Multi-Relaxation-Time Lattice Boltzmann Metodu kullanılarak 100 ila 1000 arasındaki Reynolds sayılarında kapakla yönlendirilen oyuk akışının simülasyonu

Çok Gevşetme Zamanı Örgü Boltzmann Metodu (MRT LBM), bir kapak tahrikli boşlukta sabit viskoz sıkışmaz akışın sayısal olarak simule edilmesi için kullanılır. Simülasyonlar, 100 ile 1000 arasında bir dizi Reynold sayısına göre gerçekleştirilir. Simülasyon sonuçları, birincil ana vorteksin ve iki yan vorteksin yerini açıkça gösteren akış akış çizgileri, içindeki diğer bölümlerin farklı bölümlerinde yatay ve dikey hız bileşen profillerini içerir. boşluk ve vorteks merkezlerinin yeri. Sayısal sonuçlar, yayınlanan sonuçlara göre mukayese edilir ve mükemmel bir anlaşma gösterir. Simülasyon sonuçları, yayınlanmış literatürde bildirilmeyen bir dizi Reynold sayısı için verilmiştir. Sunulan sonuçlar Reynolds sayısının bildirilen aralığında diğer sayısal yöntemlerin kıyaslanması için kullanılabilir. MRT LBM, açık bir yöntem olmanın avantajlarına sahip olduğu, karmaşık sınırları kolaylıkla ele alabileceği ve paralelleştirilebildiği için kullanılır.

Simulation of the lid-driven cavity flow at Reynolds numbers between 100 and 1000 using the Multi-Relaxation-Time Lattice Boltzmann Method

The Multi-Relaxation-Time Lattice Boltzmann Method (MRT LBM) is used to numerically simulate the steady viscous incompressible flow in a lid-driven cavity. The simulations are performed for a range of Reynolds numbers between 100 and 1000. The simulation results include the flow streamlines which clearly show the location of the primary main vortex and the two side vortices, the horizontal and vertical velocity component profiles at different sections inside the cavity and the location of the vortices centers. The numerical results are compared against published results and show a perfect agreement. The simulation results are given for a range of Reynolds numbers not reported in the published literature. The presented results can be used for benchmarking other numerical methods in the reported range of the Reynolds number. The MRT LBM is used because it has the advantages of being an explicit method, can deal easily with complex boundaries and is highly parallelizable.

