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

Abstract

Abstract. 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.

Reduced Order Models for conduction and radiation inside semi-transparent media via the Modal Identification Method

“…The MIM also requires the knowledge of the local governing equations. In the MIM approach, the ROM equations may also be written down using a Galerkin projection [10], [12] but only the form of these equations is important. The components of the ROM constitutive elements are not computed using their literal expressions like in POD-Galerkin, they are identified through a parameter estimation problem corresponding to the minimization of a quadratic functional based on the difference between reference output data, on the one hand, and on the ROM outputs corresponding to the same inputs, on the other hand [8].…”

“…As an example, real time thermal regulation within 0.01°C of an ultra-high precision metrology system was successfully performed by model predictive control using in-situ built ROMs [11]. MIM has also been used to build ROMs for non-isothermal flows, for instance a 2D laminar mixed convection flow around a heated circular cylinder [12]. In the frame of characterization of melted polymer flows, a thermo-rheological ROM for a pseudo-plastic fluid flow in a circular runner, taking into account transport, conduction and heat dissipation due to viscous effects in high shear zones, was developed in [13].…”

“…[9] [10][11] [12] [13]. The MIM consists of three main steps:1) Defining the structure of the ROM equations able to adequately describe the involved physics (see section 4);…”

Reduced order model of a two-phase loop thermosyphon by modal identification method

“…for computing a 2D incompressible steady laminar flow over a backward-facing step and associated unsteady forced heat convection. A 2D laminar mixed convection flow around a heated circular cylinder has also been studied in [27]. More recently, ROMs built by MIM from in-situ measurements have been used for efficient handling of real time state feedback control of Multi-Input-Multi-Output thermal systems.…”

Thermo-rheological reduced order models for non-Newtonian fluid flows with power-law viscosity via the modal identification method

“…The present paper is a follow-up of our previous work on model reduction for generalized Newtonian fluids [14], where references to other existing model reduction methods (many of them having not been yet applied to non-Newtonian fluid flows) can be found. In the present work, the Modal Identification Method (MIM) [14] [15] [16] [17] [18] [19] is used to build ROMs. As in many model reduction methods, each variable field (e.g.…”