Online determination of transient thermal stresses in critical steam turbine components using a two-step algorithm

The article presents a novel algorithm for robust calculation of thermal stresses in steam turbine components during transient operating conditions. Stress calculations are performed in 2 steps: in the first step an unsteady radial temperature distribution in the component model is computed, and based on this thermal stresses at critical locations are determined in the second step. The radial temperature distribution is obtained by solving the Fourier-Kirchhoff equation for a cylinder or sphere by means of a finite difference method. The thermal stresses are computed using the Duhamel integral and Green functions evaluated with a constant heat transfer coe?cient and used with an equivalent steam temperature obtained from the surface heat flux.     

Monitoring of transient temperature and thermal stresses in pressure components of steam boilers

Two methods of solving the transient inverse heat conduction problens in complex shaped elements are presented in this paper. The time-space temperature distribution in whole element cross-section is reconstructed using the measured temperature histories at several points placed inside the element or on its easily accessible outer surface. Thermal stresses are then evaluated involving Finite Element Analysis. In both methods the heat transfer coefficient at the element inner surface is the unknown value. Four examples are presented, two for one method showing the high accuracy of the presented methods and possibility of their practical application.     

基于传热系数反求法的船用柴油机组合活塞热分析

建立了柴油机组合活塞的2D有限元模型,并利用传热系数反求法对该模型进行热分析。在仿真分析中,将活塞头部外表面传热系数定义为设计参数,实测温度与仿真温度的差值定义为目标函数。通过仿真计算得到了活塞头部外表面传热系数的分布,并利用反求法得到的传热系数对有限元模型进行热分析,仿真结果与实测温度吻合;传热系数反求法收敛迅速,可以有效用于活塞及其他内燃机零部件的温度分布和热负荷分析。     

Transient stress analysis of sandwich plate and shell panels with functionally graded material core under thermal shock

A finite element formulation for stress analysis of functionally graded material (FGM) sandwich plates and shell panels under thermal shock is presented in this work. A higher-order layerwise theory in conjunction with Sanders’ approximation for shells is used to develop the finite element formulation for transient stress analysis of FGM sandwich panels. The top and the bottom surfaces of FGM sandwich panels are made of pure ceramic and metal, respectively, and core of the sandwich is assumed to be made of FGM. The temperature profile in the thickness direction of the panels is considered to be varying as per the Fourier’s law of heat conduction equation for unsteady state. The heat conduction equations are solved using the central difference method in conjunction with the Crank–Nicolson approach. Transient thermal displacements of the sandwich panels are obtained using Newmark average acceleration method and the transient thermal stresses are obtained using stress–strain relations, subsequently. Results obtained from the present layerwise finite element formulations are first validated with available solutions in literature. Parametric studies are taken up to study the effects of volume fraction index, temperature dependency of material properties, core thickness, panel configuration, geometric and thermal boundary conditions on transient thermal stresses of FGM sandwich plates and shells.     

汽轮机转子温度场和热应力的动态分析

将空心的汽轮机转子简化成长圆筒壁模型，在一定的假设条件下得到了描述其导热特性的微分方程。利用复频域分析方法求解了长圆筒壁的一维动态导热特性，并根据热弹性理论得到了转子温度场和热应力的传递函数。进而对内表面绝热、外表面为阶跃温度输入和内、外表面都为阶跃温度输入的两种情况下转子温度场和热应力的变化进行了计算和分析。计算结果表明，采用对转子内、外表面同时加热或冷却的方法，能够在不增加热应力的条件下，加速转子达到温度平衡状态，有利于缩短汽轮机组的开停机时间，并提高跟踪机组负荷变化的灵活性。     

A simplified approach for the thermoelastic large deflection in the thin clamped annular sector plate

The present article is concerned with analysis of large deflection of a heated thin annular sector plate with clamped edges under transient temperature distribution using Berger’s approximate methods. The prescribed surface temperature is at the top face of the plate whereas the bottom face is kept at zero temperature. In this study, the Laplace transform as well as the classical method have been used for the solution of heat conduction equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained using resultant bending moment and resultant forces per unit length. The calculations are obtained for the aluminium plate in the form of an infinite series involving Bessel functions, and the numerical results for temperature, deflection, resultant bending moments, and thermal stresses have been illustrated by graphs.     

