Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session H26: Flow Control: Sensor Placement and Shape Optimization |
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Chair: Krithika Manohar, Caltech Room: 608 |
Monday, November 25, 2019 8:00AM - 8:13AM |
H26.00001: Optimal sensor and actuator placement using model reduction Krithika Manohar, J. Nathan Kutz, Steven Brunton The optimal placement of sensors and actuators, given a constrained budget, is a NP-hard combinatorial search in the number of candidate locations. This combinatorial complexity quickly becomes intractable for large-scale complex systems. However, physical systems often possess low-rank underlying structure which can be harnessed for efficient sensor placement. We describe a greedy matrix pivoting scheme that exploits the proper orthogonal decomposition of the dynamics to efficiently place sensors, and extend this method to actuator placement for control using balanced model reduction of observability and controllability gramians. The resulting placements are demonstrably close to known optimal placements for feedback control in a linearized Ginzburg-Landau model. The method is also applied to sensor placement for a Bayesian inverse problem in atmospheric source dispersion. [Preview Abstract] |
Monday, November 25, 2019 8:13AM - 8:26AM |
H26.00002: Sensor selection for feedback control of transient energy growth in wall-bounded shear flows Huaijin Yao, Yiyang Sun, Maziar S. Hemati Laminar-to-turbulent transition in wall-bounded shear flows can be suppressed by reducing transient energy growth~(TEG) of small flow perturbations using feedback control. Previous studies on TEG reduction have made use of shear-stress measurements at the walls to design sensor-based output feedback control laws. Within the context of linear quadratic optimal control methods, output feedback strategies based on wall shear-stress sensors alone are unable to achieve comparable TEG performance to full-information controllers. Here, we show that TEG performance for linear quadratic output feedback control strategies can be improved by selecting an alternative set of sensors for feedback. Two systematic approaches for performing the requisite sensor selection task will be presented. All results are demonstrated within the context of a sub-critical channel flow, actuated using wall-normal blowing and suction from the upper and lower walls. [Preview Abstract] |
Monday, November 25, 2019 8:26AM - 8:39AM |
H26.00003: Greedy sensor placement with cost constraints and noise Emily Clark, Travis Askham, Steven Brunton, Nathan Kutz The problem of optimally placing sensors under a cost constraint arises naturally in the design of industrial and commercial products, as well as in scientific experiments, including the reconstruction of fluid flows from incomplete measurements. We consider a relaxation of the full optimization formulation of this problem and extend a well-established greedy algorithm for the optimal sensor placement problem without cost constraints. We then modify our framework to account for the more realistic case of noisy measurements, and consider the problem of placing two different types of sensors: expensive high-fidelity sensors, and cheaper, noisier sensors. We develop guidelines for choosing the number and location of each type given a set budget. We demonstrate the effectiveness our methods on data sets related to fluid mechanics, geophysical fluid flows, and facial recognition. [Preview Abstract] |
Monday, November 25, 2019 8:39AM - 8:52AM |
H26.00004: Multi-Rate and Multi-Fidelity Sensor Fusion for Wall-Bounded Turbulent Flow Reconstruction Mengying Wang, C. Vamsi Krishna, Mitul Luhar, Maziar S. Hemati Experimental instrumentation is rarely able to resolve the breadth of spatial and temporal scales in turbulent flows of practical interest. In this study, we propose to fuse measurements from multi-rate and multi-fidelity sensors with predictions from a physics-based model to reconstruct a wall-bounded turbulent flow. A ``fast" filter is used to fuse high-temporal low-spatial resolution measurements (e.g., hot-wire anemometers) with predictions from a model based on rapid distortion theory. Then, a ``slow" filter updates these estimates to improve spatial fidelity each time a low-temporal high-spatial resolution measurement (e.g., particle image velocimetry) becomes available. Construction of the filter from first principles requires knowledge of modeling errors and noise statistics, which can be difficult to characterize. Here, we show that a covariance matching technique can be used to identify the proposed filters directly from the available sensor measurements, avoiding the need to model and quantify uncertainties a priori. We demonstrate the approach using direct numerical simulation of a turbulent channel flow from the Johns Hopkins Turbulence Database. The role of sensor placement on reconstruction performance is also investigated. [Preview Abstract] |
