A two-dimensional inverse heat conduction problem in estimating the fluid temperature in a pipeline

An inverse heat conduction problem (IHCP) was investigated in the two-dimensional section of a pipe elbow with thermal stratification to estimate the unknown transient fluid temperatures near the inner wall of the pipeline. An inverse algorithm based on the conjugate gradient method (CGM) was proposed to solve the IHCP using temperature measurements on the outer wall. In order to examine the accuracy of estimations, some comparisons have been made in this case. The temperatures obtained from the solution of the direct heat conduction problem (DHCP) using the finite element method (FEM) were pseudo-experimental input data on the outer wall for the IHCP. Comparisons of the estimated fluid temperatures with experimental fluid temperatures near the inner wall showed that the IHCP could accurately capture the actual temperature in form of the frequency of the temperature fluctuations. The analysis also showed that the IHCP needed at least 13 measurement points for the average absolute error to be dramatically reduced for the present IHCP with 37 nodes on each half of the pipe wall.     

Two-dimensional non-linear inverse heat conduction problem based on the singular value decomposition

In this paper an efficient sequential method is developed in order to estimate the unknown boundary condition on the surface of a body from transient temperature measurements inside the solid. This numerical approach for solving an inverse heat conduction problem (IHCP) takes into account two-dimensional problems, planar or axisymmetric cylindrical, composite materials with irregular boundaries and temperature-dependent thermal properties. The unknown surface condition is assumed to have abrupt changes at unknown times. The regularization procedure used for the solution of the IHCP is based on the singular value decomposition technique. An overall estimate of error is defined in order to find the optimal estimation in the 2D IHCP (linear and non-linear). The stability and accuracy of the scheme presented is evaluated by comparison with the Function Specification Method. This comparative study has been carried out using numerically simulated data, and the parameters considered include shape of input, noise level of measurement, size of time step and temperature-dependent thermal properties. A good agreement was found between both methods. Beside this, the slight differences on estimations and number of future temperatures are discussed in this paper.     

锅炉主蒸汽管道蠕变非线性有限元分析

对长期处于高温高压状态下运行的管道而言，高温蠕变是其寿命损耗的主要内在因素。本文以一余热锅炉主蒸汽管道为研究对象，建立了该管道蠕变有限元模型，研究和分析了该主汽管在高温蠕变作用下的应力分布规律，探讨了管道内输送流体的压力和温度与其蠕变量的关系。结果表明，当温度超过490℃时或压力达到10MPa时蠕变较为明显。     

600MW锅炉机组膜式水冷壁壁温的试验研究及理论分析

在６００ＭＷ锅炉机组水冷壁热力试验的基础上,为找到使壁温发生波动的根本原因,利用有限元分析的方法对低倍率锅炉膜式水冷壁管壁温度分布随传热工况的动态变化进行了分析。分析表明：导致水冷壁管壁温度波动最根本的原因是管内传热恶化;单面受热水冷壁在管内发生传热恶化时其向火这内外壁温差随时间的波动较小,而水冷壁周向温差则随向炎侧外壁的壁温波动而剧烈波动。     

反演高温腔体内壁面温度波动的辐射边界导热反问题

在工业生产中有很多情况需要获得高温腔体内壁温度波动,但在内壁面安装测温装置进行直接测量非常困难,一般通过测量外壁温度再进行反演计算间接获得。而已有反演计算方法未考虑高温壁面与周围环境之间的辐射传热,给反演计算结果带来一定误差,为此建立了考虑辐射边界条件的反演高温腔体内壁面温度波动的导热反问题数学模型,并构造了两组数值试验对数学模型的效果进行检验。计算结果表明,建立的数学模型能够很好的由高温腔体外壁面温度反演得到内壁面温度波动情况。     

Measurement of Transient Fluid Temperature in a Pipeline

The aim of this paper is to develop a method of determining the heat transfer coefficients on the inner surface of the pipeline and outer surface of the thermometer used to measure the temperature of a fluid flowing under high pressure. The method is based on the solutions to the inverse heat conduction problems for the thermometer and the pipeline wall. The heat transfer coefficients are determined based on the measurement of the temperature of a cylindrical metal thermometer and the temperature of the wall of a cylindrical pipeline. The temperature sensor is located in the pipeline wall close to the inner surface. The correlations for the Nusselt numbers used to determine heat transfer coefficients on the outer surface of the thermometer and the inner surface of the pipeline contain unknown coefficients which are found using the least squares method. The unknown coefficients are selected so that the sum of the squares of differences between the fluid temperature determined based on the measurement of the temperature of the pipeline wall and the fluid temperature obtained from measurements inside the thermometer, calculated for several dozen set time points, is as small as possible.     

