Simulation of unsteady viscous flow-structure interaction
The design of slender structures such as longspan bridges, masts, offshore risers and cables is strongly influenced by their response behaviour when subjected to unsteady loads due to wind, waves and current. Simulation of the behaviour of a viscous flow past a structural cross section is of great importance to engineers concerned with the design of such structures. Offshore engineers are concerned with estimating the magnitude of structural forces induced by the most severe storm-induced wave events. Numerous studies have been conducted in an effort to estimate the structural forces induced by both regular and irregular waves. However, estimation of the maximum extreme wave-induced structural forces, particularly for relatively small diameter horizontal components, has received less attention. Since the most widely used method for estimating the force experienced by a bluff body subjected to wave loading is the empirical drag-inertia equation developed by Morison, O’ Brien, Johnson, and Schaaf (1950), it is important to determine whether this equation is adequate to describe the forces imposed by extremely large ocean waves. A method is presented for the simulation of incompressible viscous flow past acylinder using a stream function vorticity-transport formulation discretised on a cutcell quadtree mesh. A cut-cell technique is employed to provide accurate boundary representation and to facilitate the simulation of flow past a moving boundary. The finite volume discretisation consists of second-order accurate central difference approximations within uncut flow cells and a polynomial reconstruction technique within the cut-cells that are intersected by the solid boundary. Several preliminary validation tests concerned with flow past a circular cylinder are presented to confirm the accuracy of the numerical model. Firstly, the cut-cell discretisation is applied to the solution of the Euler equations and is shown to be almost second order accurate. Comparisons of wake geometry and force coefficients for steady and oscillatory flows at low Reynolds number are then made with existing results, and show satisfactory agreement. Preliminary tests are presented to assess the accuracy of a cut-cell based method for simulating flow past a circular body that moves across a background mesh. A series of experiments is also presented concerned with the measurement of theforce experienced by a circular cylinder undergoing a pre-defined two-dimensionalmotion within a still fluid. The cylinder trajectory is representative of the motionof a fluid particle beneath an idealised large ocean wave as defined by the NewWave formulation (Tromans et al. 1991). It is observed that, whilst the magnitude of high frequency vortex induced force fluctuations varies with the ratio of wave amplitude to cylinder diameter (A=D) and the wave spectrum shape, the overall shape of both x- and y-direction force time histories is very similar for all wave groups for which the underlying spectrum has the same shape. For all of the two-dimensional cylinder motions considered, the spectrum of both measured forces closely approximates the spectrum of uq (where u is a component of the velocity vector and q the absolute velocity) and, as a result, the vector form of the well known equation developed by Morison et al. (1950) is shown to provide a satisfactory estimate of the cartesian force components. The high frequency component of the force that is not captured by the Morison et al. equation is clearly identified as a lift-type force in the radial direction. For design purposes, a reasonable estimate of the magnitude of the peak force is obtained by neglecting inertial forces and employing a drag coefficient CD = 1.0.