Noise-producing Region Research Articles

Measurements of the single-point and joint turbulence statistics of high subsonic jets using hot-wire anemometry

This paper describes a systematic and comprehensive hot-wire investigation into the turbulent statistics of low-, moderate- and high-speed subsonic jets. Experiments were performed to obtain the one-point and two-point statistics of a single-stream, unheated jet turbulence field over a broad region of the jet plume. Results show that hot-wires can be used to measure both the one-point and two-point statistics of the high turbulence intensity, noise-producing regions of unheated, compressible, subsonic jets. For the two-point measurements, probe pairings are performed over the three orthogonal axes. Analysis of the experimental data reveals four main conclusions: (1) both the statistical and joint moments of the turbulence scale well with the local jet shear layer half-width; (2) a simple relationship exists between the statistics of the velocity fluctuations and the square of the velocity fluctuations; (3) a simple relationship exists between the longitudinal and transverse length-scales, and (4) a semi-empirical model has been developed to predict the cross-correlation coefficients, power spectral density, frequency-dependent length-scales and coherence decay of the turbulent velocity field. From the second and third conclusions, it is shown that, in the locations near an eddy’s centre of rotation (i.e. the midpoint of the jet shear layer), the turbulence statistics can be described as quasi-homogeneous and quasi-frozen. The joint statistical moments, therefore, can be inferred simply from single-point tests. These results will help to develop models for predicting jet mixing noise, highlighting the situations in which the simplifying assumptions are inadequate.Graphical abstract

Transfer mechanisms from stochastic turbulence to organized acoustic radiation in a supersonic jet

We examine the three-dimensional energy-exchange mechanisms between stochastic turbulence and an organized radiating wavepacket, and subsequent scattering and transmission of acoustic energy. A validated round-jet large-eddy simulation (LES) is subjected to Kovásznay-type decomposition into hydrodynamic, acoustic and thermal modes, as encapsulated in the generalized framework of the momentum potential theory (MPT). The results are first assimilated with known and postulated aspects of jet-noise dynamics to provide an alternative perspective. Subsequently, new insights are derived on acoustic-energy generation and transport processes. The prolonged axial and azimuthal spatio-temporal coherence of the jittering acoustic mode, which manifests as a wavepacket, and the localization of its energy to the low-order azimuthal modes (m=0,1 and 2) are shown to arise naturally in the decomposed field. The spatial supports of the internal and radiating components of the acoustic-mode are identified with dynamic mode decomposition (DMD). The resulting spectra are observed to be similar to those of the global instability modes of the mean flow. In contrast, the hydrodynamic mode, which is the primary source of energy in this cold jet, has broadband spectral structure and limited spatio-temporal coherence. This knowledge is then leveraged to analyze and quantify sound scattering versus transmission through energy interactions between the relatively chaotic hydrodynamic mode and its stimulation of an ordered response in the acoustic mode. Surface integral analyses reveal the mechanisms by which the omni-directional nature of the turbulent scattering is established. The acoustic mode plays a central role in imparting directionality to the acoustic transmission process, with its axisymmetric component contributing to downstream and shallow angle radiation and higher azimuthal modes contributing increasingly to sideline radiation. Volumetric integral analyses combine these observations to show that the unorganized hydrodynamic mode generates localized noise-producing regions, resulting in a coherent form of sound radiation from the jet.

A low-dimensional approach to closed-loop control of a Mach 0.6 jet

Simultaneous time-resolved measurements of the near-field hydrodynamic pressure field, 2-component streamwise velocity field, and far-field acoustics are taken for an un-heated, axisymmetric Mach 0.6 jet in co-flow. Synthetic jet actuators placed around the periphery of the nozzle lip provide localized perturbations to the shear layer. The goal of this study was to develop an understanding of how the acoustic nature of the jet responds to unsteady shear layer excitation, and subsequently how this can be used to reduce the far-field noise. Review of the cross-correlations between the most energetic low-order spatial Fourier modes of the pressure and the far-field region reveals that mode 0 has a strong correlation and mode 1 has a weak correlation with the far-field. These modes are emulated with the synthetic jet array and used as drivers of the developing shear layer. In open loop forcing configurations, there is energy transfer among spatial scales, enhanced mixing, a reconfiguration of the low-dimensional spatial structure, and an increase in the overall sound pressure level (OASPL). In the closed loop configuration, changes to these quantities are more subtle but there is a reduction in the overall fluctuating sound pressure level OASPLf by 1.35 dB. It is argued that this reduction is correlated with the closed loop control feeding back the dynamical low-order information measured in the largest noise producing region.

