Inverse Heat Transfer Procedure Research Articles

Inverse method for simultaneously estimating multi-parameters of heat flux and of temperature-dependent thermal conductivities inside melting furnaces

The purpose of this study is to predict the time-varying protective bank that coats the internal surface of the refractory brick walls of a melting furnace. An inverse heat transfer procedure is presented for predicting simultaneously operating and thermal parameters of a melting furnace. These parameters are the external heat transfer coefficient, the thermal conductivity of the phase change material (PCM) and the time-varying heat load of the furnace. Once these parameters are estimated, the time-varying protective PCM bank can be predicted. The melting and solidification of the PCM is modeled with the enthalpy method. The inverse problem is handled with the Levenberg-Marquardt Method (LMM) combined to the Broyden method (BM). The models are validated and the effect of the position of the temperature sensor embedded in the furnace wall, of the data capture frequency and of the measurement noise, is investigated. A statistical analysis for the parameter estimation is also carried out. Analysis of the results yielded recommendations concerning the location of the embedded sensor and the data capture frequency.

Solution of inverse radiation-conduction problems using a Kalman filter coupled with the recursive least–square estimator

This paper presents a non–intrusive inverse heat transfer procedure for predicting the time–varying heat flux on the surface of semitransparent media. Inverse radiation–conduction problems were analyzed using a Kalman filter coupled with a recursive least–square estimator (KF–RLSE). Since its unique capability to make fast predictions, KF–RLSE can be easily integrated to existing real–time control systems of industrial facilities. The performance of KF–RLSE was examined thoroughly in a series of numerical simulations in two semitransparent materials (i.e. the glass with black coating and the ceramic of zirconium dioxide ZrO2) to extract the time–varying surface heat flux on–line from the measured temperature history at boundary. Results showed that the proposed method can predict the unknown boundary flux with an acceptable error. The influence of different parameters on the accuracy and stability of the predicted heat flux was also investigated. Results indicated that the sensor location, process noise covariance and absorption coefficient exerted stronger effects on retrieval results compared with other parameters.

An inverse heat transfer method for predicting the thermal characteristics of a molten material reactor

An inverse heat transfer procedure is presented for predicting the time-varying thickness of the protective bank that covers the lining of the refractory brick walls of a molten material reactor. The inverse method predicts simultaneously influential thermo-physical properties of the reactor such as the thermal conductivity of the refractory brick wall, the thermal conductivity of the solid and of the liquid layers of the phase change material, and the time-varying reactor heat load. The inverse method rests on the Levenberg-Marquardt Method (LMM) combined with the Broyden method (BM). The effect (1) of the initial guesses for the unknown LMM polynomial parameters, (2) of the noise on the recorded temperature data, (3) of the location of the temperature sensors embedded into the brick wall and (4) of the number of recorded temperature data on the inverse predictions is investigated. Recommendations are then made concerning the installation and the operation of the temperature sensors.

An Effective Inverse Heat Transfer Procedure Based on Evolutionary Algorithms to Determine Cooling Conditions of a Steel Continuous Casting Machine

The inverse modeling of heat transfer is a useful tool in analyzing contact heat transfer at the ingot surfaces during the continuous casting process. The determination of the boundary conditions involves an experimental work consisting in the evaluation of the thermal history, generally at the casting surface, experimentally provided by infrared pyrometers. Additionally, numerical simulations, based on the solution of the 2D transient heat conduction equation, are performed in order to be inversely solved in response to the measured thermal data furnished by the sensor. Due to computational time consumption during simulations in searching cooling conditions, this work proposes an interaction between natural inspired algorithms, called evolutionary algorithms, and the numerical model in order to speed up the searching process. The present work aims to compare three algorithms, namely genetic algorithm, improved stochastic ranking evolutionary strategy, and evolutionary strategy with Cauchy distribution. The latter develops a metaheuristic version of an evolutionary strategy workflow, using a Cauchy random number function to generate each individual, instead of the usual uniform distribution function available in almost all programming languages. The surface temperature, solid shell, and molten pool profiles from the determined cooling conditions are analyzed in terms of casting quality.

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.

Heat transfer measurements in a supersonic wind tunnel through inverse temperature data reduction: application to a backward facing step

An inverse heat transfer data reduction method is presented, which allows performing quantitative heat transfer measurements using pre-heated models in a blow-down supersonic wind tunnel. The flow under investigation is a backward-facing step (BFS) at Mach 3. Temperature measurements are performed by means of infrared thermography. The inverse heat transfer procedure is used to calculate the surface heat flux from the measured surface temperature in time by taking into account multi-dimensional and unsteady conduction effects. The robustness and sensitivity of the data reduction algorithm is assessed using synthetic experiments where aspects such as measurement noise, calibration errors, conductivity errors, etc. are addressed. The BFS flow is investigated for laminar, transitional and turbulent-separating boundary layers. It is found that for the laminar and transitional cases, the Stanton number and normalized separation length are influenced by the step height. For turbulent separation, this is only marginally the case; however the Stanton number downstream of reattachment increases with step height. For the transitional separation, large heat transfer peaks are measured at reattachment, of magnitude up to twice the reference values for a developed turbulent boundary layer.

