Academic literature on the topic 'Axisymmetric subsonic flow structure'

This paper describes a numerical analysis of gas-droplet two-phase subsonic free jets in the axisymmetric system. Thermal coupling through heat transfer to droplets, as well as momentum coupling through aerodynamic drag responsible for droplet motion, is taken into account in the present numerical model. The Navier-Stokes equations for a gas-phase interacting with particle phase are solved by a time-dependent difference technique and the particle-phase is solved by a discrete particle cloud model. The jet flow structures of mixture composed of air and water-droplets with 1 μm, 5 μm, and 30 μm, respectively, in diameter are calculated with a single particle size. Some of significant characteristics for the two-phase subsonic free jets are pointed out, in particular, focusing upon the effect of particle size on the flow structure.

Measuring the fluctuating static pressure within a jet has the potential to depict in-flow sources of the jet noise. In this work, the fluctuating static pressure of a subsonic axisymmetric jet was experimentally investigated using a 1/8” microphone with an aerodynamically shaped nose cone. The power spectra of the fluctuating pressure are found to follow the -7/3 scaling law at the jet centerline with the decay rate varying as the probe approaches the acoustic near field. Profiles of skewness and kurtosis reveal strong intermittency inside the jet shear layer. By applying a continuous wavelet transform (CWT), time-localized footprints of the acoustic sources were detected from the pressure fluctuations. To decompose the fluctuating pressure into the hydrodynamic component and its acoustic counterpart, two techniques based on the CWT are adopted. In the first method the hydrodynamic pressure is isolated by maximizing the correlation with the synchronously measured turbulent velocity, while the second method originates from the Gaussian nature of the acoustic pressure where the separation threshold is determined empirically. Similar results are obtained from both separation techniques, and each pressure component dominates a certain frequency band compared to the global spectrum. Furthermore, cross-spectra between the fluctuating pressure and the turbulent velocity were calculated, and spectral peaks appearing around Strouhal number of 0.4 are indicative of the footprint of the convecting coherent structures inside the jet mixing layer.

This paper presents a parallel numerical and experimental study of rotating stall cells in an axial compressor. Based on previous theoretical and experimental studies stressing the importance of fluid inertia and momentum exchange mechanisms in rotating stall, a numerical simulation using the Euler equations is conducted. Unsteady two-dimensional solutions of rotating stall behavior are obtained in a one-stage low subsonic axial compressor. The structure and speed of propagation of one fully developed rotating stall cell together with its associated unsteady static pressure and throughflow field distributions are presented. The numerical capture of a stalled flow region starting from a stable high-flow operating point with an axisymmetric flow distribution and evolving at a reduced mass flow operating point into a rotating stall pattern is also discussed. The experimental data (flow visualization, time-averaged and unsteady row-by-row static pressure measurements) acquired in a four-stage water model of a subsonic axial compressor cover a complete characteristic line ranging from high mass flow in the stable regime to zero throughflow. Stall inception is presented together with clearly marked different operating zones within the unstable regime. For one operating point in the unstable regime, the speed of propagation of the cell as well as the static pressure spikes at the front and rear boundaries of the rotating stall cell are compared between computations, measurements, and an idealized theory based on momentum exchange between blade rows entering and leaving the stalled cell. In addition, the time evolution of the pressure trace at the rotor/stator interface is presented. This study seems to support the assumption that the cell structure and general mechanism of full-span rotating stall propagation are essentially governed by inertial effects and momentum exchange between the sound and stalled flow at the cell edges.

This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein 2003 JFM 488 , 315–333. ( doi:10.1017/S0022112003004890 )) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (Ma). The analogy shows that the exact formula for the acoustic pressure is given by a convolution product of a propagator tensor (determined by the vector Green's function of the adjoint linearized Euler equations for a given jet mean flow) and a generalized source term representing the jet turbulence field. Using a low-frequency/small spread rate asymptotic expansion of the propagator, mean flow non-parallelism enters the lowest order Green's function solution via the streamwise component of the mean flow advection vector in a hyperbolic partial differential equation. We then address the predictive capability of the solution to this partial differential equation when used in the analogy through first-of-its-kind numerical calculations when an experimentally verified model of the turbulence source structure is used together with Reynolds-averaged Navier–Stokes solutions for the jet mean flow. Our noise predictions show a reasonable level of accuracy in the peak noise direction at Ma = 0.9, for Strouhal numbers up to about 0.6, and at Ma = 0.5 using modified source coefficients. Possible reasons for this are discussed. Moreover, the prediction range can be extended beyond unity Strouhal number by using an approximate composite asymptotic formula for the vector Green's function that reduces to the locally parallel flow limit at high frequencies. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.

