Numerical investigation of distinct flow modes in a wide-gap spherical annulus using OpenMP

Abstract

Spherical Couette flow (SCF) between two rotating concentric spheres has many applications in different fields of Mathematics, Physics, and Engineering. The transitions occurring in this flow phenomena have the relevancy with geophysical motions. In this paper, we use the time-dependent three-dimensional incompressible Navier–Stokes equations (3D-INSEs) to investigate distinct flow modes for a wide-gap clearance ratio (CR) . An Artificial Compressibility method has been used along with three implicit solvers, i.e. alternating direction implicit (ADI), line Gauss–Seidel (LGS), and point Gauss–Seidel (PGS). We apply the basic techniques of OpenMP to our Fortran code. First, we make a performance comparison of the three implicit solvers running on a single central processing unit (CPU) with that of the multi-core CPUs using Open Multi-Processing (OpenMP) to choose the best solver for the simulation of the SCF problem. The comparison shows that the ADI solver is the most efficient solver compared to LGS and PGS solvers. Using the most efficient parallel ADI solver, we compute distinct flow modes for this wide gap in a range of Reynolds number between . For this wide gap, first we obtain the basic 0-vortex flow (0-VF) at . By increasing the the flow becomes symmetric 1-vortex flow (1-VF) and asymmetric spiral 1-VF at and respectively. The flow returns back to super critical basic flow at . Further increasing the the flow becomes spiral 0-VF with m = 4 and m = 5 spiral waves at and respectively. Increasing the further the flow finally becomes turbulent. For this CR, we have first time numerically simulate these flow transitions from basic flow to super critical spiral basic flow with increasing . Abbreviations: ACM: artificial compressibility method; ADI: alternating directionimplicit; CPU: central processing unit; CR: clearance ratio; CVD: circumferentialvelocity distribution; INSEs: incompressible Navier–Stokes equations; LGS: lineGauss–Seidel; OpenMP: open multi-processing; PGS: point Gauss–Seidel; Re: Reynoldsnumber; SCF: spherical Couette flow; SG: spherical-gaps; TG: Taylor–Gortler; TVF:Taylor vortex flow; 0-VF: 0-vortex flow; 1-VF: 1-vortex flow; WENO: weightedessentially non-oscillatory.