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Experimental characterization of near transition region in rotating-disk boundary layer
Benoît Pier, Muhammad Ehtisham Siddiqui, Julian F. Scott, Lionel Le Penven, Alexandre Azouzi, Patrick Dutheil, Roger Michelet
To cite this version:
Benoît Pier, Muhammad Ehtisham Siddiqui, Julian F. Scott, Lionel Le Penven, Alexandre Azouzi, et
al.. Experimental characterization of near transition region in rotating-disk boundary layer. Euromech
Fluid Mechanics Conference 7, Sep 2008, Manchester, United Kingdom. �hal-00632342�
Experimental characterization of near transition region in rotating-disk boundary layer
Benoˆıt PIER
∗, M. Ehtisham SIDDIQUI
∗, Lionel LE PENVEN
∗, Julian SCOTT
∗, Alexandre AZOUZI
∗, Patrick DUTHEIL
∗, Roger MICHELET
∗The flow due an infinite disk rotating in otherwise still fluid has served as the archetypical configuration for the study of three-dimensional boundary layers and is known to display a sharp transition from laminar to turbulent flow at a nondimen- sional critical radiusR≃510. Using linear stability analysis, this location was found by Lingwood1 to precisely coincide with the onset of local absolute instability at Rca≃507. More recently2, a fully nonlinear analysis and a secondary stability analy- sis have further contributed to the understanding of the complex dynamics prevailing near the transition station.
The present experimental investigation has been undertaken to confront these theoretical results with detailed observations of the transition region.
The experimental arrangement consists of a 50 cm diameter disk that is rotated at constant angular speeds, up to 1500 rpm. Time-resolved local measurements of the azimuthal velocity component are performed by a constant temperature hot wire probe mounted on a two-axes traversing mechanism, achieving displacements in the radial and axial directions with a precision of 20µm and 2µm respectively.
Spectral analysis of the azimuthal velocity time series confirms that transition from the laminar boundary layer (flat spectra) to the turbulent r´egime (characteristic power laws) occurs near the radial locationR≃510. However, an intermediate weakly nonlinear r´egime has also been identified, characterized by a harmonic spectrum.
This r´egime is observed in the lower part of the boundary layer, close to the disk surface, starts around R≃470 and survives up toR≃530 (plots (1a) and (1b)). In contrast, above this near wall region, towards the outer edge of the boundary layer, the transition from laminar to turbulent r´egimes is seen to occur very suddenly over 500< R <510 (plot 1c). An interpretation of this intermediate r´egime in terms of linear and nonlinear instability waves will be proposed.
∗Laboratoire de m´ecanique des fluides et d’acoustique; CNRS—Universit´e de Lyon; ´Ecole centrale de Lyon; 36 avenue Guy-de-Collongue ; F-69134 ´Ecully cedex.
1Lingwood,J. Fluid Mech. 299, 17 (1995).
2Pier,J. Fluid Mech.487, 315 (2003).
(a)
1 102 104 106 108
0 100 200 ω/Ω
R= 550 540 530 520 510 510
500 490 480 470
(b)
1 102 104 106 108
0 100 200 ω/Ω
R= 550 540 530 520 510 520
510 500
(c)
1 102 104 106 108
0 100 200 ω/Ω
R= 550 540 530 520 510
Figure 1: Fourier power spectra of velocity time series at R= 460, 470, . . . , 550 for different positions within the boundary layer: (a) Z= 2, (b)Z = 3.5, (c)Z = 5.
