Manuel Girault

Comparison of Two Nonlinear Model Reduction Techniques: The Modal Identification Method and the Branch Eigenmodes Reduction Method

This article shows the comparison of two modal reduction techniques, the modal identification method and the branch eigenmodes reduction method. The objective of these methods is to reduce the number of states representing the system evolution in order to decrease the computational time necessary for the simulation. After a presentation of both techniques, a comparison is made on a 3-D nonlinear transient thermal diffusive system. Results given by the two reduced models are compared to those given by the detailed model. The accuracy of both reduced models, as well as the gain in computational time, are analyzed for each configuration.

The Use of Model Reduction and Function Decomposition for Identifying Boundary Conditions of A Linear Thermal System

This numerical study deals with the identification of space and time varying inputs applied to a linear diffusive thermal system. Such an Inverse Heat Conduction Problem (IHCP) is ill-posed, its resolution is difficult for a large amount of unknowns and requires large memory size and computing time for multidimensional cases. Consequently, we propose a procedure to reduce both the number of unknowns and the model order. A 2D example is presented, with a heat flux density φ(y,t) to be identified from simulated transient temperature measurements. Starting from a Classical Detailed Model (CDM), two steps are performed. Firstly, a decomposition of the spatial distribution of φ on a functions basis leads to a small number of unknowns. Secondly, a Reduced Model (RM) is built using the Modal Identification Method. When RM is used to solve the inverse problem instead of CDM, computing time is drastically reduced (up to a factor 1000) whilst preserving accuracy. A procedure to determine the number of unknown coefficients is proposed. The inversion algorithm is sequential and requires no iterations. Future time steps with a function specification are used as a regularisation procedure. Tikhonovs regularisation is needed with CDM but not with RM.

Reduced Order Modeling by Modal Identification Method and POD-Galerkin approach of the heated circular cylinder wake in mixed convection

When dealing with control of thermal systems, the first step in the design of a model-based controller is the development of a model which accurately captures heat transfer dynamics. Classical high-fidelity models directly derived from the application of conservation laws on the discretized space domain, lead to sets of Ordinary Differential Equations in time whose size is usually too huge for practical implementation of real-time control. A variety of techniques have been developed for building low order models, involving a small number of degrees of freedom compared to high-fidelity models. Here, we focus on two approaches: Modal Identification Method, mainly used in heat transfer, and a POD-Galerkin method, based on Proper Orthogonal Decomposition and traditionally employed in fluid mechanics. The objective of this work is to compare on a simple 2D mixed convection problem, the accuracy of the reduced order models derived by both methods for describing the flow dynamics. Results are presented for the heated circular cylinder wake at a Reynolds number equal to 200 and a Richardson number equal to 2. Velocity and temperature fields at different time instants, computed with a reference Finite Element model, are used as data for both approaches.

Parametric low-order models in transient heat diffusion by MIM. Estimation of thermal conductivity in a 2D slab

Classical modeling methods based on spatial discretization of local governing equations lead to fine meshes, resulting in large size models which require huge computing times. In applications such as on-line inverse or real-time feedback control problems, this issue becomes crucial. Several techniques have been developed for building low-order models, involving a smaller set of equations and able to reproduce the thermal behavior of a reference large-size model or an actual system, whatever the time-varying boundary conditions and/or heat source terms, or for a range of values of a thermophysical parameter. But low-order models able to mimic heat transfer dynamics for both a time-varying thermal load and a physical parameter range are not frequently encountered. Such a problem is addressed here, through an extension of the Modal Identification Method. The approach is illustrated on a simple linear 2D transient heat diffusion problem, with a time-varying heat flux density applied on one side and a thermal conductivity in the 15 to 45 W.m−1.K−1 range. The low-order model is used for the estimation of the thermal conductivity from the knowledge of both the applied heat flux and a simulated transient temperature measurement on the opposite side. The approach remains valid for 3D cases in complex geometries involving more independent thermal loads.

Identification of velocity distribution in a turbulent flow inside parallel-plate ducts from wall temperature measurements

An Inverse Heat Convection Problem is investigated in this numerical study. Turbulent forced convection is considered, with a hydrodynamically fully developed, thermally developing, incompressible, constant property flow inside a parallel-plate duct. Velocity and effective diffusivity distributions of the turbulent model are characterised by a Reynolds number b + based on the shear stress velocity. The identification of b + from simulated wall temperature measurements is presented. A heat flux density is applied along the channel length and temperature responses are taken at the wall external surface. Heat transfer has to act as a small but measurable perturbation of the flow. The inverse problem is recast into an optimisation problem solved with a Quasi-Newton method. Reynolds numbers 105 and 106, corresponding to two different values of b + , are considered. Effects of sensor number and location, as well as magnitude of measurement error on the estimation accuracy, are examined.