ИСТИНА

Background Oriented Schlieren method (BOS) [1] is a promising way of obtaining quantitative data about density field in gas and liquid flows. Applications include high-speed gas-dynamics with shocks, convective flows and other transport phenomena. The essence of the method is comparison of two images of the same background, taken with and without the investigated transparent object between the camera and the background. The key role in achieving reliable data is played by the nature of background and details of computer post-processing. However, very little is known about data accuracy for a given background type. The object of the present paper is investigation of the resultant density field accuracy for various background types by series of virtual experiments. First, the image distortion due to known density disturbance is evaluated. Various kinds of disturbance are used: thermal plume, plane shock wave, thermal boundary layer. The distorted image is obtained by rearranging pixels in the original image according to calculated displacements. Then, two images are processed using multi-pass cross-correlation algorithm, commonly used in PIV. Density field is restored by solving Poisson equation with adequate Neumann boundary conditions. Local and total relative errors are determined by comparison with known exact solution. Simulations are performed for various backgrounds: regular and irregular dot patterns, linear backgrounds, wavelet-noise pattern proposed in [2], natural backgrounds. It is found that in order to provide better accuracy the background should meet two major requirements: i) it should have period larger than the observed displacement or interrogation window size, ii) it should not have large blocks of uniform color. Additional filtering enhancing accuracy in presence of such blocks is proposed and discussed. Also, the effect of possible image blur due to low depth-of-field in a real experiment is simulated. The feature specific for BOS method in liquids is Gladstone-Dale constant dependence on density and temperature which can be neglected in gases but yields about 25% of displacement in liquids. Poisson equation for refraction index is derived without making use of Gladstone-Dale law. Temperature and density fields are found via empirical equation of state and expression for refraction index under constant pressure assumption. It is shown that BOS method sensitivity is larger in liquids than in gases. Experimental examples are given both for gas and liquid. REFERENCES [1] G.E.A. Meier, “Computerized background-oriented schlieren”, Exp. Fluids, Vol. 33, pp. 181-187, (2002). [2] B. Atcheson, W. Heidrich and I. Ihrke, “An evaluation of optical flow algorithms for background oriented schlieren imaging”, Exp. Fluids, Vol. 46, pp. 467-476, (2009).