Rachelle Speth

Finite-time Lyapunov exponent-based analysis for compressible flows

The finite-time Lyapunov exponent (FTLE) technique has shown substantial success in analyzing incompressible flows by capturing the dynamics of coherent structures. Recent applications include river and ocean flow patterns, respiratory tract dynamics, and bio-inspired propulsors. In the present work, we extend FTLE to the compressible flow regime so that coherent structures, which travel at convective speeds, can be associated with waves traveling at acoustic speeds. This is particularly helpful in the study of jet acoustics. We first show that with a suitable choice of integration time interval, FTLE can extract wave dynamics from the velocity field. The integration time thus acts as a pseudo-filter separating coherent structures from waves. Results are confirmed by examining forward and backward FTLE coefficients for several simple, well-known acoustic fields. Next, we use this analysis to identify events associated with intermittency in jet noise pressure probe data. Although intermittent events are known to be dominant causes of jet noise, their direct source in the turbulent jet flow has remained unexplained. To this end, a Large-Eddy Simulation of a Mach 0.9 jet is subjected to FTLE to simultaneously examine, and thus expose, the causal relationship between coherent structures and the corresponding acoustic waves. Results show that intermittent events are associated with entrainment in the initial roll up region and emissive events downstream of the potential-core collapse. Instantaneous acoustic disturbances are observed to be primarily induced near the collapse of the potential core and continue propagating towards the far-field at the experimentally observed, approximately 30° angle relative to the jet axis.

Near Field Pressure and Associated Coherent Structures of Excited Jets

Large Eddy Simulations (LES) were performed for Mach 0.9 and 1.3 cold jets to associate the structures of the shear layer with near field pressure fluctuations. The jets were excited by Localized Arc Filament Plasma Actuators (LAFPAs) arranged around the periphery of the nozzle with the axisymmetric (m = 0) mode. Excitation frequencies of St = fD/Uj = 0.05 to 0.25 (close to the column mode frequency) were computed for each Mach number. The St = 0.05 produces one pulse that propagates downstream without interacting with previously emitted pulses. This is referred to as the the impulse response. The St = 0.25 frequency exhibits subsequent pulse interactions. Simulation data for both Mach numbers was collected along three arrays at different radial locations. Strong agreement was found for the near field response to excitation and the mean center-line axial velocity between the subsonic simulations and the experiments. The experiment and simulations depict a large hydrodynamic wave downstream of the exit moving at the speed of convection near the shear layer consisting of a large peak followed by a large trough after the actuator pulse. For the highest excitation frequency, the interaction between structures yields an almost sinusoidal wave in the near field. These hydrodynamic waves are associated to the phase-averaged flow structure which includes a series of rollers and ribs and the associated dilatation field. The structure interactions from subsequent pulses results in a quasi-linear superposition of the impulse jet response (St = 0.05) to actuation. Auto-correlations and two-point correlations describe the development and interaction between adjacent structures in time and space.Copyright

Nozzle-Exit Boundary-Layer Effects on a Controlled Supersonic Jet

The effect of nozzle-exit boundary-layer thickness on the evolution of a round Mach 1.3, Reynolds number 1×106 jet is examined without and with control. For the latter, the flapping mode is considered at the preferred column mode frequency (Strouhal number=0.3). The boundary-layer thickness is varied from a very small value to 25% of the diameter. For the no-control cases, the distance between the nozzle lip and the initial appearance of breakdown is proportional to the boundary-layer thickness, which is consistent with theory and previous results by other researchers at Mach 0.9. However, the subsequent growth toward the centerline is faster for the thicker boundary layers. With flapping mode control, increasing the thickness of the boundary layer has different effects on the flapping and nonflapping planes. The rapid spreading of the jet observed on the flapping plane with thin boundary layers is greatly diminished as the nozzle-exit layer is thickened. Conversely, the rate of spreading on the nonflappi...

Correlation of Near Field Pressure With Coherent Structures in an Excited Mach 1.3 Jet

Large Eddy Simulations (LES) were performed of a Mach 1.3 cold jet excited by plasma actuators arranged on the periphery of a round nozzle exit to understand the effect of excitation on the near field sound and shear layer structures. The flow is excited with the axisymmetric (m = 0) mode at 0.525% duty cycle. The time period between pulses was varied from a very low value, where the response is expected to be similar to that due to an impulse, to a value near the preferred column mode value where the response is highly non-linear. Simulation data was collected at points on three arrays radiating 8.6° to the horizontal, originating at radial distances of 1.126D, 2.126D and 5.76D respectively. Detailed auto and two-point correlations of measurements on these rakes have been examined. In the first set of observations, different points were considered on Array 1. The auto-correlations clearly show the existence and growth of structures with excitation. At the lowest frequency, the effect of individual pulses is distinct, confirming that at this value, the response is similar to that of an impulse. At the highest frequency, the interaction between structures yields an almost sinusoidal value. In the second set of observations, two point correlations of each point on the innermost array were obtained with the downstream point of the outer-most array where the signal is purely acoustic. The analysis indicate that the highest correlation occurs with the region immediately downstream of the potential core collapse as well as with the point immediately beneath (sideline). The features observed in the statistical analysis are connected to the phase averaged flow structure which includes a series of rollers and ribs and associated dilatational field.Copyright

A Study of the Noise Source Mechanisms in an Excited Mach 0.9 Jet - Complementary Experimental and Computational Analysis

Coordinated experimental and numerical results are analyzed concurrently to explore the dynamics of large-scale structures and the resultant effect on the acoustic signals in a Mach 0.9 jet. The results comprise an unheated jet which is being excited by plasma actuators in order to produce coherent structures with a well-defined phase. The dynamic interactions of the generated large-scale structures are investigated using phase-averaging and iso-levels of Q-criterion. The near-field is then decomposed into its constitutive hydrodynamic and acoustic components using a spatio-temporal wavelet transform. Two-point correlations between the full and decomposed near-field, and the nearand far-field acoustic signals are utilized to identify the dominant acoustic source regions in both jets. Our previous experimental work had shown that each individual actuation event produced a temporally and spatially localized pressure fluctuation in the irrotational near-field, which was termed the impulse response of the jet. The response of the jet to periodic excitation could be reconstructed from a linear superposition of this impulse response. Results also showed that the nearand far-acoustic fields are also governed by this quasi-linear mechanism (though this does not imply that the noise generation process itself is necessarily linear). The preliminary analysis of the numerical results found that this same principle applied inside the jet shear layer (at jet lipline), albeit with less accuracy; suggesting that the structure interactions are largely linear in nature.