Inverse estimation of heat flux and temperature in multi-layer gun barrel

In this paper, we present an inverse method, an input estimation method, to recursively estimate both the time varied heat flux and the inner wall temperature in the chamber. The algorithm includes the use of the Kalman filter to derive a regression model between the biased residual innovation and the heat flux through a given heat conduction state space model. Based on this regression model, the Recursive Least Squares Estimator (RLSE) is proposed to extract the time-varying heat flux on-line as the input. Computational results show that the proposed method exhibits a good estimation performance and highly facilitates practical implementation.     

Online estimation of multicomponent heat flux using a system identification technique

In this work system identification techniques are used to map the two-dimensional heat flux into the temperatures through a linear model supported by theoretical and numerical results. The basis of this analysis is a discrete version of the Burggraf Method saying a single component heat flux is a linear combination of the temperatures around the time of its occurrence. Taking the same approach, a linear model (i.e. a linear artificial neural network (ANN)) is employed to estimate a multicomponent heat flux as a linear function of the temperatures. A known heat flux is imposed to the direct model, then the history of heat flux-temperature data are fit to the linear mathematical model (i.e. a linear ANN) using system identification techniques. The achieved model estimates the heat flux based on a series of past and future temperatures and the estimated heat flux components are in a good agreement with the exact ones. Finally, the effect of some important factors on the results is investigated. The proposed solution to inverse heat conduction problems does not need thermophysical and geometrical parameters of the system and is robust against noises. It merely needs some series of heat flux-temperature data from solution of a reliable direct numerical model or experiment.     

Artificial neural network modelling of the thermal performance of a compact heat exchanger

This paper reports the use of artificial neural network models to simulate the thermal performance of a compact, fin-tube heat exchanger with air and water/ethylene glycol anti-freeze mixtures as the working fluids. The model predictions were compared with experimental data over a range of flow rates and inlet temperatures and with various ethylene glycol concentrations. In addition, the inlet air flow was distorted by obstructing part of the inlet ducting near the front face of the exchanger. The artificial neural networks were able to predict the overall rate of heat transfer in the exchanger with a high degree of accuracy and in this respect were found to be superior over conventional non-linear regression models in capturing the underlying non-linearity in the data. Moreover the detailed spatial variations in outlet air temperature were also adequately predicted. The results indicate that appropriately trained neural networks can simulate both the overall and “local” characteristics of the compact heat exchanger. In addition the paper demonstrates how an alternative type of neural network, the so-called Self-Organising-Map (SOM), can be employed for heat exchanger condition monitoring by identifying and classifying the deterioration in exchanger performance which, in this case, was associated with different levels of inlet obstruction.     

Theoretical and numerical investigation of flow stability in porous materials applied as volumetric solar receivers

This article reports results of a theoretical analysis as well as a numerical study investigating the occurrence of flow instabilities in porous materials applied as volumetric solar receivers. After a short introduction into the technology of volumetric solar receivers, which are aimed to supply heat for a steam turbine process to generate electricity, the general requirements of materials applied as solar volumetric receivers are reviewed. Finally, the main methods and results of the two studies are reported. In the theoretical analysis it is shown that heat conductivity as well as permeability properties of the porous materials have significant influence on the probability of the occurrence of flow instabilities. The numerical study has been performed to investigate the occurrence of unstable flow in heated ceramic foam materials. In the simulations a constant heat flow of radiation, that is absorbed in a defined volume, and constant permeability coefficients are assumed. Boundary conditions similar to those of the 10 MW Solucar Solar project have been chosen. In a three dimensional, heterogeneous two phase heat transfer model it was possible to simulate local overheating of the porous structure. The parameters heat conductivity, turbulent permeability coefficient and radial dispersion coefficient have been varied systematically. Consequently, for a heat flux density of 1 MW/m² a parameter chart could be generated, showing the possible occurrence of “unstable” or “stable” thermal and fluid mechanical behaviour. These numerical results are beneficial for the design of optimized materials for volumetric receivers.     

