Numerical Studies on the Sound Radiation by the Shocklets in the Two-dimensional Mixing Layer

摘要

Due to the large requirement of computational recourses, the direct noiserncomputations (DNC) on the problems like spatially-developing mixing layers arernseldom reported before 1990s. In 1994, Colonius used direct numerical simulationrnto study the sound field of a two-dimensional (2D) mixing layer with a splittingrnplate. Afterwards, Colonius and Mitchell made simulations on the 2D planarrnmixing layer and supersonic jets with subsonic vs. supersonic speeds. Thernevolution of the energy of the disturbances and the attributes likeof sound sourcernand directivity were analyzed. Later the computations using acoustic analogy werernalso conducted by them. Bogey et al. investigated the sound generation of the 2Drnplanar mixing layer using LES, and so did Moser et al. The latter paid morernattention on the thermal effects originated from the isothermal and non-isothermalrndistributions. Sharma & Lele also studied the thermal effect of the acoustic field ofrnthe 2D mixing layer, and the GAA method from Goldstein was used to study thernsound source characteristics. In recent years, the works of Lin Zhou were observedrnto study the sensitivity of the noise to the initial disturbances in the mixing layer. Inrnthis paper, the effect of different disturbance patterns has been studied regarding arnmixing layer with transonic convective Mach number. Four cases are investigated,rni.e., disturbances with one fundamental frequency (ω_0), ω_0 plus 1/2ω_0, ω_0 plusrn1/3ω_0, and ω_0 plus 2/3ω_0. Different patterns of vortex development evolved fromrnKelvin-Helmholz instability are obtained, which are ones of single vortex manner,rnvortex pairing, and triple vortex merging. For each type of vortex evolvement,rnshocklets are induced. Analysis has been conducted on hydrodynamic and acousticrnfeatures. Regarding the hydrodynamic part, the energy of disturbances and variousrnthickness of the mixing layer are investigated. On the aspect of acousticrncounterpart, the sound source and directivity with respect to different modal arernanalyzed. The sound pressure levels in the region far away from the mixing layersrnare computed, and the attenuations of the disturbances are studied with therncomparison with the “1/r~(-1/2)” law. The detailed analyses are made on thernrelationship between the shocklet movement and sound generation, which appearrnquit unique and different for the ordinary one in subsonic mixing layers.