Heat transfer in rod bundles cooled by supercritical water – Experimental data and correlations

Calculations to substantiate the characteristics of a reactor cooled by water with supercritical steam parameters and an adjustable neutron spectrum require clarification of data on heat transfer characteristics. The features and data on heat transfer in round pipes and rod bundles at supercritical pressures (SCP) are considered. In analysis of hydrodynamics and heat transfer dates with the flow of water of supercritical parameters in round pipes, an area of both more intense and degraded convective heat transfer was detected compared to subcritical pressures. It is assumed that one of the reasons for the deteriorated heat exchange is the presence of a near-wall layer consisting of a "gas" phase with low thermal conductivity and a central flow region in the form of a liquid-like phase having a lower temperature. A brief review of data on heat transfer in round tubes and rod bundles with SCP is presented. Since experiments on water are complex and expensive, many results, including the SSC RF - IPPE, were obtained on model media (CO2 and freon-12). Shown that despite the diversity of recommendations on the boundary regime with the deterioration of heat transfer, the proposed ratios give a different dependence of the heat flux density on the mass velocity. They do not consider the influence of such parameters as pressure, channel geometry, temperature of heat exchange surface, etc., they are obtained for a narrow range of parameters. And only extensive analytical studies of Yu.A. Zeigarnik et al. (JIHT RAS, NRU "MEI") allowed to summarize the data on heat transfer in round pipes at SCP. Only limited data was obtained by Russian, Ukrainian and Chinese specialists in heat transfer in bundles with a small number of pipes. The results of Chinese experts have shown that heat transfer in rod bundles at supercritical water pressures is higher and more stable than when water moves in pipes and annular channels. In close bundles, the deterioration of heat transfer occurred at low mass velocities and high heat fluxes, and in widespread deterioration of heat transfer was not observed. The growth of heat transfer in the rod bundles is promoted by mixing with spacer and mixing grids, which destroy the wall barrier layer, which prevents the transfer of heat under supercritical pressure from the wall to the center of the flow. The accumulation of new experimental data and additional analysis of research are necessary. A description and technical characteristics of the thermo-hydraulic facilities of the SCP on water (SVD-1 and SVD-2) and freon-12 (STF) available at SSC RF - IPPE is provided. The results of experiments at SSC RF - IPPE and technical approach and methodology of future experiments in hydrodynamics and heat transfer at SCP is presented and discussed.

An experiment has recently been performed at Xi’an Jiaotong University to study the wall temperature and pressure drop at supercritical pressures with upward flow of water inside a 2×2 rod bundle. A fuel-assembly simulator with four heated rods was installed inside a square channel with rounded corner. The outer diameter of each heated rod is 8 mm with an effective heated length of 600 mm. Experimental parameters covered the pressure of 23–28 MPa, mass flux of 350–1000 kg/m2s and heat flux on the rod surface of 200–1000 kW/m2. According to the experimental data, it was found that the circumferential wall temperature distribution of a heated rod is not uniform. The temperature difference between the maximum and the minimum varies with heat flux and/or mass flux. Heat transfer characteristics of supercritical water in bundle were discussed with respect to various heat fluxes. The effect of heat flux on heat transfer in rod bundles is similar with that in tubes or annuli. In addition, flow resistance reflected in the form of pressure loss has also been studied. Experimental results showed that the total pressure drop increases with bulk enthalpy and mass flux. Four heat transfer correlations developed for supercritical pressures water were compared with the present test data. Predictions of Jackson correlation agrees closely with the experimental data.

Experimental investigation of heat transfer from a 2 × 2 rod bundle to supercritical pressure water

Experimental and numerical investigation on heat transfer of supercritical water flowing upward in 2 × 2 rod bundles

Mixed convection heat transfer in a 5 × 5 rod bundles

Development of a correlation for mixed convection heat transfer in rod bundles

The flow and heat transfer in rod bundles are of vital importance in the reactor design. Studies on the turbulent flow in tight lattice have presented the quasi periodic large scale vortex structure is highly accounted for the local flow and heat transfer and turbulent mixing in rod bundles. In this work, the Unsteady Reynolds Averaged Navier–Stokes (URANS) simulation with the Reynolds Stress Model (RSM) is adopted to simulate the flow and vortex structure in rod bundles. The vortex structure in sparse lattice with nonuniform wall roughness is also investigated and compared with that in tight lattice. The results indicate that the quasi periodic large scale vortex structure and flow pulsation are available in both tight lattice and the sparse lattice with non-uniform wall roughness. Due to the existence of the vortex structure, the heat transfer in spare lattice is enhanced.