Transient thermal stress analysis of a functionally graded thick hollow cylinder with temperature-dependent material properties

This article deals with the study of temperature distribution and thermal stresses of a functionally graded thick hollow cylinder with temperature dependent material properties. All the material properties except Poisson’s ratio are assumed to be dependent on temperature and spatial coordinate z. The two-dimensional transient heat conduction equation is solved under convective heat transfer condition with varying point heat source. The influence of inhomogeneity parameters on the thermal and mechanical behavior is examined. Numerical computations are performed for ceramic-metal-based functionally graded material, in which alumina is selected as ceramic and nickel as metal.     

某船用锅炉联箱在复杂换热条件下的瞬态温度场有限元分析

本文利用瞬态温度场的基本理论和非线性有限元方法,对某船用主锅炉联箱在复杂换热条件下的对流换热系数成功地进行了反算,并以此对锅炉联箱进行了三维等值带温度场的非线性有限元分析,给出了其温度分布三维彩图。     

Thermoelastic study of a functionally graded annular fin with variable thermal parameters using semiexact solution

Abstract

In this paper, the thermoelastic behavior of a functionally graded material (FGM) annular fin is investigated. The material properties of the annular fin are assumed to vary radially. The heat transfer coefficient and internal heat generation are considered to be functions of temperature. A closed form solution of nonlinear heat transfer equation for the FGM fin is obtained using the homotopy perturbation method (HPM) which leads to nonuniform temperature distributions within the fin. The temperature field is then coupled with the classical theory of elasticity and the associated thermal stresses are derived analytically. For the correctness of the present closed form solution for the stress field, the results are compared with the ANSYS-based finite element method (FEM) solution. The present HPM-based closed form solution of the stress field exhibits a good agreement with the FEM results. The effect of various thermal parameters such as the thermogeometric parameter, conduction-radiation parameter, internal heat generation parameter, coefficient of variation of thermal conductivity, and the coefficient of thermal expansion on the thermal stresses are discussed. The results are presented in both nondimensional and dimensional form. The dimensional stress analysis discloses the suitability of FGM as the fin material in practical applications.     

Mathematical modelling of the transient response of pipeline

Steam pipelines applied in power units operate at high pressures and temperatures. In addition, to stress from the pipeline pressure also arise high thermal stresses in transient states such as start-up, shutdown or a load change of the power unit. Time-varying stresses are often the cause of the occurrence of fatigue cracks since the plastic deformations appear at the stress concentration regions. To determine the transient temperature of the steam along the steam flow path and axisymmetric temperature distribution in the pipeline wall, a numerical model of pipeline heating was proposed. To determine the transient temperature of the steam and pipeline wall the finite volume method (FVM) was used Writing the energy conservation equations for control areas around all the nodes gives a system of ordinary differential equations with respect to time. The system of ordinary differential equations of the first order was solved by the Runge-Kutta method of the fourth order to give the time-temperature changes at the nodes lying in the area of the wall and steam. The steam pressure distribution along pipeline was determined from the solution of the momentum conservation equation. Based on the calculated temperature distribution, thermal stresses were determined. The friction factor was calculated using the correlations of Churchill and Haaland, which were proposed for pipes with a rough inner surface. To assess the accuracy of the proposed model, numerical calculations were also performed for the thin-walled pipe, and the results were compared to the exact analytical solution. Comparison of the results shows that the accuracy of the proposed model of pipeline heating is very satisfactory. The paper presents examples of the determination of the transient temperature of the steam and the wall.     

Calculations of Flow Boiling Heat Transfer in a Minichannel Based on Liquid Crystal and Infrared Thermography Data

ABSTRACT

This paper analyzes results concerning flow boiling heat transfer in two parallel, asymmetrically heated vertical minichannels. The heating element for FC-72 Fluorinert flowing in the minichannels was a thin foil with an enhanced surface on the side in contact with the fluid. In one minichannel, changes in the temperature on the smooth side of the foil were monitored using liquid crystal thermography. Changes in the temperature on the outer surface of the glass in one minichannel and on the foil in the other minichannel were observed using infrared thermography. The heat transfer coefficient at the foil–fluid interface was calculated on the basis of one- and two-dimensional heat transfer models. In the two-dimensional method, the distribution of temperature on the enhanced side of the foil was determined by solving the inverse heat conduction problem. The governing equations were solved using the finite-element method combined with the Trefftz functions used as shape functions. The temperature measurement points were located at the boundary nodes of elements. Local values of the heat transfer coefficient calculated with the one- and two-dimensional models were analyzed in the function of the distance from the minichannel inlet. The values obtained with the two models were similar.     

