Natural convection heat transfer from a horizontal cylinder in liquid sodium: Part 2: generalized correlation for laminar natural convection heat transfer

Rigorous numerical solution of natural convection heat transfer, from a horizontal cylinder with uniform surface heat flux or with uniform surface temperature, to liquid sodium was derived by solving the fundamental equations for laminar natural convection heat transfer without the boundary layer approximation. It was made clear that the local and average Nusselt numbers experimentally obtained and reported in part 1 of this paper were described well by the numerical solutions for uniform surface heat fluxes, but that those for uniform surface temperatures could not describe the angular distribution of the local Nusselt numbers and about 10% underpredicted the average Nusselt numbers. Generalized correlation for natural convection heat transfer from a horizontal cylinder with a uniform surface heat flux in liquid metals was presented based on the rigorous theoretical values for a wide range of Rayleigh numbers. It was confirmed that the correlation can describe the authors’ and other workers’ experimental data on horizontal cylinders in various kinds of liquid metals for a wide range of Rayleigh numbers. Another correlation for a horizontal cylinder with a uniform surface temperature in liquid metals, which may be applicable for special cases such as natural convection heat transfer in a sodium-to-sodium heat exchanger etc. was also presented based on the rigorous theoretical values for a wide range of Rayleigh numbers. These correlations can also describe the rigorous numerical solutions for non-metallic liquids and gases for the Prandtl numbers up to 10.     

Condensation heat transfer characteristic in the presence of noncondensable gas on natural convection at high pressure

The steam-gas pressurizer in integrated small reactors experiences very complicated thermal-hydraulic phenomena. Especially, the condensation heat transfer with noncondensable gas under natural convection is an important factor to evaluate the pressurizer behavior. However, few studies have investigated the condensation in the presence of noncondensable gas at high pressure. In this study, therefore, a theoretical model is proposed to estimate the condensation heat transfer at high pressure using the heat and mass transfer analogy. For the high pressure effect, the steam and nitrogen gas tables are used directly to determine the density of the gas mixture and the heat and mass transfer analogy based on mass approach is applied instead of that based on the ideal gas law. A comparison of the results from the proposed model with experimental data obtained from Seoul National University indicates that the condensation heat transfer coefficients increase with increasing system pressure and with decreasing mass fraction of the nitrogen gas. The proposed model is also compared with other conventional correlations proposed in the literature. The proposed model demonstrates the capability to predict the condensation heat transfer coefficients at high pressure better than any other correlation. Finally, the condensate rate is compared to verify the application of the heat and mass transfer analogy at high pressure. The comparison results confirm that the heat and mass transfer analogy can be applied to evaluate the condensation heat and mass transfer at high pressure.     

Topical BAM cask design evaluation using drop tests and numerical calculations: accidental cask drop without impact limiters onto storage building foundation

Abstract

Cask impacts without impact limiters onto unyielding targets result in totally different mechanical reactions from those of relatively smooth impacts using impact limiters. During the licensing procedure of the new GNS CASTOR HAW 28M design for vitrified high activity waste, BAM therefore decided to perform an additional drop test with a 1 : 2 scale test cask (CASTOR HAW/TB2). In spite of a small drop height of only 0˙3 m onto the unyielding target of the BAM drop test facility, which conservatively covers any storage building foundation, the impact caused considerable stresses to the cask structure with high stress and strain rates. This paper presents the evaluation strategy of BAM including the drop test results and the development and qualification of appropriate finite element modelling to achieve sufficient agreement between test and calculation results. Further steps include mechanical analyses of reduced and full scale cask designs to determine the most critically stressed areas of the structure, verify scaling factors and demonstrate safety with respect to cask integrity and tightness.     

