scholarly journals Development of the model to determine the fuel temperature field in a two-dimensional problem statement

2019 ◽  
Vol 5 (3) ◽  
pp. 219-224 ◽  
Author(s):  
Vladimir A. Gorbunov ◽  
Natalya B. Ivanova ◽  
Nikita A. Lonshakov ◽  
Yaroslav V. Belov
Keyword(s):  
Temperature Field ◽  
Analytical Solution ◽  
Numerical Models ◽  
Reactor Core ◽  
Comsol Multiphysics ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Fuel Temperature ◽  
Problem Statement ◽  
Fuel Rods

Water-cooled water-moderated reactors (VVER) are widely used at Russian nuclear power plants. The VVER reactor core is formed by fuel assemblies consisting of fuel rods. The fuel in fuel rods is uranium dioxide. The safety of the reactor operation is ensured through stringent requirements for the maximum nuclear fuel temperature. Calculation of temperature fields within the reactor core requires associated problems to be solved to determine the internal energy release in fuel based on neutronic characteristics. Dedicated software for such calculations is not available to a broad range of users. At the present time, there are numerical thermophysical modeling packages available for training or noncommercial applications which are used extensively, including Elcut, Flow Vision, Ansys Fluent, and Comsol Multiphysics. Verification of the obtained results is becoming an important issue in building models using these calculation packages. An analytical solution was obtained as part of the study for the fuel temperature field determination. A program was developed in MathCAD based on this solution. A model was developed in Comsol Multiphysics to determine the fuel temperature field with constant thermophysical properties in a two-dimensional problem statement. The numerical model was verified using the analytical solution. The influence of the number of the grid nodes on the solution accuracy was established. The analytical solution can be used to determine the fuel temperature field at any radial coordinate of the reactor. The temperature field determination model developed in MathCAD can be used to verify numerical models of the fuel temperature field determination developed in dedicated packages.

scholarly journals Development of the model to determine the fuel temperature field in a two-dimensional problem statement

2019 ◽  
Vol 2019 (2) ◽  
pp. 174-184
Author(s):  
Vladimir Alexandrovich Gorbynov ◽  
Natalya Borisovna Ivanova ◽  
Nikita Andreevich Lonshakov ◽  
Yaroslav Viktorovich Belov
Keyword(s):  
Temperature Field ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Fuel Temperature ◽  
Problem Statement

scholarly journals Assessment of radiation heat transfer influence on parameters of temperature fields of various design fuel rods

Vestnik IGEU ◽  
2021 ◽  
pp. 23-31
Author(s):  
V.A. Gorbynov ◽  
S.G. Andrianov ◽  
S.S. Konovaltseva
Keyword(s):  
Heat Transfer ◽  
Radiation Heat Transfer ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Radiation Heat ◽  
Problem Statement ◽  
Fuel Rods ◽  
Fuel Rod ◽  
The Impact

VVER-1000 reactors use cylindrical smooth-core fuel rods. Previously, a model to determe the fuel rod temperature field in a two-dimensional problem statement has been developed and verified. However, modelling assumptions do not consider the influence of variable thermophysical properties, radiation heat transfer, and the opening in the fuel rod on the final parameters of the temperature fields. The impact assessment is an urgent task to improve the economic efficiency of the fuel cycle and the capacity of power units. To develop models and study the features of energy release in nuclear reactors, a numerical package of thermophysical modeling COMSOL Multiphysics software is used. The simulation of temperature fields is performed based on the heat equation with an internal heat source, under the boundary conditions of the second kind at the ends of the fuel rod and the boundary conditions of the third kind on the side surface of the rod. Аn axisymmetric model in two-dimensional problem statement and a three-dimensional model of the fuel rod are developed. The temperature distribution fields are determined by the finite element method. The results of calculations of various design fuel rods are presented. The results have showen that the radiation heat transfer significantly affects the maximum fuel temperature (UO2). The impact degree of variability of thermophysical properties and radiation heat transfer is determined. It was found that the temperature characteristics under different specified conditions have a difference in the range of 15,5–282,0 K (0,8–14,4 %). The developed models are reliable and confirmed by the previously verified model, the characteristics of the fuel assembly used on the VVER-1000 units. The results presented can be used for mathematical modeling of heat transfer processes, both during the modernization of the equipment in operation, and during the development, design, and operation, which will increase the efficiency of electric energy generation at the power unit of a nuclear power plant.

