Thermal conductivity of rare earth-uranium ternary oxides of the type RE6UO12

The knowledge of thermophysical properties of the rare earth uranium ternary oxides of the type RE₆UO₁₂ (RE=La, Gd and Dy) is essential to understand the fuel performance during reactor operation and for modeling fuel behavior. Literature on the high temperature properties of this compound is not available and there is no report at all on the thermal conductivity of these compounds. Hence a study of thermal conductivity of this compound has been taken up. The compounds were synthesized by a solution combustion method using metal nitrates and urea. Thermal diffusivity of these compounds was measured by the laser flash method in the temperature range 673-1373 K. The specific heat data was computed using Neumann-Kopp’s law. Thermal conductivity was calculated using the measured thermal diffusivity value, density and specific heat data for different temperatures. The temperature dependence of thermal conductivity and the implication of structural aspects of these compounds on the data are discussed here.     

Effect of temperature on steel and concrete for PCRV's

The effect of temperature on the physical and mechanical properties of typical steels and concretes which are used in PCRV design are presented. Special consideration has been given to the properties and phenomena concerning thermal behaviour, e.g. thermal diffusivity and conductivity, specific heat, density, thermal expansion and decomposition effects. Data from the literature and recent test results will be discussed. A temperature range from 20°C up to the melting points of the materials is considered.     

Thermal conductivity of neptunium dioxide

The thermal diffusivity of neptunium dioxide was measured in the temperature range from 473 to 1473 K by using a laser flash method. The thermal diffusivity slightly decreased with increasing temperature in the temperature range investigated. The heat capacity of NpO₂ was measured in the temperature range from 334 to 1071 K by using a drop calorimetry method. The heat capacity of NpO₂ determined in this study was slightly larger than that of UO₂ and about 7% smaller than that of PuO₂. The thermal conductivity of NpO₂ was determined from the thermal diffusivity, the heat capacity and the bulk density. It was found that the thermal conductivity of NpO₂ from 873 to 1473 K lay between those of UO₂ and PuO₂.     

Effect of fluid Prandtl number on heat transfer characteristics in internally heated liquid pools with Rayleigh numbers up to 10

This paper presents an analysis of effects of the fluid Prandtl number (Pr) on natural convection heat transfer in volumetrically heated liquid pools. Experimental and computational studies performed in the past are reviewed, with particular emphasis on the analysis of Pr number effects. As a practical exercise, numerical analysis is performed for two-dimensional square, semicircular and elliptical enclosures, and for three-dimensional semicircular and hemispherical cavities, to investigate the physics of the effect of the Pr number on heat transfer in internally heated liquid pools with Rayleigh numbers up to 10¹². It was found that the fluid Prandtl number has a small effect on heat transfer in the convection-dominated regions (near the top surface and side walls) of the enclosures. The decrease of the Pr number leads to the decrease of the top and side wall Nusselt (Nu) numbers. The effects of the Pr number on the Nu number at the bottom surface of the enclosures are found to be significant and they become larger with increasing Rayleigh numbers. Two physical mechanisms, i.e. thermal diffusivity and kinematic viscosity phenomena, have been proposed to explain the fluid Prandtl number effects. Calculational results have been used to quantify the significance and the area of influence for each mechanism. Also, strong dependence on the geometry (curvilinearity) of the downward cooled pool surface has been found.     

Analytical Modelling of Overpack of Enriched Uranium Hexafluoride Package in a Fire Event

Abstract

A fissile package must be subjected to a fire test at 800°C for 30 min. For a package that contains enriched uranium hexafluoride (UF₆), the temperature of the contents has to be kept below 121°C in order to avoid rupture of the 30B cylinder. A previous study on heat transfer mechanisms in an enriched UF₆ package type ‘DOT-21PF-1’ found that decomposed gas with a temperature of around 100°C generated from heated penolic foam thermal insulator was a major heat source heating the cylinder in the initial period of the fire test, in addition to the heat conducted from the outer surface through the thermal insulator into the interior of the package. Mitsubishi Materiass Corporation has developed a new packaging for enriched UF₆ ‘MST-30’ that also uses phenolic foam as the thermal insulator, and has pelformdd a fire test at 800°C for 30 min, which also indicated the temperature history of the package interior affected by heating from the decomposed gas. In this study, a laboratory test was carried out to identify the kind of gas generated from the heated phenoiic foam. The test found that the decomposed gas was water vapour. Since water vapour has a large latent heat, it has a large heat transfer coefficient when it condenses on a cool surface. By taking the water vapour heating mechanssm into account, an analytical model was developed for MST-30 to simulate the measured cylinder temperature history. Analytical models for evaluaiing the cylinder temperature under the 800°C/30 min fire test considering conservativeness are also presented.     

