Jean-Luc Battaglia

Solving an inverse heat conduction problem using a non-integer identified model

Abstract An inverse heat conduction problem in a system is solved using a non-integer identified model as the direct model for the estimation procedure. This method is efficient when some governing parameters of the heat transfer equations, such as thermal conductivity or thermal resistance, are not known precisely. Reliability of the inversion depends on the precision of the identified model. From considerations on the analytical solutions in simple cases and on the definition of non-integer (or fractional) derivative, the non-integer model appears to be the most adapted. However, some experiments do need to be carried out on the physical thermal system before it can be identified. An application that consists in estimating the heat flux in a turning tool insert during machining is presented. First, identification is performed using a specific apparatus that permits a simultaneous measurement of temperature and heat flux in the insert. Then, during machining, heat flux can be estimated from temperature using this identified model.

Estimation of heat flux and temperature in a tool during turning

The heat flux and the temperature at the tip of a tool used in a turning process are estimated from temperature measurements in an interior point of the tool insert. Instead of using a classical direct model of the transient thermal behaviour of the tool, two models that express the heat flux and the temperature at the tip of the insert according to the interior temperature are identified. These models are expressed in a recursive transfer function form. The identification of the parameters in the two models has been performed for a specific apparatus that permits controlling the heat flux and the temperature at the tip of the insert. In a second stage, the inverse heat conduction problem in the tool is solved both using an exact matching method, a sequential function specification method and a sequential regularization method in order to identify the heat flux and the temperature during a turning process.

A modal approach to solve inverse heat conduction problems

A method that greatly improves the stability of the IHCP solution is presented. The two principal features of the method are first that the same time step is used to solve the direct and inverse problems. Secondly, the direct model is designed in order to lead to the best estimation according to the location of the sensors. The method is based on the decomposition of the dynamic part of the thermal field on the modal basis of the heat diffusion operator. The stability of the solution is improved by eliminating the modes whose time constants are smaller than the lag time; that is the time of diffusion from the heated surface to the nearest sensor. An interesting consequence is that the reduced model requires less computation time than the complete one in a sequential estimation procedure.

Transient Heat Flux Measurements in High Enthalpy Air Plasma Flows Using a Non-Integer System Identification Approach

Recent results of the adaption of the non-integer system identification (Nisi) approach for heat flux measurements are reported. An advanced sensor design has been applied to the plasma windtunnel facilities at Institut fur Raumfahrtsysteme (IRS). It is shown that the previously published advantages of the new approach hold for the high enthalpy environment of these facilities. The sensor in use was calibrated prior to its operation at IRS using laser radiation. From these calibration measurements performed at Trefle Laboratory in Bordeaux, France, the impulse response is calculated which fully identifies the thermal behavior of the sensor. As a conclusion, further improvement is seen in the use of shielded thermocouples which avoids an impact of the electromagnetic noise of the plasma generator on the sensor signal.

Temperature-dependent thermal characterization of Ge2Sb2Te5 and related interfaces by the photothermal radiometry technique

The thermal conductivity of Ge2Sb2Te5 (GST) layers, as well as the thermal boundary resistance at the interface between the GST and amorphous SiO2, were measured using a PhotoThermal Radiometry experiment. The two phase-changes of the Ge2Sb2Te5 were retrieved, starting from the amorphous and sweeping to the fcc crystalline state at 130 °C and then to the hcp crystalline state at 310 °C. The thermal conductivity resulted to be constant in the amorphous phase, whereas it evolved between the two crystalline states. The thermal boundary resistance at the GST-SiO2 interface was estimated to be higher for the hcp phase than for the amorphous and fcc ones.

Thermal diffusivity of a metallic thin layer using the time-domain thermo reflectance technique

The time domain thermo reflectance (TDTR) is widely used in the field of acoustic and thermal characterization of thin layers at the nano and micro scale. In this paper, we propose to derive a simple analytical expression of the thermal diffusivity of the layer. This relation is based on the analytical solution of one-dimensional heat transfer in the medium using integral transforms. For metals, the two-temperature model shows that the capacitance effect at the short times is essentially governed by the electronic contribution.