한국지반공학회논문집 (Journal of the Korean Geotechnical Society)

  • 제33권2호
  • /
  • Pages.35-47
  • /
  • 2017
  • /
  • 1229-2427(pISSN)
  • /
  • 2288-646X(eISSN)
한국지반공학회 (Korean Geotechnical Society)
권호 표지
DOI QR코드

DOI QR Code

지반내 자연대류에 대한 수치해석적 논의

Numerical Discussion on Natural Convection in Soils

  • 신호성 (울산대학교 건설환경공학부)
  • Shin, Hosung (Dept. of Civil & Environmental Engrg., Univ. of Ulsan)
  • 투고 : 2017.01.11
  • 심사 : 2017.02.17
  • 발행 : 2017.02.28
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

지반의 열적 거동은 대부분 열전도에 국한되어 연구가 진행되었으며, 자연대류 현상에 대한 연구는 매우 미비한 실정이다. 지반의 온도증가는 간극수의 밀도변화에 따른 부력을 유발하여 자연대류를 발생시키게 된다. 유체역학 관점에서 다공질 재료내의 자연대류 해석의 제약조건에 대하여 논의하고, 거시적 관점에서 완전 결합된 열-수리-역학적인 지배방정식을 이용한 대류현상에 대한 수치해석 기법을 제시하였다. 실내 열전도도 측정을 위한 탐침기 실험에 대한 수치실험은 자연대류를 무시하고 평가된 열전도도의 불확실성에 대하여 논의하고, 모델식과의 오류를 최소화하기 위한 적정한 실험조건을 제시하였다. 해저 전력선의 매설은 해저면 0.2m 깊이에서의 온도상승을 $2^{\circ}C$로 제한하고 있으나, 투수성이 큰 지반재료에 대한 수치해석결과는 기준온도를 초과하는 것으로 나타났다. 해저면의 온도와 열-수리-역학적 물성은 전력선의 매설설계에 중요한 설계인자이며 자연대류의 영향을 고려하여야 한다. 특히, 큰 투수성을 갖는 지반내에 열원이 존재하는 경우, 간극수의 밀도변화에 따른 자연대류가 중요한 열전달의 인자가 되므로 이를 고려한 해석을 수행하여야 한다.

Thermal behavior of soils is mainly focused on thermal conduction, and the study of natural convection is very limited. Increase of soil temperature causes natural convection due to buoyancy from density change of pore water. The limitations of the analysis using fluid dynamics for natural convection in the porous media is discussed and a new numerical analysis is presented for natural convection in porous media using THM governing equations fully coupled in the macroscopic view. Numerical experiments for thermal probe show increase in the uncertainty of thermal conductivity estimated without considering natural convection, and suggest appropriate experimental procedures to minimize errors between analytical model and numerical results. Burial of submarine power cable should not exceed the temperature changes of $2^{\circ}C$ at the depth of 0.2 m under the seabed, but numerical analysis for high permeable ground exceeds this criterion. Temperature and THM properties of the seafloor are important design factors for the burial of power cable, and in this case effects of natural convection should be considered. Especially, in the presence of heat sources in soils with high permeability, natural convection due to the variation of density of pore water should be considered as an important heat transfer mechanism.

