Modeling of heat and fluid flow in granular layers using high-order compact schemes and volume penalization method

References

• T. Baumann and S. Zunft, “Properties of granular materials as heat transfer and storage medium in CSP application,” Solar Energy Mater. Solar Cells, vol. 143, pp. 38–47, 2015. DOI:10.1016/j.solmat.2015.06.037.
   Web of Science ®Google Scholar
• Z. Ma, G. C. Glatzmaier, and M. Mehos, “Development of solid particle thermal energy storage for concentrating solar power plants that use fluidized bed technology,” Energy Procedia, vol. 49, pp. 898–907, 2014. DOI:10.1016/j.egypro.2014.03.097.
   Google Scholar
• P. Ratuszny, “Thermal energy storage in granular deposits,” presented at the International Conference Energy, Environment and Material Systems (EEMS 2017), Polanica-Zdroj, Poland, 2017. DOI:10.1051/e3sconf/20171901022.
   Google Scholar
• S. Lvarez de Miguel, J. Gonzalez-Aguilara, and M. Romero, “100-Wh multi-purpose particle reactor for thermochemical heat storage in concentrating solar power plants,” Energy Procedia, vol. 49, pp. 676–683, 2014. DOI:10.1016/j.egypro.2014.03.073.
   Google Scholar
• D. M. Yancy-Caballero, L. T. Biegler, and R. Guirardello, “Large-scale DAE-constrained optimization applied to a modified spoute d b e d reactor for ethylene production from methane,” Comput. Chem. Eng., vol. 113, pp. 162–183, 2018. DOI:10.1016/j.compchemeng.2018.03.017.
   Web of Science ®Google Scholar
• T. Hoffmann, C. Rieck, A. Bück, M. Peglow, and E. Tsotsas, “Influence of granule porosity during fluidized bed spray granulation,” Procedia Eng., vol. 102, pp. 458–467, 2015. DOI:10.1016/j.proeng.2015.01.189.
   Google Scholar
• E. Diez, K. Meyer, A. Bück, E. Tsotsas, and S. Heinrich, “Influence of process conditions on the product properties in a continuous fluidized bed spray granulation process,” Chem. Eng. Res. Des., vol. 139, pp. 104–115, 2018. DOI:10.1016/j.cherd.2018.09.032.
   Web of Science ®Google Scholar
• E. Szymanek, T. Blaszczyk, M. R. Hall, P. K. Dehdezi, and J. Leszczynski, “Modelling and analysis of heat transfer trough 1D complex granular system,” Granular Matter, vol. 16, no. 5, pp. 687–694, 2014. DOI:10.1007/s10035-014-0517-1.
   Web of Science ®Google Scholar
• J. M. Hainsworth and L. A. G. Aylmore, “The use of computer assisted tomography to determine spatial distribution of soil water content,” Soil Res., vol. 21, no. 4, pp. 435–443, 1983. DOI:10.1071/SR9830435.
   Web of Science ®Google Scholar
• W. P. Breugem, V. van Dijk, and R. Delfos, “Flows through real porous media: X-ray computed tomography, experiments, and numerical simulations,” J. Fluids Eng., vol. 136, no. 4, pp. 040902-1–040902-8, 2014. DOI:10.1115/1.4025311.
   Web of Science ®Google Scholar
• W. Sobieski et al., Granularne osrodki porowate. Katedra Mechaniki i Podstaw Konstrukcji Maszyn. Olsztyn: Wydzia Nauk Technicznych Uniwersytet Warmisko-Mazurski w Olsztynie, 2016.
   Google Scholar
• M. Massoudi, “On the heat flux vector for flowing granular materials. I, II,” Math. Methods Appl. Sci., vol. 29, no. 13, pp. 1585–1598, pp. 1599–1613, 2006. DOI:10.1002/mma.745.
   Google Scholar
• D. Arumuga Perumala and A. K. Dass, “A review on the development of lattice Boltzmann computation of macro fluid flows and heat transfer,” Alexandria Eng. J., vol. 54, no. 4, pp. 955–971, 2015. DOI:10.1016/j.aej.2015.07.015.
   Web of Science ®Google Scholar
• W. L. Vargas and J. J. McCarthy, “Heat conduction in granular materials,” AIChE J., vol. 47, no. 5, pp. 1052–1059, 2001. DOI:10.1002/aic.690470511.
