Search Results (3)

A transient stability flow analysis is performed using the unsteady laminar boundary layer equations. The flow dynamics are studied via the Navier–Stokes equations. In the case of external spatially developing flow, the differential equations are reduced via Prandtl or boundary-layer assumptions, consisting of continuity and momentum conservation equations. Prescription of streamwise pressure gradients (decelerating and accelerating flows) is carried out by an impulsively started Falkner–Skan (FS) or wedge-flow similarity flow solution in the case of flat plate or a Blasius solution for particular zero-pressure gradient case. The obtained mean streamwise velocity and its derivatives from FS flows are then inserted into the well-known Orr–Sommerfeld equation of small disturbances at different dimensionless times ($\tau$). Finally, the corresponding eigenvalues are dynamically computed for temporal stability analysis. A finite difference algorithm is effectively applied to solve the Orr–Sommerfeld equations. It is observed that flow acceleration or favorable pressure gradients (FPGs) lead to a significantly shorter transient period before reaching steady-state conditions, as the developed shear layer is notably thinner compared to cases with adverse pressure gradients (APGs). During the transient phase (i.e., for $\tau <1$), the majority of the flow modifications are confined to the innermost 20–25% of the boundary layer, in proximity to the wall. In the context of temporal flow stability, the magnitude of the pressure gradient is pivotal in determining the streamwise extent of the Tollmien–Schlichting (TS) waves. In highly accelerated laminar flows, these waves experience considerable elongation. Conversely, under the influence of a strong adverse pressure gradient, the characteristic streamwise length of the smallest unstable wavelength, which is necessary for destabilization via TS waves, is significantly reduced. Furthermore, flows subjected to acceleration ($\beta$ > 0) exhibit a higher propensity to transition towards a more stable state during the initial transient phase. For instance, the time response required to reach the steady-state critical Reynolds number was approximately 1$\tau$ for $\beta$ = 0.18 (FPG) and $\tau$ = 6.8 for $\beta$ = −0.18 (APG). Full article

A high-fidelity computational analysis carefully validated against concurrently obtained experimental results is employed to examine self-noise radiation of airfoils at transitional flow regimes, with a focus on elucidating the connection between the unsteady behavior of the laminar separation bubble (LSB) and the acoustic feedback-loop (AFL) resonant interactions observed in the airfoil boundary layers. The employed parametric study examines AFL sensitivity to the changes in the upstream flow conditions and the airfoil loading. Implicit Large-Eddy Simulations are performed for a NACA-0012 airfoil in selected transitional-flow regimes for which experimental measurements recorded characteristic multiple-tone acoustic spectra with a dual ladder-type frequency structure. The switch between the tone-producing and no-tone-producing regimes is traced to the LSB size and position as a function of the flow Reynolds number and the airfoil angle of attack, and further substantiated by the linear stability analysis. The results indicate a strong multi-tonal airfoil noise radiation associated with the AFL and attributed to the switch from the slowly-growing Tollmien–Schlichting to the fast-growing Kelvin–Helmholtz instabilities occurring in thin LSB regions when those are localized near the trailing-edge (TE) on either side of the airfoil. Such a process eventually results in the nonlinearly saturated flapping vortical modes (“rollers”) that scatter into acoustic waves at the TE. Full article

We discuss herein recent experimental and numerical studies examining resonant flow-acoustic feedback–loop interactions in transitional airfoils (i.e., possessing a notable area of laminar-to-turbulent boundary-layer transition) characteristic of low-to-medium Reynolds number flow regimes. Such interactions are commonly attributed to the viscous dynamics of the convected boundary-layer structures scattering into acoustic waves at the trailing edge which propagate upstream and re-excite the convected vortical structures. While it has been long suspected that the acoustic feedback mechanism is responsible for the highly pronounced, often multi-tonal response, the exact reason of how the boundary-layer instability structures could reach a sufficient degree of amplification to sustain the feedback-loop process and exhibit specific tonal signature remained unclear. This review thus pays particular attention to the critical role of the separation bubble in the feedback process and emphasizes the complementary roles of the experimental and numerical works in elucidating an intricate connection between the airfoil radiated tonal acoustic signature and the properties of the separation zones as determined by airfoil geometry and flow regimes. Full article