키워드

참고문헌

  1. Anderson, K., Shafahi, M., McGann, S., and Pakdee, W. (2014), "Numerical Simulation of 3-D Free Convection in Porous Media due to Combined Surface Forced Convection and Internal Heat Generation", 5th International conference on porous media and their applications in science, engineering and industry.
  2. Ardelean, M. and Minnebo, P. (2015), HVDC submarine power cables in the world: State-of-the-art knowledge, Office of the European Union.
  3. Auriault, J. L. (2009), "On the Domain of Validity of Brinkman's Equation", Transp. Porous Media, Vol.79, pp.215-223. https://doi.org/10.1007/s11242-008-9308-7
  4. Bear, J. (1990), Introduction to modeling of transport phenomena in porous media, Dordrecht, Kluwer Academic Publishers, p.553.
  5. Bear, J. (1972), Dynamics of Fluids in Porous Media. American Elsevier Publishing Company, Inc., New York, NY, USA, p.764.
  6. Bidarmaghz, A. and Narsilio, G.A. (2016), "Shallow Geothermal Energy: Emerging Convective Phenomena in Permeable Saturated Soils", Geotechnique Letters, Vol.5, No.2, pp.1-5.
  7. Blake, K., Bejan, A., and Poulikakos, D. (1984), "Natural Convection Near $4^{\circ}C$ in a Water-saturated Porous Layer Heated from Below", Int J Heat Mass Transf., Vol.27, No.12, pp.2355-2364. https://doi.org/10.1016/0017-9310(84)90094-2
  8. Caltagirone, J.P., Meyer, G., and Mojtabi, A. (1981), "Structurations Thermoconvectives Tridimensionnelles Dans une Couche Poreuse Horizontale", J. Mecanique, Vol.20, pp.219-232.
  9. Cathie, D.N., Jaeck, C., Ballard, J.C., and Wintgens, J.F. (2005), "Pipeline Geotechnics: State of the Art", Proc. International Symposium on Frontiers in Offshore Geotechnics (ISFOG) Perth, Australia, pp.95-114.
  10. Chakraborty, S., Talimi, V., Muzychka, Y., and McAffee, R. (2016), "Modeling of Heat Loss from Offshore Buried Pipeline through Experimental Investigations and Numerical Analysis", Arctic Technology Conference.
  11. Cheng, P. (1978), Heat transfer in geothermal systems, Advances in Heat Transfer, p.105.
  12. Choi, W. and Ooka, R. (2014), "The Effect of Natural Convection on Thermal Response Test", Ashrae Trans., Vol.120, p.14-C047.
  13. Choi, W. and Ooka, R. (2016), "Effect of Natural Convection on Thermal Response Test Conducted in Saturated Porous Formation: Comparison of Gravel-backfilled and Cement-grouted Borehole Heat Exchangers", Renewable Energy, 96(A), pp.891-903. https://doi.org/10.1016/j.renene.2016.05.040
  14. Dang, L. and Leong, W.H. (2015), "Thermal Conductivity Probe - Part I - A Theoretical Error Analysis", Int. J. Heat Mass Transfer, Vol.86, pp.992-1003. https://doi.org/10.1016/j.ijheatmasstransfer.2015.03.020
  15. Engstrom, M. and Nordell, B. (2016), "Temperature-driven Groundwater Convection in Cold Climates", Hydrogeology Journal, Vol.24, No.5, pp.1245-1253. https://doi.org/10.1007/s10040-016-1420-0
  16. Farouki, O.T. (1981), Thermal Properties of Soils (No. CRRELMONO-81-1). Cold regions research and engineering lab.
  17. Gehlin, S.E.A. and Hellstrom, G. (2003), "Influence on Thermal Response Test by Groundwater Flow in Vertical Fractures in Hard Rock", Renew Energy, Vol.28, No.14, pp.2221-2238. https://doi.org/10.1016/S0960-1481(03)00128-9
  18. Gens, A. and Olivella, S. (2001), "THM phenomena in saturated and unsaturated porous media", Revue Francaise de Genie Civil, 5:6, pp.693-717. https://doi.org/10.1080/12795119.2001.9692323
  19. Grosan, T., Revnic, C., Pop, I., and Ingham, D.B. (2009), "Magnetic Field and Internal Heat Generation Effects on the Free Convection in a Rectangular Cavity Filled with a Porous Medium", International Journal of Heat and Mass Transfer, 52(5-6), pp.1525-1533. https://doi.org/10.1016/j.ijheatmasstransfer.2008.08.011
