Linear and nonlinear processes in two-dimensional mixing layer dynamics and sound radiation

Abstract

In this study, we consider the effects of linear and nonlinear instability waves on the near-field dynamics and aeroacoustics of two-dimensional laminar compressible mixing layers. Through a combination of direct computations, linear and nonlinear stability calculations, we demonstrate the significant role of nonlinear mechanisms in accurately describing the behaviour of instability waves. In turn, these processes have a major impact on sound generation mechanisms such as Mach wave radiation and vortex pairing sound. Our simulations show that the mean flow correction, which is required in order to accurately describe the dynamics of large-scale vortical structures, is intrinsically tied to the nonlinear modal interactions and accurate prediction of saturation amplitudes of instability waves. In addition, nonlinear interactions are largely responsible for the excitation and development of higher harmonics in the flow which contribute to the acoustic radiation. Two flow regimes are considered: In supersonic shear layers, where the far-field sound is determined by the instability wave solution at sufficiently high Mach numbers, it is shown that these nonlinear effects directly impact the Mach wave radiation. In subsonic shear layers, correctly capturing the near-field vortical structures and the interactions of the subharmonic and fundamental modes become critical due to the vortex pairing sound generation process. In this regime, a method is proposed to combine the instability wave solution with the Lilley–Goldstein acoustic analogy in order to predict far-field sound.

Wavepacket models for supersonic jet noise

“…In the supersonic jets modelled here, the disparity of wavelengths in the two regions is not large (see figure 6, and also figure 8 appearing later), so that PSE is able to approximate both domains. The noise field associated with subsonic shear layers does not satisfy this condition: this explains the corresponding failure of PSE reported by Cheung & Lele (2009). …”

“…Apart from the issue of intermittency, the consideration of the supersonic jet affords the direct acoustic modelling with PSE in another manner. Cheung & Lele (2009) demonstrated that PSE successfully predicts the acoustic field in a laminar supersonic mixing layer, but fails in a subsonic case: a hybrid PSE-acoustic analogy approach was used to circumvent the latter problem. This behaviour is explicated in our subsequent discussion.…”

Global linear stability of a model subsonic jet

“…This method therefore does not directly yield the acoustic field, although it can be recovered from an acoustic analogy. 10 Owing to the increasing computing power modal and non-modal studies of fully non-parallel flows have recently become accessible, in particular through the use of matrixfree methods. 7,15,17,22,27 In the present study, a modal stability analysis of axisymmetric perturbations is performed in order to elucidate the physical origin of the preferred mode.…”

On the governing equations for the compressing process and its coupling with other processes

“…First, at the foundation level is the vectorial velocity equation (20) or (21). Although redundant for the shearing process, it is a good preparation for the compressing process because all dynamic/thermodynamic variables except the squared sound speed are removed therefrom, and the coupling mechanisms with shearing and entropy processes are clearly exhibited.…”