Inverse estimation of spatially and temporally varying heating boundary conditions of a two-dimensional object

In many dynamic heat transfer situations, the temperature at the heated boundary is not directly measurable and can be obtained by solving an inverse heat conduction problem (IHCP) based on measured temperature or/and heat flux at the accessible boundary. In this study, IHCP in a two-dimensional rectangular object is solved by using the conjugate gradient method (CGM) with temperature and heat flux measured at the boundary opposite to the heated boundary. The inverse problem is formulated in such a way that the heat flux at heated boundary is chosen as the unknown function to be recovered, and the temperature at the heated boundary is computed as a byproduct of the IHCP solution. The measurement data, i.e., the temperature and heat flux at the opposite boundary, are obtained by numerically solving a direct problem where the heated boundary of the object is subjected to spatially and temporally varying heat flux. The robustness of the formulated IHCP algorithm is tested for different profiles of heat fluxes along with different random errors of the measured heat flux at the opposite boundary. The effects of the uncertainties of the thermophysical properties and back-surface temperature measurement on inverse solutions are also examined.     

Transient heat flux measurement analysis from coaxial thermocouples at convective based step heat load

The measurement of surface heating rate is an imperative parameter in the force convection ground-based facility for short duration investigation due to the heat transfer rate is changing rapidly. The coaxial thermocouples are suitable to measure the transient heat flux in fast varying heat transfer application because of having fast response time in the range microseconds or less. In this addition, the K-type, E-type, and J-type of coaxial thermocouples are contrived as well as the thermal coefficient resistance (TCR) and sensitivity (S) has been calculated from oil-bath based technique. These handmade coaxial thermocouples are exposed in a forced convection flow facility having three different input step heat loads as well as their transient heat fluxes are estimated using one-dimensional heat conduction modeling for the semi-infinite body. The numerical simulation has also been carried out with the analogous experimental parameters using ANSYS-FLUENT v.15.0 and compared with the outcome of the experimental approach and it is found that the average value of the transient temperatures having 0.3% error and surface heat flux recovered from this temperature is 10%. This study reveals the measuring ability of these handmade coaxial thermocouples at low temperature and low velocity on short duration transient measurements.     

A SERIAL SOLUTION FOR THE 2-D INVERSE HEAT CONDUCTION PROBLEM FOR ESTIMATING MULTIPLE HEAT FLUX COMPONENTS

A serial algorithm for the inverse heat conduction problem (IHCP) has been developed to estimate the individual flux components, one by one, at the unknown boundary, based on the function specification method. The sensitivity coefficient defined in this algorithm brings out the influence of the heat flux components independent of each other. The objective function minimizes the difference in the measured temperature and the contribution of the individual flux component to the thermal field at the sensor location. The serial algorithm developed here could be used with data from both overspecified and underspecified sensors with respect to the number of flux components. The method was tested for delineating independent heat fluxes at the boundary of a two-dimensional solid for both space- and time-varying heat fluxes. Simulated thermal histories obtained from direct solution were used as inputs for the inverse problem for characterizing the new algorithm.

Three types of analyses were done on the results of the IHCP, focused on (1) the convergence of error in estimated temperatures at the different sensor locations, (2) overall error in estimated temperatures for the whole domain, and (3) the total heat energy transferred across the boundary. It is shown that the optimum configuration of independent unknown fluxes is given by the one with minimum energy estimates across the boundary, for both cases.     

热电偶测量误差综述

介绍了使用热电偶进行温度测量过程中 ,影响热电偶准确度的因素及清除方法 ,以及热电偶参考端温度变化所引起误差及修正方法 ,最后给出了提高温度测量准确度的方法     

Role of a single shield in thermocouple measurements in hot air flow

To investigate the role of a single shield on steady temperature measurement using thermocouples in hot air flow,a methodology for solving convection,conduction,and radiation in one single model is provided.In order to compare with the experimental results,a cylindrical computational domain is established,which is the same size with the hot calibration wind-tunnel.In the computational domain,two kinds of thermocouples,the bare-bead and the single-shielded thermocouples,are simulated respectively.Surface temperature distribution and the temperature measurement bias of the two typical thermocouplcs are compared.The simulation results indicate that:1)The existence of the shield reduces bead siurface heat flux and changes the direction of wires inner heat conduction in a colder surrounding;2) The existence of the shield redes the temperature measurement bias both by improving bead surface temperature and by reducing surface temperature gradient;3) The shield effectively reduces the effect of the ambient temperature on the temperature measurement bias;4) The shield effectively reduces the influence of airflow velocity on the temperature measurement bias.     

