Charles E. Tinney

The near pressure field of co-axial subsonic jets

Results are presented from pressure measurements performed in the irrotational near field of unbounded co-axial jets. Measurements were made for a variety of velocity and temperature ratios, and configurations both with and without serrations on the secondary nozzle lip. The principal objective of the study is to better understand the near pressure field of the jet, what it can tell us regarding the underlying turbulence structure, and in particular how it can be related to the source mechanisms of the flow. A preliminary analysis of the axial, temporal and azimuthal structure of the pressure field shows it to be highly organized, with axial spatial modes (obtained by proper orthogonal decomposition) which resemble Fourier modes. The effects of serrations on the pressure fluctuations comprise a global reduction in level, a change in the axial energy distribution, and a modification of the evolution of the characteristic time scales. A further analysis in frequency–wavenumber space is then performed, and a filtering operation is used to separate the convective and propagative footprints of the pressure field. This operation reveals two distinct signatures in the propagating component of the field: a low-frequency component which radiates at small angles to the flow axis and is characterized by extensive axial coherence, and a less-coherent high-frequency component which primarily radiates in sideline directions. The serrations are found to reduce the energy of the axially coherent propagating component, but its structure remains fundamentally unchanged; the high-frequency component is found to be enhanced. A further effect of the serrations involves a relative increase of the mean-square pressure level of the acoustic component – integrated over the measurement domain – with respect to the hydrodynamic component. The effect of increasing the velocity and temperature of the primary jet involves a relative increase in the acoustic component of the near field, while the hydrodynamic component remains relatively unchanged: this shows that the additional acoustic energy is generated by the mixing region which is produced by the interaction of the inner and the outer shear layers, whereas the hydrodynamic component of the near field is primarily driven by the outer shear layer.

Low-dimensional characteristics of a transonic jet. Part 2. Estimate and far-field prediction

Complementary low-dimensional techniques are modified to estimate the most energetic turbulent features of a Mach 0.85 axisymmetric jet in the flows near-field regions via spectral linear stochastic estimation. This model estimate is three-dimensional, comprises all three components of the velocity field and is time resolved. The technique employs the pressure field as the unconditional input, measured within the hydrodynamic periphery of the jet flow where signatures (pressure) are known to comprise a reasonable footprint of the turbulent large-scale structure. Spectral estimation coefficients are derived from the joint second-order statistics between coefficients that are representative of the low-order pressure field (Fourier-azimuthal decomposition) and of the low-order velocity field (proper orthogonal decomposition). A bursting-like event is observed in the low-dimensional estimate and is similar to what was found in the low-speed jet studies of others. A number of low-dimensional estimates are created using different velocity-pressure mode combinations from which predictions of the far-field acoustics are invoked using Lighthills analogy. The overall sound pressure level (OASPL) directivity is determined from the far-field prediction, which comprises qualitatively similar trends when compared to direct measurements at r/D=75. Retarded time topologies of the predicted field at 90° and 30° are also shown to manifest, respectively, high- and low-frequency wave-like motions when using a combination of only the low-order velocity modes (m = 0, 1, 2). This work thus constitutes a first step in developing low-dimensional and dynamical system models from hydrodynamic pressure signatures for estimating and predicting the behaviour of the energy-containing events that govern many of the physical constituents of turbulent flows.

A time-resolved estimate of the turbulence and sound source mechanisms in a subsonic jet flow

A dynamical estimate of the axial component of a Mach 0.60 axisymmetric jets turbulent velocity field is presented here using spectral linear stochastic estimation. The pressure field surrounding the exit of the jet is employed as the unconditional parameter in the estimation technique. A sub-grid interpolation method is used to improve the spatial resolution of the estimate. The model estimate is time-resolved and reconstructed using a purely experimental database. A decomposition of the model estimate using POD and Fourier-azimuthal techniques identifies the turbulent velocity modes that are responsible for driving the near-field pressure when compared with direct measurements of the jets modal features. In effect, the signatures left in the near pressure field by the turbulence are a result of the low-order structure, the higher azimuthal modes being inefficient in driving the hydrodynamic pressure. A direct calculation of the source field using a Lighthill approach is performed, from which the low-d...

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.

Identifying noisy and quiet modes in a jet

In the current jet noise study, an empirical modal decomposition is proposed which distills the noisy and quiet modes of the flow field. In particular, the POD of flows is generalised for an optimal resolution of the far-field noise as opposed to a least-order representation of the hydrodynamic fluctuation level. This decomposition technique, which we call ‘most observable decomposition (MOD)’, is based on a linear cause-eect relationship between the hydrodynamics (cause) and the far-field acoustics (observed eect). In the current study, this relationship is identified from a linear stochastic estimation between the flow field and the far-field pressure — taking into account the propagation time of sound. We employ MOD to turbulent jet noise at Ma = 0.9, Re = 3600 using CFD/CAA data from RWTH Aachen. While more than 350 POD modes are necessary to capture only 50% of the flow fluctuation energy, a mere 24 MOD modes resolve 90% of the far-field acoustics. Evidently, far-field noise acts as filter which ‘sees’ only a low-dimensional subspace of the flow and ‘ignores’ silent subspaces which contain a large amount of fluctuation energy. The MOD methodology yields ‘least-order’ representations of any other observable as well — assuming a linear relationship between flow and observable.

