Direct numerical simulations were performed to investigate the behavior of laminar separation bubbles subject to vertical gusts in an airfoil flow. Oscillating boundary-layer flows containing gusts—including unsteady pressure gradients—were prescribed via boundary conditions as well as forcing terms on a domain located in the upper rear section of a natural laminar flow airfoil. For this hybrid approach, unsteady Reynolds-averaged Navier-Stokes (URANS) simulations of the entire flowfield were carried out in conjunction with the so-called disturbance velocity approach, providing transient boundary conditions for the direct numerical simulation. A steady-state reference case with a Reynolds number of [Formula: see text] is compared and validated with results from wind tunnel experiments. Results of simulations at four different gust frequencies [Formula: see text] at the same amplitude [Formula: see text], each with and without additional disturbances to the boundary layer introducing oblique resonance, are presented and discussed in this paper. The time-dependent behavior of convective instability modes is evaluated by using the continuous wavelet transform and linear stability theory with an unsteady extension. Furthermore, the contribution of the absolute instability—which appears to be larger in the case of oscillating flow compared to the steady-state case—is discussed. Lock-in effects are identified at high gust frequencies.
Wind tunnel investigations of how Natural Laminar Flow (NLF) airfoils respond to atmospheric turbulence require the generation of turbulence, whose relevant characteristics resemble those in the atmosphere. The lower, convective part of the atmospheric boundary layer is characterized by low to medium levels of turbulence. The current study focuses on the small scales of this turbulence. Detailed hot-wire measurements have been performed to characterize the properties of the turbulence generated by grids mounted in the settling chamber of the Laminar Wind Tunnel (LWT). In the test section, the very low base turbulence level of Tuu ≅ 0.02% (10 ≤ f ≤ 5000 Hz) is incrementally increased by the grids up to Tuu ≅ 0.5%. The turbulence spectrum in the u-direction shows the typical suppression of larger scales due to the contraction between grids and test section. Still, the generated turbulence provides a good mapping of the spectrum measured in flight for most of the frequency range 500 ≤ f ≤ 3000 Hz, where Tollmien-Schlichting (TS)-amplification occurs for typical NLF airfoils. The spectra in v and w-direction exhibit distinct inertial subranges with slopes being less steep compared to the − 5/3 slope of the Kolmogorov spectrum. The normalized spectra in u-direction collapse together well for all grids, whereas in v- and w-directions the inertial- and dissipative subranges are more clearly distinguished for the coarser grids. It is demonstrated that the dissipation rate ε is a suitable parameter for comparing the wind tunnel turbulence with the atmospheric turbulence in the frequency range of interest. By employing the grids, turbulence in the range 4.4 × 10–7 ≤ ε ≤ 0.40 m2/s3 at free-stream velocity U∞ = 40 m/s can be generated in the LWT, which covers representative dissipation rates of free flight NLF applications. In the x-direction, the spectra of the v and w-components develop progressively more pronounced inertial- and dissipative subranges, and the energy below f ≈ 400 Hz decreases. In contrast, the spectral energy of the u-component increases across the whole frequency range, when moving downstream. This behavior can be explained by the combination of energy transport along the Kolmogorov cascade and the incipient return to an isotropic state. Graphic Abstract
Natural laminar flow airfoils have achieved such a level of refinement that further optimisation and subsequent wind tunnel testing need to regard the specific free-stream turbulence to be expected during operation. This requires the characterisation of this turbulence in terms of those properties which are relevant for boundary layer receptivity and subsequent transition. These parameters of turbulence change with environmental conditions and, in case of aircraft, along the flight profile. This study investigates the free-stream turbulence relevant for the case of sailplane airfoils. In-flight measurements with a constant temperature anemometer x-wire probe were conducted during cross-country flights in Central Europe and provided 22 h of flight data, covering thermalling phases as well as straight flight legs. Longitudinal and transversal velocity fluctuations were recorded well into the dissipation range. The special challenges of operating a constant temperature anemometer probe continuously for several hours are addressed. The permanent unsteadiness of the inflow poses challenges for the evaluation, but also provides a broad database of measured turbulence levels. The quality of the measurements is shown by verifying some of the predictions of Kolmogorov's inertial range theories. Free-stream turbulence in thermalling phases is sufficiently homogeneous to be described accurately, as the dissipation range fluctuates only in a limited range and follows a log-normal distribution. On the straight flight legs, the turbulence depends on the convective activity along the flight path. In general, within the convective part of the atmosphere, turbulence levels are found to be significantly larger than in low-turbulence wind tunnels. Graphical abstract
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