Evaluation of Cooling Capability in a Heated Narrow Flow Passage

A numerical method for the thermal hydraulic phenomena in a narrow flow passage is developed to evaluate the gap cooling capability. Based on a drift flux model, the two-dimensional gas-liquid two-phase flow in the annular and hemispherical heated narrow flow passages is modeled. The drift velocity correlation is combined with the flooding correlation, which describes physical phenomena under cooling limits. Experiment on thermal hydraulic phenomena in the heated narrow flow passage is performed. Boiling two-phase flow behavior and dryout phenomena are observed. The critical heat flux data is obtained from measurement of the heating surface temperature. Counter-current two-phase flow, which is a key phenomenon in the gap cooling mechanism, is reproduced by the numerical analysis appropriately. The critical heat flux is predicted by assuming that deficiency of the liquid supply against the gas upward flow leads to occurrence of dryout. Validity of the newly developed numerical method is demonstrated through comparison of the predicted critical heat flux with the present and existing data in the gap width range from 0.5 to 5 mm and the pressure range from 1 to 50 bar.     

Post-dryout heat transfer: Physical mechanisms and a survey of prediction methods

Significant thermal non-equilibrium has been observed in the post-dryout regime. The degree of thermal non-equilibrium depends primarily on liquid-vapor interaction, and the heated surface temperature is controlled by the near-wall vapor velocity, vapor superheat and liquid-wall interaction. The possible mechanisms of post-dryout heat transfer and the state of the art for predicting post-dryout temperatures are described. The semi-theoretical approach is the most promising for simple geometries. Four empirical methods of predicting post-dryout temperatures are discussed. A bibliography and a table of all known post-dryout heat transfer correlations are presented.     

A method of evaluating local turbulent diffusivity of heat in a gridded fuel subassembly

In evaluating the turbulent diffusivity of heat associated with the coolant flow past a grid spacer within an FBR fuel subassembly, a heat diffusion technique is usually employed. However, measurement of subchannel bulk coolant temperature using thermocouples usually involves difficulty due to a steep and non-linear temperature gradient in the subchannels adjacent to a heater pin.A series solution of the heat conduction equation for the coolant flow in subchannels past a grid spacer and a heated section of a dummy fuel pin was derived under a slug flow approximation where the boundary conditions on dummy fuel pins were satisfied by means of the point-matching technique. The solution may be utilized in analyzing the turbulent diffusivity of heat within subchannel coolant flow as a function of distance from a grid spacer based on the measured temperature distribution on the wall of dummy fuel pins, which may be obtained without affecting the subchannel coolant temperature.In an illustrative example, the turbulent diffusivity of heat was most exaggerated at about 50 mm beyond a grid spacer and was approximately five times larger than the corresponding diffusivity without a grid spacer.     

Influence of thermal properties of zirconia shroud on analysis of PHEBUS FPT0 bundle degradation test with ICARE2 code

In the FPT0 test of the PHEBUS/FP program, it was observed that the fraction of liquefied UO₂ reached 50%, which is much larger than the expected maximum value of 20%. Most of the post-test analyses with various computer codes underpredicted the bundle temperature during a late phase and could not reproduce such a large core degradation. In most of the previous analyses, the shroud thermal conductivity evaluated based on the Pears' ZrO₂ specific heat data and the thermal diffusivity measured by JAERI was used. However, recent thermal property data books adopt a lower specific heat than measured by Coughlin and King's at high temperature. The present analyses with ICARE2 showed that the FPT0 bundle behavior could be mostly reproduced by using the shroud thermal conductivity based on Coughlin and King's. If the present calculation is assumed to be correct enough, the shroud thermal conductivity at high temperature could be smaller than the current evaluation based on the Pears' data. Since the shroud thermal conductivity has thus a strong effect on the bundle behavior, further measurement and evaluation of the thermal properties of the shroud are highly recommended.     

