The backward-facing step in a streamwise periodic channel as shown in Figure 1 is based on the
geometry given by Issa. The step height is S = 4.9 mm. A constant bulk velocity
UB = 0.14 m/s is forced by a constant volume force chosen as F = 0.4
m/s2. The dynamic viscosity of the fluid is 1.456e-5
kg/m/s, with a density of 1 kg/m3. With the hydraulic diameter D =
2*H1 of the channel above the step the Reynolds-Number of the flow is
Re = 100.Figure 1. Sketch of the Backward-Facing Step from Adami et al (lengths
in mm). See Adami
et al
Numerical Setup
Two particle resolutions are simulated, with a cutoff length rc°=°0.2*S
for the coarser and rc°=°0.1*S for the finer resolution. For the initial
particle configuration, the particles are distributed on a Cartesian grid. The walls
boundary conditions are imposed according to the methodology described by Adami et
al.
Results
In Figure 2 the flow in
the recirculation region behind the step is visualized with emphasis on the
recirculation bubble.Figure 2. Visualization of the Flow Behind the Step for the Fine
Resolution at Steady-State
The velocity profiles at the positions P1 to P4 (see Figure 1) are shown in
Figure 3. Both
simulations show very good agreement with the reference profiles by Issa.Figure 3. Velocity Profiles at the Reference Positions P1 to P4 (from
left to right)
S. Adami, H. Hu and N. Adams, "A generalized wall
boundary condition for smoothed particle hydrodynamics," Journal of
Computational Physics, vol. 231, pp. 7057-7075, 2012.
R. Issa, Numerical assessment of smoothed particle
hydrodynamics gridless method for incompressible flows and its extension to
turbulent flows, PhD Thesis: University of Manchester, 2005.
S. Adami, X. Hu and N. Adams, "A transport-velocity
formulation for smoothed particle hydrodynamics," Journal of Computational
Physics, vol. 241, pp. 292-307, 2013.
