Table of Contents

• Abstract
  
  
• Introduction
  
  
• Convection in Rotating Frames
  
  
• The Experiment
  
  
• Results
  
  
• Conclusions
  
  
• Acknowledgements
  
  
• References
  
  

Two coaxial Plexiglas^TM cylinders having radii R₀=15 cm and R₁=7.5 cm are separately rotated about a common axis. The annular test space is the region bounded below by the jet port plate and above by a transparent plastic window. The window is called a witness plate because it allows one to view the rising jet through an optically flat surface. Figure 1 shows the experiment with its rotational axis vertical, and Fig. 2 is a schematic of the apparatus. For the small port discussed below, the annular height was 12.5 cm and for the large port it was 10 cm. The outer cylinder was rotated at 1/2 Hz, resulting in a peripheral velocity of ~ 50 cm/s. The pulsed jets were injected with a velocity of ~ 10 cm/s. Consequently, the Reynolds number for the Ω-flow is Re ≅ 10⁵ and Re ≅ 10⁴ for the jets. We designed the experiment to have the largest Re feasible in order to simulate turbulent effects, but also designed for the ease of video recording at 30 Hz. These modest velocities resulted in negligible centrifugal and pulsed jet drive pressures. This is in contrast to the liquid sodium experiment where these pressures approach the structural limit of materials.

 

Figure 1: Figure 1 shows the Pulsed Jet Rotation Experiment with its camera mounts, electrical communications, air supply, and the cylinder drive systems.

 

Figure 2: Figure 2 shows a schematic of the Pulsed Jet Rotation Experiment. An air pressure pulse forces a pulse of water out of the inner cylinder, through the plenum ports and then through the jet port. This forms a rising vortex ring that simulates an expanding plume. The inner and outer cylinder can be rotated together and separately. The pulsed jet can be observed from the side and co-rotating with the outer cylinder from the top.

Two different diameters of jet ports were used. The small port diameter, d_SP=3.3 cm, was chosen such that the entraining jet would not interact with the cylinder walls prior to impinging upon the witness plate. This allowed the pulsed jet to fully develop by entrainment and radial divergence independent of wall interference. The large port diameter, d_LP=4.8 cm, was chosen such that when the jet impinged on the witness plate, its diameter equaled the width of the annulus. This was the maximum size possible that would allow an entraining jet to rise symmetrically through the annular space, impinge on the witness plate, and rotate. Since the experiment was designed to simulate the flow fields that we believe are requisite for the sodium dynamo, the pulsed jet produced by d_LP would then maximize the magnetic flux displaced and rotated by the jet. The jet is driven by a pulse of air exerting pressure on the water within the inner cylinder. The water is then forced out through radial ports at the base of the inner cylinder into the plenum and then through an orifice as a pulsed jet. At the termination of the pressure pulse, gravity forces the water, now at a different height in the annular and inner cylinder volumes, to return slowly through the same ports, reaching equilibrium in a few seconds. For calibration purposes a pressure transducer measured the pressure of the air applied on the fluid within the inner cylinder.

The outer cylinder assembly consists of the port plate and the hydrogen electrolysis anode and cathode for flow visualization by pulsed hydrogen electrolysis from a tungsten wire. The tungsten wire is stretched across the jet port on the top of the port plate for the large port and at 2.5 cm above the port for the small port. The distance that the jet travels from the wire to the witness plate was therefore 10 cm in either case. The wire is centered across the jet port and is tangent to a circle about the cylinder's axis. The outer cylinder also provides mechanical support for the camera mounts.

A DC voltage supply, 200-400 volts, was used to supply pulsed voltage, of 0.1 and 0.5 second duration, for the hydrogen electrolysis. The short pulse produced a thin sheet, ~ 1 cm in height, of bubbles. The long pulse allows a wider range, ~ 5 cm, of pulsed jet length to be monitored in order to demonstrate the integral behavior of it. The relative delay between the pulsed jet initiation and the electrolysis pulse allowed for the observation of different jet regions.

A TV and VHS/VCR system for real-time viewing and secondary image recording was used in conjunction with a DV camcorder. The camcorder records a digital image internally, and in addition, the analog output of the DV camcorder was transmitted via slip rings and a coax cable to the real-time viewing monitor. This system permitted convenient, single-frame replay capability of the studio-quality VHS/VCR and allowed for quantitative analysis of individual pulsed jets.

A. Flow Visualization Methods

Two flow visualization methods were employed in the experiment: pulsed hydrogen electrolysis from a 50 μm tungsten wire in an aqueous Na₂SO₄ solution (Merzkirch¹³) and dispersed guanidine¹⁴ in water. Hydrogen electrolysis creates a thin sheet of ~ 50 μm diameter bubbles. Hydrogen electrolysis was used primarily to reveal the average behavior of the near laminar flow at the head of the jet. The pattern of these small bubbles that outlines the jet is rapidly lost in the turbulence within the jet. Guanidine dispersed in water was used to emphasize the turbulently entraining fluid. Guanidine, a pearlescent material of micron-size platelets, produces an image of the entire pulsed jet. The modulation of this image emphasizes the the largest shear in the flow. Since this largest shear occurs primarily at the boundary of the eddies, guanidine outlines the turbulence within the jet and thus it outlines the entrainment boundary of the jet. In addition, it shows the turbulence as the jet strikes the witness plate. The electrolysis bubbles are even more random in pattern in this region. The guanidine images show the average differential rotation of the turbulent fluid in the pulsed jet.

Both methods reveal a coherent counter-rotation of the flow, either within the laminar flow ahead of the rising jet, or in the turbulent divergent flow when the jet strikes the witness plate. The linear array of bubbles produced by electrolysis remains clearly a line during rotation of the jet when it is embedded in the near-laminar flow at the head of the jet. We will show in forthcoming images the clear sequential rotation of the line of bubbles. In contrast, when the jet strikes the witness plate only the guanidine shows the average behavior of the flow. The average rotation of the turbulence was readily discerned from analysis of the original 30 Hz image series.

These two different measurements are important to the sodium dynamo experiment. First, the toroidal magnetic flux will be lifted ahead of the pulsed jet and will be rotated by a large, but finite angle. Second, the flux embedded in the turbulent jet will also be lifted and rotated coherently upon striking the end wall.