Data-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art.

Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control

Employing extremum seeking (ES) for seeking minima of control Lyapunov function (CLF) candidates, we develop 1) the first systematic design of ES controllers for unstable plants, 2) a simple non-model based universal feedback law that emulates, in an average sense, the “ $L_{g}V$ controllers” for stabilization with inverse optimality, and 3) a new strategy for stabilization of systems with unknown control directions, as an alternative to Nussbaum gain controllers that lack exponential stability, lack transient performance guarantees, and lack robustness to changes in the control direction. The stability analysis that underlies our designs is inspired by an analysis approach synthesized in a recent work by Durr, Stankovic, and Johansson, which combines a Lie bracket averaging result of Gurvits and Li with a semiglobal practical stability result under small parametric perturbations by Moreau and Aeyels.

Minimum-Seeking for CLFs: Universal Semiglobally Stabilizing Feedback Under Unknown Control Directions

Review of design optimization methods for turbomachinery aerodynamics

http://flyingv.ucsd.edu/papers/PDF/186.pdf

Extremum seeking with bounded update rates

Stereo particle image velocimetry measurements focus on the flow structure and turbulence within the tip leakage vortex (TLV) of an axial waterjet pump rotor. Unobstructed optical access to the sample area is achieved by matching the optical refractive index of the transparent pump with that of the fluid. Data obtained in closely spaced planes enable us to reconstruct the 3D TLV structure, including all components of the mean vorticity and strain-rate tensor along with the Reynolds stresses and associated turbulence production rates. The flow in the tip region is highly three-dimensional, and the characteristics of the TLV and leakage flow vary significantly along the blade tip chordwise direction. The TLV starts to roll up along the suction side tip corner of the blade, and it propagates within the passage toward the pressure side of the neighboring blade. A shear layer with increasing length connects the TLV to the blade tip and initially feeds vorticity into it. During initial rollup, the TLV involves entrainment of a few vortex filaments with predominantly circumferential vorticity from the blade tip. Being shed from the blade, these filaments also have high circumferential velocity and appear as swirling jets. The circumferential velocity in the TLV core is also substantially higher than that in the surrounding passage flow, but the velocity peak does not coincide with the point of maximum vorticity. When entrainment of filaments stops in the aft part of the passage, newly forming filaments wrap around the core in helical trajectories. In ensemble-averaged data, these filaments generate a vortical region that surrounds the TLV with vorticity that is perpendicular to that in the vortex core. Turbulence within the TLV is highly anisotropic and spatially non-uniform. Trends can be traced to high turbulent kinetic energy and turbulent shear stresses, e.g., in the shear layer containing the vortex filaments and the contraction region situated along the line where the leakage backflow meets the throughflow, causing separation of the boundary layer at the pump casing. Upon exposure to adverse pressure gradients in the aft part of the passage, at 0.65–0.7 chord fraction in the present conditions, the TLV bursts into a broad turbulent array of widely distributed vortex filaments.

Three-dimensional flow structures and associated turbulence in the tip region of a waterjet pump rotor blade

DOI: 10.2514/1.J050931 In this contribution the impact of active flow control by means of pulsed blowing in a critically loaded compressor cascadewillbedescribed.Becauseofthehighloadingoftheblades,afullythree-dimensionalandcomplex flowfieldis developing. Experimental investigations with active flow control were undertaken to increase the turning and the pressure rise of the stator cascade, by suppressing separation phenomena in the passage flowfield. Two different concepts of actuators were used. First, pulsed blowing out of the endwalls was used to reduce the secondary flow structures. Second, the flow was excited with actuators flush-mounted on the blade’s suction surface. The best performance was reached by using both actuator concepts in combination. A multivariable closed-loop control approach was used to control both separation phenomena simultaneously. Heavy disturbances could be compensated and a stabilization of the cascade operation point was achieved.

