Session AJ: Flow Control I

Chair: Joseph Katz, Johns Hopkins University
Room: Long Beach Convention Center 201A

 Sunday, November 21, 2010 8:00AM - 8:13AM AJ.00001: An Approach to Reduced-Order Modeling for Flows with Upstream Actuation Guy Ben-Dov , Arne J. Pearlstein We construct a forced ODE system from the linearized Navier-Stokes and continuity equations, using a proper orthogonal decomposition (POD) in the \textit{frequency domain} and in space. Given any laminar steady flow in a specified domain, superimposing a small (linear) time-dependent flow, forced through some part of the boundary (e.g., by blowing and suction or by synthetic jets) can be used as an actuator to actively control perturbations that may arise in the flow. Using the actuator-driven flow on the upstream boundary as an inlet condition, we compute the impulse response of the linearized PDEs in the frequency domain over a wide range of frequency. The decomposition allows substitution of the resulting modes into the PDEs, and Galerkin projection to ODEs. The approach is demonstrated for the flow over an open cavity at a moderate Reynolds number, where the actuator input is introduced by blowing and suction through a small part of the boundary at the upstream upper part of the cavity. Sunday, November 21, 2010 8:13AM - 8:26AM AJ.00002: System reduction strategy for Galerkin models of fluid flows Michael Schlegel , Bernd R. Noack , Marek Morzynski , Gilead Tadmor We propose a system reduction strategy for control-oriented, spectral and Galerkin models of incompressible fluid flows. Key enabler is a finite-time thermodynamics (FTT) closure for the first and second moments. This FTT-based approach leads to dynamic models of lower order, based on a partition in slow, dominant and fast modes. In the reduced models, slow dynamics are incorporated as nonlinear manifold consistent with mean-field theory. Fast dynamics are stochastically treated and can be lumped in nonlinear eddy viscosity approaches. The employed interaction models between slow, dominant and fast dynamics respect momentum and energy balance equations in a mathematically rigorous manner --- unlike unsteady Reynolds- averaged Navier-Stokes models or Smagorinsky-type reductions of the Navier-Stokes equation. The proposed system reduction strategy is employed to shear flows. Sunday, November 21, 2010 8:26AM - 8:39AM AJ.00003: Methods for the solution of very large flow-control problems that bypass open-loop model reduction Paolo Luchini , Thomas Bewley The numerical discretization of the Navier-Stokes equations may easily lead to millions, or hundreds of millions, degrees of freedom. For the optimal control of such a problem, one is faced with either the solution of the full Riccati equation, numerically intractable for large systems, or with openloop model reduction, which may fail to capture the dynamics of interest. Here we present recent developments in our group about a third alternative: the Riccati-less solution of the unreduced optimal flow-control problem. These include a minimal-energy control algorithm based on the unstable eigenvectors alone, an iterative algorithm for the feedback kernel when the control is of much lower dimension than the state, and an iterative procedure for the leading eigenvalues and eigenvectors of the direct-adjoint Hamiltonian matrix that bypasses the solution of the Riccati equation. Sunday, November 21, 2010 8:39AM - 8:52AM AJ.00004: A least order model for temporally-developing compressible shear layers Bashar Qawasmeh , Mingjun Wei A modified Proper Orthogonal Decomposition/Galerkin projection method has been successfully used to obtain models at very low dimension for incompressible temporal shear layers (Wei and Rowley, 2009). In this study, we applied a similar approach on compressible shear layers. To factor out the downstream viscous growth and then obtain models at lower dimension, our modified POD/Galerkin approach includes a dynamically scaling variable counting the overall thickness variation by viscosity. For compressible flow, we changed to use an inner product with both kinetic and thermal energy (Rowley, Colonius, Murray, 2004), then got the Galerkin model from the projection of the isentropic Navier-Stokes equations. The compressible model shows the capability to capture shear layer dynamics similarly but also slightly better than its incompressible version. More importantly, certain compressible characteristics is still kept in the new model. Sunday, November 21, 2010 8:52AM - 9:05AM AJ.00005: Time Delay in the Lift Response to Actuation and Its Effect on Controller Bandwidth David Williams , Tim Colonius , Wesley Kerstens , Vien Quach The transient lift responses of two- and three-dimensional wings subjected to pulse-like disturbances are used to obtain a measure of the separated flow system time delay. Data from different investigators (Amitay{\&}Glezer, 2002, Darabi{\&}Wygnanski, 2004, Williams, et al. 2009) using different wing geometries and different actuators are compared, which show that the transient lift measurements share certain common features. All the data scale with the convective time scale, t+=tU/c. An initial reversal in lift occurs immediately after actuation, which is followed by a rapid growth in lift to reach maximum lift at t+=3. A slow relaxation from maximum lift back to the undisturbed separated flow state occurs by t+=15. The initial lift reversal is associated with a time delay in the plant (separated flow system.) The time delay is related to the formation of a leading edge vortex and its convection time. The transient lift time delay limits the bandwidth for a given control architecture, which results in two important implications. First there is a practical upper limit for actuator bandwidth, and second, a different control architecture will be necessary to achieve closed-loop control on the shorter fluid-dynamic time scales. Sunday, November 21, 2010 9:05AM - 9:18AM AJ.00006: A Comparison of Model Reduction Approaches for Feedback Control Design of Thermal Flows in Buildings Jeff Borggaard , Sunil Ahuja , John Burns , Eugene Cliff , Amit Surana The application of distributed parameter control to spatiotemporal thermo-fluid systems requires the use of model reduction