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.     

Enhancement of thermal efficiency and cost effectiveness by development of melting furnace by revamping and troubleshooting fuel‐fired furnace

Technological development of furnaces over conventional melting methods of diesel or gas‐fired furnaces is necessary. These furnaces have large amount of heat losses and hence their thermal efficiency is very low. Moreover, these furnaces do not produce good quality melt because of the chances of embedment of impurities from after‐combustion gases and agitation. The time required for melting in such furnaces is more. Also, insulation is not provided and there are heat losses which increase the time of melting. An electric resistance heating furnace is developed which overcomes all the problems associated with the fuel‐fired conventional furnace. The thermal efficiency of this developed furnace is found to increase quite drastically up to 85%, which is by about 33% more than conventional furnace; while reducing the operating cost of furnace. This benefits industry overall by profit of 70% and certainly can replace the existing conventional fuel‐fired furnaces.     

What is the most suitable fixed grid solidification method for handling time-varying inverse Stefan problems in high temperature industrial furnaces?

This paper presents a simple inverse heat transfer method for predicting the time-varying bank thickness of the phase change protective layer inside a high temperature furnace. The direct problem is handled with the single phase method which is neglecting the latent heat. The inverse method rests on the Adjoint Problem and the Conjugate Gradient Method. It is shown that the iterative inverse procedure based on the single phase method predicts a virtual incident heat flux in the liquid zone that yields accurate time-varying bank predictions. Results also indicate that the benefits of the virtual iterative approach are twofold: the CPU time required for solving the inverse problem is reduced and the lagging effect inherent to the inversion is diminished for non isothermal phase change processes. For typical melting furnace operating conditions, it is shown that the virtual approach doubles the allowable diagnostic frequency for predicting the time-varying bank thickness.     

燃烧室内三维温度场的辐射反问题

本文提出了一种在介质辐射特性已知的条件下,由壁面入射辐射热流的测量值反演燃烧室内三维温度场的方法。该方法是在辐射传递方程离散坐标近似的基础上,用求目标函数极小值的共轭梯度法进行反演计算。通过对吸收系数、散射不对称因子、反照率、壁面黑度和燃烧室大小尺寸等参数对反演精度影响的分析,结果表明,即使存在随机测量误差,这些参数对温度场反演精度的影响也不大,本文所提出的方法可较精确地反演燃烧室内三维温度场。     

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.     

Performance Evaluation of Two Heat Transfer Models of a Walking Beam Type Reheat Furnace

Two different heat transfer models for predicting the transient heat transfer characteristics of the slabs in a walking beam type reheat furnace are compared in this work. The prediction of heat flux on the slab surface and the temperature distribution inside the slab have been determined by considering thermal radiation in the furnace chamber and transient heat conduction in the slab. Both models have been compared for their accuracy and computational time. The furnace is modeled as an enclosure with a radiatively participating medium. In the first model, the three-dimensional (3D) transient heat conduction equation with a radiative heat flux boundary condition is solved using an in-house code. The radiative heat flux incident on the slab surface required in the boundary condition of the conduction code is calculated using the commercial software FLUENT. The second model uses entirely FLUENT along with a user-defined function, which has been developed to account for the movement of slabs. The results obtained from both models have a maximum temperature difference of 2.25%, whereas the computational time for the first model is 3 h and that for the second model is approximately 100 h.     

Prediction of protective banks in high temperature smelting furnaces by inverse heat transfer

An inverse phase change heat transfer method has been developed for predicting the time evolution of banks covering the surface of refractory brick walls inside high temperature smelting furnaces. The presence of these banks is indispensable as they serve as a protective barrier against the highly corrosive slag, thereby maintaining the structural integrity of the furnace and prolonging its active life. The numerical model rests on the conjugate gradient solution method with the adjoint equation. It predicts banks thickness and motion relying on the thermal conditions prevailing outside the furnace and temperature measurements taken at one location inside the brick wall. Simulations are carried out to examine the effect of different parameters on the predictive capabilities of the method. Results reveal that the method remains accurate in spite of the fact that the temperature measurements inside the wall are noisy and are taken at depth of few centimetres only. An example showing how the present inverse method can be used to warn on the imminent loss of the protective bank during the operation of a smelting furnace is then provided.     