Active Separation Control with Pulsed Jets in a Critically Loaded Compressor Cascade

The paper presents experimental and numerical results for a highly loaded, low speed, linear compressor cascade with active flow control. Three active flow control concepts by means of steady jets, pulsed jets, and zero mass flow jets (synthetic jets) are investigated at two different forcing locations, i.e. at the end walls and the blade suction side. Investigations are performed at the design incidence for jet-to-inlet velocity ratios from approximately 0.7 to 3.0 and two different Reynolds numbers. Detailed flow field data are collected using a five-hole pressure probe, pressure tabs on the blade surfaces, and time-resolved particle image velocimetry. Unsteady Reynolds-Averaged Navier-Stokes simulations are performed for a wide range of flow control parameters. The experimental and numerical results are used to understand the interaction between the jet and the passage flow. Variation of jet amplitude, forcing frequency, and blowing angle of the different control concepts at both locations allows determination of beneficial control parameters and offers a comparison between similar control approaches. The paper combines the advantages of an expensive but accurate experiment and a fast but limited numerical simulation.Copyright © 2011 by ASME

Active Flow Control Concepts on a Highly Loaded Subsonic Compressor Cascade: Résumé of Experimental and Numerical Results

This paper presents results of numerical investigations carried out to explore the benefit of endwall boundary layer removal from critical regions of highly-loaded axial compressor blade rows. At the loading level of modern aero-engine compressors the performance is primarily determined by three-dimensional flow phenomena occuring in the endwall regions. 3DNS simulations were conducted on both a rotor and a stator test case in order to evaluate basic effects and the practical value of bleeding air from specific locations at the casing endwall. The results of the numerical survey demonstrated substantial benefits of relatively small bleed rates to the local flow field and to the performance of the two blade rows. On the rotor, boundary layer fluid was removed from the main flow path through an axisymmetric slot in the casing over the rotor tip. This proved to give some control over the tip leakage vortex flow and the associated loss generation. On the stator, boundary layer fluid was taken from the flow path through a single bleed hole within the passage. Two alternative off-take configurations were evaluated, revealing a large impact of the bleed hole shape and location on the cross-passage flow and the suction side corner separation. On both blade rows investigated, rotor and stator, boundary layer removal resulted in a reduction of local reverse flow, blockage and losses in the respective near-casing region. This paper gives insight into changes occuring in the 3D passage flow field near the casing and summarises the effects on the radial matching and pitchwise-averaged performance parameters, namely loss and deviation of the rotor and stator when suction is active. Primary focus is put on the aerodynamics in the blade rows in the main flow path; details of the internal flow structure within the bleed off-take cavities/ports are not discussed here.Copyright © 2005 by ASME

Numerical Investigation of Endwall Boundary Layer Removal on Highly-Loaded Axial Compressor Blade Rows

This article presents the potential of active flow control to increase the aerodynamic performance of highly loaded turbomachinery compressor blades. Experimental investigations on a large-scale compressor cascade equipped with 30 synthetic jet actuators mounted to the sidewalls and the blades themselves have been carried out. Results for a variation of the inflow angle, the jet amplitude, and the actuation frequency are presented. The wake measurements show total pressure loss reductions of nearly 10 per cent for the synthetic jet actuation. An efficiency calculation reveals that the energy saved by actuation is nearly twice the energy consumption of the synthetic jets.

/pdf/active-flow-control-by-means-of-synthetic-jets-on-a-highly-4g8hs2g841.pdf

Active flow control by means of synthetic jets on a highly loaded compressor cascade

This paper describes the impact of active separation control by means of pulsed blowing in a highly loaded compressor cascade. Experimental investigations with AFC were undertaken in order to increase the performance of the stator cascade. Two different concepts of actuation were tried. At first, pulsed blowing out of the casing was used to reduce the secondary flow structures. Secondly, the flow was excited with actuators mounted on the blade’s suction side, suppressing the pressure-induced flow separation. In a final step, both actuator concepts were combined with selected excitation amplitudes and frequencies. These demonstrations show that the gain achieved in both actuator concepts can be combined, using certain excitation parameters and no interaction with negative effects occur.

Marius Swoboda

Papers

Active Separation Control with Pulsed Jets in a Critically Loaded Compressor Cascade

Active Flow Control Concepts on a Highly Loaded Subsonic Compressor Cascade: Résumé of Experimental and Numerical Results

Numerical Investigation of Endwall Boundary Layer Removal on Highly-Loaded Axial Compressor Blade Rows

Active flow control by means of synthetic jets on a highly loaded compressor cascade

Experimental AFC Approaches on a Highly Loaded Compressor Cascade