Mark Glauser

Low-dimensional characteristics of a transonic jet. Part 2. Estimate and far-field prediction

Complementary low-dimensional techniques are modified to estimate the most energetic turbulent features of a Mach 0.85 axisymmetric jet in the flows near-field regions via spectral linear stochastic estimation. This model estimate is three-dimensional, comprises all three components of the velocity field and is time resolved. The technique employs the pressure field as the unconditional input, measured within the hydrodynamic periphery of the jet flow where signatures (pressure) are known to comprise a reasonable footprint of the turbulent large-scale structure. Spectral estimation coefficients are derived from the joint second-order statistics between coefficients that are representative of the low-order pressure field (Fourier-azimuthal decomposition) and of the low-order velocity field (proper orthogonal decomposition). A bursting-like event is observed in the low-dimensional estimate and is similar to what was found in the low-speed jet studies of others. A number of low-dimensional estimates are created using different velocity-pressure mode combinations from which predictions of the far-field acoustics are invoked using Lighthills analogy. The overall sound pressure level (OASPL) directivity is determined from the far-field prediction, which comprises qualitatively similar trends when compared to direct measurements at r/D=75. Retarded time topologies of the predicted field at 90° and 30° are also shown to manifest, respectively, high- and low-frequency wave-like motions when using a combination of only the low-order velocity modes (m = 0, 1, 2). This work thus constitutes a first step in developing low-dimensional and dynamical system models from hydrodynamic pressure signatures for estimating and predicting the behaviour of the energy-containing events that govern many of the physical constituents of turbulent flows.

A time-resolved estimate of the turbulence and sound source mechanisms in a subsonic jet flow

A dynamical estimate of the axial component of a Mach 0.60 axisymmetric jets turbulent velocity field is presented here using spectral linear stochastic estimation. The pressure field surrounding the exit of the jet is employed as the unconditional parameter in the estimation technique. A sub-grid interpolation method is used to improve the spatial resolution of the estimate. The model estimate is time-resolved and reconstructed using a purely experimental database. A decomposition of the model estimate using POD and Fourier-azimuthal techniques identifies the turbulent velocity modes that are responsible for driving the near-field pressure when compared with direct measurements of the jets modal features. In effect, the signatures left in the near pressure field by the turbulence are a result of the low-order structure, the higher azimuthal modes being inefficient in driving the hydrodynamic pressure. A direct calculation of the source field using a Lighthill approach is performed, from which the low-d...

TWO-POINT CORRELATIONS OF THE NEAR AND FAR-FIELD PRESSURE IN A TRANSONIC JET

To better understand the relationship between the near-field pressure and the acoustic far-field, multi-point measurements of the near-field pressure around the periphery of a cold Mach 0.85 round jet are compared to simultaneous multi-point farfield acoustic pressure measurements. The results indicate that the near-field pressure is low dimensional and the instantaneous contribution from both azimuthal mode 0 and 1 is sufficient to accurately recover the dynamics of the near-field pressure. Correlations of the acoustic far-field with the contribution of each azimuthal mode to the near field pressure, however, indicate that only azimuthal mode 0 is well correlated with the far-field pressure, suggesting that the acoustic source in the jet is predominantly axisymmetric. The correlation of the higher azimuthal pressure modes with the far-field acoustic pressure is extremely poor suggesting that the axisymmetric source is weakened by the presence of higher azimuthal modes in the near field of the jet.

Experimental Development of a Reduced-Order Model for Flow Separation Control

Practical methods to enable control of turbulent ∞ows in a closed-loop sense are developed with a direct application in this case to ∞ow separation control over an airfoil. The tools used to reduce the dimension and complexity of the problems are based on the Proper Orthogonal Decomposition (POD) and on measurement algorithms derived from the Linear Stochastic Estimation (LSE). Signiflcant progress has been made in the measurement techniques that enable a practical estimation of an entire velocity fleld from surface pressure measurements. This in turn, permits a more accurate representation of the system when developing dynamical systems based on experimental data. The ultimate goal is to derive a plant that accurately represents the ∞ow dynamics and that contains an actuation input explicitly.

Cross-Spectral Analysis of the Pressure in a Mach 0.85 Turbulent Jet

Measurements of the near-field pressure in an unheatedMach 0.85 round jet were performed simultaneously with far-field acoustic pressure measurements at Syracuse University’s Skytop Anechoic Chamber facility to directly quantify the strength and frequency content of the propagating portion of the jet’s near-field pressure. The largest contributions were determined to be at the lower wave numbers commonly associated with hydrodynamic pressure fluctuations. This indicates that large low-frequency hydrodynamic fluctuations are obscuring a significant source of acoustic fluctuations in the jet and dictates that care must be taken when using single point measurements of nearfield pressure spectral decay to differentiate between acoustic (propagating) and hydrodynamic (nonpropagating) fluctuations.