  20. Horton, C.W. and Rogers, F.T. (1945), "Convection Currents in a Porous Medium", J. Appl. Phys., Vol.16, pp.367-370. https://doi.org/10.1063/1.1707601
  21. Ingham, D.B. and Pop I. (2005), Transport phenomena in porous media, Elsevier, Oxford.
  22. Johansen, O. (1975), Thermal conductivity of soils, Ph.D. thesis, Trondheim, Norway (CRREL Draft Translation 637, 1977), ADA 044002.
  23. Khosrokhavar, R. (2016), Mechanisms for $CO_2$ sequestration in geological formations, Springer Theses.
  24. Koorevaar, P., Menelik, G., and Dirksen, C. (1983), Elements of soil physics. Elsevier Science Publishers B.V. (North-Holland).
  25. Kundu, P. (1990), Fluid mechanics, Academic Press, New York, p.355.
  26. Kwon, S.Y. and Lee, S. (2012), "Precise Measurement of Thermal Conductivity of Liquid Over a Wide Temperature Range Using a Transient Hot-wire Technique by Uncertainty Analysis", Thermochim. Acta, Vol.542, pp.18-23. https://doi.org/10.1016/j.tca.2011.12.015
  27. Lapwood, E.R. (1948), "Convection of a Fluid in a Porous Medium", Proc. Camb. Phil. Soc., Vol.44, pp.508-521. https://doi.org/10.1017/S030500410002452X
  28. Lewis, R.W., Nithiarasu, P., and Seetharamu, K. N. (2004), Fundamentals of the Finite Element Method for Heat and Fluid Flow, Wiley, p.356.
  29. Lundgren, T.S. (1972), "Slow Flow through Stationary Random Beds and Suspensions of Spheres", J. Fluid Mech., Vol.51, pp. 273-299. https://doi.org/10.1017/S002211207200120X
  30. Malkovsky, V.I. and Pek, A.A. (2015), "Onset of Fault-bounded Free Thermal Convection in a Fluid-saturated Horizontal Permeable Porous Layer", Transport in Porous Media, Vol.110, pp.25-39. https://doi.org/10.1007/s11242-015-0555-0
  31. Manohar, K., Yarbrough, D.W., and Booth, J.R. (2000), "Measurement of Apparent Thermal Conductivity by the Thermal Probe Method", J. Test. Eval., Vol.28, No.5, pp.345-351. https://doi.org/10.1520/JTE12123J
  32. MeiBner, K., Schabelon, H., Bellebaum, J., and Sordyl, H. (2006), Impacts of submarine cables on the marine environment -A literature review.
  33. Nield, D.A. and Bejan, A. (2006), Convection in porous media, Springer, New York.
  34. Nithiarasu, P., Seetharamu, K.N., and Sundararajan, T. (1997), "Natural Convective Heat Transfer in an Enclosure Filled with Fluid Saturated Variable Porosity Medium", Int. J. Heat Mass Transfer, Vol.40, No.16, pp.3955-3967. https://doi.org/10.1016/S0017-9310(97)00008-2
  35. Simmons, C.T. (2005), "Variable Density Groundwater Flow: from Current Challenges to Future Possibilities", Hydrogeol. J., Vol.13, pp.116-119. https://doi.org/10.1007/s10040-004-0408-3
  36. Tarnawski, V.R., Momose, T., and Leong, W.H. (2011), "Thermal Conductivity of Standard Sands II. Saturated Conditions", Int J Thermophys, Vol.32, No.5, pp.984-1005. https://doi.org/10.1007/s10765-011-0975-1
  37. Vadasz, P. (2008), Emerging topics in heat and mass transfer in porous media, Springer, New York.
  38. Vafai, K. (2005), Handbook of porous media, Taylor & Francis, Boca Raton, FL.
  39. Van Dam, R.L., Simmons, C.T., Hyndman, D.W., and Wood, W.W. (2009), "Natural Free Convection in Porous Media: First Field Documentation in Groundwater", Geophys. Res. Lett., Vol.36, L11403. https://doi.org/10.1029/2008GL036906
  40. Wang, L., Hyodo, A., Sakai, S., and Suekane, T. (2016), "Threedimensional Visualization of Natural Convection in Porous Media", Energy Procedia, Vol.86, pp.460-468. https://doi.org/10.1016/j.egypro.2016.01.047
  41. Worzyk, T. (2009), Submarine power cables: Design, installation, repair, environmental aspects (Power systems), Springer, p.318.