Monitoring of transient 3D temperature distribution and thermal stress in pressure elements based on the wall temperature measurement

Abstract

Two methods for monitoring the thermal stresses in pressure components of thermal power plants are presented. In the first method, the transient temperature distribution in the pressure component is determined by measuring the transient wall temperature at several points located on the outer insulated surface of the component. The transient temperature distribution in the pressure component, including the temperature of the inner surface is determined from the solution of the inverse heat conduction problem (IHCP). In the first method, there is no need to know the temperature of the fluid and the heat transfer coefficient. In the second method, thermal stresses in a pressure component with a complicated shape are computed using the finite element method (FEM) based on experimentally estimated fluid temperature and known heat transfer coefficient. A new thermometer with good dynamic properties has been developed and applied in practice, providing a much more accurate measurement of the temperature of the flowing fluid in comparison with standard thermometers. The heat transfer coefficient on the inner surface of a pressure element can be determined from the empirical relationships available in the literature. A numerical-experimental method of determination of the transient heat transfer coefficient based on the solution of the 3D-inverse heat conduction problem has also been proposed. The heat transfer coefficient on the internal surface of a pressure element is determined based on an experimentally determined local transient temperature distribution on the external surface of the element or the basis of wall temperature measurement at six points located near the internal surface if fluid temperature changes are fast. Examples of determining thermal and pressure stresses in the thick-walled horizontal superheater header and the horizontal header of the steam cooler in a power boiler with the use of real measurement data are presented.     

Heat Transfer Analysis of Functionally Graded Hollow Cylinders Subjected to an Axisymmetric Moving Boundary Heat Flux

The transient heat transfer analysis of functionally graded (FG) hollow cylinders subjected to a distributed heat flux with a moving front boundary on its inner surface is presented. The heat flux is assumed to be axisymmetric, and its front boundary moves along the axis of the cylinder. A method composed of the finite element and differential quadrature methods is employed to discretize the governing equations in the spatial domain. After demonstrating the convergence and accuracy of the method, the effects of different parameters on the temperature distribution and time history of the temperature at different points of FG cylinder are investigated.     

Two dimensional steady-state inverse heat conduction problems

In this work we estimate the surface temperature in two dimensional steady-state in a rectangular region by two different methods, the singular value decomposition (SVD) with boundary element method (BEM) and the least-squares approach with integral transform method (ITM). The BEM method is efficient for solving inverse heat conduction problems (IHCP) because only the boundary of the region needs to be discretized. Furthermore, both temperature and heat flux at the unknown boundary are estimated at the same time. The least-squares technique involves solving the equations constructed from the measured temperature and the exact solution. The measured data are simulated by adding random errors to the exact solution of the direct problem. The effects of random errors on the accuracy of the predictions are examined. The sensitivity coefficients are also presented to illustrate the effect of sensor location on the estimated surface conditions. Numerical experiments are given to demonstrate the accuracy of the present approaches.     

Investigation of the temperature field induced in the process of friction of a composite pad and a homogeneous disc

The analytical model for the determination of transient temperature field and heat fluxes in friction elements of brakes (pad/disc) is presented. It is assumed that one friction element is composed of a multi-layer composite strip, and the second element is a homogeneous semi-space. The solution to a non-stationary thermal problem of friction is obtained for a tribosystem with heat generation on a surface of contact and convective heat exchange with an environment on outer surface of a strip. The influences of composite parameters, for example, reinforcement fraction in the cross-section of periodic cells and the ratio of the conductivities of matrix and fibers, on the maximal temperature are studied.     

Heat transfer in a conical cylinder with porous medium

In this paper, numerical study of heat transfer in a conical annular cylinder fixed with saturated porous medium is presented. The heat transfer is assumed to take place by natural convection and radiation. The inner surface of conical cylinder is maintained at uniform wall temperature. The governing partial differential equations are non-dimensionalised using suitable non-dimensional parameters and then solved by using finite element method. The porous medium is divided using triangular elements with uneven element size. A computer software is used to solve the coupled momentum and energy equations in an iterative manner. The results are discussed for various values of geometric and physical parameters of porous medium with emphasis on cone angle of the cylinder. It is seen that the cone angle plays a vital role in heat transfer from the hot surface to porous medium.     

Heat transfer coefficient of wheel rim of large capacity steam turbines

A way of calculating the overall equivalent heat transfer coefficient of wheel rims of large capacity steam turbines is presented. The method and formula to calculate the mean forced convection heat-transfer coefficient of the surface of the blade and for the bottom wall of the blade passage, are introduced. The heat transmission from the blade to the rim was simplified by analogy to heat transmission in the fins. A fin heat transfer model was then used to calculate the equivalent heat transfer coefficient of the blade passage. The overall equivalent heat transfer coefficient of the wheel rim was then calculated using a cylindrical surface model. A practical calculation example was presented. The proposed method helps determine the heat transfer boundary conditions in finite element analyses of temperature and thermal stress fields of steam turbine rotors.     