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[1]. Witherden, F.D. and A. Jameson. Future Directions of Computational Fluid Dynamics. in 23rd AIAA Computational Fluid Dynamics Conference. 2017.
[2]. Li, Y., et al., Coupled computational fluid dynamics/multibody dynamics method for wind turbine aero-servo-elastic simulation including drivetrain dynamics. Renewable Energy, 2017. 101: p. 1037-1051.
[3]. Rutkowski, D.R., et al., Surgical planning for living donor liver transplant using 4D flow MRI, computational fluid dynamics and in vitro experiments. Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2017: p. 1-11.
[4]. Fortunato, L., et al., In-situ assessment of biofilm formation in submerged membrane system using optical coherence tomography and computational fluid dynamics. Journal of Membrane Science, 2017. 521: p. 84-94.
[5]. Boulard, T., et al., Modelling of micrometeorology, canopy transpiration and photosynthesis in a closed greenhouse using computational fluid dynamics. Biosystems Engineering, 2017. 158: p. 110-133.
[6]. Tao, Y., K. Inthavong, and J. Tu, Computational fluid dynamics study of human-induced wake and particle dispersion in indoor environment. Indoor and Built Environment, 2017. 26(2): p. 185-198.
[7]. Mahmood, R., et al., Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver. Advances in Mathematical Physics, 2017.
[8]. Abu-Nada, E. and A.J. Chamkha, Mixed convection flow of a nanofluid in a lid-driven cavity with a wavy wall. International Communications in Heat and Mass Transfer, 2014. 57: p. 36-47.
[9]. 9. Botella, O. and R. Peyret, Benchmark spectral results on the lid-driven cavity flow. Computers & Fluids, 1998. 27(4): p. 421-433.
[10]. Grillet, A.M., et al., Modeling of viscoelastic lid driven cavity flow using finite element simulations. Journal of Non-Newtonian Fluid Mechanics, 1999. 88(1): p. 99- 131.
[11]. Benyahia, S., et al., Simulation of particles and gas flow behavior in the riser section of a circulating fluidized bed using the kinetic theory approach for the particulate phase. Powder Technology, 2000. 112(1): p. 24-33.
[12]. Alex, J., et al., Analysis and design of suitable model structures for activated sludge tanks with circulating flow. Water science and technology, 1999. 39(4): p. 55- 60.
[13]. Perumal, D.A. and A.K. Dass, Application of lattice Boltzmann method for incompressible viscous flows. Applied Mathematical Modelling, 2013. 37(6): p. 4075- 4092.
[14]. Schreiber, R. and H.B. Keller, Driven cavity flows by efficient numerical techniques. Journal of Computational Physics, 1983. 49(2): p. 310-333.
[15]. Hou, S., et al., Simulation of Cavity Flow by the Lattice Boltzmann Method. Journal of Computational Physics, 1995. 118(2): p. 329-347.
[16]. Chen, S. and G.D. Doolen, LATTICE BOLTZMANN METHOD FOR FLUID FLOWS. Annual Review of Fluid Mechanics, 1998. 30(1): p. 329-364.
[17]. He, Y., et al., Lattice Boltzmann method and its applications in engineering thermophysics. Chinese Science Bulletin, 2009. 54(22): p. 4117.
[18]. Li, Q., et al., Lattice Boltzmann methods for multiphase flow and phase-change heat transfer. Progress in Energy and Combustion Science, 2016. 52: p. 62-105.
[19]. Bao, J. and L. Schaefer, Lattice Boltzmann equation model for multi-component multi-phase flow with high density ratios. Applied Mathematical Modelling, 2013. 37(4): p. 1860-1871.
[20]. Psihogios, J., et al., A Lattice Boltzmann study of nonnewtonian flow in digitally reconstructed porous domains. Transport in Porous Media, 2007. 70(2): p. 279-292.
[21]. Wang, C.-H. and J.-R. Ho, A lattice Boltzmann approach for the non-Newtonian effect in the blood flow. Computers & Mathematics with Applications, 2011. 62(1): p. 75-86.
[22]. Hao, J. and L. Zhu, A lattice Boltzmann based implicit immersed boundary method for fluid–structure interaction. Computers & Mathematics with Applications, 2010. 59(1): p. 185-193.
[23]. Yang, J. and E.S. Boek, A comparison study of multicomponent Lattice Boltzmann models for flow in porous media applications. Computers & Mathematics with Applications, 2013. 65(6): p. 882-890.
[24]. Fakhari, A., D. Bolster, and L.-S. Luo, A weighted multiple-relaxation-time lattice Boltzmann method for multiphase flows and its application to partial coalescence cascades. Journal of Computational Physics, 2017. 341: p. 22-43.
[25]. Zhuo, C. and P. Sagaut, Acoustic multipole sources for the regularized lattice Boltzmann method: Comparison with multiple-relaxation-time models in the inviscid limit. Physical Review E, 2017. 95(6): p. 063301.
[26]. Hu, Y., et al., A multiple-relaxation-time lattice Boltzmann model for the flow and heat transfer in a hydrodynamically and thermally anisotropic porous medium. International Journal of Heat and Mass Transfer, 2017. 104: p. 544-558.
[27]. Liu, Q., Y.-L. He, and Q. Li, Enthalpy-based multiplerelaxation-time lattice Boltzmann method for solidliquid phase-change heat transfer in metal foams. Physical Review E, 2017. 96(2): p. 023303.
[28]. Bhatnagar, P.L., E.P. Gross, and M. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Physical review, 1954. 94(3): p. 511.
[29]. Vanka, S.P., Block-implicit multigrid solution of NavierStokes equations in primitive variables. Journal of Computational Physics, 1986. 65(1): p. 138-158.
[30]. Ghia, U., K.N. Ghia, and C.T. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 1982. 48(3): p. 387-411.
[31]. Gupta, M.M. and J.C. Kalita, A new paradigm for solving Navier–Stokes equations: streamfunction–velocity formulation. Journal of Computational Physics, 2005. 207(1): p. 52-68.