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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 goldgof@csee.usf.edu korzhova@scee.usf.edu G.Sisoev@bham.ac.uk

Abstract

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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