*2.1. Geometry and Mesh Generation*

Figure 2 illustrates the geometry of VGs used on the NREL S809 airfoil. The main VG parameters are *h* = 5 mm, *d*/*h* = 3.5, *D*/*h* = 7, *L*/*h* = 3, and β = 18◦, based on the VG design methodology [4,5]. Two chordwise locations are considered: *x*VG/*c* = 15% (single-row); *x*VG/*c* = 15% and 40% (double-row). *x*VG is measured between the leading edges of airfoil and VGs, and *c* is the airfoil chord length.

**Figure 2.** Schematic of the rectangular vane-type vortex generators in a counter-rotating configuration. (**a**) Isometric view; (**b**) planar view.

The present numerical modelling is essentially the same as that in our previous works [23,25]. Table 1 gives the main features of the mesh. The computational mesh includes only one pair of VGs (Figure 3), and the translational periodic boundary condition is used on spanwise boundaries. The mesh dependency study has been done by the General Richardson Extrapolation method [23]. The selected mesh with single-row VGs has about 1000 cells on each VG vane. There are 200 × 190 × 80 points in the wrap-around, normal, and spanwise directions, respectively. The Reynolds number is <sup>1</sup> <sup>×</sup> 106 (i.e., *<sup>c</sup>* <sup>=</sup> 0.457 m and *<sup>U</sup>*<sup>0</sup> <sup>=</sup> 33.68 m/s), where *<sup>U</sup>*<sup>0</sup> is the freestream velocity.

**Table 1.** Main features of the computational mesh.


**Figure 3.** Boundary-layer and surface mesh of the airfoil with single-row VGs.
