zbMATH — the first resource for mathematics

Fluid flow in wall-driven enclosures with corrugated bottom. (English) Zbl 1390.76553
Summary: In this article, incompressible, continuum regime, viscous flow of Newtonian fluid in two-dimensional (2D) wall-driven enclosures consisting of regular, square shaped, corrugations on the bottom wall is studied numerically. Steady and consistent simulation results are obtained using kinetic theory based lattice Boltzmann equation method (LBM) and solution of Navier-Stokes equation based on fictitious domain method (FDM). First, numerical validation is performed by comparing LBM and FDM results for velocity profiles at particular sections inside the enclosures and vertical velocity gradient at the top of the corrugation cavity. Flow features are then compared for variations in Reynolds number, bottom-wall corrugation height and number of these corrugations. Further, complex eddy dynamics with respect to input parameters and geometry is discussed in detail. Flow transition Reynolds numbers showing distinct flow behavior are found. The numerical results obtained are verified and appear to be consistent with the previously published results for 2D flow inside slender and shallow cavity enclosures.

76M20 Finite difference methods applied to problems in fluid mechanics
76M28 Particle methods and lattice-gas methods
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI
[1] Stasiek, J. A., Experimental studies of heat transfer and fluid flow across corrugated-undulated heat exchanger surfaces, Int J Heat Mass Transf, 41, 899-914, (1998)
[2] Benjamin, T. B., Shearing flow over a wavy boundary, J Fluid Mech, 6, 161-205, (1959) · Zbl 0093.19106
[3] Pan, F.; Acrivos, A., Steady flows in rectangular cavities, J Fluid Mech, 28, 643-655, (1967)
[4] Savvides, C. N.; Gerrand, J. H., Numerical analysis of the flow through a corrugated tube with application to arterial prostheses, J Fluid Mech, 138, 129-160, (1984) · Zbl 0548.76117
[5] Ralph, M. E., Oscillatory flows in wavy-walled tubes, J Fluid Mech, 168, 515-540, (1986)
[6] Stone, K.; Vanka, S. P., Numerical study of developing flow and heat transfer in a wavy passage, J Fluids Eng, 121, 713-719, (1999)
[7] Niavarani, A.; Priezjev, N. V., The effective slip length and vortex formation in laminar flow over a rough surface, Phys Fluids, 21, 052105-1-052105-10, (2009) · Zbl 1183.76385
[8] Vlachogiannis, M.; Bontozoglou, V., Experiments on laminar film flow along a periodic wall, J Fluid Mech, 457, 133-156, (2002) · Zbl 0993.76503
[9] Luo, H.; Pozrikidis, C., Shear-driven and channel flow of a liquid film over a corrugated or indented wall, J Fluid Mech, 556, 167-188, (2006) · Zbl 1147.76570
[10] Kusumaatmaja, H.; Vrancken, R. J.; Bastiaansen, C. W.M.; Yeomans, J. M., Anisotropic drop morphologies on corrugated surfaces, Langmuir, 24, 14, 7299-7308, (2008)
[11] Sahu, K. C.; Vanka, S. P., A multiphase lattice Boltzmann study of buoyancy-induced mixing in a tilted channel, Comput Fluids, 50, 1, 199-215, (2011) · Zbl 1271.76272
[12] Amon, C. H.; Patera, A. T., Numerical calculation of stable three-dimensional tertiary states in grooved-channel flow, Phys Fluids A, 1, 12, 2005-2009, (1989)
[13] Nishimura, T.; Kunitsugu, K., Three-dimensionality of grooved channel flows at intermediate Reynolds numbers, ExpFluids, 31, 1, 34-44, (2001)
[14] Frisch, U.; Hasslacher, B.; Pomeau, Y., Lattice-gas automata for the Navier-Stokes equation, Phys Rev Lett, 56, 1505-1508, (1986)
[15] Qian, Y. H.; Succi, S.; Orszag, S. A., Recent advances in lattice Boltzmann computing, Annu Rev Comput Phys, 3, 195-242, (1995)
[16] He, X.; Luo, L. S., Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation, Phys Rev E, 56, R6811-R6817, (1997)
[17] He, X.; Luo, L. S., Lattice Boltzmann model for the incompressible Navier-Stokes equation, J Stat Phys, 88, 927-944, (1997) · Zbl 0939.82042
[18] Chen, S. Y.; Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu Rev Fluid Mech, 30, 329-364, (1998)
[19] Guo Z. and Shu C. Lattice Boltzmann method and its applications in engineering (advances in computational fluid dynamics)2013; 3.