Prediction of the ledge thickness inside a high-temperature metallurgical reactor using a virtual sensor

A non-intrusive inverse heat transfer procedure for predicting the time-varying thickness of the phase-change ledge on the inner surface of the walls of a high-temperature metallurgical reactor is presented. An extended Kalman filter with augmented state is coupled with a nonlinear state-space model of the reactor in order to estimate on-line the position of the phase front. The data are collected by a heat flux sensor located inside or outside of the reactor wall. This non-intrusive method can be seen as a virtual sensor which is defined as the combination of an estimation algorithm with measurements for the estimation of 'hard to measure' on-line process variables. The inverse prediction of the ledge thickness with the virtual sensor is thoroughly tested for typical operating conditions that prevail inside an industrial facility. Due to the fact that the melting/solidification process inside the reactor is highly nonlinear, results show that the accuracy of the state-space identification and the virtual sensor estimation is far superior when a nonlinear state-space model and the extended Kalman filter are employed, as opposed to a linear state-space model and the classic Kalman filter. In the former, it is shown that the discrepancy between the exact and the estimated ledge thickness remains smaller than 10% at all times.

An unscented Kalman filter inverse heat transfer method for the prediction of the ledge thickness inside high-temperature metallurgical reactors

A non-intrusive inverse heat transfer procedure for predicting the time-varying thickness 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 a heat flux sensor embedded in the reactor wall. The virtual sensor comprises a state observer (Kalman filter) coupled to a state-space model of the reactor. Three different virtual sensors are thoroughly tested: (1) an unscented Kalman filter with a nonlinear state-space model, (2) an extended Kalman filter with a nonlinear state-space model, and (3) a linear Kalman filter with a linear state-space model. Results show that the virtual sensor composed of the unscented Kalman filter yields the best results for the operating conditions that prevail inside industrial facilities. Its predictions are more accurate than that of the linear Kalman filter, more stable than that of the extended Kalman filter, and its CPU time requirement is comparable to that of the other sensors.

Determination of Thermal Conductivity of Mn-Al Powder Compacts using An Inverse Heat Transfer Procedure

AbstractThe effective thermal conductivities of various Mn-Al powder compact compositions were measured using an Inverse Heat Transfer Procedure, and extensive validation work was also carried out. Specially fabricated cylindrical compact specimens were used equipped with two thermocouples at strategic locations. The porosity of these specimens was also measured.The estimated effective thermal conductivities of various Mn-Al compacts were in the range of 5.5 to 10.5 W m−1 °C−1, which are much lower than that of Al (237 W m−1 °C−1), and close to that of Mn (7.8 W m−1 °C−1). The effective thermal conductivities of Mn-Al powder compacts decreased with an increase in the compact's Mn composition and porosity. Within the examined temperature range of 250 to 600 °C, the effect of temperature on the effective thermal conductivity was minimal. A purely theoretically derived prediction of Mn-Al compact thermal conductivity is substantially higher than the estimates of using the IHTP.

Control of the ledge thickness in high-temperature metallurgical reactors using a virtual sensor

A non-intrusive inverse heat transfer procedure for predicting the time-varying thickness of the phase change ledge on the inside surface of the walls of a high-temperature metallurgical reactor is presented. A Kalman filter, based on a state-space representation of the reactor, is coupled with a recursive least-square estimator in order to estimate online the position of the phase front. The data are collected by a heat flux sensor located inside or outside of the reactor wall. The inverse method, used here as a virtual sensor, is coupled to a classic proportional–integral controller in order to control the ledge thickness by regulating the air cooling applied on the outside surface of the reactor wall. The virtual sensor and the control strategy are thoroughly tested for typical phase change conditions that prevail inside industrial facilities. Results show that a virtual sensor that relies on a heat flux sensor embedded inside the reactor wall provides more accurate and stable information, but at a price of a more complicated installation. In that case, it is shown that the discrepancy between the exact and the estimated ledge thicknesses remains smaller than 3% at all times, and that the control strategy ensures a null steady-state tracking error, a maximum tracking error less than 10%, no overshoot and no significant time lag.

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.

Comparisons of the Effects of Air and Helium on Heat Transfer at the Metal-Mold Interface

The effect of helium on heat transfer at the metal-mold interface was studied using a unique casting apparatus. Temperature, as well as displacement, measurements were carried out. The heat-transfer coefficient (HTC) at the metal-mold interface was deduced using an inverse heat-transfer procedure. Comparisons of heat-transfer characteristics were made between aluminum-based alloys solidified with and without helium at the metal-mold interface. These comparisons indicated that the onset of the metal-mold gap developed faster under helium conditions than without helium. The time decrease for the onset of the metal-mold gap with and without helium conditions can be as large as 34 pct. In addition, the average heat-transfer coefficient, from the beginning of the casting until the onset of the metal-mold gap, was higher by as much as 48 pct in the castings using helium compared to castings without the use of helium. The impact of helium on heat transfer relative to air was found to be largest with higher mold roughness. Equations were developed from the onset of the metal-mold gap, which relate the HTC against the size of the gap. These equations had the form $$ h\, = \,\frac{1} {{a*G\, + \,b}}\, + \,c $$ . It was also found that at the onset of metal-mold gap, the rate of the heat-transfer coefficient decrease is higher at the early stages of gap development than at the later stages of gap formation.