   Web of Science ®Google Scholar
• R. Brociek and D. Slota, “Application and comparison of the intelligent algorithms to solve the fractional heat conduction inverse problem," Inf. Technol. Control, vol. 45, no. 2, pp. 184–194, 2016.
   Google Scholar
• T. Blaszczyk, E. Kotela, and J. Leszczyski, “Application of the fractional oscillator equation to simulations of granular flow in a silo,” Comput. Methods Mater. Sci., vol. 11, pp. 64–67, 2011.
   Google Scholar
• H. P. A. Calis, J. Nijenhuis, B. C. Paikert, F. M. Dautzenberg, and C. M. van den Bleek, “CFD modelling and experimental validation of pressure drop and flow profile in a novel structured catalytic reactor packing,” Chem. Eng. Sci., vol. 56, no. 4, pp. 1713–1720, 2001. DOI:10.1016/S0009-2509(00)00400-0.
   Web of Science ®Google Scholar
• L. W. Rong, K. J. Dong, and A. B. Yu, “Lattice-Boltzmann simulation of fluid flow through packed beds of uniform spheres: Effect of porosity,” Chem. Eng. Sci., vol. 99, pp. 44–58, 2013. DOI:10.1016/j.ces.2013.05.036.
   Web of Science ®Google Scholar
• J. Yang, J. Wu, L. Zhou, and Q. Wang, “Computational study of flow and heat transfer in composite packed beds of spheres with low tube to particle diameter ratio,” Nuclear Eng. Des., vol. 300, pp. 85–96, 2016. DOI:10.1016/j.nucengdes.2015.10.030.
   Web of Science ®Google Scholar
• S. Bale, et al., “Spatially resolved mass transfer coefficient for moderate Reynolds number flows in packed beds: Wall effects,” Int. J. Heat Mass Transf., vol. 110, pp. 406–415, 2017. DOI:10.1016/j.ijheatmasstransfer.2017.03.052.
   Web of Science ®Google Scholar
• B. D. Wood et al., “A comparison of measured and modeled velocity fields for a laminar flow in a porous medium,” Adv. Water Resour., vol. 85, pp. 45–63, 2015. DOI:10.1016/j.advwatres.2015.08.013.
   Web of Science ®Google Scholar
• A. Sadikin, N. A. M. Yunus, K. Abdullah, and A. N. Mohammed, “Numerical study of flow past a solid sphere at moderate Reynolds number,” Appl. Mech. Mater., vol. 660, pp. 674–678, 2014. DOI:10.4028/www.scientific.net/AMM.660.674.
   Google Scholar
• L. Prahl, A. Jadoon, and J. Revstedt, “Interaction between two spheres placed in tandem arrangement in steady and pulsating flow,” Int. J. Multiphase Flow, vol. 35, no. 10, pp. 963–969, 2009. DOI:10.1016/j.ijmultiphaseflow.2009.05.001.
   Web of Science ®Google Scholar
• Z. Qi, S. Kuang, L. Rong, and A. Yu, “Lattice Boltzmann investigation of the wake effect on the interaction between particle and power-law fluid flow,” Powder Technol., vol. 326, pp. 208–221, 2018. DOI:10.1016/j.powtec.2017.12.015.
   Web of Science ®Google Scholar
• D. Toghraie, M. Afrand, A. D. Zadeh, and H. A. Akbari, “Numerical investigation on the flow and heat transfer of a multi-lobe particle and equivalent spherical particles in a packed bed with considering the wall effects,” Int. J. Mech. Sci., vol. 138–139, pp. 350–367, 2018. DOI:10.1016/j.ijmecsci.2018.02.019.
   Web of Science ®Google Scholar
• L. Shiyang, J. Yang, and Q. Wang, “Large eddy simulation of flow and heat transfer past two side-by-side spheres,” Appl. Thermal Eng., vol. 121, pp. 810–819, 2017. DOI:10.1016/j.applthermaleng.2017.04.065.
   Web of Science ®Google Scholar
• M. Ozgoren, “Flow structures around an equilateral triangle arrangement of three spheres,” Int. J. Multiphase Flow, vol. 53, pp. 54–64, 2013. DOI:10.1016/j.ijmultiphaseflow.2013.02.001.
