A complex-valued resonance model for axisymmetric screech tones in supersonic jets

We model the resonance mechanism underpinning generation of A1 and A2 screech tones in an under-expanded supersonic jet. Starting from the resonance model recently proposed by \cite{mancinelli2019screech}, where the upstream-travelling wave is a neutrally-stable guided jet mode, we here present a more complete linear-stability-based model for screech prediction. We study temperature and shear-layer thickness effects and show that, in order to accurately describe the experimental data, the effect of the finite thickness of the shear layer must be incorporated in the jet-dynamics model. We then present an improved resonance model for screech-frequency predictions in which both downstream- and upstream-travelling waves may have complex wavenumber and frequency. This resonance model requires knowledge of the reflection coefficients at the upstream and downstream locations of the resonance loop. We explore the effect of the reflection coefficients on the resonance model and propose an approach for their identification. The complex-mode model identifies limited regions of frequency-flow parameter space for which the resonance loop is amplified in time, a necessary condition for the resonance to be sustained. This model provides an improved description of the experimental measurements.Comment: 28 pages, 20 figure

Large-scale streaky structures in turbulent jets

International audienceStreaks have been found to be an important part of wall turbulence dynamics. In this paper, we extend the analysis for unbounded shear flows, in particular a M = 0.4 round jet, using measurements taken using dual-plane, time-resolved, stereoscopic particle image velocimetry taken at pairs of jet cross-sections, allowing the evaluation of the cross-spectral density of streamwise velocity fluctuations resolved into azimuthal Fourier modes. From the streamwise velocity results, two analyses are performed: the evaluation of wavenumber spectra (assuming Taylor's hypothesis for the streamwise coordinate) and a spectral proper orthogonal decomposition (SPOD) of the velocity field using PIV planes in several axial stations. The methods complement each other, leading to the conclusion that large-scale streaky structures are also present in turbulent jets where they experience large growth in the streamwise direction, energetic structures extending up to eight diameters from the nozzle exit. Leading SPOD modes highlight the large-scale, streaky shape of the structures, whose aspect ratio (streamwise over azimuthal length) is about 15. The data was further analysed using SPOD, resolvent and transient-growth analyses, good agreement being observed between the models and the leading SPOD mode for the wavenumbers considered. The models also indicate that the lift-up mechanism is active in turbulent jets, with streamwise vortices leading to streaks. The results show that large-scale streaks are a relevant part of the jet dynamics

Screech-tone prediction using upstream-travelling jet modes

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Experimental investigation of thrust vectoring by flow separation control on a rectangular M = 1.45 jet

A crossflow jet actuator is used on the smallest dimension of he exhaust of a rectangular nozzle. By this way separation is introduced, creating asymetry and vectorizing the main flow. PIV measurements were performed for several fluidic injection rates. Effects of the manipulation on the main flow are discussed

Jet-edge interaction tones

Motivated by the problem of jet-flap interaction noise, we study the tonal dynamics that occur when a sharp edge is placed in the hydrodynamic nearfield of an isothermal turbulent jet. We perform hydrodynamic and acoustic pressure measurements in order to characterise the tones as a function of Mach number and streamwise edge position. The distribution of spectral peaks observed, as a function of Mach number, cannot be explained using the usual edge-tone scenario, in which resonance is underpinned by coupling between downstream-travelling Kelvin-Helmholtz wavepackets and upstream-travelling sound waves. We show, rather, that the strongest tones are due to coupling between the former and upstream-travelling jet modes recently studied by Towne et al. (2017) and Schmidt et al. (2017). We also study the band-limited nature of the resonance, showing a high-frequency cut-off to be due to the frequency dependence of the upstream-travelling waves. At high Mach number these become evanescent above a certain frequency, whereas at low Mach number they become progressively trapped with increasing frequency, a consequence of which is their not being reflected in the nozzle plane. Additionally, a weaker, low-frequency, forced-resonance regime is identified that involves the same upstream travelling jet modes but that couple, in this instance, with downstream-travelling sound waves. It is suggested that the existence of two resonance regimes may be due to the non-modal nature of wavepacket dynamics at low-frequency.Comment: 21 pages, 15 figure

