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An efficient immersed boundary method for fluid flow simulations with moving boundaries. (English) Zbl 1427.76212
Summary: An efficient immersed boundary (IB) method is presented for the direct numerical simulation of fluid flow past a pair of circular cylinders and rigid particulate flows. The cylinders are settled in either a tandem or side-by-side arrangement. The grid applied in this paper involves an uneven Cartesian grid, and local differential quadrature (LDQ) is employed to discretize the governing equations. Specifically, a solid in a target region is embedded into the Cartesian grid, and linear interpolation is adopted to calculate the IB and the virtual force on the cell center. The virtual force is substituted into the governing equations to determine the effect of the solid in the IB. The parameters for numerical calculation are the Reynolds number (10-200) and the Prandtl number of air (0.7). The spacing intervals of the tandem arrangement and side-by-side arrangement are $$g^* = 1.5-4$$ and $$s^* = 1.5-4$$, respectively. According to the aforementioned conditions, the local Nusselt number and average Nusselt number of the cylinder surface in each arrangement are calculated to investigate how dissimilar flow conditions and spacing intervals between the cylinders influence the effect of heat transfer enhancement. In addition, the present model is applied to simulate the sedimentation of one particle and two particles in a box. Related changes in the flow field of fluid-particles interaction are also discussed.

MSC:
 76M99 Basic methods in fluid mechanics 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 76D05 Navier-Stokes equations for incompressible viscous fluids
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 [1] Zdravkovich, M. M., Review of flow interference between two circular cylinders in various arrangements, ASME J. Fluids Eng., 99, 717-731, (1977) [2] Bearman, P. W.; Wadcock, A. J., The interaction between a pair of circular cylinders normal to a stream, J. Fluid Mech., 61, 499-511, (1973) [3] Williamson, C. H.K., Evolution of a single wake behind a pair of bluff bodies, J. Fluid Mech., 159, 1-18, (1985) [4] Meneghini, J. R.; Saltara, F.; Siqueira, C. L.R.; Ferrari, J. A., Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements, J. Fluids Struct., 15, 327-350, (2001) [5] Saravanan, S.; Vidhya Kumar, A. R., Natural convection in square cavity with heat generating baffles, Appl. Math. Comput., 244, 1-9, (2014) · Zbl 1335.76048 [6] Eckert, E. R.G.; Soehngen, E., Distribution of heat transfer coefficients around circular cylinders in crossflow at Reynolds numbers from 20 to 500, Trans. ASME, 75, 343-347, (1952) [7] Momose, K.; Kimoto, H., Forced convection heat transfer from a heated circular cylinder with arbitrary surface temperature distributions, Heat Transf.-Asian Res., 28, 484-499, (1999) [8] Bharti, R. P.; Chhabra, R. P.; Eswaran, V., A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder, Heat Mass Transf., 43, 639-648, (2007) [9] Zhang, N.; Zheng, Z. C.; Eckels, S., Study of heat-transfer on the surface of a circular cylinder in flow using an immersed-boundary method, Int. J. Heat Fluid Flow, 29, 1558-1566, (2008) [10] Chang, M. W.; Finlayson, B. A., Heat transfer in flow past cylinders at Re<150 Part I. calculations for constant fluid properties, Numer. Heat Transf., 12, 179-198, (1987) · Zbl 0623.76098 [11] Rosales, J. L.; Ortega, A.; Humphrey, J. A.C., A numerical investigation of the convective heat transfer in unsteady laminar flow past a single and tandem pair of square cylinders in a channel, Numer. Heat Transf. A, 38, 443-465, (2000) [12] Chaitanya, N. S.K.; Dhiman, A. K., Non-Newtonian power-law flow and heat transfer across a pair of