### Numerical simulation of multiple steady and unsteady flow modes in a medium-gap spherical Couette flow

Suhail Abbas, Li Yuan, Abdullah Shah
2019 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,
more » ... 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.