Wall Pressure Unsteadiness and Side Loads in Overexpanded Rocket Nozzles

Surveys of both the static and dynamic wall pressure signatures on the interior surface of a sub-scale, cold-flow and thrust optimized parabolic nozzle are conducted during fixed nozzle pressure ratios corresponding to FSS and RSS states. The motive is to develop a better understanding for the sources of off-axis loads during the transient start-up of overexpanded rocket nozzles. During FSS state, pressure spectra reveal frequency content resembling SWTBLI. Presumably, when the internal flow is in RSS state, separation bubbles are trapped by shocks and expansion waves; interactions between the separated flow regions and the waves produce asymmetric pressure distributions. An analysis of the azimuthal modes reveals how the breathing mode encompasses most of the resolved energy and that the side load inducing mode is coherent with the response moment measured by strain gauges mounted upstream of the nozzle on a flexible tube. Finally, the unsteady pressure is locally more energetic during RSS, albeit direct measurements of the response moments indicate higher side load activity when in FSS state. It is postulated that these discrepancies are attributed to cancellation effects between annular separation bubbles.

Low-dimensional azimuthal characteristics of suddenly expanding axisymmetric flows

Two rakes of cross-wire probes were used to capture the two-point velocity statistics in a flow through an axisymmetric sudden expansion. The expansion ratio of the facility is 3, and has a constant geometry. Measurements were acquired at a Reynolds number equal to 54000, based on centreline velocity and inlet pipe diameter. The two-point velocity correlations were obtained along a plane normal to the flow (r, 0), at eleven downstream step-height positions spanning from the recirculating region, through reattachment, and into the redeveloping region of the flow. Measurements were acquired by means of a flying-hot-wire technique to overcome rectification errors near the outer wall of the pipe where flow recirculations were greatest. A mixed application of proper orthogonal (in radius) and Fourier decomposition (in azimuth) was performed at each streamwise location to provide insight into the dynamics of the most energetic modes in all regions of the flow. This multi-point analysis reveals that the flow evolves from the Fourier-azimuthal mode m = 2 (containing the largest amount of turbulent kinetic energy) in the recirculating region, to m = 1 in the reattachment and redeveloping regions of the flow. An eigenvector reconstruction of the kernel, using the most energetic modes from the decomposition, displays the spatial dependence of the Fourier-azimuthal modes and the characteristics that govern the turbulent shear layer and recirculating regions of the flow.

Nonlinear Noise Propagation from a Fully Expanded Mach 3 Jet

The high-intensity noise radiated by an unheated and fully expanded Mach 3 jet is investigated experimentally using arrays of microphones placed in the acoustic near and far far–field of the jet. Under these conditions Mach wave radiation is the most prominent component of turbulent mixing noise in this shock-free supersonic jet. Measurements of the pressure time series are acquired along a grid in the (x,r)-plane in order to quantify the degree of non-linearity in the pressure waveforms. The topography of the OASPL reveal a highly directive sound propagation path emanating from the post-potential core region at x/Dj = 20 and along 45 � from the jet axis; this coincides with the Mach wave radiation angle that is expected of this flow. Likewise, the spatial growth saturation and decay of the OASPL due to wave steepening is shown to peak around 127Dj from the source field identified in the post-potential core region. Various metrics for quantifying the degree of nonlinearity in the acoustic waveforms are computed and include skewness of the pressure derivative, wave steepening factor and the number of zero crossings per unit time. Each metric is shown to produce a slightly unique propagation path, albeit they all follow along similar paths as the OASPL. A second effort focuses on employing an augmented Burgers equation to numerically propagate the temporal waveform at 60Dj outward to a distance of 140Dj (along the same 45 � path coinciding with the maximum OASPL). Both linear and nonlinear forms of the algorithm are employed and include effects of absorption, dispersion and geometrical spreading. Comparison of the predicted and measured waveforms and spectra reveal how the sound radiation is fairly linear over the spatial domain considered in this study.

The effect of heat on turbulent mixing noise in supersonic jets

The most prominent component of turbulent mixing noise in jets is associated with Mach wave radiation. Large-turbulence structures radiate Mach waves efficiently when they convect supersonic relative to the ambient. An experimental study is conducted on an unheated (T0 = 286.6K) and heated (T0 = 1020.6K) fully expanded Mach 1.553 jet to investigate the effect of heat on this radiation process. The acoustic near-field was captured using a line array that comprised ten microphones situated in the hydrodynamic periphery of the dominant sound producing region, which is located downstream of the collapse of the potential core. Space-time correlations revealed a convective speed of the pressure signatures that was slightly larger than sonic, relative to the ambient, for the unheated jet, while being around M = 1.48 for the heated jet; Mach wave radiation occurred in both cases. A far-field circular arc array with a radius of 58.5 jet exit diameters was centered at the jet exit and consisted of twelve microphones ranging from 20 to 135 relative to the jet axis. A linear coherence and temporal correlation study unveiled mechanisms by which the nearand far-field pressures are coupled. Mach wave radiation is a fairly linear process. From arrival times of the acoustic disturbances traveling from nearto far-field it was found that propagation speeds were uniform in the heated case, while variations in speed, up to 15% above the ambient sound speed, were found for the unheated case.

A study in the near pressure field of co-axial subsonic jets

An experimental investigation of the near pressure field of unbounded subsonic jets has been performed. The near-field pressure was sampled, using linear and azimuthal arrays, on conical surfaces surrounding free jets generated by (1) a single axisymmetric nozzle, (2) a co-axial short-cowl nozzle, and (3) a co-axial short-cowl nozzle with serrations (the co-axial experiments were performed as part of the EU program, CoJeN (AST3-CT-2003-502790), where velocity and temperature-ratios were varied). The objective of the study is to better understand differences in the structure of the flows in terms of their sound production mechanisms. A model representation of the source mechanism associated with coherentstructures in the flow is considered, using both the pressure fluctuations themselves and the pressure-derivative source term from Curle’s acoustic analogy. A filtering operation is then applied in order to identify the structure of the radiating source field.