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The origin of the tubular jet

Published online by Cambridge University Press:  26 March 2008

RAYMOND BERGMANN ,
ERIK DE JONG ,
JEAN-BAPTISTE CHOIMET ,
DEVARAJ VAN DER MEER  and
DETLEF LOHSE
RAYMOND BERGMANN
Affiliation:
Physics of Fluids Group, Department of Applied Physics, Impact Institute, and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
ERIK DE JONG
Affiliation:
Physics of Fluids Group, Department of Applied Physics, Impact Institute, and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
JEAN-BAPTISTE CHOIMET
Affiliation:
Physics of Fluids Group, Department of Applied Physics, Impact Institute, and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
DEVARAJ VAN DER MEER
Affiliation:
Physics of Fluids Group, Department of Applied Physics, Impact Institute, and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
DETLEF LOHSE
Affiliation:
Physics of Fluids Group, Department of Applied Physics, Impact Institute, and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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Abstract

A vertical cylindrical tube is partially immersed in a water-filled container and pressurized to lower the fluid level inside the tube. A sudden release of the pressure in the tube creates a singularity on top of the rising free surface. At the very beginning of the process a jet emerges at the centre of the surface, the strength of which strongly depends on the initial shape of the meniscus. Here, the time-evolution of the complex shape of the free surface and the flow around the cylindrical tube are analysed using high-speed imaging, particle image velocimetry, and numerical simulations. The tubular jet is found to be created by the following series of events, which eventually lead to the flow focusing at the tube's centre. A circular surface wave, produced by the funnelling of flow into the tube, is pushed inwards by the radial flow directly underneath the surface. As the wave moves inward and eventually collapses at the centre of the tube, a bump of fluid grows in the centre due to the converging flow in the bulk. This converging flow continues to feed the jet after the circular wave has collapsed. The singularity of the wave collapse is manifested in the initial sharp tip of the jet. All of the above events are traced back to a single origin: the convergence of the flow as it enters the tube. Movies are available with the online version of the paper.

JFM classification

Wakes/Jets: Jets Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 600 , 10 April 2008 , pp. 19 - 43
Copyright
Copyright © Cambridge University Press 2008

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Bergmann et al. supplementary material

Movie 1(a-c). A vertical cylindrical tube of inner radius R = 25 mm is partially immersed to a depth H of 200 mm in a water-filled container and pressurized to lower the meniscus level inside the tube. After a sudden release of the pressure the temporal evolution of the free surface is shown for initial meniscus heights of h = 14 mm (a), h = 0 mm (b), and h = -6 mm (c). The dotted white line indicates the position of the bottom of the tube and the solid yellow line is the depth of the centre of the initial meniscus: (a) h > 0 produces no jet, just a small bump of liquid is visible in the centre of the tube; (b) h ≈ 0 produces a sharp jet; (c) h < 0 produces a detached rising water column, from which a strong jet erupts. In all cases the distance L from the bottom of the tube to the bottom of the container is much larger than R.

Download Bergmann et al. supplementary material(Video)
Video 673.9 KB

Bergmann et al. supplementary material

Movie 1(a-c). A vertical cylindrical tube of inner radius R = 25 mm is partially immersed to a depth H of 200 mm in a water-filled container and pressurized to lower the meniscus level inside the tube. After a sudden release of the pressure the temporal evolution of the free surface is shown for initial meniscus heights of h = 14 mm (a), h = 0 mm (b), and h = -6 mm (c). The dotted white line indicates the position of the bottom of the tube and the solid yellow line is the depth of the centre of the initial meniscus: (a) h > 0 produces no jet, just a small bump of liquid is visible in the centre of the tube; (b) h ≈ 0 produces a sharp jet; (c) h < 0 produces a detached rising water column, from which a strong jet erupts. In all cases the distance L from the bottom of the tube to the bottom of the container is much larger than R.

Download Bergmann et al. supplementary material(Video)
Video 629.8 KB

Bergmann et al. supplementary material

Movie 1(a-c). A vertical cylindrical tube of inner radius R = 25 mm is partially immersed to a depth H of 200 mm in a water-filled container and pressurized to lower the meniscus level inside the tube. After a sudden release of the pressure the temporal evolution of the free surface is shown for initial meniscus heights of h = 14 mm (a), h = 0 mm (b), and h = -6 mm (c). The dotted white line indicates the position of the bottom of the tube and the solid yellow line is the depth of the centre of the initial meniscus: (a) h > 0 produces no jet, just a small bump of liquid is visible in the centre of the tube; (b) h ≈ 0 produces a sharp jet; (c) h < 0 produces a detached rising water column, from which a strong jet erupts. In all cases the distance L from the bottom of the tube to the bottom of the container is much larger than R.

