Abstract
The present numerical investigation deals with the flow across two square cylinders placed in staggered alignment at fixed Reynolds number (Re) of 160 and varying gap spacings (g*) from 0 to 6. Numerical computations are conducted by employing the two-dimensional single-relaxation-time lattice Boltzmann method (SRT-LBM). The complex phenomena of vortex shedding are explored for different g* and outcomes are presented as vorticity snapshots, time-history analysis of drag and lift coefficients (CD and CL) and power spectra analysis of CL. Five flow patterns are observed which are named as: single bluff body flow, quasi periodic flow, chaotic flow, in-phase/anti-phase modulated flow and synchronized flow. The fluid forces are irregular for all flow patterns except for synchronized flow where lift is periodic due to synchronization of flow. It is observed that presence of an upstream cylinder in the near vicinity of downstream cylinder increases the drag at small gap spacing and vice versa.
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Aboueian, J. and Sohankar, A. (2017). “Identification of flow regimes around two staggered square cylinders by a numerical study.” Theoretical and Computational Fluid Dynamics, Vol. 31, No. 3, pp. 295–315, DOI: 10.1007/s00162-017-0424-2.
Agrawal, A. Djenidi, L., and Antonia, R. A. (2006). “Investigation of flow around a pair of side by side square cylinders using the lattice Boltzmann method.” Computers & Fluids, Vol. 35, No. 10, pp. 1093–1107, DOI: 10.1016/j.compfluid.2005.05.008.
Bhatnagar, P. L. Gross, E. P., and Krook, M. (1954). “A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems.” Physical Review, Vol. 94. No. 3, pp. 511–514, DOI: 10.1103/PhysRev.94.511.
Burattini, P. and Agrawal, A. (2013). “Wake interaction between two side by side square cylinders in channel flow.” Computers & Fluids, Vol. 77. No. 1, pp. 134–142, DOI: 10.1016/j.compfluid.2013.02.014.
Chen, Y., Cai, Q., Xia, Z., Wang, M., and Chen, S. (2013). “Momentumexchange method in lattice Boltzmann simulations of particle-fluid interactions.” Physical Review E, Vol. 88, No. 1, p. 013303, DOI: 10.1103/PhysRevE.88.013303.
Fredsoe, J. and Sumer, M. B. (1997). “Hydrodynamics around cylindrical structures.” World scientific Publishing, Vol. 26, DOI: 10.1142/6248.
Gera, B. Sharma, P. K., and Singh, R. K. (2010). “CFD analysis of 2D unsteady flow around a square cylinder.” International Journal of Applied Engineering Research, Vol. 3. No. 1, pp. 602–612, DOI: 10.1051/itmconf/20181602003.
Guo, Z. and Chang, S. (2013). “Lattice Boltzmann method and its applications in engineering.” World Scientific, Vol. 3, DOI: 10.1142/8806.
Guo, Z., Liu, H., Luo, L. S., and Xu, K. (2008). “A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows.” Journal of Computational Physics, Vol, 227, No. 10, pp. 4955–4976, DOI: 10.1016/j.jcp.2008.01.024.
Islam, S. U., Abbasi, W. S., and Rahman, H. (2014). “Force statistics and Wake Structure Mechanism of flow around a square cylinder at low Reynolds numbers.” International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering, Vol. 8, No. 8, pp. 1417–1423, DOI: 10.5281/zenodo.1094333.
Islam, S. U., Abbasi, W. S., Rahman, H., and Naheed, R. (2016). “Numerical investigation of wake modes for flow past three tandem cylinders using the multi-relaxation-time lattice Boltzmann method for different gap spacings.” Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 38, No. 3, pp. 799–812, DOI: 10.1007/s40430-014-0282-4.
Islam, S. U., Nazeer, G., Islam, Z. U., Ying, Z. C., and Manzoor, R. (2017). “Transitions in the flow patterns and aerodynamic characteristics of the flow around staggered rows of cylinders.” PLOS One, Vol. 12, No. 10, p. e0184169, DOI: 10.1371/journal.pone.0184169.