Two-dimensional simulations of natural convection/radiation heat transfer for BWR assembly within isothermal enclosure

Abstract

The current scoping study identifies the significant heat transfer effects for a 7 × 7 boiling water reactor (BWR) assembly within an isothermal basket opening inside a transport cask. A two-dimensional finite volume mesh is constructed that models the assembly components and cover gas. Computational fluid dynamics (CFD) simulations calculate the buoyancy induced gas motion, conduction and radiation within the components. Simulations use different basket surface temperatures, fuel heat generation rates and cladding surface emissivities, for both nitrogen and helium cover gases at atmospheric pressure. An analytical conduction/radiation model is developed for the thermal resistance between the channel and basket. Results using buoyancy induced gas motion compared to stagnant gas simulations show that natural convection is significant only at low basket temperatures, with nitrogen gas. Helium and high basket temperature simulations exhibit no significant temperature reduction from natural convection. Simulations with varying cladding emissivity ? show that a 10% increase in ? causes a 7˙2% decrease in the interior temperature difference for nitrogen and a 5˙3% decrease for helium.     

Numerical investigation of natural convection characteristics of a heat pipe-cooled passive residual heat removal system for molten salt reactors

The limited availability of studies on the natural convection heat transfer characteristics of fluoride salt has hindered progress in the design of passive residual heat removal systems(PRHRS) for molten salt reactors. This paper presents results from a numerical investigation of natural convection heat transfer characteristics of fluoride salt and heat pipes in the drain tank of a PRHRS. Simulation results are compared with experimental data,demonstrating the accuracy of the calculation methodo...     

Experimental investigation on narrow gap heat transfer with porous media under downward-facing horizontal heated surface

An experimental study of horizontal narrow gap heat transfer of porous media under a round downward-facing heated plate has been carried out, using water as the working fluid. The boiling curves are obtained with different gap size, plate diameter and solid spherules. The results show that the heat transfer increases significantly with porous media in the gap especially under boiling condition, and the occurrence of pool boiling crisis would be brought forward when the gap size is very small. The results also indicate that the heat transfer in horizontal narrow gap can be enhanced by increasing the ratio of gap size to plate diameter and using porous media with high thermal conductivity. Based on the mechanism of heat transfer of porous media, the correlations for natural convection and nucleate boiling are proposed to predict the heat flux.     

Experimental and numerical investigation of counter-current stratified flows in horizontal channels

Counter-current flow regimes of air and water are investigated in the WENKA test facility at the Forschungszentrum Karlsruhe. With the fluorescent-particle image velocimetry (PIV) measurement technique, velocity and velocity fluctuations are measured up to the free surface. A statistical model is presented to correlate the measured void fraction with the turbulent kinetic energy calculated from the measured velocity fluctuations. The experimental data are used to develop a phase interaction model to simulate stratified flows. Two different approaches are compared for turbulence modelling. The Prandtl mixing length model and an extended k–ω model for the two-phase region are applied to supercritical flow conditions.     

Natural convection heat transfer of water on a horizontal downward facing stainless steel disk in a gap under atmospheric pressure conditions

An experimental study on natural convection heat transfer on a horizontal downward facing heated surface in a water gap has been carried out under atmospheric pressure conditions. A total of 7204 experimental data points are correlated using Rayleigh versus Nusselt number correlations in various forms, based on different independent variables. The effects of different characteristic lengths and film temperatures are discussed. The buoyancy force acts as a resistance force for natural convection heat transfer on a downward facing horizontal heated surface in a confined space. For the estimation of the natural convection heat transfer under the present conditions, empirical correlations in which Nusselt number is expressed as a function of Rayleigh number, or Rayleigh and Prandtl numbers both, may be used. However, the best accuracy is provided by an empirical correlation which expresses the Nusselt number as a function of the Rayleigh and Prandtl numbers, as well as the gap width-to-heated surface diameter ratio; and uses the temperature difference between the heated surface and the ambient fluid in the definition of Rayleigh number. The characteristic length is the gap size and the film temperature is the average fluid temperature.     

