Lattice Boltzmann Method: Applications to Fluid Structure Interaction Problems

Abstract

Lattice Boltzmann Method: Applications to Fluid Structure Interaction Problems In this numerical study fluid structure interaction problems are analyzed using the lattice Boltzmann method (LBM). For this purpose, firstly LBM is discussed in details. After that numerical computations are performed, using a two-dimensional code based on LBM, for the unsteady and incompressible flow past a single-, two-, three- and four square cylinders at different Reynolds numbers (Re) and gap spacings (g) in order to study the important characteristics of fluid structure interaction. The numerical computations are carried out at Re in the range 1 to 200 while g is taken in the range 0.5 to 17. Different features of fluid structure interaction like transition in flow states, different wake modes and flow induced forces are captured in an efficient way using the LBM. The results are presented in the form of vorticity contours visualization, streamlines, temporal histories of drag and lift coefficients and power spectrum of lift coefficients. Also the variation of physical parameters like mean drag coefficient (Cdmean), Strouhal number (St), root-mean square values of drag and lift coefficients (Cdrms and Clrms) with Re and g is presented. For the flow past a single square cylinder it is found that the flow remains in a steady state up to Re = 50. The unsteadiness starts between Re = 50 and 55 with formation of weaker vortices. The flow becomes fully periodic at Re = 60. Also it is found that the computational domain has a great influence on the flow characteristics. The size of computational domain may be different in case of a single and multiple bodies in the flow field. For the flow past two inline square cylinders three different states of flow are found by varying Re in the range 1 to 110 at g = 2, 3.5 and 5: (a) steady state, (b) quasi steady state and (c) unsteady state. The first cylinder (c1) has greater Cdmean, less Cdrms and Clrms values as compared to those of c2. Also both cylinders have similar values of St. In steady state flow the St is not found at all values of Re and g. The characteristics of flow past three inline square cylinders are studied in three different ways: Firstly, effect of equal spacing is analyzed at a fixed value of Re, secondly, the effect of Re is analyzed at different fixed values of spacing, and thirdly, the effect of unequal spacing is analyzed at different Re. Five different modes of wake x are found by varying g in the range 0.5 to 17 at Re = 75: (a) Steady wake, (b) Quasi steady wake, (c) Sparse Karman vortex street, (d) Non-fully developed vortex street in single row and (e) Non-fully developed vortex street in double row. It is found that g = 3 is the drag inversion (DI) or critical spacing value where abrupt changes in flow characteristics occur. By varying Re in the range 90 to 175 at different values of g in the range 0.5 to 6 seven different flow patterns are found: (a) Single bluff body, (b) Quasi unsteady flow, (c) Shear layer reattachment, (d) Weakly interactive vortex shedding, (e) Strongly interactive vortex shedding, (f) Secondary vortex formation and (g) Critical flow. Re = 90 and 140 are found to be critical values of Re. Also it is observed that the DI spacing decreases with increment in Re. The Clrms of all cylinders are generally found to be greater than the corresponding Cdrms values. At different combinations of unequal spacing between the cylinders four major trends of shear layers are observed: (a) without roll up in both gaps, (b) without roll up in first gap and roll up in second gap, (c) roll up in first gap and without roll up in second gap and (d) roll up in both gaps. The values of Cdmean and St of c1 at unequal spacing combinations are higher than the corresponding values of c1 at equal spacing. At the spacing combinations (g1, g2) = (1, 1.5) and (g1, g2) = (1.5, 1), Re = 75 is observed to be the critical value of Re. Moreover, it is observed that the spacing combinations (g1, g2) = (3, 4) and (g1, g2) = (4, 3) are sensitive for the physical parameters. For the flow around four square cylinders, arranged in an inline square configuration, four main patterns of flow are observed in the range of Re from 60 to 175 at three different spacings g =1, 3 and 6: (a) steady flow, (b) stable shielding flow, (c) wiggling shielding flow, and (d) vortex shedding flow. At g = 1, a strong interaction of jet flow is observed which disappears as the spacing increases. In the steady and stable shielding flow patterns the Cdmean values, for all cylinders, are found to be greater than those of other flow patterns. The upstream cylinders (c1 and c2) are found to have similar flow characteristics to each other. Also the downstream cylinders (c3 and c4) have similar characteristics to each other. The downstream cylinders have higher values of Cdrms and Clrms as compared to the corresponding Cdrms and Clrms values of upstream cylinders. Furthermore, the results of current study are compared with those of other researchers and found to be in good agreement. Reduction in the values of physical parameters observed due to addition of bodies in the flow field.