Abstract
A laboratory experiment of transient thermal convection in a 1-m-high cell was conducted to compare the length and time scales of plume development to theory. The temperature field was resolved to less than 1 mm and was measured by dissolving a solution of thermochromic crystals into the water–glycerin working fluid. The time-dependent experiment was run by applying heat at the bottom boundary that eventually was \(6\,^\circ \)C above the background temperature of the fluid. After development of a thermal boundary layer, the instability became visible at 26 min, with the development of 11, 3–4 cm width plumes growing from the boundary layer. The initially rapid growth rate reached a limiting velocity of approximately 0.5 cm min\(^{-1}\), and then decelerated throughout the experiment. Plumes interacted primarily by merging together; by the end of the experiment only three plumes were present. The Nusselt number at the onset of convection was 10, although it dropped to 4 after 45 min, which would be expected of a barely unstable system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Hue can be extracted from images captured by a true color, digital camera; however, internal filtering is sometimes applied prior to saving the data, which would alter the \(RGB\) data.
References
Bear, J.: Dynamics of Fluids in Porous Media, p. 764. Dover (corrected reprint of 1972 Elsevier ed.), New York (1988)
Bejan, A.: Convection Heat Transfer, 3rd edn. Wiley, New York (2004)
Carslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids. Oxford University Press, London (1959)
Ciofalo, M., Signorino, M., Simiano, M.: Tomographic particle-image velocimetry and thermography in Rayleigh–Bénard convection using suspended thermochromic liquid crystals and digital image processing. Exp. Fluids 34, 156–172 (2003)
Elder, J.W.: Steady free convection in a porous medium heated from below. J. Fluid Mech. 27, 29–48 (1967a)
Elder, J.W.: Transient convection in a porous medium. J. Fluid Mech. 27, 609–623 (1967b)
Foster, T.D.: Onset of convection in a layer of fluid cooled from above. Phys. Fluids 8(10), 1770–1774 (1965)
Gonzalez, R.C., Woods, R.E., Eddins, S.L.: Digital Image Processing Using MATLAB. Gatesmark Publishing, Knoxville (2009)
Graham, M.D., Steen, P.H.: Plume formation and resonant bifurcations in porous-media convection. J. Fluid Mech. 272, 67–89 (1994)
Green, L.L., Foster, T.D.: Secondary convection in a Hele–Shaw cell. J. Fluid Mech. 71, 675–687 (1975)
Horton, C.W., Rogers, F.T.: Convection currents in a porous medium. J. Appl. Phys. 16, 367–370 (1945)
Howard, L.N.: Convection at high Rayleigh number. In: Görtler, H. (ed.) Applied Mechanics, Proceedings of the 11th. International Congress of Applied Mechanics, Munich, Federal Republic of Germany, August 1964, pp. 1109–1115 (1966)
Kowalewski, T.A., Ligrani, P., Dreizler, A., Schulz, C., Fey, U.: Temperature and heat flux. In: Tropea, C., Yarin, A., Foss, J.F. (eds.) Springer Handbook of Experimental Fluid Mechanics, pp. 487–561. Springer, Berlin (2007)
Lapwood, E.R.: Convection of a fluid in a porous medium. Proc. Camb. Philos. Soc. 44, 408–521 (1948)
Miner, C.S., Dalton, N.N.: Glycerol. Reinhold Publ. Corp., New York (1953)
Nield, D.A.: Onset of thermohaline convection in a porous medium. Water Resour. Res. 11, 553–560 (1968)
Nield, D.A., Bejan, A.: Convection in Porous Media. Springer, New York (2006)
Phillips, O.M.: Geological Fluid Mechanics. Cambridge University Press, Cambridge (2009)
Raffel, M., Willert, C.E., Kompenhans, J.: Particle Image Velocimetry. Springer, Berlin (1998)
Riaz, A., Hesse, M., Tchelepi, H.A., Orr, F.M.: Onset of convection in a gravitationally unstable diffusive boundary layer in porous media. J. Fluid Mech. 548, 87–111 (2006)
Tritton, D.J.: Physical Fluid Dynamics. Oxford Science Publications, Oxford (1988)
Wooding, R.A.: Convection in a saturated porous medium at large Reynolds number or Péclet number. J. Fluid Mech. 15, 527–544 (1963)
Wooding, R.A., Tyler, S.W., White, I.: Convection in groundwater below an evaporating salt lake: 1. Onset of instability. Water Resour. Res. 33, 1199–1217 (1997a)
Wooding, R.A., Tyler, S.W., White, I., Anderson, P.A.: Convection in groundwater below an evaporating salt lake: 2. Evolution of fingers or plumes. Water Resour. Res. 33, 1219–1228 (1997b)
Acknowledgments
Financial support for this research was provided by the U.S. National Science Foundation under Award EAR 0309618. We thank two anonymous reviewers for their comments which greatly improved the manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cooper, C.A., Crews, J.B., Schumer, R. et al. Experimental Investigation of Transient Thermal Convection in Porous Media. Transp Porous Med 104, 335–347 (2014). https://doi.org/10.1007/s11242-014-0337-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-014-0337-0