On the disturbance evolution downstream of a cylindrical roughness element

Abstract

Roughness-induced transition is one of the main parameters contributing to performance loss of airfoils. Within this paper, the disturbance evolution downstream of a single, cylindrical roughness element, which is placed in a laminar boundary layer in an airfoil leading edge region, is investigated. The experiments focus on medium height roughness elements with respect to the local boundary layer displacement thickness. Hence, transition is not directly tripped at the roughness element. The roughness diameter is comparable to the streamwise wavelength of the most amplified (linear) disturbance eigenmodes. The vortical structures observed downstream of the roughness are in agreement with previous findings in the literature. In the near roughness wake, a distinct growth of high-frequency (fundamental) modes, that is modes with a high n-factor at the roughness location, is observed. In the far roughness wake, these fundamental modes recover linear stability characteristics due to a possible relaxation of the mean flow. However, an interaction of particularly two-dimensional fundamental modes and by the roughness interference excited oblique fundamental modes results in an excitation of subharmonic type, low-frequency combination modes, which are associated with a phase-locked interaction mechanism. Depending on the initial growth of the fundamental modes in the near wake, the low-frequency modes can experience a nonlinear growth in the far roughness wake and, thereby, trip turbulence. The fundamental mode growth rate in the near wake in turn is a weak function of the disturbance frequency and of the pressure gradient, whereas it is decisively increasing with the roughness height, that is with the mean flow distortion caused by the roughness.

Nonlinear Mode Interactions in the Wake of a Medium Height Roughness Element

“…In order to ensure phase synchronism for the disturbance excitation the same clock is used for all 128 channels of the signal generator. In the reference case (zero roughness height), the streamwise evolution of the excited TS-waves complies well with linear theory within the measurement domain 16 . At the roughness position, the standard deviation of the TS-wave amplitude and phase in spanwise direction is 8% of the mean amplitude and 6.8 • for the TS-wave phase, i.d.…”

“…An effective contraction ratio of 20:1 and several screens in the inlet section lead to a low longitudinal turbulence level of T u x = 0.02 % for a frequency range of f = 10 − 5000 Hz and a free stream velocity of u ∞ = 30 m/s. The closed test section has a cross section of 0.73 × 2.73 m 2 and a length of 3.15 m. The diffusor section is equipped with noise absorbing foam substantially reducing the background noise level in the test section 13 . During the measurements the free stream velocity and not the Reynolds number was kept constant due to the quadratic influence of the nondimensional frequency parameter F = 2π f ν/u 2 ∞ on the free stream velocity (with ν being the kinematic viscosity).…”

Investigation on the wake flow instability behind isolated roughness elements on the forebody of a blunt generic reentry capsule

“…However, the amplitude in the favourable pressure gradient (FPG) case is slightly lower compared with the zero (ZPG) and adverse pressure (APG) cases. For the far wake region (s/d > 4), the authors report that the leading mode is damped in the FPG case, whereas in the ZPG and APG cases, the amplitude remains at a nearly constant level before being slightly damped [30]. A stabilizing in §uence of the FPG is also mentioned in [9].…”

“…The distinct decay of the dominant wake modes is most likely attributed to the strong favourable pressure gradient. Recently, Plogmann et al [30] experimentally investigated the e¨ect of di¨erent pressure gradients on the mode amplitudes behind a cylindrical roughness element. The authors reveal that in the near wake of the roughness (s/d < 4), the amplitude of the leading mode is very weakly dependent on the pressure gradient.…”

Verification and validation of a Direct Numerical Simulation code

“…An increasing instability leads to transition to turbulence. Experimental and numerical studies are being used to explain and predict this phenomenon [7][8][9][10].…”