thickness walls, inlet mass flux, and helix diameter. The finite-thickness wall barely affected local heat transfer in the straight tube with inlet mass flux of 1,260 kg/(m2 s) whereas the local heat transfer in the helical tube was very different with relative difference in q/qav between the inside and bottom, caused by the centrifugal force, is 36%. In helical tubes, the heat transfer coefficients in the inner bar were the lowest, with a low fluid velocity under the effect of the centrifugal force. The buoyancy and centrifugal force in the helical tubes caused non-uniformity in the wall temperature; however, when the fluid temperature increased below the pseudo-critical temperature, the temperature distributions showed an increasing trend. The non-uniformities in the wall temperature distributions decreased as the centrifugal force increased, and they were suppressed by the finite-thickness wall.

Performance analysis of heat transfer for supercritical water cooled in various inclined tubes

In this paper, the heat transfer performance of supercritical water (SCW) cooled in various inclined tubes was investigated numerically. The simulation was conducted using the shear stress transport (SST) k-ω model and it was verified using measured data. The inclination angle ranges from vertically downward flow (θ = -90°) to vertically upward flow (θ = 90°). The effects of mass flux, operating pressure and inclination angle on SCW heat transfer were presented. The analysis indicated that buoyancy had little influence on the flow heat transfer in the gas-like region (Tb > Tpc) and it became more significant in the liquid-like region (Tb < Tpc), especially at low mass flux. The secondary flow induced by buoyancy distorted the velocity field, achieving better heat transfer performance at the top surface. It sharpened the velocity field and intensified the heat transfer in the upward flow. The inclined flow with θ = 60° provided the best heat transfer performance among the various inclined flows. Moreover, the buoyancy effect could be alleviated and the heat transfer could be improved with increasing of mass flux. When the mean bulk enthalpy was slightly superior to the pseudo-critical enthalpy (Hb > Hpc), the heat transfer coefficient reached peak. Not only did the specific heat increase but also the velocity gradient and turbulent kinetic energy increased with decreasing pressure, which enhanced the heat transfer. The buoyancy effect was evaluated using the empirical parameters Gr/Re2 and Gr/Re2.7, and results showed that the Gr/Re2.7 had better prediction accuracy.

Numerical investigations of corrugated tube and Fe3O4 nanoparticles on the mitigation effects of supercritical water heat transfer deterioration

When faced with high thermal loads, the dramatic variations in supercritical water (SCW) thermophysical properties can lead to heat transfer deterioration (HTD). Therefore, the present paper first proposes a new mechanism of HTD based on the pseudo boiling theory, and then numerically investigates the mitigation effects of nanoparticles and corrugations on the HTD. By the investigation of SCW in vertically upward smooth tube, the mechanism study illustrates that the pseudo film with the characteristics of low turbulence intensity and thermal conductivity induces the HTD, and the pseudo two-phase flow instability dominates the growth and dissipation of pseudo film. With the help of nanoparticles and corrugations, the wall temperature has a maximum decrease of 348 K, the wall temperature peak mitigation ratio was 33.5%, and the maximum heat transfer enhancement is 164%. Since the corrugations within the corrugated tube (CT) does not change the growth rate of pseudo film, "HTD cycles" occurs in the CT with large corrugation pitch and further deteriorates the overall heat transfer performance. By the inhibition of pseudo film growth and enhancement of gas-like SCW thermal conductivity, the coupling effect of nanoparticles and corrugations can effectively suppress the HTD as well as "HTD cycles".

Study on Convective Heat Transfer of Supercritical Water in Annular Square Channel

Supercritical water, known for its abrupt changes in fluid properties near the pseudocritical region, has always posed a design challenge, leading to enhancement or deterioration in heat transfer. Additionally, the lack of complete understanding of the thermodynamic behavior of supercritical water near the pseudocritical zone, unlike in the subcritical zone, highlights the necessity of a systematic study. Hence, this paper focuses on characterizing the convective upward flow and heat transfer characteristics inside a vertical smooth annular square channel. The numerical analysis uses a steady-state, pressure-based, compressible, Newtonian solver with body force term and two-equation turbulence model to study the influence of variation in pressure, heat flux, and heat-to-mass flux ratios. The flow characteristics and heat transfer behavior of deteriorated, normal, and enhanced heat transfer modes are studied. The heat transfer deterioration is suppressed with the increase in pressure; however, it increases with the increase in inlet bulk temperature. The supercritical boiling number that determines the heat transfer mode is calculated and analyzed for the square annulus section. The evolution of the flow in different heat transfer modes differs based on the effect of buoyancy on the velocity field and the turbulence. The calculated Nusselt numbers match the existing Jackson and Hall correlation well with a maximum absolute error of 9.91%.