Heat Transfer of Bingham Fluids in an Annular Duct with Viscous Dissipation

ABSTRACT

Analytical expressions for the velocity and temperature profiles in a fully-developed laminar Poiseuille flow through a concentric annular duct of a Bingham fluid with constant wall heat flux at the inner and outer wall, in the presence of viscous dissipation are deduced and presented. It is found that the proportion of the heat generated by viscous dissipation near the outer wall increases with an increase of the dimensionless flow parameter, and a decrease of the duct radius ratio. The Nusselt numbers are first calculated based on a single bulk temperature for the entire duct cross section. The possibility of performing calculations of the relevant parameters discussed in this work is available via the Supplementary Material as an Excel file. Also in this work a new approach is employed, where two different bulk temperatures are used, one for each side of the radial location in the temperature profile whose derivative is zero. With this new approach the Nusselt number behavior is free of either unphysical discontinuities or negative values. As a consequence, the Nusselt number values better reflect the actual heat transfer coefficient at the walls and are more comparable with the heat transfer inside ducts when the temperature profile is symmetric.     

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.     

Limiting Nusselt numbers for laminar forced convection in asymmetrically heated annuli with viscous dissipation

Analytical expressions for the Nusselt number at the inner and outer pipes, kept at unequal temperatures, for laminar forced convection through annuli including viscous dissipation have been obtained in the conduction limit. This article examines the dependence of the limiting Nusselt numbers on the Brinkman number and the degree of asymmetry in inner and outer pipe temperatures. Further, the limiting temperature profile obtained when viscous dissipation is included serves the purpose of providing the downstream boundary condition needed in solving the elliptic form of conservation of thermal energy equation that arises when axial conduction is included.     

Heat Transfer Analysis for a Concentric Tube Heat Exchanger Including the Wall Axial Conduction

The effect of wall axial conduction on the heat transfer in a concentric tube heat exchanger is examined for the inner flow laminar flow regime. The procedure used for the current analysis combines the analytical solution for the inner fluid with a numerical approximation for the wall conduction and has the capability of handling the temperature variation for the outer fluid. Both parallel and counterflow cases are evaluated for the analysis, and results are presented in terms of the axial variations of fluids and wall temperatures. Effects of the heat capacity rate ratio of the fluids on the temperature variations and on the mean heat flux are also pointed out. The effect of the exchanger length is included for the analysis. It is concluded that the total heat transfer between the fluids is greatly influenced by the wall axial conduction for the counterflow arrangement and is not ignorable when the heat capacity rate ratio of fluids are smaller than unity.     

不同散热条件下微燃烧的数值模拟

散热是影响微尺度燃烧器燃烧稳定性的重要因素之一.本实验通过在一个长40 mm、内径2 mm、外径4 mm的石英玻璃直圆管表面施加不同的外部吹风温度,控制其表面散热.研究4、107、756℃外部风温下,微燃烧器的工作性能,其中燃料混合气体流量为0.16、0.28、0.32 L/min.实验测得燃烧器壁面温度,结合数值模拟研究内部燃烧过程.计算结果显示,提高燃料流量或外部风温可以提升反应强度、抑制熄火.如在风温107℃时,燃料气体当量配比下,当流量由0.16 L/min上升到0.32 L/min时,峰值温度由1538 K上升到1620 K;在流量0.28 L/min时,燃料气体当量配比下,当外部风温由4℃上升到756℃时,峰值温度由1592 K上升到1731K.     

Estimation of exhaust gas temperature of the rocket nozzle using hybrid approach

In this paper the theoretical model is built for ZEpHyR (ZARM Experimental Hybrid Rocket) main engine which is being developed at ZARM institute, Bremen, Germany. The theoretical model is used to estimate the temperature of exhaust gas. The Conjugate Gradient Method (CGM) with Adjoint Problem for Function Estimation iterative technique is used to solve the Inverse Heat Conduction Problem (IHCP) to estimate the heat flux and internal wall temperature at the throat section of the nozzle. Bartz equation is used to calculate the convective heat transfer coefficient. The exhaust gas temperature is determined using the estimated heat flux, the wall temperature at internal surface of nozzle and the heat transfer coefficient. The accuracy of CGM iterative scheme to solve the IHCP is also investigated and its results are presented.     

Effects of different loads on structure stress of “L”-type large-diameter buried pipe network based on fluid-structure-heat coupling

Large-diameter buried pipeline is widely used because of its energy-saving advantage and high efficiency. In this paper, “L”-type heat pipe network was taken as the research object, which was studied using the flow–heat–solid coupling method. The ANSYS Workbench platform was used to simulate heat transfer and the flow of the medium in the pipe network. The pressure and temperature of the flow field and the temperature, equivalent stress of the solid structure under different conditions were calculated, and the force characteristics of pipe network and elbow under coupled and non-coupled loads were compared. Results show the maximum equivalent stress was located at inner wall surface of the short-arm anchor end. The equivalent stress of the inner wall was larger than that of the outer wall at the same position. The stress of the straight pipe of the pipe network was mainly affected by the temperature of the fluid, whereas the stress of elbow was mainly affected by the pressure. The stress distribution of the pipe network was influenced by the temperature and pressure loads coupled and the coupling effect was stronger with the higher pressure and temperature of the medium, but the coupling effect had its limit.     