Spatial Correlations in a Transonic Jet

properties. The data are presented from two separate experiments; one with the light sheet orientated in the streamwise direction (r–x plane) and one with the light sheet perpendicular to the flow direction (r–� plane). The instrument’s characteristics allow for the calculation and subsequent analysis of the two-point spatial correlations which are known to be relevant to the source terms in acoustics analogies where sound production is concerned. An examination of the spatial correlations demonstrates the averaged spatial evolution of the jet’s large-scale turbulent structures throughout the noise producing region. In particular, the (r–x) spatial dependence of the axial and azimuthal normal stresses manifest a oblique structure in the mixing layer regions of the flow, whereas the radial normalstressesevolvemoreuniformlytowardtheendofthepotentialcore.Quadrupolesourcetermsrelevanttothe soundproduction mechanismsare alsocalculated from which their spatial distributions areanalyzed with zerotime delay.Theanalysisofthesesourcetermsatx=D � 4showhowthepeakenergyfortheshear-noisecomponentresides on the high-speed side of the shear layer around r=D � 0:33, whereas the self-noise terms peak along the lip-line at r=D � 0:5,andaremostenergeticforthestreamwiseandazimuthalcomponentsofthevelocity.Tofullyevaluatethe quadrupole sources of noise, the space-time correlations of the full three-dimensional turbulent flowfield are required which are currently not available from experiments.

Simulation of oxide trapping noise in submicron n-channel MOSFETs

Carrier trapping via tunneling into the gate oxide was implemented into a partial differential equation-based semiconductor device simulator to analyze the 1/f-like noise in silicon MOSFETs. Local noise sources are calculated using the carrier tunneling rates between trap centers in the oxide and those at the interface. Using the Green's transfer function approach, noise contributions from each node in the oxide mesh to the overall noise at the specified contact terminals are simulated. Unlike traditional 1/f noise analyses in MOSFETs, the simulator is capable of simulating noise for a wide range of bias voltages and device structures. The simulation results show that for an uniformly doped channel, the region in the oxide above the pinch-off point in saturation is most critical for low frequency noise generation while for a graded channel device the source side of the gate oxide region becomes important. By comparing the simulation results with the measured noise data, the oxide defect density in the noise producing regions can be profiled.

A MODELLING OF THE NOISE FROM SIMPLE COAXIAL JETS, PART I: WITH UNHEATED PRIMARY FLOW

The work described in this paper forms a portion of an on-going fundamental study of coaxial jet noise both statically and in flight. Three principal noise-producing regions are identified and their mean flow and turbulence characteristics classified from published data. The noise production from each region is then calculated by using single jet prediction methods for flows of similar mean velocity and turbulence profiles. The initial test of this prediction scheme has been conducted by comparison with data from an unheated, co-planar, coaxial jet configuration. The agreement, in terms of one-third octave spectral predictions, is significantly better than 1 dB over a wide range of both angle of observation and velocity ratio.

Turbulence suppression in free turbulent shear flows under controlled excitation. Part 2. Jet-noise reduction

It is shown that reduction of broadband (even total) far-field jet noise can be achieved via controlled excitation of a jet at a frequency in the range 0.01 < Stθ < 0.02, where Stθ is the Strouhal number based on the exit momentum thickness of the shear layer. Hot-wire measurements in the noise-producing region of the jet reveal that the noise suppression is a direct consequence of turbulence suppression, produced by early saturation and breakdown of maximally growing instability modes.

