An unconditionally stable, explicit algorithm for finite-element heat conduction analysis

The stable explicit algorithm of Saul'ev is extended to the finite element heat conduction transient analysis. With the use of matrix notation, the algorithm is generalized so that it can be applied to both finite difference and finite element analysis in any number of spatial dimensions. Accuracy and stability are discussed using basic properties of the capacitance and the conductance matrix. A two-dimensional example is included and the results are compared with the Crank-Nicolson method.     

Transient heat conduction problems in inhomogeneous media discretized by means of boundary-volume element

An integral equation formulation is presented for the transient heat conduction problems in inhomogeneous media. The material constants are assumed to be prescribed as arbitrary, continuous and differentiable functions of position vector. The governing integral equations are derived from the weighted residual statement of the problems in which the fundamental solution to the corresponding heat conduction problems in homogeneous media is used as the weight function. The whole domain of interest is discretized into a series of boundary-volume-time elements, and then a set of linear simultaneous equations are obtained. Their solutions yield the temperature in the whole domain as well as the heat flux on the boundary.     

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.     

Finite element analysis of linear and nonlinear heat transfer

The finite element method is rapidly becoming a popular procedure for the evaluation of thermal stresses in complex structures. In linear analysis the method has been used extensively and has been coupled with stress analysis computer programs in order to automate thermal stress analysis. However, for the method to be effective, efficient numerical techniques need to be used. The purpose of this paper is to survey the recent developments in linear heat transfer analysis and, specifically, to present the techniques that permit the practical analysis of large and complex three-dimensional heat conduction problems. Typical practical problems are described and solution times are presented. In the analysis of systems with nonlinear thermal properties the method has had limited application. In this paper the general formulation of the incremental equations used in nonlinear heat transfer analysis are presented. An efficient numerical solution of the equations is given. Several types of nonlinearities are discussed and the solutions of some typical problems are presented.     

Elbow stress indices using finite element analysis

Existing ASME Code provisions allow for an experimentally determined collapse load. This collapse (limit) load can then be used in the Code equation defining stress indices to obtain a stress index experimentally. This paper describes a research project to investigate the use of inelastic finite element analysis, rather than experiments, to obtain the collapse load. An example is given for a 2-in., schedule 40, long radius, 90°, stainless steel elbow with 10-in.-long straight pipes on each end. A B₂ index is found using this approach which is nearly 50% lower than the one obtained using the Code equation for B₂.     

Smearing in an axisymmetric finite element structural analysis application to the GCFR steam generator cavity closure plug

A methodical technique for smearing material properties in an elastic finite element analysis to derive an approximate axisymmetric model of a structure is presented. In this process, material properties are smeared circumferentially about an axis of symmetry in the structure's outline. Attention is given to the subsequent problem of unsmearing the results to obtain an estimate of circumferential variation in the solution. The scheme is illustrated with an application to an analysis of a GCFR steam generator cavity closure plug.     

Finite element analysis of a finite-strain plasticity problem

A finite-strain plasticity analysis was performed of an engraving process in a plastic rotating band during the firing of a gun projectile. The aim was to verify a nonlinear feature of the NIFDI/RB code: plastic large deformation analysis of nearly incompressible materials using a deformation theory of plasticity approach and a total Lagrangian scheme.     

脉冲强磁体中应力的有限元分析

提高脉冲磁场强度的主要障碍是磁体中巨大的应力,而脉冲磁体中应力的产生和作用过程比较复杂,要准确地计算出来很困难。采用有限元法对脉冲磁体中的应力进行分析,计算中全面考虑了预应力、电磁力、热应力等情况。通过计算,得出了,一些设计脉冲磁体的基本原则。     

Finite element analysis of steady-state nonlinear heat transfer problems

A method of analysis and the associated computer program are presented for the purpose of solving steady-state nonlinear heat transfer problems in two-dimensional structures. The nonlinearity arises from the dependence of the thermal conductivities on temperature as well as from the presence of rediative heat transfer between parts of the structure. The problem is formulated in terms of an integral of conductivity and solved in an iterative way via the finite element concept. Several examples are given to illustrate the validity and practicality of the suggested solution technique.     

Discontinuity stress analysis of pressure vessels using the finite element method

In pressure vessels the centre lines of the cylinder and dome portions often do not coincide thereby leading to a discontinuity at their junction. Structural analysis of such a structure assuming the centrelines of the cylinder and dome portions to be coincident leads to an incorrect estimation of stress and displacement distributions around the discontinuity. To predict accurately the stress and displacement distributions around the discontinuity, an iterative finite element scheme is developed in this paper using a conical shell finite element. The method is applied to two typical pressure vessels, one with hemispherical end domes and the other with ellipsoidal end domes. It is found that the solution converges in a few iterations.     

