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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:55:59 +0000Numerically nonreflecting boundary conditions for multidimensional aeroacoustic computations
https://resolver.caltech.edu/CaltechAUTHORS:20190726-104731244
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}]}
Year: 1998
DOI: 10.2514/6.1998-2220
Many compressible flow and aeroacoustic computations rely on accurate nonreflecting or radiation boundary conditions. When the equations and boundary conditions are discretized using a finite- difference scheme, the dispersive nature of the discretized equations can lead to spurious numerical reflections not seen in the continuous boundary value problem. These reflections can lead to poor convergence to a stationary state, and can lead to self-forcing of flows. We have constructed numerically nonreflecting boundary conditions which account for the particular finite-difference scheme used, and are designed to minimize these spurious numerical reflections. These extend our earlier work on one- dimensional boundary conditions to the multidimensional case. Stable boundary conditions which are nonreflecting to arbitrarily high-order-of-accuracy are obtained. Various test cases are presented which show excellent results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4mf66-2m871Numerical investigation of the flow past a cavity
https://resolver.caltech.edu/CaltechAUTHORS:20190726-104730595
Authors: {'items': [{'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Basu-A-J', 'name': {'family': 'Basu', 'given': 'Amit J.'}}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}]}
Year: 1999
DOI: 10.2514/6.1999-1912
Numerical simulations are used to investigate the resonant instabilities in the flow past an open cavity. The compressible Navier-Stokes equations are solved directly (no turbulence model) for two-dimensional cavities with laminar boundary layers upstream. The computational domain is large enough to directly resolve a portion of the radiated acoustic field. The results show a transition from a shear layer mode, for shorter cavities and lower Mach numbers, to a wake mode for longer cavities and higher Mach numbers. The shear layer mode is well characterized by Rossiter modes. The wake mode is characterized instead by a large-scale vortex shedding with Strouhal number independent of the Mach number. The vortex shedding causes the boundary layer to periodically separate upstream of the cavity. The wake mode oscillation is similar to that reported by Gharib and Roshko (J. Fluid Mech., 177, 1987) for incompressible ow with a laminar upstream boundary layer. The results suggest that laminar separation upstream of the cavity edge is the cause of the transition to wake mode.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c363f-5m005Computation of Sound Generation and Flow/Acoustic Instabilities in the Flow Past an Open Cavity
https://resolver.caltech.edu/CaltechAUTHORS:20190726-104730500
Authors: {'items': [{'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Basu-A-J', 'name': {'family': 'Basu', 'given': 'Amit J.'}}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}]}
Year: 1999
The modes of oscillation and radiated acoustic fields of compressible flows over open cavities are investigated computationally. The compressible Navier-Stokes equations are solved directly (no turbulence model) for two dimensional open cavities with laminar boundary layers upstream. The computational domain is large enough to directly resolve a portion of the radiated acoustic field. The results show a bifurcation from a shear layer mode, for shorter cavities and lower Mach numbers, to a wake mode for longer cavities and higher Mach numbers. The shear layer mode is well characterized by Rossiter modes and these oscillations lead to intense upstream acoustic radiation dominated by a single frequency. The wake mode is characterized instead by a large-scale vortex shedding with Strouhal number nearly independent the Mach number. The vortex shedding causes the boundary layer to periodically separate upstream of the cavity. Acoustic radiation is more intense, with multiple frequencies present. The wake mode oscillation is similar to that reported by Gharib & Roshko (1987) for incompressible cavity flows with laminar upstream boundary layers.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/emfpy-s6r46Discretely Nonreflecting Boundary Conditions for Linear Hyperbolic Systems
https://resolver.caltech.edu/CaltechAUTHORS:20190726-104729508
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}]}
Year: 2000
DOI: 10.1006/jcph.1999.6383