   Web of Science ®Google Scholar
• P. Yu, Y. Zeng, T. S. Lee, H. X. Bai, and H. T. Low, “Wake structure for flow past and through a porous square cylinder,” Int. J. Heat Fluid Flow, vol. 31, no. 2, pp. 141–153, 2010. DOI:10.1016/j.ijheatfluidflow.2009.12.009.
   Web of Science ®Google Scholar
• J. Yang, Q. Wang, M. Zeng, and A. Nakayama, “Computational study of forced convective heat transfer in structured packed beds with spherical or ellipsoidal particles,” Chem. Eng. Sci., vol. 65, no. 2, pp. 726–738, 2010. DOI:10.1016/j.ces.2009.09.026.
   Web of Science ®Google Scholar
• S. W. Perng, H. W. Wu, R. H. Wang, and T. C. Jue, “Unsteady convection heat transfer for a porous square cylinder varying cylinder-to-channel height ratio,” Int. J. Thermal Sci., vol. 50, no. 10, pp. 2006–2015, 2011. DOI:10.1016/j.ijthermalsci.2011.02.018.
   Web of Science ®Google Scholar
• A. G. Dixon, M. Ertan, T. M. Nijemeisland, and E. H. Stitt, “Systematic mesh development for 3D CFD simulation of fixed beds: Single sphere study,” Comput. Chem. Eng., vol. 35, no. 7, pp. 1171–1185, 2011. DOI:10.1016/j.compchemeng.2010.12.006.
   Web of Science ®Google Scholar
• S. Dhinakaran and J. Ponmozhi, “Heat transfer from a permeable square cylinder to a flowing fluid,” Energy Conversion Manag., vol. 52, no. 5, pp. 2170–2182, 2011. DOI:10.1016/j.enconman.2010.12.027.
   Web of Science ®Google Scholar
• A. Richter and P. A. Nikrityuk, “New correlations for heat and fluid flow past ellipsoidal and cubic particles at different angles of attack,” Powder Technol., vol. 249, pp. 463–474, 2013. DOI:10.1016/j.powtec.2013.08.044.
   Web of Science ®Google Scholar
• M. Nijemeisland and A. G. Dixon, “CFD study of fluid flow and wall heat transfer in a fixed bed of spheres,” Amer. Inst. Chem. Eng. J., vol. 50, no. 5, pp. 906–921, 2004.
   Google Scholar
• Z. Minhua, D. He, and G. Zhongfeng, “Computational study of flow and heat transfer in fixed beds with cylindrical particles for low tube to particle diameter ratios,” Chem. Eng. Res. Des., vol. 132, pp. 149–161, 2018.
   Web of Science ®Google Scholar
• E. A. Fadlun, R. Verzicco, P. Orlandi, and J. Mohd-Yusof, “Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations,” J. Comput. Phys., vol. 161, no. 1, pp. 35–60, 2000. DOI:10.1006/jcph.2000.6484.
   Web of Science ®Google Scholar
• R. Mittal and G. Iaccarino, “Immersed boundary methods,” Ann. Rev. Fluid Mech., vol. 37, no. 1, pp. 239–261, 2005. DOI:10.1146/annurev.fluid.37.061903.175743.
   Web of Science ®Google Scholar
• J. R. Pacheco, A. Pacheco-Vega, T. Rodić, and R. E. Peck, “Numerical simulations of heat transfer and Fluid flow problems using an immersed-boundary finite-volume method on non-staggered grids,” Numeric. Heat Transf. Part B: Fundam., vol. 48, no. 1, pp. 1–24, 2005. DOI:10.1080/10407790590935975.
   Web of Science ®Google Scholar
• D. Pan, “An immersed boundary method on unstructured Cartesian meshes for incompressible flows with heat transfer,” Numeric. Heat Transf. Part B: Fundam., vol. 49, no. 3, pp. 277–297, 2006. DOI:10.1080/10407790500290709.
   Web of Science ®Google Scholar
• D. Kinoshita, A. da Silveira Neto, F. P. Mariano, R. A. P. da Silva, and R. Serfaty, “A novel immersed boundary/Fourier pseudospectral method for flows with thermal effects,” Numeric. Heat Transf. Part B: Fundam., vol. 69, no. 4, pp. 312–333, 2016. DOI:10.1080/10407790.2015.1104199.