Meshless element free Galerkin method for unsteady nonlinear heat transfer problems

In this paper, meshless element free Galerkin (EFG) method has been extended to obtain the numerical solution of nonlinear, unsteady heat transfer problems with temperature dependent material properties. The thermal conductivity, specific heat and density of the material are assumed to vary linearly with the temperature. Quasi-linearization scheme has been used to obtain the nonlinear solution whereas backward difference method is used for the time integration. The essential boundary conditions have been enforced by Lagrange multiplier technique. The meshless formulation has been presented for a nonlinear 3-D heat transfer problem. In 1-D, the results obtained by EFG method are compared with those obtained by finite element and analytical methods whereas in 2-D and 3-D, the results are compared with those obtained by finite element method.     

Techniques for detailed heat transfer measurements in cold supersonic blowdown tunnels using thermochromic liquid crystals

The paper presents methods for measurement of convective heat transfer distributions in a “cold flow” supersonic blowdown wind tunnel. The techniques involve use of the difference between model surface temperature and adiabatic wall temperature as the driving temperature difference for heat transfer and no active heating or cooling of the test gas or model is required. Thermochromic liquid crystals are used for surface temperature indication and results presented from experiments in a Mach 3 flow indicate that measurements of the surface heat transfer distribution under swept shock wave boundary layer interactions can be made.     

Melting of a phase change material in concentric horizontal annuli of arbitrary cross-section

Results are presented of a finite element computational study of the free convection-dominated melting of a pure phase change material contained in concentric horizontal annuli of the following configurations: (a) square external tube with a circular tube inside — annulus type A and (b) circular external tube with a square tube inside — annulus type B. Effects of the Rayleigh number as well as heating of the inside, outside or both walls at a temperature above the melting point of the material were studied. Flow and temperature patterns within the melt, local heat flux distributions at the heating surface and the cumulative energy charged as a function of time are presented and discussed.     

Study of mixed convection in an annular vertical cylinder filled with saturated porous medium,using thermal non-equilibrium model

The present study deals with numerical investigation of effects of different parameters on enhancement or retardation of the heat transfer rate in an annular vertical cylinder filled with saturated porous medium. The heat transfer is assumed to take place by mixed convection mode. The thermal non-equilibrium approach is considered. The inner surface of the annular cylinder is maintained at constant wall temperature whereas the outer surface remains at ambient temperature. The governing partial differential equations are solved using finite element method. The results are discussed for the effects of Peclet number, interphase heat transfer co-efficient and thermal conductivity ratio.     

Solution of the inverse heat conduction problem described by the Poisson equation for a cooled gas-turbine blade

The presented paper describes a method of solving the inverse problems of heat conduction, consisting in solving the Poisson equation for a simply connected region instead of the Laplace equation for a multiply connected one, like a gas-turbine blade provided with cooling channels. The considered method consists in determining unknown values of the source (heat sink) power in the cooling channels for a given external heat transfer situation to achieve as close as possible an isothermal outer surface. Afterwards the temperature and heat flux distributions at the cooling channel walls are determined. Since the unknown source power is sought, the problem is an inverse one. Taking into account the sought values the method is reckoned among the class of the fictitious source methods and presents an optimization scheme. Using an exemplary gas turbine blade cooling configuration, the results of the calculation obtained with this method have been compared to the results achieved with an inverse method using the boundary element method for a multiple connected region.The results obtained with both methods within the optimization scheme approximated each other. Nevertheless, the results for the inverse method shown in the present paper gave nearly no oscillations, which is important in case of the blades with other geometric features of the cooling channels.     

大功率汽轮机叶轮轮缘传热系数的研究

提出了大功率汽轮机叶轮轮缘总传热系数的计算方法.介绍了汽轮机动叶片叶身平均对流换热表面传热系数和叶片流道下壁面对流换热表面传热系数的计算方法和计算公式.把汽轮机叶片对叶轮的传热简化为肋片传热,使用肋片传热模型计算汽轮机叶片流道的等效传热系数,采用圆筒壁模型计算汽轮机叶轮轮缘的总传热系数,并给出了应用实例.在汽轮机转子的温度场与热应力场有限元分析中,该计算方法为确定叶轮轮缘的传热边界条件提供了依据.     

Conduction based calibration of handmade platinum thin film heat transfer gauges for transient measurements

Heat transfer measurement using thin film gauges (TFG) is the most prevalently used technique for determination of surface heat flux. They are best suited for short duration transient surface temperature measurements and typically used in the applications where convection is a dominant mode of heat transfer such as gas turbine engines, high speed flights etc. However, in few interdisciplinary research areas, there are practical issues and difficulties in exposing the gauges for convection based measurements. These present investigations are aimed at exploring the possibility of using thin film gauges for short duration conduction based transient measurements with pure conduction mode of heat transfer. A simple calibration set-up has been used to supply known heat flux of different magnitudes to the thin film gauges that are fabricated in-house with platinum as sensing element and pyrex as an insulating substrate. Experimentally recorded temperature signals from the gauges are compared with simulated temperature histories obtained through finite element analysis. Convoluted integral of one-dimensional heat conduction equation is used to predict the surface heat flux and compared with input heat loads. The presently developed calibration setup is seen to be very useful for conduction based measurements of thin film gauges.     