Many compressible flow and aeroacoustic computations rely on accurate nonreflecting or radiation boundary conditions. When the equations and boundary conditions are discretized using a finite-difference scheme, the dispersive nature of the discretized equations can lead to spurious numerical reflections not seen in the continuous boundary value problem. Here we construct discretely nonreflecting boundary conditions, which account for the particular finite-difference scheme used, and are designed to minimize these spurious numerical reflections. Stable boundary conditions that are local and nonreflecting to arbitrarily high order of accuracy are obtained, and test cases are presented for the linearized Euler equations. For the cases presented. reflections for a pressure pulse leaving the boundary are reduced by up to two orders of magnitude over typical ad hoc closures, and for a vorticity pulse, reflections are reduced by up to four orders of magnitude.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ag9g2-5de13POD Based Models of Self-Sustained Oscillations in the Flow Past an Open Cavity
https://resolver.caltech.edu/CaltechAUTHORS:20190726-104731320
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}]}
Year: 2000
DOI: 10.2514/6.2000-1969
The goal of this work is to provide accurate dynamical models of oscillations in the flow past a rectangular cavity, for the purpose of bifurcation analysis and control. We have performed an extensive set of direct numerical simulations which provide the data used to derive and evaluate the models. Based on the method of Proper Orthogonal Decomposition (POD) and Galerkin projection, we obtain low-order models (from 6 to 60 states) which capture the dynamics very accurately over a few periods of oscillation, but deviate for long time.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n9cw0-6z661Reconstruction equations and the Karhunen–Loève expansion for systems with symmetry
https://resolver.caltech.edu/CaltechAUTHORS:20100913-105958467
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}]}
Year: 2000
DOI: 10.1016/S0167-2789(00)00042-7
We present a method for applying the Karhunen–Loève decomposition to systems with continuous symmetry. The techniques in this paper contribute to the general procedure of removing variables associated with the symmetry of a problem, and related ideas have been used in previous works both to identify coherent structures in solutions of PDEs, and to derive low-order models via Galerkin projection. The main result of this paper is to derive a simple and easily implementable set of reconstruction equationswhich close the system of ODEs produced by Galerkin projection. The geometric interpretation of the method closely parallels techniques used in geometric phases and reconstruction techniques in geometric mechanics. We apply the method to the Kuramoto–Sivashinsky equation and are able to derive accurate models of considerably lower dimension than are possible with the traditional Karhunen–Loève expansion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mvwyn-fnf79Reconstruction Equations and the Karhunen-Loève
Expansion for Systems with Symmetry
https://resolver.caltech.edu/CaltechAUTHORS:20101025-090642137
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}]}
Year: 2000
DOI: 10.1016/S0167-2789(00)00042-7
We present a method for applying the Karhunen-Lo`eve decomposition to
systems with continuous symmetry. The techniques in this paper contribute to
the general procedure of removing variables associated with the symmetry of a
problem, and related ideas have been used in previous works both to identify
coherent structures in solutions of PDEs, and to derive low-order models via
Galerkin projection. The main result of this paper is to derive a simple and
easily implementable set of reconstruction equations which close the system of
ODEs produced by Galerkin projection. The geometric interpretation of the
method closely parallels techniques used in geometric phases and reconstruction
techniques in geometric mechanics. We apply the method to the Kuramoto-
Sivashinsky equation and are able to derive accurate models of considerably
lower dimension than are possible with the traditional Karhunen-Loève expansion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vnr3y-9ah91Dynamical models for control of cavity oscillations
https://resolver.caltech.edu/CaltechAUTHORS:20190726-104731145
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}]}
Year: 2001
DOI: 10.2514/6.2001-2126
We investigate nonlinear dynamical models for self-sustained oscillations in the flow past a rectangular cavity. The models are based on the method of Proper Orthogonal Decomposition (POD) and Galerkin projection, and we introduce an inner product and formulation of the equations of motion which enables one to use vector-valued POD modes for compressible flows. We obtain models between 3 and 20 states, which accurately describe both the short-time and long-time dynamics. This is a substantial improvement over previous models based on scalar-valued POD modes, which capture the dynamics for short time, but deviate for long time.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/476q0-75d28Variational integrators for degenerate Lagrangians, with application to point vortices
https://resolver.caltech.edu/CaltechAUTHORS:20101007-083427136
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}]}
Year: 2002
DOI: 10.1109/CDC.2002.1184735
We develop discrete mechanics and variational integrators
for a class of degenerate Lagrangian systems,
and apply these integrators to a system of
point vortices. Excellent numerical behavior is observed.
