scholarly journals A reduced-order model of three-dimensional unsteady flow in a cavity based on the resolvent operator

2016 ◽  
Vol 798 ◽  
Author(s):  
F. Gómez ◽  
H. M. Blackburn ◽  
M. Rudman ◽  
A. S. Sharma ◽  
B. J. McKeon
Keyword(s):  
Time Series Data ◽  
Three Dimensional ◽  
Dynamical Behaviour ◽  
Reduced Order Model ◽  
Series Data ◽  
Mean Flow ◽  
Order Model ◽  
Full Field ◽  
Reduced Order ◽  
The Mean

A novel reduced-order model for time-varying nonlinear flows arising from a resolvent decomposition based on the time-mean flow is proposed. The inputs required for the model are the mean-flow field and a small set of velocity time-series data obtained at isolated measurement points, which are used to fix relevant frequencies, amplitudes and phases of a limited number of resolvent modes that, together with the mean flow, constitute the reduced-order model. The technique is applied to derive a model for the unsteady three-dimensional flow in a lid-driven cavity at a Reynolds number of 1200 that is based on the two-dimensional mean flow, three resolvent modes selected at the most active spanwise wavenumber, and either one or two velocity probe signals. The least-squares full-field error of the reconstructed velocity obtained using the model and two point velocity probes is of the order of 5 % of the lid velocity, and the dynamical behaviour of the reconstructed flow is qualitatively similar to that of the complete flow.

Decentralized Control of a Tower Crane

1999 ◽  
Author(s):  
Kiyoshi Takagi ◽  
Hidekazu Nishimura
Keyword(s):  
Decentralized Control ◽  
Three Dimensional ◽  
Reduced Order Model ◽  
Flexible Structure ◽  
Order Model ◽  
Modeling And Control ◽  
Reduced Order ◽  
Tower Crane ◽  
Three Dimensional Models ◽  
And Control

Abstract This paper deals with modeling and control of a crane mounted on a tower-like flexible structure. A fast transfer of the load causes the sway of the load rope and the vibration of the flexible structure. Our object is to control both the sway and the vibration by the inherent capability of the tower crane. This paper makes its three-dimensional models for simulation and reduced-order-model in order to design the decentralized control system. Then, we design the decentralized H∞ compensator and verify the efficiency by simulations and experiments.

Design of a Kangaroo Inspired Hopping Robot for Unrestricted Locomotion and Controller Development

2019 ◽  
Author(s):  
Austin Curtis ◽  
James Mynderse ◽  
Hamid Vejdani
Keyword(s):  
Frequency Response ◽  
Three Dimensional ◽  
Reduced Order Model ◽  
Design Parameters ◽  
Order Model ◽  
Reduced Order ◽  
Gait Performance ◽  
System Parameters ◽  
Hopping Robot ◽  
The Relationship

Abstract Inspired by the agility and maneuverability of running kangaroos, a prototype robot was developed using a reduced order model to constrain the system. Both passive and active models were used to understand the relationship between system parameters and gait performance. A frequency response experiment was performed on the prototype to quantify the relationship between design parameters and system responses. Additionally, preliminary tail controllers were tested. Based on the results of the initial platform, a new robot was designed and built as a platform for the study of three dimensional hopping.

Using Functional Gains for Optimal Sensor Placement in Fluid-Structure Interaction

2009 ◽  
Author(s):  
Imran Akhtar ◽  
Jeff Borggaard ◽  
John A. Burns ◽  
Lizette Zietsman
Keyword(s):  
Differential Equations ◽  
Stokes Equations ◽  
Reduced Order Model ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Mean Flow ◽  
Order Model ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Functional Gains