Energy Management in Car Underhood Compartment—Temperature and Heat Flux Analysis of Car Inclination Effects

It has been shown by the authors that car inclination influences the temperatures of different underhood components. Here these effects are analyzed by heat-flux measurements. The results of underhood temperature and heat-flux measurements carried out on a passenger vehicle in wind-tunnel S4 of Saint-Cyr l’Ecole are presented. The underhood compartment of the vehicle is instrumented with 40 surface and air thermocouples and 20 flux meters of normal gradient. Experiments are performed with a specific technique for separate measurement of convective and radiative heat fluxes. Three car position configurations are tested: flat, uphill, and downhill positions. Measurements are made for three different thermal functioning modes. Fluxmetric analysis based on overall heat flux as well as on separate convective and radiative heat fluxes is reported here in order to establish the effects and variation tendencies of car inclination on the temperature–heat flux pair. For most of the tested positions in the underhood top region, the car inclination improves convective heat transfer and penalizes radiative heat transfer. The reduction in radiative heat transfer dominates the convective heat-transfer improvement, resulting in augmentation of the overall heat flux as well as the temperature.     

Measurement of high gas-stream temperature using dynamic thermocouples

The dynamic probe technique using the transient response of a thermocouple is one of the methods of measuring high temperature flowing gases. In this paper, the complete dynamic response of a thermocouple has been solved consisting of convective, conductive, and radiative terms. The solution has been used to arrive at correction factors for actual experimental data. The use of dynamic thermocouples in the measurement of temperature profiles has also been illustrated by experiment. The model is verified at lower temperatures using a bunsen flame.     

Experiments on the influence of intake conditions on local instantaneous heat flux in reciprocating internal combustion engines

The present study tries to be a contribution for the development of more precise theoretical models for predicting the dissipation of heat through the combustion chamber walls of reciprocating (internal combustion) IC engines. A fast response thermocouple was embedded in the combustion chamber of a single cylinder engine to measure instantaneous wall temperatures. The heat flux was obtained by solving the one-dimensional transient energy equation with transient boundary conditions using the Fast Fourier Transform. The engine was tested under different operating conditions to evaluate the sensitivity of the measurement procedure to variations of three relevant combustion parameters: injection pressure, air temperature and oxygen concentration at the intake. The local heat flux obtained was compared with other relevant parameters that characterize the thermal behaviour of engines, showing, in most of the cases, correlation among them. The results showed that the instantaneous heat flux through the walls and hence the local wall temperatures are strongly affected by the ignition delay and the start of combustion.     

A data method using the inner temperature difference to improve the stability of the inverse heat conduction problems

Abstract

This article proposes a method to construct two series systems for improving the stability of the inverse heat conduction problems (IHCP) in a finite slab. The transfer function between the surface heat flux or temperature and the inner temperature difference is respectively obtained by Laplace transform technique firstly. Then the series systems which can solve IHCP based on the inner temperature difference are constructed by replacing the unsuitable zero and pole points of the transfer function approximated by è approximation. Finally the effects of the series systems are evaluated by a typical example. The results of the evaluation show that this method can obtain the surface heat flux and temperature by the inner temperature difference, and enhance the response speed of the measurement system at the same time. In addition this method can also improve the signal to noise ratio (SNR) of the inverse solutions by selectively amplifying the high SNR parts of the inner temperature difference. The present work provides an effective method to improve the stability of IHCP.     

Heat flux estimation of a plasma rocket helicon source by solution of the inverse heat conduction problem

A solution of the inverse heat conduction problem (IHCP) by the steepest descent method is carried out in order to determine the waste heat flux from a helicon plasma discharge using transient surface temperature measurements obtained from infrared thermography. The infrared camera data is calibrated against thermocouple data and mapped to real locations on the observed surface. The magnitude and distribution of the heat flux to the gas containment tube in the helicon is investigated as the applied power, gas flow rate, magnetic field distribution and neutral gas are varied.     

Thermal quadrupoles approach for two-dimensional heat flux estimation using infrared and thermocouple measurements on the JET tokamak

This paper presents several 2D heat flux calculation methods applied to temperature data of one of the most exposed plasma facing components of the JET tokamak. We have two temperature diagnostics: a high time resolution infrared system is used to measure the surface temperature and two embedded thermocouples to measure the temperature in the bulk at 1 cm depth from the surface. A direct calculation is possible using the surface temperature but the presence of thin carbon layers disturb the measurements and leads us to make an inverse computation of the heat flux using the thermocouple data.     