A longer term goal is to use these integration
methods in the context of control of mechanical
systems, such as coordinated groups of underwater
vehicles. In fact, numerical evidence given
in related problems, such as those in [2] shows that
in the presence of external forces, these methods
give superior predictions of energy behavior.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fq9h3-fhc45Model-based control of cavity oscillations. I - Experiments
https://resolver.caltech.edu/CaltechAUTHORS:20190718-165126408
Authors: {'items': [{'id': 'Williams-D-R', 'name': {'family': 'Williams', 'given': 'David R.'}}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}, {'id': 'MacMartin-D-G', 'name': {'family': 'MacMartin', 'given': 'Douglas G.'}, 'orcid': '0000-0003-1987-9417'}, {'id': 'Fabris-Drazin', 'name': {'family': 'Fabris', 'given': 'Drazin'}}, {'id': 'Albertson-Julie', 'name': {'family': 'Albertson', 'given': 'Julie'}}]}
Year: 2002
DOI: 10.2514/6.2002-971
An experimental investigation of acoustic mode noise suppression was conducted in a cavity using a digital controller with a linear control algorithm. The control algorithm was based on flow field physics similar to the Rossiter model for acoustic resonance. Details of the controller and results from its implementation are presented in the companion paper by Rowley, et al.
Here the experiments and some details of the flow field development are described, which were done primarily at Mach number 0.34 corresponding to single mode resonance in the cavity. A novel method using feedback control to suppress the resonant mode and open-loop forcing to inject a non-resonant mode was developed for system identification. The results were used to obtain empirical transfer functions of the components of resonance, and measurements of the shear layer growth for use in the design of the control algorithm.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/r6jj4-0v905On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities
https://resolver.caltech.edu/CaltechAUTHORS:ROWjfm02
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Basu-A-J', 'name': {'family': 'Basu', 'given': 'Amit J.'}}]}
Year: 2002
DOI: 10.1017/S0022112001007534
Numerical simulations are used to investigate the resonant instabilities in two-dimensional flow past an open cavity. The compressible Navier–Stokes equations are solved directly (no turbulence model) for cavities with laminar boundary layers upstream. The computational domain is large enough to directly resolve a portion of the radiated acoustic field, which is shown to be in good visual agreement with schlieren photographs from experiments at several different Mach numbers. The results show a transition from a shear-layer mode, primarily for shorter cavities and lower Mach numbers, to a wake mode for longer cavities and higher Mach numbers. The shear-layer mode is characterized well by the acoustic feedback process described by Rossiter (1964), and disturbances in the shear layer compare well with predictions based on linear stability analysis of the Kelvin–Helmholtz mode. The wake mode is characterized instead by a large-scale vortex shedding with Strouhal number independent of Mach number. The wake mode oscillation is similar in many ways to that reported by Gharib & Roshko (1987) for incompressible flow with a laminar upstream boundary layer. Transition to wake mode occurs as the length and/or depth of the cavity becomes large compared to the upstream boundary-layer thickness, or as the Mach and/or Reynolds numbers are raised. Under these conditions, it is shown that the Kelvin–Helmholtz instability grows to sufficient strength that a strong recirculating flow is induced in the cavity. The resulting mean flow is similar to wake profiles that are absolutely unstable, and absolute instability may provide an explanation of the hydrodynamic feedback mechanism that leads to wake mode. Predictive criteria for the onset of shear-layer oscillations (from steady flow) and for the transition to wake mode are developed based on linear theory for amplification rates in the shear layer, and a simple model for the acoustic efficiency of edge scattering.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jzmer-yr644Model-based control of cavity oscillations. II - System identification and analysis
https://resolver.caltech.edu/CaltechAUTHORS:20190709-092100972
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Williams-D-R', 'name': {'family': 'Williams', 'given': 'David R.'}}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}, {'id': 'MacMartin-D-G', 'name': {'family': 'MacMartin', 'given': 'Douglas G.'}, 'orcid': '0000-0003-1987-9417'}, {'id': 'Fabris-Drazin', 'name': {'family': 'Fabris', 'given': 'Drazin'}}]}
Year: 2002
DOI: 10.2514/6.2002-972
Experiments using active control to reduce oscillations in the flow past a rectangular cavity have uncovered surprising phenomena: in the controlled system, often new frequencies of oscillation appear, and often the main frequency of oscillation is split into two sideband frequencies. The goal of this paper is to explain these effects using physics-based models, and to use these ideas to guide control design.
