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Image Processing of the Film Fluid Flow in a Spinning Disk Reactor

Dmitry Goldgof, Valentina Korzhova, Grigori Sisoev

Department of Computer and Science University of South Florida, USA School of Mathematics

University of Birmingham, UK


This paper presents novel video-based algorithms for de- tection and tracking of spiral waves of fluid in a spinning disk reactor. One of the algorithms is based on process- ing of experimental video data consisting of the discrete field of disk point coordinates and its intensities. An- other algorithm is based on the mathematical models of Navier-Stokes type for the thin film flow. Comparison of the results for these two algorithms is made. Ill-posed problems of estimation of characteristics of wave regimes such as a radial velocity component and inclination an- gles are considered. To estimate errors of the respective estimates, the so-called quasi-optimal method is imple- mented.

1. Introduction

The flow of a liquid film over a rapidly rotating horizon- tal disk has been used in many industrial applications. They range from a magnetic disk with a thin lubricant film to processes involving heat or mass transfer between expanded liquid and surrounded gas, blood oxygenation, and cooling devices.

Experimental observations [1, 2, 3, 4, 5] have demon- strated that at a small flow-rate, a smooth film is formed, and at a moderately higher flow-rate, circumferential waves moving from the disk center to the disk periph- ery are formed. Further increasing flow rate leads to the appearance of spiral waves unwinding in the direction of rotation [6].

Theoretical explanation of experimental results has received increasing attention in recent published re- search. In recent papers [9, 10, 11] an evolution system of equations to model axis-symmetric finite-amplitude waves was derived and analyzed; this model was ex- tended for non-axis-symmetric flows to explain the exper- imental results. Nevertheless, the theory here is based on a general system of the Navier-Stokes equations, which are very difficult to investigate. Therefore, many prob- lems should be treated by parallel application of theo-

retical and experimental approaches: sensitivity of wave regimes to flow conditions and the three-dimensional structures observed in experiments.

Recently, work has begun in an effort to combine pre- cise experimental setup, theoretical derivation, and ba- sic image analysis techniques [5].The motion analysis of non-rigid objects and the analysis of fluid-like motion were attempted [12, 13, 14, 15]. For the fast fluid-like motion in the air, having turbulent character, detection of interface between fluid and air is important. A special so-called particle image velocimetry (PIV) technique was developed [16] to measure the kinematics of turbulent fluid flow in controlled laboratory experiments. Given a typical ensemble of PIV images, the aim is to calculate the instantaneous interface, including the instantaneous velocity on the surface of the fluid with air contact, effi- ciently and with a reasonable degree of accuracy. Algo- rithms used are typically based on a filter-like approach. In practice, however, experimental data, obtained for a sequence of time instants, contain information that, gen- erally speaking, differs from the model variables.

Algorithms and analysis of spiral waves in a spinning disk reactor are presented in [17]. Also, the character- istics of wave regimes such as wavelength and inclina- tion angles and their accuracy were estimated and results computed from video data were compared with results predicted by the theoretical model [11].

The purpose of this paper is to develop an automated system of detecting and tracking of the film flow over a spinning disk with intention of detecting regimes of the fluid flow, to develop the respective algorithms for that system; in particular, to calculate fluid flow parameter such as a radial velocity component and to compare them with the solution of the mathematical models. In this pa- per, combination of direct visualization with image anal- ysis software, utilizing results and methods of mathemat- ical modeling, is suggested.

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