Yvon Jarny

A General Optimization Method using Adjoint Equation for Solving Multidimensional Inverse Heat Conduction

Abstract A three-dimensional formulation is presented to solve inverse heat conduction as a general optimization problem by applying the adjoint equation approach coupled to the conjugate gradient algorithm. The formulation consists of the sensitivity problem, the adjoint problem and the gradient equations. A solution algorithm is presented for the estimation of the surface condition (i.e. heat flux or temperature), space dependent thermal conductivity and heat capacity from the knowledge of transient temperature recordings taken within the solid. In this approach, no a priori information is needed about the unknown function to be determined. It is shown that the problems involving a priori information about the unknown function become special cases of this general approach.

An inverse analysis to estimate linearly temperature dependent thermal conductivity components and heat capacity of an orthotropic medium

Abstract An inverse analysis is used to estimate linearly temperature dependent thermal conductivity components k x ( T ), k y ( T ) and specific heat capacity C ( T ) per unit volume for an orthotropic solid. Simulated measured transient temperature data are generated by adding random errors to the exact temperatures computed from the solution of the two-dimensional, direct transient heat conduction problem. An iterative procedure, based on minimizing a sum of squares function with the Levenberg-Marquardt iterative procedure is used to solve the inverse problem.

Estimation of thermal conductivity of thermoplastics under moulding conditions: an apparatus and an inverse algorithm

The thermal conductivity of thermoplastics is measured under moulding conditions (high pressure and high temperature). A specific apparatus has been designed and is described. A parameter estimation method is used for the experimental data processing. It is based on the resolution of a 1-D non-linear inverse conduction problem. The optimisation algorithm developed to solve the problem, is efficient and stable. Confidence intervals of the estimated parameters take into account errors both in the temperature measurements and in the parameters of the model. Heat capacity is estimated from calorimetric measurements, error analysis on the estimated conductivity is discussed, especially in the phase change interval. Numerical validation and experimental examples are presented.

Estimation of effective thermal conductivity tensor from composite microstructure images

The determination of the effective thermal properties of inhomogeneous materials is a long-standing problem of continuously interest. The impressive number of methods developed to measure or estimate the thermal properties of composite materials clearly exhibits the importance given to their knowledge. Homogenization models are a cheap way to determine or predict them. Many different approaches of homogenization were developed, but the last advances are credited to numerical methods. In this study, a new computational model is developed to estimate the 2D thermal conductivity tensor and the thermal main directions of a pure carbon/epoxy unidirectional composite. This tool is based on real composite microstructure.

Implementation of an inverse method for identification of reticulation kinetics from temperature measurements on a thick sample

Abstract The aim of this article is to identify a reaction function involved in a model of vulcanization by using experimental study on thick pieces of rubber. The methods of determination of the parameters of the model are described, the inverse method is explained, results are given and commented on.

Uniform Cooling and Part Warpage Reduction in Injection Molding Thanks to the Design of an Effective Cooling System

In this paper, a new methodology for the design of effective cooling system of thermoplastic injection tools is proposed. It is named MCOOL® for Morpho Cooling. It allows the design of the cooling channels in the mold with no a priori on the number, the size, the shape of the channels and the temperature of the coolant before performing the optimization. Numerical and experimental results obtained on a mold manufactured thanks to this methodology are compared with those coming from a conventional design. The criteria used to discriminate the results are based on the uniformity of the temperature field in the molded part and on the final warpage of the part.

Estimation Of Rheological Law By Inverse Method From Flow And Temperature Measurements With An Extrusion Die

Simulation quality is determined by the knowledge of the parameters of the model. Yet the rheological models for polymer are often not very accurate, since the viscosity measurements are made under approximations as homogeneous temperature and empirical corrections as Bagley one. Furthermore rheological behaviors are often traduced by mathematical laws as the Cross or the Carreau‐Yasuda ones, whose parameters are fitted from viscosity values, obtained with corrected experimental data, and not appropriate for each polymer. To correct these defaults, a table‐like rheological model is proposed. This choice makes easier the estimation of model parameters, since each parameter has the same order of magnitude. As the mathematical shape of the model is not imposed, the estimation process is appropriate for each polymer. The proposed method consists in minimizing the quadratic norm of the difference between calculated variables and measured data. In this study an extrusion die is simulated, in order to provide us...

Estimation of the initial temperature field during cooling of a 1-d three layer body

A method is developed to determine the initial spatial distribution T 0(x) of the temperature field in the central layer of a body from temperature measurement histories recorded in both side layers of the same body. The resolution of this inverse heat conduction problem is based on the minimization of a L-S criterion by using conjugate gradient algorithms. The practical case involving non perfect thermal conditions between the layers is analyzed.

Inverse method for the cooling system design in injection moulding – application to a ‘T-shaped’ piece

The designing of the cooling channels in the thermoplastic injection process is one of the most important steps during mould design. Indeed, inappropriate cooling will lead to defects in the piece and a low production rate. In this paper, a new approach for the design of cooling channels is presented. Based on morphological concepts, the idea of regulation by cooling surface is considered. The first part of the methodology leads to the optimal determination of fluid temperature distribution along the cooling surface in order to minimise a cost function composed of two terms linked to the quality of the piece and the productivity of the process. The conjugate gradient algorithm coupled with a Lagrangian approach is implemented for the determination of the optimal fluid temperature distribution. The method is applied to design the cooling system of a ‘T-shaped’ piece, and numerical results are then compared with those available in the literature for the same piece shape and the same injection moulding conditions.

Methodology for the Design of Cooling Channels in Thermoplastic Injection Moulding Process

Injection is one of the most used processes to manufacture thermoplastic parts. The design of the cooling channels in this process is of great importance during the mould design. Indeed, an inappropriate cooling will lead to defects in the part and a low production rate. In this paper, a new approach for the design of the cooling channels is assessed. Based on morphological concepts, the idea of regulation by cooling surface is introduced. The thermal behaviour of the mould can be restricted on the spatial domain delimited by the cooling surface on which a spatial temperature distribution is imposed. The first step of the methodology leads to the optimal determination of the fluid temperature distribution along the cooling surface in order to minimize a cost function composed of two terms linked to the quality of the part and the productivity of the process. The conjugate gradient algorithm coupled with a Lagrangian technique is implemented for the determination of fluid temperature parameters. However, the obtained solution is not workable in practice. The second step consists then in building real channels from this optimal distribution. The shape, location and fluid temperature level of these channels are determined a posteriori from the thermal analysis of the temperature field in the mould domain located between the plastic part and the cooling surface. Channels are builded by using the contours of isotherms in the thermal steady-state area of the mould. It becomes then possible to design the cooling channels with no a priori on the numbers, the location of these channels and on the temperature of the coolant fluid. The methodology is first illustrated with a 2D part. Results are compared with literature.Copyright