UBC Theses and Dissertations
Finite element analysis of viscous flow and rigid body interaction Irani, Mehernosh Boman
A finite element method is developed to analyse the interaction of a two-dimensional viscous fluid and an elastically supported rigid body. The stream function form of the Navier-Stokes equations is discretized using 18 degree of freedom C¹ triangular elements. For each fluid element in contact with the body consistent surface traction vectors are derived in terms of the nodal variables to represent the force coupling terms in the equations of motion of the body. Thus a system of nonlinear differential equations is obtained for the coupled fluid-mass system. For the first order solution of the nonlinear problem by the perturbation method, the equations are linearized and the linear problem is solved. In the present study results for the linear problem only are presented, which are valid for "zero" Reynolds number or very slow flow. The problem of a square shaped mass which is excited by a harmonic force in otherwise still fluid and supported by an elastic spring in the direction of its motion is studied. A simple dimensional analysis shows that the response is a function of three basic non-dimensional parameters, namely, (a) the effective viscosity, (b) the ratio of the forcing frequency to the natural frequency of the spring-mass system in vacua, and, (c) the mass to fluid density ratio. A parametric study of the response in terms of these basic non-dimensional parameters is carried out. The influence of the fluid on the response of the mass, represented as added mass and effective damping, is also studied as a function of the frequency Reynolds number. The effect of the fluid, in the form of added mass and damping, is clearly evident in the shift of the resonance peaks of the amplitude response curves of the mass. In the absence of known results no quantitative estimate of the accuracy of the method could be made. But the values of the added mass obtained at high frequencies came to within ten per cent of the predictions by inviscid flow theory. This indicates good accuracy at least in this limiting case.
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