This paper uses a discrete-vortex code to examine a shear layer's response to forcing at its origin. The code and its thermodynamic overlay have been used in previous studies to predict the optically-aberrating characteristics of relatively-high-Mach-number, subsonic shear layers that can be classified as weakly compressible. The results reported in this study are again directed toward the shear layer's optical characteristics; however, the intent was to use forcing to create periodic aberrating fields, referred to as "regularized" shear-layer aberrations. The study shows that the use of single-frequency forcing produces a regularized shear layer for distances preceding the point where the unforced shear layer's natural frequency occurs. In the case of the forced shear layer, a greater thickness is produced closer to its point of origin until collapsing onto the unforced shear layer thickness past the point of regularization. The aberration periodicity is shown to have lower robustness toward the furthest downstream extent of regularization due to uncontrolled pairing. This region is made more regular by applying both fundamental and subharmonic forcing at the shear layer's origin; however, such subharmonic forcing is sensitive to the phasing of the fundamental to that of the subharmonic.
Non-uniform, variable-density fields, resulting from compressibility effects in turbulent flows, are the source of aero-optical distortions which cause significant reductions in optical system performance. Adaptive-Optics (AO) is a technique used to correct for such spatially and temporally varying aberrations on an optical beam by applying a conjugate waveform correction to the beam. Traditional AO systems are bandwidth limited by real-time processing issues and wavefront sensor limitations. This paper presents an alternative AO approach using a phase-locked-loop control strategy. By using flow control to regularize the shear layer and its corresponding optical wavefront, the bandwidth necessary to make realtime corrections is effectively reduced by producing a more periodic and predictable optical signal. A feedback control approach has been simulated numerically performing real-time corrections to an aberrating wavefront due to propagation through a free shear layer. Several cases were studied for a variety of upper and lower Mach numbers. The numerical results show significant increases in the time-averaged Strehl ratio for the cases where the regularized wavefront contained a single dominant frequency. Further increases in the Strehl ratios were achieved after additionally removing tip/tilt. It was noted that tip/tilt error must be removed post AO corrections rather than prior in order to maintain a traveling wavefront necessary for this control strategy. In the highest Mach number case studied, regularization of the shear layer produced an optical wavefront containing both fundamental and subharmonic frequencies. Higher Mach number cases, such as this, may require the use of two frequency control which is currently being investigated further. Nomenclature OPL= Optical Path Length OPD = Optical Path Difference n = index-of-refraction p = pressure ρ = density u = velocity in x direction, along the streamwise direction v = velocity in y direction, perpendicular to the flow direction T = temperature T ad = initial temperature calculated using the adiabatic relation p ∞ = free stream pressure γ = specific heat ratio θ = jitter angle f n = optical natural frequency Λ n = optical coherence length U c = convective velocity
This paper uses a discrete-vortex code to examine a shear layer's response to forcing at its origin and to develop a relationship between a shear layer's optical characteristics and the commonly used characteristic growth length, vorticity thickness. The code and its thermodynamic overlay have been used in previous studies to predict the optically aberrating characteristics of relatively high-Mach-number, subsonic shear layers that can be classified as weakly compressible. A weighted-average natural frequency is introduced and used to characterize the unforced shear layer in terms of an optical characteristic length referred to as optical coherence length. It is shown that optical coherence length is related to vorticity thickness by a factor of approximately 3.18. The study also shows that the use of single-frequency forcing produces a regularized shear layer for distances preceding the point at which the unforced shear layer's natural frequency matches the forcing frequency. In the case of the forced shear layer, a greater thickness is produced closer to its point of origin until collapsing onto the unforced shear-layer thickness past the point of regularization. The aberration periodicity is shown to have lower robustness toward the furthest downstream extent of regularization due to uncontrolled pairing. Nomenclature A = aperture of laser beam, amplitude of forcing C = vorticity thickness growth rate constant C = optical coherence length growth rate constant f f = forcing frequency f n = natural optical frequency K GD = Gladstone-Dale constant n = index of refraction R = velocity ratio s = density ratio U c = convective velocity, u U u L =2 u L = lower freestream velocity in the x direction u U = upper freestream velocity in the y direction x = streamwise or flow direction y = normal direction to the plane of the shear layer, perpendicular to the main flow vis = shear-layer thickness ! = vorticity thickness = momentum thickness j = jitter angle n = optical coherence length = dimensionless velocity ratio L = lower stream density U = upper stream density = phase shift of forcing function
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