Correcting lateral heat conduction effect in image-based heat flux measurements as an inverse problem

The image deconvolution method is developed, which is coupled with the one-dimensional (1D) analytical inverse method to calculate more accurate heat flux fields by correcting the lateral heat conduction effect in image-based surface temperature measurements. The theoretical foundation is a convolution-type integral equation with a Gaussian filter (kernel) that relates a heat flux field obtained by using the 1D inverse method on a surface to the true heat flux field. The accuracy of this method is evaluated and the standard deviation in the Gaussian filter is determined for different materials through simulations. This method is used to calculate heat flux fields in temperature-sensitive-paint measurements on a 7°-half-angle circular cone at Mach 6 in a short-duration hypersonic wind tunnel. In addition, a simple method is proposed to solve a projection problem associated with image deconvolution for a highly curved developable surface.     

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.     

Input Estimation Method in the Use of Electronic Device Temperature Prediction and Heat Flux Inverse Estimation

The input estimation method (IEM) is proposed in this research to estimate the real-time time-variant core heat flux of electronic components. The IEM is an on-line real-time estimation method, which combines the Kalman filter mechanism and recursive least-square estimation (RLSE). On the premise that there exists both system processing error and measurement error, using temperature measurements measured from the exterior of the device package, the core time-variant heat flux of the device can be precisely estimated inversely.     

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.     

A general calculation method for plate heat exchangers

The possibilities of process stream guidance within plate heat exchangers are very complex. There exist constructional solutions, in which the process-streams are led through stream-passages connected in series or parallel. Other constructions realize the heat transfer between more than two process streams. Known are also constructions, where the stream passages are spirals. All these constructions deviate more or less from the ideal principle of uniflow or counterflow guidance. While the approximate interpretation of plate heat exchangers is solved methodically, the only methods used for the calculation of existing apparatus are either mathematically extremely exacting or not generally valid. To analyse the behaviour of plate heat exchangers, exact and easy to apply calculation methods are required. This article presents a general calculation method for the stationary simulation of plate heat exchangers of any type required. The method allows a mathematically exact determination of the temperature profiles of types of apparatus mentioned above. In a further step the proposed method can also be used for the simulation of the heat flux along the walls of the plates as well as the dispersion in the passages. The basic idea of the presented method is the simulation of a heat exchanger network with generalized operating characteristics. The “classic formulas” of this operating characteristic are given in this method as special cases. The general calculation method for plate heat exchangers can be used without any iteration. Only the consideration of temperature dependent properties as well as phase transitions require iterations. This method is characterized by a great numerical stability.     

Artificial neural network techniques for the determination of condensation heat transfer characteristics during downward annular flow of R134a inside a vertical smooth tube

In this study, the best artificial intelligence method is investigated to estimate the measured convective heat transfer coefficient and pressure drop of R134a flowing downward inside a vertical smooth copper tube having an inner diameter of 8.1 mm and a length of 500 mm during annular flow numerically. R134a and water are used as working fluids in the tube side and annular side of a double tube heat exchanger, respectively. The ANN training sets have the experimental data of in-tube condensation tests including six different mass fluxes of R134a such as 260, 300, 340, 400, 456 and 515 kg m^− 2 s^− 1, two different saturation temperatures of R134a such as 40 and 50 °C and heat fluxes ranging from 10.16 to 66.61 kW m^− 2. The quality of the refrigerant in the test section is calculated considering the temperature and pressure obtained from the experiment. The pressure drop across the test section is directly measured by a differential pressure transducer. Input of the ANNs are the measured values of test section such as mass flux, heat flux, the temperature difference between the tube wall and saturation temperature, average vapor quality, while the outputs of the ANNs are the experimental condensation heat transfer coefficient and measured pressure drop in the analysis. Condensation heat transfer characteristics of R134a are modeled to decide the best approach using several artificial neural network (ANN) methods such as multilayer perceptron (MLP), radial basis networks (RBFN), generalized regression neural network (GRNN) and adaptive neuro-fuzzy inference system (ANFIS). Elimination process of the ANN methods is performed by means of 183 data points, divided into two sets randomly, obtained in the experiments. Sets of test and training/validation include 33 and 120/30 data points respectively for the elimination process. Validation process, in terms of various experimental conditions, is done by means of 368 experimental data points having 68 data points for test set and 300 data points for training set. In training phase, 5-fold cross validation is used to determine the best value of ANNs control parameters. The ANNs performances were measured by means of relative error criteria with the usage of unknown test sets. The performance of the method of multi layer perceptron (MLP) with 5-13-1 architecture and radial basis function networks (RBFN) were found to be in good agreement, predicting the experimental condensation heat transfer coefficient and pressure drop with their deviations being within the range of ± 5% for all tested conditions. Dependency of outputs of the ANNs from input values is also investigated in the paper.     

