Influence of texture on the analysis of thermoelastic/plastic anisotropy and the initial yielding of zircaloy tubes

Averaging procedures are developed to obtain texture factors relating the thermoelastic properties of single crystals of zirconium to polycrystalline properties. The effect of various approximations to the elastic properties of poly crystalline material and various assumed yield criteria on the transition from elastic to plastic behavior for a tube subjected to various boundary conditions is examined. It is found that thermal anisotropy has a greater effect on the elastic-plastic transition than does elastic anisotropy. The choice of yield condition can also affect appreciably the predicted yielding behavior of a tube.     

A three-dimensional method for integrated transient analysis of reactor-piping systems

A three-dimensional method for integrated hydrodynamic, structural, and thermal analyses of reactor-piping systems is presented. The hydrodynamics are analyzed in a reference frame fixed to the piping and are treated with a two-dimensional Eulerian finite-difference technique. The structural responses are calculated with a three-dimensional co-rotational finite-element methodology. Interaction between fluid and structure is accounted for by iteratively enforcing the interface boundary conditions.A thermal transient capability has been developed. A system energy equation is used to compute the coolant temperatures due to convection. A radial heat-conduction equation is employed to establish the temperature profile throughout the pipe-wall thickness. The constitutive equation used for the thermal-mechanical stress calculation is suited for a large number of materials under various loading conditions, such as those having thermal, plastic, and viscous effects. The flow surface, which defined the purely elastic regime, can be arbitrarily small; an associated flow rule is utilized for regimes of material plasticity.Three sample problems are presented to illustrate this method. The first one calculates the piping response under the seismic excitation. The second one validates the heat-conduction model. The third problem deals with a coupled hydrodynamic-structural-thermal analysis of a piping system. Results are discussed in detail.     

Thermal analysis of plates with circular inclusions

A least square boundary point matching method is employed to determine the temperature distributions and deformations of rectangular plates with circular elastic inclusions. Solutions for two problems have been obtained. The first problem is concerned with the determination of the temperature distribution in a finite rectangular plate having a circular inclusion and subjected to prescribed temperature distribution and thermal conditions along the edges. The plate is heated uniformly through the thickness. The second problem is concerned with the deflection and moment distribution in the same plate model with simply supported edges and prescribed temperature variation across the thickness but no temperature variation over the plate surface. Numerical results are presented.     

Moisture propagation and resulting stress in heated concrete walls

A mathematical model to simulate the coupled heat and mass transfer in heated porous media, as well as the resulting stress, is described. A finite element analysis, assuming homogeneous elastic material, is used to study the temperature and pore pressure distribution, and the rate of moisture propagation through a concrete containment wall under different time-dependent temperature boundary conditions. Results are also presented for the internal stresses caused by the presence of temperature gradients, pore pressure and the release of chemically bound water at high temperatures. Stress analysis calculations are superimposed over the calculations of the moisture propagation. The temperature, pore pressure and volume change resulting from the loss of bound water, as derived by the thermal mass transport calculation, are used as input for the stress analysis.     

Stochastic thermal stress analysis of clad cylindrical fuel elements

After a review of deterministic elastic thermal stress analysis by means of the displacement method for a cylindrical system in which the temperature distribution is not only radially variable but azimuthally and axially variable also, a method is shown for the determination of the statistical moments of the stress components when (a) the outer boundary of the cladding is a stochastic quantity, and (b) the uncertainties in the elastic and thermal constants of the materials and in the magnitude of the heat generation term are taken into account. A typical model is proposed for describing the statistics of the outer radius of the cladding which is a stochastic variable owing to uncertainties produced by the extrusion process. The theory is illustrated by means of a simple example by examining a meaningful reliability index and the relative importance of each of the uncertainties.     

On the effect of boundary conditions on finite deflections of heated annuli exhibiting temperature-dependent properties

The present study concerns nonlinear deflection analyses of axisymmetrically heated annular plates for several boundary conditions at the outer radius. Temperature-dependent mechanical and thermal properties of plates are considered within the frame of orthotropic elasticity theory. It is pointed out by numerical calculations that the temperature-dependent effect on finite deflections differs markedly for distinct boundary conditions.     

Thermal stresses in a spherical shell with a conical nozzle

A thermal stress problem of a spherical shell with a conical nozzle is solved using a continuum approach. The thermal loading consists of a steady temperature which is uniform on the inner and outer surfaces of the shell and the conical nozzle but may vary linearly across the thickness. The thermal stress problem is converted to an equivalent boundary value problem and boundary conditions are specified at the junction of the spherical shell and conical nozzle. The stresses are obtained for a uniform increase in temperature and for a linear variation of temperature across the thickness of the shell, and are presented in graphical form for ready use.     