Development of a 2D conduction code for a finned fuel element analysis

The fuel element of KMRR (Korea Multi-purpose Research Reactor) has 8 longitudinal, rectangular fins to enhance the heat transfer performance. The existence of these fins makes it difficult to analyze the heat transfer phenomena within the fuel element using the conventional one-dimensional heat conduction model. As the uncertainty in the computation of the maximum sheath temperature significantly affects the core thermal margin, a computer code, called, TEMP2D, which is based on a two-dimensional heat conduction model has been developed to deal with the finned element and validated. This computer code TEMP2D has a fully implicit numerical scheme and can solve both the steady state and transient problems such as the changes in coolant thermal-hydraulic conditions and fuel pin power. The code accuracy, which proved to be an excellent one, was verified by comparing its results with those from two widely accepted computer codes, MARC and ADINA. The result of this code calculation has been used to compute the KMRR core thermal margin and to develop a correlation for the equivalent 1D heated diameter which can reproduce the maximum cladding temperature (or heat flux) at various steady states when used in the 1D heat conduction model.     

Thermal stresses in rectangular plates: Variational and finite element solutions

This paper deals with the development of an approximate method for the analysis of thermal stresses in rectangular plates (plane stress problem) and an evaluation of the relative accuracy of the finite element method. The stress function is expanded in terms of polynomial coordinate functions which identically satisfy the boundary conditions, and a variational approach is used to determine the expansion coefficients. The results are in good agreement with a finite element approach.     

Forced convection heat transfer in rectangular ducts—general case of wall resistances and peripheral conduction for ventilation cooling of nuclear waste repositories

A numerical solution for laminar flow heat transfer between a flowing gas and its containing rectangular duct has been obtained for many different boundary conditions which may arise in nuclear waste repository ventilation corridors. The problem has been solved for the cases of insulation on no walls, one wall, two walls, and three walls with various finite resistances on the remaining walls. Simplifications are made to decouple the convective heat transfer problem from the far field conduction problem, but peripheral conduction is retained. Results have been obtained for several duct aspect ratios in the thermal entrance and in the fully developed regions, including the constant temperature cases. When one wall is insulated and the other three are at constant temperature, the maximum temperature occurs in the fluid rather than on the insulated wall. This maximum moves toward the insulated wall with increasing axial distance. Nusselt numbers for the same constant flux on all four walls with peripheral conduction lie in a narrow band bounded by zero and infinite peripheral conduction cases. A dimensionless wall conduction group of four can be considered infinite for the purpose of estimating fully developed Nusselt numbers to within an accuracy of 3%. A decrease in wall and bulk temperatures by finite wall conduction has been demonstrated for the case of a black body radiation boundary condition. Nusselt numbers for the case of constant temperature on the top and bottom walls and constant heat flux on the side walls exhibited unexpected behavior.     

Steady-state heat conduction in slabs, cylindrical and spherical shells with non-uniform heat generation

A comparison is made between temperature drops in cylindrical and spherical shells and in slabs in the cases of uniform and non-uniform internal heat generation with the same total amount of heat. One boundary is assumed to. be insulated; the rate of internal heat generation may be an arbitrary function of the radius. The (variational) ratio between the relative difference in temperature drops (in the non-uniform and uniform cases) and a (dimensionless) measure of the non-uniformity in heat generation is found to vary between narrow bounds which depend only upon the geometry. When the power density is better known, the bounds on the variational ratio get closer together. Similar derivations are made for the average temperature when one boundary is insulated or when both boundaries are at the same temperature. Kernels allowing the exact computation of temperatures of interest are listed in tables for various geometries and boundary conditions.     

矩形通道干涸点传热特性试验研究

在中国核动力研究设计院流动传热基础试验平台上进行了矩形通道干涸点传热试验。通过对各种热工水力参数的试验研究,得出结论:(1)随着进口含汽率的增加,干涸点热流密度减小,含汽率增加,壁面温度降低,传热系数减小;(2)随着质量流速的增大,干涸点热流密度增大,含汽率减小,壁面温度升高,传热系数增大;(3)随着系统压力的升高,干涸点热流密度增大,含汽率增加,壁面温度升高,传热系数增大。由试验数据与现有经验关系式的比较,发现这些关系式适合中高压、中低质量流速工况,而对低压、高质量流速工况存在较大的偏差。在古塔杰拉奇关系式的基础上,引入矩形通道尺寸和进口焓等影响传热的因素,得出了适用于矩形通道的干涸关系式。关系式与试验数据吻合良好。     

Finite element nonlinear heat transfer analysis using a stable explicit method

The explicit stable method of Saulev is applied to nonlinear finite element heat conduction. Several nonlinear example problems are considered which include temperature-varying material properties and radiation boundary conditions.     

A finite element formulation for thermal stress analysis. Part II: Finite element formulation

This paper deals with the development of a variational principle which can be used for solving problems related to the thermoelastic behavior of solids and is the first of the two part series. The formulation is based on the introduction of a new quantity defined as heat displacement and related to temperature in the same manner as the mechanical displacement is related to strain. The introduction of such a quantity allows the heat conduction equations to be written in a form equivalent to the equation of motion, and the equations of coupled thermoelasticity to be written in a unified form. The obtained equations are used to write a variational formulation which, together with the concept of generalized coordinates, yield a set of differential equations with the time as the independent variable. These equations can be used to formulate a finite element solution for thermoelastic problems. This is done in the second part.     

Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics.Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.     

Hydrodynamic transition delay in rectangular channels under high heat flux

When upgrading a research nuclear reactor for a higher power output it can be expected that the cooling flow rate has to be increased. In the case of a reactor designed with a laminar cooling flow this upgrade may take the flow into the transition hydrodynamic regime.