Large–Eddy Simulation of the Flow Inside a Scour Hole Around a Circular Cylinder Using a Cut Cell Immersed Boundary Method

Abstract

We present a novel symmetry-preserving cut cell finite volume method which is a three-dimensional generalisation of the method by Dröge and Verstappen (Int J Numer Method Fluids 47:979–985, 2005). A colour-coding scheme for the three-dimensional cut momentum cell faces reduces the number of possible cut cell configurations. A cell merging strategy is employed to alleviate time step constraints. We demonstrate the energy conservation property of the convective and pressure gradient terms, and the second-order spatial convergence with suitable benchmark cases. We used the scheme to perform highly resolved large–eddy simulations of the flow inside a scour hole around a circular cylinder mounted vertically in a flume. The simulation results are extensively compared to a stereoscopic particle image velocimetry experiment of the same configuration performed by Jenssen and Manhart (Exp Fluids 61:217, 2020). We demonstrate that for the investigated Reynolds numbers (20,000 and 40,000) nearly converged solutions are obtained; however at large computational efforts (up to 2.35 billion cells for the higher Reynolds number). It turns out that the flow topology of the horseshoe vortex system is strongly dependent on the grid resolution. For simulation results obtained on the finest grid, the mean flow and turbulence quantities agree well with the experiment. We investigate the shape and turbulence structure of the horseshoe vortex based on three-dimensional fields, and discuss the distribution of the mean and standard deviation of the wall shear stress in the scour hole and the implications for the physics of the scouring process over a sand bed.

Flow topology in the gap and wake of convex curved tandem cylinders

“…MGLET is based on a finite volume formulation of the incompressible Navier-Stokes equations, and uses a staggered Cartesian grid (Manhart 2004). Solid bodies are introduced through an immersed boundary method (Peller et al 2006), where the boundary is discretised using a cut-cell approach (Unglehrt et al 2022). A third-order low-storage explicit Runge-Kutta time integration scheme is used for time stepping, and the Poisson equation is solved using an iterative, strongly implicit procedure.…”

“…2006), where the boundary is discretised using a cut-cell approach (Unglehrt et al. 2022). A third-order low-storage explicit Runge–Kutta time integration scheme is used for time stepping, and the Poisson equation is solved using an iterative, strongly implicit procedure.…”