Unsteady vortex shedding behind a circular cylinder
Compare Strouhal number and force coefficients against published experimental data at Re = 200.
Case type
Verification
Reynolds number
2.0 × 10² (dimensionless)
Solver
pimpleFoam (OpenFOAM v2312)
Turbulence model
2-D laminar (no model)
Mesh cells
48 000
Time scheme
Backward, second-order implicit
Research Motivation
Cylinder vortex shedding is one of the most studied benchmark problems in unsteady incompressible flow. A correct simulation must capture the Strouhal number and the time-averaged lift and drag coefficients within experimental scatter. This case serves as a sanity check for any new laminar solver setup.
Problem Statement
A rigid circular cylinder of diameter D is immersed in a uniform cross-flow at Reynolds number Re = 200. The flow is laminar, two-dimensional and unsteady. The objective is to predict the shedding frequency and mean hydrodynamic forces.
Geometry & Mesh
The computational domain extends 20D upstream, 40D downstream and 20D in the cross-flow direction. The cylinder surface is resolved with 240 points, and the outer boundary uses a characteristic boundary condition to minimize reflection.
Figure 1: Near-wall mesh refinement and wake region grading.
Mesh: 48 000 cellsSource: Demo
Boundary Conditions
Inlet velocity is fixed to U∞ = 1 m/s. The cylinder surface uses a no-slip wall. The top and bottom boundaries are symmetry planes. The outlet uses a zero-gradient pressure condition with a reference value of 0 Pa.
Results
The flow develops a stable von Kármán vortex street after approximately 15 convective times. The vorticity field shown in the hero image captures the alternating shedding pattern clearly.
Figure 2: Lift coefficient history used for Strouhal extraction via FFT.
Validation
The table below compares computed quantities against experimental and numerical references commonly cited for this Reynolds number. All values are dimensionless.
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Quantity
Reference source
Reference value
CFD value
Relative error
Result
Strouhal number St
Williamson & Roshko (1988)
0.195–0.200
0.197
1.0 %
Pass
Mean drag coefficient Cd
Tritton (1959)
1.31–1.36
1.34
1.5 %
Pass
RMS lift coefficient Cl'
Liu et al. (1998)
0.62–0.70
0.66
5.7 %
Pass
Data & Reproduction
The case files, post-processing scripts and figure data are provided below. This is demo content; downloads are placeholders.
