2.6.1. Plasma Numbers

Critical Re must be determined through experiments or numerical simulations for each configuration. The maximum of *Ma*, Peclet number (Pe), Re, and Prandtl number (Pr), calculated in each cell of meshes for the whole of simulation time in an arc of 200 A, are shown in Figure 5. *Ma* is much less than 0.3. Pe, the product of the Re and Pr, is very large. The studied case is, however, similar to the flow inside a cylinder, where for 41 ≤ Re ≤ 10<sup>3</sup> an unsteady but predictable LF with counter-rotating vortices shed periodically from the cylinder is observed [81]. If Re > 103, vortices will be unstable, resulting in a turbulent wake behind the cylinder that is 'unpredictable' [81]. There is a transition to an entirely TF. As the stream begins to transfer to the turbulence regime, fluctuations appear in the flow, even though the inlet flow rate does not change with time. Then, it is no longer possible to assume time-invariant flow. So, it is compulsory to solve the time-dependent Navier-Stokes (TDNS) equations.

**Figure 5.** Maximum of cell Peclet number (Pe), Mach number (*Ma*), cell Reynolds number (Re), and cell Prandtl number (Pr) for the whole of simulation in 200 *Apeak* arc.
