Three-dimensional instabilities in compressible flow over open cavities

Direct numerical simulations are performed to investigate the three-dimensional stability of compressible flow over open cavities. A linear stability analysis is conducted to search for three-dimensional global instabilities of the two-dimensional mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of flow conditions and cavity aspect ratios. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately one cavity depth and oscillates with a frequency about one order of magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities previously reported in flows over backward-facing steps, lid-driven cavity flows and Couette flows. Results from three-dimensional simulations of the nonlinear compressible Navier–Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. The results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows

Three-Dimensional Linear Stability Analysis of Cavity Flows

Numerical Simulations of the two- and three-dimensional linearized Navier–Stokes equations are performed to investigate instabilities of open cavity flows that are homogeneous in the spanwise direction. First, the onset of two-dimensional cavity instability is characterized over a range of Mach numbers, Reynolds numbers and cavity aspect ratios. The resulting oscillations are consistent with the typical Rossiter flow/acoustic resonant modes. We then identify the presence of three-dimensional instabilities of the two-dimensional basic flow and study their dependence on the parameter space. In general, the most amplified three-dimensional mode has a spanwise wavelength scaling with the cavity depth, and a frequency typically an order-of-magnitude smaller than two-dimensional Rossiter modes. The instability appears to arise from a generic centrifugal instability mechanism associated with a large vortex in the two-dimensional basic flow that occupies the downstream portion within the cavity

Direct Numerical Simulations of Three-Dimensional Cavity Flows

Three-dimensional direct numerical simulations of the full compressible Navier–Stokes equations are performed for cavities that are homogeneous in the spanwise direction. The formation of oscillating spanwise structures is observed inside the cavity. We show that this 3D instability arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. In general, the three-dimensional mode has a spanwise wavelength of approximately 1 cavity depth and oscillates with a frequency about an order-of-magnitude lower than 2D Rossiter (flow/acoustics) instabilities. The 3D mode properties are in excellent agreement with predictions from our previous linear stability analysis. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. We connect these results with the observation of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows. Preliminary results on the connections between the 3D centrifugal instabilities and the presence/suppression of the wake mode are also presented

Acoustic Properties of Porous Coatings for Hypersonic Boundary-Layer Control

Numerical simulations are performed to investigate the interaction of acoustic waves with an array of equally spaced two-dimensional microcavities on an otherwise flat plate without external boundary-layer flow. This acoustic scattering problem is important in the design of ultrasonic absorptive coatings for hypersonic laminar flow control. The reflection coefficient, characterizing the ratio of the reflected wave amplitude to the incident wave amplitude, is computed as a function of the acoustic wave frequency and angle of incidence, for coatings of different porosities, at various acoustic Reynolds numbers relevant to hypersonic flight. Overall, the numerical results validate predictions from existing theoretical modeling. In general, the amplitude of the reflection coefficient has local minima at some specific frequencies. A simple model to predict these frequencies is presented. The simulations also highlight the presence of resonant acoustic modes caused by coupling of small-scale scattered waves near the coating surface. Finally, the cavity depth and the porosity are identified as the most important parameters for coating design. Guidelines for the choice of these parameters are suggested

Direct Numerical Simulations of Three-Dimensional Cavity Flows

Three-dimensional direct numerical simulations of the full compressible Navier–Stokes equations are performed for cavities that are homogeneous in the spanwise direction. The formation of oscillating spanwise structures is observed inside the cavity. We show that this 3D instability arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. In general, the three-dimensional mode has a spanwise wavelength of approximately 1 cavity depth and oscillates with a frequency about an order-of-magnitude lower than 2D Rossiter (flow/acoustics) instabilities. The 3D mode properties are in excellent agreement with predictions from our previous linear stability analysis. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. We connect these results with the observation of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows. Preliminary results on the connections between the 3D centrifugal instabilities and the presence/suppression of the wake mode are also presented

Second-mode attenuation and cancellation by porous coatings in a high-speed boundary layer

Numerical simulations of the linear and nonlinear two-dimensional Navier–Stokes equations, and linear stability theory are used to parametrically investigate hypersonic boundary layers over ultrasonic absorptive coatings. The porous coatings consist of a uniform array of rectangular pores (slots) with a range of porosities and pore aspect ratios. For the numerical simulations, temporally (rather than spatially) evolving boundary layers are considered and we provide evidence that this approximation is appropriate for slowly growing second-mode instabilities. We consider coatings operating in the typical regime where the pores are relatively deep and acoustic waves and second-mode instabilities are attenuated by viscous effects inside the pores, as well as regimes with phase cancellation or reinforcement associated with reflection of acoustic waves from the bottom of the pores. These conditions are defined as attenuative and cancellation/reinforcement regimes, respectively. The focus of the present study is on the cases which have not been systematically studied in the past, namely the reinforcement regime (which represents a worst-case scenario, i.e. minimal second-mode damping) and the cancellation regime (which corresponds to the configuration with the most potential improvement). For all but one of the cases considered, the linear simulations show good agreement with the results of linear instability theory that employs an approximate porous-wall boundary condition, and confirm that the porous coating stabilizing performance is directly related to their acoustic scattering performance. A particular case with relatively shallow pores and very high porosity showed the existence of a shorter-wavelength instability that was not initially predicted by theory. Our analysis shows that this new mode is associated with acoustic resonances in the pores and can be more unstable than the second mode. Modifications to the theoretical model are suggested to account for the new mode and to provide estimates of the porous coating parameters that avoid this detrimental instability. Finally, nonlinear simulations confirm the conclusions of the linear analysis; in particular, we did not observe any tripping of the boundary layer by small-scale disturbances associated with individual pores

