Abstract
Macroscopic parameters such as effective thermal conductivity (ETC) is an important parameter which is affected by micro and meso level behaviour of particulate materials, and has been extensively examined in the past decades. In this paper, a new lattice based numerical model is developed to predict the ETC of sand and modified high thermal backfill material for energy transportation used for underground power cables. 2D and 3D simulations are performed to analyse and detect differences resulting from model simplification. The thermal conductivity of the granular mixture is determined numerically considering the volume and the shape of the each constituting portion. The new numerical method is validated with transient needle measurements and the existing theoretical and semi empirical models for thermal conductivity prediction sand and the modified backfill material for dry condition. The numerical prediction and the measured values are in agreement to a large extent.
Similar content being viewed by others
References
Gangadhara Rao MVBB, Singh DN (1999) A generalized relationship to estimate thermal resistivity of soils. Can Geotech J 36(4):767–773. https://doi.org/10.1139/t99-037
Shrestha D, Hailemariam H, Wuttke F (2016) Enhancement of soil thermal conductivity in dry condition. Proceedings of the 1st International Conference on Energy Geotechnics, 29–31 August 2016, Kiel, Germany. https://doi.org/10.1201/b21938-64
Smith WO (1942) The thermal conductivity of dry soil. Soil Sci 53(6):435–460 June 1942
Mickley AS (1949) The thermal movement of moisture in soil. Trans Am Inst Electr Eng 68:330–335
De Vries DA (1952) The thermal conductivity of soil. Mededelingen van de Landbouwhogeschool te Wageningen 52(1):1–73 translated by Building Research Station (Library Communication No. 759), England
Farouki OT (1981) Thermal properties of soils, CRREL Monograph 81-1, US Army Corps of Engineers, Cold Regions Research and Engineering Laboratory, Hanover, N.H
Johansen O (1975) Thermal conductivity of soils, Ph.D. diss. Norwegian Univ. of Science and Technol., Trondheim (CRREL draft transl. 637, 1977)
Côté J, Konrad JM (2005a) A generalized thermal conductivity model for soils and construction materials. Can Geotech J 42:443–458
Lu S, Ren T, Gong Y, Horton R (2007) An improved model for predicting soil thermal conductivity from water content at room temperature. Soil Sci Soc Am J 71:8–14
Balland V, Arp PA (2005) Modelling soil thermal conductivities over a wide range of conditions. J Environ Eng Sci 4(6):549–558. https://doi.org/10.1139/s05-007
Tarnawski VR, Momose T, Leong WH, Bovesecchi G, Coppa P (2009) Thermal conductivity of standard sands. Part I. dry-state conditions. Int J Thermo Phys 30:949. https://doi.org/10.1007/s10765-009-0596-0
Woodside W, Messmer JH (1961) Thermal conductivity of porous media. I. Unconsolidated sands. J Appl Phys 32:1688. https://doi.org/10.1063/1.1728419
Abyzov AM, Goryunov AV, Shakhov FM (2013) Effective thermal conductivity of disperse materials. I. Compliance of common models with experimental data. Int J Heat Mass Transf. https://doi.org/10.1016/j.ijheatmasstransfer.2013.08.045
Xu Y, Ray G, Abdel-Magidn B (2006) Thermal behavior of single-walled carbon nanotube polymer-matrix composites. Compos Part A 37:114–121
Kumlutas D, Tavman I (2006) A numerical and experimental study on thermal conductivity of particle filled polymer composites. J Thermoplast Compos 19:441–455
Karkri M, Garnier B, Boudenne A (2011) Numerical and experimental study of the thermo physical properties of spheres composite materials. High Temp High Pressures 40(1):61–84
