Mathematical Models for Impinging Jets
In this paper are discussed mathematical models for the liquid film generated by impinging jets. These models describe only the film shape under special assumptions about processes. Attention is stressed on the interaction of the liquid film with some obs
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Summary. In this paper are discussed mathematical models for the liquid film generated by impinging jets. These models describe only the film shape under special assumptions about processes. Attention is stressed on the interaction of the liquid film with some obstacle. The idea is to generalize existing models and to investigate qualitative behavior of liquid film using numerical experiments. G.l. Taylor [Ta159][Talll59] found that the liquid film generated by impinging jets is very sensitive to properties of the wire which was used as an obstacle. The aim of this presentation is to propose a modification of the Taylor's model, which allows to simulate the film shape in cases when the angle between jets is different from 180°. Numerical results obtained by discussed models give two different shapes of the liquid film similar as in Taylors experiments. These two shapes depend on the regime: either droplets are produced close to the obstacle or not. The difference between two regimes becomes larger if the angle between jets decreases. Existence of such two regimes can be very essential for some applications of impinging jets, if the generated liquid film can have a contact with obstacles.
Key words: Impinging jets, liquid film, obstacle, simulation
Introduction Recently impinging jets are used as impinging-jet injectors for droplet generation [LHJ99, RAP95, IP91]. The main characteristics of the impinging jets, which are interesting for developers of corresponding devices, are the shape of the liquid film and the droplet distribution. Fundamentals of the liquid sheet formed during impinging of jets can be found in papers of Taylor [Tal59, Tall59, Taiii59, Ta60]. The principal scheme of the droplet generation process by impinging jets can be seen in Fig. 1. Two impinging jets with the radius R and with velocity U build a liquid film. Point B characterizes the position of an obstacle. r 0 is the distance from the obstacle to the stagnation point. Droplets can be generated on the film boundary. Different shapes of the film can be obtained in dependence of the angle between jets (20). A. Buikis et al. (eds.), Progress in Industrial Mathematics at ECMI 2002 © Springer-Verlag Berlin Heidelberg 2004
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u ~
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u Fig. 1. Interaction of the liquid film formed by impinging jets with an obstacle. Point B will also later show the position of obstacle.
In the practice there exist devices, where a contact of the liquid sheet with some surfaces can not be avoided. Taylor [Taiii59] did analysis about the interaction of a wire with the liquid sheet. Other authors mainly are working with free liquid sheets. Taylors results about interaction of the liquid film with wires are very important. He proposed that the shape of a disturbed liquid film by a small obstacle will be determined by antisymmetrical waves which can remain at rest. He observed two possible development of the film boundary, in dependence of the wire diameter and wetability. Taylor proposed mathematical models and did experiments for the case () = 1r
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