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Continuum thermodynamic modeling of drying capillary particulate materials via an edge-based algorithm. (English) Zbl 1091.76068
Summary: The numerical modeling of the coupled heat and mass transfer processes prevalent in drying non-hygroscopic and hygroscopic capillary particulate materials is dealt with. A set of volume averaged governing equations is employed for this purpose. An improved unstructured hybrid vertex-centered edge-based finite volume algorithm is used for spatial discretization. Enhancements include reformulation of boundary integral flux-averaging in conjunction with the use of a compact stencil in the computation of diffusive terms. A significant increase in accuracy is demonstrated. For validation purposes the drying of a non-hygroscopic brick and hygroscopic extruded corn meal are modeled. Predicted results for the former case are shown to compare reasonable well with experimental data while for the latter case a very good agreement is obtained.

MSC:
76T30 Three or more component flows
76M12 Finite volume methods applied to problems in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
80A22 Stefan problems, phase changes, etc.
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[1] Keey, R.B., Drying principals and practice, (1972), Pergamon Press Oxford
[2] Leyland, S.P., Research procedures and history of the water based shell development programme, Internal memorandum–rolls-royce plc, (1996), Precision Casting Facility Derby
[3] Malan, A.G.; Lewis, R.W.; Ransing, R.S., Investigation into the thermodynamic continuum modeling of investment casting shell-mould drying, Preliminary research report–rolls-royce plc, (2002), Precision Casting Facility Derby
[4] R.W. Lewis, K. Morgan, H.R. Thomas, A non-linear analysis of shrinkage stresses in porous materials. In: Proceedings of the 1st International Conference on Numerical Methods in Thermal Problems, pp. 515-526, Swansea, 1979
[5] M. Fortes, M.R. Okos, A non-equilibrium thermodynamics approach to transport phenomena in capillary porous media. In: Proceedings of the 1st International Symposium on Drying, McGill University, Montreal, Canada, 1978
[6] Ferguson, W.J.; Lewis, R.W.; Tomosy, L., Finite element analysis of freeze-drying of a coffee sample, Comput. methods appl. mech. engrg., 108, 3-4, 341-352, (1993) · Zbl 0844.76050
[7] Lewis, R.W.; Morgan, K.; Thomas, H.R., The non-linear modelling of drying-induced stresses in porous bodies, Adv. drying, 2, 233-268, (1983)
[8] Lewis, R.W.; Morgan, K.; Thomas, H.R.; Seetharamu, K.N., The finite element method in heat transfer analysis, (1996), John Wiley & Sons Ltd. Chichester · Zbl 0847.65072
[9] Turner, I.W.; Ferguson, W.J., An unstructured mesh cell-centered control volume method for simulating heat and mass transfer in porous media: application to softwood drying, part I: the isotropic model, Appl. math. model., 19, 654-667, (1995) · Zbl 0841.76074
[10] Philip, J.R.; de Vries, D.A., Moisture movement in porous materials under temperature gradients, Trans. am. geophys. union, 38, 2, 222-232, (1957)
[11] Luikov, A.V., Heat and mass transfer in capillary-porous bodies, Int. J. heat mass transfer, 9, 139-152, (1966) · Zbl 0980.80500
[12] Whitaker, S., Advances in heat transfer–coupled transport phenomena in multi-phase systems: A theory of drying, vol. 31, (1998), Academic Press New York
[13] Kallel, F.; Galanis, N.; Perrin, B.; Javelas, R., Effects of moisture on temperature during drying of consolidated porous materials, Trans. ASME, 115, 724-733, (1993)
[14] Sbarbella, L.; Imregun, M., An efficient discretization of viscous fluxes on unstructured mixed-element grids, Comm. numer. methods engrg., 16, 839-849, (2000) · Zbl 1015.76051
[15] Sørensen, K.A.; Hassan, O.; Morgan, K.; Weatherill, N.P., Agglomerated multigrid on hybrid unstructured meshes for compressible flow, Int. J. num. methods fluids, 40, 3-4, 593-603, (2002) · Zbl 1019.76030
[16] Khawaja, A.; Kallinderis, Y., Hybrid grid generation for turbomachinery and aerospace applications, Int. J. num. methods engrg., 49, 1-2, 145-166, (2000) · Zbl 0980.76073
[17] Luo, H.; Baum, J.D.; Löhner, R., Edge-based finite-element scheme for the Euler equations, Aiaa, 32, 6, 1183-1190, (1994) · Zbl 0810.76037
[18] Zhao, Y.; Zhang, B., A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Int. J. num. methods engrg., 37, 3323-3341, (1994)
[19] T.J. Barth, D.C. Jespersen, The design and application of upwind schemes to unstructured meshes. In: AIAA Paper, vol. 89-0366, 1989
[20] Mavriplis, D.J., Three dimensional multigrid Reynolds-averaged Navier-Stokes solver for unstructured meshes, Aiaa j., 3, 445-453, (1995) · Zbl 0824.76049
[21] J. Peraire, K. Morgan, M. Vadhati, J. Peiró, The construction and behavior of some unstructured grid algorithms for compressible flows, in: K.W. Morton, M.J. Baines (Eds.), ICFD Conference on Numerical Methods in Fluid Dynamics, Oxford, 1992
[22] R.C. Swanson, E. Turkel. Multistage schemes with multigrid for Euler and Navier-Stokes equations, NASA Technical Paper 3631, 1997
[23] Malan, A.G.; Lewism, R.W., Modeling coupled heat and mass transfer in drying non-hygroscopic capillary particulate materials, Comm. num. methods engrg., 19, 9, 669-677, (2003) · Zbl 1032.80009
[24] Fletcher, C.A.J., Computational techniques for fluid dynamics, vol. I, (1991), Springer-Verlag Berlin · Zbl 0706.76001
[25] P.I. Crumpton, P. Moinier, M.B. Giles, An unstructured algorithm for high Reynolds number flows on highly stretched meshes, in: C. Taylor, J.T. Cross (Eds.), Numerical Methods in Laminar and Turbulent Flow, 1997, pp. 561-572
[26] Murugesan, K.; Seetharamu, K.N.; Narayana, P.A.A.; Thomas, H.R.; Ferguson, W.J., Study of shrinkage stresses for drying brick as a conjugate problem, Int. J. numer. methods engrg., 48, 1, 37-53, (2000) · Zbl 0977.74018
[27] Perrin, B.; Javelas, R., Simultaneous heat and mass-transfer in consolidated materials used in civil engineering, Int. J. heat mass transfer, 30, 2, 297-309, (1987)
[28] Fortes, M.; Okos, M.R., Heat and mass transfer in hygroscopic capillary extruded products, Aiche j., 27, 2, 255-262, (1981)
[29] M. Vahdati, K. Morgan, J. Peraire, O. Hassan, A cell-vertex upwind unstructured grid solution procedure for high-speed compressible viscous flow. In: Proceedings International Conference on Hypersonic Aerodynamics, Royal Aeronautical Society, London, 1989, pp. 12.1-12.22
[30] Malan, A.G.; Lewis, R.W.; Nithiarasu, P., Unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: part I. theory and implementation, Int. J. num. methods engrg., 54, 5, 695-714, (2002) · Zbl 1098.76581
[31] Murugesan, K.; Seetharamu, K.N.; Narayana, P.A.A., A one dimensional analysis of convective drying of porous materials, Heat mass transfer, 32, 1-2, 81-88, (1996)
[32] Sherwood, T.K.; Pigford, R.L., Absorption and extraction, (1952), McGraw-Hill Book Company Inc. New York
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