Adjoint-based control of turbulent jet noise

Noise is an important factor in certifying an airplane and more restrictive noise regulations have demanded the design of quieter aircraft, with much of the emphasis focused on lower jet-noise emission. Previous passive and active noise-reduction strategies required parametric experiments or cut-and-try approaches, a fact largely attributed to the complexity of turbulence as a source of sound and to the subtlety of the sound-production mechanism. Both aeroacoustic theory and high-fidelity simulation have demonstrated that turbulence-generated noise can be predicted with sufficient accuracy; however, they have not been able to generally guide noise-reduction efforts so far. Adjoint-based optimization provides a unique and useful tool to pursue jet-noise reduction in a systematic approach. The adjoint of the perturbed and linearized Navier--Stokes equations is crafted to provide the control sensitivity in a direction of decreasing noise. Thus, despite the complexity of jet turbulence in the physical space, noise-reducing controls can be directly explored in a control parameter space. Prior work has shown that adjoint-based controls are capable of significantly suppressing the noise from two-dimensional subsonic free shear flows via a subtle modification of large-scale vortex dynamics. The adjoint-based optimization is used here to reduce the sound radiation of a pressure-matched Mach 1.3 cold jet computed using high-fidelity, non-dissipative, high-order finite differences on generalized curvilinear meshes. A large-eddy approximation is conducted with the smallest scales of turbulent motion approximated using the dynamic Smagorinsky sub-grid-scale model. For the time horizon over which the control is applied, the most intense noise events are almost completely removed. At a jet exhaust angle of 30 degree, the far-field peak spectral noise reduction is 5.6 dB at the jet column mode frequency and the overall sound pressure level is reduced by 1.6 dB. At the 90 degree (sideline) angle, the noise reduction is insignificant; however, there is no adverse noise increase as has commonly been found in experimental noise-reduction efforts. Fourier spectral analysis and the proper orthogonal decomposition are used to investigate the jet turbulence before and after the noise-reducing control is applied. The large-scale coherent vortical motion is slightly, but importantly, adjusted to reduce the noise. Most notably, vortex coalescence is demonstrated to be associated with the intermittent sound-generating mechanisms. The intermittently loud acoustic radiation is removed by a space–time localized control that alters a tearing-like vortex interaction which appears to lead to vortex coalescence for the uncontrolled jet. There are no proofs available concerning convergence to a global minimum of the radiated sound, and thus far the control applied to this turbulent jet has failed to achieve the same ~10 dB seen in previous studies of two-dimensional subsonic mixing layers. This is attributed to the greater complexity and less deterministic character of true three-dimensional turbulence. However, the reductions found are comparable to the best engineered devices without any increase at the quieter angles