Наближена оцінка температурного стану керамічного ядерного палива в циліндричних твелах та впливу на нього процесів і параметрів конструкцій активної зони реактора

The approximate mathematical model of the temperature state of ceramic nuclear fuels in cylindrical fuel elements was proposed in the form of linear ordinary differential equation and the boundary conditions. The theory of heat conduction and assumptions about the axial symmetry and absence of heat flows along axis of fuel element, which allow to simplify the common equations in cylindrical coordinates, are the basis of the proposed simplified mathematical model for approximate estimating the temperature state of the nuclear fuel. The intensity of volume heat sources in fuel element was taken into account by using the average values corresponding with the heat power and the structural characteristics of a nuclear reactor core. The conception about the heat transfer coefficient was used for modeling interaction between the fuel and the heat carrier. This heat transfer coefficient depends on characteristic sizes and heat conductions of constituted materials of the fuel element and allows to estimate influence of these on the temperature state of the nuclear fuel. The analytical solution for the temperature of a ceramic fuel in cylindrical fuel elements was obtained and was used for researching. It was shown that the heat conductivity of the fuel has significantly influences both the average temperature and the difference between the inner and outer temperatures in the fuel pellet. At the same time, other parameters have significant influence only on the average temperature of the fuel pellet. Due to these, it is necessary to consider the temperature dependence of the thermal conductivities of the materials constituted the fuel elements for more precisely estimations the temperature state of the fuel pellets, which will lead to nonlinear equations will required the numerical methods for their solving.На основі математичної моделі теплопровідності з урахуванням ряду гіпотез спрощення отримані наближені кількісні оцінки температурного стану керамічного ядерного палива в активній зоні ядерного енергетичного реактора. Досліджено вплив на температурний стан ядерного палива температури теплоносія, тепловіддачі від оболонки твела до теплоносія, теплопровідності оболонки, газового наповнювача твела, керамічного палива, а також розмірів палива. Показано, що теплопровідності палива і конструкційних матеріалів твела мають найбільший вплив на температурний стан керамічного ядерного палива

Наближена оцінка температурного стану керамічного ядерного палива в циліндричних твелах та впливу на нього процесів і параметрів конструкцій активної зони реактора

The approximate mathematical model of the temperature state of ceramic nuclear fuels in cylindrical fuel elements was proposed in the form of linear ordinary differential equation and the boundary conditions. The theory of heat conduction and assumptions about the axial symmetry and absence of heat flows along axis of fuel element, which allow to simplify the common equations in cylindrical coordinates, are the basis of the proposed simplified mathematical model for approximate estimating the temperature state of the nuclear fuel. The intensity of volume heat sources in fuel element was taken into account by using the average values corresponding with the heat power and the structural characteristics of a nuclear reactor core. The conception about the heat transfer coefficient was used for modeling interaction between the fuel and the heat carrier. This heat transfer coefficient depends on characteristic sizes and heat conductions of constituted materials of the fuel element and allows to estimate influence of these on the temperature state of the nuclear fuel. The analytical solution for the temperature of a ceramic fuel in cylindrical fuel elements was obtained and was used for researching. It was shown that the heat conductivity of the fuel has significantly influences both the average temperature and the difference between the inner and outer temperatures in the fuel pellet. At the same time, other parameters have significant influence only on the average temperature of the fuel pellet. Due to these, it is necessary to consider the temperature dependence of the thermal conductivities of the materials constituted the fuel elements for more precisely estimations the temperature state of the fuel pellets, which will lead to nonlinear equations will required the numerical methods for their solving.На основі математичної моделі теплопровідності з урахуванням ряду гіпотез спрощення отримані наближені кількісні оцінки температурного стану керамічного ядерного палива в активній зоні ядерного енергетичного реактора. Досліджено вплив на температурний стан ядерного палива температури теплоносія, тепловіддачі від оболонки твела до теплоносія, теплопровідності оболонки, газового наповнювача твела, керамічного палива, а також розмірів палива. Показано, що теплопровідності палива і конструкційних матеріалів твела мають найбільший вплив на температурний стан керамічного ядерного палива

Mathematical Modeling of Mitral Valve Dynamics: Nonlinear vs Linear Models

A tractable mathematical model of the valve dynamics is developed for the real time computations and in silico planning of the biomechanically consistent surgery on the ruptured chordae of the mitral valve. The geometry and dynamics of the heart contraction and valve closure are restored by digitization of the 2d echocardiography data measured on a patient. The chordae are modeled as branched systems of viscoelastic strings with zero bending rigidity. Both linear and nonlinear rheology of the heart tissues are considered. The corresponding numerical procedure is worked out. The developed model can be used for comparative study of different existing strategy of surgical restoration for individual patients as well as for fast real time computations of optimal location of the neochordae directly during the surgery