Thermo-mechanical simulation for nozzle header of once-through steam generator by experiment and finite element method

The thermo-mechanical behaviour of the nozzle header of a steam generator developed for an integral reactor was investigated using experimental and finite element methods. The nozzle feedwater header suffers from severe thermal transient loadings during the operation of the nuclear reactor. The nozzle header is exposed to the low temperature inlet feedwater and the high temperature outlet superheated steam and the other side of the nozzle header contacts with the high temperature primary coolant. The temperature gradients result in high thermal stresses in the nozzle header. The thermal transient loading has been simulated in a test loop. The input and thermo-hydraulic parameters of the primary and the secondary system were. Strain gauges and thermocouples attached to the highly stressed region monitored the thermo-mechanical behaviour of the nozzle header. In parallel with the experimental study, the transient behaviour of the nozzle header was simulated by utilizing a commercial finite element code. The fluid temperature and pressure obtained from the test loop were used as inputs to the finite element analysis. As a result of this investigation, the thermo-mechanical load carrying capacity of the developed steam generator nozzle header was proved numerically and experimentally.     

Analytical solution for transient temperature and thermal stresses within convective multilayer disks with time-dependent internal heat generation,Part I: Methodology

This work deals with the exact solution for asymmetric transient problem of heat conduction and accordingly thermal stresses within multilayer hollow or solid disks which lose heat by convection to the surrounding ambient. The combination of the separation of variables method (SVM) and Duhamel's theorem is applied to the heat conduction problem which provides a versatile technique. The temperature distribution is obtained by the SVM which concerns the heat conduction problem with time-independent internal heat generation. Applying Duhamel's theorem on the previous solution, temperature distribution with time-dependent internal heat generation can be achieved. Accordingly, assuming plane stress condition, radial and tangential stresses are obtained which are incorporated into the equivalent tensile stress formulation to calculate von Mises stress. The comprehensive methodology described here can be useful addition for many new emerging fields in which both transient and steady-state temperature distributions and thermal stresses for composite disks are important.     

Numerical analysis of heat transfer and flow field around cross-flow heat exchanger tube with fouling

Fouling is one of the main problems of heat transfer which can be described as the accumulation on the heat exchanger tubes, i.e.; ash deposits on the heat exchanger unit of the boiler. A decrease in heat transfer rate by this deposition causes loss in system efficiency and leads to increasing in operating and maintenance costs. This problem concerns with the coupling among conduction heat transfer mode between solid of different types, conjugate heat transfer at the interface of solid and fluid, and the conduction/convection heat transfer mode in the fluid which can not be solved analytically. In this paper, fouling effect on heat transfer around a cylinder in cross flow has been studied numerically by using conjugate heat transfer approach. Unlike other numerical techniques in existing literatures, an unstructured control volume finite element method (CVFEM) has been developed in this present work. The study deals with laminar flow where the Reynolds number is limited in the range that the flow field over the cylinder is laminar and steady. We concern the fouling shape as an eccentric annulus with constant thermal properties. The local heat transfer coefficient, temperature distribution and mean heat transfer coefficient along the fouling surface are given for concentric and eccentric cases. From the results, we have found that the heat transfer rate of cross-flow heat exchanger depends on the eccentricity and thermal conductivity ratio between the fouling material and fluid. The effect of eccentric is dominant in the region near the front stagnation point due to high temperature and velocity gradients. The mean Nusselt number varies in asymptotic fashion with the thermal conductivity ratio. Fluid Prandtl number has a prominent effect on the distribution of local Nusselt number and the temperature along the fouling surface.     