Nuclear coupled thermal–hydraulic analysis of parallel channel density wave instabilities in a supercritical water reactor

In an attempt to obtain a realistic estimate of the density wave instability (DWI) thresholds of a typical supercritical water reactor (SCWR) in its relevant operating regime, the present numerical framework accounts for the nonlinear interdependence among the thermal–hydraulic (TH), neutronic and fuel dynamic field variables, by solving the coupled multi-physics conservation equations in a time-domain where the TH, neutron point-kinetic (NPK) and fuel heat conduction (FHC) solvers are integrated through coolant density and fuel temperature reactivity feedback coefficients, and supercritical water (SCW) heat transfer coefficient (HTC). The time dependent and radially non-uniform, but axially uniform reactor power distribution among the different fuel assemblies (FAs) are incorporated in the numerical framework by the employment of NPK solver and considering the existence of several parallel channels in the reactor core where every channel represents a group of FAs of similar reactor power assembled in a single region. The integrated model is next compared against the available numerical results to access its capability in analyzing thermal-hydraulically induced DWIs while being influenced with the neutronic reactivity feedback effects. Nuclear coupled core-wide and regional density wave oscillations (DWOs), two modes of parallel channel DWIs, are finally analyzed with the purpose to determine the effect of temporal reactor power variation and the channel to channel interactions on the stability thresholds of the SCWR under consideration. The conclusions are drawn and reported accordingly.

Numerical modeling on heat transfer of supercritical water in cooled horizontal circular tube

As an efficient and energy-saving fluid, supercritical water (SCW) has great potential in power plants. In this paper, the cooling heat transfer of SCW in horizontal tube was investigated numerically. The two highly recommended models (Re-Normalization Group (RNG) k-ε model and Shear Stress Transport (SST) k-ω model) are validated against experiments and it is observed that the SST k-ω model is closer to the experimental data. The cooling heat transfer characteristics of the SCW in horizontal tubes are revealed and the effects of heat flux, mass flux, tube diameter and buoyancy on the heat transfer performance are investigated. Results demonstrated that the heat transfer coefficient (HTC) peaks when bulk enthalpy (Hb) slightly greater than the pseudo-critical enthalpy (Hpc). Heat flux affected SCW heat transfer at Hb>Hpc and had no significant effect at Hb<Hpc. Higher HTC and more uniform wall temperatures could be achieved by increasing the mass flux. Temperature and velocity stratification could be observed, and the wall temperature at the top was higher than the bottom due to the buoyancy effect. The secondary flow induced by buoyancy force disturbed the velocity field, drawing better heat transfer performance at the top surface. The HTC discrepancy between at the top and bottom could be well explained by the field synergy principle. Finally, two buoyancy criteria were compared and the results indicated that Ri=Gr/Re2 could better predict the buoyancy effect for SCW cooling flow in the whole enthalpy regimes. The conclusions can provide guidelines for further design of supercritical water heat exchangers.

Numerical study of heat transfer and fluid flow of supercritical water in twisted spiral tubes

ABSTRACT Supercritical water (SCW) as fluid with enough potential abilities such as high thermal efficiency can be replaced in water cooling systems. However, helical pipes are the most common type of swirl generators used for heat transfer enhancement, and their geometrical parameters contribute significantly to the compactness and efficiency of heat exchangers. In this study, for the Reynolds ranges of 8000–20000, a numerical study is performed to investigate SCW flow within circular tube, twisted oval tube and twisted multi-lobe tubes. Effects of such parameters as cross-section shapes and lobed numbers on heat transfer performance and flow physics of different spiral tubes were investigated. Results indicated SCW has a contradictory behavior with ordinary water. The results showed that twisted tri-lobed tubes had higher average Nusselt number than circular tube and twisted oval tube, which was 53% and 41%, respectively. Also in these tubes the larger radius of connecting arc and the smaller length of major axis conclude the higher amount like 4%-6% of heat flux due to the enhancement of swirling fluid flow in the pipe and the heat flux. By increasing the number of lobes, the swirling flow rate that is bounded by the lobes will increase.