Inverse Thermo-Mechanical Analysis of a Functionally Graded Fin

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent base heat flux of a functionally graded fin from the knowledge of temperature measurements taken within the fin. Subsequently, the distributions of temperature and thermal stresses in the fin can be determined as well. It is assumed that no prior information is available on the functional form of the unknown base 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. The influence of measurement errors and measurement location upon the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent base heat flux, temperature distributions, and thermal stresses can be obtained for the test case considered in this study.     

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.     

A Principal Component Analysis and neural network based non-iterative method for inverse conjugate natural convection

Inverse Heat Transfer Problems (IHTP) are characterized by estimation of unknown quantities by utilizing any given information of the system. In this study, the inverse problem of estimation of boundary heat flux for a given temperature distribution on the walls of a two dimensional square cavity with a finite wall thickness is considered. A non-iterative method is applied utilizing Artificial Neural Network (ANN) and Principal Component Analysis (PCA) to estimate the parameters that define the boundary heat flux. The forward model is numerically solved with Fluent 6.3 for known values of a linearly varying boundary heat flux and the temperature distribution thus obtained is utilized to train the ANN for the inverse model. A parametric study is carried out to determine the effect of the thermal conductivity of the top and bottom walls on the flow and temperature distribution in the cavity. PCA analysis is carried out to reduce the dimensions of the input data set for the inverse model. These reduced dimensions are used to train the network and due to low dimensionality of the input, the effort required to train the network is considerably less. The trained networks are finally used to estimate boundary heat flux for any desired temperature distribution on the top and bottom walls. Additionally, covariance analysis is carried out in order to estimate the required number of temperatures during an experiment, on the top and bottom walls for the prediction of heat flux with a reasonable accuracy. The inverse model with covariance analysis is compared with the inverse model with PCA and both the methods are found to be equally potent.     

Study of heat and mass transfer in integrated thermal management controller (ITMC) employed in waste heat recovery application

In the waste heat recovery process, heat source temperature control and thermal management are always required to ensure safety and high efficiency of the waste heat recovery system. To this aim, the conventional method is to establish a series of independent heat transfer units and adopt a complex control strategy, which makes the system very complex and only applicable for a specific object. The concept of “integrated thermal management controller” (ITMC) is presented in this work to provide a novel method to solve the above problems. A two-dimensional heat and mass transfer model is developed to analyze and predict the operation performance of the ITMC. The numerical analysis indicates good heat source temperature control and thermal management performance of the ITMC. In addition, an experimental prototype is established, and test data are presented, which agree well with the numerical results and verify the correctness of the model.     

AN INPUT ESTIMATION APPROACH TO ON-LINE TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEMS

Abstract

An on-line methodology to solve two-dimensional inverse heat conduction problems (IHCP) is presented. A new input estimation approach based on the Kalman filtering technique is developed to estimate the two separate unknown heat flux inputs on the two boundaries in real time. A recursive relation between the observed value of the residual sequence with unknown heat flux and the theoretical residual sequence of the Kalman filter that assumes known heat flux is formulated. A real-time least-squares algorithm is derived that uses the residual innovation sequence to compute the magnitude of heat flux. This recursive approach facilitates practical implementation, and its capabilities are demonstrated in several typical cases with discontinuous and time-varying heat flux inputs.     

