Ph.D. (Engg):Tonal acoustic radiation from turbulent subsonic jets

Acoustic tones in the near field of a Mach 0.9, Reynolds number 10^6 round jet are investigated using large-eddy simulations (LES) performed with the explicit filtering LES (EFLES) approach. The jet is issued into the ambient through a cylindrical nozzle. Pressure spectra at observer locations in the upstream direction reveal the presence of tones which are 15–20 dB more intense than the background turbulent mixing noise. Spectral Proper Orthogonal Decomposition (SPOD) of the pressure field in the near-nozzle region reveals two distinct categories of tones. The first category comprises tones whose frequency corresponds to high order radial and azimuthal ductmodes of the nozzle. Their spatial amplitude distribution revealed by SPOD at these frequencies show significant support within the nozzle as expected for the natural hard-wall duct modes. These duct modes are scattered at the nozzle lip and radiate in the upstream direction and explain the tonal radiation observed in the LES at their corresponding frequencies. This mechanism has been extensively studied using Wiener-Hopf models applied to a cylindrical vortex sheet (Munt, 1977; Rienstra, 2003; Samanta and Freund, 2008). The second category of tones observed have frequencies that are not hard wall duct mode frequencises. Their spatial amplitude distribution revelaed by SPOD for these frequencies is characterized by significant support within the jet potential core. Empirical dispersion relations constructed from the LES suggest that these tones arise from resonance in the potential core due to coupling between the upstream-propagating guided jet mode (GJM) and the upstream- and downstream-propagating duct-like modes (Schmidt et al., 2017; Towne et al., 2017) near the upper cut-off frequency of the guided jet mode (Bogey, 2021). However, the mechanism by which tones radiate from the potential core has not yet been established. This motivates the theoretical investigation in this thesis that focuses on the dynamics of the guided jet mode and its interaction with the nozzle lip leading to tonal upstream acoustic radiation. The interaction between the GJM and the nozzle lip is analyzed using a Wiener–Hopf formulation with the jet modelled as a semi-infinite cylindrical vortex sheet and the nozzle with a vanishingly-thin sharp edge. When the GJMs are cut-on, these solutions show that an incident GJM is reflected as a downstream-traveling soft-duct mode, a scattered Kelvin–Helmholtz (K–H) mode and a transmitted upstream-traveling hard-wall duct mode. The reflective efficiency of GJM increases with frequency and is greatest near their upper cut-off frequency. This explains why tones associated with potential core resonance occur near the upper cut-off frequency of the GJM. In addition, the GJM is scattered as acoustic waves to the far field, primarily in the upstream direction. The scattered wavefronts are most intense along the outer nozzle wall. The scattered waves propagate to the far field where they generate distinctive directivity patterns that show excellent agreement with the LES-computed far-field directivity reported by Bogey (2021). These results provide a mechanistic explanation for how tones generated by potential core resonance radiate to the far field through scattering of the guided jet mode at the nozzle lip. Acoustic tones in the near field of a Mach 0.9, Reynolds number 10^6 round jet are investigated using large-eddy simulations (LES) performed with the explicit filtering LES (EFLES) approach. The jet is issued into the ambient through a cylindrical nozzle. Pressure spectra at observer locations in the upstream direction reveal the presence of tones which are 15–20 dB more intense than the background turbulent mixing noise. Spectral Proper Orthogonal Decomposition (SPOD) of the pressure field in the near-nozzle region reveals two distinct categories of tones. The first category comprises tones whose frequency corresponds to high order radial and azimuthal ductmodes of the nozzle. Their spatial amplitude distribution revealed by SPOD at these frequencies show significant support within the nozzle as expected for the natural hard-wall duct modes. These duct modes are scattered at the nozzle lip and radiate in the upstream direction and explain the tonal radiation observed in the LES at their corresponding frequencies. This mechanism has been extensively studied using Wiener-Hopf models applied to a cylindrical vortex sheet (Munt, 1977; Rienstra, 2003; Samanta and Freund, 2008). The second category of tones observed have frequencies that are not hard wall duct mode frequencises. Their spatial amplitude distribution revealed by SPOD for these frequencies is characterized by significant support within the jet potential core. Empirical dispersion relations constructed from the LES suggest that these tones arise from resonance in the potential core due to coupling between the upstream-propagating guided jet mode (GJM) and the upstream- and downstream-propagating duct-like modes (Schmidt et al., 2017; Towne et al., 2017) near the upper cut-off frequency of the guided jet mode (Bogey, 2021). However, the mechanism by which tones radiate from the potential core has not yet been established. This motivates the theoretical investigation in this thesis that focuses on the dynamics of the guided jet mode and its interaction with the nozzle lip leading to tonal upstream acoustic radiation. The interaction between the GJM and the nozzle lip is analyzed using a Wiener–Hopf formulation with the jet modelled as a semi-infinite cylindrical vortex sheet and the nozzle with a vanishingly-thin sharp edge. When the GJMs are cut-on, these solutions show that an incident GJM is reflected as a downstream-traveling soft-duct mode, a scattered Kelvin–Helmholtz (K–H) mode and a transmitted upstream-traveling hard-wall duct mode. The reflective efficiency of GJM increases with frequency and is greatest near their upper cut-off frequency. This explains why tones associated with potential core resonance occur near the upper cut-off frequency of the GJM. In addition, the GJM is scattered as acoustic waves to the far field, primarily in the upstream direction. The scattered wavefronts are most intense along the outer nozzle wall. The scattered waves propagate to the far field where they generate distinctive directivity patterns that show excellent agreement with the LES-computed far-field directivity reported by Bogey (2021). These results provide a mechanistic explanation for how tones generated by potential core resonance radiate to the far field through scattering of the guided jet mode at the nozzle lip. Comparison of the Wiener–Hopf predictions with the LES-computed pressure spectra in the present investigation reveals excellent agreement at lower frequencies but deviations at higher frequencies. At lower frequencies, the SPOD modes are qualitatively similar to the corresponding Wiener–Hopf solutions. In contrast, at higher frequencies, the scattered waves originating from the nozzle lip undergo secondary scattering at the slanted section of the outer nozzle wall, causing them to lift away from the wall. The findings suggest two possible strategies for mitigating the tones generated by the potential core resonance: (i) modifying the nozzle-lip geometry and (ii) modifying the outer nozzle-wall geometry.

Speaker: NAGA SARAS CHANDAN VEMPATI

Research Supervisor: Santosh Hemchandra