Detection of hot spot through inverse thermal analysis in superconducting RF cavities

An inverse heat conduction problem in a superconducting radio frequency (SRF) cavity is examined. A localized defect is simulated as a point-heating source on the inner surface (RF surface) of the evacuated niobium cavity. Liquid helium acts as a coolant on the outer surface of the cavity. By measuring the outer surface temperature profile of the cavity using relatively few sensors, the temperature and location of a hot spot on the inner surface of the niobium are calculated using an inverse heat conduction technique. The inverse method requires a direct solution of a three-dimensional heat conduction problem through the cavity wall thickness along with temperature measurements from sensors on the outer surface of the cavity, which is immersed in liquid helium. A non-linear parameter estimation program then estimates the unknown location and temperature rise of the hot spot inside the cavity. The validation of the technique has been done through an experiment conducted on a niobium sample at room temperature.     

Measurement of ice movement in water using electrical capacitance tomography

The permafrost with the highest altitude and largest area in the mid and low latitude is located in the Qinghai-Tibet Plateau. As most frozen soils contain ice particles which are very sensitive to temperature and other external parameters, thus influencing the stability of the embankment in permafrost regions, it is very important to develop techniques to prevent damages to railway embankments due to thaw settlement. In this paper, the electrical capacitance sensors are designed to study the freezing front movement in a vessel and ice movement in water, which is the first step to apply the ECT system to the study of frozen soil. Two sensor arrangements are put into use. First, the traditional closed electrode sensors are put into use. In this arrangement, the electrodes are attached to the outside of the pipe or vessel, and the cross-sectional distribution of ice and water could be reconstructed from the capacitances measured. Also, the ice moving track at the cross section could be reflected thoroughly. Since the traditional closed electrode sensors can not meet the needs of measuring the ice freezing front movement, a new electrode sensors structure, that is, the unclosed electrode sensors are designed to satisfy the specific test of frozen soil. In this arrangement, several pairs of electrodes are arranged along the height of the vessel. A sudden decrease in the measured capacitance is observed when the freezing front advances past the electrodes. Therefore, according to the capacitance variation, the ice movement can be reflected. In summary, electrical capacitance tomography has the advantages of being non-intrusive. With different electrode sensor arrangement, ice movement and ice freezing front can be obtained. The electrical capacitance sensor system can be applied to investigate the complicated phenomena in frozen soil.     

含甲烷水合物沉积物电–声响应特性联合探测：装置开发与实验研究

为了满足开展天然气水合物模拟实验、测试电学和声学特性参数以及建立特性参数与含水合物饱和度之间关系的需求，开发了一套电–声响应特性联合探测实验装置，以海沙模拟松散沉积物开展了甲烷水合物生成和分解模拟实验，联合探测了电学和声学参数，分析了被测体系的电学和声学响应特性。研究表明：（1）通过电–声响应联合探测实验装置能够同步获取宽频率范围电学阻抗谱和超声波接收信号波形；（2）通过设计电声复合传感器及其阵列式排布方式和“分时轮流”工作模式能够获取电学和声学参数的空间分布信息；（3）基于所提出的波动百分比和相关系数指标对不同频率阻抗模值进行评价所获得的100 kHz阻抗模值随含水合物饱和度的增加先减小后增大，经过有效压力校正后的超声波接收信号波动幅度值随含水合物饱和度的增加而升高；（4）上述两者分别可以作为分析和建立与含水合物饱和度之间关系的电学和声学有效特征参数。所开发的实验装置为将来开展含水合物复杂沉积物的模拟实验与测试工作提供了必要条件，所得到的电学和声学有效特征参数为含水合物饱和度计算模型的建立奠定了基础。     

New noise rejection techniques on pulse-by-pulse basis for on-linepartial discharge measurement of turbine generators

On-line partial discharge tests for turbine generators are useful for recognizing abnormal or deteriorated stator winding insulation without a machine outage. One problem related to such a test is additional installation of sensors. We propose that wires of a resistance temperature detector (RTD) embedded in a stator slot are applied as a partial discharge sensor in the form of an RF coupler. The other problem is electrical noise that is a pulse similar to partial discharge in frequency characteristic and has higher amplitude than partial discharge. The sensors in two steam turbine generators showed enough sensitivity and broad frequency bandwidth to facilitate the elimination of noise from the partial discharge measurement. Two new techniques of noise rejection on a pulse-by-pulse basis are investigated with the multiple sensors. One is founded on the correlation between pulse height in two frequency bands. The other is based on the correlation between pulse height from the two partial discharge sensors. It was found that each noise rejection technique was successful in a trial testing     