Monday, November 25, 2019 8:52AM - 9:05AM |
H26.00005: ABSTRACT WITHDRAWN |
Monday, November 25, 2019 9:05AM - 9:18AM |
H26.00006: Shape optimization of stirrers for mixing binary fluids Maximilian Eggl, Peter Schmid Mixing is an omnipresent process in a wide-range of industrial applications. It thus seems prudent to devise techniques for optimizing mixing processes under time and energy constraints. To this end, we present a computational framework based on nonlinear direct-adjoint looping for the enhancement of mixing efficiency in a binary fluid system. The governing equations consist of the nonlinear Navier-Stokes equations, complemented by an evolution equation for a passive scalar. Immersed and moving stirrers are treated by a Brinkman-penalization technique, and the full system of equations is solved using a Fourier-based pseudospectral approach. The adjoint equations provide gradient and sensitivity information which is used to improve an initial mixing strategy, based on shape, rotational and path modifications. We utilise a Fourier-based approach for parameterising and optimising the embedded stirrers and consider a variety of geometries to achieve enhanced mixing efficiency. We study a restricted optimisation space by limiting the time for mixing and the rotational velocities of all stirrers. In all cases, non-intuitive shapes produced better mixing. [Preview Abstract] |
Monday, November 25, 2019 9:18AM - 9:31AM |
H26.00007: A minimal model for riblet geometry optimization Mitul Luhar, Andrew Chavarin Recent work shows that the forcing-response gain for resolvent modes resembling the energetic near-wall cycle is a useful predictor of overall drag reduction performance over riblets. Riblet sizes and shapes identified as being optimal in previous high-fidelity simulations and experiments are found to minimize gain for this resolvent mode. Building on this observation, we develop a geometry optimization framework for streamwise constant riblets. The shape and size of the riblets is parametrized using Bezier curves. A gradient-based search algorithm is employed to identify curve parameters that minimize amplification of the near-wall mode. Unsurprisingly, this procedure identifies scalloped and blade-like geometries as being optimal. Moreover, when scaled in inner units, the optimal sizes for these geometries are found to be insensitive to Reynolds number. Preliminary optimization results that take manufacturability constraints into account are presented briefly. Physical mechanisms responsible for performance deterioration are discussed in the context of the resolvent-based predictions. [Preview Abstract] |
Monday, November 25, 2019 9:31AM - 9:44AM |
H26.00008: Solution to shape design of unsteady natural convection fields to control time history of flow velocity Eiji Katamine, Takashi Aoki This paper presents a numerical solution to shape design of unsteady natural convection fields to control time history of flow velocity. The square error integral between the actual time history of flow velocity and the prescribed time history of flow velocity on the prescribed sub-domain during the specified period of time is used as the objective functional. Shape gradient of the shape design problem is derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping is carried out by the traction method proposed as an approach to solving shape optimization problems.Numerical analyses program for the shape design is developed based on FreeFem++, and the validity of proposed method is confirmed by results of 2D numerical analyses. [Preview Abstract] |
Monday, November 25, 2019 9:44AM - 9:57AM |
H26.00009: A model-based investigation of the effect of actuator geometry on boundary layer flows Igal Gluzman, Dennice Gayme An input-output approach is used to study actuated boundary layers arising from different types of input signals and actuator geometries. We obtain the manipulated flow fields through the Navier-Stokes equations linearized about a given base flow with the spatial geometry of the actuator represented as an array of localized input sources organized in the pattern of interest. The actuated fields are then obtained by superposing the response of each localized source in the array pattern, e.g., a saw tooth plasma actuator whose signal varies in intensity over the geometry. Actuation signals including a single pulse, a train of pulses, and a continuous input are modeled through analytical solutions of the LNS system. As an example, a steady-state step response is used to reproduce the stationary actuated flow-fields due to different plasma actuator configurations in transitional boundary layers. The model is found to reproduce the vortical and streamwise velocity structures obtained in experimental and simulation studies qualitatively well. Our results demonstrate the promise of such an analytical tool in determining beneficial actuator configurations prior to detailed experimental or high fidelity simulations, which are too costly for expansive parametric studies. [Preview Abstract] |