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.     

Analytical developments in the Wong–Fung–Tam–Gao radiation model of thermal diffusivity

When the thermal diffusivity, χ, of a thin film on a substrate is measured by means of the mirage method, the photothermal deflection of the probe beam is determined by the heat radiation field contributed by the film and the substrate, heated by the pump beam. A two-dimensional algorithm is here presented in order to deduce the measure of the diffusivities of the film and the substrate in one set of mirage detection from the experimental data.     

Specific heat,thermal diffusivity and thermal conductivity of synroc,perovskite, zirconolite and barium hollandite

The thermal diffusivity, specific heat and thermal conductivity of cold-pressed and sintered (CPS) perovskite (CaTiO₃), zirconolite (CaZrTi₂O₇), barium hollandite (BaAL₂Ti₆O₁₆), SYNROC-B and SYNROC-C were measured in the temperature ranges 20–700°C (thermal diffusivity) and 20–500°C (specific heat and thermal conductivity). The property values, falling in the broad range of titanates, decrease in the order perovskite>hollandite>zirconolite. Values of SYNROC-B are close to those for hollandite, while values for SYNROC-C are closer to those for zirconolite.The heat transport properties of hot-pressed SYNROC-C are directional. For heat flow parallel to the hot-pressing direction, property values are 12% lower than for CPS SYNROC-C. Perpendicular to the hot-pressing direction, values are 12% higher.     

Convection heat transfer anisotropy in a bubbling viscous pool—Application to molten core-concrete interaction

In the absence of bubbling, natural convection in an internally heated pool is largely anisotropic. There are large heat transfers to the upper and lateral walls, while the heat transfer to the cooled lower surface is small. Bubbling is a well-known mean of increasing the heat transfer coefficients, especially at the lower wall. The heat transfer between an internally heated pool and its walls has been experimentally studied while air bubbles were produced through a grid drilled with holes installed at the lower interface. Sugar solutions have been used as simulant the high temperature corium melts that would be produced during molten core-concrete interaction with respect to [Deckwer, W.-D.,1992. Bubble Column Reactors. John Wiley & Sons, Chichester (English Translation)] heat transfer model. Without any gas bubbling, natural convection in the pool exhibits a large anisotropy with a small heat transfer to the bottom wall. This is due to the building of a thermal gradient through the pool height. Bubbling with superficial gas velocity as low as 1 mm/s is sufficient to destabilize these layers in water and homogenize the pool. For more viscous fluids, it has been possible to determine a threshold between these regimes.     

Radiation effects in thermal properties of polymers. An analytical review. I. Polyethylene

The information about radiation effects on the thermal properties of polymeric materials is of special interest since: (1) the temperature regime of technical structural units operated in the radiation fields is determined in many respects by the values of the material thermal constants and the rate of their degradation; (2) the temperature and dose dependencies of heat conductivity and, especially, heat capacity characterize the polymer structure. The data on radiation effects on the thermal conductivity, heat capacity and diffusivity, linear thermal expansion, density, crystallinity degree, heat and temperature of phase transitions are presented in this review only for polyethylene of high and low density, as a very famous and typical semi-crystalline polymer. It is supposed to deal in the future with such problems as reversible radiation effects on heat capacity, analytical models of the radiation-induced changes and anisotropy effects on the thermal conductivity, accumulated radiation energy (“heat defect”) and an important problem of specific action of different kinds of radiation on the thermal properties of polymers.     

Steady state and transient temperature profiles in a multishell spherical system heated internally by reactor-grade plutonium

Steady state and transient temperature distributions are analysed for multishell spherical systems which are heated in their inner part by the alpha-particle heat power of reactor-grade plutonium. Different geometrical thickness of the spherical shells and temperature dependent thermal material properties are assumed. Boundary conditions at the surface of the multishell system are natural convection by air and thermal radiation or cooling by cryogenic liquids. In addition, cooling by internal thermally conducting structures in outer shells is investigated by applying an approximate heat conduction model. The steady state and transient temperature distributions allow defining limits for alpha-particle heat power at different outer boundary conditions for which e.g. the melting points or other temperature limits of different materials are exceeded.     

