Background Material & Preliminary Tasks
for Students Interested in Thesis Research in Reduced Order Models and Feedback Control in Fluid Flow Systems
Gilead Tadmor
ECE / Mathematics / CDSP
Northeastern University
Contents
1 Background
The following description is an edited version of excerpts from the web site http://www7.nationalacademies.org/usnctam/Fluid Dynamics.html.
Fluid (i.e., liquids and gases) flow systems are of an immense importance over an extremely wide range of man-made devices, as well as natural contexts. Fluid motions are responsible for most of the transport and mixing (of materials or properties) that take place in the environment, in industrial processes, in vehicles, and in living organisms. Hence, they are responsible for most of the energy required to power aircraft, ships and automobiles, to pump oil through pipelines and so forth. In the environment, fluid motion is responsible for most of the transport of pollutants (thermal, particulate and chemical) from place to place, as well as for making life possible by transporting oxygen and carbon dioxide and heat from the places where they are produced to the places where they will be used or rejected. In industrial processes, it is largely responsible for the rates at which many processes proceed, and for the uniformity of the resulting product. Research in fluid mechanics has as its ultimate goal improvement in our ability to predict and control all of these situations, so as to improve our ability to design devices (for example, aircraft gas turbines, automobile engines) and to regulate (for example, industrial emissions). If fluid motions appear to be ubiquitous, one might recall that the ancient Greek philosophers postulated that there were but four elements, air, earth, fire, and water. Of the four, three are fluid states, and the fourth, Earth, is not only saturated with water in the thin continental skins on which we live, but is mostly liquid metal just below the continents.
The efficiency of fluid flow systems therefore bears on energy efficiency, performance measures, structural integrity and durability, and environmental impact such as chemical pollution, green-house gas emissions and acoustic noise. It will not be an exaggeration to state that the economic and environmental impacts of even seemingly small improvements (e.g., few percents of turbulence-induced drag over aircrafts, ships and submarines or automobiles) can reach epic proportions. This is the goal of fluid flow control. For examples, 60% or more, of the energy consumed by cars at cruise speed, is used to counteract aerodynamic drag. Recent unofficial experimental results showed that open loop actuation can reduce this component by 20%. It is hoped that feedback control will be able to further improve this performance.
Flow control is still in its infancy. What is envisioned are, surfaces covered with micro-devices that can sense the state of the flow, and actuators that can influence the flow, introducing disturbances at just the right time to increase or reduce the mixing of high- and low-speed fluid, (making the flow follow the contour of a wing, for example, or increasing the rate at which combustion takes place in an engine) or reducing the drag. One of the most important aspects of this process is the interpretation of the sensor input, and the decisions regarding what disturbance to introduce, when and where (known as the control algorithm). This requires an acute understanding of the structure of the flow; such an understanding is obtained by the use of dynamical systems theory, which allows the construction of relatively simple (though still complicated) models of the flows.
2 Common Themes in Current Projects in My Group
The work we do is focused on obtaining low order models, suitable for the design of dynamic observers and feedback design in fluid flow systems, and, indeed, on design, based on the use of such models. Our work is done in close collaboration with teams from the Berlin (Germany) and Poznan (Poland) Universities of Technology, Rensselaer Polytechnic Institute (RPI), Illinois Institute of Technology (IIT), Princeton University and the California Institute of Technology (Caltech).
The work done with the Berlin-Poznan team is funded by NSF. It concerns both basic research, using relatively simple flow configurations as benchmarks, and the application of our findings in experimental work on critical engineering applications. Specifically, we considered the instability of 2D wake flows, such as the flow behind a circular cylinder, the flow behind a backward facing step and the flow over a high lift wing configuration. Physical examples for wake flow instability include the instability behind an automobile, the landing gear of an airplane, the wake behind a boat and behind support pillars for bridges and drilling rigs. Physical examples for the flow over a backward facing step include the flow over a corner shaped buildings, abrupt widening of air ducts and the flow of mixed fuel and air into a combustor. Key to this work is the search for dominant coherent structures in the flow. The high lift wing configuration is used by large commercial airplanes during takeoff and landing, when flaps at the rear (trailing edge) of the wing and slats at the front (leading) edge are extended. These structures are used in the development of very low order models. Understanding their dynamics help determine the validity range of the model and provides guidelines for control design.
Work with RPI is focused on direct extraction of simplified models from physical first principles, such as from the governing Navier-Stokes equations. Here we focus on the ideal mixing shear layer.
Work with the Caltech-IIT-Princeton team concerns methods to implement engineered counterparts of control strategies used by insects and small birds. These bio-fliers achieve flight agility and performance that far surpass man-made aircraft. Our goal is to understand the physics of these control mechanisms and find ways to implement them in autonomous micro air vehicles. The team includes experimentalists (Caltech, IIT), computational fluid dynamics experts (Caltech), and dynamics and control experts (Princeton, NU).
3 What Would Research in Fluid Flow Control Involve
The research will involve a mix of numerical work, analytic work on dynamic data compression, system identification and control design.
Numerical work. In the most part we rely on partner institutions to develop computational fluid dynamics (CFD) simulation models, and to provide us with experimental data. At NU we ran simulations with moderate order models, provided to us by our collaborating partners, collect data from such simulations and from partner institutions, and process collected data. This involves programming in Fortran, Matlab and possibly, C++. Interested students should be capable to program and be willing to learn using languages with which they are less familiar (such as Fortran).
Analytic data compression and system identification. Here we live in the conceptual world of distributed parameter systems, whose state takes values in L2(W), where W is the spatial domain. This requires having and / or interest to acquire proficiency with the basic vocabulary of Hilbert spaces of signals, signal processing and estimation, concepts of projections and sub-space approximations, basic operator theory, and dynamical systems. We also borrow from the world of random variables.
Observer and Feedback Design. Although the objective is feedback control design, at this point our main interest is not on the use of sophisticated design methods. Rather, we aim to understand the restrictions due to the physics of the system and the validity envelope of the model, and match these restrictions by design. We strive to be guided by concepts of energy flow, for the most efficient way to impact system dynamics, and to extract useful, real-time data from few, noisy sensors. This work requires relatively basic knowledge of control theory, some signal processing, and the ability to understand what a nonlinear ordinary differential equation tells us about the system.
Experiments. Physical and large scale numerical experiments are carried by partner institutions. NU team members should collaborate with these partners, defining guidelines for experiments, such as by providing controller and observer design, selecting operating points we want tested, and exchanging raw and processed data.
Initiative. Team members are expected to be self driven problem solvers, and collaborative team members. They are expected to do what it take to solve practical / administrative problems, suggest new ideas in research, follow the literature, and provide periodic reports to the local team, as well as to the team at-large.
4 What Do I Do if I Am Interested in Joining the Team?