Experiments on Supersonic Jet Noise

The noise generated by a 1-in. supersonic jet was investigated at nominal jet Mach numbers of 1.5, 2.0, and 2.5. In particular, a quantity W, referred to as the apparent source strength per unit length, was determined along the jet axis using a directional microphone system. The integrated value of W along the jet axis was found to agree with the sound intensity obtained by a conventional microphone. This result is consistent with the a priori assumption that the jet may be described in terms of independent, spatially compact acoustic sources. The main finding of the investigation is the discovery of two distinct intense noise-producing regions in a jet having supersonic source velocities: the upstream region associated with Mach wave radiation, and a zone, located downstream of the potential cone, exhibiting radiation similar in character to that of a subsonic jet. An estimate of the radiated intensity associated with the Mach waves also is made.

Orderly structure in jet turbulence

Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating.

The effect of vortex generators on the noise-producing region of a jet

The flow downstream of a nozzle was disturbed by a ring of delta wings arranged so that their trailing vortices were approximately in the centre-line of the mixing layer that springs from the jet exit. This flow was considered somewhat similar to that from a noisesuppressing nozzle fitted with teeth. The mean flow and the turbulent velocities have been measured over the important noise-producing regions of a subsonic jet with and without the delta wings. In order to be able to draw conclusions about the differences in the noise generated from these two flows, the properties of the fluctuating turbulent stresses were also measured. Significant reductions were observed in the magnitude of the one fluctuating turbulent stress measured and its integral length scales with the delta wings present. The measured reduction in noise from the nozzle fitted with delta wings was attributed to these changes.

Fluctuating turbulent stresses in the noise-producing region of a jet

Measurements of the fluctuating turbulent stresses (uiuj)’ in the mixing layer of a two-dimensional jet are presented. These include the intensity, spatial correlation and the wave-number frequency spectra of the fluctuating stresses.The acoustic spectrum perpendicular to the axis of a jet can be approximated with the aid of assumptions about jet similarity and a knowledge of the four-dimensional wave-number frequency spectrum at zero wave-number. In the present paper the four-dimensional spectrum was inferred from measured two-dimensional spectra and the self-noise spectrum perpendicular to a round jet estimated. Good agreement was obtained with measured acoustic spectra.

Turbulence in the noise-producing region of a circular jet

The flow in the noise-producing region of a circular jet is found to be dominated by a group of large eddies, containing nearly a quarter of the turbulent shear stress in the quasi-plane region of the shear layer: their contribution to the shear stress decreases as the effects of axisymmetry become noticeable at more than about two diameters downstream of the nozzle. These large eddies appear to be almost entirely responsible for the irrotational fluctuations near the nozzle, which, for this and other reasons, are larger relative to the reference dynamic pressure than in other shear flows. As a consequence of this, the convection velocity near the high- and low-velocity edges of the flow is biased towards the mean velocity in the high-intensity region. The dominance of the large eddies therefore explains the measurements of near-field pressure fluctuations by Franklin & Foxwell (1958), and of convection velocity by Davies, Barratt & Fisher (1963) and the present authors. The strength of these large eddies, compared with those in the boundary layer or wake, is remarkable.The large eddies appear to be mixing-jets similar to those found by Grant (1958) in the wake, but with their projection in the (y, z)-plane inclined at about 45° to the y (radial) axis instead of lying along the y-axis as in the wake.It is suggested that the augmentation of these large eddies by artificial means could be used to increase the mixing rate and permit the reduction of jet noise by means of acceptably short ejector shrouds.The medium-scale motion is found to be far from isotropic in scales, although the two scales associated with a given vorticity component are more nearly equal. This phenomenon is also noticeable in the wake.It is found that the departure from self-preservation, which starts when the shear layer thickness is no longer small compared with the nozzle radius, does not grossly affect the region of high turbulence intensity and maximum noise production until this region itself is no longer small compared with the radius. The maximum shear stress seven diameters downstream of the exit is still 70% of its value near the exit, and the non-dimensional mean velocity gradient is practically unchanged.