6 results
Flow dynamics and wall-pressure signatures in a high-Reynolds-number overexpanded nozzle with free shock separation
- E. Martelli, L. Saccoccio, P. P. Ciottoli, C. E. Tinney, W. J. Baars, M. Bernardini
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- Journal:
- Journal of Fluid Mechanics / Volume 895 / 25 July 2020
- Published online by Cambridge University Press:
- 26 May 2020, A29
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A delayed detached eddy simulation of an overexpanded nozzle flow with shock-induced separation is carried out at a Reynolds number of $1.7\times 10^{7}$, based on nozzle throat diameter and stagnation chamber properties. In this flow, self-sustained shock oscillations induce local unsteady loads on the nozzle wall as well as global off-axis forces. Despite several studies in the last few decades, a clear physical understanding of the factors driving this unsteadiness is still lacking. The geometry under investigation is a subscale truncated ideal contour nozzle, which was experimentally tested at the University of Texas at Austin at a nozzle pressure ratio of 30. Under these conditions, the nozzle operates in a highly overexpanded state and comprises a conical separation shock that merges to form a Mach disk at the nozzle centre. The delayed detached eddy simulation model agrees well with the experimental results in terms of mean and fluctuating wall-pressure statistics. Wall-pressure spectra reveal a large bump at low frequencies associated with an axisymmetric (piston-like) motion of the shock system, followed by a broad and high-amplitude peak at higher frequencies associated with the Mach waves produced by turbulent eddies convecting through the detached shear layer. Moreover, a distinct peak at an intermediate frequency (${\sim}1~\text{kHz}$) persists in the wall-pressure spectra downstream of the separation shock. A Fourier-based analysis performed in both time and space (azimuthal wavenumber) reveals that this intermediate-frequency peak is associated with the $m=1$ (non-symmetric) pressure mode and is thus related to the generation of aerodynamic side loads. It is then shown how the unsteady Mach disk motion is characterized by an intense vortex shedding activity that, together with the vortical structures of the annular shear layer, contributes to the sustainment of an aeroacoustic feedback loop occurring within the nozzle.
On cumulative nonlinear acoustic waveform distortions from high-speed jets
- W. J. Baars, C. E. Tinney, M. S. Wochner, M. F. Hamilton
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- Journal:
- Journal of Fluid Mechanics / Volume 749 / 25 June 2014
- Published online by Cambridge University Press:
- 19 May 2014, pp. 331-366
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A model is proposed for predicting the presence of cumulative nonlinear distortions in the acoustic waveforms produced by high-speed jet flows. The model relies on the conventional definition of the acoustic shock formation distance and employs an effective Gol’dberg number $\Lambda $ for diverging acoustic waves. The latter properly accounts for spherical spreading, whereas the classical Gol’dberg number $\Gamma $ is restricted to plane wave applications. Scaling laws are then derived to account for the effects imposed by jet exit conditions of practical interest and includes Mach number, temperature ratio, Strouhal number and an absolute observer distance relative to a broadband Gaussian source. Surveys of the acoustic pressure produced by a laboratory-scale, shock-free and unheated Mach 3 jet are used to support findings of the model. Acoustic waveforms are acquired on a two-dimensional grid extending out to 145 nozzle diameters from the jet exit plane. Various statistical metrics are employed to examine the degree of local and cumulative nonlinearity in the measured waveforms and their temporal derivatives. This includes a wave steepening factor (WSF), skewness, kurtosis and the normalized quadrature spectral density. The analysed data are shown to collapse reasonably well along rays emanating from the post-potential-core region of the jet. An application of the generalized Burgers equation is used to demonstrate the effect of cumulative nonlinear distortion on an arbitrary acoustic waveform produced by a high-convective-Mach-number supersonic jet. It is advocated that cumulative nonlinear distortion effects during far-field sound propagation are too subtle in this range-restricted environment and over the region covered, which may be true for other laboratory-scale jet noise facilities.
Low-dimensional characteristics of a transonic jet. Part 2. Estimate and far-field prediction
- C. E. TINNEY, L. S. UKEILEY, M. N. GLAUSER
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- Journal:
- Journal of Fluid Mechanics / Volume 615 / 25 November 2008
- Published online by Cambridge University Press:
- 25 November 2008, pp. 53-92
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Complementary low-dimensional techniques are modified to estimate the most energetic turbulent features of a Mach 0.85 axisymmetric jet in the flow's 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 Lighthill's 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.
Low-dimensional characteristics of a transonic jet. Part 1. Proper orthogonal decomposition
- C. E. TINNEY, M. N. GLAUSER, L. S. UKEILEY
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- Journal:
- Journal of Fluid Mechanics / Volume 612 / 10 October 2008
- Published online by Cambridge University Press:
- 10 October 2008, pp. 107-141
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An experimental investigation concerning the most energetic turbulent features of the flow exiting from an axisymmetric converging nozzle at Mach 0.85 and ambient temperature is discussed using planar optical measurement techniques. The arrangement of the particle image velocimetry (PIV) system allows for all three components of the velocity field to be captured along the (r, θ)-plane of the jet at discrete streamwise locations between x/D=3.0 and 8.0 in 0.25 diameter increments. The ensemble-averaged (time-suppressed) two-point full Reynolds stress matrix is constructed from which the integral eigenvalue problem of the proper orthogonal decomposition (POD) is applied using both scalar and vector forms of the technique. A grid sensitivity study indicates that the POD eigenvalues converge safely to within 1% of their expected value when the discretization of the spatial grid is less than 30% of the integral length scale or 10% of the shear-layer width. The first POD eigenvalue from the scalar decomposition of the streamwise component is shown to agree with previous investigations for a range of Reynolds numbers and Mach numbers with a peak in azimuthal mode 5 at x/D=3.0, and a gradual shift to azimuthal mode 2 by x/D=8.0. The eigenvalues from the scalar POD of the radial and azimuthal components are shown to be much lower-dimensional with most of their energy residing in the first few azimuthal modes, that is modes 0, 1 and 2, with little change in the relative energies along the streamwise direction. From the vector decomposition, the azimuthal eigenspectra of the first two POD modes shift from a peak in azimuthal mode 5 at x/D=3.0, followed by a gradual decay to azimuthal mode 2 at x/D=8.0, the differences in the peak energies being very subtle. The conclusion from these findings is that when the Mach number is subsonic and the Reynolds number sufficiently large, the structure of the turbulent jet behaves independently of these factors.
The near pressure field of co-axial subsonic jets
- C. E. TINNEY, P. JORDAN
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- Journal:
- Journal of Fluid Mechanics / Volume 611 / 25 September 2008
- Published online by Cambridge University Press:
- 25 September 2008, pp. 175-204
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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 azimuthal characteristics of suddenly expanding axisymmetric flows
- C. E. TINNEY, M. N. GLAUSER, E. L. EATON, J. A. TAYLOR
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- Journal:
- Journal of Fluid Mechanics / Volume 567 / 25 November 2006
- Published online by Cambridge University Press:
- 19 October 2006, pp. 141-155
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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 54 000, based on centreline velocity and inlet pipe diameter. The two-point velocity correlations were obtained along a plane normal to the flow ($r,\theta$), 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.