PHYSICS OF FLUIDS 24, 086101 (2012)
Near-exit ﬂow physics of a moderately overpressured jet
and Stephen A. Solovitz
Department of Aerospace and Mechanical Engineering, University of Arizona,
Tucson, Arizona 85719, USA
Department of Mechanical Engineering, Washington State University Vancouver,
Vancouver, Washington 98686, USA
(Received 18 January 2012; accepted 16 July 2012; published online 14 August 2012)
The developing region of high-speed jets is studied using particle image velocimetry
methods. Ensemble-averaged and ﬂuctuating velocity proﬁles were measured at a
range of exit pressures, from a subsonic pressure-balanced case to an overpressured
condition 3.2 times atmospheric. When pressure-balanced, the mean ﬂow structure
showed gradual development to a bell-shaped proﬁle at approximately 8 diameters
downstream, but the turbulent Reynolds stresses were far below self-similar levels.
When overpressured, the mean structure displayed a series of compressions and
expansions, including a normal shock, and the ﬂow was far from Gaussian after
8 downstream diameters. The turbulent stresses were more suppressed than in the
pressure-balanced jet, with little change exhibited in the jet core except very near the
normal shock. Instantaneous vorticity contours also showed that the shear layer was
divided into two bands at overpressure. This suggests that the turbulent eddies driving
entrainment in the near-exit region were substantially weaker than in the self-similar
region, which would result in lower mass ﬂow from the ambient.
Institute of Physics.[http://dx.doi.org/10.1063/1.4745005]
Volcanic eruptions release high-pressure gases and particulates into the atmosphere at high
speed, often at sonic conditions. Initially, this mixture is negatively buoyant relative to the surround-
ings, which impedes its vertical rise. However, based on mass and momentum conservation, the jet
also entrains lower-density ambient air. If there is enough entrainment, the mixture density becomes
sub-atmospheric, and the plume becomes positively buoyant. Hence, the magnitude of entrainment
can determine whether a volcanic jet either collapses or grows to the stratosphere.
Under self-similar conditions, both jets and buoyant plumes are easily modeled using an en-
trainment ratio, α, which is a relation between entrained velocities and jet speeds. The entrained
velocity is a measure of the inward, radial velocity for the ambient air, typically scaled using the jet
half-width. This latter value is the radial location where the axial velocity is one-half of the centerline
jet speed. (Ironically, the radial velocity is often not inward at this location, but the scaling is still
common.) When fully developed, this ratio is a constant, equal to about 0.054 for jets and 0.09
These empirical values have been effectively employed in one-dimensional analytical
models, which produce reasonable estimates for plume height and collapse criteria.
Near the exit, the jet ﬂow structure is far from self-similar for two reasons. First, the jet velocity
proﬁle develops over an axial distance on the order of 30 jet diameters, and the shear layer is thinner
during this process. Because mixing layer eddies drive the entrainment process, their reduced size
leads to lower entrainment, on the order of 50% of self-similar levels.
Second, these jets are typically overpressured, where exit pressures are above atmospheric
levels. Under these circumstances, the ﬂuid must expand to atmospheric pressure after the exit,
This research was performed while at the Washington State University, Vancouver.
Author to whom correspondence should be addressed. Electronic mail: email@example.com.
2012 American Institute of Physics24, 086101-1