Short communicationHeat transfer coefficients of natural volcanic clasts
Introduction
Heat transfer from particles to the surrounding gas during explosive volcanic eruptions affects the buoyancy of the gas–particle mixture and the gas pressure (e.g., Woods and Bursik, 1991). Thus the rate of heat transfer can influence the runout of pyroclastic density currents and elutriation of fine ash. The time scale over which particles cool also affects their degassing (Hort and Gardner, 2000), oxidation (Tait et al., 1998), expansion and quenching (Kaminski and Jaupart, 1997). For these reasons, numerical simulations of pyroclastic density currents and explosive eruptions often include models for particle–gas heat transfer (e.g., Dobran et al., 1993, Neri and Macedonio, 1996, Dartevelle et al., 2004, Dufek and Bergantz, 2007a).
Heat transfer properties are typically characterized by a so-called “heat transfer coefficient”, and are usually measured for spherical, non-porous particles (e.g., Mallory, 1969, Touloukian and Ho, 1972). In contrast, natural volcanic particles are irregular in shape and porous. Particle shape can alter heat transfer coefficients by changing the properties of the thermal boundary layer around particles across which heat is conducted. Porous particles may also alter heat transfer coefficients by allowing increased airflow through the particle pores, thereby expediting cooling.
Here we performed a series of laboratory experiments to determine the sensitivity of volcanic particle heat transfer coefficients to variations of permeability and density. We find values that can differ by factors exceeding 3 compared with standard engineering values for spherical particles. We also present an example numerical simulation in which we assess the role of error or uncertainty in the heat transfer coefficient on the depositional temperature of centimeter-sized clasts.
Section snippets
Samples
We measured heat transfer coefficients for a range of natural volcanic particles to encompass different densities and permeabilities. We also made the same measurements on glass spheres in order to compare our results with well-established literature values (e.g., Whitaker, 1972).
The volcanic samples are air fall from the ∼ 850 BP Glass Mountain eruption at Medicine Lake volcano, California (numbered samples), and basaltic scoria from Coso, California (Scoria 1 and 2). Sample properties are
Methods
Heat transfer coefficients were measured by recording the cooling rates of the particles shown in Fig. 1 and listed in Table 1. A 1 mm diameter thermocouple wire was inserted into a 1 mm diameter hole drilled into the interior of each sample. We heated samples to 200 °C in a convection oven. Once the internal temperature reading from the thermocouple was steady, we removed the sample from the oven and recorded its cooling. We monitor internal temperature with the thermocouple and the surface
Results
Fig. 2 shows one example of the temperature measurements collected for a cooling particle. The data shown is for sample 22 subjected to a wind speed of 3.5 m/s with an ambient temperature of 25 °C. In order to characterize particle cooling, we calculate a dimensionless heat loss, or Nusselt number, defined aswhere the thermal conductivity of air kair is 0.0257 Wm− 1 K− 1. To calculate H, we calculated the best-fit line that relates the logarithmic temperature difference from Eq. (1) and
Discussion
In Fig. 4 we show model predictions given by Eq. (7) for the highest and lowest density natural clasts. Also shown is the equivalent relationship, Eq. (5), for spherical particles. There are two ways in which the heat transfer coefficients for natural clasts differ from those of the glass beads. First, for the non-porous particles, the heat transfer coefficient for natural clasts is higher than that for spherical particles owing to the increased surface area to volume ratio for non-spherical
Conclusions
We measured heat transfer coefficients for natural volcanic clasts. We find that particle permeability has no significant effect but density matters for high wind speeds. Pumice particles cool about 3 times more slowly than their dense equivalents at wind speeds (relative velocity between particles and surrounding gas) of 10 m/s. We propose that Eqs. (7) be used in numerical simulations that include such heat transfer processes (e.g., Dobran et al., 1993, Neri and Macedonio, 1996 Dartevelle et
Acknowledgements
We thank the Berkeley Undergraduate Research Apprenticeship Program and NSF grants 0809564 (WS and MM) and 0809321 (JD) for support. Ameeta Patel helped with the lab measurements. We thank M. Hort and an anonymous reviewer for comments on the manuscript.
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