Experimental study of rotating-disk boundary-layer flow with surface roughness

Abstract

Rotating-disk boundary-layer flow is known to be locally absolutely unstable at R > 507 as shown by Lingwood (J. Fluid Mech., vol. 299, 1995, pp. 17-33) and, for the clean-disk condition, experimental observations show that the onset of transition is highly reproducible at that Reynolds number. However, experiments also show convectively unstable stationary vortices due to cross-flow instability triggered by unavoidable surface roughness of the disk. We show that if the surface is sufficiently rough, laminar-turbulent transition can occur via a convectively unstable route ahead of the onset of absolute instability. In the present work we compare the laminarturbulent transition processes with and without artificial surface roughnesses. The differences are clearly captured in the spectra of velocity time series. With the artificial surface roughness elements, the stationary-disturbance component is dominant in the spectra, whereas both stationary and travelling components are represented in spectra for the clean-disk condition. The wall-normal profile of the disturbance velocity for the travelling mode observed for a clean disk is in excellent agreement with the critical absolute instability eigenfunction from local theory; the wall-normal stationary-disturbance profile, by contrast, is distinct and the experimentally measured profile matches the stationary convective instability eigenfunction. The results from the clean-disk condition are compared with theoretical studies of global behaviours in spatially developing flow and found to be in good qualitative agreement. The details of stationary disturbances are also discussed and it is shown that the radial growth rate is in excellent agreement with linear stability theory. Finally, large stationary structures in the breakdown region are described.

Relation Between Convective Instability and Global Instability on a Rotating Disk

“…(6). The distribution matches very well with the experimental data of Imayama et al [21]. xp(αRe), where α is the growth rate.…”

“…The finding that the wavenumber and the frequency are both 32 indicates that the 32 spiral vortices are stationary with respect to the disk surface, which is consistent with the previously reported experimental results. Both in our computation, in which the flow field was excited by artificial disturbance at an upstream location of Re ~ 255, and the experimental data of Imayama et al [20,21], in which the disturbance was only naturally provided from the disk surface, the velocity fluctuations were stationary with respect to the disk surfaces and their wavenumbers or the number of spiral vortices were similar. It can be judged that the velocity fluctuation in this computation grew by the convective instability as in experiments.…”

“…According to the theoretical study by Malik [9], the critical Reynolds number for the stationary cross-flow convective type instability is 285.36. In experimental studies, 28 ~ 32 spiral vortices are observed [20,21]. In experiments, because of minute roughness on the disk surfaces, stationary disturbances are always supplied.…”

On the global nonlinear instability of the rotating-disk flow over a finite domain

“…For r > r end the flow will have entered the nonlinear region and r end thus separates the linear and nonlinear regions. In experiments, Imayama et al (2013) defined the transitional Reynolds number (also including Imayama et al 2012Imayama et al , 2014Imayama et al , 2016 from their power spectra where the first harmonic of the stationary vortices reaches an amplitude of 10 −6 . Using this threshold for the onset of nonlinearity in our simulations, it will be shown that the first harmonics of the travelling disturbances reach the same amplitude in our corresponding spectra at our position r end .…”

Boundary-layer transition over a rotating broad cone

“…[5]. Slightly later the transition scenario on the disk was further investigated experimentally [6] and via direct numerical simulations [7], and it was conjectured that an absolute secondary instability on top of the primary vortices was likely to be the trigger for transition.…”