UFR 2-14 Best Practice Advice

Fluid-structure interaction in turbulent flow past cylinder/plate configuration II

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Best Practice Advice

Numerical Modelling

CFD

• Discretization accuracy: In order to perform LES predictions it is required that spatial and temporal discretization are both at least of second-order accuracy. It is also important that the numerical schemes applied possesses low numerical diffusion (and dispersion) properties in order to resolve all the scales and not to dampen them out. A predictor-corrector scheme (projection method) of second-order accuracy forms the kernel of the fluid solver. In the predictor step an explicit Runge-Kutta scheme advances the momentum equation in time. This explicit method is chosen because of its accuracy, speed and low memory consumption. The discretization in space is done with second order central discretization scheme without any flux blending.

• Grid resolution: The second critical issue to perform LES is the grid resolution. The mesh near the wall, in the free-shear layers and also in the interior flow domain has to be fine enough. For wall-resolved LES the recommendations given by Piomelli and Chasnov (1996) should be followed or outperformed, e.g., $y^{+}<2,\;\Delta x^{+}<50,\;\Delta z^{+}<50-150$. In the present investigation a block-structured grid for the subset case is used. The entire grid consists of about 14 million control volumes (CVs). The first cell center is located at a distance of $\Delta y/D\approx 6.8\times 10^{-4}$. It was found to be sufficient to resolve the flow accurately at walls as well as in the free shear layers. Similar to the classical flow around a cylinder also in the present configuration it is important to resolve the region close to the separation point and the evolving shear layer region adequately.

• Grid quality: The third point is the quality of the grid. Smoothness and orthogonality is a very important issue for LES computations. In order to capture separations and reattachments at the cylinder and on the plate reliably, the orthogonality of the curvilinear grid in the vicinity of the walls has to be high. For deforming grids such as in the present FSI case, it is furthermore crucial to keep a high quality grid after strong grid movements and deformations.

• Inlet boundary condition: At the inlet a constant streamwise velocity is set as inflow condition without adding any perturbations. The choice of zero turbulence level is based on the consideration that, in general, small perturbations imposed at the inlet will anyway not reach the cylinder due to the coarseness of the grid at the outer boundaries. Therefore, all inflow fluctuations will be highly damped. However, since the flow is assumed to be sub-critical and the inflow turbulence level measured in the experimental setup found to be rather small, the neglect of inflow perturbations is of no relevance.

• Outlet boundary condition: A convective outflow boundary condition is favored allowing vortices to leave the integration domain without significant disturbances (Breuer, 2002). The convection velocity is set to uinflow.

• Boundary conditions at the lateral sides: In the subset case a reasonable approximation already applied in Breuer et al. (2012) is to use periodic boundary conditions in spanwise direction for both the fluid and the structure. For LES predictions periodic boundary conditions represent an often used measure in order to avoid the formulation of appropriate inflow and outflow boundary conditions. The approximation is valid as long as the turbulent flow is homogeneous in the specific direction and the width of the domain is sufficiently large. The latter can be proven by predicting two-point correlations, which have to drop towards zero within the half-width of the domain. The impact of periodic boundary conditions on the CSD predictions are discussed below. For the full case periodic boundary conditions can no longer be used. Instead, the lateral boundaries are assumed as slip walls (similar to the upper and lower walls) since the full resolution of the boundary layers would be again too costly. Furthermore, the assumption of the slip wall is consistent with the disregard of the small gap between the flexible structure and the side walls.

CSD

• Grid resolution: In the present investigation shell elements were used. A grid study on a simple structure case has shown that a mesh with $30\times 10$ shell elements for the subset case was sufficient.

• Non-linear deformation: In the present test case the deformations of the flexible structure are large. Therefore, in the realized computations geometrical non-linearities are taken into account with the CSD solver Carat++.

• Time discretization: In the present study the standard Newmark algorithm was sufficient.

• Boundary conditions at the cylinder: At the rigid cylinder a clamped support is realized and all degrees of freedom are equal to zero.

• Boundary conditions at the trailing edge: On the downstream trailing-edge side, the rubber plate is free to move and all nodes have the full set of six degrees of freedom.

• Boundary conditions at the lateral sides: The edges which are aligned to the main flow direction are using special boundary conditions, as explained in details in Section Numerical CFD Setup.

FSI

• FSI subiterations: When the FSI phenomenon is fully developed, 5 FSI subiterations are sufficient to reach a FSI convergence criterion set to $\varepsilon _{\text{FSI}}=10^{-4}$ for the L2 norm of the displacement differences.

• Unterrelaxation: To stabilize and speed up the FSI convergence a static unterrelaxation on the displacement is used. A constant underrelaxation factor of ω = 0.5 is considered for the displacements. The loads are transferred without underrelaxation.

Recommendations for Future Work

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Contributed by: Andreas Kalmbach, Guillaume De Nayer, Michael Breuer — Helmut-Schmidt Universität Hamburg

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