Lift on a sphere in shear flow near flat channel bed

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Virginia Tech


The lift and drag forces exerting on a sphere immersed in a shear flow above a flat channel bed are evaluated by solving the steady three-dimensional Navier-Stokes equations. The numerical technique which combines the Newton iteration method and the finite element method is used to solve the non-linear Navier-Stokes equations. The technique first linearizes the non-linear terms in the partial differential equations, then solves the linearized equations by the finite element method. The Newton iteration method is used to linearize the non-linear equations. Since the iteration method requires a good initial guess, the linear solution of the partial differential equations is used for the initial guess, where the linear solution is the obtained by solving the differential equations without non-linear terms. The computer model developed can evaluate the lift coefficients of a sphere stationed at various distance from the channel bed. The computational results agree very well with the experimental measurements cited in the literature. The lift coefficient of the sphere changes with the undisturbed approaching velocity profile as well as the gap ratio which is the ratio of the distance between the sphere and the channel bed and the diameter of sphere. For fixed gap ratios, higher Reynolds number gives smaller lift coefficient than that of the lower Reynolds number. On the other hand, the lift coefficient also changes with the diameter of sphere for each fixed gap ratio. For small gap ratios, the lift coefficient increases as the diameter of sphere increases. For large gap ratios, the lift coefficient increases in the negative (downward) direction as the diameter of sphere increases.