A method to measure time lag constants of heat conduction equations

Technique based on frequency response is suggested for the measuring of time lag constants in heat conduction problem. Steady state temperature distribution at a semi infinite medium subjected to periodic heat flux for non-Fourier, Dual Phase Lag, and T wave models are found and thermal impedances are acquired. The time lags of these models can be found by measuring thermal impedance. Because of the difficulties concerning generating and measuring high frequencies, it is focused on the minimum required frequency to achieve a suitable accuracy. Some notes and a procedure are proposed to determine time lags of mentioned models with desired accuracy.     

APPLICATION OF OPTIMIZATION METHODS FOR SOLVING INVERSE PHASE-CHANGE PROBLEMS

Several optimization algorithms in conjunction with a control-volume method (for discretization) and a least-square method (for improving accuracy and stability) have been considered to solve the inverse phase-change problem for the example of the welding process. The results show that quite an accurate solution can be obtained when the sensors are placed near the interface region. The most important feature of the approach is that the liquid-solid interface as well as the temperature distribution within the solid region can be obtained from the temperature data at a number of sensors located in the solid region, without considering heat transfer and fluid flow in a molten zone. The validity of the numerical solution of the inverse problem is checked by comparing the results with direct solution of the problem. The inverse approach to phase-change problems has many potential applications that are of great technological significance.     

Fast inverse prediction of phase change banks in high temperature furnaces with a Kalman filter coupled with a recursive least-square estimator

An inverse heat transfer procedure for predicting the time-varying thickness of phase-change banks on the inside surface of the walls of high temperature furnaces is presented. The main feature of the inverse method is its unique capability of making fast predictions so that it can be easily integrated to existing real-time control systems of industrial facilities. The method rests on fast computing state-space models (direct model) that are designed to mimic the response of a full finite-difference model of the phase change problem. A Kalman filter coupled with a recursive least-square estimator (inverse method) is employed to estimate the time-varying phase front position from the data collected by a temperature and/or heat flux sensor located in the furnace wall. The inverse heat transfer procedure is thoroughly tested for typical phase change conditions that prevail inside industrial facilities. The effect of the sensor type (temperature sensor or heat flux sensor), of its location and of the measurement noise on the accuracy and stability of the predicted bank thickness is investigated. It is shown that the proposed inverse heat transfer procedure becomes increasingly reliable and accurate for predicting the bank thickness as it shrinks. This feature is of the utmost interest for preventing the sudden and accidental loss of the protective banks of industrial furnaces filled with molten material. Recommendations are also made concerning the type and location of sensors.     

Developments in gas sensor technology for hydrogen safety

Gas sensors are applied for facilitating the safe use of hydrogen in, for example, fuel cell and hydrogen fuelled vehicles. New sensor developments, aimed at meeting the increasingly stringent performance requirements in emerging applications, are reviewed. The strategy of combining different detection principles, i.e. sensors based on electrochemical cells, semiconductors or field effects in combination with thermal conductivity sensing or catalytic combustion elements, in one new measuring system is reported. This extends the dynamic measuring range of the sensor while improving sensor reliability to achieve higher safety integrity through diverse redundancy. The application of new nanoscaled materials, nanowires, carbon tubes and graphene as well as the improvements in electronic components and optical elements are evaluated in view of key operating parameters such as measuring range, sensor response time and low working temperature.     

INVERSE TRANSIENT THERMOELASTIC PROBLEM FOR A COMPOSITE CIRCULAR DISK

The present article deals with the application of a piezoelectric material as a sensor of thermomechanical disturbance. We consider a composite circular disk constructed of a transversely isotropic layer onto which a piezoceramic layer of crystal class 6mm is perfectly bonded. An inverse transient thermoelastic problem is solved to determine the unknown transient heating temperature distribution on the surface of the transversely isotropic layer, when the distribution of the electric potential difference across the piezoceramic layer is known. A finite difference method with respect to the time variable is employed to solve this inverse problem. The thermoelastic fields in the transversely isotropic and piezoceramic layers are analyzed by means of a transversely isotropic potential function method and a piezothermoelastic potential function method, respectively. Numerical results are presented for the time variation of the inferred heating temperature distribution and the corresponding distributions of temperature, displacements, stresses, and electric displacements.     