Laminar combined convection heat transfer of liquid sodium flowing through a single horizontal row of cooling tubes in the direction of gravity

The laminar combined convection heat transfer of the liquid sodium which flows through a single horizontal row of cooling tubes in the direction of gravity are studied using numerical analysis. The heat transfer characteristics at large Reynolds numbers are improved when Richardson numbers (= GR/Re²) are increased and the improvement rate is enlarged with an increase in value. The temperature field at small Reynolds numbers does not exhibit much change even when the Richardson number reaches a high value. Consequently the Nusselt numbers do not differ from those of forced convection. In other words, in a decay heat removal system at a low velocity, there is a possibility that an improvement in the heat transfer characteristics by combined convection cannot be expected even in a system with a large Richardson number.     

Optimized trajectories of the transfer cask system in ITER

The transfer cask system (TCS) is one of the remote handling systems that will operate in ITER, transporting heavy and highly activated in-vessel components between the tokamak building and the hot cell building. A motion planning methodology for the TCS was developed, providing smooth paths that maximize the clearance to obstacles and that incorporate manoeuvres whenever necessary. This paper presents the results of the TCS planning algorithm with trajectories computed for nominal operations. The length of the journey, the velocity, the time duration, and the risk of collision were evaluated individually for each trajectory. A summary of all results, conclusions and future work are presented and discussed.     

Interaction of natural convection flow in multiple open cavities formed due to horizontal fins

Natural convection heat transfer from a stack of horizontal open cavities formed due to fins attached to equipment has been investigated for a wide range of Rayleigh number, cavity spacing and number of cavities in the stack. The interaction between natural convection from one cavity with other cavities in the stack is the focus of the study. Conservation equations of mass, momentum and energy have been solved using a finite volume solver. Ideal gas assumption is invoked to account for density variation of air. Numerical results have been validated with published solutions for a single isolated cavity. It is seen that the heat transfer from a stack of cavities is less than that predicted for isolated cavities. Due to pre-heating effect of fluid reaching the entrance of the upper cavities from the bottom ones, the heat transfer from upper cavities deteriorates. This deterioration is found to exhibit strong dependence on Rayleigh number and fin spacing. The dimensionless optimum fin spacing which yields the maximum heat transfer is found to be 2.5 for Ra ? 10⁴ and it is 0.5 for Ra ? 10⁵. The reduction in Nusselt number from the top cavity compared to that in the bottom cavity is in the range of 65% at the highest Rayleigh number studied.     

A design guide for calculating liquid-metal turbulent forced convection heat transfer with non-uniform heat fluxes and transients

Calculation of turbulent forced convection heat transfer in ducts during non-uniform wall heat fluxes and transients is of interest to the national liquid-metal fast breeder nuclear reactor program. This paper presents an improved method whereby such heat transfer can be determined during analysis and design. Since the method involves the use of fully developed, steady-state heat transfer coefficients, several dimensionless coefficients and selected physical properties, tables, graphs, or equations are included for the convenience of the designer. Application of the improved method is specialized to four geometries of interest: circular tube, parallel-plate channel, annular space, and approximation of pin or rod bundle.     

窄环隙内强迫对流换热特性的实验研究

对窄环隙内强迫对流换热特性进行了实验研究。实验结果表明,在紊流区窄环隙可以强化换热;当Re<150时,发生传热恶化。对窄环隙内加热流体和冷却流体强迫对流换热特性进行分析,可以为窄环隙内对流换热的进一步研究提供基础。     

Characterization of heat transfer processes in a melt pool convection and vessel-creep experiment