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

On The Theory Of Bending Of A Thick Orthotropic Plate Without Consideration Of Simplifying Hypothesis

2011 ◽  
Vol 3 ◽  
Author(s):  
Makhamatali Koraboyevich Usarov
Keyword(s):  
Analytical Solution ◽  
Orthotropic Plate ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Orthotropic Plates

The problem of bending of a thick orthotropic plate is considered as a three-dimensional problem of the theory ofelasticity. On the basic of the method of expansion of thesolution into the series, a three-dimensional problem isreduced to two independent two –dimensional problems.The theory of thick orthotropic plates free from simplifiedhypothesis is developed: An analytical solution of equationis given. Maximum values of displacements and stressesfor upper, middle and lower surfaces of the plate are calculated.

Discussion of Boundary Conditions of Transpiration Cooling Problems Using Analytical Solution of LTNE Model

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Jianhua Wang ◽  
Junxiang Shi
Keyword(s):  
Temperature Field ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Coolant Temperature ◽  
Transpiration Cooling ◽  
Dimensional Problem ◽  
Gas Temperature ◽  
One Dimensional ◽  
Hot Gas ◽  
Hot Surface

To compare five kinds of different boundary conditions (BCs), an analytical solution of a steady and one-dimensional problem of transpiration cooling described by a local thermal nonequilibrium (LTNE) model is presented in this work. The influence of the five BCs on temperature field and thermal effectiveness is discussed using the analytical solution. Two physical criteria, if the analytical solution of coolant temperature may be higher than hot gas temperature at steady state and if the variation trend of thermal effectiveness with coolant mass flow rate at hot surface is reasonable, are used to estimate the five BCs. Through the discussions, it is confirmed which BCs at all conditions are usable, which BCs under certain conditions are usable, and which BCs are thoroughly unreasonable.

scholarly journals ANALYTICAL SOLUTION OF A 2D TRANSIENT HEAT CONDUCTION PROBLEM USING GREEN´S FUNCTIONS

2020 ◽  
Vol 19 (1) ◽  
pp. 66
Author(s):  
J. R. F. Oliveira ◽  
J. A. dos Santos Jr. ◽  
J. G. do Nascimento ◽  
S. S. Ribeiro ◽  
G. C. Oliveira ◽  
...  
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Heat Fluxes ◽  
Two Dimensional ◽  
One Dimensional ◽  
Transient Heat Conduction Problem

Through the present work the authors determined the analytical solution of a transient two-dimensional heat conduction problem using Green’s Functions (GF). This method is very useful for solving cases where heat conduction is transient and whose boundary conditions vary with time. Boundary conditions of the problem in question, with rectangular geometry, are of the prescribed temperature type - prescribed flow in the direction x and prescribed flow - prescribed flow in the direction y, implying in the corresponding GF given by GX21Y22. The initial temperature of the space domain is assumed to be different from the prescribed temperature occurring at one of the boundaries along x. The temperature field solution of the two-dimensional problem was determined. The intrinsic verification of this solution was made by comparing the solution of a 1D problem. This was to consider the incident heat fluxes at y = 0 and y = 2b tending to zero, thus making the problem one-dimensional, with corresponding GF given by GX21. When comparing the results obtained in both cases, for a time of t = 1 s, it was seen that the temperature field of both was very similar, which validates the solution obtained for the 2D problem.

Numerical-Analytical Solution of Two-Dimensional Problem for Elastic Radially Inhomogeneous Thick-Walled Cylinder

2015 ◽  
Vol 752-753 ◽  
pp. 642-647 ◽  
Author(s):  
Vladimir I. Andreev
Keyword(s):  
Cylindrical Shell ◽  
Analytical Solution ◽  
Axisymmetric Problem ◽  
Infinite System ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Uniform Load ◽  
Radially Inhomogeneous ◽  
Walled Cylinder

In the [1,2] was considered method of separating of variables in three-dimensional problem for radially inhomogeneous cylinder. This problem solves in terms of displacements and reduced to infinite system of ordinary differential equations. The paper deals with the partially case – two-dimensional axisymmetric problem of the calculation of thick-walled cylindrical shell loaded by non-uniform load on the outer surface.

scholarly journals Engineering Margin in Calculations of Energy Release in VVER-1000 core

2018 ◽  
pp. 20-26
Author(s):  
A.M. Abdullayev ◽  
A.I. Zhukov ◽  
S.V. Maryokhin ◽  
S.D. Riabchykov
Keyword(s):  
Energy Release ◽  
Three Dimensional ◽  
Measurement Data ◽  
Reactor Core ◽  
Small Scale ◽  
Two Dimensional ◽  
Fuel Rods ◽  
Fuel Rod ◽  
The Core ◽  
Fuel Assemblies

