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

Abstract

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.

The Impulse Response of a High-Speed Jet Forced with Localized Arc Filament Plasma Actuators

“…The critical ky value reported in the literature varies considerably and is approximately 2 for low subsonic jets, 12, 29, 30 and 3.5 for a Mach 0.85 jet. 31,32 The St D ≈ 0.6 demarcation in the spectra presented in Figure 5(a) translates to ky values between 3.3 and 3.8 for the range of Mach numbers studied here, which agrees well with results in the literature.…”

On the convection velocity of source events related to supersonic jet crackle

“…Norum & Seiner (1982) report U c = 0.7U j is suitable for matching far-field acoustic measurements while Troutt & McLaughlin (1982) report 0.8U j based on hot-wire measurements of the jet itself. Tinney, Ukeiley & Glauser (2008) used a proper orthogonal decomposition to show that U c varied from 0.6U j to 0.8U j across the radial extent of the jet shear layer. Thurow et al (2008) provides a review of numerous experiments that have undertaken to measure the convective velocity in the shear layer citing efforts that used traditional two-point space-time correlations, optical measurements of the Mach wave angles emanating from the eddies and time-correlated sequences of flow visualization images.…”

On cumulative nonlinear acoustic waveform distortions from high-speed jets

“…Here we have chosen to assume U c = 0.8U j , which was motivated by the findings of McLaughlin et al (1975) and Troutt & McLaughlin (1982) who showed phase velocities of the axial instability waves to be of this magnitude over a broad range of wavenumbers; similar findings were reported by Kerhervé, Fitzpatrick & Jordan (2006). A recent study by Tinney, Ukeiley & Glauser (2008), based on near-field pressure and velocity correlations, has also shown how low-mode-number disturbances, residing on the high-speed sides of the annular shear layer, convect at speeds near 0.8U j . These low-mode-number events correlate well with the far-field pressure (Hall et al 2009).…”

“…A typical source size is estimated to span the width of the shear layer in the post-potential-core region of the flow. Given the relatively linear growth of the jet shear layer (roughly 0.10 x; see Tinney et al 2008), an emission-point location scale of s = r 0 /D j = 2.5 is expected and is assumed to hold over a range of jet conditions. The resultant shock formation distance and effective Gol'dberg number for this laboratory-scale study are determined to be r L (s = 2.5) = 18.0 m and Λ L (s = 2.5) = 0.15.…”