The results of an integral experiment on melt pool convection and vessel-creep deformation are presented and analyzed. The experiment is performed on a test facility, named Failure Of REactor VEssel Retention (FOREVER). The facility employs a 1/10-scaled 15Mo3-(German)-steel vessel of 400-mm diameter, 15-mm wall thickness and 750-mm height. A high-temperature (1300 °C) oxide melt is prepared in a SiC-crucible placed in a 50 kW induction furnace and is, then, poured into the 1/10th scale vessel. A MoSi₂ 50 kW electric heater is employed in the melt pool to heat and maintain its temperature at 1200 °C. The vessel is pressurized with argon at the desired pressure. In the FOREVER/C1 experiment, the vessel wall, maintained at about 900 °C and pressurized to 26 bars, was subjected to creep deformation in a 24-h non-stop test. The FOREVER/C1 test is the first integral experiment, in which a decay-heated oxidic naturally-convecting melt pool was maintained in long-term contact with the hemispherical lower head of a pressurized, creeping, steel vessel. A sizeable database was obtained on melt pool temperatures, melt pool energy split, heat transfer rates, heat flux distribution on the melt (crust)–vessel contact surface, vessel temperatures and, in particular the vessel wall creep rate as a function of time. The paper provides information on the FOREVER/C1 measured thermal characteristics and analysis of the observed thermal behavior. The coupled nature of thermal and mechanical processes, as well as the effect of other system conditions (such as depressurization) on the melt pool and vessel temperature responses are analyzed.     

Heat transfer performance tests using a half scale horizontal storage module

Spent nuclear fuel generated at nuclear power plants must be safely stored during interim storage periods. A horizontal storage module to safely store the spent nuclear fuel should be able to adequately emit the decay heat from the spent nuclear fuel. The horizontal storage module must ensure that the temperatures of the spent nuclear fuel assemblies are maintained within the allowable values for normal, off-normal, and accident conditions. Therefore, the horizontal storage module must be designed including heat removal capabilities with an appropriate reliability. However, the thermal conductivity of concrete is not good and the allowable temperature of concrete is lower than that of steel. Therefore, heat transfer performance tests were performed to evaluate the heat transfer performance in accordance with the ratio of the outlet to inlet of the air as well as the direction of the inlet and outlet of the air in the horizontal storage module. The influence that the direction of the inlet and outlet of the air reaches to the heat transfer performance was estimated to be minimal. The overall heat removal efficiencies were reduced as the mass flow rate at the outlet was reduced.     

Implementation of burn-up credit approach for transport and storage cask

Abstract

TN International currently uses burn-up credit methodology for the design of casks dedicated to the transport of pressurised water reactor uranium oxide spent fuel assemblies. As long as the fuel enrichment of the pressurised water reactor fuel assemblies was sufficiently low, a burn-up credit methodology based on the sole consideration of actinides and the use of a partial burn-up was satisfactory to cover the needs without necessity to design new casks. Nevertheless, the continuous increase in the fuel enrichment during the last decade has led TN International to continue the investigations on the burn-up credit methodology to limit both the increase in the neutron poison content in the new basket designs and the burn-up constraints attached to the acceptability of the fuel assemblies for transport. The strategy of TN International was then to take benefit of the large negative reactivity reserves, which might be gained by the consideration of the fission products coming from the fuel irradiation. A big step forward has recently been reached by TN International on this field with the definition of an advanced burn-up credit methodology based on the consideration of relevant fission products recommended by OECD. In the meantime, TN International has taken the opportunity to use such burn-up credit approach in the design of the TN 24 E transport and storage cask developed for the German nuclear power plants. The relevant task has been carried out according to the German standard DIN 25712 for burn-up credit application. The present paper will describe the basic principles of the burn-up credit methodology implemented by TN International such as:

(i) the current state of the art concerning the burn-up credit application in the criticality assessment

(ii) the basic approach used for the implementation of the advanced burn-up credit methodology (bounding axial burn-up profiles, fuel irradiation parameters, fission products, etc.)

(iii) the area of validity of the TN International burn-up credit approach with fission products

(iv) example of application of the burn-up credit methodology for the design of the TN 24 E transport and storage cask under licensing in Germany

(v) the perspectives of development of the burn-up credit methodology.