Compressible Cavity Flows Research Articles

A Novel Reduced-Order Model for Predicting Compressible Cavity Flows

Compressible cavity flows exist widely in aeronautical vehicles. The cost of the computational fluid dynamics to solve compressible cavity flows is high. To address this issue, in this work, a novel reduced-order model (ROM) combining proper orthogonal decomposition (POD) with the long short-term memory (LSTM) neural network named LSTM-ROM for predicting the compressible cavity flows is proposed. First, POD is used to provide a low-dimensional subspace. Then, the LSTM neural network is designed to predict the POD coefficients with time evolution. The results show that the LSTM-ROM can accurately predict the POD coefficients for a long time and capture the shock wave structures at supersonic speed. The predicted density and normal velocity field are consistent with those simulated by direct numerical simulation (DNS). The calculation time of LSTM-ROM is almost one-seventh of that of DNS. By comparing the performance of LSTM-ROM with that of dynamic mode decomposition (DMD) and multilayer perceptron (MLP), it is found that the root mean square errors of density and normal velocity field predicted by LSTM-ROM are smaller than those predicted by DMD and MLP. In addition, the LSTM-ROM can accurately and efficiently predict the flows over cavities with different inclination angles at subsonic speed. Therefore, the LSTM-ROM is an accurate and efficient method for predicting the compressible cavity flows, which lays a foundation for other complex flows.

Effect of vortex and entropy sources in sound generation for compressible cavity flow

The present study reports the effect of different source terms on the near and far-field acoustic characteristics of compressible flow over a rectangular cavity using hybrid computational aeroacoustics methodology. We use a low dispersive and dissipative compressible fluid flow solver in conjunction with an acoustic perturbation equation solver based on the spectral/hp element method. The hybrid approach involves calculating the base fields and the acoustic sources from a fluid simulation in the first step. In the next step, the acoustic solver utilizes the variables to predict the acoustic propagation due to the given sources. The validation of the methodology against benchmark cases provides quite accurate results while compared against the existing literature. The study is then extended to assess the importance of the entropy source term for the flow over a rectangular cavity. The predictions of hybrid simulations with vortex and entropy source terms reproduce the perturbation pressure values very close to the existing direct numerical simulation results. Moreover, the results suggest that the use of just the vortex source terms over-predicts the perturbation pressure near the source region. Finally, we have carried out detailed simulations with all the source terms to investigate the noise sources for compressible flow over the cavity for different Mach number ranges (M=0.4,0.5,0.6,0.7,1.5). The obtained acoustic spectra and the sound directivity are in close agreement with the reference experiment.

Spatial distribution of pressure resonance in compressible cavity flow

The development of the unsteady pressure field on the floor of a rectangular cavity was studied at Mach 0.9 using high-frequency pressure-sensitive paint. Power spectral amplitudes at each cavity resonance exhibit a spatial distribution with a streamwise-oscillatory pattern; additional maxima and minima appear as the mode number is increased. This spatial distribution also appears in the propagation velocity of modal pressure disturbances. This behaviour was tied to the superposition of a downstream-propagating shear-layer disturbance and an upstream-propagating acoustic wave of different amplitudes and convection velocities, consistent with the classical Rossiter model. The summation of these waves generates a net downstream-travelling wave whose amplitude and phase velocity are modulated by a fixed envelope within the cavity. This travelling-wave interpretation of the Rossiter model correctly predicts the instantaneous modal pressure behaviour in the cavity. Subtle spanwise variations in the modal pressure behaviour were also observed, which could be attributed to a shift in the resonance pattern as a result of spillage effects at the edges of the finite-width cavity.

Identification of the formation of resonant tones in compressible cavity flows

Identification of the fluid dynamic mechanisms responsible for the formation of resonant tones in a cavity flow is challenging. Time-frequency non-linear analysis techniques were applied to the post-processing of pressure signals recorded on the floor of a rectangular cavity at a transonic Mach number. The results obtained, confirmed that the resonant peaks in the spectrum were produced by the interaction of a carrier frequency (and its harmonics) and a modulating frequency. High-order spectral analysis, based on the instantaneous wavelet bi-coherence method, was able to identify, at individual samples in the pressure–time signal, that the interaction between the fundamental frequency and the amplitude modulation frequency was responsible for the creation of the Rossier–Heller tones. The same technique was also able to correlate the mode switching phenomenon, as well as the deactivation of the resonant tones during the temporal evolution of the signal.

