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.     

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...     

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.     

Numerical simulation of coupling heat transfer and thermal stress for spent fuel dry storage cask with different power distribution and tilt angles

Dry storage containers must be secured and reliable during long-term storage, and the effect of decay heat released from the internal spent fuel on the cask has become an important research topic. In this paper, a 3D computational fluid dynamics model is presented, and the accuracy of the calculation is verified, with computational errors of less than 6.2%. The thermal stress of the dry storage cask was estimated by coupling it with a transient temperature field. The total power remained constan...     

Natural convection heat transfer from horizontal rod bundles in liquid sodium. Part 2: Correlations for horizontal rod bundles based on theoretical results

Natural convection heat transfer from horizontal rod bundles in N_xm × N_ym arrays (N_xm, N_ym = 5–9) in liquid sodium was numerically analyzed for three types of the bundle geometry (in-line rows, staggered rows I and II). The unsteady laminar two-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady state. The PHOENICS code was used for the calculation considering the temperature dependence of thermophysical properties concerned. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, R_f, ranging from 0.0637 to 63.1 (q = 1×10⁴ to 7×10⁶ W/m²). S_x/D and S_y/D for the rod bundle, which are the ratios of the distance between center axes on the abscissa and the ordinate to the rod diameter, respectively, were ranged from 1.6 to 2.5 on each bundle geometry. The spatial distribution of Nusselt numbers, Nu, on horizontal rods of a bundle was clarified. The average value of Nusselt number, Nu_av, for three types of bundle geometry with various values of S_x/D and S_y/D were calculated to examine the effect of the array size, S/D and R_f on heat transfer. The bundle geometry for the higher Nu_av value under the condition of S_x/D×S_y/D = 4 was examined by changing the ratio of S_x/S_y. A correlation for Nu_av for the three types of bundle geometry above mentioned including the effects of S_x/D and S_y/D was developed. The correlation can describe the theoretical values of Nu_av for the three types of bundle geometry in N_xm × N_ym arrays (N_xm, N_ym = 5–9) for S_x/D and S_y/D ranging from 1.6 to 2.5 within 10% difference.     

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.     

Interaction between natural convection and condensation heat transfer in the passive containment cooling condensers of the ESBWR reactor

The passive containment cooling condensers (PCCC) are the crucial part of several new reactor designs. In this paper we have developed several models to compute the heat transfer coefficients for the following cases: (i) condensation in presence of noncondensable gases inside the PCCC tubes; (ii) laminar natural convection for vertical cylinders; (iii) turbulent natural convection for vertical cylinders. These models have been implemented in the TRAC-BF1 code, and we have studied the interaction between the conservation regime inside the condenser tubes and the natural convection outside.     

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.     

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.     

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.     

Natural convection heat transfer from horizontal rod bundles in liquid sodium. Part 1: Correlations for two parallel horizontal cylinders based on experimental and theoretical results

Natural convection heat transfer coefficients on two parallel horizontal test cylinders in liquid sodium were obtained experimentally and theoretically for various setting angles, γ, between vertical direction and the plane including both of these cylinders’ axes, over the range of 0°–90°. Both test cylinders are 7.6 mm in diameter and 50 mm in heated length with the ratio of the distance between each cylinder axis to the cylinder diameter, S/D, of 2. Theoretical equations for laminar natural convection heat transfer from the two horizontal cylinders were numerically solved for the same conditions as the experimental ones. The average Nusselt numbers Nu on the cylinders obtained experimentally were compared with the corresponding theoretical values on the Nu versus modified Rayleigh number R_f [= Gr*Pr²/(4?+?9Pr^1/2?+ 10Pr)] graph. The experimental values of Nu for the upper cylinder are about 20% lower than those for the lower cylinder at γ = 0° for the range of R_f tested here. The value of Nu for the upper cylinder becomes higher and approaches that for the lower cylinder with the increase in γ over the range of 0°–90°: the values for each cylinder agree with each other at γ = 90°. The values of Nu for the lower cylinder at each γ are almost in agreement with those for a single cylinder. The theoretical values of Nu on two cylinders except those for R_f < 4 at γ = 0° are in agreement with the experimental data at each γ with the deviations less than 15%. Correlations for two cylinders were obtained as functions of S/D and γ based on the theoretical solutions. A combined correlation for multi-cylinders in a vertical array based on the correlations for two cylinders was developed. The values by the correlation agree with the theoretical solution for the multi-cylinders for R_f ranging from 4.7 to 63 within 10% difference.     

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.