We have examined the behavior of solid particles in an annulus. A circular, square and elliptic shaped particle is analysed separately and in pairs. Behaviour of two circular particles moving inside two concentric moving cylinders having an internal obstacle is analysed. The interaction of particle with the fluid and circular obstacle is carried out inside a fixed circular mesh using an Eulerian approach. The coupled fluid and particles system is handled using fictitious boundary method. The hydrodynamic forces acting on the fictitious boundaries (particles) are calculated using an explicit volume integral approach. A collision model proposed by Glowinski et al. is used to prevent particle-wall, particle-particle and particle-obstacle overlapping and collision. The particulate flow is computed using multigrid finite element solver FEATFLOW.
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Abbasi WS, Islam SU, Rahman H, Manzoor R (2018) Numerical investigation of fluid-solid interaction for flow around three square cylinders. AIP Adv 8(2):025221
Bayraktar E, Mierka O, Platte F, Kuzmin D, Turek S (2011) Numerical aspects and implementation of population balance equations coupled with turbulent fluid dynamics. Comput Chem Eng 35(11):2204–2217
Crowley TJ, Meadows Edward S, Evangelos K, Doyle III, Francis J (2000) Control of particle size distribution described by a population balance model of semibatch emulsion polymerization. J Process Control 10(5):419–432
Dyko Mark P, Kambiz V, Kader Mojtabi A (1999) A numerical and experimental investigation of stability of natural convective flows within a horizontal annulus. J Fluid Mech 381:27–61
Glowinski R, Pan TW, Hesla TI, Joseph DD (1999) A distributed lagrange multiplier/fictitious domain method for particulate flows. Int J Multiph Flow 25(5):755–794
Grigull U, Hauf (1966) Natural convection in horizontal cylindrical annuli. In: The 3rd international heat transfer conference
Hackbusch W (2003) Multi-grid methods and applications. Springer series in computational mathematics. SpringerSpringer, Berlin
Hirt CW, Amsden AA, Cook JL (1974) An arbitrary Lagrangian–Eulerian computing method for all flow speeds. J Comput Phys 14(3):227–253
Hu HH, Joseph DD, Crochet MJ (1992) Direct simulation of fluid particle motions. Theoret Comput Fluid Dyn 3:285–306
Hu H, Patankar NA, Zhu MY (2001) Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian–Eulerian technique. J Comput Phys 169(2):427–462
Hu Y, Li D, Shu S, Niu X (2015) Study of multiple steady solutions for the 2d natural convection in a concentric horizontal annulus with a constant heat flux wall using immersed boundary-lattice Boltzmann method. Int J Heat Mass Transf 81:591–601
Jabeen S, Usman K, Walayat K (2019) Numerical investigations for a chain of particles settling in a channel. Comput Part Mech 7:1–13
John V (2002) Higher order finite element methods and multigrid solvers in a benchmark problem for the 3d Navier–Stokes equations. Int J Numeri Methods Fluids 40:775–798
Kim SS, Karrila SJ (1991) Microhydrodynamics: principles and selected applications, 2nd edn. Butterworth-Heinemann, Boston
Kuehn TH, Goldstein RJ (1976) An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders. J Fluid Mech 74(4):695–719
Lopez JM, Marques F, Mercader I, Batiste O (2007) Onset of convection in a moderate aspect-ratio rotating cylinder: Eckhaus–Benjamin–Feir instability. J Fluid Mech 590:187–208
Maury B (1996) Characteristics ale method for the unsteady 3d Navier–Stokes equations with a free surface. Int J Comput Fluid Dyn 6:175–188
Maury B (1997) A many-body lubrication model. J Comput Appl Math 325(9):1053–1058
Mishra BK, Rajamani K (1992) The discrete element method for the simulation of ball mills. Appl Math Model 16(11):598–604
Munjiza A, Owen DRJ, Bicanic N (1995) A combined finite-discrete element method in transient dynamics of fracturing solids. Eng Comput 12:145–174
Nguyen T, Vasseur P, Robillard L (1982) Natural convection between horizontal concentric cylinders with density inversion of water for low Rayleigh numbers. Int J Heat Mass Transf 25(10):1559–1568
Osher S, Fedkiw RP (2001) Level set methods: an overview and some recent results. J Comput Phys 169(2):463–502
Patankar NA, Singh P, Joseph DD, Glowinski R, Pan TW (2000) A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows. Int J Multiph Flow 26:1509–1524
Pillapakkam SB, Singh P (2001) A level-set method for computing solutions to viscoelastic two-phase flow. J Comput Phys 174(2):552–578