Download Bergmann et al. supplementary material(Video)
Video 723.2 KB

Bergmann et al. supplementary material

Movie 1(a-c). A vertical cylindrical tube of inner radius R = 25 mm is partially immersed to a depth H of 200 mm in a water-filled container and pressurized to lower the meniscus level inside the tube. After a sudden release of the pressure the temporal evolution of the free surface is shown for initial meniscus heights of h = 14 mm (a), h = 0 mm (b), and h = -6 mm (c). The dotted white line indicates the position of the bottom of the tube and the solid yellow line is the depth of the centre of the initial meniscus: (a) h > 0 produces no jet, just a small bump of liquid is visible in the centre of the tube; (b) h ≈ 0 produces a sharp jet; (c) h < 0 produces a detached rising water column, from which a strong jet erupts. In all cases the distance L from the bottom of the tube to the bottom of the container is much larger than R.

Download Bergmann et al. supplementary material(Video)
Video 706 KB

Bergmann et al. supplementary material

Movie 1(a-c). A vertical cylindrical tube of inner radius R = 25 mm is partially immersed to a depth H of 200 mm in a water-filled container and pressurized to lower the meniscus level inside the tube. After a sudden release of the pressure the temporal evolution of the free surface is shown for initial meniscus heights of h = 14 mm (a), h = 0 mm (b), and h = -6 mm (c). The dotted white line indicates the position of the bottom of the tube and the solid yellow line is the depth of the centre of the initial meniscus: (a) h > 0 produces no jet, just a small bump of liquid is visible in the centre of the tube; (b) h ≈ 0 produces a sharp jet; (c) h < 0 produces a detached rising water column, from which a strong jet erupts. In all cases the distance L from the bottom of the tube to the bottom of the container is much larger than R.

Download Bergmann et al. supplementary material(Video)
Video 800.2 KB

Bergmann et al. supplementary material

Movie 1(a-c). A vertical cylindrical tube of inner radius R = 25 mm is partially immersed to a depth H of 200 mm in a water-filled container and pressurized to lower the meniscus level inside the tube. After a sudden release of the pressure the temporal evolution of the free surface is shown for initial meniscus heights of h = 14 mm (a), h = 0 mm (b), and h = -6 mm (c). The dotted white line indicates the position of the bottom of the tube and the solid yellow line is the depth of the centre of the initial meniscus: (a) h > 0 produces no jet, just a small bump of liquid is visible in the centre of the tube; (b) h ≈ 0 produces a sharp jet; (c) h < 0 produces a detached rising water column, from which a strong jet erupts. In all cases the distance L from the bottom of the tube to the bottom of the container is much larger than R.

Download Bergmann et al. supplementary material(Video)
Video 797.7 KB

Bergmann et al. supplementary material

Movie 2. The evolution of the free surface after the pressure release seen from below for h = 0 mm (experimental conditions: R = 25 mm, L >> R, H = 300 mm). A circular surface wave is seen to travel inward and its collapse produces the initial the initial sharp tip of the jet.

Download Bergmann et al. supplementary material(Video)
Video 403 KB

Bergmann et al. supplementary material

Movie 2. The evolution of the free surface after the pressure release seen from below for h = 0 mm (experimental conditions: R = 25 mm, L >> R, H = 300 mm). A circular surface wave is seen to travel inward and its collapse produces the initial the initial sharp tip of the jet.

Download Bergmann et al. supplementary material(Video)
Video 355.4 KB

Bergmann et al. supplementary material

Movie 3. The closure of the circular wave viewed from above at an angle for h = 0 mm (experimental conditions: R = 25 mm, L >> R, H = 200 mm). The rim moves as a wall of fluid over the undisturbed inner region of the interface, similar to a hydraulic jump. The jet is initiated when the bottom of the fluid wall reaches the centre.

Download Bergmann et al. supplementary material(Video)
Video 1.2 MB

Bergmann et al. supplementary material

Movie 3. The closure of the circular wave viewed from above at an angle for h = 0 mm (experimental conditions: R = 25 mm, L >> R, H = 200 mm). The rim moves as a wall of fluid over the undisturbed inner region of the interface, similar to a hydraulic jump. The jet is initiated when the bottom of the fluid wall reaches the centre.

Download Bergmann et al. supplementary material(Video)
Video 2.2 MB