Stereoscopic three-component particle image velocimetry (3C-PIV) measurements have been made in a turbulent round jet to investigate the spatio-temporal correlations that are the origin of aerodynamic noise. Restricting attention to subsonic, isothermal jets, measurements were taken in a water flow experiment where, for the same Reynolds number and nozzle size, the shortest time scale of the dynamically important turbulent structures is more than an order of magnitude greater that in equivalent airflow experiments, greatly facilitating time-resolved PIV measurements. Results obtained (for a jet nozzle diameter and velocity of 40 mm and $1~\text{m}~\text{s}^{-1}$, giving $\mathit{Re}=4\times 10^{4}$) show that, on the basis of both single-point statistics and two-point quantities (correlation functions, integral length scales) the present incompressible flow data are in excellent agreement with published compressible, subsonic airflow measurements. The 3C-PIV data are first compared to higher-spatial-resolution 2C-PIV data and observed to be in good agreement, although some deterioration in quality for higher-order correlations caused by high-frequency noise in the 3C-PIV data is noted. A filter method to correct for this is proposed, based on proper orthogonal decomposition (POD) of the 3C-PIV data. The corrected data are then used to construct correlation maps at the second- and fourth-order level for all velocity components. The present data are in accordance with existing hot-wire measurements, but provide significantly more detailed information on correlation components than has previously been available. The measured relative magnitudes of various components of the two-point fourth-order turbulence correlation coefficient ($R_{ij,kl}$) – the fundamental building block for free shear flow aerodynamic noise sources – are presented and represent a valuable source of validation data for acoustic source modelling. The relationship between fourth-order and second-order velocity correlations is also examined, based on an assumption of a quasi-Gaussian nearly normal p.d.f. for the velocity fluctuations. The present results indicate that this approximation shows reasonable agreement for the measured relative magnitudes of several correlation components; however, areas of discrepancy are identified, indicating the need for work on alternative models such as the shell turbulence concept of Afsar (Eur. J. Mech. (B/Fluids), vol. 31, 2012, pp. 129–139).

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.

Numerical simulation of a compressible mixing layer past an axisymmetric trailing edge is carried out for a Reynolds number based on the diameter of the trailing edge approximately equal to 2.9 × 106. The free-stream Mach number at separation is equal to 2.46, which corresponds to experiments and leads to high levels of compressibility. The present work focuses on the evolution of the turbulence field through extra strain rates and on the unsteady features of the annular shear layer. Both time-averaged and instantaneous data are used to obtain further insight into the dynamics of the flow. An investigation of the time-averaged flow field reveals an important shear-layer growth rate in its initial stage and a strong anisotropy of the turbulent field. The convection velocity of the vortices is found to be somewhat higher than the estimated isentropic value. This corroborates findings on the domination of the supersonic mode in planar supersonic/subsonic mixing layers. The development of the shear layer leads to a rapid decrease of the anisotropy until the onset of streamline realignment with the axis. Due to the increase of the axisymmetric constraints, an adverse pressure gradient originates from the change in streamline curvature. This recompression is found to slow down the eddy convection. The foot shock pattern features several convected shocks emanating from the upper side of the vortices, which merge into a recompression shock in the free stream. Then, the flow accelerates and the compressibility levels quickly drop in the turbulent developing wake. Some evidence of the existence of large-scale structures in the near wake is found through the domination of the azimuthal mode m = 1 for a Strouhal number based on trailing-edge diameter equal to 0.26.