Monday, November 25, 2019 9:57AM - 10:10AM |
H26.00010: Adjoint-based Interfacial Control of Axisymmetric Viscous Drops Alexandru Fikl, Daniel J. Bodony We develop a continuous adjoint formulation for the control of the deformation of a clean, neutrally buoyant droplet in Stokes flow. The focus is on constant surface tension-driven flows, where the interface is deformed with the local fluid velocity. We apply well-known results from the field of shape optimization to rigorously derive the optimality conditions for a wide range of interfacial problems. In the cases of interest, we make use of boundary integral methods as a natural choice for the numerical discretization of the flow variables. In the static case, our methodology is tested on several tracking-type cost functionals, corresponding to classic shape optimization problems. We show agreement with black-box finite difference-based gradients and accurate minimization of the cost functionals. Finally, we show that the methodology also applies to the control of the unsteady droplet deformation, controlled by external forcing in the form of the Capillary number. [Preview Abstract] |
Monday, November 25, 2019 10:10AM - 10:23AM |
H26.00011: A new Drunken Sailor perspective and Spontaneously Singular Control approach for Lagrangian particles (buoyancy-controlled balloons) in highly stratified turbulence Thomas Bewley, Paolo Luchini, Gianluca Meneghello We will discuss recent progress in an ambitious project proposing a low-cost balloon observation system for sustained (in time), broadly distributed (in space), in-situ (between 1-8km altitude), real-time (from data acquisition to NCAR within 20 minutes) measurement of hurricane development. The high density (in space \& time) of measurements from such a robotic sensor vehicle swarm (100 or more vehicles persisting for 5 days) will be invaluable in improving our ability to estimate and forecast such extreme and dangerous atmospheric events. Recent work has focused on a decentralized strategy for rejecting small-scale disturbances of the sensor balloons (acting as Lagrangian tracers in the horizontal directions) that arise due to unresolved turbulent flowfield fluctuations with a concomitant $\omega^{-2}$ spectrum. This is done by modeling the balloon velocities (note: NOT positions) with a statistical random walk away from those planned by the coordinating MPC formulation. Implementing a realistic control penalty, $<|u|>$, in this setting gives a curious (and, practically implementable!) Spontaneously Singular Control strategy (on-off); this strategy is ultimately to be combined in a hierarchical setting with centralized MPC coordination of the large-scale balloon trajectories. [Preview Abstract] |
Monday, November 25, 2019 10:23AM - 10:36AM |
H26.00012: Enhanced scalar transport through predictive reorientation of flow fields Ruud Lensvelt, Michel Speetjens, Henk Nijmeijer Enhancements to scalar transport by fluid flows involves improved redistribution of heat/chemicals through advection. Improvements will be beneficial for a large span of industrial applications ranging from inline mixing in food production to subsurface resource extraction. A common feature in the applications of interest is reorientation of boundary driven laminar base flows to promote scalar transport. In conventional approaches a fixed, periodic reorientation scheme (in space or time) is optimized to accomplish chaotic advection. However, it is unclear whether such approaches produce the most effective promotion of transport in the presence of significant diffusion and/or chemical reactions. In this work, we explore an optimization scheme to predict the optimal orientation to enhance scalar transport over a certain time horizon. Spectral decomposition of the base flow allows for a compact model to ensure efficient prediction of the scalar field in this scheme. We investigate boundary heating of a cold fluid in a 2D circular domain with reorientation of the base flow based on both schemes. The optimization approach shows significant acceleration towards homogenization of the scalar field which demonstrates its potential to improve transport with reorientation of flow fields. [Preview Abstract] |
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