The inverse problem for the dipole field

The inverse problem for an electromagnetic field produced by a dipole is solved. It is assumed that the field of an arbitrary changing dipole is known. Obtained formulae allow calculation of the position and dynamics of the dipole which produces the measured field. The derived results can be used in investigations on radiative process in solids caused by changing of the charge distribution. For example, generation of the electromagnetic field caused by oscillations of atoms or electron gas at the trace of a particle channeling in a crystal, or fields arising at solids cracking or dislocation formation - in any case when one is interested in the details of the dipole field source.     

Transient thermal stresses in a bonded composite hollow circular cylinder under symmetrical temperature distribution

A general treatise for the transient thermal stress problem of a composite circular cylinder made by bonding is described under a symmetrical temperature distribution. Analysis is developed by stress function method by the aid of Laplace transforms. Numerical examples are illustrated for the hollow composite cylinder with several radius-ratios made by the different materials due to transient heating at the internal surface by liquid.     

An application of the LTSN method on an inverse problem in hydrologic optics

Simultaneous estimation of bioluminescence source term and boundary conditions from in situ irradiance data is presented. Inverse analysis is performed by solving a nonlinear optimization problem, where the objective function is given by the square difference between experimental and computed data plus a regularization term. The forward problem is tackled with the LTS_N method that numerically solves the radiative transfer equation. The experimental data are simulated with synthetic data corrupted with noise.     

Calculating the transient temperature field in a reactor tube and the thermoelastic stresses in the fuel element cladding

Approximate analytic methods are given for calculating the transient temperature field in the fuel elements and the coolant temperatures at any point along the reactor tube, as well as the transient thermoelastic stresses in the cladding of a cylindrical fuel element. The coolant temperature at the input to the tube is constant, and the coolant undergoes no changes in state of aggregation. The approximate methods are illustrated by examples.Results are given, for comparison, of accurate calculations of the same examples made with a rapid calculating machine.List of symbols time - r; z coordinates (radius, distance along tube) - r₁; r₂ internal and external radii of fuel element cladding respectively - H total active length of fuel element - a₁; ₁;c _{1 1} coefficients of temperature conductivity, heat conductivity, specific heat capacity and specific gravity of fissionable material respectively - a₂; ₂; C_p2; ₂ cladding parameters - a; ; c_p; coolant parameters - mean cladding radius - f:f₂ cross-sectional area of tube for coolant and cladding respectively - w coolant velocity - coefficient of heat release to coolant - t (r, ); (); () fuel temperature, mean temperature over cross section of cladding, and coolant temperature at pointz. along tube respectively - qv() specific volume of coolant at pointz - values averaged overz - quantities at the initial instant of time - ₃ delay time - _n time required for coolant to go from z=0 to the point in question     

Investigation of the thermal inertia and thermal stresses of heat-transferring elements in a solid-coolant nuclear reactor

Computational studies of specific questions arising when solids are used in nuclear reactors as the cooling medium are described. The concept of using approximately 1 mm in diameter spherical heat-carrying elements made of pyrolytic carbon coated graphite as a medium for transmitting heat from a fuel element to a steam generator is examined. A computational analysis of the internal stresses arising in 1–10 mm in diameter spherical elements transferring heat and the temperature lag of the heat-carrying elements relative to the temperature of the medium under cyclic heating and cooling is performed. The results of experimental studies were used to determine the boundary conditions of the problem. Supplying heat uniformly over the surface and through a finite number of contact points, which is characteristic for a fill consisting of spherical particles, was modeled. The transmission of heat through a finite number of contacts results in a complicated stress state of the heat-transmitting elements and a higher thermal inertia. It is shown that the internal stresses are weak in small heat-carrying particles, but when the diameter is increased to 10 mm the stresses from thermal cycling become comparable to the ultimate strength.     

