Heat flux identification using reduced model and the adjoint method. Application to a brake disk rotating at variable velocity

International audienceIn previous works [1], reduced models have been used for solving inverse problems, characterized by a complex geometry requiring a large number of nodes and / or an objective of online identification. The treated application was a brake disc in two-dimensional representation, in rotation at variable speed. The dissipated heat flux at the pad-disk interface had been identified by Beck's method. We present here a similar application using the adjoint method. The modal reduction is done by using special bases (called branch bases) that offer the advantage of dealing with nonlinear problems and / or unsteady parameters. Adjoint method provides particularly accurate results in this configuration

Réduction de modèle par identification en convection forcée pour des systèmes soumis à des conditions aux limites thermiques instationnaires : application à l'écoulement le long d'une marche avec contrôle thermique par retour d'état

The numerical work described in this thesis deals with model reduction in the field of heat transfer and fluid mechanics. The reduced models being solved rapidly, they can be coupled with some optimal algorithms. The construction of reduced models is performed based on the Modal Identification Method (MIM) that has been developed in our laboratory for many years. This method is based on the state representation under a modal form. The reduced model is identified through the minimization of a function containing the parameters of the model and based on the difference between the outputs of a detailed model and those of a reduced one. An application is proposed dealing on a flow over a backward-facing step, with a time-varying heat flux density applied upstream of the step. Reduction modelling leads to important reduction of simulation times, still while maintaining a very good accuracy. We then propose an approach combining the theory of optimal control with the model obtained by the MIM. This approach is used to find, on-line, the fluxes applied upstream the step such that the obtained temperature stays as close as possible to the set point.Les travaux numériques décrits dans ce mémoire portent sur la réduction de modèle dans le domaine de la thermique et de la mécanique des fluides. Ces modèles réduits étant rapides en temps d'exécution, ils permettent la mise en place d'algorithmes de contrôle optimal. La construction des modèles réduits est réalisée à partir de la Méthode d'Identification Modale (MIM) développée au laboratoire depuis de nombreuses années. Cette méthode s'appuie sur la représentation d'état sous forme modale : le modèle réduit est identifié à travers la minimisation d'une fonctionnelle comprenant les paramètres du modèle et basée sur l'écart entre les réponses du modèle détaillé et celles du modèle réduit. Une application est proposée sur un écoulement le long d'une marche descendante, avec un flux de chauffage intervenant en amont de la marche. On montre comment on peut réduire de façon importante les temps de simulation, tout en gardant une très bonne précision. Sur cette application, nous proposons également une approche combinant la théorie de la commande optimale avec les modèles réduits obtenus par la MIM. Cette approche est utilisée pour trouver une loi de commande en flux permettant de maintenir un profil de température proche d'une consigne dans l'écoulement en aval de la marche

On the use of reduced models obtained through identification for feedback optimal control problems in a heat convection–diffusion problem

International audienceThis paper deals with the use of reduced models for solving some optimal control problems. More precisely, the reduced model is obtained through the modal identification method. The test case which the algorithms is tested on is based on the flow over a backward-facing step. Though the reduction for the velocity fields for different Reynolds numbers is treated elsewhere [1], only the convection–diffusion equation for the energy problem is treated here. The model reduction is obtained through the solution of a gradient-type optimization problem where the objective function gradient is computed through the adjoint-state method. The obtained reduced models are validated before being coupled to optimal control algorithms. In this paper the feedback optimal control problem is considered. A Riccati equation is solved along with the Kalman gain equation. Additionally, a Kalman filter is performed to reconstruct the reduced state through previous and actual measurements. The numerical test case shows the ability of the proposed approach to control systems through the use of reduced models obtained by the modal identification method

Réduction de modèle par identification en convection forcée pour des systèmes soumis à des conditions aux limites thermiques instationnaires (application à l'écoulement le long d'une marche avec contrôle thermique par retour d'état)

Les travaux numériques décrits dans ce mémoire portent sur la réduction de modèle dans le domaine de la thermique et de la mécanique des fluides. Ces modèles réduits étant rapides en temps d'exécution, ils permettent la mise en place d'algorithmes de contrôle optimal. La construction des Modèles Réduits est réalisée à partir de la Méthode d Identification Modale (MIM) développée au laboratoire depuis de nombreuses années. Cette méthode s'appuie sur la représentation d'état sous forme modale : le modèle réduit est identifié à travers la minimisation d'une fonctionnelle comprenant les paramètres du modèle et basée sur l'écart entre les réponses du modèle détaillé et celles du modèle réduit. Une application est proposée sur un écoulement le long d'une marche descendante, avec un flux de chauffage intervenant en amont de la marche. On montre comment on peut réduire de façon importante les temps de simulation, tout en gardant une très bonne précision. Sur cette application, nous proposons également une approche combinant la théorie de la commande optimale avec les modèles réduits obtenus par la MIM. Cette approche est utilisée pour trouver une loi de commande en flux permettant de maintenir un profil de température proche d'une consigne dans l'écoulement en aval de la marche.The numerical work described in this thesis deals with model reduction in the field of heat transfer and fluid mechanics. The Reduced Models being solved rapidly, they can be coupled with some optimal control algorithms. The construction of Reduced Models is performed based on the Modal Identification Method (MIM) that has been developed in our laboratory for many years. This method is based on the state representation under a modal form. The reduced model is identified through the minimization of a function containing the parameters of the model and based on the difference between the outputs of a detailed model and those of a reduced one. An application is proposed dealing on a flow over a backward-facing step, with a time-varying heat flux density applied upstream of the step. Reduction modelling leads to important reduction of simulation times, still while maintaining a very good accuracy. When then propose an approach combining the theory of optimal control with the model obtained by the MIM. This approach is used to find, on-line, the fluxes applied upstream the step such that obtained temperature stays as close as possible to the set point.POITIERS-BU Sciences (861942102) / SudocSudocFranceF