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...

Boundary Feedback Flow Control: Proportional Control with Potential Application to Aero-Optics

A large percentage of the losses in performance and effectiveness of airborne optical systems are caused by turbulence. In an effort to reduce these adverse effects in airborne optical systems, we are exploring the use of both openand closed-loop flow control over a cylindrical turret. A series of experiments were performed at a Reynolds number of 2 10, based on the turret’s diameter and freestream velocity, which corresponds to aMach number of 0.3. The three-dimensional turret contained an actuation system that consists of 17 synthetic jets placed upstream from the leading edge of the aperture. Initially, a large database containing no control and open-loop control was obtained. These data sets provide a rich ensemble for the development and application of a simple proportional closed-loop control with the use of proper orthogonal decomposition. Surface pressuremeasurements were acquired across the aperture region for all cases studied. Results from the open-loop test demonstrate a reduction of 19.6% in the root-mean-square values when compared to the baseline case. The closed-loop flow control results show that the root-mean-square pressure fluctuations are reduced by 25.7%, the integral scales are significantly reduced, and the flow is driven toward homogeneity.

A SNAPSHOT DECOMPOSITION METHOD FOR REDUCED ORDER MODELING AND BOUNDARY FEEDBACK CONTROL.

Abstract : In this paper, we develop a reduced basis construction method that allows for separate consideration of baseline and actuated dynamics in the reduced modeling process. A prototype initial boundary value problem, governed by the two-dimensional Burgers equation, is formulated to demonstrate the utility of the method in a boundary control setting. Comparisons are done between reduced and full order solutions under open-loop boundary actuation to illustrate advantages gained by separate consideration of actuated dynamics. A tracking control problem is specified using a linear quadratic regulator formulation. Comparisons of feedback control effectiveness are done to demonstrate benefits in control effectiveness obtained from separate consideration of actuated dynamics during model reduction.

Simulation-Guided, Model-Based Feedback Flow Control for a Pitching Turret

Closed-loop systems have been developed for controlling the flow above a three-dimensional turret while the hemispherical top of the turret rotates about the pitch axis. Separation and concomitant turbulence levels incurred through the pitching cycle were altered by suction jet slots circumscribing the aperture, which served as control input; an array of pressure sensors on the turret surface provided the controller with information about the state of the flow above the surface. The control objective was to minimize the separation and turbulence in the dynamic environment created by the articulating turret. The closed-loop control systems included dynamical and measurement-based estimators, regulators, filters, and compensators. These components were developed using both computational and experimental data, and the control systemswere evaluated through a series of control-in-the-loop computation-fluid-dynamics simulations and wind-tunnel runs. The implementation of this suction flow-control system resulted in a decrease of fluctuating velocity over the flat optical aperture. Initial simple proportional and the advanced proportional-integral closed-loop control systems were able to decrease the fluctuating velocity more efficiently than the steady suction of open-loop control. The more-advanced closed-loop controllers showed a better ability to track the trends of the separation and turbulence levels as the hemisphere of the turret pitched. The development of the controller design and numerical demonstration of the closed-loop feedback system is described in a companion paper.

The Evolution of the Most Energetic Modes in a High Subsonic Mach Number Turbulent Jet

Low dimensional techniques are applied to the compressible turbulent mixing layer in the sound source regions of the ∞ow from a cold (75 o F) Mach 0.85 jet (z/D=3 to 8) using POD and Fourier decomposition. Measurements are acquired along the streamwise cross plane (r, µ) using a multi-component PIV system with an azimuthal grid spacing of 10 o to prevent aliasing of the Fourier-azimuthal modes. The decomposition is performed using single, two and three component forms of the POD (u-streamwise, v-radial, w-azimuthal) applied in radius. Fourier decomposition is applied along the azimuthal direction because of the mean periodic nature of axisymmetric ∞ows. The relative distribution of energy from this joint technique is shown to be consistent with Glauser & George 5 and Jung et al 8 who used the scalar (u) form in the incompressible axisymmetric mixing layer, and Ukeiley et al 18 who used a vector form (streamwise and radial component) in the compressible Mach 0.30 & 0.60 axisymmetric jet. The dominant Fourier-azimuthal modes in the current investigation at z/D=3 and z/D=8 are m = 5 and m = 2, respectively, and is similar to the previous flndings whereby the mean energy shifts to lower modes with the growth of the mixing layer. Using the flndings from this low-dimensional analysis, a Modifled form of Bonnet et al’s 2 Complementary Technique is employed to reconstruct temporally, the evolution of the joint technique’s expansion coe‐cients via Adrian’s 1 Linear Stochastic Estimation.