An analytical study of heat transfer in a finite tissue region with two blood vessels and general Dirichlet boundary conditions

Vessel–vessel and vessel–tissue heat transfer rates are defined and explicitly quantified, for the first time, for a uniformly heated, finite, circular tissue region with two arbitrarily imbedded circular vessels and general Dirichlet boundary conditions. These heat transfer rates are obtained using an exact analytical solution for the tissue temperature field that is derived herein. Based on these heat transfer rates two different types of Poisson conduction shape factors (PCSFs) are defined. One is related to the vessel–vessel heat transfer rate (VVPCSF) and the other is related to the vessel–tissue heat transfer rates (VTPCSF). Two, conventional, alternative formulations for the VTPCSFs are studied; one is based on the difference between the average vessel wall and tissue boundary temperatures, and the other on the difference between the average vessel wall and the average tissue matrix temperatures. The effects of the angularly varying, non-uniform boundary conditions, the source term and the diameters and locations of the two vessels on these heat transfer rates and PCSFs are studied for the typical case of vessels cooling a tissue; i.e., when the average vessel wall boundary temperatures are lower than the average tissue boundary temperature. Results show that first, the effects of vessel wall temperature fluctuations on both the vessel–vessel and the vessel–tissue heat transfer rates are significant. Second, unlike the vessel wall temperature fluctuations, fluctuations at the outer tissue boundary affect only the vessel–tissue heat transfer rates. They do not affect the vessel–vessel heat transfer rates. Third, when strong fluctuations are present on the vessel walls and outer tissue boundary the shape factors are dependent on the shape of the fluctuations, and are thus very problem specific. Further, the analytical solution procedure used to derive the solution for the temperature field and the methodology developed to quantify the heat transfer rates are general and can be extended for the case of ‘N’ arbitrarily located vessels.     

Non-iterative estimation of heat transfer coefficients using artificial neural network models

The Inverse Heat Conduction Problem (IHCP) dealing with the estimation of the heat transfer coefficient for a solid /fluid assembly from the knowledge of inside temperature was accomplished using an artificial neural network (ANN). Two cases were considered: (a) a cube with constant thermophysical properties and (b) a semi-infinite plate with temperature dependent thermal conductivity resulting in linear and nonlinear problem, respectively. The Direct Heat Conduction Problems (DHCP) of transient heat conduction in a cube and in a semi-infinite plate with a convective boundary condition were solved. The dimensionless temperature-time history at a known location was then correlated with the corresponding dimensionless heat transfer coefficient/Biot number using appropriate ANN models. Two different models were developed for each case i.e. for a cube and a semi-infinite plate. In the first one, the ANN model was trained to predict Biot number from the slope of the dimensionless temperature ratio versus Fourier number. In the second, an ANN model was developed to predict the dimensionless heat transfer coefficient from non-dimensional temperature. In addition, the training data sets were transformed using a trigonometric function to improve the prediction performance of the ANN model. The developed models may offer significant advantages when dealing with repetitive estimation of heat transfer coefficient. The proposed approach was tested for transient experiments. A ‘parameter estimation’ approach was used to obtain Biot number from experimental data.     

Thermocouple Data in the Inverse Heat Conduction Problem

The presence of thermocouples inside a heat-conducting body will distort the temperature field in the body and may lead to significant bias in the temperature measurement. If temperature histories obtained from thermocouples are used in the inverse heat conduction problem (IHCP), errors are propagated into the IHCP results. The bias in the thermocouple measurements can be removed through use of appropriate detailed thermocouple models to account for the dynamics of the sensor measurement. The results of these models can be used to generate correction kernels to eliminate bias in the thermocouple reading, or can be applied as sensitivity coefficients in the IHCP directly. Three-dimensional and axisymmetric models are compared and contrasted and a simple sensitivity study is conducted to evaluate the significance of thermal property selection on the temperature correction and subsequent heat flux estimation. In this paper, a high-fidelity thermocouple model is used to account for thermocouple bias in an experiment to measure heat fluxes from solidifying aluminum to a sand mold. Correction kernels are obtained that are used to demonstrate the magnitude of the temperature measurement bias created by the thermocouples. The corrected temperatures are used in the IHCP to compute the surface heat flux. A comparison to IHCP results using uncorrected temperatures shows the impact of the bias correction on the computed heat fluxes.     