Thermal Fluid-Structure Interaction Analysis for the Upper Structure of LMFRs

This paper describes a thermal fluid-structure interaction analysis code FLUSH that calculates both thermal-hydraulics and thermal structure response at the same time. This code has been developed to evaluate the thermal responses of the upper structures of LMFRs, using two different analysis codes of α-FLOW and FINAS. The heat flux on the boundary surface of the fluid region and the temperature on the boundary of the structure region are exchanged in every iterative cycle as the new boundary conditions, and finally the unified thermal fields are calculated. The different mesh method and the detail thermal radiation model were also developed to apply for the large scale models.

The 2-D model of the basic experiment for the cover gas thermal-hydraulics was calculated to verify this iterative method. The calculated average temperature on the boundary agreed well with the experimental results. The 3-D large scale models of the out-of-pile experiment for MONJU shield plug were also calculated to verify this method. The calculated temperature both in the annulus and the shield plug agreed well with the experiments. These studies showed that this iterative method of FLUSH was very effective for the predictions in the strong coupled thermal fields.     

A thermal stress mechanism for the fragmentation of molten UO2 upon contact with sodium coolant

An important aspect of fuel-coolant interaction problems relative to various hypothetical LMFBR accidents is the fragmentation of molten oxide fuel on contact with sodium coolant. In order to properly analyze the kinetics of such an event, an understanding of the breakup process and an estimate of the size and dispersion of such fragmented fuel must be known. A thermal stress initiated mechanism for fragmentation is presented using elastic stress theory for the cases of both temperature-dependent and independent mechanical properties. Included is a study of the effect of the choice of surface heat transfer boundary condition and the compressibility of the unsolidified inner core. Results of parametric calculations indicate that the thermal stresses induced in the thin outer shell and the pressurization of the inner molten core are potentially responsible for the fragmentation. For UO₂ in Na the calculated stresses are extremely high, while for aluminum in water they are much smaller and a strong function of the surface heat transfer boundary condition. Qualitatively, these results compare favorably with small scale dropping experiments, that is, molten UO₂ quenched in Na undergoes fragmentation while aluminum in water usually results in little breakup. The experimentally observed increase in breakup with decreasing coolant temperature is also in qualitative agreement with the thermal stress-induced mode of fragmentation.     

Group theory transformation for Soret and Dufour effects on free convective heat and mass transfer with thermophoresis and chemical reaction over a porous stretching surface in the presence of heat source/sink

The group theoretic method is applied for solving the problem of combined effect of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a porous stretching surface in the presence of thermophoresis particle deposition with variable stream conditions. The application of one-parameter groups reduces the number of independent variables by one and consequently, the system of governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. The equations along with the boundary conditions are solved numerically by using Runge Kutta Gill integration scheme with shooting technique. Impact of Soret and Dufour effects in the presence of thermophoresis particle deposition with chemical reaction plays an important role on the flow field. The results thus obtained are presented graphically and discussed.     

用薄层模型求解离心机流场的端盖边界条件

文章分析用Onsager的薄层模型研究离心机中流场时,端盖边界条件的不同对流场求解的影响。端盖边界条件可有两种形式,一种由分析端盖上水平Ekman边界层得到(称为原始形式),另一种由对原始形式求导后得到(称为导数形式)。目前使用的是导数形式。然而,求导运算损失了原始形式边界条件中包含的部分信息,并复杂化了边界条件。在端盖上分别有热驱动、供取料情况下,分别对流场进行求解来分析两种形式边界条件的差别。结果表明,使用不同形式的边界条件所得流场总体上不同,为避免导数形式中的信息损失,建议使用原始形式。     

Thermal stresses in a cylindrical shell containing a circular hole or a rigid inclusion

The thermal stress problem of a circular discontinuity in a cylindrical shell has been solved by continuum approach. Two types of discontinuities are considered: (i) a circular hole and (ii) a circular regid inclusion. The effect of a uniform temperature or a linearly varying temperature across the thickness has been studied. The problem is converted into an equivalent boundary value problem and boundary conditions are specified around the discontinuity. The results are presented in a graphical form for ready use.     

Subject index to volume 90

The temperature distribution and thermal stress behavior in the blind end-plate of the rotating fluidized reactor are analyzed using free traction boundary conditions. Parametric effects are discussed and the order of maximum stress is estimated without considering centrifugal stresses.     

End-plate temperatures and thermal stress distributions in the rotating fluidized bed reactor

The temperature distribution and thermal stress behavior in the blind end-plate of the rotating fluidized reactor are analyzed using free traction boundary conditions. Parametric effects are discussed and the order of maximum stress is estimated without considering centrifugal stresses.     