Potapov Alexander V, Hunt Melany L, Campbell Charles S (2001) Liquid-solid flows using smoothed particle hydrodynamics and the discrete element method. Powder Technol 116(2–3):204–213
Powe RE, Carley CT, Bishop EH (1969) Free convective flow patterns in cylindrical annuli. J Heat Transf 91(3):310–314
Sarrate J, Huerta A, Donea J (2001) Arbitrary Lagrangian–Eulerian formulation for fluid-rigid body interaction. Comput Methods Appl Mech Eng 190(24):3171–3188
Sarthou A, Vincent S, Caltagirone JP, Angot P (2008) Eulerian–Lagrangian grid coupling and penalty methods for the simulation of multiphase flows interacting with complex objects. Int J Numer Methods Fluids 56(8):1093–1099
Singh P, Hesla TI, Joseph DD (2003) Distributed Lagrange multiplier method for particulate flows with collisions. Int J Multiph Flow 29(3):495–509
Sommerfeld M (2001) Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence. Int J Multiph Flow 27(10):1829–1858
Stefan T (1996) A comparative study of time-stepping techniques for the incompressible Navier–Stokes equations: from fully implicit non-linear schemes to semi-implicit projection methods. Int J Numer Methods Fluids 22(10):987–1011
Stefan T (1997) On discrete projection methods for the incompressible Navier–Stokes equations: an algorithmical approach. Comput Methods Appl Mech Eng 143(3):271–288
Turek S, Wan D, Rivkind L S (2003) The fictitious boundary method for the implicit treatment of Dirichlet boundary conditions with applications to incompressible flow simulations. In: Challenges in scientific computing—CISC 2002 (Eberhard Baensch, ed.), Lecture notes in computational science and engineering, vol 35. Springer, Berlin, pp 37–68 (English)
Usman K, Walayat K, Wang Z, Liu M (2017) A multigrid finite element fictitious boundary method for fluid-solid two-phase flows. In: The 8th international conference on computational mehtods (ICCM2017) (Advances in Computational Engineering Science, ed.), ScienTech Publisher
Usman K (2013) Numerical analysis of collision models in 2d particulate flow. Technische Universität Dortmund, Fakultät für Mathematik, Ph.D. Thesis
Usman K, Ali J, Mahmood R, Bilal DS, Jabeen S, Asmat J (2020) Study of a falling rigid particle passing around obstacles in a fluid channel. Int J Comput Fluid Dyn
Walayat K, Wang Z, Usman K, Liu M (2018) An efficient multi-grid finite element fictitious boundary method for particulate flows with thermal convection. Int J Heat Mass Transf 126:452–465
Walayat K, Zhang Z, Usman K, Chang J, Liu M (2019) Fully resolved simulations of thermal convective suspensions of elliptic particles using a multigrid fictitious boundary method. Int J Heat Mass Transf 139:802–821
Wan D, Turek S (2007) Fictitious boundary and moving mesh methods for the numerical simulation of rigid particulate flows. J Comput Phys 222(1):28–56
Wan D, Turek S (2006) Direct numerical simulation of particulate flow via multigrid fem techniques and the fictitious boundary method. Int J Numer Methods Fluids 51(5):531–566
Wan D, Turek S (2007) An efficient multigrid-fem method for the simulation of solid-liquid two phase flows. J Comput Appl Math 203(2):561–580
Wan D, Turek S, Rivkind LS (2004) An efficient multigrid fem solution technique for incompressible flow with moving rigid bodies. In: Miloslav F, Vit D, Petr K, Karel N (eds) Numerical mathematics and advanced applications. Springer, Berlin, pp 844–853 English
Wei Y, Wang Z, Qian Y, Guo W (2018) Study on bifurcation and dual solutions in natural convection in a horizontal annulus with rotating inner cylinder using thermal immersed boundary-lattice boltzmann method. Entropy (Basel, Switzerland) 20(10):733
Wendt John F (ed) (2009) Computational fluid dynamics. Springer, Berlin
Yoo J (1999) Prandtl number effect on bifurcation and dual solutions in natural convection in a horizontal annulus. Int J Heat Mass Transf 42(17):3279–3290
Yoo J-S (1998) Natural convection in a narrow horizontal cylindrical annulus: \(pr \le 0.3\). Int J Heat Mass Transf 41(20):3055–3073
Zhang N, Zheng ZC (2007) A collision model for a large number of particles with significantly different sizes. J Phys D Appl Phys 40:2603–2616
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Jabeen, S., Usman, K. & Shahid, M. Numerical study of general shape particles in a concentric annular duct having inner obstacle. Comp. Part. Mech. (2021). https://doi.org/10.1007/s40571-021-00423-z
- Particulate flow
- Direct numerical simulation
- Fictitious boundary method
- Finite element method