Investigation of Flow Structures around surface mounted cylinders (bridge piers) on flat beds or deformed beds corresponding to equilibrium scour conditions using Large Eddy Simulation (LES).

In this study, large eddy simulation (LES) is used to investigate the horseshoe vortex (HV) system together with unsteady wake around a circular cylinder mounted on a bed surface. The goal is to investigate the fundamental physical phenomena present in this flow, focusing on the characterization of the structure of the HV system under different flow conditions (e.g., laminar vs. turbulent incoming boundary layer, flat bed corresponding to conditions at the start of the scouring process vs. deformed bed corresponding to equilibrium conditions at the end of the scour process in the case of loose beds).

A recently developed massively parallel LES flow solver (Mahesh, Constantinescu and Moin, JCP 2004) is used in this work.  The finite-volume solver uses a predictor-corrector formulation which discretely conserves energy on unstructured grids.  This property insures robustness at high Reynolds numbers without introduction of numerical dissipation (central discretizations are used for all terms including the convective ones in the momentum equations).  The dynamic Smagorinsky sub-grid scale model is used to account for turbulence effects.  Thus, the model does not contain any adjustable constant.

Three cases are considered.  In all of them the depth of the channel away from the scour area is 1.2D, D is the cylinder diameter.  The mesh size is close to 5 million cells in all these simulations.  It contains only hexahedra but the topology is unstructured (a paving technique was used to maintain high mesh quality).

Figure: Computational mesh (mesh_view_1.tif  and mesh_viev_2.tif)

(1) Circular cylinder is located on flat bed and inlet velocity profile is laminar. Reynolds number defined with the mean upstream channel velocity and cylinder diameter is Re=5,000 (Case 1).

(2) Circular cylinder is located on flat bed and inlet velocity profile is fully turbulent (instantaneous velocity fields from a previous LES simulation in a periodic channel are fed through inlet section). Re=18,000 (Case 2).

(3) The circular cylinder is located on scoured bed corresponding to equilibrium conditions.  Inlet velocity profile is fully turbulent. The deformed bed bathymetry is obtained from experiments. Re=18,000 (Case 3).  
 

Case 1

Figure: General view of the computational domain.  (def_sketch.jpg)

Figure: Horseshoe vortices in the laminar breakaway regime visualized by instantaneous 3-D streamlines.  (Horseshoe_ribbon.jpg)

Movie: Animation showing the streamlines and out-of-plane vorticity contours at several planes cutting through the main coherent structures part of the horseshoe vortex system. (4_planes_str_vor.avi)

Figure.  Structure of periodic horseshoe vortex system (str_in_period_3.tif)

Movie: Animation showing the dynamics of horseshoe vortices in a plane parallel to bed cutting through the cores of the main HV.  Contours of in-plane vorticity and vertical velocity are used to visualize these structures.  (horseshoe_cut_black&white.avi)
 

Case 2

Figure: General view of the computational domain. (domain_view_ext_abst.jpg)

Movie: Animation showing the evolution of HV system in five azimuthal planes around cylinder using 2-D streamlines and out-of-plane vorticity contours a) f=0; b) f=30; c)f=45; d)f=60; e) f=90. (flat_bed_5_planes_turb.avi)

Movie: Animation showing the shedding of vortex tubes from detached shear layers in near-wake of the cylinder in different horizontal planes starting from the free surface (y/D=1.2). (flat_bed_6_y_planes_turb.avi)

Movie: Visualization of horseshoe vortex system around cylinder (flat_bed_turb_horseshoe_cut..)

Movie: Animation showing the large scale vortex shedding using eddy viscosity contours. (flat_bed_turb_y_plane_shed…)

Figure: Friction velocity contours on the bed a) instantaneous; b) mean. c) Mean bed shear stress contours. (y_0_0017_inst_mean_utau_c…)

Figure: R.m.s. of resolved pressure fluctuations & resolved turbulent kinetic energy in planes a) f=0; b) f=30; c) f=60; d) f=90 showing the extent of the horseshoe vortex system at the base of the cylinder. (stat_4_planes.jpg)
 

Case 3

Figure:  Bed bathymetry corresponding to equilibrium conditions (pier_def_bed_view.tif)

Figure: Horseshoe vortices visualized with 3-D streamlines (horseshoe_ribbon.jpg and horseshoe_def.tif).

Figure: Contours of vertical velocity in a plane parallel to the bed (z/D=0.07) used to visualize interaction between the legs of the horseshoe vortices, the detached shear layers and wake behind cylinder. (def_bed_zd_0_31_plane…)

Movie: Animation showing the evolution of the horseshoe vortex inside the scour hole in symmetry plane.  (plane_y_0.avi)

Movie: Animation showing the distribution of bed shear velocity near the cylinder. (shr_stress_turb_def.avi)

Figure: Bed shear velocity time series for two points situated in the scour region showing large variability of instantaneous values around the mean. (shear_vel_time_series.jpg)