Piping specific analysis of stresses due to thermal stratification

Within the framework of the ‘Component Specific Analysis of Mechanical Behaviour’, the nuclear codes and standards, e.g. KTA Standard KTA 3201.2 on Components of the Reactor Coolant Pressure Boundary of Light Water Reactors (Design and Analysis) allow a simplified stress and fatigue analysis for piping by applying the stress index method. The equations supplementary to present KTA Standard given in this context can be used for the consideration of the thermal loads arising from piston flow but not of those from thermal stratification. Thermal stratification occurs e.g. in the surge line of pressurised water reactors during start-up and shut-down processes. This phenomenon is explained and its effects are described. The equations supplementary to the present KTA Standard are derived which enable the consideration of the load case ‘thermal stratification’ in the simplified stress and fatigue analysis. Their applicability is demonstrated by a numeric example.     

Effect of shear deformation on thermal stresses in cylindrical shells

A theory of cylindrical shell including the shear deformation is developed and its effect on the thermal displacements and the thermal stresses are investigated. The theory presented in this work is a refined version of the Donnell type improved theory given earlier and a reduction method of the system of equation with five unknowns to one with three unknowns is proposed. In numerical examples for cylindrical shells under heat sources the thermal displacements and the thermal stresses in the present and the Donnell type theories are examined and are discussed together with those in the classical theories.     

Three-dimensional transport theory: An analytical solution for the internal beam searchlight problem, II

Multidimensional semi-analytical particle transport benchmarks to provide highly accurate standards of assessment are few and far between. Because of a well-established 1D theory for the analytical solution of the transport equation, it is sometimes possible however, to “bootstrap” 1D solutions to give more comprehensive solution representations. Here, we propose the internal searchlight problem in a half space, designated ISLP/HS, as a multidimensional benchmark to be constructed from 1D solutions. This is a variation of the usual SLP/HS where a source emits within the half space rather than striking its surface. Our primary interest is in the exiting intensity at the free surface established through a new Fn formulation. The benchmark features true 2/3D particle transport through integration of a point kernel to simulate 2/3D source emission. In this way, we accommodate a solid or hollow cylindrical source and a general line source in addition to the standard point, ring and disk sources featured in previous investigations.     

Criteria for comparison of methods of solution of the inverse heat conduction problem

Some criteria are presented for comparing methods of solution of the inverse heat conduction problem. These include accuracy when using exact data, insensitivity to measurement errors, and stability for small time steps. The criteria are applied to a method previously given by the author; it is shown herein that as measurement errors become larger, the time steps must increase for a given accuracy of the calculated surface heat flux or temperature. New results are also presented for a multiple number of temperature sensors. In addition, it is demonstrated how the procedure can be applied to correlated measurement errors. Some methods used by other investigators are also briefly considered.     

Initial assessment of the thermal stresses around a radioactive waste depository in hard rock

The disposal of heat emitting radioactive waste into hard rock should result in temperature rises and thermal gradients over distances of several hundred metres for several centuries. The consequent constrained thermal expansion of the rock would induce stresses which have important implications for possible water-borne leakage of radionuclides and for depository design. These problems are assessed by considering a simplified mathematical model for which analytic solutions to the temperature and stress fields are derived.     

Anisotropy of coefficient of thermal expansion of nuclear graphite under compressive stresses

The coefficient of thermal expansion (CTE) of nuclear graphite IG-110 and NBG-18 under compressive stresses of 20 MPa, 30 MPa and 40 MPa has been measured by strain gauge method and corresponding anisotropies of CTE under stresses were investigated. With the increasing compressive stresses, the CTE of IG-110 and NBG-18 parallel and perpendicular to the loading directions increased significantly and decreased gradually respectively. The corresponding CTE anisotropies of IG-110 and NBG-18 almost maintain below 1.05 and keep their original near-isotropic properties under compressive stresses maybe due to the homogeneous sensitivity of CTE to the stresses, perfect crystallites in the grains and homogeneous alignment of grains in graphite. The constant isotropic properties of graphite IG-110 and NBG-18 under stresses are beneficial for the integrity and safety of the graphite used in the reactor.     

