Supersonic Air Flow due to Solid-Liquid Impact

📝 Abstract

A solid object impacting on liquid creates a liquid jet due to the collapse of the impact cavity. Using visualization experiments with smoke particles and multiscale simulations we show that in addition a high-speed air-jet is pushed out of the cavity. Despite an impact velocity of only 1 m/s, this air-jet attains \emph{supersonic} speeds already when the cavity is slightly larger than 1 mm in diameter. The structure of the air flow resembles closely that of compressible flow through a nozzle – with the key difference that here the “nozzle” is a \emph{liquid} cavity shrinking rapidly in time.

💡 Analysis

A solid object impacting on liquid creates a liquid jet due to the collapse of the impact cavity. Using visualization experiments with smoke particles and multiscale simulations we show that in addition a high-speed air-jet is pushed out of the cavity. Despite an impact velocity of only 1 m/s, this air-jet attains \emph{supersonic} speeds already when the cavity is slightly larger than 1 mm in diameter. The structure of the air flow resembles closely that of compressible flow through a nozzle – with the key difference that here the “nozzle” is a \emph{liquid} cavity shrinking rapidly in time.

📄 Content

arXiv:0909.3777v2 [physics.flu-dyn] 21 Jan 2010 Supersonic Air Flow due to Solid-Liquid Impact Stephan Gekle,1 Ivo R. Peters,1 Jos´e Manuel Gordillo,2 Devaraj van der Meer,1 and Detlef Lohse1 1 Department of Applied Physics and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands 2 ´Area de Mec´anica de Fluidos, Departamento de Ingener´ıa Aeroespacial y Mec´anica de Fluidos, Universidad de Sevilla, Avda. de los Descubrimientos s/n 41092, Sevilla, Spain (Dated: October 30, 2018) A solid object impacting on liquid creates a liquid jet due to the collapse of the impact cavity. Using visualization experiments with smoke particles and multiscale simulations we show that in addition a high-speed air-jet is pushed out of the cavity. Despite an impact velocity of only 1 m/s, this air-jet attains supersonic speeds already when the cavity is slightly larger than 1 mm in diameter. The structure of the air flow resembles closely that of compressible flow through a nozzle – with the key difference that here the “nozzle” is a liquid cavity shrinking rapidly in time. PACS numbers: 47.55.D-, 47.60.Kz, 47.11.St, 47.80.Jk Taking a stone and throwing it onto the quiescent sur- face of a lake triggers a spectacular series of events which has been the subject of scientists’ interest for more than a century [1–17]: upon impact a thin sheet of liquid (the “crown splash”) is thrown upwards along the rim of the impacting object while below the water surface a large cavity forms in the wake of the impactor. Due to the hydrostatic pressure of the surrounding liquid this cavity immediately starts to collapse and eventually closes in a single point ejecting a thin, almost needle-like liquid jet. Just prior to the ejection of the liquid jet the cavity pos- sesses a characteristic elongated “hourglass” shape with a large radius at its bottom, a thin neck region in the center, and a widening exit towards the atmosphere. This shape is very reminiscent of the converging- diverging (“de Laval”) nozzles known from aerodynam- ics as the paradigmatic picture of compressible gas flow through, e.g., supersonic jet engines. In this Letter we use a combination of experiments and numerical simula- tions to show that in addition to the very similar shape, also the structure of the air flow through the impact cav- ity resembles closely the high-speed flow of gas through such a nozzle. Not only is the flow to a good approx- imation one-dimensional, but it even attains supersonic velocities. Nevertheless, the pressure inside the cavity is merely 2% higher than the surrounding atmosphere. The key difference, however, is that in our case the “nozzle” is a liquid cavity whose shape is evolving rapidly in time – a situation for which no equivalent exists in the scientific or engineering literature. Our experimental setup consists of a thin circular disc with radius R0 = 2 cm which is pulled through the liquid surface by a linear motor mounted at the bot- tom of a large water tank [16] with a constant speed of V0 = 1 m/s. To visualize the air flow we use small glycerin droplets (diameter roughly 3 µm) produced by a commercially available smoke machine (skytec) com- monly used for light effects in theaters and discotheques. Before the start of the experiment the atmosphere above the water surface is filled with this smoke which is conse- quently entrained into the cavity by the impacting disc. A laser sheet (Larisis Magnum II, 1500mW) shining in from above illuminates a vertical plane containing the axis of symmetry of the system. A high-speed camera (Photron SA1.1) records the motion of the smoke parti- cles at up to 15,000 frames per second. Cross-correlation of subsequent images allows us to extract the velocity of the smoke which faithfully reflects the actual air speed [18]. Our setup obeys axisymmetry and we use cylindri- cal coordinates with z = 0 the level of the undisturbed free surface. In the beginning of the process (see the snapshot in Fig. 1 (a)) air is drawn into the expanding cavity behind the impacting object with velocities of the order of the impact speed. In a later stage however, this downward flux is overcompensated by the overall shrinking of the cavity volume resulting in a net flux out of the cavity. The cavity shape at the moment when the flow through the neck reverses its direction is illustrated in Fig. 1 (b). Towards the end of the cavity collapse a thin and fast air stream is pushed out through the cavity neck which is illustrated in Fig. 1 (c). From images such as those in Fig. 1 we can directly measure the air speed u up to about 10 m/s as is shown in the inset of Fig. 2. In order to determine the flow speed at even higher velocities we revert to multiscale numerical simulations. Our numerical method proceeds in two stages: an incom- pressible stage at the beginning and a compressible stage towards the end of the impact process. During the first stage both air and liquid are treated as i

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