Islam, S. U., Nazeer, G. Z., and Ying, Z. C. (2018). “Numerical investigation of flow past 17-cylinder array of square cylinders.” AIP Advances, Vol. 8, No. 6, p. 065004, DOI: 10.1063/1.5022360.
Islam, S. U., Rahman, H., Ying, Z. C., and Saha, S. A. (2016). “Comparison of wake structures and force measurements behind three side by side cylinders.” Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 38, No. 3, pp. 843–858, DOI: 10.1007/s40430-014-0297-x.
Junk, M., Axel, K., and Luo, L. S. (2005). “Asymptotic analysis of the lattice Boltzmann equation.” Journal of Computational Physics, Vol. 210, No. 2, pp. 676–704, DOI: 10.1016/j.jcp.2005.05.003.
Kang, S. (2003). “Characteristics of flow over two circular cylinders in a side by side arrangement at low Reynolds numbers.” Physics of Fluids, Vol. 15, No. 9, pp. 2486–2498, DOI: 10.1063/1.1596412.
Kang, S. (2004). “Numerical study on laminar flow over three SBS cylinders.” KSME International Journal, Vol. 18, No. 10, pp. 1869–1879, DOI: 10.1080/10407782.2018.1486645.
Lee, K. and Yang, K. S. (2009). “Flow patterns past two circular cylinders in proximity.” Computers & Fluids, Vol. 38, No. 4, pp. 778–788, DOI: 10.1016/j.compfluid.2008.07.005.
Niu, J. and Zhu, Z. (2006). “Numerical study of three-dimensional flows around two identical square cylinders in staggered arrangements.” Physics of Fluids, Vol. 18, No. 4, pp. 044106–14, DOI: 10.1063/1.2194077.
Sohankar, A. (2012). “A numerical investigation of the flow over a pair of identical square cylinders in a tandem arrangement.” International Journal for Numerical Methods in Fluids, Vol. 70. No. 10, pp. 1244–1257, DOI: 10.1002/fld.2739.
Sohankar, A., Norberg, C., and Davidson, L. (1998). “Low-Reynoldsnumber flow around a square cylinder at incidence: Study of blockage, onset of vortex shedding and outlet boundary condition.” International Journal for Numerical Methods in Fluids, Vol. 26, No. 1, pp. 39–56, DOI: 10.1002/(SICI)1097-0363(19980115)26:1< 39::AID-FLD623>3.0.CO;2-P.
Sohankar, A., Norberg, C., and Davidson, L. (1999). “Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers.” Physics of Fluids, Vol. 11, No. 2, pp. 288–306, DOI: 10.1063/1.869879.
Sukop, M. C. and Thorne, D. T. Jr. (2006). Lattice boltzmann modeling: An introduction for geoscientists and engineers, Springer, Berlin, Heidelberg, Germany, DOI: 10.1007/978-3-540-27982-2.
Sumner, D. (2010). “Two circular cylinders in cross-flow: A review.” Journal of Fluids and Structures, Vol. 26, No. 6, pp. 849–899, DOI: 10.1016/j.jfluidstructs.2010.07.001.
Sumner, D., Price, S. J., and Paidoussis, M. P. (2000). “Flow-pattern identification for two staggered circular cylinders in cross-flow.” Journal of Fluid Mechanics, Vol. 411, pp. 263–303, DOI: 10.1017/S00221120 99008137.
Yen, S. C. and Liu, J. H. (2011). “Wake flow behind two side by side square cylinders.” International Journal of Heat and Fluid Flow, Vol. 32, No. 31, pp. 41–51, DOI: 10.1016/j.ijheatfluidflow.2012.09.005.
Yu, D., Mei, R., Luo, L. S., and Shyy, W. (2003). “Viscous flow computations with the method of lattice Boltzmann equation.” Progress in Aerospace Sciences, Vol. 39, No. 5, pp. 329–367, DOI: 10.1016/S0376-0421(03)00003-4.
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Islam, S.U., Nazeer, G. & Shigri, S.H. Numerical Investigation of Different Flow Regimes for Square Cylinders in Staggered Configuration. KSCE J Civ Eng 23, 2188–2197 (2019). https://doi.org/10.1007/s12205-019-0726-6
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DOI: https://doi.org/10.1007/s12205-019-0726-6