Zachary Berger

Low-Dimensional Approach for Reconstruction of Airfoil Data via Compressive Sensing

Compressive sensing is used to compress and reconstruct a turbulent-flow particle image velocimetry database over a NACA 4412 airfoil. The spatial velocity data at a given time are sufficiently sparse in the discrete cosine transform basis, and the feasibility of compressive sensing for velocity data reconstruction is demonstrated. Application of the proper orthogonal decomposition/principal component analysis on the dataset works better than the compressive-sensing-based reconstruction approach with discrete cosine transform as the basis in terms of the reconstruction error, although the performance gap between the two schemes is not significant. Using the proper orthogonal decomposition/principal component analysis as the sparsifying basis, compressive-sensing-based velocity reconstruction is implemented, which outperformed discrete cosine transform. Compressive sensing preprocessing (filtering) with discrete cosine transform as the basis is applied to a reduced number of particle image velocimetry snap...

Correlations and wavelet based analysis of near-field and far-field pressure of a controlled high speed jet

Discussed within are the experimental results obtained via simultaneous near-field and far-field measurements of a controlled jet. A large database of both open-loop and closedloop control cases are carried out. The two most interesting investigations from the openloop (OL) and closed-loop (CL) studies are highlighted here and compared to the uncontrolled jet. For the open-loop forcing, the shear layer is seeded with an axisymmetric sinusoidal input with a frequency of 1700 Hz. For the closed-loop case, the shear layer is seeded with a sinusoidal forcing amplitude modulated with the mode-filtered near-field pressure sampled from the stream-wise location at x/D = 6. Data analysis looks at both averaged and instantaneous quantities. In an averaged sense the introduction of control significantly modifies the characteristics of the developing shear layer. Open-loop control is shown to modify the phase lag between both near-field stations with a penalty in an increase in the overall sound pressure level. The closed-loop control imparts more subtle changes to the flow field but yields a slight reduction in the acoustic pressure at the microphone closest to the jet axis. Wavelet based filtering exposes the evolution of the broadband intermittent events seen at both stations.

Analysis of high speed jet flow physics with time-resolved PIV

This work focuses on a Mach 0.6 turbulent, compressible jet flow field with simultaneously sampled near and far-field pressure, as well as 10 kHz time-resolved PIV. Experiments have been conducted in the fully anechoic chamber and jet facility at Syracuse University. The PIV measurements were taken in the streamwise plane of the jet along the center plane at various downstream locations. In addition, measurements were taken off of the center plane to obtain a three-dimensional view of the jet flow. Active flow control (both open and closed-loop) was performed in order to see the effects on the potential core length and overall sound pressure levels. Various reduced-order models have been used to analyze previous experimental data sets at Syracuse University. This paper will focus on the analysis of the flow physics, using the time-resolved velocity field coupled with the simultaneously sampled pressure. Novel modeling approaches such as observable inferred decomposition and cluster-based reduced-order modeling have been implemented in an effort to link the near-field velocity with the far-field acoustics.

Comparison of spatial and temporal resolution on high speed axisymmetric jets

The current investigation examines a 2 inch, circular, high-speed jet with two separate PIV setups simultaneously sampled with far-field pressure. Subsonic and supersonic velocity measurements are performed in the streamwise (r-z) plane of the jet with both time-resolved PIV and large window PIV configurations, taken at different times. The 10 kHz time-resolved PIV captures 1.5 streamwise diameter windows at several downstream locations. The large window PIV utilizes 3 simultaneously captured cameras stitched together to view a single interrogation window of the flow field approximately 2.5-9 streamwise diameters from the nozzle lip. Both PIV setups have an approximately 1.5 diameter spatial window in the radial direction. In this paper, we will focus on the Mach 0.6 flow in the region of the potential core collapse (z/D = 6 7.5). Low-dimensional modeling techniques in the form of proper orthogonal decomposition, Lumley (1967) and Sirovich (1987), are implemented in order to help us understand the large scale, energetic events within the flow. In previous work, the time-dependent POD modes from the TRPIV have been correlated with the far-field acoustics to determine which low-dimensional structures best relate to the noise. These correlated events are deemed as “loud” modes, Low et al. (2013). One issue is that this approach is greatly influenced by the temporal and spatial nature of the PIV. By utilizing the differences in our PIV setups, we map the convergence of POD modes based on their spatial and temporal resolution.