Simple method for monitoring transient thermal stresses in pipelines

This paper presents a seminumerical method for solving inverse heat conduction problems (IHCP) encountered in the monitoring of thermal stresses in pressurized thick-walled elements of steam boilers. The objective is to give a simple and quick method of determining transient temperature histories in thick-walled components based on temperature measurements on the outer thermally insulated surface. The method is suitable for solving one-dimensional problems. However, it can be extended to multidimensional temperature fields. The IHCP will be solved using the control volume approach. The accuracy of the method is demonstrated by comparing computational and experimental results. Gram orthogonal polynomials are used to smooth the measured time-dependent temperature and for evaluating time derivatives of noisy data with high accuracy. Due to the simplicity of the final formulations, the developed method is very useful for estimating the thermal stresses and controlling the fatigue damage of boiler components.     

3D Study of Thermal Stresses in Lead-Free Surface Mount Devices

The paper presents the study of non-uniform temperature distributions in a flip chip electronic assembly, and the use of these temperature distributions to analyse the thermal stresses in lead-free solder joints in surface mount devices. The thermal stresses in the solder joints are mainly due to the mismatch in the coefficients of thermal expansions between the component and substrate materials, and temperature gradient in the electronic assembly. The thermo-elasto-visco-plastic finite element analysis is carried out to investigate the extent of thermal stresses induced in solder joints between a surface mount component and a FR4 circuit board (substrate) under conditions of thermal cycling with the chip resistor operating at its full power condition. Three different cases of spatial temperature distributions are considered including one with an experimentally obtained non-uniform temperature distribution. A comparative study of thermal stresses is performed using a near-eutectic SnAgCu solder material for three different thermal cases.     

Determination of thermal contact resistance from transient temperature measurements

The temperature distribution in combustion engine components is highly influenced by thermal contact resistance. For the prediction and optimisation of the thermal behaviour of modern combustion engines knowledge about the contact heat transfer is crucial.Available correlations to predict the contact resistance are simplifications of the real geometric conditions and only tested for moderate pressures up to 7 MPa. Typical combustion engine applications include contact pressures up to 250 MPa.The experimental approach presented here to derive the thermal contact resistance in terms of contact heat transfer coefficients for high temperature and high pressure conditions is based on transient infrared temperature measurements. Two bodies initially at two different temperatures are brought in contact and the surface temperature histories are recorded with a high-speed infrared camera. The contact heat flux is calculated by solving the related inverse problem. From the contact heat flux and from the measured temperature jump at the interface the contact heat transfer coefficient is calculated.The inverse method used for the calculation of the heat flux is based on the analytical solution for a semi-infinite body and a step response to a Neumann boundary condition. This method provides an algorithm that is used in a sequential manner. The use of “future” temperature data greatly improve the stability of the governing equations and reduce the sensitivity to measurement errors.     

Sensitivity analysis and numerical experiments on transient test of compact heat exchanger surfaces

A single-blow transient testing technique considering the effect of longitudinal heat conduction is suggested for determining the average convection heat transfer coefficient of compact heat exchanger surface. By matching the measured outlet fluid temperature variation with similar theoretical curves, the dimensionless longitudinal conduction parameter ?_l, the time constant of the inlet fluid temperature ?⁺, and the number of heat transfer units N_tu can be determined simultaneously using the Levenberg-Marquardt nonlinear parameter estimation method. Both sensitivity analysis and numerical experiments with simulated measurements containing random errors show that the method in the present investigation provides satisfactory accuracy of the estimated parameter N_tu, which characterizes the heat transfer performance of compact heat exchanger surfaces.     

Analytical solution for transient temperature and thermal stresses within convective multilayer disks with time-dependent internal heat generation,Part II: Applications

This work investigates the analytical solution for transient temperature and thermal stresses within three circular geometries. First, the transient temperature and thermal stresses within a composite disk are addressed. Then, two examples regarding transient temperature and thermal stresses throughout circular heaters are analyzed. Pulsed and sinusoidal internal heat generations are incorporated into the second and third examples, respectively. For the composite hollow-disk example, merely the separation of variables method (SVM) is used to overcome the energy partial differential equation. For the other two examples, the combination of the SVM and Duhamel's theorem are adopted to solve the partial differential equations. Accordingly, assuming plane stress formulation, the transient thermal stresses within structures are obtained.