We present a linear model for the cavity flow, based on the physical mechanisms of the familiar Rossiter model. Experimental data indicates that under many operating conditions, the oscillations are not self-sustained, but in fact are caused by amplification of external disturbances. We present some experimental results demonstrating the peak-splitting phenomena mentioned above, use the physics-based model to study the phenomena, and discuss fundamental performance limitations which limit the achievable performance of any control scheme.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qp5x4-psg54On the choice of norm for modeling compressible flow dynamics at reduced-order using the POD
https://resolver.caltech.edu/CaltechAUTHORS:20190214-123721078
Authors: {'items': [{'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clancy W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Freund-J-B', 'name': {'family': 'Freund', 'given': 'Jonathan B.'}}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}]}
Year: 2002
DOI: 10.1109/CDC.2002.1184376
We use POD (proper orthogonal decomposition)/Galerkin projection to investigate and derive reduced-order models of the dynamics of compressible flows. We examine DNS data for two flows, a turbulent M=0.9 jet and self-sustained oscillations in the flow over an open cavity, and show how different choices of norm lead to different definitions of the energetic structures, and, for the cavity, to different reduced-order models of the dynamics. For the jet, we show that the near-field dynamics are fairly well represented by relatively few modes, but that key processes of interest, such as acoustic radiation, are not well captured by norms that are defined based on volume integrals of pressure and velocity. For the cavity flow, we demonstrate that vector-valued POD modes lead to reduced-order models that are much more effective (accurate and stable) than scalar-valued modes defined independently for different flow variables.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w3btx-2kq60Reduction and reconstruction for self-similar dynamical systems
https://resolver.caltech.edu/CaltechAUTHORS:ROWnonlin03
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Kevrekidis-I-G', 'name': {'family': 'Kevrekidis', 'given': 'Ioannis G.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}, {'id': 'Lust-K', 'name': {'family': 'Lust', 'given': 'Kurt'}}]}
Year: 2003
DOI: 10.1088/0951-7715/16/4/304
We present a general method for analysing and numerically solving partial differential equations with self-similar solutions. The method employs ideas from symmetry reduction in geometric mechanics, and involves separating the dynamics on the shape space (which determines the overall shape of the solution) from those on the group space (which determines the size and scale of the solution). The method is computationally tractable as well, allowing one to compute self-similar solutions by evolving a dynamical system to a steady state, in a scaled reference frame where the self-similarity has been factored out. More generally, bifurcation techniques can be used to find self-similar solutions, and determine their behaviour as parameters in the equations are varied.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yxzv6-6sa77Model reduction for compressible flows using POD and Galerkin projection
https://resolver.caltech.edu/CaltechAUTHORS:20190214-075224908
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}]}
Year: 2004
DOI: 10.1016/j.physd.2003.03.001
We present a framework for applying the method of proper orthogonal decomposition (POD) and Galerkin projection to compressible fluids. For incompressible flows, only the kinematic variables are important, and the techniques are well known. In a compressible flow, both the kinematic and thermodynamic variables are dynamically important, and must be included in the configuration space. We introduce an energy-based inner product which may be used to obtain POD modes for this configuration space. We then obtain an approximate version of the Navier–Stokes equations, valid for cold flows at moderate Mach number, and project these equations onto a POD basis. The resulting equations of motion are quadratic, and are much simpler than projections of the full compressible Navier–Stokes equations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2fex1-0xr95Locomotion of Articulated Bodies in a Perfect Fluid
https://resolver.caltech.edu/CaltechAUTHORS:20100819-133718721
Authors: {'items': [{'id': 'Kanso-E', 'name': {'family': 'Kanso', 'given': 'E.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'J. E.'}}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'C. W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Melli-Huber-J-B', 'name': {'family': 'Melli-Huber', 'given': 'J. B.'}}]}
Year: 2005
DOI: 10.1007/s00332-004-0650-9