Reduced Order Models for a High Speed Jet with Time-Resolved PIV

In the current investigation, we examine a turbulent, compressible jet flow field in the high subsonic range (Mach 0.85). Experiments take place in the fully anechoic jet facility at Syracuse University, where the flow field is probed in order to measure near-field hydrodynamic pressure, far-field acoustic sound, and near-field velocity. High resolution 10 kHz time-resolved particle image velocimetry (TRPIV) is implemented to gain better insight into the structures formed in the region of the collapse of the potential core of the jet. By exploring these structures in conjunction with the near and far-field pressure, low-dimensional modeling techniques are implemented. With such techniques as proper orthogonal decomposition (POD) and observable inferred decomposition (OID), we seek to gain a better understanding of how jet noise created in the near-field propagates downstream, and how control can be implemented accordingly using such approaches. It has been found that through low-dimensional modeling techniques, “loud” modes in the flow have been identified, which will be utilized through a closed-loop control methodology.

Investigation of an axisymmetric transonic jet with high resolution time-resolved PIV

In the current investigation, we examine a turbulent, compressible jet flow field at Mach 1.0. In the fully anechoic jet facility at Syracuse University, the flow field is probed in order to measure near-field hydrodynamic pressure, far-field acoustic sound, and nearfield velocity. High resolution 10 kHz time-resolved particle image velocimetry (TRPIV) is implemented to gain better insight into the structures formed in the near region of the jet. By exploring those structures present just after the collapse of the potential core, in conjunction with the near and far-field pressure, low-dimensional modeling techniques are implemented in the form of proper orthogonal decomposition (POD). With these lowdimensional models, we seek to gain a better understanding of how jet noise created in the near-field propagates downstream, and how control can be implemented accordingly using such approaches.

Investigation of "Loud" Modes in a High-Speed Jet to Identify Noise-Producing Events

The current investigation focuses on a fully compressible, axisymmetric jet operating at high subsonic conditions. The test bed of interest includes 10 kHz time-resolved particle image velocimetry coupled with simultaneously sampled near and far-field pressure measurements. The experimental results to be presented have been conducted in the Syracuse University anechoic chamber at the Skytop campus. This study focuses on identifying possible noise-producing events in the flow field by implementing reduced-order modeling techniques to extract “loud” modes in the flow. These concepts are coupled with waveletbased diagnostic tracking techniques to examine the spatial and temporal nature of the “loud” modes. For this work, Mach 0.6 and Mach 0.85 will be the focus, in an effort to understand the noise-producing structures in a subsonic jet. The overall goal of this work is to efficiently link near-field velocity with far-field acoustics to identify the interactions of the flow field responsible for far-field noise generation. Low-dimensional “loud” modes can then be implemented into closed-loop control algorithms in real-time for far-field noise suppression. This paper will focus on these “loud” modes, primarily linking the flow physics directly to the acoustics.

Cluster-based reduced-order modeling to capture intermittent dynamics of interacting wakes

Interacting flows are found in a range of aviation-relevant technologies, including flow control devices, engine combustors and augmentors, and aerodynamic control surfaces. The structure and dynamics of interacting jets and wakes, including both large-scale coherent dynamics and turbulent fluctuations, is fundamentally different from that of a single flowfield. The goal of this work is to understand large-scale, intermittent dynamics of turbulent interacting wakes and jets using an improved reduced-order modeling strategy, cluster-based reduced-order modeling (CROM), to capture these dynamics. We compare the dynamics of a three-wake system at two spacings to that of a single wake flowfield using the cluster-based method. The CROM is able to capture the expected dynamics of the single wake, and the results are analogous to those from proper orthogonal decomposition. However, CROM reveals a much more complicated set of dynamics in the interacting wake cases, including the existence of two sets of dynamics that intermittently appear and the switching points between them, that the POD was unable to detect. CROM is used to quantify these dynamics and understand the effect of bluff-body spacing on the three-wake flowfields.

