EXPERIMENTAL INVESTIGATION OF NEAR-VENT ENTRAINMENT FOR UNDEREXPANDED JETS

The growth of volcanic plumes is strongly dependent on the entrainment of surrounding air, which can alter the buoyancy of the exhaust gases. Many plumes can be successfully modeled using a simple entrainment ratio, which represents the rate of addition of ambient fluid as a constant fraction of the axial jet mass flux at distances far from the jet exit. These one-dimensional relationships are useful in rapid analysis of plume behavior, but they oversimplify the fluid mechanics involved in the plume development. Moreover, entrainment ratios have been typically measured using relatively low speed jets under laboratory conditions, while typical eruptions involve high-speed, choked flow at sonic conditions. Further, the entrainment process is somewhat muted in the near-vent region of a jet, which is a location critical to plume development in volcanoes. To improve the accuracy of entrainment models, an experiment is developed to directly measure the velocity distribution in the near-vent region of an underexpanded jet. Particle image velocimetry is applied to determine the instantaneous and time-averaged velocity fields within the jet development region, which is within the first 30 diameters downstream of its exit. The Reynolds numbers at the jet exit range well into the turbulent regime, on the order of 300,000, while the Mach numbers immediately above the vent extend from <1 to ≥1 (“underexpanded”) with pressure at the constricted vent exit ranging up to 6 atmospheres. The Reynolds number range is still below the typical value of ~10⁹ of a volcanic eruption, but the flow is well into the turbulent regime for jet flows. The measured entrainment ratios near the exit are approximately 0.02, which are significantly less than the value of 0.0535 commonly used in volcanic jet modeling. For underexpanded cases, which feature a shock cell structure downstream of the exit, there is a local peak of entrainment at the exit, while the values are reduced past the first oblique shock. These measurements demonstrate that entrainment can be influenced by the local flow physics in the near-vent region, and these results will significantly affect model predictions for volcanic plume growth, particularly as they are scaled to higher Reynolds numbers through the use of computational simulations.