Geometrical effects on the airfoil flow separation and transition

Abstract

We present results from direct numerical simulations (DNS) of incompressible flow over two airfoils, NACA-4412 and NACA-0012-64, to investigate the effects of the airfoil geometry on the flow separation and transition patterns at Re = 10 4 and 10 degrees incidence. The two chosen airfoils are geometrically similar except for maximum camber (respectively 4%C and 0 with C the chord length), which results in a larger projection area with respect to the incoming flow for the NACA-4412 airfoil, and a larger leeward surface curvature at the leading edge for the NACA-0012-64 airfoil. The governing equations are discretized using an energy conservative fourth-order spatial discretization scheme. An assessment on the two-point correlation indicates that a spanwise domain size of 0.8C is sufficiently large for the present simulations. We dis- titative eigen-system analysis on the instantaneous velocity field shows that although the flow over an airfoil is intrinsically anisotropic, the alignments between the vorticity vector and the eigenvectors of S i j and S ik S k j + Ω ik Ω k j are quite similar to those of the homogeneous isotropic turbulent flows due to the formation of vortex tubes.

Assessment of spanwise domain size effect on the transitional flow past an airfoil

“…where Re = ρU 0 C/ν is the Reynolds number; ( code has been validated and used in previous work [51,52]. In the present study, the time step size is fixed at 2.5 × 10 flow, and then an additional 50C/U 0 for data acquisition and statistics.…”

“…The coefficient is normally computed by averaging over combinations of proven that fluctuations in the spanwise direction become uncorrelated when the aspect ratio is sufficiently large [3,23,28,30,51,52].…”

“…airfoil is rescaled to unit chord length C and extended to include a sharp trailing edge and 6C, which are confirmed to be sufficiently large for such simulations [43,51,52].…”

BiGlobal linear stability analysis on low-Re flow past an airfoil at high angle of attack

“…The simulations are performed using an in-house code that has been validated in our previous works. [16][17][18] The unsteady flow pattern is presented by the instantaneous vorticity field in Figure 2. The periodic shedding of the flow is clearly observed downstream of the airfoil.…”

“…However, the generalization is accompanied by the high computational cost which restricts this method in relatively simple geometries (e.g., the work of Tezuka and Suzuki 13 and Bagheri et al 14 ). For most numerical simulations of flow past an isolated airfoil or other configurations using either the high-fidelity DNS or the large-eddy simulation (LES) approach, the computational domain is normally assumed straight in the spanwise direction and periodic boundary condition is prescribed for all primitive variables (e.g., the work of Jones et al, 7 Kitsios et al, 15 Zhang et al, 16 and Zhang and Samtaney 17,18 ). The variation of the flow along the homogeneous spanwise (z-) direction is significantly weaker than the other two inhomogeneous directions, i.e., ∂φ/∂z ≪ ∂φ/∂ x and ∂φ/∂z ≪ ∂φ/∂ y in which φ is any flow variable.…”