Flow-induced vibration in the compressible cavity flow

The cavity plays an important role in the fuel-air mixing and combustion stability inside the hypersonic scramjet. However, the high levels of time-dependent loading resulting from the supersonic cavity flow can cause intense structural vibration even damage. Experiments and numerical simulations were performed to understand the complex fluid-structure interaction in this paper. A cantilever plate with a cavity was installed as a splitter plate in the supersonic mixing layer wind tunnel. The response displacements of this cantilever plate were measured by a non-intrusive laser vibrometer. Large eddy simulation (LES) was applied to calculate the aerodynamic loading. Results show that the St number of time-dependent surface-averaged pressure difference agrees well with semi-empirical relation of Heller used to predict the resonance mode. The cantilever plate exhibits a directly dependent response to self-oscillation of supersonic cavity flow. Measurement results of displacement indicate that the vibration shape of this plate is dominantly two-dimensional.

Resonance dynamics in compressible cavity flows using time-resolved velocity and surface pressure fields

The resonance modes in Mach 0.94 turbulent flow over a cavity having a length-to-depth ratio of five were explored using time-resolved particle image velocimetry (TR-PIV) and time-resolved pressure sensitive paint (TR-PSP). Mode switching was quantified in the velocity field simultaneous with the pressure field. As the mode number increased from one through three, the resonance activity moved from a region downstream within the recirculation region to areas further upstream in the shear layer, an observation consistent with linear stability analysis. The second and third modes contained organized structures associated with shear layer vortices. Coherent structures occurring in the velocity field during modes two and three exhibited a clear modulation in size with streamwise distance. The streamwise periodicity was attributable to the interference of downstream-propagating vortical disturbances with upstream-travelling acoustic waves. The coherent structure oscillations were approximately $180^{\circ }$ out of phase with the modal surface pressure fluctuations, analogous to a standing wave. Modal propagation (or phase) velocities, based on cross-correlations of bandpass-filtered velocity fields were found for each mode. The phase velocities also showed streamwise periodicity and were greatest at regions of maximum constructive interference where coherent structures were the largest. Overall, the phase velocities increased with modal frequency, which coincided with the modal activity residing at higher portions of the cavity where the local mean flow velocity was elevated. Together, the TR-PIV and TR-PSP provide unique details not only on the distribution of modal activity throughout the cavity, but also new understanding of the resonance mechanism as observed in the velocity field.

Response of a Store with Tunable Natural Frequencies in Compressible Cavity Flow

Fluid–structure interactions that occur during aircraft internal store carriage were experimentally explored at Mach 0.58–1.47 using a generic, aerodynamic store installed in a rectangular cavity having a length-to-depth ratio of seven. The store vibrated in response to the cavity flow at its natural structural frequencies, and it exhibited a directionally dependent response to cavity resonance frequencies. Cavity tones excited the store in the streamwise and wall-normal directions consistently, whereas the spanwise response to cavity tones was much more limited. Increased surface area associated with tail fins raised vibration levels. The store had interchangeable components to vary its natural frequencies by about 10–300 Hz. By tuning natural frequencies, mode-matched cases were explored where a prominent cavity tone frequency matched a structural natural frequency of the store. Mode matching in the streamwise and wall-normal directions produced substantial increases in peak store vibrations, though the response of the store remained linear with dynamic pressure. Near mode-matched frequencies, changes in cavity tone frequencies of only 1% altered store peak vibrations by as much as a factor of two. Mode matching in the spanwise direction did little to increase vibrations.

Pressure and kinetic energy transport across the cavity mouth in resonating cavities

Basic properties of the incompressible fluid motion in a rectangular cavity located along one wall of a plane channel are considered. For Mach numbers of the order of 1×10(-3) and using the incompressible formulation, we look for observable properties that can be associated with acoustic emission, which is normally observed in this kind of flow beyond a critical value of Reynolds number. The focus is put on the energy dynamics, in particular on the accumulation of energy in the cavity which takes place in the form of pressure and kinetic energy. By increasing the external forcing, we observe that the pressure flow into the cavity increases very rapidly, then peaks. However, the flow of kinetic energy, which is many orders of magnitude lower than that of the pressure, slowly but continuously grows. This leads to the pressure-kinetic energy flows ratio reaching an asymptotic state around the value 1000 for the channel bulk speed Reynolds number. It is interesting to note that beyond this threshold when the channel flow is highly unsteady-a sort of coarse turbulent flow-a sequence of high and low pressure spots is seen to depart from the downward cavity step in the statistically averaged field. The set of spots forms a steady spatial structure, a sort of damped standing wave stretching along the spanwise direction. The line joining the centers of the spots has an inclination similar to the normal to the fronts of density or pressure waves, which are observed to propagate from the downstream cavity edge in compressible cavity flows (at Mach numbers of 1×10(2) to 1×10(3), larger than those considered here). The wavelength of the standing wave is of the order of 1/8 the cavity depth and observed at the channel bulk Reynolds number, Re~2900. In this condition, the measure of the maximum pressure differences in the cavity field shows values of the order of 1×10(-1) Pa. We interpret the presence of this sort of wave as the fingerprint of the noise emission spots which could be observed in simulations where the full compressible formulation is used. The flow is studied by means of a sequence of direct numerical simulations in the Reynolds number range 25-2900. This allows the study to span across the steady laminar regime up to a first coarse turbulent regime. These results are confirmed by the good agreement with a set of laboratory results obtained at a Reynolds number one order of magnitude larger in a different cavity geometry [M. Gharib and A. Roshko, J. Fluid Mech. 177, 501 (1987)]. This leaves room for a certain degree of qualitative universality to be associated with the present findings.