A new method for identification of thermal boundary conditions in water-wall tubes of boiler furnaces

In this paper, a method for determining fireside heat flux, heat transfer coefficient on the inner surface and temperature of water-steam mixture in water-wall tubes is developed. The unknown parameters are estimated based on the temperature measurements at a few internal locations from the solution of the inverse heat conduction problem. The non-linear least squares problem is solved numerically using the Levenberg–Marquardt method. The diameter of the measuring tube can be larger than the water-wall tube diameter. The view factor defining the distribution of the heat flux on the measuring tube circumference was determined using exact analytical formulas and numerically using ANSYS software. The method developed can also be used for an assessment of scale deposition on the inner surfaces of the water-wall tubes or slagging on the fire side.     

Estimation of front surface temperature and heat flux of a locally heated plate from distributed sensor data on the back surface

We present a new method of solving the three-dimensional inverse heat conduction (3D IHC) problem with the special geometry of a thin sheet. The 3D heat equation is first simplified to a 1D equation through modal expansions. Through a Laplace transform, algebraic relationships are obtained that express the front surface temperature and heat flux in terms of those same thermal quantities on the back surface. We expand the transfer functions as infinite products of simple polynomials using the Hadamard Factorization Theorem. The straightforward inverse Laplace transforms of these simple polynomials lead to relationships for each mode in the time domain. The time domain operations are implemented through iterative procedures to calculate the front surface quantities from the data on the back surface. The iterative procedures require numerical differentiation of noisy sensor data, which is accomplished by the Savitzky–Golay method. To handle the case when part of the back surface is not accessible to sensors, we used the least squares fit to obtain the modal temperature from the sensor data. The results from the proposed method are compared with an analytical solution and with the numerical solution of a 3D heat conduction problem with a constant net heat flux distribution on the front surface.     

Regularization methods in electrical impedance tomography technique for the two-phase flow visualization

The electrical impedance tomography (EIT) technique for the two-phase flow visualization requires the solution of a nonlinear inverse problem, which is typically ill-posed and subject to noisy data. During the solution procedure, hence, regularization methods are often introduced. This work presents a comparative study on several regularization methods to seek a suitable one for the visualization of liquid/vapor phase distribution. The images reconstructed by first order difference and implicitly scaled Levenberg-Marquardt regularizations give relatively good results even under some errors in measurement data. Also some computational issues relating EIT inverse problem are discussed.     

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。     

Prediction of the Time-Varying Ledge Profile inside a High-Temperature Metallurgical Reactor with an Unscented Kalman Filter-Based Virtual Sensor

A non-intrusive inverse heat transfer procedure for predicting the two-dimensional time-varying profile of the protective phase-change ledge on the inside surface of the walls of a high-temperature metallurgical reactor is presented. The inverse method, used here as a virtual sensor, enables the on-line estimation of the position of the solid-liquid phase front using thermal sensors embedded in the reactor wall. The virtual sensor comprises a state observer coupled to a reduced model of the reactor. Results show that the virtual sensor that yields the best prediction comprises an unscented Kalman filter, a nonlinear state-space model of thereactor, and two heat flux sensors located at the wall/ledge interface.     

Multi-parameter estimation in combined conduction–radiation from a plane parallel participating medium using genetic algorithms

An inverse conduction–radiation problem for simultaneous estimation of the conduction–radiation parameter, the optical thickness and the boundary emissivity from a knowledge of the measured temperature profile for combined conduction and radiation in a plane parallel participating medium is presented. A finite volume method is used to solve the “forward” problem, wherein the temperature profile is determined by a solution of the governing equation for a given set of parameters. The inverse problem is treated as an optimization problem, wherein, we minimize the sum of square of residuals between the measured and estimated temperatures. Genetic algorithms are used for the search. The effects of “measurement” errors on the estimated parameters, which are introduced through a random perturbation, are investigated.     

Application of Sequential Function Specification Method in Heat Flux Monitoring of Receding Solid Surfaces

Measurement of heat flux at the receding surface of materials is extremely difficult due to the presence of harsh working conditions. Under these situations, the solution of inverse heat conduction problem can be found as an efficient means of obtaining heat flux in the moving interface. This paper reports the results of applying the sequential function specification method to the problem of estimating the effect of severe thermal environments on the ablative structures. It is assumed that special sensing instruments are used to record the temperatures and the surface recession in real time of the simulated experiment. Due to high temperature regions near the ablating surface, the temperature sensors may burn out. A numerical experiment with simulated noisy measurements is used to analyze the effect of presence and/or absence of the lost sensors on the outcomes of the proposed procedure. The results introduce an efficient technique for designing heat flux gauges that work with temperature, as well as recession sensors.     