methods. The form of the optimal feedback control can inform design decisions, such as sensor and actuator selection and placement. A number of model reduction approaches for fluid systems have been put forward that are based on the proper orthogonal decomposition (POD). In this talk, we examine three approaches, the traditional POD-Galerkin model, the POD-Sensitivity model, and the Balanced-POD models. Our work is motivated by the building indoor environment control problem. Energy performance in building cooling and heating systems can be substantially improved by exploiting spatial temperature stratification and buoyancy that are prevalent in passive systems. We consider the control of airflow in a room with a passively cooled radiant ceiling and displacement ventilation provided near the room floor. For this problem, we approximate the full-order solution to compute the control gains, develop reduced-order models and associated controllers, and simulate the full-order closed-loop system for comparison with the reduced-order model-based control design. Sunday, November 21, 2010 9:18AM - 9:31AM AJ.00007: Feedback control of the cylinder wake using balanced reduced order models Simon Illingworth , Hiroshi Naito , Koji Fukagata Feedback control is most successful when an accurate model of the system-to-be-controlled is available. For fluids, this can be achieved using a reduced order model which is balanced (meaning the input-output behaviour is properly captured). With this in mind, we consider feedback control of the cylinder wake in low Reynolds number simulations. Actuation is via blowing and suction on the cylinder's surface, and a single velocity sensor in the wake is used. Balanced reduced order models are formed using the Eigensystem Realization Algorithm (ERA) at a number of Reynolds numbers. The reduced order models, validated by comparing their impulse responses to the full system, are then used in two ways. First, the gain window'' phenomenon seen in previous feedback control studies is reproduced (and therefore explained) by the models. We see that this gain window shrinks with increasing Reynolds number, the consequence being that feedback control with a simple proportional gain is not possible at higher Reynolds numbers. Second, $\mathcal{H}_\infty$ loop-shaping techniques are used to design dynamic'' controllers that are effective at higher Reynolds numbers, achieving complete suppression of vortex shedding at Reynolds numbers in excess of 100. Sunday, November 21, 2010 9:31AM - 9:44AM AJ.00008: Feedback control of transition in boundary layer Onofrio Semeraro , Shervin Bagheri , Luca Brandt , Dan S. Henningson We study the use of feedback control for the delay of laminar-turbulent transition in boundary layer. The mitigation of three-dimensional wavepackets of streaks and Tollmien-Schlichting waves is investigated numerically. The dynamics is studied from an input-output point of view: a set-up of spatially localized inputs (external disturbances and actuators) and outputs (sensor for the estimation and objective functions) is introduced for the control design. Sensors and actuators are distributed in arrays near the wall, spanning the homogeneous spanwise direction. Reduced-order models of the Navier-Stokes equations including the inputs and outputs, obtained via balanced truncation, are used to design an LQG controller. The controller provides an optimal signal that minimizes the amplitude of the perturbation downstream. Using a limited number of sensors and actuators (about 10-20 elements), the linear controller reduces substantially the energy growth of the instabilities arising in the boundary layer flows. In the final contribution, the mitigation of finite-amplitude perturbations in nonlinear simulations and the delay of the laminar-turbulent transition will be addressed. Sunday, November 21, 2010 9:44AM - 9:57AM AJ.00009: Optimal actuator and sensor placement in the linearized complex Ginzburg-Landau system Kevin Chen , Clarence Rowley The linearized complex Ginzburg-Landau equation is a model for the evolution of small fluid perturbations, such as in a bluff body wake. We control this system by implementing actuators and sensors and designing an $H_2$-optimal controller. We seek the optimal actuator and sensor placement that minimizes the $H_2$ norm of the controlled system, from flow disturbances to a cost on the perturbation and input magnitude. We formulate the gradient of the $H_2$ squared norm with respect to actuator and sensor positions, and iterate toward the optimal position. With a single actuator and sensor, it is optimal to place the actuator just upstream of the origin (e.g., the bluff body object) and the sensor just downstream. With multiple but an equal number of actuators and sensors, it is optimal to arrange them in pairs, placing actuators slightly upstream of sensors, and scattering pairs throughout the spatial domain. Global mode and Gramian analyses fail to predict the optimal placement; they produce $H_2$ norms about five times higher than at the true optimum. A wave maker formulation is better able to guess an initial condition for the iterator. Sunday, November 21, 2010 9:57AM - 10:10AM AJ.00010: Analysis of Local Flow Dynamics Using Koopman Modes Jonathan Tu , Kevin Chen , Clarence Rowley The Koopman operator is a linear operator defined for any dynamical system, be it linear or nonlinear. The corresponding Koopman modes, which can be computed using an Arnoldi-like algorithm called Dynamic Mode Decomposition (DMD), provide a means of identifying structures relevant to the local dynamics. Each mode is associated with a distinct frequency, unlike those resulting from Proper Orthogonal Decomposition (POD). Here we present a Koopman analysis of the flow past a 2-D cylinder. Using this single approach, we are able to identify modes relevant to the linearized (near-equilibrium), transient, and limit cycle (periodic shedding) dynamics. We also present a preliminary analysis of a high Reynolds number, separated flow past a flat plate with an elliptical leading edge. Koopman analysis confirms the observation that such flows are dominated by a small set of natural frequencies. The corresponding Koopman modes display familiar physical features.