Lattice Boltzmann simulation of non-Fourier heat conduction with phase change

The lattice Boltzmann method (LBM) combined with the enthalpy method is a very effective method to solve the solid–liquid phase transition problem. However, when the heat flux is very high or the time of the process is in the same order of magnitude as the relaxation time, it is necessary to consider the non-Fourier effect in heat conduction. At this time, whether the LBM-BGK format based on Bhatnagar-Gross-Krook (BGK) approximation is still valid remains to be discussed. In this paper, the hyperbolic lattice Boltzmann method (HLBM) is combined with the enthalpy method to solve the non-Fourier solid–liquid phase change problem. By solving the non-Fourier heat conduction problem and the Fourier solid–liquid phase change problem, the numerical solution is compared with the analytical solution to verify the accuracy of the algorithm. The effect of different relaxation times on the solid–liquid phase transition is analyzed. In addition, the effect of changes in thermal diffusivity due to state changes on the non-Fourier solid–liquid phase transition is discussed.     

Version étendue du filtre de Kalman discret appliquée à un problème inverse de conduction de chaleur non linéaire

An extended version of the discrete Kalman filter applied to a nonlinear inverse heat conduction problem. A nonlinear inverse heat conduction problem is resolved by using a formulation of the Kalman filter based on a statistical approach and extended to nonlinear systems. The time evolution of a surface heat flux density is reconstructed from a numerical simulation which allowed us to analyse the influence of some parameters, that condition the running of the filter, on the estimation result. A suitable choice of these parameters, guided by the filter behaviour observations, leads to a solution that remains stable when using noisy data, but that is slightly time-lagged compared to the exact function. This time-lag depends on the location of the interior temperature measurement needed for the inversion and on the model error caused by the approximation of the heat flux with a piece-wise constant function. The application of the extended Kalman filter with real measurements recorded from an experimental set-up, shows that this technique fits the stochastic structure of experimental measurements. The provided results are validated by using the Raynaud's and Bransier's inverse method and are in good agreement with the heat flux density estimated with this method.     

Estimation of heat flux and temperature distributions in a composite strip and homogeneous foundation

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 and temperature distributions for the system composed of a multi-layer composite strip and semi-infinite foundation, from the knowledge of temperature measurements taken within the strip. 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. Results show that an excellent estimation on the time-dependent heat flux can be obtained for the test case considered in this study.     

Estimation of heat flux imposed on the rake face of a cutting tool: A nonlinear,complex geometry inverse heat conduction case study

In this paper the sequential function specification method is used to estimate the transient heat flux imposed on the rake face of a cutting tool during the cutting operation with two different assumptions. In one of them the thermal conductivity is taken to be constant, and in the other one it varies with temperature. The cutting tool is modeled as a three dimensional object. The capabilities of the geometric modeling, mesh generation as well as solver of the commercial software ANSYS are utilized in order to reduce the time expended for modeling and direct heat conduction solution, in both linear and nonlinear problems. This way the inverse heat conduction algorithm employs ANSYS as a subprogram through the ANSYS Parametric Design Language (APDL). The stability as well as accuracy is compared for cases of linear and nonlinear heat conductions. The effect of nonlinearity, as well as different sensor locations is investigated in order to arrive at an optimal experimental procedure. Finally, a typical temperature data during the working condition are used to recover the heat flux at the cutting tool surface using linear as well as nonlinear solutions.     

Estimation of a Location- and Time-Dependent High-Magnitude Heat Flux in a Heat Conduction Problem Using the Kalman Filter and the Approximation Error Model

This paper aims to estimate a location- and time-dependent high-magnitude heat flux in a heat conduction problem. The heat flux is applied on a small region of a surface of a flat plate, while transient temperature measurements are taken on the opposite surface. This inverse problem is solved using the Kalman filter and a reduced forward model, obtained by simplifications of a three-dimensional and nonlinear heat conduction problem. To deal with the modeling errors of this reduced model, the Approximation Error Model is used. The results show that excellent estimates can be obtained at feasible computational times.