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SUMMARY:Transient growth induced by surface roughness in a Blasius boundar
 y layer - Lavioe\, P (Toronto)
DTSTART:20080910T105000Z
DTEND:20080910T111000Z
UID:TALK13356@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Introduction There has been much recent interest in transient 
 growth both theoretically [1-4] and experimentally [2\,5]. The present wor
 k stems from an interest in model reduction for flow control: starting wit
 h a linear physical model representative of near-wall turbulence\, the aim
  of this experiment is to devise a wall-based estimator. The inviscid tran
 sient growth instability has an optimal form of spanwise periodic streamwi
 se vortices resulting in high/low  speed streaks. Slow growth and decay in
  x and spanwise periodicity suggest a reduced requirement for mode observa
 bility. Equations (1) and (2) describe the generation of optimal modes thr
 ough the coupling term\, \, viz. \n\nExperimental Arrangement The Blasius 
 base flow is developed on a vertical cast aluminium plate with a sharp lea
 ding edge in a very low-turbulence intensity (around 0.05%) wind tunnel. A
  periodic array of roughness elements at 200 mm from the leading edge is u
 sed to perturb the base state and introduces steady steamwise vortex pairs
  approximating the optimum mode. The height\, k\, spanwise separation\, Δ
 z and diameter\, d\, of the roughness elements are all adjustable. For the
  present work\, 0.5 ≤ k ≤ 1.5\, 10 ≤ Δz ≤ 30 and 2.5 ≤ d ≤ 5.
 0 mm and the measurements are conducted over the central six elements. Two
  hot wires\, one normal and one slanted by 45 degrees to the mean flow\, a
 re used to obtain u and w in the range 250 ≤ x ≤ 700 mm. \n\nResults a
 nd Discussion Figure 1 present typical results for these experiments. Figu
 re 1(a) shows the u-disturbance spectra as a function of spanwise-wavenumb
 er. The spectrum is taken at the wall-normal location where the maximum rm
 s of the disturbance occurs below that predicted by theory [3]. For this c
 ase\, the first harmonic of the disturbance introduced is discernible for 
 the first four streamwise locations. The energy of the disturbance is obse
 rved to grow at the first streamwise location and peaks when eta is equal
  to 0.45 before it decays monotonically. Figures 1(b) and (c) show the cor
 responding disturbance contours at x = 300. The double positive peaks in t
 he u-disturbance merge into a single peak further downstream of the roughn
 ess elements. The shape of the w-disturbance is more complicated and sugge
 sts that the streamwise vortices produced by the roughness elements are ve
 ry weak by this location. \n\nThe u-component of the disturbance shows the
  effects of a spanwise shear at larger x\, the shear increasing with strea
 k amplitudes. In common with other experiments [2\,5]\, the evolution of t
 he disturbance shows significant deviation to that predicted by theory\, s
 uggesting a suboptimal initial growth. This raises questions regarding the
  receptivity mechanism of laminar boundary layers subjected to different t
 ypes of perturbations\, such as free stream turbulence or wall roughness [
 6]. In future work\, we intend to investigate this further as well as esti
 mating the v component from continuity. Simultaneous measurements of the t
 wo components of surface skin friction will also be made to enable the des
 ign of an estimator for control by surface deformation. \n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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