## NUMERICAL SIMULATION OF FLOW AROUND TWO SIDE-BY-SIDE RECTANGULAR CYLINDERS WITH VERTICAL AND HORIZONTAL OFFSETS

##### Master thesis

##### Permanent lenke

http://hdl.handle.net/11250/2614972##### Utgivelsesdato

2015##### Metadata

Vis full innførsel##### Samlinger

- Institutt for marin teknikk [2405]

##### Sammendrag

Computational Fluid Dynamics (CFD) is a common tool when investigating the effects of flow around structures. In this thesis, I have used \textit{ANSYS ICEM CFD} (Analysis System Integrated Computer Engineering and Manufacturing in Computational Fluid Dynamics) as a meshing tool. Two dimensional (2D) simulations for flow around 5:1 rectangular cylinders with Reynolds number $Re = 2x10^{5}$ was performed in \textit{OpenFOAM} (Open Field Operation and Manipulation). A 2D Unsteady Reynolds-Averaged Navier-Stokes (URANS) model and the high Reynolds number $k-\epsilon$ model was used when running the simulations in OpenFOAM. Grid-refinement, time-step and domain-size convergence studies were performed for all cases, generating the hydrodynamic values which will be used for post-processing. By using the obtained lift coefficient $C_{L}$, drag coefficient $C_D$, Strouhal number $St$, vorticity, pressure and velocity distribution, I have made an assessment of the results.
Due to the lack of any comparable studies on two 5:1 side-by-side rectangular cylinders, I analysed the flow around one single 5:1 rectangular cylinder and compared it with other sources as a validation. I saw close to identical numerical results when comparing them with the numerical simulations done by \cite*{Dahl}, 8\% reduction in Root Mean Square (RMS) lift coefficient $C_{Lrms}$, 0.3\% reduction in mean drag coefficient $\overline{C_D}$, and a similar Strouhal number. In comparison with the experimental studies by \cite*{Schewe2006} and \cite*{Schewe2009} for $Re = 2x10^{5}$ showed a 37\% decrease in $C_{Lrms}$, 6.7\% increase in $\overline{C_D}$, and a 10\% increase in $St$. I, therefore, conclude that these are useful methods for finding reliable values for two 5:1 rectangular cylinders.
Based on the mesh properties gathered from the single cylinder case, I analysed the flow around two 5:1 side-by-side rectangular cylinders with vertical offsets (VOs). I studied the hydrodynamic values for increasing vertical offset, from VO = 1 to VO = 4. There is a symmetric flow field due to the symmetry in geometry, giving equal hydrodynamic values for the top (\textit{top}) and bottom (\textit{bot}) cylinders. I will only focus on the top cylinder for the qualitative study. The mean lift coefficient showed an exponential 46.3\% decrease, from $\overline{{C_L}^{top,bot}} \approx \pm 1.7$ to $\overline{{C_L}^{top,bot}} \approx \pm 0.9305$. The negative $\overline{C_{L}^{bot}}$-value means we have a lift force acting downwards for the bottom cylinder, opposite for the top cylinder. The mean drag coefficient showed a linear 13.7\% decrease, from $\overline{C_D} \approx 1.46$ to $\overline{C_D} \approx 1.26$. The Strouhal number fluctuated between $St = 0.1373$ and $St = 0.1526$ inside a transitional range $1.5 \leq VO \leq 2.5$. From VO = 1.5 to VO = 2 we go from the generation of one common vortex shedding to two separate vortex sheddings. The velocity between the cylinder shows an exponential decrease for increasing VO. This velocity increase causes large pressure drops or suction in the cylinder boundary layer. The suction increase can be seen as larger vortices above and behind the cylinder (primary and tertiary vortices) and a decrease in the vortex below the cylinder (secondary vortex). The larger the size difference between the primary and secondary vortices, the larger the lift. In addition, the larger the tertiary vortex, the larger the drag. Inside the transitional range, we see the generation of additional "transitional tertiary vortices". We see this transition as lower mean wave heights for the lift and drag coefficients, $\overline{C_{Lh}}$ and $\overline{C_{Dh}}$, respectively. The drag and lift frequency were equal for all VOs, implying no alternation between the separation points from above and below the cylinders. The large increase in suction at the lower leading edge is only affective for a short distance at the start before it increases more rapidly, leading to a higher suction at the top leading edge. This, in turn, causes the lift to act upwards, as a repelling force between the cylinders.
By using the same mesh as for the VO = 1 case, I analysed the flow around two 5:1 side-by-side rectangular cylinders with VO = 1 and HO (horizontal offset) = 1. I saw a larger difference in the converged hydrodynamic values from the top to bottom cylinder, except for the Strouhal number. For the mean lift coefficient, I saw a 47.5\% difference, from $\overline{C_{L}}^{top} \approx 2.00$ to $\overline{C_{L}}^{bot} \approx -1.05$. For the mean pressure, I got a 6\% reduction, from $\overline{C_D}^{top} \approx 1.49$ to $\overline{C_D}^{bot} \approx 1.40$. I got a Strouhal number $St = 0.1221$, which is the same as for the single rectangular cylinder. The asymmetric geometry causes a phase shift in the drag coefficient over time for the top and bottom cylinders, which can be seen as a more "cluttered" vortex shedding. Quantitatively we see this influence as a lower mean wave height for the top cylinder and higher for the bottom cylinder compared to the VO = 1 case. It is interesting to observe the major reduction in suction occurring at the lower leading edge for the top cylinder. The back-flow from the bottom cylinder gets pushed up by the suction pressure below the top cylinder, causing a large positive pressure increase. This, in turn, gives us a shortened secondary vortex for the top cylinder together with a larger pressure decrease and secondary vortex at the upper leading edge for the bottom cylinder.
I found no direct comparable references to the flow around two side-by-side rectangular cylinders, but several in the scenarios where the fluid interaction might appear. When comparing the results done on ship-to-ship interaction for two parallel travelling ships by \cite*{fonfach2011numerical}, I saw certain similarities. These results show that the accelerated velocity between the two ship hulls causes a large suction, but the results do not indicate where specifically. This causes an attraction between the cylinders, which we would also get due to the strong suction at the beginning between the cylinders and momentum forces. More experimental and numerical data on two cylinders with vertical and horizontal offset is required. Nevertheless, the study done on two 5:1 rectangular cylinders with vertical and horizontal offset has proven to show stable and converging results which leads me to believe they can be used as a reliable source for further validation study and engineering design purposes.