Vargas WL, McCarthy JJ (2001) Heat conduction in granular materials. AICHE J 47(5):1052–1059
Yun TS, Evans TM (2010) Three-dimensional random network model for thermal conductivity in particulate materials. Comput Geotech 37:991–998
Wong JK -W, Soga K, Xu X, Delenne J-Y, 2015 Modelling fracturing process of geomaterial using lattice element method. Geomechanics from Micro to Macro 417–422. https://doi.org/10.1201/b17395-74
David F, Drouffe J-M (1988) Monte-Carlo simulations of random rigid surfaces with random lattices Nuclear Physics B (Proceedings Supplement) 4, 83–87
Puhl H (1993) Sandpiles on random lattices. Physica A 197:14–22
Lauritsen KB, Moukarzel C, Herrmann HJ (1993) Statistical laws and mechanics of Voronoi random lattices. J de Physique l France 3(9):1941–1951
Ostoja-Starzewski M, Alzebdeh K, Jasiuk I (1995) Linear elasticity of planar Delaunay networks III. Self-consistent approximations. Acta Mech 110(1–4):57–72
Gasparini DA, Ronacuse P, Powers L, Romeo A (1996) Stochastic parallel-brittle networks for modeling materials. J Eng Mech 12(2):130–137
Cheng GJ, Yu AB, Zulli P (1999) Evaluation of effective thermal conductivity from the structure of a packed bed. Chem Eng Sci 54(19):4199–4209
Yang RY, Zou RP, Yu AB, Choi SK (2006) Pore structure of the packing of fine particles. J Colloid Interface Sci 299(2):719–725
Rizvi ZH, Sattari AS, Wuttke F. (2016). Numerical analysis of heat conduction in granular geo-material using lattice element method. In Energy Geotechnics - Proceedings of the 1st International Conference on Energy Geotechnics, ICEGT 2016. https://doi.org/10.1201/b21938-58
Wuttke F, Sattari AS, Rizvi ZH, Motra HB (2016) Advanced meso-scale modelling to study the effective thermo-mechanical parameter in solid geomaterial. Springer Ser Geomech Geoeng. https://doi.org/10.1007/978-3-319-52773-4_9
Zehner P, Schlunder EU (1970) Thermal conductivity of granular materials at moderate temperatures. Chem Ing Tech 42:933–941 (In German)
Hsu CT, Cheng P, Wong KW (1994) Modified Zehner-Schlunder models for stagnant thermal conductivity of porous media. Int J Heat Mass Transf 37:2751–2759
Yovanovich MM (1973) Apparent conductivity of glass microspheres from atmospheric pressure to vacuum. ASME Paper 73-HT-43, American Society of Mechanical Engineers, New York
Fuller WB, Thomson SE (1907) The laws of proportioning concrete. Trans ASCE 59(2):67–143
Yun TS, Santamarina JC (2007) Fundamental study of thermal conduction in dry soils. Granul Matter 10(3):197–207
ASTM 5334-08 (2008) Standard test method for determination of thermal conductivity of soil and soft rock by thermal needle probe procedure, ASTM
IEEE (1992) Guide for soil thermal resistivity measurements, Inst. of Electrical and Electronics Engineers, Inc. New York
Hashin Z, Shtrikman S (1962) A Variational approach to the theory of the effective magnetic permeability of multiphase materials. J Appl Phys 33(10):3125–3131
Gori F, Corasaniti S (2004) Theoretical prediction of the thermal conductivity and temperature variation inside Mars soil analogues. Planet Space Sci 52:91–99
Maxwell JC (1954) A treatise on electricity and magnetism, third edn. Dover, New York
Acknowledgements
This research project is financially supported by the research grant BMWi/KF3067303KI3 and ZF4016802HF5 provided by the Federal Ministry of Education and Research, Germany.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rizvi, Z.H., Shrestha, D., Sattari, A.S. et al. Numerical modelling of effective thermal conductivity for modified geomaterial using lattice element method. Heat Mass Transfer 54, 483–499 (2018). https://doi.org/10.1007/s00231-017-2140-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00231-017-2140-2