529 / 2019-03-19 22:00:22

Experimental Investigation on Effect of Viscosity on Droplet Deformation Process at Low Weber Number

Deformation process; Shock wave; Viscosity

全体主题 > Interface Instabilities at Extremes

In this paper, the viscous effect on droplet deformation behavior induced by shock wave of low Weber number will be specially concerned in order to have a deep understanding of droplet deformation process. The shock wave was generated by a horizontal shock tube with high-speed shadowgraphic technique used to capture the deformation and breakup process. The experiments were carried out with three different dynamic viscosities: 10 m, 50 and 100 mPa·s. Respectively droplet diameters were kept nearly the same. The Weber number was 45, and Ohnesorge number were 0.07, 0.32 and 0.66 respectively. In every experimental operation, the high pressure section was filled with nitrogen and the low pressure section was at atmospheric pressure filled with air.
Typical images of droplet deformation process upon its interaction with the shock wave with different Oh are shown in Fig. 1. The time is dimensionalized as "T=t" "U" _"0" 〖"(" "ρ" _"l" "/" "ρ" _"g" ")" 〗^"-0.5" "/" "d" _"0" . As shown by the first row (Case 1), the deformation process can be divided into five periods (static, compression, expansion, recompression, and bag growth) according to the deformation behavior. Specifically, for a) the static period (T=0~0.13), the droplet stays the initial state with no deformation behavior. For b) the compression period (T=0.13~0.59), the droplet deforms in a way that the fluid on the windward face and the lee side is extruded towards the equator. At T=0.32, the droplet appears as a mushroom shape. The fluid keeps on flowing towards the equator, and when T is 0.53, the droplet appears much more like a flattened bowl. To quantify the droplet deformation perpendicular direction, its perpendicular direction is defined as dc. As time evolves, dc keeps on increasing while the droplet width along the flow direction keeps on decreasing. At the dimensionless time T=0.59, the shape of the droplet becomes fusiform. For c) expansion period (T=0.59~0.73), the windward face of the droplet keeps on expanding, the periphery begins to envelop the droplet and keeps expanding along the flow direction, which leads to the growth of droplet width along the flow direction d) recompression period (T=0.73~1.19). From the dimensionless time T=0.73 to 0.94, two unique deformation features occur: droplet width along the flow direction starts to decrease again and the flattened droplet begins to bend along the flow direction. In addition, the droplet carries on expanding radially, and dc keeps on increasing. From T=0.94 to 1.19, dc stays nearly the same with little change while droplet width along the flow direction keeps on decreasing. For the final e) bag growth period, (T>1.19), Bag is growing within the droplet. At T=1.36, the droplet volume reaches its maximum before breakup. The droplet shape keeps changing, small bags that grows on the surface break one by one. The breakup image at T=1.57 shows the typical multimode breakup behavior. Limited by the short shock wave tube length, the reflected shock wave comes, and is about to contact with the broken droplet at T=1.65.
For more viscous droplet, as shown by the second row (Case 2) in Fig. 1, similar deformation behaviors appear as the less viscous droplet of Case 1: a) mushroom and fusiform shape; b) droplet bending phenomenon is observed. However, it is seen that the droplet deformation is slower, and the fusiform shape is slenderer. Besides, after dc reaches the maximum, dc firstly decreases then increases from the dimensionless time T= 0.73 to 1.42. This kind of oscillation does not appear at low Oh case. From T=1.24, the droplet bag starts to grow, but the bag does not grow fully before the reflected shock wave arrives at the droplet. It can be seen that the bag breaks under the force of the reflected shock but with a ring unbroken at T=2.76.

Figure 1: Droplet deformation behavior
With the further increase of viscosity, as shown by the third row (Case 3) in Fig. 1, images show several different droplet deformation behaviors. Firstly, at T=0.40, droplet appears like a mushroom, but it much more “soft”, the appearance has a better curve shape than the low Oh cases. In addition, at T=0.70, droplet deforms into fusiform shape, whose width of the droplet (T=0.70) is much lower than the Case 1. After the action of the reflected shock wave, the droplet bag continues to grow but in a contrary direction. For the whole deformation process, the deformation behavior of Case 3 is much slower, compared to Case 1.
For better understanding the viscous effect on the droplet deformation process induced by shock wave, experiments at low Weber number on a horizontal shock tube. Three kinds of silicone oils (10, 50 and 100 mPa·s) were chosen as the experimental fluids. Upon the shock wave passing through the droplet, it experiences five periods (static, compression, expand, recompression and bag growth), detailed deformation behaviors are described with dimensionless time. With the increase of viscosity, the deformation behavior is slowed down. Besides, the oscillation phenomena are firstly observed at such low We condition.