Numerical Simulation of Aero-Optical Aberration Through a Weakly Compressible Shear Layer

Abstract

This work examines the origin of aero-optical aberration in weakly-compressible laminar, transitional and turbulent shear layers employing a high-fidelity numerical simulation approach. The flow fields are obtained using a high-order implicit large-eddy simulation methodology based on compact schemes and on low-pass filtering which provides selective dissipation at unresolved scales. The optical aberration is expressed in terms of the optical path difference (OPD) by integration through the variable index-of-refraction field. In order to discern the origin of the aberration, a regularized 2-D laminar shear layer is first considered for cases in which either the total or static temperatures of the two streams are matched. In addition, synthetic density fields generated through filtering of the computed flow, as well as a simple analytically-prescribed density interface are considered. It is shown that vastly different density fields can result in rather similar distortion suggesting that caution must be excercised when using the comparisons of OPD alone to attempt to infer the precise nature of the aberrating density field. Analysis of these results demonstrate that aberration in a regularized laminar shear layer can clearly be generated by the well-defined alternating lower and higher density zones associated with the coherent vortices (i.e. compressibility effects). However, comparable aberration can also result from the curved growing density interface between the two streams which exists due to the assumption of matched total temperature. For transitional shear layers, despite the loss of coherence and the absence of low-density regions in portions of the flow, the OPD increases downstream due to the growing undulating interface. In fact, to a great extent, the aberration can be captured by simply considering the contribution of the curved interface on the high-speed side of the shear layer. For forced turbulent shear layers, with tripped boundary layers on the splitter plate, the mean OPD decreased with increasing excitation frequency. This has implications for selecting an optimal forcing frequency when taking into consideration both the flow control actuator performance and the operating limitations of adaptive-optic systems. Finally, the issue of total temperature separation was examined. Variations in total temperature were shown to arise primarily as a result of the fluctuating pressure field induced by the moving vortices and can be accounted for using an inviscid analysis along the pathlines. Changes in total temperature correlate with the varying kinetic energy as the fluid element moves across the shear layer, and are not due to the transport of static temperature as a passive scalar. This energy separation effect was found to persist for transitional and turbulent shear layers provided the flow contained convecting coherent regions of low pressure.