Experimental simulations of the May 18, 1980 directed blast at Mount St. Helens, WA

Abstract

The 1980 directed blast at Mount St. Helens erupted from a high-pressure magma chamber into atmospheric conditions at a pressure ratio of ~150:1, producing a high-velocity dusty gas flow. Decompression from even modestly high pressure ratios (>2:1) produces supersonic flow and thus, this event was modeled as a supersonic underexpanded jet by Kieffer (1981). Steady-state underexpanded jets have a complex geometrical structure in which there is an abrupt, stationary, normal shock wave, called the Mach disk shock. For steady flow, a log-linear relationship between pressure ratio and Mach disk standoff distance, known as the Ashkenas-Sherman relation, is valid for pressure ratios above 15:1 given by x/D=0.67(Rp)^(0.5) where Rp is the pressure ratio, and x/D is the standoff distance normalized to vent diameter. The effects of unsteady discharge from a finite reservoir and application to Mount St. Helens have not been previously investigated. In order to simulate the blast, we use laboratory and numerical experiments of unsteady flow from a finite reservoir to examine jet structure. The reservoir and test section correspond to the magma chamber and ambient atmospheric conditions at Mount St. Helens respectively. We completed a series of laboratory experiments in which we varied the initial pressure ratio, reservoir length and reservoir gas (nitrogen, helium). The numerical simulations show that the Mach disk initially forms close to the vent and then travels downstream to its equilibrium position. The experiments show that as the reservoir pressure continuously decreases during the venting, or "blowdown", the Mach disk shock continuously moves back toward the reservoir after its formation at the equilibrium position. Results of these experiments indicate that above a pressure ratio of 15:1, the Mach disk standoff distance for unsteady flow falls on the empirical Ashkenas-Sherman curve for steady flow. We present a new relation for the location of the Mach disk shock for pressure ratios below 15:1 given by x/D=0.41(Rp)^(0.66). The results indicate no dependence of the normalized Mach disk location on the finiteness of the reservoir. These results may be of interest not only for high pressure eruptions such as Mount St. Helens, but to low pressure steam eruptions as well because helium is a good analog to steam.

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