Inverse heat conduction estimation of inner wall temperature fluctuations under turbulent penetration

Turbulent penetration can occur when hot and cold fluids mix in a horizontal T-junction pipe at nuclear plants. Caused by the unstable turbulent penetration, temperature fluctuations with large amplitude and high frequency can lead to time-varying wall thermal stress and even thermal fatigue on the inner wall. Numerous cases, however, exist where inner wall temperatures cannot be measured and only outer wall temperature measurements are feasible. Therefore, it is one of the popular research areas in nuclear science and engineering to estimate temperature fluctuations on the inner wall from measurements of outer wall temperatures without damaging the structure of the pipe. In this study, both the one-dimensional(1D) and the two-dimensional(2D) inverse heat conduction problem(IHCP) were solved to estimate the temperature fluctuations on the inner wall. First, numerical models of both the 1D and the 2D direct heat conduction problem(DHCP) were structured in MATLAB, based on the finite difference method with an implicit scheme. Second, both the 1D IHCP and the 2D IHCP were solved by the steepest descent method(SDM), and the DHCP results of temperatures on the outer wall were used to estimate the temperature fluctuations on the inner wall. Third, we compared the temperature fluctuations on the inner wall estimated by the 1D IHCP with those estimated by the 2D IHCP in four cases:(1) when the maximum disturbance of temperature of fluid inside the pipe was 3℃,(2) when the maximum disturbance of temperature of fluid inside the pipe was 30℃,(3) when the maximum disturbance of temperature of fluid inside the pipe was 160℃, and(4) when the fluid temperatures inside the pipe were random from 50℃ to 210℃.     

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.     

In-situ determination of the heat flux density at the glass/mould interface during a glass pressing production cycle

The glass pressing process involves heat transfer between the glass gob and the forming tool which are among the most important parameters influencing the thermo-mechanical stresses in the moulds. The present paper presents the development of the instrumentation of a mould for the measurement of temperatures during the production cycle. These measurements are exploited with an inverse method to evaluate the heat flux densities at the working surface of the mould. The influence of each process stage and of the location at the surface of the mould on the thermal loadings are described. The evaluated heat flux densities are used as boundary conditions in a finite element calculation. The validity of these results are discussed taking into account the differences between experiment and calculation, the hypothesis of the inverse method and the time response of the thermocouples.     

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 Inverse Heat Transfer Analysis of Functionally Graded Materials in Estimating Time-Dependent Surface Heat Flux

Two-dimensional transient inverse heat conduction problem (IHCP) of functionally graded materials (FGMs) is studied herein. A combination of the finite element (FE) and differential quadrature (DQ) methods as a simple, accurate, and efficient numerical method for FGMs transient heat transfer analysis is employed for solving the direct problem. In order to estimate the unknown boundary heat flux in solving the inverse problem, conjugate gradient method (CGM) in conjunction with adjoint problem is used. The results obtained show good accuracy for the estimation of boundary heat fluxes. The effects of measurement errors on the inverse solutions are also discussed.     

The emittance of yttrium-beryllium oxide thermocouple coating

The emittance of a yttrium-beryllium oxide thermocouple coating was determined by an electrical heating method and by sodium line reversal measurements in the overall temperature range 1465–1830K. The emittance determined by both methods was 0.60. Comparison of emittances measured with different sized thermocouples in one-dimensional flames implied that the appropriate thermocouple heat transfer model was a cylinder in cross flow. Good agreement was obtained between radiation-corrected temperatures measured with silica coated (emittance of 0.22) and yttrium-beryllium oxide coated thermocouples.     

Inverse estimation of the unknown base heat flux in irregular fins made of functionally graded materials

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle has been successfully applied to an irregular fin made of functionally graded materials to estimate the unknown base heat flux distributions by using temperatures at some measurement locations. The inverse results, in which three different base heat flux distributions are to be determined, have proven current method's capability to accurately estimate arbitrary fin-base heat flux distributions even measurement errors have been taken into account. The temperature data calculated from the direct problem are used to simulate the measured temperature. The influence of measurement errors upon the precision of the estimated results is also investigated. This method does not need any prior information on the unknown quantity, and results show that excellent estimations can be obtained for the test cases considered in this study.     

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.     

Design and fabrication of coaxial surface junction thermocouples for transient heat transfer measurements

Low cost coaxial surface junction thermocouples (CSJTs') have been fabricated in-house and calibrated to measure the transient surface temperature rise within a UNITEN's shock tube wall facility, consisting of K-type coaxial thermocouple elements. The aim of this paper is to explain the design technique of the CSJTs' and the difficulties that have occurred during the fabrication process. The microstructural analysis and the chemical characterization for these types of thermocouples have also been carried out to verify the surface morphology and to qualitatively evaluate the CSJT materials composition. The preliminary testing was performed to demonstrate the performance of these thermocouples to be used for measuring the surface temperatures and heat transfer rates under transient conditions. The preliminary results from shock tube tests have shown that these thermocouples have a time response on the order of microseconds and were suitable for making heat transfer measurements in highly transient conditions. It was concluded that the current construction technique produced gauges that were reliable, reproducible, rugged and inexpensive.