Supercritical pressure water has been widely used in many industrial fields, such as fossil-fired power plants and nuclear reactors because mainly of its high thermal efficiencies. Although many empirical correlations for heat transfer coefficients of supercritical pressure water have been proposed by different authors based on different experimental data base, there exist remarkable discrepancies between the predicted heat transfer coefficients of different correlations under even the same condition. Heat transfer correlations with good prediction performance are of considerable significance for developing supercritical (ultra-supercritical) pressure boilers and SCWRs. In this paper, the experimental data (about 7389 experimental data points) and 30 existing empirical correlations for heat transfer of supercritical pressure water (SCW) flowing in vertical upward tubes are collected from the open literatures. Evaluations of the prediction performance of the existing correlations are conducted based on the collected experimental data, and a detailed multi-collinearity analysis has been made on different correction factors involved in the existing correlations, and then based on the collected experimental data, a new heat transfer correlation is developed for the supercritical pressure water flowing in vertical upward tubes under normal and enhanced heat transfer mode. Compared with the existing correlations, the new correlation exhibits good prediction accuracy, with a mean absolute deviation (MAD) of 9.63%.

Experimental investigation on heat transfer deterioration of supercritical pressure water in vertically-upward internally-ribbed tubes

Single-phase convective heat transfer in rod bundles

A model has been developed to calculate the heat transfer coefficients from the fuel rods to the steam-droplet mixture typical of Boiling Water Reactors under Emergency Core Cooling System (ECCS) operation conditions during a postulated loss-of-coolant accident. The model includes the heat transfer by convection to the vapor, the radiation from the surfaces to both the water droplets and the vapor, and the effects of droplet evaporation. The combined convection and radiation heat transfer coefficient can be evaluated with respect to the characteristic droplet size. Calculations of the heat transfer coefficient based on the droplet sizes obtained from the existing literature are consistent with those determined empirically from the Full-Length-Emergency-Cooling-Heat-Transfer (FLECHT) program. The present model can also be used to assess the effects of geometrical distortions (or deviations from nominal dimensions) on the heat transfer to the cooling medium in a rod bundle.

Development of supercritical water heat-transfer correlation for vertical bare tubes

In the fuel assemblies in reactor core, the distribution of temperature is not uniform in the fuel rod along the circumferential direction. The circumferential temperature difference could be neglected for conventional assembly design but increases significantly in a tight lattice. To investigate the circumferential non-uniformity of heat transfer in rod bundles, this paper firstly establishes mathematical model and makes theoretical analyses, based on which influential non-dimensional numbers are summarized. Then, a semi-empirical correlation describing this phenomenon is proposed based on theoretical results and CFD sensitivity analyses. Finally, a three-dimensional model for cylindrical fuel is introduced in the thermal-hydraulic code to predict circumferential heat transfer non-uniformity in different geometry and flow conditions. To validate this model, some results are compared with experimental data of bundle test for subcritical and supercritical water. The three-dimensional fuel model for sub-channel code is a new numerical tool to predict the peak cladding and fuel temperature and can be applied in thermal-hydraulic analysis of fuel assemblies of tight lattice design. Copyright © 2017 John Wiley & Sons, Ltd.

Experimental data on heat transfer to supercritical pressure water presented at ISSCWR-5, 6, and 7 international symposiums—which took place in 2011–2015 in Canada, China, and Finland—and data printed in recent periodical scientific publications were analyzed. Results of experiments with annular channels and three- and four-rod bundles of heating elements positioned in square or triangular grids were examined. Methodology used for round pipes was applied at generalization of experimental data and establishing of correlations suitable for engineering analysis of heat exchange coefficient in conditions of strongly changing water properties in the near-critical pressure region. Empiric formulas describing normal heat transfer to supercritical pressure water mowing in annular channels and rod bundles were obtained. As compared to existing recommendations, suggested correlations are distinguished by specified dependency of heat exchange coefficient on density of heat flux and mass flow velocity of water near pseudo-critical temperature. Differences between computed values of heat exchange coefficient and experimental data usually do not exceed ±25%. Detailed statistical analysis of deviations between computed and experimental results at different states of supercritical pressure water flow was carried out. Peculiarities of deteriorated heat exchange were considered and their existence boundaries were defined. Experimental results obtained for these regimes were generalized using criteria by J.D. Jackson that take the influence of thermal acceleration and Archimedes forces on heat exchange processes into account. Satisfactory agreement between experimental data on heat exchange at flowing of water in annular channels and rod bundles and data for round pipes was shown.

Effect of spacer grids on CHF in nuclear rod bundles