Document Type : Original Article

Author

Aerospace Engineering Urmia University of Technology

10.22034/jast.2023.376159.1139

Abstract

Minimizing the computational cost and improving the convergence speed is the main goal of any computational design. In this regard, due to the low convergence speed of the traditional iterative method of fluid flow solution, a new method to improve the traditional iterative method is applied. In this paper, two-dimensional fluid flow in a channel with an aspect ratio of 10, uniform inlet velocity, constant outlet pressure, and no-slip conditions at the walls is studied using the Lattice-Boltzmann Method. The speed of convergence of the solution is increased by verifying that the mass flux is conserved between the inlet and each channel section. The solution time of channel flow obtained by Lattice-Boltzmann Method for Reynolds number of 100 and three types of grids 40x400, 60x600 and 80x80 are 261, 1039 and 4264 s, respectively. Based on the results, by introducing a flow rate control in each channel section of these three types of grids, the solution time is reduced by 35, 266, and 1590 seconds. This method can be implemented not only for normal but also for channel with an obstacle. According to the results, the speed of convergence increases by at least 2 times using this method

Keywords

Main Subjects

[1] A. Guittet, M. Theillard, F. Gibou, A stable projection method for the incompressible Navier-Stokes equations on arbitrary geometries and adaptive Quad/Octrees, Journal of computational physics, 292, 215–238 (2015)
[2] S.V. Patankar, D.B. Spalding, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, International Journal of Heat and Mass Transfer, 15(10), 1787–1806 (1972)
[3] H. Xiao, J. Wang, Z. Liu, W. Liu, A consistent SIMPLE algorithm with extra explicit prediction — SIMPLEC, International Journal of Heat and Mass Transfer, 120, 1255-1265 (2018)
[4] Y. Liu, F. Wang, Y. Li, Fourier analysis of the SIMPLE serials, Numerical Heat Transfer, Part B: Fundamentals, 69(3), 197-216, (2016). DOI: 10.1080/10407790.2015.1097095
[5] J. Li, Q. Zhang, Z.Q. Zhai. An efficient SIMPLER-revised algorithm for incompressible flow with unstructured grids, Numerical Heat Transfer, Part B: Fundamentals, 71(5), 425-442, (2017)
[6] M. Darwish, I. Sraj, F. Moukalled, A coupled finite volume solver for the solution of incompressible flows on unstructured grids, Journal of computational physics, 228(1), 180–201 (2009)  
[7] D. Shirokoff, R.R. Rosales, An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary, Journal of computational physics, 230(23), 8619–8646 (2011)  
[8] C.N. Xiao, F. Denner, B.G.M. van Wachem, Fully-coupled pressure-based finite volume framework for the simulation of fluid flows at all speeds in complex geometries, Journal of Computational Physics, 346, 91–130 (2017)
[9] M. Bayati, M. Tahmasebi Sarvestani, Numerical and Analytical Investigation of the Surface Evaporation Rate of the Different Nanofluids and Optimization Results by Using the RSM Method, Arabian Journal for Science and Engineering, (2022). DOI: 10.1007/s13369-022-07407-y.  
[10] P. Nithiarasu, C.B. Liu, an artificial compressibility based characteristic based split (CBS) scheme for steady and unsteady turbulent incompressible flows. Computer Methods in Applied Mechanics and Engineering, 195(23), 2961–2982 (2006)
[11] M. Napolitano, G. Pascazio, L. Quartapelle, A review of vorticity conditions in the numerical solution of the f–w equations, Computers and Fluids, 28(2), 139–185 (1999)  
[12] B. Kallemov, A. Bhalla, B. Griffith, A. Donev, An immersed boundary method for rigid bodies, Communications in Applied Mathematics and Computational Science, 11(1), 79–141 (2016)  
