Instability waves and low-frequency noise radiation in the subsonic chevron jet

Spatial instability frequency noise radiation at waves associated with low- shallow polar angles in the chevron jet are investigated and are compared to the round counterpart. The Reynolds-averaged Navier-Stokes equations are solved to obtain the mean flow fields, which serve as the baseflow for linear stability analysis. The chevron jet has more complicated instability waves than the round jet, where three types of instability modes are identified in the vicinity of the nozzle, corresponding to radial shear, azimuthal shear, and their integrated effect of the baseflow, respectively. The most unstable frequency of all chevron modes and round modes in both jets decrease as the axial location moves downstream. Besides, the azimuthal shear effect related modes are more unstable than radial shear effect related modes at low frequencies. Compared to a round jet, a chevron jet reduces the growth rate of the most unstable modes at down- stream locations. Moreover, linearized Euler equations are employed to obtain the beam pattern of pressure generated by spatially evolving instability waves at a dominant low frequency St = 0.3, and the acoustic efficiencies of these linear wavepackets are evaluated for both jets. It is found that the acoustic efficiency of linear wavepacket is able to be reduced greatly in the chevron jet, compared to the round jet.

Coherent structures and wavepackets in subsonic transitional turbulent jets

A large eddy simulation (LES) is performed for two subsonic jets with a Reynolds number of , which have different core temperatures, i.e., the cold and hot jet. The far-field overall sound pressure levels (OASPL) and noise spectra are well validated against previous experimental results. It is found that the OASPL is raised by heating at shallow angles. The most energetic coherent structures are extracted with specified frequencies using the filter based on the frequency domain variant of the snapshot method of proper orthogonal decomposition (POD). The modes have high coherence of near-field pressure for both jets, while the coherence of modes is enhanced greatly by heating. Based on the coherent structures, spatial wavepackets are educed and the characteristics of growth, saturation and decay are analyzed and compared between the two jets in detail. The results show that heating would enhance the linear growth rate for high frequency components, and nonlinear growth rates for low frequency components in general, which are responsible for higher OASPL in the hot jet. The far-field sound generated by wavepackets is computed using the Kirchhoff extrapolation, which matches well with that of LES at shallow angles. This indicates that the wavepackets associated with coherent structures are dominant sound sources in forced transitional turbulent jets. Additionally, the present POD method is proven to be a robust tool to extract the salient features of the wavepackets in turbulent flows.

Bifurcations in penetrative Rayleigh-Be′nard convection in a cylindrical container

The bifurcations of penetrative Rayleigh-B′enard convection in cylindrical containers are studied by the linear stability analysis(LSA) combined with the direct numerical simulation(DNS) method. The working ?uid is cold water near 4?C, where the Prandtl number P r is 11.57, and the aspect ratio(radius/height) of the cylinder ranges from 0.66 to 2. It is found that the critical Rayleigh number increases with the increase in the density inversion parameter θ_m. The relationship between the normalized critical Rayleigh number(Rac(θ_m)/Rac(0)) and θ_m is formulated, which is in good agreement with the stability results within a large range of θ_m. The aspect ratio has a minor effect on Rac(θ_m)/Rac(0). The bifurcation processes based on the axisymmetric solutions are also investigated. The results show that the onset of axisymmetric convection occurs through a trans-critical bifurcation due to the top-bottom symmetry breaking of the present system.Moreover, two kinds of qualitatively different steady axisymmetric solutions are identi?ed.

Mode transition and oscillation suppression in supersonic cavity flow

Supersonic flows past two-dimensional cavities with/without control are investigated by the direct numerical simulation （DNS）. For an uncontrolled cavity, as the thickness of the boundary layer declines, transition of the dominant mode from the steady mode to the Rossiter Ⅱ mode and then to the Rossiter III mode is observed due to the change of vortex-corner interactions. Meanwhile, a low frequency mode appears. However, the wake mode observed in a subsonic cavity flow is absent in the current simulation. The oscillation frequencies obtained from a global dynamic mode decomposition （DMD） approach are consistent with the local power spectral density （PSD） analysis. The dominant mode transition is clearly shown by the dynamic modes obtained from the DMD. A passive control technique of substituting the cavity trailing edge with a quarter-circle is studied. As the effective cavity length increases, the dominant mode transition from the Rossiter Ⅱ mode to the Rossiter Ⅲ mode occurs. With the control, the pressure oscillations are reduced significantly. The interaction of the shear layer and the recirculation zone is greatly weakened, combined with weaker shear layer instability, responsible for the suppression of pressure oscillations. Moreover, active control using steady subsonic mass injection upstream of a cavity leading edge can stabilize the flow.

Model reduction for supersonic cavity flow using proper orthogonal decomposition(POD)and Galerkin projection

The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.

