Short communication
Heat transfer coefficients of natural volcanic clasts

https://doi.org/10.1016/j.jvolgeores.2010.05.007Get rights and content

Abstract

Heat transfer coefficients used in numerical simulations of volcanic eruptions are typically borrowed from industrial settings where the coefficients are well determined for non-permeable, machined (spherical) materials. Volcanic clasts, in contrast, are permeable and have irregular shapes. We performed a series of laboratory experiments to determine heat transfer coefficients for natural volcanic particles. We measured the surface and interior temperatures during cooling at wind speeds ranging from 0 to 10 m/s. We also measured the permeability and density of the particles. We find that the permeability of the particles has little effect on clast cooling. In the absence of any wind, heat loss occurs by free convection, and we find no relationship between the heat transfer coefficient and particle density. However, for non-zero Reynolds numbers (finite wind speed), the heat transfer coefficient decreases with increasing porosity. We obtain a correlation for the dimensionless heat loss, or Nusselt number, of the form Nu = 2 + aRe1/2Pr1/3 where a is a density dependent coefficient given by a = 0.00022ρ + 0.31, with ρ in kg/m3, and Re and Pr are the Reynolds number and Prandtl number, respectively. Compared with non-porous particles, heat transfer coefficients for natural pumice clasts are reduced by a factor of 2–3 for particles with similar Re. Numerical simulations show that this leads to an increase in depositional temperature by 50–90 °C.

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 asNu=2Hrckairwhere 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.

References (27)

  • J. Dufek et al.

    The suspended-load and bed-load transport of particle laden gravity currents: insight from pyroclastic flows that traverse water

    J. Theor. Comput. Fluid Dyn.

    (2007)
  • J. Dufek et al.

    The dynamics and deposits generated by the Kos Plateau Tuff eruption: the controls on basal particle loss on pyroclastic flow transport

    Geochem. Geophys. Geosyst.

    (2007)
  • J. Dufek et al.

    Littoral blasts: pumice–water heat transfer and the conditions for steam explosions when pyroclastic flows enter the ocean

    J. Geophys. Res.

    (2007)
  • Cited by (20)

    • Pyroclast cooling and saturation in water

      2018, Journal of Volcanology and Geothermal Research
      Citation Excerpt :

      We find Biot numbers and heat transfer coefficients in the range of 1 − 10 and 20 − 350 W m−2K−1, respectively (Table 1). By comparison, typical heat transfer coefficients are lower for pyroclasts cooling in air, ≈ 15 W m−2K−1 (Stroberg et al., 2010) and much higher for steel, nickel, aluminum, and copper cooling in water, ≈ 103 − 104 W m−2K−1, with H decreasing with the surface temperature of the metal (Bamberger and Prinz, 1986). During stage 2 we find that clast submerged weight changes linearly with temperature (Fig. 9).

    • Impact of wind on the condition for column collapse of volcanic plumes

      2013, Earth and Planetary Science Letters
      Citation Excerpt :

      Clasts can remain mechanically coupled to and in thermal equilibrium with the gas flow when the momentum and thermal response time are small relative to the characteristic timescale of the gas flow (Crowe et al., 1997). The density, size, heat capacity, and thermal conductivity of the pyroclasts will affect these timescales (Stroberg et al., 2010). As the size, unlike the other properties, can vary over many orders of magnitude we believe this is the most important property of the pyroclasts that will affect the condition for column collapse.

    • Effects of thermal quenching on mechanical properties of pyroclasts

      2013, Journal of Volcanology and Geothermal Research
      Citation Excerpt :

      We made “quenched” samples by heating clasts to 600 °C, quenching them in water at 21 °C, drying them for 24 h at 105 °C, and then cooling them to room temperature. The quenched samples were kept in the furnace at 600 °C for 1–2 h. Using measured heat transfer coefficients for similar size pumice from the same deposit (Stroberg et al., 2010), the time scale to heat these clasts is less than 10 min. In quenching, we dropped clasts from their hot crucibles into room temperature water 2 to 3 s after removing them from the furnace.

    • Experimental study of turbulence, sedimentation, and coignimbrite mass partitioning in dilute pyroclastic density currents

      2012, Journal of Volcanology and Geothermal Research
      Citation Excerpt :

      If the segregation occurs relatively quickly, then the thermal energy of those particles is unavailable for thermal expansion of entrained air. More specifically, if the residence time of the particle within the dilute portion of the current is shorter than the timescale of thermal equilibration with the atmosphere, ~ 102 s for cm-size clasts (Stroberg et al., 2010), then some of the particle's thermal energy is removed from the current. Currents enriched in coarse or dense particles will most likely have increased deposition in proximal regions, shorter runout distances, and reduced coignimbrite fractionation compared with finer-grained currents.

    View all citing articles on Scopus
    View full text