A control volume analysis is presented in this paper to analyze the jet effect on the coflow jet airfoil with injection and suction and on the airfoil with injection only. The formulations to calculate the duct's reactionary forces that must be included for the lift and drag calculation are given. The computational fluid dynamics solutions based on the Reynolds-averaged Navier-Stokes model are used to provide the breakdowns of lift and drag contributions from the airfoil surface force integral and jet duct's reactionary forces. The results are compared with experiment for validation. The duct reactionary forces are also validated with the result of a 3-D computational fluid dynamics calculation of the complete airfoil with jet ducts and wind tunnel walls. The study indicates that the suction occurring on the airfoil suction surface of the coflow jet airfoil is more beneficial than the suction occurring through the engine inlet such as the airfoil with injection only. For the airfoil with injection only, the drag actually acted on the aircraft, or the equivalent drag, is significantly larger than the drag measured by the wind tunnel balance due to the ram drag and captured area drag when the jet is drawn from the freestream. For a coflow jet airfoil, the drag measured by the wind tunnel balance is the actual 2-D drag that the aircraft will experience. A coflow jet airfoil does not have the ram drag and captured area drag. For a coflow jet airfoil, the suction penalty is offset by the significant circulation enhancement. The coflow jet airfoil with both injection and suction yields stronger mixing, larger circulation, more filled wake, higher stall angle of attack, less drag, and lower energy expenditure.

We present wall-resolved large-eddy simulations (LES) of flow over a smooth-wall circular cylinder up to $Re_{D}=8.5\times 10^{5}$, where $Re_{D}$ is Reynolds number based on the cylinder diameter $D$ and the free-stream speed $U_{\infty }$. The stretched-vortex subgrid-scale (SGS) model is used in the entire simulation domain. For the sub-critical regime, six cases are implemented with $3.9\times 10^{3}\leqslant Re_{D}\leqslant 10^{5}$. Results are compared with experimental data for both the wall-pressure-coefficient distribution on the cylinder surface, which dominates the drag coefficient, and the skin-friction coefficient, which clearly correlates with the separation behaviour. In the super-critical regime, LES for three values of $Re_{D}$ are carried out at different resolutions. The drag-crisis phenomenon is well captured. For lower resolution, numerical discretization fluctuations are sufficient to stimulate transition, while for higher resolution, an applied boundary-layer perturbation is found to be necessary to stimulate transition. Large-eddy simulation results at $Re_{D}=8.5\times 10^{5}$, with a mesh of $8192\times 1024\times 256$, agree well with the classic experimental measurements of Achenbach (J. Fluid Mech., vol. 34, 1968, pp. 625–639) especially for the skin-friction coefficient, where a spike is produced by the laminar–turbulent transition on the top of a prior separation bubble. We document the properties of the attached-flow boundary layer on the cylinder surface as these vary with $Re_{D}$. Within the separated portion of the flow, mean-flow separation–reattachment bubbles are observed at some values of $Re_{D}$, with separation characteristics that are consistent with experimental observations. Time sequences of instantaneous surface portraits of vector skin-friction trajectory fields indicate that the unsteady counterpart of a mean-flow separation–reattachment bubble corresponds to the formation of local flow-reattachment cells, visible as coherent bundles of diverging surface streamlines.

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.

We present large-eddy simulation (LES) of flow past different airfoils with$Re_{c}$, based on the free-stream velocity and airfoil chord length, ranging from$10^{4}$to$2.1\times 10^{6}$. To avoid the challenging resolution requirements of the near-wall region, we develop a virtual wall model in generalized curvilinear coordinates and incorporate the non-equilibrium effects via proper treatment of the momentum equations. It is demonstrated that the wall model dynamically captures the instantaneous skin-friction vector field on arbitrary curved surfaces at the resolved scale. By combining the present wall model with the stretched-vortex subgrid-scale model, we apply the wall-modelled LES approach to three different airfoil cases, spanning different geometrical parameters, different attack angles and low to high$Re_{c}$. The numerical results are verified with direct numerical simulation (DNS) at low$Re_{c}$, and validated with experiment data at higher$Re_{c}$, including typical aerodynamic properties such as pressure coefficient distributions, velocity components and also more challenging measurements such as skin-friction coefficient and Reynolds stresses. All comparisons show reasonable agreement, providing a measure of validity that enables us to further probe simulation results into aspects of flow physics that are not available from experiments. Two techniques to quantify hitherto unexplored physics of flows past airfoils are employed: one is the construction of the anisotropy invariant map, and the second is skin-friction portraits with emphasis on flow transition and unsteady separation along the airfoil surface. The anisotropy maps for all three$Re_{c}$cases, show clearly that a portion of the flow field is aligned along the axisymmetric expansion line, corresponding to the turbulent boundary layer log-law behaviour and the appearance of turbulent transition. The instantaneous skin-friction portraits reveal a monotonic shrinking of the near wall structure scale. At$Re_{c}=10^{4}$, the interaction between the primary separation bubble and the secondary separation bubble contributes to turbulent transition, similar to the case of flow past a cylinder. At higher$Re_{c}=10^{5}$, the primary separation breaks into several small separation bubbles. At even higher$Re_{c}=2.1\times 10^{6}$, near the turbulent separation, the skin-friction lines show small-scale reversal flows that are similar to those observed in DNS of the flat plate turbulent separation. A notable feature of turbulent separation in flow past an airfoil is the appearance of turbulence structures and small-scale reversal flows in the spanwise direction due to the vortex shedding behaviour.

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