Mode decomposition of a noise suppressed mixing layer

Noise is generated in a two-dimensional mixing layer due to the growing of instability waves and vortex pairings. The adjoint-based control methodology has shown to be a robust tool to suppress noise radiation. The mode decomposition algorithms such as the compressible version of proper orthogonal decomposition （POD） and dynamic mode decomposition （DMD） are employed to analyze the spatial/spatial-temporal coherent structures for a consecutive data sets of the controlled mixing layer and its uncontrolled counterpart. The analyses of POD indicate that the y-direction body force control mainly modify the most energetic spatial structures, and increase the uniformity of the flow. The analyses of DMD show us prevalent frequencies and corresponding mode structures, and the stability characteristics of each mode can be obtained from DMD-spectrum. The spectral signatures illustrate that a lot of neutral/slightly damping modes emerging in uncontrolled flow within the frequency range （w 〈 0.4） are suppressed due to control, relevant spatial-temporal structures are also varied, which is coincident with the change of far-field noise spectra. From the view of mode decomposition, the action of control redistribute the energy for frequency components of ~ 〈 0.4 by weakening nonlinearities and regularizing corresponding dynamic structures in streamwise direction, and thus suppress the noise radiation. Moreover, the POD- and DMD-analysis in this study demon- strate that DMD can serve as an important supplement for POD in analyzing a time-resolved physical process.

Linear stability analysis of supersonic axisymmetric jets

Stabilities of supersonic jets are examined with different velocities, momentum thicknesses, and core temperatures. Amplification rates of instability waves at inlet are evaluated by linear stability theory （LST）. It is found that increased velocity and core temperature would increase amplification rates substantially and such influence varies for different azimuthal wavenumbers. The most unstable modes in thin momentum thickness cases usually have higher frequencies and azimuthal wavenumbers. Mode switching is observed for low azimuthal wavenumbers, but it appears merely in high velocity cases. In addition, the results provided by linear parabolized stability equations show that the mean-flow divergence affects the spatial evolution of instability waves greatly. The most amplified instability waves globally are sometimes found to be different from that given by LST.

The effects of initial perturbation to mixing-layer noise

The far-field noise radiated from mixing layers is determined by the near-field flow dynamics which is sensitive to the initial perturbation of instability introduced physically or numerically.This study focuses on the effects of the phase delay in two initial perturbations,one at the fundamental wave number and the other at its subharmonic both calculated from linear instability analysis,on the sound generation in mixing layers.When different phase delaysφ_1 changing from zero to 2πis applied on the fundamental mode,we observe different vortex merging processes（e.g.vortex pairing or tearing）.The strong nonlinear interaction in the merging process generates most of the noise from mixing layers.There shows a pattern in a period of 2πfor the response of far-field sound to the change ofφ_1.Similar effects on the dynamics and acoustics can be achieved by adding different phase delaysφ_2 to the subharmonic mode instead,however,the response repeats in a period of onlyπforφ_2.The effects of the combination of different phase delays to other parameters,including the amplitude and wave number for each perturbations,are also investigated.All the results indicate a critical role of nonlinearity in the sound generation mechanism of mixing layers.

Temperature and heat flux bounds of convection driven by non-uniform internal heating

Convection driven by a spatially non-uniform internal heat source between two horizontal isothermal walls is studied by theoretical analysis and numerical simulation,in order to explore the bounds of the temperature and the vertical heat flux.Specifically,the rigorous lower bound of the weighted average temperature<QT>is derived analytically,by decomposing the temperature field into a background profile and a fluctuation part.This bound obtained for the first time to consider non-uniform heat sources is found to be compatible with the existing bound obtained in uniform internal heat convection.Of physical importance,an analytical relationship is derived as an inequality connecting<QT>and the average vertical heat flux<wT>,by employing the average heat flux on the bottom wall(qb)as an intermediary variable.It clarifies the intrinsic relation between the lower bound of<QT>and the upper bound of<wT>,namely,these two bounds are essentially equivalent providing an easy way to obtain one from another.Furthermore,the analytical bounds are extensively demonstrated through a comprehensive series of direct numerical simulations.

Noise reduction in cavity flow by addition of porous media

Self-sustained oscillation and the sound radiation of flow over an open cavity is of great importance in nature and industry.Influences of filled porous media in the cavity are investigated numerically by using a lattice Boltzmann method in two-dimensional space.It is shown that the outcomes of the porous patch depend on the location of the patch and the original flow mode,namely shear layer(SL)and wake mode(WM).For SL flow,the porous patch either damps the vortical flow or suppresses the generation of the secondary vortex sheet on the wall.The later effect destabilizes the SL.Consequently,the radiated sound is reduced as the patch is on the trailing edge,and increased with porous patch on the floor,respectively.For flow in WM,a transition from WM to SL mode is found when the porous patch is set either on the floor or behind the leading wall.In the cases,the recirculating flow on large scale is blocked significantly due to the porous patch,therefore,the WM flow is not sustained.On the other hand,the porous patch on the trailing edge slightly weakens the sound due to dissipation.The study shows that assembling of porous media in the flow field decreases the radiated sound level only if it is done carefully.

A unified theory for gas dynamics and aeroacoustics in viscous compressible flows.PartⅡ.Sources on solid boundary

This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al.,2022),this paper studies the source of longitudinal field at solid boundary,caused by the on-wall kinematic and viscous dynamic coupling of longitudinal and transverse processes.We find that at this situation the easiest choice for the two independent thermodynamic variables is the dimensionless pressure P and temperature T.The two-level structure of boundary dynamics of longitudinal field is obtained by applying the continuity equation and its normal derivative to the surface.We show that the boundary dilatation flux represents faithfully the boundary production of vortex sound and entropy sound,and the mutual generation mechanism of the longitudinal and transverse fields on the boundary does not occur symmetrically"at the samc level,but appears along a zigzag route.At the first level,it is the pressure gradient that generates vorticity unidirectionally;while at the second level,it is the vorticity that generates dilatation unidirectionally.