Proper Orthogonal Decomposition

... the exclusive use of linear aerodynamic theories for predicting the unsteady aerodynamic forces. ... Because of this computational cost, the potential of CFD-based nonlinear aeroelastic codes ... possible however to address this limitation with the use of reduced-order models (ROMs ...

In this study, a channel with a cavity heated from below is numerically investigated for the mixed convection case for a range of Richardson numbers (Ri=0.1, 1, 5, 10, 15 and 20) and Reynolds numbers (Re=400, 500, 600, 700 and 800) in the laminar flow regime. The results are presented in terms of streamlines, isotherm plots, local Nusselt number distribution along the bottom wall of the cavity and averaged Nusselt number plots. A POD-based interpolation method is also employed to predict the flow field and heat transfer characteristic for the mixed convection case at Re=400 for a range of Richardson numbers. Excellent agreement between the field variables is obtained for the considered range (Ri=0.1, 1, 2, 5, 10, 15 and 20) and targeted (Ri=3, 7 and 12) Richardson numbers. Nusselt number variation with respect to Richardson number is also captured well with this approach of POD-based interpolation compared to the CFD calculations.

Keywords: mixed convection, interpolation, proper orthogonal decomposition, computational fluid dynamics

The strong interaction between turbulent structures arising from a plane mixing layer impinging on a circular cylinder is studied. This complex flow has been investigated by a set-up called “dual-plane” PIV that uses two 2D PIV (two-dimensional particle image velocimetry) planes acquired simultaneously. This approach allowed us to apply a 3D-POD (three-dimensional proper orthogonal decomposition) treatment. The first POD modes show the main footprint of the flow configuration, which comprises oblique structures associated with the action of the mixing layer on the near wake. The present study suggests, by analogy, that this phenomenon behaves like the dislocation observed in uniform wake flows.

Many complex fluid motions are driven by physical processes of instability, transition and turbulence dependent upon nonlinear mechanisms. Here, we solve the flow past cylinder(s) using single-block structured and overset grids by computing Navier-Stokes equation in two-dimensions. The suitability of a compact scheme in discretizing convection and diffusion terms are investigated first by looking at relevant numerical properties. Also, for the overset grid method, one of the methods is identified that shows the best results in minimizing interpolation error at sub-domain boundaries for an analytical test function. We provide extensive comparisons with experimental and other computational results for flow past a single cylinder, utilizing both single-block structured and Chimera or overset grids. Apart from showing instability of this flow calculated by these methods, we also compare the computed vorticity and velocity data using these two grids by employing the proper orthogonal decomposition (POD). We have analyzed and developed an overset grid method with compact scheme that does not need any filtering to control error. This has been ascertained by performing POD analysis. To show that the developed method is capable of handling complex geometries, we have computed flow past two cylinders in side-by-side arrangement. Results obtained capture the known flow characteristics for this arrangement well using relatively fewer number of grid points.

In this paper, an approach based on the syn-ergistic use of proper orthogonal decomposition and Kalman filtering is proposed for the online health monitoring of damaged structures. The reduced-order model of a structure is obtained during an (offline) initial training stage of monitoring; afterward, effective estimations of a possible structural damage are provided online by tracking the evolution in time of stiffness parameters and projection bases handled in the model order reduction procedure. Such tracking is accomplished via two Kalman filters: a first (extended) one to deal with the time evolution of a joint state vector , gathering the reduced-order state and the stiffness terms degraded by damage; a second one to deal with the update of the reduced-order model in case of damage evolution. Both filters exploit the information conveyed by measurements of the structural response to the external excitations. Results are reported for a (pseudo-experimental) benchmark test on an eight-story shear building. Capability and performance of the proposed approach are assessed in terms of tracked variation of the stiffness terms of the reduced-order model, identified damage location and speed-up of the whole health monitoring procedure. Keywords Structural health monitoring (SHM) · Reduced-order modeling · Damage detection · Model updating · Kalman filtering · Proper orthogonal decomposition (POD)

A reduced-order modelling (ROM) strategy is pursued to achieve a mechanistic understanding of jet flow mechanisms targeting jet noise control. Coherent flow structures of the jet are identified by the proper orthogonal decomposition (POD) and wavelet analysis. These techniques are applied to an LES data ensemble with velocity snapshots of a three-dimensional, incompressible jet at a Reynolds number of Re=3600. A low-dimensional Galerkin model of a three-dimensional jet is extracted and calibrated to the physical dynamics. To obtain the desired mechanistic understanding of jet noise generation, the loudest flow structures are distilled by a goal-oriented generalisation of the POD approach we term ’most observable decomposition’ (MOD). Thus, a reduction of the number of dynamically most important degrees of freedom by one order of magnitude is achieved. Capability of the presented ROM strategy for jet noise control is demonstrated by suppression of loud flow structures.