Alternate Designs of Ultrasonic Absorptive Coatings for Hypersonic Boundary Layer Control

Numerical simulations of the linear and nonlinear two-dimensional Navier-Stokes equations are used to parametrically investigate hypersonic boundary layers over ultrasonic absorptive coatings consisting of a uniform array of rectangular pores (slots) with a range of porosities and pore aspect ratios. Based on our previous work, we employ a temporally evolving approximation appropriate to slowly-growing second-mode instabilities. We consider coatings operating in attenuative regimes where the pores are relatively deep and acoustic waves and second mode instabilities are attenuated by viscous effects inside the pores, as well as cancellation/reinforcement regimes with alternating regions of local minima and maxima of the coating acoustic absorption, depending on the frequency of the acoustic waves. The focus is on reinforcement cases which represent a worst case scenario (minimal second-mode damping). For all but one of the cases considered, the linear simulations confirm the results of linear instability theory that employs an approximate porous-wall boundary condition. A particular case with a relatively shallow cavities and very high porosity showed the existence of a shorter wavelength instability that is not predicted by theory. Finally, nonlinear simulations of the same cases led to the same conclusions as linear analysis; in particular, we did not observe any "tripping" of the boundary layer by small scale disturbances associated with individual pores

Numerical Simulations of the Transient Flow Response of a 3D, Low-Aspect-Ratio Wing to Pulsed Actuation

Numerical simulations of the natural and actuated unsteady flow over a three-dimensional low-aspect ratio wing are performed using Lattice Boltzmann method. The LBM simulations match the flow conditions and the detailed wing geometry from previous experiments, including the actuators that are installed internally along the leading edge of the wing. The present study focuses on the transient lift response to short-duration square-wave actuation, for the wing in a uniform flow at five different angles of attack. Overall, both mean and unsteady numerical results show good agreement with the experimental data, in particular at the post-stall angle of attack 19°, where the maximum lift enhancement occurs. At that angle of attack, the effects of the actuation strength and duration are investigated. In general, the lift response to a single pulse increases with increasing actuator mass-flow rate and pulse duration

Solutions to aliasing in time-resolved flow data

Avoiding aliasing in time-resolved flow data obtained through high fidelity simulations while keeping the computational and storage costs at acceptable levels is often a challenge. Well-established solutions such as increasing the sampling rate or low-pass filtering to reduce aliasing can be prohibitively expensive for large data sets. This paper provides a set of alternative strategies for identifying and mitigating aliasing that are applicable even to large data sets. We show how time-derivative data, which can be obtained directly from the governing equations, can be used to detect aliasing and to turn the ill-posed problem of removing aliasing from data into a well-posed problem, yielding a prediction of the true spectrum. Similarly, we show how spatial filtering can be used to remove aliasing for convective systems. We also propose strategies to avoid aliasing when generating a database, including a method tailored for computing nonlinear forcing terms that arise within the resolvent framework. These methods are demonstrated using large-eddy simulation (LES) data for a subsonic turbulent jet and a non-linear Ginzburg-Landau model.Comment: 25 pages, 14 figure

Spectral analysis of jet turbulence

Informed by large-eddy simulation (LES) data and resolvent analysis of the mean flow, we examine the structure of turbulence in jets in the subsonic, transonic and supersonic regimes. Spectral (frequency-space) proper orthogonal decomposition is used to extract energy spectra and decompose the flow into energy-ranked coherent structures. The educed structures are generally well predicted by the resolvent analysis. Over a range of low frequencies and the first few azimuthal mode numbers, these jets exhibit a low-rank response characterized by Kelvin–Helmholtz (KH) type wavepackets associated with the annular shear layer up to the end of the potential core and that are excited by forcing in the very-near-nozzle shear layer. These modes too have been experimentally observed before and predicted by quasi-parallel stability theory and other approximations – they comprise a considerable portion of the total turbulent energy. At still lower frequencies, particularly for the axisymmetric mode, and again at high frequencies for all azimuthal wavenumbers, the response is not low-rank, but consists of a family of similarly amplified modes. These modes, which are primarily active downstream of the potential core, are associated with the Orr mechanism. They occur also as subdominant modes in the range of frequencies dominated by the KH response. Our global analysis helps tie together previous observations based on local spatial stability theory, and explains why quasi-parallel predictions were successful at some frequencies and azimuthal wavenumbers, but failed at others