We investigate source mechanisms for subsonic jet noise using experimentally obtained datasets of high-Reynolds-number Mach 0.4 and 0.6 turbulent jets. The focus is on the axisymmetric mode which dominates downstream sound radiation for low polar angles and the frequency range at which peak noise occurs. A linearized Euler equation (LEE) solver with an inflow boundary condition is used to generate single-frequency hydrodynamic instability waves, and the resulting near-field fluctuations and far-field acoustics are compared with those from experiments and linear parabolized stability equation (LPSE) computations. It is found that the near-field velocity fluctuations closely agree with experiments and LPSE computations up to the end of the potential core, downstream of which deviations occur, but the LEE results match experiments better than the LPSE results. Both the near-field wavepackets and the sound field are observed directly from LEE computations, but the far-field sound pressure levels (SPLs) obtained are more than an order of magnitude lower than experimental values despite close statistical agreement of the near hydrodynamic field up to the potential core region. We explore the possibility that this discrepancy is due to the mismatch between the decay of two-point coherence with increasing distance in experimental flow fluctuations and the perfect coherence in linear models. To match the near-field coherence, experimentally obtained coherence profiles are imposed on the two-point cross-spectral density (CSD) at cylindrical and conical surfaces that enclose near-field structures generated with LEEs. The surface pressure is propagated to the far field using boundary value formulations based on the linear wave equation. Coherence matching yields far-field SPLs which show improved agreement with experimental results, indicating that coherence decay is the main missing component in linear models. The CSD on the enclosing surfaces reveals that the application of a decaying coherence profile spreads the hydrodynamic component of the linear wavepacket source on to acoustic wavenumbers, resulting in a more efficient acoustic source.

AbstractNumerical investigation of a sonic jet from a blunt body opposing a supersonic flow with a free stream Mach number ${M}_{\infty } = 2. 5$ was carried out using large-eddy simulation for two total pressure ratios of the jet to the free stream, i.e. $\mathscr{P}= 0. 816$ and 1.633. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the flow phenomena, including shock/jet interaction, shock/shear-layer interaction, turbulent shear-layer evolution and coherent structures, have been studied systematically. Based on the analysis of the flow structures and features, two typical flow states, i.e. unstable and stable states corresponding to the two values of $\mathscr{P}$, are identified and the behaviours relevant to the flow states are discussed. Small-scale vortical structures mainly occur in the jet column, and large-scale vortices develop gradually in a recirculation region when the jet terminates through a Mach disk and reverses its orientation as a conical free shear layer. The turbulent fluctuations are enhanced by the rapid deviation of the shear layer and the interaction with shock waves. Moreover, the coherent structures of the flow motion are analysed using the proper orthogonal decomposition technique. It is found that the dominant mode in the cross-section plane exhibits an antisymmetric character for the unstable state and an axisymmetric one for the stable state, while statistical analysis of unsteady loads indicates that the side loads can be seen as a rotating vector uniformly distributed in the azimuthal direction. Further, we clarify a feedback mechanism whereby the unsteady motion is sustained by the upstream-propagating disturbance to the Mach disk through the recirculation subsonic region and downstream propagation in the conical shear layer. Feedback models are then proposed which can reasonably well predict the dominant frequencies of the two flow states. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the opposing jet/supersonic flow interaction.

Two temporally developing isothermal round jets at a Mach number of 0.9 and Reynolds numbers of 3125 and 12 500 are simulated in order to investigate noise generation in high-subsonic jet flows. Snapshots and statistical properties of the flow and sound fields, including mean, root-mean-square and skewness values, spectra and auto- and cross-correlations of velocity and pressure, are presented. The jet at a Reynolds number of 12 500 develops more rapidly, exhibits more fine turbulent scales and generates more high-frequency acoustic waves than the other. In both cases, however, when the jet potential core closes, mixing-layer turbulent structures intermittently intrude on the jet axis and strong low-frequency acoustic waves are emitted in the downstream direction. These waves are dominated by the axisymmetric mode and are significantly correlated with centreline flow fluctuations. These results are similar to those obtained at the end of the potential core of spatially developing jets. They suggest that the mechanism responsible for the downstream noise component of these jets also occurs in temporal jets, regardless of the Reynolds number. This mechanism is revealed by averaging the flow and pressure fields of the present jets using a sample synchronization with the minimum values of centreline velocity at potential-core closing. A spot characterized by a lower velocity and a higher level of vorticity relative to the background flow field is found to develop in the interfacial region between the mixing layer and the potential core, to strengthen rapidly and reach a peak intensity when arriving on the jet axis, and then to break down. This is accompanied by the growth and decay of a hydrodynamic pressure wave, propagating at a velocity which, initially, is close to 65 per cent of the jet velocity and slightly increases, but quickly decreases after the collapse of the high-vorticity spot in the flow. During that process, sound waves are radiated in the downstream direction.