David R. Gonzalez

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.

Large-eddy simulations of plasma-based asymmetric control of supersonic round jets

Localised arc filament plasma actuators are modelled with a validated technique to examine asymmetric control of a perfectly expanded round free jet to deflect its downstream trajectory. The nominal Mach and Reynolds numbers are 1.3 and 1 million, respectively. No-control, symmetrically controlled, and under-expanded jets are also simulated for comparison purposes. Parametric variation of actuation frequency and duty cycle indicate that asymmetric control can alter the trajectory, and, within the confines of the parameters investigated, the optimal forcing scheme was found to correspond to the jets column-mode frequency and a duty cycle of approximately 60%. Increasing frequency and duty cycle beyond these values have a detrimental effect on control, which is consistent with experimental findings. Asymmetric actuation resulted in significant mixing enhancement on the actuated side, as evidenced by the increased growth rate of the non-dimensional momentum thickness. The effectiveness of control is reduced for under-expanded jet conditions.

Analysis of the Near-Field of an Asymmetrically Controlled Supersonic Round Jet

The effects of asymmetric forcing on a supersonic, perfectly-expanded jet have been investigated with large-eddy simulations. Forcing was imposed with a semi-empirical model of the Localized Arc Filament Plasma Actuators (LAFPAs), where the effects of actuation are accounted for with a local surface-heating condition. A single forcing scheme based on the first-flapping mode in which the three of the eight equally-spaced actuators, all on the same side of the jet, are fired simultaneously was adopted. Comparison of the uncontrolled and forced time-mean flow fields reveals that increased flow entrainment on the actuated side of the jet results in a modest downward angle of the forced jet plume. Coherent structures play a critical role in the dynamics of the transitional jet as the asymmetric forcing induces the creation of a ‘superstructure’ that emerges from the interaction of the induced vortices downstream of each actuator. However, due to the lack of the out of phase forcing that is present in the mixed (first-flapping) mode of actuation, the large-scale vortical structures are biased on a single side. Spectral analysis on point data at locations very close to the nozzle exit reveals that, in the very near-field, asymmetric actuation serves to reduce the sound pressure levels on the side opposite of actuation.

Exploratory Investigation of Asymmetric Control of a Supersonic Round Jet via Plasma Actuation

Localized arc filament plasma actuators (LAFPA) have been under development in academia for several years and have been shown to be effective at modifying high-subsonic and supersonic turbulent shear layer flows. The primary focus of their application thus far has centered on affecting the flow structures responsible for noise generation in an attempt to develop quieter aircraft engines. Various studies have looked at other applications for the LAFPA, including shock-boundary layer interactions. This effort focuses on an initial computational assessment of the actuators to asymmetrically control a supersonic round jet. To this end, large-eddy simulations are adopted for a perfectly expanded Mach 1.3 jet. Preliminary results have shown that pulsing three actuators on a single side of the nozzle at the jets preferred column mode frequency and a higher harmonic generates a noticeable effect on the jet exhaust. In particular, the asymmetric instabilities imposed resulted in the generation of non-zero vertical velocity components downstream of the nozzle and, in most cases tested, a reduction in length of the potential core as compared to the baseline, no-control case. An unexpected result from the asymmetric control simulations is a reversal in the vertical velocity component in the jet. Upon exiting the nozzle, the velocities curve towards to actuation side and subsequently reverse direction, achieving a peak vertical velocity in this reversal region. It is believed that vortex interactions are primarily responsible for this phenomenon. A downward vectoring of the potential cores in the asymmetrically actuated solutions provides further evidence into the dynamics responsible for this reversal.

Development of Turbulent Inflow Boundary Conditions for Large Eddy Simulations of Rocket Motor Internal Flows

‡This paper presents results from an investigation into the development of turbulent inflow boundary conditions to be used for rocket motor internal flow simulations. The proposed inflow conditions are based on extracting fluctuating pressure magnitudes from available rocket motor static firings and applying them as one of the fluctuating thermodynamic variables at the inflow boundary. Two approaches for the coupling of pressure fluctuations were explored: first, a turbulent mean profile generated via separate Reynolds-Averaged Navier-Stokes solution was imposed at the boundary along with the mean pressure, temperature, density. The fluctuating pressure signal was then superimposed on this mean profile. The second approach consisted of incorporating the pressure fluctuations into a recycle/rescale approach for the remaining turbulent fluctuating quantities. These two boundary condition implementations were tested in a simple pipe geometry. The approach where the fluctuating pressures was the only turbulence mechanism was found to be inadequate in terms of sustaining turbulence as the flow was found to relaminarize. The recycle/rescale condition coupled with the pressure fluctuation signal was capable of sustaining turbulence throughout the simulation. However, turbulence statistics were somewhat deficient when compared to direct numerical simulation results at the flow conditions studied. Further assessment of the boundary conditions is currently underway to assess the shortcomings identified in this effort.

Contrasting Modal Decompositions of Flow Fields with & without Control

The unique attributes of Proper orthogonal (POD) and dynamic mode (DMD) decompositions are examined by considering Large-Eddy Simulations (LES) of two different turbulent flow fields comprised of a supersonic, perfectly-expanded jet (without and with control) and a subsonic NACA0015 airfoil in static stall. The objectives are not only to consider the physics of the interactions, but also to accelerate the derivation of statistical data, such as the time-mean, from the LES. The stationary (time-mean) from the LES corresponds to the dominant POD mode as anticipated, while a similar result was obtained with the neutrally-stable DMD mode. However, an amplitude-based ranking of DMD modes demonstrates that if the LES snapshots are not representative of the statistically stationary state, the mean is not represented by the dominant (primary) DMD mode. A detailed comparison is performed of the key features of these stationary modes with the ‘true’ mean-flow obtained from LES. The use of these decompositions as a means of accelerating the acquisition of a suitable mean flow is also examined. The results suggest that these techniques can accelerate the acquisition of a time-mean solution and success was also obtained on reconstruction of Reynolds shear stresses using limited data samples. A sensitivity study on the effects of data sampling parameters on the two decompositions is also described.