Three-dimensional transport theory: An analytical solution of an internal beam searchlight problem, III

We describe a method for obtaining analytical solutions and numerical results for three-dimensional one-speed neutron transport problems in a half-space containing a variety of source shapes which emit neutrons mono-directionally in the direction away from the surface. Thus this paper is a supplement to Williams [Williams, M.M.R., 2009, Three-dimensional transport theory: an analytical solution for the internal beam searchlight problem I. Annals of Nuclear Energy 36, 767–783]. For example, we consider a point source, a ring source and a disk source, and calculate the surface scalar flux as a function of the radial co-ordinate when the source is at a fixed distance from the surface. The results are in full agreement with the work of Ganapol and Kornreich [Ganapol, B.D., Kornreich, D.E., this issue. Three-dimensional transport theory: an analytical solution for the internal beam searchlight problem II. Annals of Nuclear Energy]. Diffusion theory results are also included.     

Influence of thermally induced secondary stresses on the lifetime of high temperature reactor components

The metallic components of a high-temperature reactor with operating temperatures above 880°C have to be ensured against the, in comparison to primary stresses, respectively higher secondary stresses due to loading transients. For the calculation of the damage accumulation due to primary, secondary and peak stresses, elastic methods are used in the temperature region up to 800°C. These elastic methods are too conservative at temperatures above 900°C. Therefore a simplified inelastic method is shown for calculation of the creep damage of a reformer tube with operating temperatures at about 900°C under start-up and shut-down loadings. With this method a design is possible for the calculated start-up and shut-down transients during the lifetime of the component.     

Application of the theory of random matrices to a reactor-noise problem

The stochastic equation corresponding to a nuclear reactor with random distribution of materials is written in a matrix form, in this way the probability distribution of reactivities is derived as the probability distribution of the higher eigenvalues of random matrices. The theoretical results are illustrated and validated with Monte Carlo simulations based on the diffusion equations and the matrix approach.     

The principles of nucleation theory relevant to the void swelling problem

The nucleation of small stable species is described in the problem of void growth by discrete rate equations. The purpose of this review is to clarify and draw together existing ideas on incubation dose and critical cavity radius for void nucleation and those of classical nucleation theory. When gas is being produced the problem reduces to one of calculating the incubation dose for the gas bubble-to-void transition. A general expression for the steady state nucleation rate is derived for the case when voids are formed by vacancy fluctuations which enable an effective nucleation barrier to be crossed.     

A computational-experimental investigation of the temperature field of IGR masonry

The experimental measurements of the temperature in IGR reactor masonry are analyzed, and it is shown that because of the radiation heating of the thermocouples, it is impossible to measure the temperature at the moment of a run and because of the time constant of the measuring system, it is impossible to measure the temperature during a period of 1 min after a run. The three-dimensional code TEMPO was developed to calculate the temperature field of the reactor masonry. It is shown that the code predicts the temperature field to within 10%, which is adequate for the present stage of the work. Computational results for the temperature field of the masonry are presented, 6 figures, 6 references. Translated from Atomnaya énergiya, Vol. 88, No. 4, pp. 247–251, April 2000. Original article submitted March 13, 2000.     

Influence of multiple jet cooling on the heat transfer and thermal stresses in DEMO divertor cooling finger

The divertor concept for DEMO fusion reactor is based on modular design cooled by multiple impinging jets. Such divertor should be able to withstand a surface heat flux of at least 10 MW/m² at an acceptable pumping power. To reduce the thermal loads the plasma-facing side of the divertor is build up of numerous small cooling fingers. Each cooling finger is cooled by an array of jets blowing through the holes on the steel cartridge.The size, number and arrangement of jets on the cartridge influences the heat transfer and pressure drop characteristics of the divertor. Five different cartridge designs are analyzed in the paper. The most critical parameters, such as structure temperature, heat removal ability, pressure drop, cooling efficiency and thermal stress loadings in the cooling finger are predicted for each cartridge design. A combined computational fluid dynamics and structural model was used to perform the necessary numerical analyses. The results have shown that the cartridge design with the best heat transfer and pressure drop characteristics is not also the most favorable choice from the point of view of minimum stress peaks.