   Web of Science ®Google Scholar
• A. Pacheco-Vega, J. R. Pacheco, and T. Rodić, “A general scheme for the boundary conditions in convective and diffusive heat transfer with immersed boundary methods,” J. Heat Transf., vol. 129, no. 11, pp. 1506–1516, 2007. DOI:10.1115/1.2764083.
   Web of Science ®Google Scholar
• D. Pan, “A general boundary condition treatment in immersed boundary methods for incompressible Navier–Stokes equations with heat transfer,” Numeric. Heat Transf. Part B: Fundam., vol. 61, no. 4, pp. 279–297, 2012. DOI:10.1080/10407790.2012.670560.
   Web of Science ®Google Scholar
• K. Khadra, P. Angot, S. Parneix, and J. P. Caltagirone, “Fictitious domain approach for numerical modelling of Navier–Stokes equations,” Int. J. Numeric. Methods Fluids, vol. 34, no. 8, pp. 651–684, 2000. DOI:10.1002/1097-0363(20001230)34:8<651::AID-FLD61>3.3.CO;2-4.
   Web of Science ®Google Scholar
• A. Tyliszczak, “A high-order compact difference algorithm for half-staggered grids for laminar and turbulent incompressible flows,” J. Comput. Phys., vol. 276, pp. 438–467, 2014. DOI:10.1016/j.jcp.2014.07.043.
   Web of Science ®Google Scholar
• A. Tyliszczak, “High-order compact difference algorithm on half-staggered meshes for low Mach number flows,” Comput. Fluids, vol. 127, pp. 131–145, 2016. DOI:10.1016/j.compfluid.2015.12.014.
   Web of Science ®Google Scholar
• C. A. J. Fletcher, Computational Techniques for Fluid Dynamics. Berlin Heidelberg: Springer-Verlag, 1991.
   Google Scholar
• B. Kadoch, D. Kolomenskiy, P. Angot, and K. Schneider, “A volume penalization method for incompressible flows and scalar advection diffusion with moving obstacles,” J. Computat. Phys., vol. 231, no. 12, pp. 4365–4383, 2012. DOI:10.1016/j.jcp.2012.01.036.
   Google Scholar
• A. Tyliszczak, and M. Ksiezyk, “Large eddy simulations of wall-bounded flows using a simplified immersed boundary method and high-order compact schemes,” Int. J. Numeric. Methods Fluids, vol. 87, no. 7, pp. 358–381, 2018. DOI:10.1002/fld.4496.
   Web of Science ®Google Scholar
• C. Shu, “High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD,” Int. J. Comput. Fluid Dyn., vol. 17, no. 2, pp. 107–118, 2003. DOI:10.1080/1061856031000104851.
   Web of Science ®Google Scholar
• Z. J. Wang et al., “High-order CFD methods: Current status and perspective,” Int. J. Numeric. Methods Fluids, vol. 72, no. 8, pp. 811–845, 2013. DOI:10.1002/fld.3767.
   Web of Science ®Google Scholar
• S. Lele, “Compact finite difference schemes with spectral-like resolution,” J. Comput. Phys., vol. 103, no. 1, pp. 16–42, 1992. DOI:10.1016/0021-9991(92)90324-R.
   Web of Science ®Google Scholar
• A. Tyliszczak and B. J. Geurts, “Parametric analysis of excited round jets – Numerical study, Flow Turbulence Combust., vol. 93, no. 2, pp. 221–247, 2014. DOI:10.1007/s10494-014-9544-6.
   Web of Science ®Google Scholar
• A. Tyliszczak and B. J. Geurts, “Controlled mixing enhancement in turbulent rectangular jets responding to periodically forced inflow conditions,” J. Turbulence, vol. 16, no. 8, pp. 742–771, 2015. DOI:10.1080/14685248.2015.1027345.
   Google Scholar
• A. Tyliszczak, “Parametric study of multi-armed jets,” Int. J. Heat Fluid Flow, vol. 73, p. 82, 2018. DOI:10.1016/j.ijheatfluidflow.2018.07.002.
   Web of Science ®Google Scholar