Abstract
This paper presents a comprehensive investigation into flow past a circular cylinder where compressibility and rarefaction effects play an important role. The study focuses on steady subsonic flow in the Reynolds-number range 0.1–45. Rarefaction, or non-equilibrium, effects in the slip and early transition regime are accounted for using the method of moments and results are compared to data from kinetic theory obtained from the direct simulation Monte Carlo method. Solutions obtained for incompressible continuum flow serve as a baseline to examine non-equilibrium effects on the flow features. For creeping flow, where the Reynolds number is less than unity, the drag coefficient predicted by the moment equations is in good agreement with kinetic theory for Knudsen numbers less than one. When flow separation occurs, we show that the effects of rarefaction and velocity slip delay flow separation and will reduce the size of the vortices downstream of the cylinder. When the Knudsen number is above 0.028, the vortex length shows an initial increase with the Reynolds number, as observed in the standard no-slip continuum regime. However, once the Reynolds number exceeds a critical value, the size of the downstream vortices decreases with increasing Reynolds number until they disappear. An existence criterion, which identifies the limits for the presence of the vortices, is proposed. The flow physics around the cylinder is further analysed in terms of velocity slip, pressure and skin friction coefficients, which highlights that viscous, rarefaction and compressibility effects all play a complex role. We also show that the local Knudsen number, which indicates the state of the gas around the cylinder, can differ significantly from its free-stream value and it is essential that computational studies of subsonic gas flows in the slip and early transition regime are able to account for these strong non-equilibrium effects.
Highlights
IntroductionFlow past a stationary circular cylinder is a classical problem in fluid mechanics. the geometric configuration is relatively simple, the physics associated
Flow past a stationary circular cylinder is a classical problem in fluid mechanics. the geometric configuration is relatively simple, the physics associatedNon-equilibrium effects on flow past a circular cylinder with the flow around the cylinder exhibits a range of important phenomena, such as flow separation with attached eddies and the formation of the well-known vortex street
Macroscopic sets of the NSF, regularised 13 moment equations (R13) and regularised 26 moment equations (R26) equations are solved numerically for flows past a stationary cylinder with a wide range of Reynolds and Knudsen numbers determined by the free-stream parameters, u∞, T∞ and p∞
Summary
Flow past a stationary circular cylinder is a classical problem in fluid mechanics. the geometric configuration is relatively simple, the physics associated. Canuto & Taira (2015) performed direct numerical simulation of flow past a cylinder with moderate Reynolds and Mach numbers using the compressible Navier–Stokes equations. Their flow conditions lay in the range 0 < Kn 0.037 but rarefaction effects were not considered, which could result in an overprediction of both CD and the vortex size. With several extra macroscopic governing equations, the moment method is slightly more expensive than the NSF equations to solve numerically It is much more computationally efficient than the kinetic approaches and capable of capturing the non-equilibrium effects with a high degree of accuracy in the slip and early transition regime.
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