Simulation And Instability Study Of The Flow Around Circular Cylinder

Two-dimensional flows around a circular cylinder are simulated with Computational FluidDynamics (CFD). The flows between two parallel walls at Re=26,100and flows in infinitedomain at Re=40,100are calculated respectively, when the flows of entire flow field arelaminar. The flows with secondary vortex street in infinite domain at Re=200and flows ininfinite domain at Re=200and400are simulated with large-eddy simulation respectively. Thecalculating results are compared with numerical results and experimental results in literatureand they are in good agreement. The instability of entire flow field is analyzed with the energygradient theory based on the simulation results calculated above, and conclusions obtained areas follows:(1) The criterion for pressure driven flow proposed in the energy gradient theory isvalidated, i.e., for pressure driven flow, the sufficient and necessary condition of turbulenttransition is the existence of inflection point in time average velocity profile.(2) The criterion for shear driven flow proposed in the energy gradient theory is validated,i.e., for shear driven flow, the sufficient and necessary condition of turbulent transition is theexistence of zero velocity gradients in time average velocity profile.(3) Two eddies attached at rear of the cylinder have no effect on the flow stability, when theflows between two parallel walls and in infinite domain are in steady state.(4) For the flow between two parallel walls, the flow instability in the cylinder wakeoriginates from the absolute instability in the cylinder near wake and the interaction of twoshear layers. For the flow in infinite domain, the flow instability originates from the interactionof two shear layers.(5) For the pressure driven flow and shear driven flow with Karman vortex street in thecylinder wake, the region inner a vortex firstly loses its stability. It is the inflection point(pressure driven flow) and zero velocity gradients (shear driven flow) in time average velocityprofile inner a vortex that lead to the instability.(6) It is the mechanical energy gradient that dominates the decay and disappearance ofprimary vortex street in the cylinder wake. The interaction of mechanical energy gradient and disturbance in the wake leads to the formation of secondary vortex street in the cylinder farwake.(7) The energy gradient theory is applicable to study the flow stability, including turbulenttransition and the change of flow state, for example, the flow in the cylinder wake transits tounsteady state from the steady state.