This paper is concerned with modeling the dynamics of N articulated solid bodies submerged in an ideal fluid. The model is used to analyze the locomotion of aquatic animals due to the coupling between their shape changes and the fluid dynamics in their environment. The equations of motion are obtained by making use of a two-stage reduction process which leads to significant mathematical and computational simplifications. The first reduction exploits particle relabeling symmetry: that is, the symmetry associated with the conservation of circulation for ideal, incompressible fluids. As a result, the equations of motion for the submerged solid bodies can be formulated without explicitly incorporating the fluid variables. This reduction by the fluid variables is a key difference with earlier methods, and it is appropriate since one is mainly interested in the location of the bodies, not the fluid particles. The second reduction is associated with the invariance of the dynamics under superimposed rigid motions. This invariance corresponds to the conservation of total momentum of the solid-fluid system. Due to this symmetry, the net locomotion of the solid system is realized as the sum of geometric and dynamic phases over the shape space consisting of allowable relative motions, or deformations, of the solids. In particular, reconstruction equations that govern the net locomotion at zero momentum, that is, the geometric phases, are obtained. As an illustrative example, a planar three-link mechanism is shown to propel and steer itself at zero momentum by periodically changing its shape. Two solutions are presented: one corresponds to a hydrodynamically decoupled mechanism and one is based on accurately computing the added inertias using a boundary element method. The hydrodynamically decoupled model produces smaller net motion than the more accurate model, indicating that it is important to consider the hydrodynamic interaction of the links.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/btmc2-w3m96Linear models for control of cavity flow oscillations
https://resolver.caltech.edu/CaltechAUTHORS:ROWjfm06
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Williams-D-R', 'name': {'family': 'Williams', 'given': 'David R.'}}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Murray-R-M', 'name': {'family': 'Murray', 'given': 'Richard M.'}, 'orcid': '0000-0002-5785-7481'}, {'id': 'MacMartin-D-G', 'name': {'family': 'MacMynowski', 'given': 'Douglas G.'}, 'orcid': '0000-0003-1987-9417'}]}
Year: 2006
DOI: 10.1017/S0022112005007299
Models for understanding and controlling oscillations in the flow past a rectangular cavity are developed. These models may be used to guide control designs, to understand performance limits of feedback, and to interpret experimental results. Traditionally, cavity oscillations are assumed to be self-sustained: no external disturbances are necessary to maintain the oscillations, and amplitudes are limited by nonlinearities. We present experimental data which suggests that in some regimes, the oscillations may not be self-sustained, but lightly damped: oscillations are sustained by external forcing, such as boundary-layer turbulence. In these regimes, linear models suffice to describe the behaviour, and the final amplitude of oscillations depends on the characteristics of the external disturbances. These linear models are particularly appropriate for describing cavities in which feedback has been used for noise suppression, as the oscillations are small and nonlinearities are less likely to be important. It is shown that increasing the gain too much in such feedback control experiments can lead to a peak-splitting phenomenon, which is explained by the linear models. Fundamental performance limits indicate that peak splitting is likely to occur for narrow-bandwidth actuators and controllers.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cs1cy-78146Unsteadiness in Flow over a Flat Plate at Angle-of-Attack at Low Reynolds Numbers
https://resolver.caltech.edu/CaltechAUTHORS:20190718-165127033
Authors: {'items': [{'id': 'Taira-Kunihiko', 'name': {'family': 'Taira', 'given': 'Kunihiko'}, 'orcid': '0000-0002-3762-8075'}, {'id': 'Dickson-W-B', 'name': {'family': 'Dickson', 'given': 'William B.'}}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Dickinson-M-H', 'name': {'family': 'Dickinson', 'given': 'Michael H.'}, 'orcid': '0000-0002-8587-9936'}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}]}
Year: 2007
DOI: 10.2514/6.2007-710