Conception of thermoelectric flux meters for infrared radiation measurements in industrial furnaces

To help optimise the design and command of infrared (IR) emitters which are frequently used in industrial installations [A.C. Metaxas, Foundations of Electro-Heat a Unified Approach, John Wiley, Chichester, 1996; H. Lihan, Infrared surface pasteurisation of Turkey frankfurters, Innovative Food Science and Emerging Technologies 5 (3) (2004) 345–351; F.M. Schmidt, Y. Le Maoult, S. Monteix, Modelling of infrared heating of thermoplastic sheet used in thermoforming process, Journal of Materials Processing Technology 143–144 (2003) 225–231; M.T. Brogan, P.F. Monaghan, Thermal simulation of quartz tube infrared heaters used in the processing of thermoplastic composites, Composites Part A: Applied Science and Manufacturing 27 (4) (1996) 301–306; S. Le Person, J.R. Puiggali, M. Baron, M. Roques, Near infrared drying of pharmaceutical thin films: experimental analysis of internal mass transport, Chemical Engineering and Processing 37 (3) (1998) 257–263; K. Esser, E. Haberstroh, U. Hüsgen, D. Weinand, Infrared radiation in the processing of plastics: precise adjustment—the key to productivity, Advances in Polymer Technology 7 (2) (1987) 89–128; D. Blanc, P. Laurent, J. Andrieu, J.F. Gerard, Convective and radiant (IR) curing of bulk and waterborne epoxy coatings as thin layers, part II: infrared curing polymer, Engineering and Science 39 (12) (1999) 2487–2497], this paper aims at presenting the development, the construction, the calibration, and the test of flux meters designed to make “in situ” measurements of infrared radiation in industrial furnaces. These sensors must be able to measure high heat flux in difficult thermal ambiances, and be adapted to the characterization of existing processes, therefore the output signal has to directly reflect the IR received flux. The sensible part is made with a semiconductor thermoelectric module which offers a great sensitivity. While the top part of the module is exposed to convection and infrared radiation, the bottom is stuck on a metallic mass. Three different devices have been developed. The first one uses a water cooling circuit to maintain the bottom at a constant temperature. Then, two autonomic devices are developed to allow an on-line assessment of the system state. A flux meter using a paraffin buffer to maintain the reference temperature is designed to measure global heat flux. The third device presented has a floating reference temperature and uses two thermoelectric modules. A mathematical model has also been developed in order to analyse the three different flux meters with regard to the different levels of convective and radiative heat flux. Our flux meters are relevant to test IR furnaces. They can measure up to 50 kW m⁻² heat flux in more than 120 °C ambient. Autonomous sensors can help characterise and adjust existing installations. They are also interesting tools for maintenance shift.     

Estimation of heat flux on the surface of an initially hot cylinder cooled by a laminar confined impinging jet

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown space-and time-dependent heat flux at the surface of an initially hot cylinder cooled by a laminar confined slot impinging jet from the knowledge of temperature measurements taken on the cylinder’s surface. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. The results show that an excellent estimation on the space-and time-dependent heat flux can be obtained even the distributions of thermal properties inside the cylinder is unknown.     

Thermal modeling of controlled atmosphere brazing process using virtual reality technology

In the automotive industry, heat exchangers are manufactured in large quantities. The controlled atmosphere brazing (CAB) process is one of the fastest growing processes for aluminum radiator production behind vacuum brazing and machine assembly process. In this paper, we describe a thermal model (HETCAB) to predict the transient temperature distribution in an aluminum heat exchanger while it is being brazed in a CAB furnace. This thermal model is simulated using a virtual CAB (VR CAB) furnace created using virtual reality technology. Within this VR CAB furnace, engineers can “walk” through the furnace, observe the dynamic heat exchange, manipulate the products inside the furnace, and test various parameters critical to the process. The VR CAB together with the thermal model provides a realistically simulated environment that enables engineers to control and improve the heat exchange processes, experiment with design parameters, and study the effects of various process parameters including the parameters that control product yield.     

Inverse radiation problem of temperature field in three-dimensional rectangular furnaces

The discrete ordinates method is used to developed a solution to an inverse radiation problem of temperature field in rectangular furnaces. It is assumed that, with the exception of the inhomogeneous temperature field, all aspects of the radiation transport problem are known. A method is developed to determine the inhomogeneous temperature field from specified incident radiation heat fluxes at the centers of boundary walls. The inverse problem is solved using conjugate gradient method that minimize the error between the incident radiation heat fluxes calculated and the experimental data. The results of temperature estimation show that the temperature field can be estimated accurately, even with noisy data.     

生物组织热边界条件反演研究

对肿瘤热疗过程中生物组织表面热流及内部温度协同反演进行了研究。首先介绍了激光辐照下生物组织内部光热传输模型，并采用有限体积法和离散坐标法相结合求解生物组织内光热传输问题。然后介绍了模糊推理方法基本原理，并采用改进分散模糊推理方法同时反演了激光诱导肿瘤热疗过程中生物组织表面入射热流及内部温度场。最后分析了热流形式和测量误差对反演结果的影响。结果表明，改进分散模糊推理方法可以准确地同时反演组织表面热流及内部温度分布，并具有较强稳定性和抗误差干扰能力。     

A heat-flux based “building block” approach for solving heat conduction problems

A numerical approximation of the Green’s function equation based on a heat-flux formulation is given. It is derived by assuming as a functional form of the surface heat flux a stepwise variation with space and time. The obtained approximation is very important in investigation of the inverse heat conduction problems (IHCPs) because it gives a convenient expression for the temperature in terms of the heat flux components. Additionally, it is very important for the unsteady surface element (USE) method which is a modern boundary discretization method. Green’s function approximate solution equation (GFASE) also creates ‘naturally’ fixed groups or modules of work elements called “building blocks” that may be added together to obtain space and time values of temperature. In the current case, they are subject to a partial heating by an applied surface heat flux. The “building block” solution can be derived by using the various analytical and numerical approaches available in heat conduction literature though the exact analysis is preferable, as discussed in the text. Poorly-convergent series deriving from Green’s functions approach are replaced by closed-form algebraic solutions.     