Tritium Isotope Separation by CO2 Laser Irradiation at Dry Ice Temperature

A computational method based on boundary element method (BEM) has been developed to analyze transient temperature distribution in a three-dimensional solid having non-linear boundary condition (for example boiling or thermal radiation). To obtain high numerical accuracy, the heat transfer coefficient which depends on the surface temperature was approximated as a linear combination of interpolation functions with respect to time and analytical time integration of the non-linear term included in boundary integral equation was made.

To investigate feasibility of the present method, it was applied to calculations of the temperature distribution in an infinite flat plate cooled on one side. The heat transfer co-efficient of cooling surface was in proportion to n-th power of the surface temperature. Results are (1) the method has given a stable solution for non-linear boundary value problems such as conventional BEM could not solve, (2) it has given an accurate solution for large time increment except for first time step, and (3) an optimal relaxation factor decreases with strength of non-linearity of the heat transfer coefficient.

Applying the method to thermal analysis of limiter and divertor plate installed in a fusion test facility and fusion reactor respectively, availability of the method has been confirmed.     

Simulations of heat and oxygen diffusion in UO2 nuclear fuel rods

We present finite-element simulations of coupled heat and oxygen atom diffusion for UO₂ fuel pellets. The expressions for thermal conductivity, specific heat and oxygen diffusivity for the fuel element are obtained directly from previously published correlations, or from analysis of previously published data. We examine the temperature and non-stoichiometry distributions for a varying range of conditions. Simulations are performed for steady-state and transient regime in one-dimensional (purely radial) configurations. For steady-state conditions we perform parametric studies that determine the maximum temperature in the fuel rod as a function of non-stoichiometry and heat generation rate intensity. For transient simulations, we examine the time lag in the response of the temperature and non-stoichiometry distributions with respect to sudden changes in heat generation rate intensity and oxygen removal rate. All simulations are performed with the commercial code COMSOL Multiphysics™.     

Isotopie Effect on Thermal Physical Properties of Isotopically Modified Boron Single Crystals

The measurement of specific heat and thermal conductivity at low temperature for isotopically modified boron single crystals was performed between 0.5 and 100 K using relaxation method and steady heat flow method, respectively. The results indicate that the specific heat has obvious divergences at T <5 K. At 40 K, the thermal conductivity of ¹⁰B- enriched crystal is about 570W/m-K, which is 40% larger than that of natural boron crystal. The influence of lattice vibration modes and the isotopic effect on specific heat and thermal conductivity for isotopically modified boron are discussed.     

Numerical modeling of heat and mass transport during rapid heating and vaporization of binary solids by absorbing radiation - application to UO2

Pulsed surface irradiation of an absorbing material induces a temperature transient which leads to melting and vaporization. If the target is a two-component solid that evaporates incongruently, the near-surface composition is also perturbed. A mathematical model and numerical solution scheme have been developed to simulate the heat and mass transport processes which result from rapid energy deposition in the surface of a binary solid. The response surface method was used to determine the loss of precision in such a computation due to uncertainties in the material properties at high temperatures.Application of the method to incongruently-vaporizing UO₂ irradiated by a pulsed laser demonstrated the extent of oxygen depletion of the surface and revealed the sensitivity of the computed temperatures and vaporization rates arising from lack of knowledge of the diffusivity of oxygen in liquid UO₂.     

Behaviors of Electron Heat Transportation in HT-7 Sawtoothing Plasma

It is found that in HT-7 ohmic plasma, main energy loss comes from electron heat conduction, hence quantitative data of electron heat diffusivity is a very important issue for investigation of electron heat transportation behavior in different target plasmas so as to get high performance plasma. A time-to-peak method of the heat pulse propagation originating from the sawtooth activity on the soft x-ray intensity signal has been adopted to experimentally determine electron heat diffusivity χe^HP on the HT-7 tokamak. Aiming to improve the signal-to-noise (S/N) ratio of the original signal to get a stable and reasonable electron heat diffusivity χe^HD value, some data processing methods, including average of tens of sawteeth, is discussed. The electron heat diffusivity χe^HP is larger than χe^PB which is determined from the balance of background plasma power. Based on variation of the measured electron heat diffusivity χe^HP , performances of different high confinement plasmas are analyzed.