Flow over an impulsively started low-aspect-ratio flat plate at angle-of-attack is investigated for a Reynolds number of 300. Numerical simulations, validated by a companion experiment, are performed to study the influence of aspect ratio, angle of attack, and planform geometry on the interaction of the leading-edge and tip vortices and resulting lift and drag coefficients. Aspect ratio is found to significantly influence the wake pattern and the force experienced by the plate. For large aspect ratio plates, leading-edge vortices evolved into hairpin vortices that eventually detached from the plate, interacting with the tip vortices in a complex manner. Separation of the leading-edge vortex is delayed to some extent by having convective transport of the spanwise vorticity as observed in flow over elliptic, semicircular, and delta-shaped planforms. The time at which lift achieves its maximum is observed to be fairly constant over different aspect ratios, angles of attack, and planform geometries during the initial transient. Preliminary results are also presented for flow over plates with steady actuation near the leading edge.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e5m7e-s3b33Low-Dimensional Models for Control of Leading-Edge Vortices: Equilibria and Linearized Models
https://resolver.caltech.edu/CaltechAUTHORS:20190718-165125547
Authors: {'items': [{'id': 'Ahuja-Sunil', 'name': {'family': 'Ahuja', 'given': 'Sunil'}}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Kevrekidis-I-G', 'name': {'family': 'Kevrekidis', 'given': 'Ioannis G.'}}, {'id': 'Wei-Mingjun', 'name': {'family': 'Wei', 'given': 'Mingjun'}}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Tadmor-G', 'name': {'family': 'Tadmor', 'given': 'Gilead'}}]}
Year: 2007
DOI: 10.2514/6.2007-709
When an airfoil is pitched up rapidly, a dynamic stall vortex forms at the leading edge and produces high transient lift before shedding and stall occur. The aim of this work is to develop low-dimensional models of the dynamics of these leading-edge vortices, which may be used to develop feedback laws to stabilize these vortices using closed-loop control, and maintain high lift. We first perform a numerical study of the two-dimensional incompressible flow past an airfoil at varying angles of attack, finding steady states using a timestepper-based Newton/GMRES scheme, and dominant eigenvectors using ARPACK. These steady states may be either stable or unstable; we develop models linearized about the stable steady states using a method called Balanced Proper Orthogonal Decomposition, an approximation of balanced truncation that is tractable for large systems. The balanced POD models dramatically outperform models using the standard POD/Galerkin procedure, and are used to develop observers that reconstruct the flow state from a single surface pressure measurement.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/g50jc-hpg03Unsteady Aerodynamic Forces on Small-Scale Wings: Experiments, Simulations, and Models
https://resolver.caltech.edu/CaltechAUTHORS:20190718-165125978
Authors: {'items': [{'id': 'Brunton-S-L', 'name': {'family': 'Brunton', 'given': 'Steven L.'}}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Taira-Kunihiko', 'name': {'family': 'Taira', 'given': 'Kunihiko'}, 'orcid': '0000-0002-3762-8075'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Collins-Jesse', 'name': {'family': 'Collins', 'given': 'Jesse'}}, {'id': 'Williams-D-R', 'name': {'family': 'Williams', 'given': 'David R.'}}]}
Year: 2008
DOI: 10.2514/6.2008-520
The goal of this work is to develop low order dynamical systems models for the unsteady lift and drag forces on small wings in various modes of flight, and to better understand the physical characteristics of unsteady laminar separation. Velocity field and body force data for a flat plate at static angle of attack and in sinusoidal pitch and plunge maneuvers are generated by 2D direct numerical simulations using an immersed boundary method at Re = 100. The lift of a sinusoidally plunging plate is found to deviate from the quasi-steady approximation at a reduced frequency of k = 0.5 over a range of Strouhal numbers. Lagrangian coherent structures illustrate formation and convection of a leading-edge vortex in sinusoidal pitch and plunge. A phenomenological ODE model with three states is shown to reproduce the lift on a flat plate at a static angle of attack above the stall angle. DNS for a 3D pitch-up maneuver of a rectangular plate at Re = 300 shows the effect of aspect ratio on vortical wake structure and lift. Wind tunnel experiments of a wing in single pitch-up and sinusoidal pitch maneuvers are compared with a dynamic model incorporating time delays and relaxation times to produce hysteresis.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/d2d1q-h1w55Control of a Semi-Circular Planform Wing in a "Gusting" Unsteady Free Stream Flow II: Modeling and Feedback Design
https://resolver.caltech.edu/CaltechAUTHORS:20190717-102320405
Authors: {'items': [{'id': 'Tadmor-G', 'name': {'family': 'Tadmor', 'given': 'Gilead'}}, {'id': 'Williams-D-R', 'name': {'family': 'Williams', 'given': 'David R.'}}, {'id': 'Collins-Jesse', 'name': {'family': 'Collins', 'given': 'Jesse'}}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}]}
Year: 2008
DOI: 10.2514/6.2008-3977