[13] Q. Li, K.H. Luo, Q.J. Kang, Y.L. He, Q. Chen, Q. Liu, Lattice Boltzmann methods for multiphase flow and phase-change heat transfer, Progress in Energy and Combustion Science, 52, 62–105 (2016)
[14] L. An, T.S. Zhao, Transport phenomena in alkaline direct ethanol fuel cells for sustainable energy production, Journal of power sources, 341, 199–211 (2017)
[15] Q. Luo, T. Ren, D. Liang, Discretized pressure Poisson algorithm for the steady incompressible flow on a non-staggered grid, Numerical Heat Transfer, Part B: Fundamentals, 71(6), 549-559, (2017)
[16] R. Choudhury, U.J. Das, Viscoelastic effects on the three- Dimensional hydrodynamic flow past a vertical porous plate, International Journal of Heat and Technology, 31(1), 1-8 (2013). DOI: 10.18280/ijht.310101.
[17] H. Ashrafi, N. Pourmahmoud, I. Mirzaee and N. Ahmadi. Introducing a new serpentine configuration of gas channels to enhance the performance and reduce the water flooding in the PEMFC, Iranian Journal of Chemistry and Chemical Engineering, 42(1), 192-207, (2023). DOI: 10.30492/ijcce.2022.546616.5111.
[18] j. Fan, W. Duan, L. Huang, et al., High fidelity flow field reconstruction model for incompressible fluid with physical constraints, Ocean Engineering, 280, (2023). DOI: 10.1016/j.oceaneng.2023.114597.
[19] X. Chen, Z. Chai, Y. Zhao, B. Shi, Numerical Simulation of Power-Law Fluid Flow in a Trapezoidal Cavity using the Incompressible Finite-Difference Lattice Boltzmann Method, Physics Fluid Dynamics, (2023). DOI: 10.48550/arXiv.2306.07603.
[20] S. Bhopalam Rajakumar, D. Arumuga Perumal and A. Kumar Yadav, Three-dimensional simulations of fluid flows in oscillating lid-driven cavities using lattice Boltzmann method, Fluid Dynamics Research, (2023). DOI: 10.1088/1873-7005/ace37c.
[21] Y. Zhao, F. Meng and X. Lu, Improvement of lattice Boltzmann methods based on gated recurrent unit neural network. Scientific Reports Signal, Image and Video Processing (2023). https://doi.org/10.1007/s11760-023-02543-w.
[22] M. Yang, X. Li, Optimum convergence parameters of lattice Boltzmann method for predicting effective thermal conductivity, Computer Methods in Applied Mechanics and Engineering, 394, (2022). DOI: 10.1016/j.cma.2022.114891.
[23] A. Jaramillo, V. Pessoa Mapelli and L. Cabezas-Gómez, Pseudopotential Lattice Boltzmann Method for boiling heat transfer: A mesh refinement procedure, Applied Thermal Engineering, 213, (2022). DOI: 10.1016/j.applthermaleng.2022.118705.
[24] Ji-Hao Zhang, Dong-Dong Zhang, Fu-Yun Zhao & Di Liu, Non-unique steady flow solutions for pressure correction equations applied in the regime of natural convection inside free vented enclosures, Numerical Heat Transfer; Part A: Applications, 70(2), 145-161, (2016). DOI:
 10.1080/10407782.2016.1173437
[25] E. Blosch, W. Shyy, R. Smith, The role of mass conservation in pressure-based algorithms. Numerical Heat Transfer, Part B Fundamentals, 24(4), 415-429 (1993)
[26] J.B. Liu, M. Bayati, M. Abbas, A. Rahimi, M. Naderi, Mesoscopic approach for simulating nanofluid flow and heat transfer in a finned multi-pipe heat exchanger, International Journal of Numerical Methods for Heat & Fluid Flow, 29(8), 2822-2839 (2019)
[27] M. Sukop, D. Or, Invasion percolation of single component, multiphase fluids with lattice Boltzmann models, Physica B: Condensed Matter, 338, 298–303 (2003)
[28] Q. Zou, X. He, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Physics of Fluids, 9, 1591–1598 (1997)
[29] M.C. Sukop, D.T. Thorne, Lattice Boltzmann Modeling. (2006)
[30] Guide, F. U. S. Fluent Inc. Pune, India, (2005)
[31] M. Breuer, J. Bernsdorf, T. Zeiser, F. Durst, Accurate computations of the laminar flow past a square cylinder based on two different methods: Lattice-Boltzmann and finite-volume. International Journal of Heat and Fluid Flow, 21(2), 186-196 (2000)