Edge fixing effect on the life of a vacuum chamber thin spherical cover subjected to creep damage

Within framework of the numerical studies of creep resource of a thin spherical cover of a vacuum chamber, we present mathematical formulation and the calculation method for the solution of the initial boundary value problems of the creep theory of thin shells with account of the damage accumulation process of the material. The effect of edge fixing along the normal and tangential lines to the median surface, as well as angular edge fixings, on the cover life in creep are studied under atmospheric pressure creep conditions. The calculation data obtained made it possible to determine the dependence between the cover life in creep and its edge fixing conditions: this effect is strong by the latent fracture time and weak by the allowable deflection value

Mathematical Modeling of Mitral Valve Dynamics: Nonlinear vs Linear Models

A tractable mathematical model of the valve dynamics is developed for the real time computations and in silico planning of the biomechanically consistent surgery on the ruptured chordae of the mitral valve. The geometry and dynamics of the heart contraction and valve closure are restored by digitization of the 2d echocardiography data measured on a patient. The chordae are modeled as branched systems of viscoelastic strings with zero bending rigidity. Both linear and nonlinear rheology of the heart tissues are considered. The corresponding numerical procedure is worked out. The developed model can be used for comparative study of different existing strategy of surgical restoration for individual patients as well as for fast real time computations of optimal location of the neochordae directly during the surgery

Оцінка працездатності пароперегрівачів парових котлів з урахуванням високотемпературної повзучості і рівномірної хімічної коррозии

It is proposed theoretical estimating workability of steam boilers superheaters on the base of considering the influence of a high-temperature uniform chemical corrosion on of a high-temperature creep of superheater pipes on account of stresses redistributions the pipes walls due to their thickness decreasing. The high-temperature uniform chemical corrosion is presented by the well-known time and temperature depend-ences of the height of damaged material. The high-temperature creep is considered using the well-known incremental-type theory taking into account the Cachanov-Rabotnov scalar damage parameter. It is proposed the mathematical model of state of superheaters pipes in the form of initial-boundary-value problem in the domain with the moving boundary. The differential equations, initial and boundary conditions of that problem are corresponded to the well-known in the theory of high-temperature creep. Moving of the boundary is corresponded to the well-known time dependence of the height of damaged material due to the high-temperature uniform chemical corrosion. Although, the used theory of creep and the used regularities of uniform corrosion are well-known separately, considering the influence of uniform corrosion on the creep is the complicated problem due to the moving boundary in the corresponded initial-boundary-value problem. It is shown, that the spatial variable replacement allows to reduce the proposed initial-boundary-value problem with the moving boundary to the initial-boundary-value problem with the fixed normed boundary, that allows to simplify numerical solving of the considered problem. The method of lines is discussed for solving the initial-boundary-value problem, representing the mathematical model of the state of pipes of superheaters.Пропонується теоретична оцінка працездатності пароперегрівачів парових котлів на основі врахування впливу високотемпературної рівномірної хімічної корозії на високотемпературну повзучість труб пароперегрівача через перерозподіл напружень стінок труб через зменшення їх товщини. Запропоновано математичну модель стану труб пароперегрівачів у вигляді початково-крайової задачі з рухомою границею. Показано, що заміна просторової змінної дозволяє звести запропоновану початково-крайову задачу з рухомою границею до початково-крайової задачі з фіксованою границею, що дозволяє спростити чисельне рішення даної задачі

Prediction of the corrosion cracking of structures under the conditions of high-temperature creep

On the basis of the continual model of corrosion crack growth proposed earlier and the well-known incremental-type creep theory, we make an attempt to predict the corrosion cracking of structures under the conditions of high-temperature creep. We propose the mathematical statement of the problem taking into account the influence on corrosion cracking of the properties of corrosive media and the redistribution of stresses in time caused by creep. The Bubnov–Galerkin method is applied for the solution of this problem. An example of prediction of the phenomenon of corrosion cracking in the case of creep of a pipe under the action of internal pressure is analyze

The method of R-functions in the solution of elastic problems on the basis of reissner`s mixed variational principle

A method is presented for solving boundary-value elastic problems on the basis of the variational–structural method of R-functions and Reissner’s mixed variational principle. A mathematical formulation is given to problems on the deformation of elastic bodies under mixed boundary conditions and bodies interacting with smooth rigid dies. Solutions satisfying all the boundary conditions are proposed. For undetermined components of these solutions, the resolving equations are derived and their properties are studied. A posteriori estimation of numerical solutions is made. As examples, solutions are found to a problem on the stress–strain state of a short cylinder and to a contact problem on a cylinder interacting with a smooth die. A numerical method of solving such problems is analyzed for convergence, and the accuracy of the solutions is estimated