side-by-side circular cylinders, Int. J. Heat Mass Transf., 55, 5941-5958, (2012) [13] Peskin, C. S., Flow patterns around heart valves: a numerical method, J.Comput. Phys., 10, 252-271, (1972) · Zbl 0244.92002 [14] Goldstein, D.; Handler, R.; Sirovich, L., Modeling a no-slip flow boundary with an external force field, J.Comput. Phys., 105, 354-366, (1993) · Zbl 0768.76049 [15] Mohd-Yusof, J., Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries, (Proceedings of Annual Research Briefs. Proceedings of Annual Research Briefs, Standard CA, (1997), NASA Ames Research Center/Standford University Center for Turbulence Research), 317-327 [16] Lee, S.; Jung, E., A two-chamber model of valveless pumping using the immersed boundary method, Appl. Math. Comput., 206, 876-884, (2008) · Zbl 1163.76011 [17] Guo, X.; Yao, J.; Zhong, C.; Cao, J., A hybrid adaptive-gridding immersed-boundary lattice Boltzmann method for viscous flow simulations, Appl. Math. Comput., 267, 529-553, (2015) · Zbl 1410.76355 [18] Taira, K.; Colonius, T., The immersed boundary method: a projection approach, J. Comput. Phys., 225, 2118-2137, (2007) · Zbl 1343.76027 [19] Bellman, R. E.; Kashef, B. G.; Casti, J., Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, J. Comput. Phys., 10, 40-52, (1972) · Zbl 0247.65061 [20] Shen, L. H.; Young, D. L.; Lo, D. C.; Sun, C. P., Local differential quadrature method for flow and heat transfer in 2D irregular domains, Numer. Heat Transf. B., 55, 116-134, (2009) [21] Shu, C.; Xue, H., Comparison of two approaches for implementing stream function boundary conditions in DQ simulation of natural convection in a square cavity, Int. J. Heat Fluid Flow, 19, 59, (1998) [22] Shu, C.; Wang, L.; Chew, Y. T., Numerical computation of three-dimensional incompressible Navier-Stokes equations in primitive variable form by DQ method, Int. J. Numer. Methods Fluids, 43, 345-368, (2003) · Zbl 1032.76657 [23] Lo, D. C.; Young, D. L.; Murugesan, K., GDQ method for natural convection in a square cavity using velocity-vorticity formulation, Numer. Heat Transf. B., 47, 321-341, (2005) [24] Lo, D. C.; Young, D. L.; Murugesan, K., GDQ method for natural convection in a cubic cavity using velocity-vorticity formulation, Numer. Heat Transf. B., 48, 363-386, (2005) [25] Lo, D. C., High-resolution simulations of magnetohydrodynamic free convection in an enclosure with a transverse magnetic field using a velocity-vorticity formulation, Int. Commun. Heat Mass Transf., 37, 514-523, (2010) [26] Niu, X. D.; Shu, C.; Chew, Y. T.; Peng, Y., A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows, Phys. Lett. A, 354, 173-182, (2006) · Zbl 1181.76111 [27] Calhoun, D., A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions, J. Comput. Phys., 176, 231-275, (2002) · Zbl 1130.76371 [28] Choi, J. I.; Oberoi, R. C.; Edwards, J. R.; Rosati, J. A., An immersed boundary method for complex incompressible flow, J. Comput. Phys., 224, 757-784, (2007) · Zbl 1123.76351 [29] Liu, C.; Sheng, X.; Sung, C. H., Preconditioned multigrid methods for unsteady incompressible flows, J. Comput. Phys., 139, 35-57, (1998) · Zbl 0908.76064 [30] Russel, D.; Wang, Z. J., A Cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow, J. Comput. Phys., 191, 177-205, (2003) · Zbl 1160.76389 [31] Feng, J.; Hu, H. H.; Joseph, D. D., Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid, Part 1. Sedimentation, J. Fluid Mech., 261, 95-134, (1994) · Zbl 0800.76114 [32] Wan, D. C.; Turek, S., Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method, Int. J. Numer. Methods Fluids, 51, 531-566, (2006) · Zbl 1145.76406 [33] fortes, A.; Joseph, D. D.; Lundgren, T. S., Nonlinear mechanics of fluidization of beds of spherical particles, J. Fluid Mech., 177, 467-483, (1987)
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