Functional gains are integral kernels of the standard feedback operator and are useful in control of partial differential equations (PDEs). These functional gains provide physical insight into how the control mechanism is operating. In some cases, these functional gains can provide information about the optimal placement of actuators and sensors. The study is motivated by fluid flow control and focuses on the computation of these functions. However, for practical purposes, one must be able to compute these functions for a wide variety of PDEs. For higher dimensional systems, computing these gains is at least as challenging as the original simulation problem. To reduce the complexity of the governing equations, reduced-order models are often developed by reducing the PDEs to ordinary-differential equations (ODEs). In this study, we use proper orthogonal decomposition (POD)-Galerkin based approach and develop a reduced-order model of a bluff body wake. We solve the incompressible Navier-Stokes equations, simulate the flow past a circular cylinder, and record the snapshots of the flow field. We compute the POD eigenfunctions and project the Navier-Stokes equations onto these few of these eigenfunctions to develop a reduced-order model. Later, we modify the model by introducing a control function simulating suction actuation on the cylinder surface. We linearize the model about the mean flow and apply feedback control to suppress vortex shedding. We then compute the functional gains for the applied control. We identify these gains at various stations in the wake region and suggest optimum locations for the sensors.

A Method for Reducing the Order of Nonlinear Dynamic Systems

1984 ◽  
Vol 51 (2) ◽  
pp. 391-398 ◽  
Author(s):  
S. F. Masri ◽  
R. K. Miller ◽  
H. Sassi ◽  
T. K. Caughey
Keyword(s):  
Dynamic Systems ◽  
Three Dimensional ◽  
Element Model ◽  
Random Excitation ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Dimensional Finite Element ◽  
Restoring Forces ◽  
Three Dimensional Finite Element

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.

Analysis of Vibration of a Tank Caused by an Explosion

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
M. Utsumi ◽  
H. Tazuke
Keyword(s):  
Fluid Motion ◽  
Three Dimensional ◽  
Longitudinal Axis ◽  
Reduced Order Model ◽  
Fe Model ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Large Tank ◽  
The Galerkin Method

The vibration of a large tank caused by an explosion that occurs at a place apart from the tank is analyzed. Because the tank is double-walled and the liquid is contained in the inner shell, the vibration of the outer shell subjected to the explosion-induced pressure wave that travels outside the tank is analyzed without considering the liquid. A cylindrical tank with a spherical roof is considered as a realistic three-dimensional (3D) model, and a computationally efficient semi-analytical method that is applicable to the 3D geometry of the tank–fluid interface is investigated. First, cylindrical coordinates are introduced such that the longitudinal axis intersects the center of the tank base and is normal to the explosion source plane, thereby defining the inner and outer radii of the analysis domain of the fluid motion. Next, the solutions are expressed in terms of coordinate-dependent eigenvalues and a reduced order model is developed by applying the Galerkin method to the governing equations that take into account the compressibility and nonlinearity of the fluid motion. The method is verified by comparing with earlier results obtained by a numerical method. We also analyze the vibration of the tank shell by developing its finite element (FE) model and transforming the model into modal equations to develop a reduced order model for the fluid–tank system.

Experimental Investigation on the Loss Production Mechanisms in Transitional Boundary Layers

2020 ◽  
Author(s):  
M. Dellacasagrande ◽  
D. Lengani ◽  
D. Simoni ◽  
M. Ubaldi ◽  
P. Zunino
Keyword(s):  
Boundary Layer ◽  
Strain Rate ◽  
Boundary Layers ◽  
Separated Flow ◽  
Reduced Order Model ◽  
Mean Flow ◽  
Order Model ◽  
Data Set ◽  
Reduced Order ◽  
Stress Tensors

