A numerical model of the motion of a curved flexible fibre in a shear flow

grantor: University of TorontoA general method to simulate the motion of initially curled flexible fibres in 2-D flows is developed. Equations of motion are formulated for a curled elastic fibre in a fluid flow using Hamilton's Principle. The non-linear integro-differential equations contain an unknown deflection variable that is discretized using a half-range Fourier Sine series representation. The first (kinematic) approximation is obtained by setting the inertia terms to zero. The resulting inertialess equations are solved using a Runge-Kutta method implemented in a C++ code. The validity of the numerical model was tested against analytic theory and existing transient results for essentially straight fibres, i.e. fibres with small radii of curvature and large angles. Excellent agreement was achieved. The numerical model was then applied to simulate fibre motion into a screen slot. For similar fibre parameters, it was found that significantly more curled fibres entered the slot than their straight counterparts.M.A.Sc