Coherent structure and shock-vortex interaction in the screeching supersonic jet.
thesisposted on 28.02.2017 by Mitchell, Daniel Michael
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This body of work describes an experimental investigation into coherent structures and aeroacoustic feedback loops in underexpanded supersonic jets. The work includes a study of additional error terms in Particle Image Velocimetry (PIV) measurements due to the presence of shock waves within the flow, a detailed campaign of acoustic and time-resolved schlieren measurements as well as planar PIV measurements. An error analysis is conducted for the application of PIV to shock containing flows. The effect of size distribution within a seed material on measured relaxation time is examined, with polydisperse particles of the same median diameter shown to possess a significantly higher relaxation time than their monodisperse counterparts when measured via a PIV algorithm. The influence of a shock wave induced velocity gradient within a PIV interrogation window on the correlation function is also examined using the Noiseless Cross Correlation Function of Soria (2006). The presence of a shock is shown to introduce an artificial fluctuation into the measurement of velocity. This fluctuation is a function of the shock position, shock strength, spatial ratio and particle distribution. When the shock is located at the middle of the window, the magnitude of the fluctuation increases monotonically with increasing spatial ratio, increases asymptotically with shock strength, and decreases for increasing particle polydispersity. When the shock is located at the upstream edge of the window, the magnitude of the artificial fluctuation is highest for intermediate spatial ratios, going to zero at infinitely high and low values. In this instance particle polydispersity acts to increase the magnitude of fluctuations in measured velocity. In both cases particle polydispersity serves to broaden the PDF of measured velocity. For the theoretical cases presented herein, with a shock located within the interrogation window, the root mean square of the artificial velocity fluctuations reaches values in excess of 30% of the freestream velocity. For the specific experiments presented later in the work, the magnitude of the artificial velocity fluctuation is less than 10%. Both the schlieren technique and PIV are applied to the study of the instability modes of screeching axisymmetric jets. Jets at four pressure ratios: NPR = [2.2, 2.6, 3.4, 4.2] are studied, and the dominant modes identified as A2, B, C and C respectively. Three distinct modes at NPR = 2.2 are identified, one axisymmetric and two lateral, with screech Strouhal numbers of 0.71, 0.51 and 0.2 respectively. At NPR = 2.6 a dominant lateral mode is identified with St = 0.42. This mode proves the least amenable to measurement with the PIV technique, as the direction of lateral oscillation precesses around the axis somewhat randomly. Helical modes at NPR = 3.4 and 4.2 are studied, with St = 0.39 and 0.35 respectively. The presence of a large Mach disk at NPR = 4.2 is not shown to qualitatively change the dynamics of the screech process. The production of discrete acoustic tones by the interaction between embedded shocks and convected vortices is directly visualized. The motion of vortices is seen to create a disturbance wave at the shock reflection point of an upstream shock cell, this disturbance convects to the jet core and forms the basis for an evanescent convecting shockwave downstream. The flattening of this shock wave during the passage of the vortex results in a strong acceleration of the shock-tip, which moves in a whip-like manner and generates a strong upstream travelling acoustic wave. Analysis of the skewness and kurtosis of the axial velocity probability density functions is shown to be able to identify locations of intense sound generation. The second, third and fourth shock cells are shown to be the dominant noise sources.