Abstract The present paper discusses the results of a large experimental data set describing transitional boundary layers. Time resolved Particle Image Velocimetry (PIV) measurements have been adopted to survey the boundary layer developing over a flat plate under prescribed adverse pressure gradients typical of turbomachinery components. The tests have been performed while varying the pressure gradient, the Reynolds number and the inlet free-stream turbulence intensity (FSTI). Two exemplary cases, referring to bypass and separated flow transition, are discussed by means of principal axis analysis and proper orthogonal decomposition (POD). The POD is used to provide statistical representation of the flow structures and to compute the turbulence production (i.e., the mean flow energy dissipation) due to the dynamical features observed for the different transition types. Reduced order model representations of the flow field are provided and their contribution to the total turbulence kinetic energy production is isolated. This analysis is closed by the inspection of the eigenvectors of the strain rate and Reynolds stress tensors. For the separated flow case, it is shown that the eigenvectors of strain rate and shear tensor are almost perfectly aligned downstream of the maximum displacement of the bubble. The reduced order model reconstruction of the Kelvin-Helmholtz shed vortices provides the largest part of the overall TKE production. For the high FSTI induced transition, the eigenvectors of the shear and stress tensors do not have the same direction. The loss generation is related to the local maximum Reynolds normal stress in the streamwise direction, induced by the boundary layer streaks and their breakdown.

scholarly journals A Reduced-Order Model for the Vibration Analysis of Mistuned Blade–Disc–Shaft Assembly

2019 ◽  
Vol 9 (22) ◽  
pp. 4762
Author(s):  
Wang ◽  
Bi ◽  
Zheng
Keyword(s):  
Vibration Analysis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Normal Modes ◽  
Order Reduction ◽  
Symmetry Analysis ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Reduced Order

An effective reduced-order model is presented in this paper for the vibration analysis of a mistuned blade–disc–shaft assembly considering the flexibility of the shaft and the rotordynamic effects. For the sake of accurate modeling and quantitative analysis, three-dimensional (3D) finite element models were employed in obtaining the governing equations of motion with the Coriolis force, centrifugal stiffening, and spin softening effects taken into account. Then, an efficient model order reduction technique based on the coordinate projection by normal modes of tuned assembly and cyclic symmetry analysis was developed for mistuned blade–disc–shaft assembly. The criterion of whether one matrix could be incorporated in cyclic symmetry analysis is presented. During the modeling, the mistuning in blade and disc was taken into account and dealt with independently. In mistuning projection, the blade and disc parts were both projected onto their tuned counterparts of the sector model, where the boundary conditions were set to be fixed and free, respectively. Finally, an example of a blade–disc–shaft assembly was employed to validate the effectiveness of the presented method in free and forced vibration analysis.

scholarly journals An Eddy–Zonal Flow Feedback Model for Propagating Annular Modes

2021 ◽  
Vol 78 (1) ◽  
pp. 249-267
Author(s):  
Sandro W. Lubis ◽  
Pedram Hassanzadeh
Keyword(s):  
Large Scale ◽  
Interaction Mechanism ◽  
Zonal Flow ◽  
Reanalysis Data ◽  
Reduced Order Model ◽  
Mean Flow ◽  
Order Model ◽  
Reduced Order ◽  
Annular Modes ◽  
Lag Times

AbstractThe variability of the zonal-mean large-scale extratropical circulation is often studied using individual modes obtained from empirical orthogonal function (EOF) analyses. The prevailing reduced-order model of the leading EOF (EOF1) of zonal-mean zonal wind, called the annular mode, consists of an eddy–mean flow interaction mechanism that results in a positive feedback of EOF1 onto itself. However, a few studies have pointed out that under some circumstances in observations and GCMs, strong couplings exist between EOF1 and EOF2 at some lag times, resulting in decaying-oscillatory, or propagating, annular modes. Here, we introduce a reduced-order model for coupled EOF1 and EOF2 that accounts for potential cross-EOF eddy–zonal flow feedbacks. Using the analytical solution of this model, we derive conditions for the existence of the propagating regime based on the feedback strengths. Using this model, and idealized GCMs and stochastic prototypes, we show that cross-EOF feedbacks play an important role in controlling the persistence of the annular modes by setting the frequency of the oscillation. We find that stronger cross-EOF feedbacks lead to less persistent annular modes. Applying the coupled-EOF model to the Southern Hemisphere reanalysis data shows the existence of strong cross-EOF feedbacks. The results highlight the importance of considering the coupling of EOFs and cross-EOF feedbacks to fully understand the natural and forced variability of the zonal-mean large-scale circulation.

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