Effect of slip on vortex shedding from a circular cylinder in a gas flow

Most studies of vortex shedding from a circular cylinder in a gas flow have explicitly or implicitly assumed that the no-slip condition applies on the cylinder surface. To investigate the effect of slip, vortex shedding is simulated using molecular gas dynamics (the direct simulation Monte Carlo method) and computational fluid dynamics (the incompressible Navier-Stokes equations with a slip boundary condition). A Reynolds number of 100, a Mach number of 0.3, and a corresponding Knudsen number of 0.0048 are examined. For these conditions, compressibility effects are small, and periodic laminar vortex shedding is obtained. Slip on the cylinder is varied using combinations of diffuse and specular molecular reflections with accommodation coefficients from zero (maximum slip) to unity (minimum slip). Although unrealistic, bounce-back molecular reflections are also examined because they approximate the no-slip boundary condition (zero slip). The results from both methods are in reasonable agreement. The shedding frequency increases slightly as the accommodation coefficient is decreased, and shedding ceases at low accommodation coefficients (large slip). The streamwise and transverse forces decrease as the accommodation coefficient is decreased. Based on the good agreement between the two methods, computational fluid dynamics is used to determine the critical accommodation coefficient below which vortex shedding ceases for Reynolds numbers of 60–100 at a Mach number of 0.3. Conditions to observe the effect of slip on vortex shedding appear to be experimentally realizable, although challenging.

Figure 1

Conditions for simulating vortex shedding produced by a gas flow over a circular cylinder with slip.

Figure 2

Processes employed for molecular reflection from the cylinder surface.

Figure 3

DSMC force histories for bounce-back (left) and specular (right) molecular reflections. By a nondimensional time of ∼100, either periodic vortex shedding or steady flow is established.

Figure 4

DSMC (left) and CFD (right) force histories at late times with periodic vortex shedding. The frequency and the amplitude for both methods depend similarly on the amount of slip.

Figure 5

DSMC and CFD vortex-shedding frequencies versus accommodation. Both methods yield frequencies that increase similarly with increasing slip (decreasing accommodation).

Figure 6

DSMC and CFD forces versus accommodation. Both methods yield forces that decrease similarly with increasing slip (decreasing accommodation) relative to zero-slip values.

Figure 7

DSMC and CFD forces at $\mathrm{Ma}=0.3$ (left) and $\mathrm{Ma}=0.1$ (right) for an accommodation of unity. The frequencies and amplitudes agree more closely at lower Mach and Knudsen numbers.

Figure 8

DSMC (upper) and CFD (lower) velocity fields at $\mathrm{Ma}=0.1$ and unity accommodation.

Figure 9

CFD results for the saturation amplitude and the mean and steady recirculation lengths (points of zero velocity on the centerline) versus accommodation coefficient.

Figure 10

CFD results for the critical accommodation coefficient (below which vortex shedding ceases) and the recirculation length at this value (the neutral condition) as functions of the Reynolds number, with curves drawn to guide the eye.