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Research Papers: Multiphase Flows

Experimental Study of Near-Field Entrainment of Moderately Overpressured Jets

[+] Author and Article Information
Stephen A. Solovitz1

 Washington State University Vancouver, 14204 NE Salmon Creek Avenue, VELS 130F Vancouver, WA 98686stevesol@vancouver.wsu.edu

Larry G. Mastin

 USGS Cascade Volcanoes Observatory 1300 SE Cardinal Court, Bldg. 10, Suite 100, Vancouver, WA 98686lgmastin@usgs.gov

Farhad Saffaraval

 Washington State University Vancouver, 14204 NE Salmon Creek Avenue, Vancouver, WA 98686,f-saffaraval@vancouver.wsu.edu

1

Corresponding author.

J. Fluids Eng 133(5), 051304 (Jun 07, 2011) (12 pages) doi:10.1115/1.4004083 History: Received June 24, 2010; Revised April 20, 2011; Published June 07, 2011; Online June 07, 2011

Particle image velocimetry (PIV) experiments have been conducted to study the velocity flow fields in the developing flow region of high-speed jets. These velocity distributions were examined to determine the entrained mass flow over a range of geometric and flow conditions, including overpressured cases up to an overpressure ratio of 2.83. In the region near the jet exit, all measured flows exhibited the same entrainment up until the location of the first shock when overpressured. Beyond this location, the entrainment was reduced with increasing overpressure ratio, falling to approximately 60% of the magnitudes seen when subsonic. Since entrainment ratios based on lower speed, subsonic results are typically used in one-dimensional volcanological models of plume development, the current analytical methods will underestimate the likelihood of column collapse. In addition, the concept of the entrainment ratio normalization is examined in detail, as several key assumptions in this methodology do not apply when overpressured.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 3

Schematic of experimental apparatus

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Figure 4

Ensemble-averaged PIV velocity contours normalized by the exit sonic speed at steady state conditions at ReD  = 1.82 × 105 and M = 0.80 for the jet core. Contour lines are spaced 0.05 apart. For most of the imaged region, the half width location is located at approximately U/a = 0.40.

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Figure 5

Ensemble-averaged PIV velocity profiles normalized by the exit sonic speed at steady state conditions at ReD  = 1.82 × 105 and M = 0.80 at various axial locations, showing (a) axial velocities in the jet core and (b) radial velocity magnitudes in the ambient

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Figure 6

Ensemble-averaged PIV velocity contours normalized by the exit sonic speed at steady state conditions at ReD  = 4.17 × 105 and K = 1.71 for the jet core. Contour lines are spaced 0.1 apart.

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Figure 7

Ensemble-averaged centerline velocity normalized by the exit sonic speed, Uc /a, as a function of normalized distance from the exit, x/D, at steady state conditions for a 9.25-mm diameter jet at a range of inlet pressures. The experimental uncertainty is ± 5.2%.

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Figure 8

Ensemble-averaged centerline velocity normalized by the exit sonic speed, Uc /a, as a function of normalized distance from the exit, x/D, at steady state conditions for ReD  = 3.04 × 105 and K = 1.22 compared with data from Chuech [23] and Cumber [24]. The measurements agree within the experimental uncertainty of ± 5.2%.

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Figure 9

Ensemble-averaged PIV velocity contours normalized by the exit sonic speed at steady state conditions at ReD  = 4.67 × 105 and K = 2.55 for the jet core. Contour lines are spaced 0.1 apart.

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Figure 10

Ensemble-averaged centerline velocity normalized by the exit sonic speed, Uc /a, as a function of normalized distance from the exit, x/D, at steady state conditions for a 6.83-mm diameter jet at a range of inlet pressures. The experimental uncertainty is ± 5.2%.

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Figure 11

Comparison of the axial location where the centerline line falls below sonic speed, xcrit /D, for a range of overpressure ratios, K, for a 2.71-mm diameter jet

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Figure 12

Entrainment ratio based on the measured profile for a 9.25-mm diameter jet at subsonic and overpressured conditions. The experimental uncertainty is ± 10.5%.

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Figure 13

Entrainment ratio based on a tophat profile for a 9.25-mm diameter jet at subsonic and overpressured conditions

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Figure 14

Entrained mass flow rate normalized by the exit mass flow for a 9.25-mm diameter jet at subsonic and overpressured conditions. Also shown are estimates assuming the typical α = 0.06. The metric μent is linearly related to the local entrainment ratio, αlocal , although it uses exit conditions rather than local values. The experimental uncertainty is ± 8.8%.

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Figure 15

Entrained mass flow rate normalized by the exit mass flow for a 6.83-mm diameter jet at subsonic conditions compared to curves from Liepmann and Gharib [19], Ricou and Spalding [32], and Crow and Champagne [33]. The metric μent is linearly related to the local entrainment ratio, αlocal , although it uses exit conditions rather than local values. The measurements agree within the experimental uncertainty of ± 8.8%.

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Figure 16

Entrained mass flow rate normalized by the exit mass flow for a 6.83-mm diameter jet at a range of inlet pressures. The experimental uncertainty is ± 8.8%.

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Figure 1

(a) Ascent of a buoyant volcanic plume at Mount St. Helens, July 22, 1980. (b) Pyroclastic flow for a collapsing volcanic plume at Mount St. Helens, August 7, 1980 (photos by the U. S. Geological Survey).

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Figure 2

Schematic of an overpressured jet exiting from a nozzle (adapted from Ogden [3])

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