TECHNICAL PAPER Numerical investigation of different aspect ratios for flow past three inline rectangular cylinders Shams Ul Islam 1 • Raheela Manzoor 1 • Zhou Chao Ying 2 • Zia Ul Islam 3 Received: 22 December 2015 / Accepted: 1 August 2018 / Published online: 7 August 2018 Ó The Brazilian Society of Mechanical Sciences and Engineering 2018 Abstract In this paper, numerical investigations are carried out to study the effect of aspect ratios (AR = length/height) for flow past three rectangular cylinders aligned inline at different gap spacings (g) using lattice Boltzmann method. The aspect ratio is varied between 0.25 and 3, gap spacing is taken in the range from 0.5 to 7 and the Reynolds number is fixed at 150. With the help of present numerical investigation, it is found that the variation of forces with different AR and g is governed by six distinct flow patterns: (1) shear layer reattachment flow; (2) steady flow; (3) quasi-steady flow; (4) strongly interactive vortex shedding flow; (5) two-row vortex street flow; and (6) critical flow pattern. It is observed that the development of vortices, interferences of the free shear layers and the wake vortices distribution of three cylinders play a vital role in the variation of shedding frequencies and fluid forces. Consequently, the cylinders placed at downstream usually experience serious fluctuating forces due to unsteady wakes generated by the upstream cylinders. Also, the upstream cylinder normally experiences larger mean drag force as compared to the downstream ones. The sudden jumps in mean drag coefficients and Strouhal numbers with their maximum and minimum values are identified, respectively. The upstream and middle cylinders force coefficients strongly affected due to critical aspect ratios at different fixed gap spacings. It is observed that the wake transition at early stages significantly changes by changing the aspect ratios for fixed gap spacings. The results also show that the middle and downstream cylinders experience negative drag force for some aspect ratios and gap spacings. Furthermore, the dependence of the critical gap spacing on the aspect ratios is also discussed. Keywords Aspect ratios Á Force coefficients Á Flow patterns Á Gap spacings Á Inline rectangular cylinders Á Lattice Boltzmann method List of symbols AR Aspect ratio C d Drag coefficient C l Lift coefficient C 1 Upstream cylinder C 2 Middle cylinder C 3 Downstream cylinder C dmean Mean drag coefficient C drms Root-mean-square value of drag coefficient C lrms Root-mean-square value of lift coefficient C s Speed of sound d Diameter of the cylinder e i Velocity directions f i Particle density distribution function f i (eq) Equilibrium distribution function F x In-line force component F y Transverse force component f s Vortex shedding frequency g Gap spacing H Height of the computational domain L Length of the computational domain L d Downstream position L u Upstream position P Pressure Re Reynolds number s Surface-to-surface distance between cylinders S t Strouhal number Technical Editor: Andre ´ Cavalieri. & Shams Ul Islam islam_shams@comsats.edu.pk 1 Mathematics Department, COMSATS University, Islamabad 44000, Pakistan 2 Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen University Town, Shenzhen 518055, China 3 Mechanical Engineering Department, Capital University of Science and Technology, Islamabad 44000, Pakistan 123 Journal of the Brazilian Society of Mechanical Sciences and Engineering (2018) 40:410 https://doi.org/10.1007/s40430-018-1334-y