Active flow control has been demonstrated in Part I of this article to modify the lift, drag and pitching moments on a semi-circular wing during "gusting" flow conditions. The low aspect ratio wing, AR = 2.54, is mounted on a captive trajectory system that responds to the instantaneous lift force and pitching moment and the "gusting" flow is simulated by a 0.2 Hz oscillation of the free stream speed of the wind tunnel. The mean chord Reynolds number of the wing is 70,600. Active flow control occurs along the leading edge of the airfoil, which contains 16 spatially localized micro-valve actuators. Details of the experimental setup, a quasi steady state lift model and results involving open-loop proof of concept validation are provided in Part I of this paper. Here we outline principles and considerations associated with close loop design that will be discussed in our talk.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6h8ep-hra38Closed-Loop Control of Leading Edge Vorticity on a 3D Wing: Simulations and Low-Dimensional Models
https://resolver.caltech.edu/CaltechAUTHORS:20190717-102320932
Authors: {'items': [{'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Ahuja-Sunil', 'name': {'family': 'Ahuja', 'given': 'Sunil'}}, {'id': 'Taira-Kunihiko', 'name': {'family': 'Taira', 'given': 'Kunihiko'}, 'orcid': '0000-0002-3762-8075'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}]}
Year: 2008
DOI: 10.2514/6.2008-3981
We study model-based feedback control of the low-Reynolds-number flow over a flat plate at large angles of attack, in both two and three dimensions. Our long-term goal is to be able to manipulate the leading-edge vortices that form on low-aspect-ratio wings at high angles of attack, and that often contribute to exceptionally large lift coefficients. Intwo-dimensional simulations, we present a model-based feedback controller that uses an observer to reconstruct the entire flow field from velocity measurements at three locations, and stabilizes the flow at an angle of attack for which the natural flow state is periodic shedding. In three-dimensional simulations, we use open-loop forcing to study actuator placement, and conclude that trailing-edge actuation is more effective than leading-edge actuation in influencing the forces on the plate, as well as the wake structures. Finally, we present initial results towards extending our model-based control design to the 3D setting, and apply a selective frequency damping method to find unstable equilibrium flow fields in 3D simulations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/v3r9s-ztr60Low Reynolds Number Wing Response to an Oscillating Freestream With and Without Feed Forward Control
https://resolver.caltech.edu/CaltechAUTHORS:20190717-102319638
Authors: {'items': [{'id': 'Williams-D', 'name': {'family': 'Williams', 'given': 'David'}}, {'id': 'Quach-V', 'name': {'family': 'Quach', 'given': 'Vien'}}, {'id': 'Kerstens-W', 'name': {'family': 'Kerstens', 'given': 'Wesley'}}, {'id': 'Buntain-S', 'name': {'family': 'Buntain', 'given': 'Seth'}}, {'id': 'Tadmor-G', 'name': {'family': 'Tadmor', 'given': 'Gilead'}}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}]}
Year: 2009
DOI: 10.2514/6.2009-143
The unsteady lift of a low Reynolds number wing in an oscillating freestream is documented in terms of its amplitude and phase. The phase variation of the lift relative to the freestream velocity shows a larger phase difference than predicted by classical unsteady flow theory. A constant time delay between the lift and the actuator was observed to be τ^+ = t_(delay)U/c = 5.3 when normalized by the freestream speed and chord. Feed forward control of pulsed-jet actuators is used to modulate the lift coefficient of the wing, in an attempt to suppress the lift oscillations. Suppression of the fluctuating lift at the fundamental frequency was partially successful, but additional "noise" was added to harmonics of the lift signal by the controller.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pxaz0-anz31Lock-On to a High-Lift State with Oscillatory Forcing in a Three-Dimensional Wake Flow
https://resolver.caltech.edu/CaltechAUTHORS:20190214-083422063
Authors: {'items': [{'id': 'Taira-Kunihiko', 'name': {'family': 'Taira', 'given': 'Kunihiko'}, 'orcid': '0000-0002-3762-8075'}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}]}
Year: 2010
DOI: 10.1007/978-3-642-11735-0_6
Flow control is applied to a three-dimensional post-stall flow around a rectangular low-aspect-ratio wing. Steady actuation is used to examine effective flow control setups that modify the vortex dynamics in the wake and achieve increase in lift. For one of the setups, oscillatory forcing is then used to examine the influence of actuation frequency. It is found that sinusoidal actuation requires less momentum to the flow field to achieve lift increase compared to steady momentum injection. There are two observed ranges of forcing frequency at which the flow locks onto period-one and period-two high-lift states. Discussions of the ongoing work on stabilizing separated flow about these periodic high-lift states are offered.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/h606f-x2q76Feedback Control of High-Lift State for A Low-Aspect-Ratio Wing