The qualitative and quantitative assessment of the thermal reactivity feedbacks occurring in a nuclear reactor is a crucial issue for the time-dependent evolution of the system and, in turn, it has a great impact on the development and validation of advanced control techniques. In the present work, in order to overcome the limitations of the classic Point Kinetics adopted in the control simulators, a spatial neutronics model, representing the neutron flux as sum of a spatial basis weighted by time-dependent coefficients, has been considered. The reference reactor is ALFRED, the European demonstrator of the Lead-cooled Fast Reactor technology. Average cross-sections for each Fuel Assembly, calculated by means of a Monte Carlo code, have been used to solve the partial differential equations of the neutron diffusion, exploiting the capabilities of the COMSOL software. Once obtained the spatial functions, the set of equations for studying the reactivity effects has been implemented in the MATLAB environment. Among the several temperature reactivity feedbacks, specific attention has been paid to the Doppler effect in the fuel and to the lead density effect. Several spatial bases have been calculated and their capability of representing the reactivity variation have been assessed.

Introduction: There is considerable evidence that shows that the Martian atmosphere behaves in a more regular fashion than its terrestrial counterpart [1, 2, 3, 4]. This evidence leads to the hypothesis of theMartian climate attractor being of a relatively low dimension, which, in turn, would imply the possibility of describing the state of the atmosphere by means of a relatively few degrees of freedom. We explore this hypothesis by assuming that the atmospheric total energy (TE), i.e. the sum of kinetic energy and total potential energy (gravitational potential energy plus internal energy), is confined in a few coherent structures which dynamically interact nonlinearly with each other.

The main idea of flow control is the improvement of aerodynamic characteristics of flow. This study analyzes the laminar flow over a two-dimensional (2D) circular cylinder and its control by air blowing from several slots located on the cylinder surface, computationally. The Computational Fluid Dynamics (CFD) results are validated using the experimental results available in the literature for Strouhal number, time-averaged drag coefficient and pressure coefficient distribution around the cylinder. Air blowing from four slots on the cylinder with a velocity of 50% of the free-stream velocity yields a reduction of the drag coefficient by 9%. Flow structures are separated according to their frequency content by Proper Orthogonal Decomposition (POD) method. It is seen from POD results that 99% of the total energy content can be modeled by considering only four most energetic POD modes of the flow. POD analysis of the controlled cases also show that the flow structure around the cylinder changes with the help of air blowing. For real-time flow control applications, it is important to predict the flow based on surface sensors, placed at a few discrete points. In this study, optimum sensor locations on the cylinder surface are also obtained by utilization of a one-dimensional POD analysis based on surface pressure data obtained from CFD results.

Keywords: computational fluid dynamics; CFD; cylinder; vortex; von Karman vortex street; flow control; proper orthogonal decomposition; POD

The mixing layer–wake interaction is studied experimentally in the framework of two flow configurations. For the first one, the initial conditions of the mixing layer are modified by using a thick trailing edge, a wake effect is therefore superimposed to the mixing layer from its beginning (blunt trailing edge). In the second flow configuration, a canonical mixing layer is perturbed in its asymptotic region by the wake of a cylinder arranged perpendicular to the plane of the mixing layer. These interactions are analyzed mainly by using two-point velocity correlations and the proper orthogonal decomposition (POD). These two flow configurations differ by the degree of complexity they involve: the former is mainly 2D while the latter is highly 3D. The blunt trailing edge configuration is analyzed by using rakes of hot wire probes. This flow configuration is found to be considerably different when compared to a conventional mixing layer. It appears in particular that the scale of the large structures depends only on the trailing edge thickness and does not grow in its downstream evolution. A criterion, based on POD, is proposed in order to separate wake–mixing layer dominant areas of the downstream evolution of the flow. The complex 3D dynamical behaviour resulting from the interaction between the canonical plane mixing layer and the wake of a cylinder is investigated using data arising from particle image velocimetry measurements. An analysis of the velocity correlations shows different length scales in the regions dominated by wake like structures and shear layer type structures. In order to characterize the particular organization in the plane of symmetry, a POD-Galerkin projection of the Navier–Stokes equations is performed in this plane. This leads to a low-dimensional dynamical system that allows the analysis of the relationship between the dominant frequencies to be performed. A reconstruction of the dominant periodic motion suspected from previous studies is then retrieved.

Abstract We study the spatiotemporal dynamics of flow separation in a planar diffuser to extract reduced-order models that may be used to guide active separa-tion control. Proper orthogonal decomposition of numerical simulation data revealed organized dynam-ics of the large-...

In this paper a systematic modeling and control approach for flow problems is considered. A nonlinear Galerkin model is obtained from the partial differential equations (PDEs) describing the flow; and a Linear Parameter Varying (LPV) model is constructed to approximate the Galerkin model, where the parameter variation of the LPV model is controller by an adaptation mechanism. The LPV model is then treated as a surrogate on which the control design is carried out, where the parameter variations provide a range of uncertainty in which the control design must perform satisfactorily. It is shown that if certain conditions are met, then such a controller design will succeed when applied to the nonlinear Galerkin model. The ideas developed in the present paper are illustrated through a flow control example governed by the Navier-Stokes (NS) PDEs, where it is observed that a controller design based on the proposed approach is successful in achieving a desired regulation within the flow dom...