Numerical simulation of multiple steady and unsteady flow modes in a medium-gap spherical Couette flow
Journal of the Brazilian Society of Mechanical Sciences and Engineering
We study the multiple steady and unsteady flow modes in a medium-gap spherical Couette flow (SCF) by solving the three-dimensional incompressible Navier-Stokes equations. We have used an artificial compressibility method with an implicit line Gauss-Seidel scheme. The simulations are performed in SCF with only the inner sphere rotating. A mediumgap clearance ratio, = R 2 − R 1 ∕R 1 = 0.25, has been used to investigate various flow states in a range of Reynolds numbers, Re ∈ [400, 6500] . First,
... 00, 6500] . First, we compute the 0-vortex basic flow directly from the Stokes flow as an initial condition. This flow exists up to Re = 4900 after which it evolves into spiral 0-vortex flows with wavenumber s p = 3, 4 in the range Re ∈ [4900, 6000] , and then the flows become turbulent when Re > 6000 . Second, we obtain the steady 1-vortex flow by using the 1-vortex flow at Re = 700 for = 0.18 as the initial conditions and found that it exists for Re ∈ [480, 4300] . The 1-vortex flow becomes wavy 1-vortex in the range Re ∈ [4400, 5000] . Further increasing the Reynolds number, we obtain new spiral waves of wavenumber s p = 3 for Re ∈ [5000, 6000] . The flow becomes turbulent when Re > 6000 . Third, we obtain the steady 2-vortex flow by using the 2-vortex flow at Re = 900 for = 0.18 as the initial conditions and found that it exists for Re ∈ [700, 1900] . With increasing Reynolds number the 2-vortex flow becomes partially wavy 2-vortex in the small range Re ∈ [1900, 2100] . We obtain distorted spiral wavy 2-vortex in the range Re ∈ [4000, 5000] . when Re > 6000 the flow evolves into spiral 0-vortex flow and becomes turbulent. The present flow scenarios with increasing Re agree well with the experimental results and further we obtain new flow states for the 1-vortex and 2-vortex flows.