Estimation of local Mach number in compressible flows of dense organic vapors using Gabor filters and Radon transforms for the post-processing of schlieren images

Abstract

Images of compressible flows can be post-processed with digital imaging techniques to obtain accurate quantitative information about variables characterizing the flow. For example, the local flow Mach number can be obtained from the angle of Mach lines visualized with the schlieren method. These techniques were recently applied to supersonic flows of dense organic vapors, with the objective of obtaining accurate data to validate theory and CFD codes. Non-ideal compressible fluid dynamics (NICFD) is concerned with these flows, for which therefore the thermodynamic properties of the fluid can be modeled only with equations that are more complex than the ideal gas relations. NICFD flows are relevant, e.g., for applications in the power and chemical industry. However, currently employed image post-processing techniques used to obtain the local Mach number or shock wave angle from schlieren images, like the Hough transform, suffer from few drawbacks, namely a long computational time to obtain the relevant quantities and improvable accuracy. The investigation reported here concerns the application of known digital image processing methods to schlieren images, in this case Gabor filters and Radon transforms, to obtain the local Mach number and the shockwave angle of flows in NICFD conditions. The selected test case is the supersonic expansion of the dense vapor of hexamethyldisiloxane flowing through the nozzle test section of the ORCHID facility in operation at the Propulsion and Power laboratory of Delft University of Technology. The investigated digital image processing techniques provide values of the local Mach number with comparable uncertainty (within \(5\%)\) as the Hough transform approach. Moreover, Mach line orientations are computed for the whole field of view, together with Mach line wavelength. It was also proven that these methods are suitable for discerning Mach line orientation even in the case of very complex flow fields, with coexisting Mach waves and shock waves.