[20] Kaufman, A.; Fan, Z.; Petkov, K., Implementing the lattice Boltzmann model on commodity graphics hardware, J Stat Mech, 2009, 06, P06016, (2009)
[21] Hong, P.-Y.; Huang, L.-M.; Lin, L.-S.; Lin, C.-A., Scalable multi-relaxation-time lattice Boltzmann simulations on multi-GPU cluster, Comput Fluids, 110, 1-8, (2015) · Zbl 1390.76720
[22] Vanka, S. P.; Shinn, A. F.; Sahu, K. C., Computational fluid dynamics using graphics processing units: challenges and opportunities, ASME 2011 international mechanical engineering congress and exposition, 429-437, (2011), American Society of Mechanical Engineers
[23] Lin, L.-S.; Chang, H.-W.; Lin, C.-A., Multi relaxation time lattice Boltzmann simulations of transition in deep 2D lid driven cavity using GPU, Comput Fluids, 80, 381-387, (2013)
[24] Chang, H.-W.; Hong, P.-Y.; Lin, L.-S.; Lin, C.-A., Simulations of flow instability in three dimensional deep cavities with multi relaxation time lattice Boltzmann method on graphic processing units, Comput Fluids, 88, 866-871, (2013) · Zbl 1391.76600
[25] Glowinski, R.; Pan, T.-W.; Periaux, J., A fictitious domain method for Dirichlet problem and applications, Comput Methods Appl MechEng, 111, 283-303, (1994) · Zbl 0845.73078
[26] Khadra, K.; Angot, P.; Parneix, S.; Caltagirone, J.-P., Fictitious domain approach for numerical modelling of Navier-Stokes equations, Int J Numer Methods Fluids, 34, 651-684, (2000) · Zbl 1032.76041
[27] Glowinski, R.; Pan, T.-W.; Hesla, T. I.; Joseph, D. D.; Periaux, J., A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow, J Comput Phys, 169, 363-426, (2001) · Zbl 1047.76097
[28] Haeri, S.; Shrimpton, J. S., A new implicit fictitious domain method for the simulation of flow in complex geometries with heat transfer, J Comput Phys, 237, 21-45, (2013) · Zbl 1286.65117
[29] Glowinski, R.; Pan, T.-W.; Periaux, J., A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations, Comput Methods Appl MechEng, 114, 133-148, (1994) · Zbl 0845.76069
[30] Brenner, G.; Al-Zoubi, A.; Mukinovic, M.; Schwarze, H.; Swoboda, S., Numerical simulation of surface roughness effects in laminar lubrication using the lattice Boltzmann method, J Tribol, 127, 603-610, (2007)
[31] Al-Zoubi, A.; Brenner, G., Simulating fluid flow over sinusoidal surfaces using the lattice Boltzmann method, Comput Math Appl, 55, 1365-1376, (2008) · Zbl 1142.76447
[32] Varnik, F.; Dorner, D.; Raabe, D., Roughness-induced flow instability: a lattice Boltzmann study, J Fluid Mech, 573, 191-209, (2007) · Zbl 1119.76331
[33] Patil, D. V.; Lakshmisha, K. N.; Rogg, B., Lattice Boltzmann simulation of lid-driven flow in deep cavities, Comput Fluids, 35, 10, 1116-1125, (2006) · Zbl 1177.76324
[34] Ding, L.; Shi, W.; Luo, H., Numerical simulation of viscous flow over non-smooth surfaces, Comput Math Appl, 61, 3703-3710, (2011) · Zbl 1225.76227
[35] Bhatnagar, P. L.; Gross, E. P.; Krook, M., A model for collision processes in gases.I. small amplitude processes in charged and neutral one-component systems, Phys Rev, 94, 511-525, (1954) · Zbl 0055.23609
[36] Qian, Y. H.; D’Humires, D.; Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys Lett, 17, 479-484, (1992) · Zbl 1116.76419
[37] Ning, Y.; Premnath, K. N.; Patil, D. V., Numerical study of the properties of the central moment lattice Boltzmann method, Int J Numer Methods Fluids, 82, 59-90, (2016)
[38] Geier, M.; Schönherr, M.; Pasquali, A.; Krafczyk, M., The cumulant lattice Boltzmann equation in three dimensions: theory and validation, Comput Math Appl, 70, 4, 507-547, (2015)
[39] Haeri, S.; Shrimpton, J. S., On the application of immersed boundary, fictitious domain and body-conformal mesh methods to many particle multiphase flows, Int J Multiphase Flow, 40, 38-55, (2012)
[40] Haeri, S.; Shrimpton, J. S., A correlation for the calculation of the local Nusselt number around circular cylinders in the range 10 ≤ re ≤ 250 and 0.1 ≤ pr ≤ 40, Int J Heat Mass Transf, 59, 219-229, (2013)
[41] Haeri, S.; Shrimpton, J. S., Fully resolved simulation of particle deposition and heat transfer in a differentially heated cavity, Int J Heat Fluid Flow, 50, 1-14, (2014)
[42] Thantanapally, C.; Singh, S.; Patil, D. V.; Succi, S.; Ansumali, S., Quasiequilibrium lattice Boltzmann models with tunable Prandtl number for incompressible hydrodynamics, Int J Mod Phys C, 24, 12, 1340004, (2013)
[43] Succi, S., The lattice Boltzmann equation for fluid dynamics and beyond, Oxford University Press, Oxford, (2001) · Zbl 0990.76001
[44] Ansumali, S.; Karlin, I. V.; Frouzakis, C. E.; Boulouchos, K. B., Entropic lattice Boltzmann method for microflows, Physica A, 359, 289-305, (2006)
[45] Patil, D. V.; Lakshmisha, K. N., Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J Comput Phys, 228, 14, 5262-5279, (2009) · Zbl 1280.76054
[46] Moffatt, H. K., Viscous and resistive eddies near a sharp corner, J Fluid Mech, 18, 01, 1-18, (1964) · Zbl 0118.20501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.