Estimation of Heat Flux and Thermal Stresses in Functionally Graded Hollow Circular Cylinders

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat flux at the inner surface of a functionally graded hollow circular cylinder from the knowledge of temperature measurements taken within the cylinder. Subsequently, the distributions of temperature and thermal stresses in the cylinder can be determined as well. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. Results show that an excellent estimation on the time-dependent heat flux, temperature distributions, and thermal stresses can be obtained for the test case considered in this study.     

Neural Computation to Estimate Heat Flux in an Atmospheric Plasma Spray Process

Temperature is a key parameter in the thermal spray process and is a consequence of the heat flux experienced by the workpiece. This paper deals with the estimation of the heat flux transmitted to a workpiece from an atmospheric plasma spray torch during the preheating process often implemented in thermal spraying. An inverse heat conduction problem solution using a conjugate gradient method was considered to determine the heat flux starting from a known temperature distribution. Results from the later method were used to train an artificial neural network to discover correlations between selected processing parameters and heat flux.     

订单生产对加热炉提出全新要求

对湘钢宽厚板加热炉进行了热平衡测试,其热效率为60.09%,可比单耗37.35kgce/t,在国内同类型加热炉能耗比较中处于中上水平。分析了订单化生产对加热炉经济指标造成的影响,湘钢宽厚板厂加热炉比国内先进同类型加热炉氧化烧损率高0.8%～0.9%,而炉底强度低300～600kg/(m2.h)。针对订单化生产对加热炉操作提出全新要求,湘钢需要不断优化生产组织,提高板坯质量,实施热送热装,完善加热炉操作控制。     

我国锻造工业炉的现状及发展趋势

阐述了铸造工业炉燃料构成，炉型结构，燃烧装置，余热利用，耐火材料及热工控制等方面的技术现状，以及煤炉改造及高性能锻造工业炉的发展趋势。     

Prediction of the heat flux profile on the furnace wall of circulating fluidized bed boilers

The purpose of this work is to investigate and develop a correlation for predicting the profile of heat flux on the crest of the membrane water wall tube along the height of circulating fluidized bed furnaces. The heat conduction equation for the tube was solved numerically under various operating conditions and furnace sizes. It was found that the temperature and heat flux profiles decreased rapidly in the region above the secondary air ports and then were found to be nearly constant. In addition, the heat flux increased as the Froude number increased or as the bed particle to the furnace diameter ratio decreased. The results were used to develop a correlation for predicting the heat flux profiles of the boilers having capacities from 12 MW_th to 165 MW_th in terms of dimensionless temperature, the Froude number, the diameter ratio and the height from the ports to the total height ratio.     

On Configuration of Load in Radiant Furnace for Uniform Thermal Conditions

This work aimed to investigate the boundary design problem for uniform thermal conditions, when multiple three-dimensional (3-D) design objects (DOs) are placed inside the radiant furnace, and to explore the suitable configuration of DOs located inside the radiant furnace. Also the objective includes ascertaining the limit of maximum numbers of DOs that can be accommodated to get the uniform thermal conditions. To accomplish this task, 19 cases are evaluated, consisting of the different number of DOs with various configurations, located on the bottom surface of the furnace enclosure. Each case is treated as an inverse boundary design problem separately. The radiative information is calculated using the radiation element method by ray emission model (REM²). The microgenetic algorithm (MGA) is used as an optimization tool. The specularity effect of the surfaces of heaters, of surfaces of radiant enclosure, and of the DOs is taken into account. The suitability of the configuration of DOs is shown by comparing the estimated heat flux distribution on DOs. The effect of different heater power ranges on the uniformity of the heat flux distribution on DOs is discussed. With a sample case, the optimal heater power setting that produces the desired uniform thermal conditions on DOs is also given. In the present boundary design problems, to obtain the uniform thermal conditions, a pronounced effect of the configuration of DOs and the numbers of DOs is observed.     

燃烧产物辐射特性的误差对炉内辐射传热计算精度的影响

本文用离散坐标法对含吸收散射性介质矩形空腔内的３维辐射传递过程进行了模拟，并编写了相应的数值计算程序。利用该程序分析了介质的吸收系数、散射系数、相函数、光谱特性及壁面灰渣沉积层黑度的不确定性对矩形燃烧室内烟气温度及热流计算精度的影响。结果表明计算精度很大程度上取决于燃烧产物辐射特性的取值精度，特别是壁面灰渣沉积层黑度的取值精度。在煤粉燃烧室中，介质的散射不宜忽略。