A method for calculating the engineering margin factor (EMF) in calculations of the energy release in the core of VVER-1000 reactors is proposed in the paper. The analysis of various approaches in the calculation of EMF is carried out and various factors influencing EMF and the ways of their consideration —deterministic and statistical — are determined. The main attention is paid to the influence of gaps between the fuel assemblies on the energy release of fuel rods and the contribution of this factor to the EMF. The limitations and conservatism of two-dimensional small-scale calculations of the energy release of fuel rods in case of deviation of the gap size between the fuel assemblies from the design one are shown. A three-dimensional approach to calculating the contribution of gaps to the EMF is proposed. The approach is based on detailed measurements of the shape of fuel assemblies removed from the core performed at Zaporizhzhya NPP [13]; simulation of the distribution of gaps in the reactor core [16] using measurement data; two-dimensional calculations of the energy release of fuel rods in separate fuel assemblies, surrounded by gaps of different widths, with mirroring boundary conditions; three-dimensional calculations of energy release of fuel rods in fuel assemblies in the reactor core. Two-dimensional and three-dimensional calculations are performed by the wellknown ALPHA-H/PHOENIX-H/ANC-H codes. The proposed approach allows considering not only the change in the fuel rod power, particularly of the peripheral rods, which is inherent in the currently used methods of calculating EMF, but also takes into account the change in the power of the fuel assemblies in the core, which makes the proposed method more realistic and removes the excessive conservatism of EMF calculations and, thereby, allows improving fuel efficiency. For fuel assemblies produced by Westinghouse, it is proposed to use full EMF: for fuel rod power (FΔH) 1.111 and for fuel rod linear power (FQ) 1.173. The use of the BEACONTM monitoring system makes it possible to further reduce the EMF: for fuel rod power (FΔH) - up to 1.084 and for fuel rod linear power (FQ) - up to 1.121.

scholarly journals Displacements Caused by the Temperature in Multicomponent, Multi-Layered Periodic Material Structures

2020 ◽  
Vol 22 (3) ◽  
pp. 809-820 ◽  
Author(s):  
Vazgen Bagdasaryan ◽  
Monika Wągrowska ◽  
Olga Szlachetka
Keyword(s):  
Temperature Field ◽  
Boundary Value Problem ◽  
Thermal Stresses ◽  
Boundary Value ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Periodic Composites ◽  
Modelling Procedure ◽  
Tolerance Modelling ◽  
Model Equations

AbstractThe present study aims to analyse a two-dimensional problem of displacements in theory of thermal stresses for multicomponent, multi-layered periodic composites. The model equations are obtained within the framework of the tolerance modelling procedure. These equations allow to determine the distribution of displacements caused by the temperature field in the theory of thermal stresses. The paper presents an example of a solution of a boundary value problem.

scholarly journals Mathematical modeling of well operation in the case of two-dimensional filtration in an anisotropic heterogeneous layer

2020 ◽  
pp. 87-95
Author(s):  
Д.Г. Лекомцев ◽  
В.Ф. Пивень
Keyword(s):  
Mathematical Modeling ◽  
Analytical Solution ◽  
Affine Transformation ◽  
Integral Relation ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
System Of Integral Equations ◽  
Well Production ◽  
Rank Tensor ◽  
Heterogeneous Layer

Поставлена плоская (двумерная) задача о математическом моделировании работы скважины в анизотропном неоднородном пласте грунта с раздельной анизотропией и неоднородностью, когда контур питания произвольный. Рассматривается совершенная скважина, когда она полностью вскрывает пласт своей рабочей частью (фильтром). Проницаемость грунта характеризуется тензором второго ранга, компоненты которого моделируются степенной функцией координат. Гомеоморфным аффинным преобразованием координат эта задача приводится к каноническому виду, что значительно упрощает ее исследование. Получено в конечном виде аналитическое решение задачи о дебите скважины с конкретным эллиптическим контуром питания, а также в случае, когда контур питания удален в бесконечность. В случае произвольного гладкого контура питания задача о дебите редуцирована к системе сингулярного интегрального уравнения и интегрального соотношения, которая решена численно методом дискретных особенностей. Исследовано влияние на дебит анизотропии, неоднородности пласта и формы контура питания. A flat (two-dimensional) problem has been posed on the mathematical modeling of well in an anisotropic inhomogeneous reservoir of soil with separate anisotropy and heterogeneity when the power contour is arbitrary. The considered well completely opens the formation with its working part (filter). Such a well is called perfect. The permeability of the soil is characterized by a second-rank tensor whose components are modeled by a power function of the coordinates. With a homeomorphic affine transformation of coordinates, this problem is reduced to a canonical form which greatly simplifies its study. An analytical solution of the problem of well production with an elliptical power contour is obtained in the final form as well as in the case when the power contour is removed to infinity. In the general case, the problem is reduced to a system of integral equations and the integral relation. The results were obtained in the general case using the discrete singularities method. The influence on the flow rate of anisotropy, heterogeneity of the reservoir and the shape of the power contour was studied.

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