https://resolver.caltech.edu/CaltechAUTHORS:20190717-102320131
Authors: {'items': [{'id': 'Taira-Kunihiko', 'name': {'family': 'Taira', 'given': 'Kunihiko'}, 'orcid': '0000-0002-3762-8075'}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}]}
Year: 2010
DOI: 10.2514/6.2010-357
The objective of this study is to employ feedback control to maximize time-average lift on a low-aspect-ratio wing by directly modifying the three-dimensional dynamics of the wake vortices. Flow control around such wing at post-stall angles of attack is numerically investigated at a low Reynolds number of 300 with blowing along the trailing edge. Motivated by the existence of time-periodic high-lift states under open-loop control with periodic excitation, the extremum seeking algorithm is considered for designing feedback control to lock the flow onto such high-lift states. Preliminary results are presented where the close-loop control is able to seek the optimal actuation frequency and yield high lift.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m7ghj-7ct15Lift Enhancement for Low-Aspect-Ratio Wings with Periodic Excitation
https://resolver.caltech.edu/CaltechAUTHORS:20100831-130506686
Authors: {'items': [{'id': 'Taira-Kunihiko', 'name': {'family': 'Taira', 'given': 'Kunihiko'}, 'orcid': '0000-0002-3762-8075'}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'Williams-D-R', 'name': {'family': 'Williams', 'given': 'David R.'}}]}
Year: 2010
DOI: 10.2514/1.J050248
In an effort to enhance lift on low-aspect-ratio rectangular flat-plate wings in low-Reynolds-number
post-stall flows, periodic injection of momentum is considered along the trailing edge in this numerical
study. The purpose of actuation is not to reattach the flow but to change the dynamics of the wake
vortices such that the resulting lift force is increased. Periodic forcing is observed to be effective
in increasing lift for various aspect ratios and angles of attack, achieving a similar lift enhancement
attained by steady forcing with less momentum input. Through the investigation on the influence of
the actuation frequency, it is also found that there exists a frequency at which the flow locks on to a
time-periodic high-lift state.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kjydr-yaz92Modal Analysis of Fluid Flows: An Overview
https://resolver.caltech.edu/CaltechAUTHORS:20171213-075938896
Authors: {'items': [{'id': 'Taira-Kunihiko', 'name': {'family': 'Taira', 'given': 'Kunihiko'}, 'orcid': '0000-0002-3762-8075'}, {'id': 'Brunton-S-L', 'name': {'family': 'Brunton', 'given': 'Steven L.'}}, {'id': 'Dawson-S-T-M', 'name': {'family': 'Dawson', 'given': 'Scott T. M.'}, 'orcid': '0000-0002-0020-2097'}, {'id': 'Rowley-C-W', 'name': {'family': 'Rowley', 'given': 'Clarence W.'}, 'orcid': '0000-0002-9099-5739'}, {'id': 'Colonius-T', 'name': {'family': 'Colonius', 'given': 'Tim'}, 'orcid': '0000-0003-0326-3909'}, {'id': 'McKeon-B-J', 'name': {'family': 'McKeon', 'given': 'Beverley J.'}, 'orcid': '0000-0003-4220-1583'}, {'id': 'Schmidt-O-T', 'name': {'family': 'Schmidt', 'given': 'Oliver T.'}, 'orcid': '0000-0002-7097-0235'}, {'id': 'Gordeyev-S', 'name': {'family': 'Gordeyev', 'given': 'Stanislav'}}, {'id': 'Theofilis-V', 'name': {'family': 'Theofilis', 'given': 'Vassilios'}}, {'id': 'Ukeiley-L-S', 'name': {'family': 'Ukeiley', 'given': 'Lawrence S.'}}]}
Year: 2017
DOI: 10.2514/1.J056060
Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features. It has become common practice in the analysis of these flows to look for and extract physically important features, or modes, as a first step in the analysis. This step typically starts with a modal decomposition of an experimental or numerical dataset of the flowfield, or of an operator relevant to the system. We describe herein some of the dominant techniques for accomplishing these modal decompositions and analyses that have seen a surge of activity in recent decades [1–8]. For a nonexpert, keeping track of recent developments can be daunting, and the intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community. In particular, we present a brief overview of several of the well-established techniques and clearly lay the framework of these methods using familiar linear algebra. The modal analysis techniques covered in this paper include the proper orthogonal decomposition (POD), balanced proper orthogonal decomposition (balanced POD), dynamic mode decomposition (DMD), Koopman analysis, global linear stability analysis, and resolvent analysis.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q7fn7-mdy41