The Stability And Sound Generation Of Compressible Free Shear Layers

In the realm of Aeronautics and Astronautics, aeroacoustic noise generated by free shear flows such as jet plume of vehicles, wake vortices, which causes severe environmental pol-lution. Consequently, it attracts widely concerns from engineering and academy community in recent decades. In the present work, instability characteristics of temporally and spatially developing flow like plane mixing layer, wake etc, are investigated by linear stability analysis and direct numerical simulation, and we are particularly focusing on studying connections of the near-field large-scale vortical structures, far field noise and instability waves. Our main work includes following aspects:(1) For a temporally developing flow, we derive a new acoustic analogy model in the framework of Lighthill’s analogy, which establishes a direct link between near-field dynam-ics and far-field noise, and it can reveal the internal mechanism of flow-induced noise:the pressure gradient in the near field exerts a force of compression or expansion on a fluid ele-ment, and such a force together with the same-direction velocity produces the power for sound generation. Using this formulation, we explained topological structures of sound sources at different evolution stages for a temporally developing mixing layer, which depict that our defined sound sources are mainly concentrate in the outside of the vortex structure/in a s-mall transverse region after averaging in the streamwise direction at the stage of vortex-roll, pairing and viscous damping.(2) Direct numerical simulation is performed for a temporally developing mixing layer, and the effects of initial perturbations to near-field dynamics and far-field noise are investi-gated. The results show that:In the case of single instability wave, near-field dynamics and far-field noise is dominated by viscous damping, if the amplitude of perturbation is small enough. When the amplitude increased, near-field dynamics and far-field noise transitioned from viscous damping to the instability wave mechanism. Regardless of using an instability wave of a high/low wavenumber, the instability wave always plays a dominant role in near-field dynamics and far-field noise. The difference is the former leads to a faster decay to viscous damping, whereas the latter cause stronger noise production and a longer time period to viscous damping; In the case of two instability waves, linear mechanism holds the leading position for small amplitude perturbations, but the nonlinear mechanism gradually takes the place of it as the increasing of amplitudes. In nonlinear mechanism, different phase-shifts between instability waves lead to different behaviors of the near-field dynamics, and hence induce various intensity of far-field noise. It is worth noting that near-field dynamics and2This work was supported by the National Nature Science Foundation(Grant No.11072238), Innovative Foundation of University of Science and Technology of China, the111Project of China (Grant No. B07033) and Foundation of China Scholarship Council. far-field noise change periodically with phase-shift in the case of sub-harmonic resonance.(3) The connections of near-field dynamics, far-field noise and inflow forcing are studied for a spatially developing mixing/jet. The results indicate that:In multiple vortex interactions occurring in a plane mixing layer, the intensity and directivity of noise induced by a single vortex depend on the inflow forcing frequency. Acoustic intensity induced by two-vortex in-teractions is relying on parameters of amplitude and phase shift etc, but its directivity exhibit no dependency. However, both acoustic intensity and directivity appear to be very sensitive to changes in near-field for triple/quadruple vortex interactions; Forced by different scales of instability waves, distinctly different acoustic intensity and directivity are induced due to fun-damentally different nonlinear process, although the flow downstream has a same frequency. In parallel jet, as we impose a symmetric and an antisymmetric inflow forcing respectively, the induced near-field behaviors are quite different, but their acoustic directivities remain the same, except for a small difference in acoustic intensity.(4) Stability analysis is utilized for a temporally developing swirling jet. Using the numerical solution of compressible boundary layer equation as the base flow, we carefully examined the effects of swirl intensity, jet temperature and co-flow to stability characteristics of a compressible viscous swirling jet via solving linear stability equation by high-resolution spectral collocation method. The results demonstrate that:As the increasing of swirl inten-sity, or reducing of core temperature of the jet, it is found that the growth rate of the most unstable shear mode will be promoted; When increasing swirl intensity or core temperature, the most unstable centrifugal mode becomes much more unstable; In swirl jet and wake, we find their most unstable spiral and rotation direction are contradict to each other.(5) The effects of parameters of instability waves with sub-harmonic resonance to near-field dynamics and far-field noise are investigated for a round jet/swirling jet. The results exhibit that:The phase shift of instability wave has an effect on acoustic intensity, but does-n’t change its directivity. Using the same forcing conditions, the development of vortical structures for a swirling/non-swirling jet are nearly identical, aside from negative vorticity structures emerging in downstream for a swirling flow. In addition, it should be mentioned that acoustic intensity in far-field for swirling jet is weaker than non-swirl jet.