Numerical investigation on deteriorated heat transfer of supercritical water flowing upward in tubes with variable cross-sectional geometries

To mitigate Deteriorated Heat Transfer (DHT) of Supercritical Water (SCW) upward flow, tubes with variable cross-sectional geometries are numerically investigated. Three types of variable cross-sectional geometries: converging channel, diverging channel, and periodic geometries, are modelled. Results of wall temperature in the smooth channel are compared with experimental data, and good agreements are obtained. The wall temperature effects of convergent and divergent channels of various proportions and periodic geometries of various amplitudes are investigated. Thermo-Hydraulic Performance Evaluation Criterion (PEC) is proposed to evaluate the performance of the studied geometries using dimensionless parameters Nu/Nu0, f/f0, and PEC = (Nu/Nu0)/(f/f0)1/3. The results indicated that the convergent channels suppress and delay DHT downstream, while opposite effects are observed for divergent channels. Periodic geometries, which have alternating convergent and divergent sections, suppress DHT with minimal pressure drop. 1st temperature peak is reduced by 200 K with 1 mm of outlet radius reduction for the convergent channel. Average PEC is enhanced by 60% with 0.5 mm A of periodic geometry. It is discovered that the convergent section can suppress DHT, and the mitigation effect is proportional to the size of convergence. It is concluded that, since the DHT caused by buoyancy-induced flow laminarization has flattened the cross-sectional velocity profile, the convergent section reverts the laminarization to the normal velocity profile by the nozzle acceleration effect. Nozzle acceleration also increases Turbulent Kinetic Energy (TKE) in the boundary layer which further enhances turbulent heat transfer.

Bayesian network analysis of heat transfer deterioration in supercritical water

Using the experimental data of supercritical water heat transfer, a Bayesian network is constructed for various parameters which affect the heat transfer deterioration (HTD)in supercritical water. Through the Bayesian network model, it is concluded that the most direct factors are the actual heat transfer coefficient and the Pr number, and the factors which are most closely related to HTD are thermal conductivity, dynamic viscosity, Reynolds number and heating power. The interaction of various parameters results in the complexity and changeability of the situation. The Bayesian network is capable of showing the effect of various factors under different conditions, and then it comes to make reasonable inferences and analysis on the possibility of HTD in supercritical water with different condition parameters. Then the mechanism analysis of the effect is carried out.

Numerical Investigation on Deteriorated Heat Transfer of Supercritical Water Flowing Upward in Tubes with Variable Cross-Sectional Geometries

Numerical Investigation on Deteriorated Heat Transfer of Supercritical Water Flowing Upward in Tubes with Variable Cross-Sectional Geometries

Numerical Investigations of Corrugated Tube and Fe3o4 Nanoparticles on the Mitigation Effects of Supercritical Water Heat Transfer Deterioration

Numerical Investigations of Corrugated Tube and Fe3o4 Nanoparticles on the Mitigation Effects of Supercritical Water Heat Transfer Deterioration

Numerical Verifications on Heat Transfer to Supercritical Water Flowing Upward in a 4-m Long Bare Vertical Tube

Abstract Thermal efficiency and safety of generation-IV nuclear-power-reactor concept supercritical water-cooled reactor (SCWR) are largely dependent on the coupled supercritical water (SCW) thermophysical properties and heat transfer performance in the supercritical region. This paper presents the numerical investigation of the heat-transfer characteristics of SCW flow in a 4-m long circular tube (ID = 10 mm) based on computational fluid dynamics. Numerical model for SCW was established in this analysis and forced-convection heat transfer was studied at different operating conditions. The data were collected at pressure of about 24 MPa, inlet temperatures from 320 to 350 °C, mass flux from 1000 to 1500 kg/m2·s, and heat flux up to 1500 kW/m2. Results of numerical simulation predict the experimental data with reasonable accuracy. A dimensional analysis was conducted to derive the general form of an empirical supercritical water heat-transfer correlation. The decrease of turbulent viscosity due to the decrease of density leads to a lower turbulent diffusion and turbulent kinetic energy, which inhibits heat transfer. The increased wall temperature and localized heat transfer deterioration (HTD) would occur as the liquid in the core of the tube is isolated for the low-density fluid adheres to the near-wall region, which is characterized by low thermal capacity.

