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

A computational study to define the phenomena that lead to the onset of short length-scale (spike) rotating stall disturbances has been carried out. Based on unsteady simulations, we hypothesize there are two conditions necessary for the formation of spike disturbances, both of which are linked to the tip clearance flow. One is that the interface between the tip clearance and oncoming flows becomes parallel to the leading-edge plane. The second is the initiation of backflow, stemming from the fluid in adjacent passages, at the trailing-edge plane. The two criteria also imply a circumferential length scale for spike disturbances. The hypothesis and scenario developed are consistent with numerical simulations and experimental observations of axial compressor stall inception. A comparison of calculations for multiple blades with those for single passages also allows statements to be made about the utility of single passage computations as a descriptor of compressor stall.

Criteria for Spike Initiated Rotating Stall

Extremum seeking is a form of adaptive control where the steady-state input-output characteristic is optimized, without requiring any explicit knowledge about this input-output characteristic other than that it exists and that it has an extremum. Because extremum seeking is model free, it has proven to be both robust and effective in many different application domains. Equally being model free, there are clear limitations to what can be achieved. Perhaps paradoxically, although being model free, extremum seeking is a gradient based optimization technique. Extremum seeking relies on an appropriate exploration of the process to be optimized to provide the user with an approximate gradient, and hence the means to locate an extremum. These observations are elucidated in the paper. Using averaging and time-scale separation ideas more generally, the main behavioral characteristics of the simplest (model free) extremum seeking algorithm are established.

Extremum seeking from 1922 to 2010

Rotating instabilities (RI) have been observed in axial flow fans, centrifugal compressors as well as in low-speed and high-speed axial compressors. They are responsible for the excitation of high amplitude rotor blade vibrations and noise generation. This flow phenomenon moves relative to the rotor blades and causes periodic vortex separations at the blade tips and an axial reversed flow through the tip clearance of the rotor blades.The paper describes experimental investigations of RI in the Dresden Low-Speed Research Compressor (LSRC). The objective is to show that the fluctuation of the blade tip vortex is responsible for the origination of this flow phenomenon.RI have been found at operating points near the stability limit of the compressor with relatively large tip clearance of the rotor blades. The application of time-resolving sensors in both fixed and rotating frame of reference enables a detailed description of the circumferential structure and the spatial development of this unsteady flow phenomenon, which is limited to the blade tip region.Laser-Doppler-Anemometry (LDA) within the rotor blade passages and within the tip clearance as well as unsteady pressure measurements on the rotor blades show the structure of the blade tip vortex.It will be shown that the periodical interaction of the blade tip vortex of one blade with the flow at the adjacent blade is responsible for the generation of a rotating structure with high mode orders, termed as rotating instability (RI).Copyright © 2000 by ASME

Rotating Instabilities in an Axial Compressor Originating From the Fluctuating Blade Tip Vortex

This paper reports on an experimental and numerical investigation aimed at understanding the mechanisms of rotating instabilities in a low speed axial flow compressor. The phenomena of rotating instabilities in the current compressor were first identified with an experimental study. Then, an unsteady numerical method was applied to confirm the phenomena and to interrogate the physical mechanisms behind them. The experimental study was conducted with high-resolution pressure measurements at different clearances, employing a double phase-averaging technique. The numerical investigation was performed with an unsteady 3-D Navier-Stokes method that solves for the entire blade row. The current study reveals that a vortex structure forms near the leading edge plane. This vortex is the result of interactions among the classical tip-clearance flow, axially reversed endwall flow, and the incoming flow. The vortex travels from the suction side to the pressure side of the passage at roughly half of the rotor speed. The formation and movement of this vortex seem to be the main causes of unsteadiness when rotating instability develops. Due to the nature of this vortex, the classical tip-clearance flow does not spill over into the following blade passage. This behavior of the tip-clearance flow is why the compressor operates in a stable mode even with the rotating instability, unlike traditional rotating stall phenomena.Copyright © 2001 by ASME

An Experimental and Numerical Investigation Into the Mechanisms of Rotating Instability

An experimental study is described to investigate the negative effects of the tip clearance gap on the aerodynamic and acoustic performance of axial turbomachines. In addition to the increased broadband levels reported in the literature when the tip clearance is enlarged, significant level increases were observed within narrow frequency bands below the blade passing frequency. Measurements of the pressure and velocity fluctuations in the vicinity of the blade tips reveal that the tip clearance noise is associated with a rotating flow instability at the blade tip, which in turn is only present under reversed flow conditions in the tip clearance gap. A turbulence generator inserted into the tip clearance gap is found to be effective in eliminating the tip clearance noise and in improving the aerodynamic performance.

Experimental study of tip clearance losses and noise in axial turbomachines and their reduction

Rotating blade flow instability as a source of noise in axial turbomachines

Sound Generation in Centrifugal Compressors

Sound fields in the inlet and outlet ducts of axial fans, compressors, and aircraft engines propagate as higher‐order acoustical modes in a wide‐frequency range Decomposition of the sound field into azimuthal and radial modes permits direct conclusions on the sound generation processes and can lead to the identification of aerodynamic source areas An established experimental method for assessing the sound field is to circumferentially traverse a radial microphone rake over 360 degrees, to measure the sound pressure in the duct at multiple circumferential and radial positions On the inlet side of a turbo‐machine this procedure cannot be employed because the wake of the rake would disturb the inlet flow conditions of the machine and alter its acoustic characteristics Computer simulations have shown that the radial mode structure of the sound field can also be determined by measuring the sound pressure only at the inner duct wall, but at different axial locations In this paper, experiments are described where the sound field in the outlet duct of an axial‐flow fan is measured once with the conventional radial microphone rake and a second time with wall‐flush mounted microphones Subsequent radial mode analyses are carried out for both sets of measurement data to experimentally verify the new method

Wolfgang Neise

Papers

An Experimental and Numerical Investigation Into the Mechanisms of Rotating Instability

Experimental study of tip clearance losses and noise in axial turbomachines and their reduction

Rotating blade flow instability as a source of noise in axial turbomachines

Sound Generation in Centrifugal Compressors

Experimental verification of a radial mode analysis technique using wall‐flush mounted sensors