Nonlinear jet-flap interactions: a dynamical-systems analysis

International audienceWe analyze the temporal dynamics associated with the jet-flap interactions by carrying-out a dynamical-systems analysis. The experimental cases are characterized by three different setups of the jet-flap system, running in the range M a = 0.6 − 1.0. The analysis is based on data presented by Jordan et al., 1 where the self-sustained oscillations were analyzed by means of linear models. Nonlinear competition among the modes was observed: here we analyze this interplay by investigating the system using statistical tools, phase portraits, Poincaré sections, and return maps. We estimate the minimal number of degrees of freedom necessary for the description of a nonlinear model. The correlation dimension is assessed for four representative cases. Finally, we analyze the toroidal geometry in the phase-space and identify the main ingredients necessary for nonlinear reduced-order models of this system

Reflection coefficients and screech-tone prediction in supersonic jets

International audienceWe study and model the resonance mechanism underlying the generation of A1 and A2 screech modes in an under-expanded supersonic jet. Following our previous work [1], where upstream-travelling guided jet modes were used to provide closure of the screech resonance loop, we here consider a more complete model in which both wavenumbers and frequencies of the upstream-and downstream-travelling waves are complex. The new model requires knowledge of the upstream and downstream reflection coefficients, which are treated as parameters and identified using the experimental data. The new screech model is shown to provide a more complete description of the measured data. I. Nomenclature c ∞ = Ambient speed of sound k = Dimensionless streamwise wavenumber ω = Non-dimensional frequency m = Order of the azimuthal Fourier mode n r = Radial order of the guided jet modes St = Nozzle diameter-based Strouhal number M a = Acoustic Mach number M j = Jet Mach number U j = Jet velocity T = Jet-to-ambient temperature ratio k K H = Kelvin-Helmholtz instability mode k p = Guided jet mode L 1 = Length of the first shock cell L s = Location of the s th shock cell Re = Nozzle diameter-based Reynolds number D = Nozzle diameter r = Radial distance from the nozzle axis SPSL = Sound Pressure Spectrum Level

Dynamics of a pre-stalled windturbine blade using control of circulation at the trailing-edge

Wind turbines are installed in the strongly inhomogeneous and unsteady turbulent atmospheric boundary layer. This induces unsteady mechanical loads at different characteristic time scales from seconds to minutes which limit significantly their life time. The present work, supported by the SMARTEOLE ANR project, focuses on the flow control strategies at the blade scale, to manipulate lift and thus alleviate some of these loads. For this purpose, a NACA654-421 airfoil profile has been modified : the trailing edge has been rounded to take advantage of Coanda effects and the camber has been increased to compensate the loss of lift due to the trailing edge modifications. The lift control is obtained by fluidic injection via 42 1x1 mm micro-jets placed at the trailing edge along the entire span of the wing. An experiment has been conducted to identify both static and dynamic performances of the proposed control mechanism. The experimental campaign consisted in chordwise unsteady pressure measurements as well as aerodymics forces measurements. The preliminary results of the mean quantities indicate that the lift gain obtained is proportional to the fluidic injection, which is of interest when closed-loop control is to be considered. In a second series of measurements, we focus on the step-response of the flow to the actuation. The lift response is shown to behave as a first order dynamics and we show that the response time of lift is of the order of 3 convective time units. This is about three times faster than what is usually observed for boundary layer reattachement process

Large eddy simulation for jet noise: the importance of getting the boundary layer right

Large eddy simulations of an isothermal Mach 0.9 jet issued from a convergent-straight nozzle are performed at Reynolds number 1 × 10^6. The flow configuration and operating conditions match the companion experiment conducted at the PPRIME Institute, Poitiers. To replicate the effects of the boundary layer trip present in the experiment and to ensure a turbulent jet, localized adaptive mesh refinement, synthetic turbulence, and wall modeling are used inside the nozzle. This leads to fully turbulent nozzle-exit boundary layers and results in significant improvements for the flow field and sound predictions, compared to those obtained from the typical approach based on laminar flow assumption in the nozzle. The far-field noise spectra now match the experimental measurements to within 0.5 dB for relevant angles and frequencies. As a next step toward better understanding of turbulent jet noise, the large database collected during the simulation is currently being used for reduced order modeling and wavepacket analysis