Heat transfer characteristics of supercritical water in channels: A systematic literature review of 20 years of research

• More experiments are required to validate the existing the turbulence model. • Turbulence model with Algebraic heat flux model (AHFM) may be promising. • Heat transfer peak occurs as the fluid approaches the pseudo-critical temperature. • To achieve the high accuracy, piecewise correlation may be an effective method. • Internally ribbed tube combined with inclined angles may be a research direction. Supercritical water (SCW) is one of the high-profile fluids between scholars, which has great potential in the thermal industry. Therefore, it may serve as a promising fluid utilized in nuclear and boiler systems. This paper presents a comprehensive review in terms of the published literature on supercritical water heat transfer in channels. Three types of heat transfer, involving normal, enhanced and deteriorated heat transfer, are classified in this article. Firstly, the thermo-physical properties of supercritical water are illustrated to explain the reasons for the different heat transfer behavior. Heat transfer enhancement and deterioration appear to have greater potential and draw some researchers’ interest. In short, transformation of geometry or operating conditions, such as, channel structure, mass flux and heat flux, would induce variations of thermo-physical properties. Consequently, heat transfer performance can be significantly affected. The heat transfer characterization and affecting factors were evaluated. Some unusual phenomena were explained. Then, the developed heat transfer coefficients (HTC) were compared with the experimental data available in the open literature. The results indicated that the reliable accuracy could be achieved through these correlations except the pseudo-critical region. Additionally, the mechanism and the onset of heat transfer deterioration were revealed and estimated. Finally, this review also identifies the current challenges regarding this research through analysis and comparison. These challenges deserve to be efficiently solved and optimized to enhance supercritical water heat transfer in the future.

Experiemental Study on Heat Transfer of Supercritical Water in Triangular Channel of Reactor Core with Spacer Grid

The experimental study on supercritical water flow heat transfer is carried out for the vertical upward triangular sub-channels in the supercritical water cooled reactor core with spacer grid. The fuel bundle diameter and pitch ratio of this sub-channel used are 8 mm and 1.4 respectively. The parameters adopted in the research include heat flux (q) ranging from 600 kW/m2, pressure (P) ranging from 23-28 MPa, and mass flow rate (G) ranging from 700-1,300 kg/(m2·s). This study analyzes the effect of such thermal parameters as heat flux, pressure and mass flow rate on the heat transfer characteristics of supercritical water. According to the experimental results, with the mass flow rate at the spacer grid increasing, the fluid disturbance increases and the heat transfer coefficient rises significantly; under the supercritical pressure, the inner surface temperature increases with the increasing pressure, and consequently, the peak heat transfer coefficient decreases; as the peak heat transfer coefficient reduces at an excessively high heat flux, the heat transfer performance can be improved when the heat flux is reduced properly; increasing the mass flow rate causes the drop of inner surface temperature and the increase of peak heat transfer coefficient, and thus can significantly improve the heat transfer performance; and the pressure change has little effect on the heat transfer characteristics in the vicinity of spacer grid, and however, the system safety can be improved by increasing the pressure properly.

Modeling of heat transfer of supercritical water in helical finned double pipe

Supercritical water (SCW) is a promising fluid for achieving high thermal efficiency. In the present work, the SST k-ω turbulence model is employed to numerically simulate flow and heat transfer behavior of supercritical water in horizontal double pipe with helical fins. Grid independence test was firstly carried out and then model was validated with experimental data. Different combinations of width, height and pitch in helical double pipe numerical model, width varying from 2 mm to 4 mm, height ranging from 2 mm to 6 mm and pitch available from 15 mm to 25 mm, were examined. In addition, effects of buoyancy force, hot fluid temperature and mass flux on the heat transfer performance were investigated. Buoyancy disturbs the flow field by inducing secondary flow. The flow field is symmetrically distributed on the tube-side. In contrast, the presence of the fins in shell-side breaks the symmetrical distribution and generates a swirling flow at the top of the fins. The results indicated that the peak tube-side and overall heat transfer coefficients emerged at hot fluid slightly greater than the pseudo-critical point temperature. Moreover, the overall heat transfer coefficient improved as mass flux on both the tube-side and the shell-side. However, the shell-side would induce a greater magnitude. Also, the shell-side pressure drop closely related to the shape factor and increased with it. The performance evaluation criterion for case 8 and case 9 were 2.08 and 1.88, respectively. Nevertheless, the pressure drop of case 8 was more than twice case 9. Consequently, case 9 may be an optimal configuration simultaneously considering the coupling effect of heat transfer and pressure drop.