Turbulent Flow Physics and Control: The Role of Big Data Analyses Tools

We are studying several problems involving turbulence and big data that range from more efficient and lower noise in next generation jet propulsion systems to bio-inspired concepts for energy production. Specific examples include flows over airfoils (flapping and stationary) and other complex bodies such as turrets and high-speed jet flows. These research activities involve the collection of massive amounts of data from multi-scale computer simulations and/or large-scale experiments. Such experiments/simulations routinely produce terabytes of multi-modal data (velocity, pressure, acoustics, etc.) in fractions of a second. Time-resolved particle image velocimetry data, for example, has requirements of 10 kHz or higher sampling rates in time along with spatial resolution requirements over a broad range of spatial scales observed in high Reynolds and Mach number turbulent flows. Common questions that arise include: How do we compare and contrast data that have different levels of granularity, density (or sparseness), and distribution (e.g. uniform, checkered, lattice, random, etc.)? Can we combine such fields that span in space and time to develop a holistic systems-level understanding? This is important in linking numerical simulations that apply lenses with varying magnifications to the same system, as well as integrating qualitative and quantitative experimental observations with computer simulations. We will discuss our general efforts to apply big data analyses/modeling tools (the “right filters”) to identify patterns and predictive models rather than just a posteriori trends, statistics, and distributions. Our advanced tools include proper orthogonal decomposition, stochastic estimation, optimal inferred decomposition, wavelet analysis, and Lagrangian coherent structure methods which we are using for understanding, modeling, and controlling such flows. In this paper we focus on high Reynolds and Mach number jets, both axisymmetric and more complex. We have also utilized compressive sensing to examine high-dimensional airfoil data but will not discuss those results here and instead refer the reader to other papers in this volume which focus on this approach in some detail.

Investigation of POD bases for flow control on disk wakes

This work investigates the effects of flow control on the near wake region of a disk in a water flow, utilizing the POD reconstructed time dependent velocity fields. Velocity measurements were collected using time resolved particle image velocimetry (TRPIV) at a Reynolds number of 20,000 based on the disk diameter, both with and without control. An open-loop control was applied via periodic synthetic jet excitation from the disk edge. With the advantage of a time resolved velocity database, we have the ability to reconstruct the time dependent velocity field in the wake of the disk. This reconstruction is done for the baseline and controlled cases using various POD truncations to observe velocity reconstructions, based on the overall energy of the system. In doing so, we will consider the convergence rate of the spatial eigenvalues when conducting our POD reconstruction of the fluctuating velocity field, for both the baseline and controlled cases. Since a complex flow exists in the wake of the disk, the goal will be to form a state space representation of the flow in the form of a linear time invariant (LTI) system. This model is simply a linearization of the flow around the baseline. Furthermore, our knowledge of the input control signal will allow us to predict the flow at a later instant in time. We would like to extract the most energetic modes of the system and thereby form our observer-based controller to close the loop. In order to accomplish this, and with a rich open-loop dataset at our disposal, we will first form the POD reconstruction of the baseline. We then form a new basis, obtained by taking the actuated (controlled) data and subtracting from it the components of the flow that fall in the subspace spanned by the baseline flow. This will characterize the flow field by capturing the effect of the control input (actuation), from which the parameters of the LTI system can be identified. Preliminary POD reconstruction shows that 60% of the energy is recovered from 20 POD modes of the total 511 modes for the baseline case; similarly 60% of the energy is also recovered from 100 POD modes of the total 1,024 modes for the actuated case.Copyright