Effect of dynamic load on heat transfer characteristic of a two‐phase pipe boiling flow

An experimental investigation was performed to obtain the flow and heat transfer characteristics of a single‐phase water flow and a two‐phase pipe boiling water flow under dynamic load in the present work. By analyzing the fluid resistance, effective heat, flow pattern, and heat transfer coefficient of the experimental data, the effects of dynamic load on the flow and heat transfer characteristics of single‐phase water and two‐phase boiling water flow were investigated. The results show that the dynamic load significantly influences the flow characteristic and boiling heat transfer of the two‐phase pipe flow. It will enhance the fluid resistance and heat dissipation toward the ambient environment, and reduce the heat transferred to the two‐phase fluid. The impact mixing flow caused by the dynamic load breaks the uniform and varying principle of the wall temperatures. As a result of that, the greater the dynamic load, the lower the wall inner bottom temperature and the higher the wall inner top temperature in a certain extent. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20378     

Transient solution of temperature field of conjugate laminar forced convection heat transfer in functionally graded hollow cylinder

In this study, the numerical analysis of conjugate heat transfer of laminar flow in a functionally graded hollow cylinder (FGHC) made of metal/ceramic for a two‐dimensional fluid and wall conduction subject to Newton boundary condition is considered. The fluid and FGHC energy equations are coupled through the continuity of temperature and heat flux at the inner wall‐fluid interface while the outer surface is subject to convective heat transfer. The continuity, momentum, and energy equations of the fluid are discretized using the finite volume approach. The effects of fluid and functionally graded material parameters, such as volume fraction index, volume composition, time history, wall‐to‐fluid thermal diffusivity ratio, wall‐to‐fluid thermal conductivity ratio, Biot number, Peclet number, and Prandtl number are investigated on the temperature field in the FGHC. The result shows that on account of the inhomogeneity of the material property, the volume fraction index has a significant effect on the other parameters and the temperature variation along the thickness. The lower the volume fraction index, the higher the inner wall (metal side) temperature, and the temperature gradient along the thickness. However, except for the variation in the wall‐to‐fluid thermal conductivity ratio, the lower the volumetric fraction, the lower the outer wall (ceramic side) temperature distribution.     

中深层地热地埋管实际运行影响因素研究

为研究中深层地热地埋管运行的影响因素,分析西咸新区中深层地热地埋管供暖系统的长期运行结果,并结合关中地区地质数据,建立深度为2510 m的中深层地埋管换热器全尺寸模型,采用数值模拟法研究实际岩层分布下地埋管的运行、结构和材料因素对其取热能力的影响。结果表明,西咸新区某项目1号地埋管和2号地埋管两个地埋管,其平均取热功率均在310 kW以上,具有优良的取热能力。地埋管进水温度随季节变化明显,并引起用户侧负荷及热泵回水温度的波动。在结构方面,随内管径由63 mm增至125 mm,平均出口水温和换热功率分别降低1.9%和4.8%,但内管径过小将影响内管运行的安全性,综合安全和换热两方面因素,最佳内管径应选取ϕ110 × 10mm规格;随外管径由168.3 mm增至244.5 mm,平均出口水温和换热功率分别增加3.5%和9%,综合成本和换热两方面因素,最佳外管径应选取ϕ 177.8 × 19 mm规格;在运行方面,地埋管出口水温随着流量的增加而减小,换热功率随着流量增加而增加;出口水温随着进水温度的升高而上升,换热功率也随之减小。在材料方面,减小内管导热系数和增加固井材料导热系数均能增加地埋管出口水温和换热功率,考虑换热功率变化和成本因素,在工程中导热系数为0.42 W/（m∙K）的内管和导热系数为3 W/（m∙K）左右的固井材料。     

High temperature jacketed piping: Review of the suited thermal models and comparison with experimental results

A comparison is presented between a theoretical model and the experimental data of the thermal performance of a jacketed pipe which belongs to an experimental facility aimed at testing the critical components of the externally fired combined cycle (EFCC) technology.The pipe consists of two concentric tubes, the inner with hot air (nominal conditions above 1000 °C) and the outer with cold water, whose function is to make the inner tube wall temperature to be tolerated by a traditional steel (e.g. an AISI series stainless steel).A proper model is identified to calculate the fluid temperatures at the pipe exit, by considering a spatial discretization of the system, such that on each resulting section a differential equation is iteratively solved which gets as boundary conditions the output values arising from the preceding section.The model predictions are compared to the data coming from an experimental facility, resulting in a good agreement: about 87% of the air side (and 92% of the water side) experimental data is falling within a ±8% deviation band from the expected values. Such difference is widely acceptable, being probably due to the uncertainties connected with to the use of closed-form correlations for calculating the convective heat transfer coefficients.