Aero-optical Effects Of The Supersonic Shear Layers

With the developments in airborne laser systems and optical imaging systems, theaero-optical aberrations caused by the compressibility of high speed flows have attactedmuch attention. According to the relevant engneering applications, the aero-opticaleffects of the supersonic mixing layer and boundary layer are chosen as the subject ofthis thesis. From the viewpoints of basic phenomena and basic concepts, the currentstatus and content of the aero-optics of the shear layers are reviewed, including theexperiemtnal measurements, numerical simulations, and the control and correction.Based on the nano-particle-based planar laser scattering (NPLS) technique, andcombining the tools of theoretical analysis and numerical simulation, the aero-opticalaberrations are investigated from the viewpoints of the spatial structure, temporalevolution and adaptive optical correction. The main results of this thesis aresummarized as follows.Firstly, the aero-optical aberration of the supersonic mixing layer is investigated fromthe viewpoints of spatial structure and temporal evolution. Depending on the structureof flow field, the type of the correlation function is Gaussian or exponential type. Thestructure function exibites evident power law behavior over wide range of distance. Thefar-field propagation of Gaussian beam passing through the mixing layer is simulated byFourier transform, and the Strehl ratio is calculated. The beam centre and beam spreadaround the centre in far-field are calculated with the statistics of the tilt of the distortedwave-front. The coherent structures of the optical path length (OPL) are extracted bythree methods, including the methods of thresholding the coefficients of orthogonalwavelet transform and wavelet packet transform, and preserving a number of waveletpacket coefficients with largest amplitudes determined by the entropy dimension. Theirperformances are compared and the method with wavelet packet prevails. A model forthe temporal evolution of OPD in a short time interval is described. With the advantageof proper orthogonal decomposition (POD) in capturing the energy of a signal, the firstfew coefficients are assumed to be linear with time and the others are modeled by theGaussian statistics. As an application, this model is used to compute the short-exposureoptical transfer function of the mixing layer. The results imply that the imagingdistortion mainly occurs at low frequrncies and that the influence of phase modulation isevident.Secondly, the aero-optical aberration of the supersonic turbulent boundary layer isinvestigated from the viewpoint of spatial structure. The power spectrum of therefractive index along streamwise direction shows evident power behavior in a broadregion of wavenumber, and the power exponent varies from-1.9to-1.7in thelogarithmic region. The length of dominant structures is revealed using the pre-multiplied spectrum, and the length of the largest structure we found is about1.2δ (δis the thickness of the boundary layer). The characteristic length along normal directionis studied with the linking equation in aero-optics. This length is defined with normalintegral of correlation coefficient, and the results with two slightly different definitionsof correlation coefficient are compared. The structure function of the refractive indexalong streamwise direction is computed, and the Tatarski model is examined to fit theexperimental results. In order to fit the experiment better, a modification of the Tatarskimodel is suggested, and the power density spectrum of the refractive index is computedand analyzed.A universal form of the power spectrum of the2D OPD of the supersonic turbulentboundary layer is proposed. According to the structure function of1D OPD and thelocally homogeneous isotropic assumption, an analytic expression for the2D powerspectrum is obtained. The universality of the expression is argued, and its validity ischecked by the comparison with experiment. With this theoretical model and theexperiment, the behavior of the spectrum of1D OPD is also examined, and adescription of the normalized spectrum of the jitter signal is offered. One noticeablefeature of this model is that the model parameters can be obtained from the basicparameters of the flow, which simplifies the numerical simulation dramatically.The higher order structure functions of OPL are computed and analyzed within theframework of She-Leveque (SL) hierarchical symmetry assumption. The results indicatethat the OPL obeys this assumption, but with parameter β depending on q. The scalingexponent of SF ζ(q) is computed and compared with the theoretical prediction of SLmodel. The experimental results agree with the theoretical model quite well for large q.The curve ζ(q) we obtained is convex for small q, and the deviation from the experimentresults can not be neglected. The anomalous hehavior of ζ(q) for small q is attributed tothe large scale structure of OPL.The statistc of the tilt of the aberrated wavefront is examined by analyzing thewandering of beam certre after far-field propagation through the boundary layer of thesided wall. When the diameter of the beam propagating through the flow is smallcompared with the boundary layer thickness, the probability density functions (PDF) ofthe tilts are centered and can be approximated with Gaussian distribution. For largerbeam diameter, the PDF of the tilt in spanwise direction can still be regarded as centeredand Gaussian, but the deviation from Gaussian distribution of the PDF of the tilt instreamwise direction is evident. The correlation of the tilts in the two directions isinvestigated by computing the correlation coefficient, and the results indicate that thecorrelation is positive and strong for small beam diameter and becomes positive andweak for large beam diameter. These characters are explained by the hairpin vorticesstructures in the boundary layer, which prevail and meander for very long streamwisedistance. Finally, the correction of the aero-optical aberration of supersonic mixing layer withadaptive optics (AO) is examined with numerical method. Based on the direct numericalsimulation of supersonic mixing layer, an AO system for correcting the aero-opticalaberration is described, and its performance is tested with simulation. The AO system isbased on the optimization of distributed Strehl ratios and the stochastic parallel gradientdescent (SPGD) algorithm. Two strategies are suggested to improve the performance ofSPGD algorithm for its use in aero-optics. The first one is using an iteration processkeeping finite memory by introducing a memory factor, and the second is based on thefrozen hypothesis, and is implemented by shifting the phase on the deformable mirrorwith the convective speed. With these modifications, the performance of AO isimproved, and the aero-optical aberration can be corrected to some noticeable extent.