CFD analysis of thermal-hydraulic behavior in SCWR typical flow channels

Investigations on thermal-hydraulic behavior in SCWR fuel assembly have obtained a significant attention in the international SCWR community. However, there is still a lack of understanding and ability to predict the heat transfer behavior of supercritical water. In this paper, CFD analysis is carried out to study the flow and heat transfer behavior of supercritical water in sub-channels of both square and triangular rod bundles. Effect of various parameters, e.g. thermal boundary conditions and pitch-to-diameter ratio on the thermal-hydraulic behavior is investigated. Two boundary conditions, i.e., constant heat flux at the outer surface of cladding and constant heat density in the fuel pin are applied. The results show that the structure of the secondary flow mainly depends on the rod bundle configuration as well as the pitch-to-diameter ratio, whereas, the amplitude of the secondary flow is affected by the thermal boundary conditions, as well. The secondary flow is much stronger in a square lattice than that in a triangular lattice. The turbulence behavior is similar in both square and triangular lattices. The dependence of the amplitude of the turbulent velocity fluctuation across the gap on Reynolds number becomes prominent in both lattices as the pitch-to-diameter ratio increases. The effect of thermal boundary conditions on turbulent velocity fluctuation is negligibly small. For both lattices with small pitch-to-diameter ratios (P/D < 1.3), the mixing coefficient is about 0.022. Both secondary flow and turbulent mixing show unusual behavior in the vicinity of the pseudo-critical point. Further investigation is needed. A strong circumferential non-uniformity of wall temperature and heat transfer is observed in tight lattices at constant heat flux boundary conditions, especially in square lattices. In the case with constant heat density of fuel pin, the circumferential conductive heat transfer significantly reduces the non-uniformity of circumferential distribution of wall temperature and heat transfer, which is favorable for the design of SCWR fuel assemblies.     

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.     

Transient thermal stresses in an orthotropic finite rectangular plate due to arbitrary surface heat-generations

The transient thermal stresses in an orthotropic finite rectangular plate due to arbitrary surface heat-generations on two edges are studied by means of the Airy stress function.The purposes of this paper are to present a method of determining the transient thermal stresses in an orthotropic rectangular plate with four edges of distinct thermal boundary condition of the third kind which exactly satisfy the traction-free conditions of shear stress over all boundaries including four corners of the plate, and to consider the effects of the anisotropies of material properties and the convective heat transfer on the upper and lower surfaces on the thermal stress distribution.     

Effects of Boundary Conditions on Thermal Response of a Cellulose Acetate Layer Using Hottel’s Zonal Method

Energy can transfer internally by radiation in addition to conduction in translucent polymers. Since radiant propagation is very rapid, it can provide energy within the layer more quickly than diffusion by heat conduction. Thus, the transient thermal response of a layer for combined radiative and conduction may be extremely different from that of conduction alone. In this paper, the behavior of a heat conducting, absorbing, and emitting layer of Cellulose Acetate layer is investigated during the transient interval when both conductive and radiative heat transfer are considered. Specifically, the effects of boundary conditions on the response of the layer are considered here. These boundary conditions include both conductive boundary conditions, such as convection coefficient and convective fluid temperature, and radiation boundary conditions, like radiation surrounding temperature and specular reflectivity. To this end, the governing differential equations including the equation of radiative heat transfer within the material coupled to the transient energy equation with radiative terms are presented. The solution procedure is based on nodal analysis and Hottel’s zonal method extended by the ray tracing method. The transient energy equation including the radiative internal energy source is solved using a time marching finite difference procedure with variable space and time increments.     

Development of the FHR advanced natural circulation analysis code and application to FHR safety analysis

The University of California, Berkeley (UCB) is performing thermal hydraulics safety analysis to develop the technical basis for design and licensing of fluoride-salt-cooled, high-temperature reactors (FHRs). FHR designs investigated by UCB use natural circulation for emergency, passive decay heat removal when normal decay heat removal systems fail. The FHR advanced natural circulation analysis (FANCY) code has been developed for assessment of passive decay heat removal capability and safety analysis of these innovative system designs. The FANCY code uses a one-dimensional, semi-implicit scheme to solve for pressure-linked mass, momentum and energy conservation equations. Graph theory is used to automatically generate a staggered mesh for complicated pipe network systems. Heat structure models have been implemented for three types of boundary conditions (Dirichlet, Neumann and Robin boundary conditions). Heat structures can be composed of several layers of different materials, and are used for simulation of heat structure temperature distribution and heat transfer rate. Control models are used to simulate sequences of events or trips of safety systems. A proportional-integral controller is also used to automatically make thermal hydraulic systems reach desired steady state conditions. A point kinetics model is used to model reactor kinetics behavior with temperature reactivity feedback. The underlying large sparse linear systems in these models are efficiently solved by using direct and iterative solvers provided by the SuperLU code on high performance machines. Input interfaces are designed to increase the flexibility of simulation for complicated thermal hydraulic systems. This paper mainly focuses on the methodology used to develop the FANCY code, and safety analysis of the Mark 1 pebble-bed FHR under development at UCB is performed.