A three-dimensional inverse problem in estimating the applied heat flux of a titanium drilling – Theoretical and experimental studies

The applied heat flux on the drilling surface of drilling tool is estimated in the present three-dimensional inverse heat conduction problem. The inverse algorithm utilizing the Steepest Descent Method (SDM) and a general purpose commercial code CFX4.4 is applied successfully in this study based on the simulated and measured temperature distributions with time at four sensors embedded on the drilling surfaces. The numerical experiments are considered at the first stage to illustrate the validity of inverse determination of the unknown heat flux using exact and error measurements. Experimental data are then used to estimate the actual heat flux along the drilling edge at two different drill peripheral cutting speeds. Results of both the numerical and experimental examinations show that the reliable estimated heat flux can be obtained by using the present inverse algorithm.     

Solution of the Initial Inverse Problems in the Heat Equation Using the Finite Difference Method with Positivity-Preserving Padé Schemes

The classical inverse problem of recovering the initial temperature distribution from the final temperature distribution is extremely ill-posed. We propose a class of numerical schemes based on positivity-preserving Padé approximations to solve initial inverse problems in the heat equation. We also utilize a partial fraction decomposition technique to solve the problem more efficiently when higher order Padé approximations are used. We apply the proposed numerical schemes on the parabolic heat equation. Our aim is to model the problem as a direct problem and use our numerical schemes to recover the initial profile in a stable and efficient way.     

SIMULTANEOUS ESTIMATION OF INLET TEMPERATURE AND WALL HEAT FLUX IN TURBULENT CIRCULAR PIPE FLOW

An inverse heat convection problem is solved for simultaneous estimation of unknown inlet temperature and wall heat flux in a thermally developing, hydrodynamically developed turbulent flow in a circular pipe based on temperature measurements obtained at several different locations in the stream. The direct problem of turbulent forced convection is solved with a finite difference method with appropriate algebraic turbulence modelling. Although we seek for two unknown functions, we formulate the inverse problem as one of parameter estimation through the representation of the unknown inlet temperature profile and the wall heat flux distribution by one-dimensional finite element interpolation. Nodal values of the inlet temperature and the wall heat flux at chosen positions are determined as unknown parameters through the Levenberg–Marquardt algorithm for minimization procedure. Numerical results for several testing cases with different magnitudes of measurement errors are examined by using simulated experimental data. The effects of the number and the locations of the temperature measurement points are discussed.     

Determination of temperature wall functions for high Rayleigh number flows using asymptotics: A systematic approach

This paper presents a systematic approach to determine temperature wall functions for high Rayleigh number flows using asymptotics. An asymptotic analysis of the flow and heat transfer in the near wall region forms the basis for the development of the wall functions. Appropriate normalization of the variables followed by asymptotic matching of the temperature gradients of the inner and outer layers in the overlap region leads to a logarithmic temperature profile as a wall function that has undetermined constants. A key classification that has been made in the present study is the introduction of (1) The direct problem and (2) The inverse problem. The former means that temperature profiles, either from experiments or Direct Numerical Simulations (DNS), are available and the wall function problem finally reduces to one of determining certain constants in a general wall function formula. More radical and of more interest, is the inverse problem. The idea behind this it is that when a temperature profile can be recast into a Nusselt–Rayleigh correlation, it should be perfectly possible for one to start from a Nusselt–Rayleigh correlation and end up with a wall function for temperature. This approach again will have undetermined constants that can be calibrated from either experimental or DNS data. The main advantage of using the inverse problem is the dispensation of the need to measure temperatures accurately within the boundary layer. For both the direct and inverse problems, a graded treatment to determine the constants is presented. The treatment at its highest level will result in a parameter estimation problem that can be posed as an optimization problem. The optimization problem is then solved by state of the art techniques like Levenberg–Marquardt algorithm and Genetic algorithms (GA) and the solutions are compared. While for the direct problem, the approach is illustrated for the infinite channel problem (a simple flow), for the inverse problem, the approach is elucidated for the Rayleigh–Bénard problem (a complex flow). Finally, a blending procedure to arrive at a universal temperature profile that is valid in the viscous sublayer, buffer and the overlap layers is suggested. The key ideas of (1) using optimization techniques for determining the constants in the wall function and (2) obtaining wall functions from the Nusselt numbers by the inverse approach are expected to be useful for a wide class of problems involving natural convection.