Corner Singularity Dynamics and Regularity of Compressible Viscous Navier--Stokes Flows

We show unique existence (global in time) and regularity of solutions to the Navier--Stokes equations for compressible viscous flows with nonzero initial and Dirichlet boundary data on polygonal domains. The solution is constructed by the inverse of the sum of two operators taken from Da Prato and Grisvard [J. Math. Pures Appl. (9), 54 (1975), pp. 305--387] and, applying to the inverse the corner singularity result of the Lamé system and the Laplace with parameters, is split into singular and regular parts. The orders of the leading corner singularities for the velocity are the same as those of the Lamé system, and the one for the temperature is the same as that for the Laplace operator. The coefficients of the singularities, called the stress intensity functions, are constructed, and the remainders are shown to have increased regularities. Consequently the derivatives of the flow variables may blow up along the trajectory curves starting near the nonconvex vertices, so the dynamical behaviors will be steeply changed there. The corner singularities are also propagated into the region by the transport character of the continuity equation. The explicit expression of singularities near the corners may be employed in a direct estimation of compressible cavity flow oscillations, for instance, the resonant amplitude tones near corners.

Low-frequency components and modulation processes in compressible cavity flows

The modulated character of cavity-flow oscillations is investigated through a so-called modulation analysis of spectral distributions. The approach is based on a recently proposed viewpoint on the Rossiter formula and concerns mid- to high-subsonic flows in shallow cavities. For this type of configuration, the spectra are mainly characterized by the presence of several dominant peaks (Rossiter modes) that are not in a harmonic relation but uniformly spaced at a distance equal to the fundamental frequency of the oscillation mechanism (aero-acoustic feedback loop). This feature is interpreted as the result of an amplitude modulation process and related to variations in the vortex–corner interaction in the downstream part of the cavity ( γ modulation). A lower frequency modulation is identified through the secondary peak distribution. A detailed analysis of the spectral structure confirms the presence of a component at the corresponding frequency value ( Δ f mode). The assumption of a specific coupling between the two modulation processes is investigated. It leads to a new approximate form for the γ-modulation ratio that allows an explicit expression of the Rossiter constant γ related to aspect ratio of the cavity ( L/D).

Compressible cavity flow oscillation due to shear layer instabilities and pressure feedback

A computational analysis was performed on a compressible flow oscillation due to shear layer instabilities over a cavity and pressure feedback in a cavity of length-to-depth ratio 3 at Mach 1.5 and 2.5. The mass-averaged NavierStokes equations were solved. Turbulence closure was achieved using a k-u> model with compressibility corrections. Self-sustained oscillations were produced. Negative form drag coefficient was observed within an oscillatory cycle due to mass ejection from the cavity near the trailing edge and vortex production near the leading edge. The shock wave-expansion wave interaction patterns, modes of the oscillation, sound pressure level, and time-averaged surface pressure were compared with experimental results of previous investigations and good agreement was achieved, particularly the time-averaged pressure. The prediction showed a marked improvement over earlier analysis.

Navier-Stokes Calculations of Transonic Flows Past Cavities

Presented in this paper is a computational investigation of subsonic and transonic flows past three-dimensional deep and transitional cavities. Simulations of these self-induced oscillatory flows have been generated through time-accurate solutions of the Reynolds averaged, full Navier-Stokes equations, using the explicit MacCormack scheme. The Reynolds stresses have been included through the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties. The results of an experimental investigation have been used not only to validate the time-averaged results, but also to investigate the effects of varying the Mach number and the incoming boundary-layer thickness. Time series analyses have been performed for the instantaneous pressure values on the cavity floor and compared with the results obtained by a predictive formula. While most of the comparisons have been favorable, some discrepancies have been observed, particularly on the rear face. The present results help understanding the three-dimensional and unsteady features of the separations, vortices, the shear layer, as well as some of the aeroacoustic phenomena of compressible cavity flows.