Numerical investigation of flow around straight cylinders with inclination
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- Institutt for marin teknikk 
In this master thesis the validity of the independence principle(I.P) on an inclined infinite circular cylinder has been investigated. Normalized Reynolds numbers 150 and 1000 for inclination angles 0°-65° were studied. Themain objective was to investigate wake dynamics for an inclined circular cylinder that eventually lead to the break down of the independence principle. Reynolds number 150 has been the primary focus in this study. Wake behaviour, as well as individual velocity components, were investigated. The inclined circular cylinders were also compared to equivalent elliptic cylinders to improve the understanding of the limitationsof the I.P. The simulations were carried out using the computer software MGLET, whichsolves the incompressible Navier-Stokes equations on a staggered non-equidistant Cartesian grid. The infinite circular cylinder was modelled by periodic boundary conditions, and the body implemented by the use of an Immersed Boundary Method. Zonal grid and periodic boundary conditions on the top and bottom of the computational domain prohibits the use of an inclined circular cylinder. The inclination of the cylinder is therefore given by inclining the inflow and keeping the cylinder straight For Re_n = 150 the simulations resulted in a break down of the independence principle between 35° and 45°. The break down is characterized by a deviation in the Strouhal number, as well as the lift coefficient. Measured flow quantities were normalized, and compared to the quantities of the normal flow in order to investigate the validity of the independence principle. For the pressure coefficient a deviation was only noticeable at angles larger than 45°. This deviation could be caused by the transient effects associated with the breakdown of I.P. The drag coefficient seem to be well predicted by the I.P for all investigated angles at this Reynolds number. As the inclination angle increases the r.m.s of the lift coefficient, C_L, decreases in magnitude. The decrease is due to the increased three-dimensionality of the flow as the inclination angle is increased. v- and w-velocities are phase shifted behind the cylinder in the spanwise direction and no longer independent of z when the independence principle breaks down. This means that the vortices along the cylinder are not shed simultaneously, which contributes to the drop observed. The shedding angles on the vortex filaments were found to remain constant at an angle of 61° for angles where I.P was found invalid. This non-physically locked shedding angle is assumed to be caused by the periodic boundary conditions. When the flow becomes inclined the periodic boundary conditions do not account for the inclination. It is believed that the angle locking is due to the boundary condition being too stiff for this flow configuration. Flow around elliptic cylinders in normal flow equivalent to inclination angles 35°-65° were simulated. Good agreementwith the literature was achievedwhen verifying the results. Comparisons against the inclined circular cylinders resulted in the the ellipses in normal flow being unsuitable to represent inclined circular cylinders. This result is in agreement with the literature, and lack of three-dimensionality is to blame. For Re_n = 1000 the independence principle was found to be valid for all flow quantities, except the r.m.s lift coefficient, C_L, up to an inclination angle of 55°. The deviation in C_L is suspected to be due to a combination of inclination angle and Reynolds number, for which both have been found to reduce the correlation length. Increased validity range for the independence principle is assumed to be caused by the boundary layer becoming thinner for increasing Reynolds number. The required simulation time has been evaluated by comparing contour lines for omega_z, by evaluating the differences visually. Simulation time was found sufficient for t = 300s. Indications of locked shedding angles in the vortex filaments, as for Re_n = 150, were not found for this Reynolds number. Periodic boundary conditions are thusconsidered less stiff, and plausible as no indication of solution pollution is found.