Fluid temperature distribution inside a flat mini-channel: Semi-analytical wall transfer functions and estimation from temperatures of external faces

International audienceModelling fluid flow and heat transfer inside a mini- or micro-channel constitutes a challenge because it requires taking into account many effects that do not occur in traditional macrostructured systems. A semi-analytical heat transfer model that takes into account conduction and advection in the fluid as well as conduction in the solid walls (conjugate heat transfer) of a flat mini-channel is first derived and verified. It is based on Fourier transforms of the temperature and normal flux in the direction of the Poiseuille flow. It allows to relate its bulk temperature Tb(x) to external surface sources by two transfer functions without the use of any internal heat transfer coefficient distribution, whatever the location of these sources. The second part of the paper is devoted to the use of this model in an inverse way, that is to retrieve the Tb(x) distribution starting from the additional observation of the noised synthetic temperature profiles over the external faces of both walls of the channel. Estimations of the average velocity and of the external heat transfer coefficient are first implemented. The temperature and flux distributions over the internal faces of the walls are estimated by an inverse method then, before a reconstruction of the internal bulk temperature profile

INVERSE PROBLEM OF FLUID TEMPERATURE ESTIMATION INSIDE A FLAT MINI-CHANNEL STARTING FROM TEMPERATURE MEASUREMENTS OVER ITS EXTERNAL WALLS

International audienceModelling fluid flow and heat transfer inside a mini-or micro-channel constitutes a challenge because it requires taking into account many effects that do not occur in traditional macrostructured systems. In a mini-channel, presence of solid walls, whose volume fraction is not negligible, modifies heat diffusion (conjugated heat transfer): this means that traditional Nusselt correlations for forced convection have to be revisited, because the heat flux distribution at the wall is not always normal to it and the location of the heat source modifies the distribution of the heat transfer coefficient in the flow direction. Our objective is to characterize the mean velocity U and the heat transfer coefficient of external exchange h and to describe the bulk temperature distribution T b (x). The inverse method makes it possible to go back to this information starting from measurement of the temperature fields on the two external faces of the channel and a corresponding model through the minimization of a criterion. In this work, the temperature fields can be obtained either by a numerical model or by an experimental model by infrared thermography. Before an experimental validation by infrared thermography, we perform numerical simulations and a sensitivity analysis of the external temperature fields to the mean flow velocity U and to the external heat transfer coefficient h. The temperature and flux distributions over the internal faces of the walls are estimated by an inverse method then

Heat flux identification using reduced model and the adjoint method. Application to a brake disk rotating at variable velocity

International audienceIn previous works [1], reduced models have been used for solving inverse problems, characterized by a complex geometry requiring a large number of nodes and / or an objective of online identification. The treated application was a brake disc in two-dimensional representation, in rotation at variable speed. The dissipated heat flux at the pad-disk interface had been identified by Beck's method. We present here a similar application using the adjoint method. The modal reduction is done by using special bases (called branch bases) that offer the advantage of dealing with nonlinear problems and / or unsteady parameters. Adjoint method provides particularly accurate results in this configuration

Inverse convection in a flat mini-channel: towards estimation of fluid bulk temperature distribution with infrared thermography

International audienceThis study deals with the solution of an inverse problem in a flat mini-channel of of 1 mm thickness. At this scale, the difficulty is to introduce non-intrusive sensors. The sensors can modify the local flow and therefore the heat transfer. Our objective is to characterize the mean velocity U and the heat transfer coefficient of external exchange h in order to recover the bulk temperature distribution T b (x). The inverse method makes it possible to go back to this information starting from measurement of the temperature fields on the two external faces of the channel and from a corresponding model through the minimization of a least square criterion. In this work, the temperature fields can be obtained either by a numerical model or by infrared thermography. Before an experimental validation by infrared thermography, we perform numerical simulations and a sensitivity analysis of the external temperature fields to the mean flow velocity U and to the external heat transfer coefficient h. The temperature and flux distributions over the internal faces of the walls are estimated by an inverse method then

On-line indirect thermal measurement in a radiant furnace by a reduced modal model

International audienceWe propose an original method to recover the whole thermal field of a heated object on a furnace from a few measurement points. The radiant thermal source is first identified via a low order reduced model based on AROMM (Amalgam Reduced Order Modal Model) method. From this identified temperature, the thermal field is then recovered by direct simulation using a reduced model of higher order which leads to a better precision. This process is applied to a complex titanium object heated by two radiant panels placed in the furnace. From two measurement points, the temperature of the heated object is recovered on-line, with a mean error below 3K

Identification of radiant source in an enclosure by reduced model

International audienceAbstract We propose an original method to recover from a few measurement points the integrity of the temperature field of a furnace heated by a radiant thermal source. The radiant thermal source is first identified via a low order reduced model based on based on AROMM (Amalgam Reduced Order Modal Model) method which preserves the integrity of the geometry. The minimization is performed via a trust-region reflective least squares algorithm implemented in MATLAB “lsqcurvefit” function. From that identified heat flux, the integrity of the thermal field is then recovered by direct simulation thanks to a reduced model of higher rank to have a better precision. The treated application is a complex titanium piece heated by two radiant panels placed in a furnace. With four measuring points, the temperature of the whole thermal scene is retrieved at all times with an average error around 1 K on the studied object