Averaging approach for microchannel heat sinks subject to the uniform wall temperature condition

The present paper is devoted to modeling methods for thermal analysis of microchannel heat sinks. The averaging approach presented in earlier works for the case of constant surface heat flux is extended to the problems subject to the uniform wall temperature condition. The solutions for velocity and temperature distributions are obtained by solving one-dimensional averaged governing equations without resorting to a two-dimensional direct numerical simulation. General solutions for both high-aspect-ratio and low-aspect-ratio microchannel heat sinks are presented. Asymptotic solutions in high-aspect-ratio and low-aspect-ratio limits are also given in explicit form. The solutions presented in the paper are validated by comparing them with the results of direct numerical simulation. The friction factors, Nusselt numbers and thermal resistances for microchannel heat sinks with a uniform base temperature are obtained from the presented solutions. The effects of the aspect ratio and the porosity on the friction factor and the Nusselt number are presented. Finally, characteristics of the thermal resistance of the microchannel heat sink are discussed.     

Modeling of Heat Transfer Across the Interface in Two-Fluid Flows

A model is presented in this article to deal with heat transfer across the interface separating two immiscible fluids. It is suitable to be incorporated into interface-tracking methods, such as volume-of-fluid (VOF) methods, because a sharp interface is available in these approaches. The temperature at the interface and the heat flux through it are calculated in such a way that the continuity of the two properties at the contact surface is satisfied explicitly. With use of these values, the temperature either at the centroid or on a face of the interface cell can be estimated, which serves as Dirichlet boundary condition for the energy equation. The temperature field is then calculated by solving the energy equations for the two fluids simultaneously in an implicit way. This method is first assessed via testing on two heat conduction problems in which two solids are in contact. Good agreement between numerical solutions and theory is obtained. To demonstrate its capability, it is applied to two kinds of heat transfer problems, one being the collapse of a heated water column in a cavity, and the other the falling of a molten tin droplet in an oil tank. The effect of fluid flow on the heat transfer is clearly illustrated.     

Investigation of the heat balance of bipolar NiMH-batteries

Heat generation plays an important role for energy storage systems like batteries in electric and hybrid vehicles. In order to investigate the thermal and electrical behaviour the batteries were exposed to cycling programs including various methods of battery cooling by flowing air. Two different experimental methods were presented to study the establishing of the heat balance. The second part of the paper describes the simulation of the temperature distribution by using finite element methods (FEM). The electric and thermal battery model was compared with results obtained from temperature measurements at four selected points during battery cycling.     

Numerical analysis of fluid flow due to mixed convection in a lid-driven cavity having a heated circular hollow cylinder

Mixed convection heat transfer in a lid-driven cavity along with a heated circular hollow cylinder positioned at the center of the cavity has been analyzed numerically. The present study simulates a realistic system such as air-cooled electronic equipment with a heat component or an oven with heater. A Galerkin weighted residual finite element method with a Newton–Raphson iterative algorithm is adopted to solve the governing equations. The computation is carried out for wide ranges of the Richardson numbers, cylinder diameter and solid fluid thermal conductivity ratio. Results are presented in the form of streamlines, isothermal lines, average Nusselt number at the heated surface and fluid temperature in the cavity for the mentioned parameters. It is found that the flow field and temperature distribution strongly depend on the cylinder diameter and also the solid–fluid thermal conductivity ratio at the three convective regimes.     

Numerical Investigation of Saturated Flow Boiling in Microchannels by the Lattice Boltzmann Method

Bubble formation in saturated flow boiling in 2D microchannels, generated from a microheater under constant wall heat flux or constant wall temperature conditions, is studied numerically based on a newly developed lattice Boltzmann model for liquid-vapor phase change. Simulations are carried out to study effects of inlet velocity, contact angle, and heater size on saturated flow boiling of water under constant wall heat flux conditions. Important information, such as effects of static contact angle on nucleation time and nucleation temperature, which was unable to be obtained by other numerical simulation methods, is obtained. Furthermore, effects of inlet velocity, contact angle, and superheat on nucleate boiling heat transfer in steady flow boiling of water under constant wall temperature conditions are also presented. It is found that the nucleate boiling heat transfer at the microheater is higher if the heater surface is more hydrophilic, because the superheated vapor at the hydrophilic wall has a thinner thermal boundary layer and a larger thermal conductivity.     

Frictional heating during braking in a three-element tribosystem

A three-element model of braking process is proposed. In order to determine the temperature fields in each element of the model, the analytical solution of a boundary-value problem of heat conduction for tribosystem, consisting of the semi-space, sliding with the time-dependent velocity (braking at uniform retardation) on a surface of the strip deposited on a semi-infinite foundation, is obtained. The results of the numerical analysis for different materials applied in a braking system, cast iron–FMK-11 metal ceramics–steel, are presented.     

An inverse estimation of surface temperature using the maximum entropy method

The maximum entropy method (MEM) is applied to estimation of surface temperature from temperature readings. The inverse heat conduction problem is reformulated for MEM and a three-phase solution method utilizing the successive quadratic programming (SQP) is addressed. Computational results by the proposed MEM are presented and compared with results by the conventional methods.