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Flow visualization of supersonic mixing layer has been studied based on the high spatiotemporal resolution Nano-based Planar Laser Scattering (NPLS) method in SML-1 wind tunnel. The corresponding images distinctly reproduced the flow structure of laminar, transitional and turbulent region, with which the fractal measurement can be implemented. Two methods of measuring fractal dimension were introduced and compared. The fractal dimension of the transitional region and the fully developing turbulence region of supersonic mixing layer were measured based on the box-counting method. In the transitional region, the fractal dimension will increase with turbulent intensity. In the fully developing turbulent region, the fractal dimension will not vary apparently for different flow structures, which embodies the self-similarity of supersonic turbulence. NPLS, turbulence mixing layer, fractal dimensionRecently, applications of fractal theory in fluid dynamics are widely studied. The objects with fractal characteristic have no characteristic scale and often exhibit self-similarity of different scales, which are suitable to depict turbulence. Sreenivasan and Meneveau introduced the fractal theory into experimental fluid dynamics, and analyzed the fractal dimension of low speed shear layer, jet, wake and boundary layer [1] . Sreenivasan discussed the fractal and multifractal description and measurement of turbulent flow [2] . Turcotte analyzed the energy spectral of temperature fluctuation of sea with the fractal theory [3] . Takeno measured the fractal dimension of the surface of flame [4] . Lane-Serff measured the fractal structure of the round jet and plume [5] . Frederiksen acquired vast experimental data of the turbulent round jet based on LIF technique, from which fractal characteristics of turbulence were discussed in detail [6][7][8][9] . Now, fractal studies of low speed flow based on experimental images have produced many valuable results, and the application of the fractal models in CFD are evolving [10,11] , but up to now, no reference has reported any fractal studies of supersonic turbulent mixing layer from the point of view of experiments.

Due to the influence of shock wave and turbulence, supersonic density field exhibits strongly inhomogeneous and unsteady characteristics. Applying traditional density field measurement techniques to supersonic flows yields three problems: low spatiotemporal resolution, limitation of measuring 3D density field, and low signal to noise ratio (SNR). A new method based on Nano-based Planar Laser Scattering (NPLS) technique is proposed in this paper to measure supersonic density field. This method measures planar transient density field in 3D supersonic flow by calibrating the relationship between density and concentration of tracer particles, which would display the density fluctuation due to the influence of shock waves and vortexes. The application of this new method to density field measurement of supersonic optical bow cap is introduced in this paper, and the results reveal shock wave, turbulent boundary layer in the flow with the spatial resolution of 93.2 μm/pixel. By analyzing the results at interval of 5 μs, temporal evolution of density field can be observed.

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The interaction between shock wave and turbulence has been studied in supersonic turbulent mix layer wind tunnel. The interaction between oblique shock wave and turbulent boundary layer and the influence of large vortex in mix layer on oblique shock wave have been observed by NPLS technique. From NPLS image, not only complex flow structure is observed but also time-dependent supersonic flow visualization is realized. The mechanism of interaction between shock wave and turbulence is discussed based on high quality NPLS image.shock wave, turbulent boundary layer, turbulent mix layerThe interaction between shock wave and turbulence is one of the most complex phenomena in supersonic flow. A study on it can help to understand the mechanism of shock wave and turbulence flow more deeply. This phenomenon often presents in supersonic turbulent mix layer flow. While pressure is equivalent between two layers, the primary characteristics are the generating and developing of coherent structure. If not equal, interaction between shock wave and turbulent mix layer and boundary layer will appear, which will lead to a very complex flow field. Generally speaking, the interaction between shock wave and turbulence can be classified as: interaction between shock wave and homogeneous turbulence, interaction between shock wave and turbulent jet, and interaction between shock wave and turbulent boundary layer, etc. [1] . Interactions between shock wave and turbulent boundary layer and mix layer are studied in this paper.Rose and Johson studied the interaction between shock wave and turbulent boundary layer [2] . An oblique shock wave was generated at the opposite wall to that of the boundary layer by a sharp edge in their experiment, but no high resolution turbulence image was acquired. Andreopoulos and Muck, Erengil and Dolling, and Beresh also studied it with different methods with the influence of pressure fluctuation and movement of large scale structure taken into account [3][4][5] , but more detailed analysis could not be realized because of the limitation of resolution. Settles, Hayakawa and Samimy have studied the interaction between oblique shock wave and turbulent mix layer. In their experiments, the turbulent mix layer is generated from a concave, and oblique shock wave is generated by a sharp edge. But they only dealt with the influence of Mach number on turbulent intensity due to limitations of testing system [6][7][8] . There are also some computational results on the interaction between shock wave and turbulence. Horstman and Visbal attempted to predict the flow structure using Reynolds-averaged Navier-Stokes methods, but the result showed that the predicted turbulent intensity was not accuracy. More recently, LES and DNS have been invoked to study the interaction between shock wave and turbulence with the development of computer technology. Ducros has studied the interaction between normal shock wave and homogeneous turbulence with LES [9] . Adams studied the interaction between shock

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The density field measurement of supersonic mixing layer based on the nanoparticle-based planar laser scattering method was studied. The calibration of experimental images was analyzed, and the relation between tracer particles concentration and local density of flowfield was calibrated with oblique shockwave experiment. According to the characteristic of mixing layer images, the influence of uneven light intensity distribution was calibrated. With these calibration methods, the density field of supersonic mixing layer with convective Mach number at 0.12 was measured. By analyzing the spanwise vortical structures and streamwise density field, the three dimensional (3D) density field was approximately reconstructed, which apparently reflected the 3D structure of supersonic mixing layer.supersonic mixing layer, density field measurement, nanoparticles scattering Citation:Zhao Y X, Yi S H, Tian L F, et al. Density field measurement and approximate reconstruction of supersonic mixing layer.

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