Stability Calculations of the Three-Dimensional Boundary Layer Flow on a Rotating Disk

Structure of Absolute Instability in 3-D Boundary Layers: Part 2. Application to Rotating-Disk Flow.

“…1 that the maximumgrowth-rate curves (solid lines) obtained from spatial stability analysis break off nearly at R = 420; the broken lines from temporal theory show no singular behavior in the range of Reynolds numbers concerned. 4) This result indicates the appearance of singular points in the region of larger Reynolds numbers of rotating-disk flow, in accordance with the previous studies. 3,5) In this paper, therefore, attention is directed to the flow on a rotating disk, and investigation is made about whether absolute instability can occur in this three-dimensional flow.…”

“…As is well c 2001 The Japan Society for Aeronautical and Space Sciences known, the classical spatial theory of linear stability assigns real values of ω and β and determines a complex value of α, whose imaginary part α i indicates spatial damping rate in the positive X direction. The maximum-growth-rate curves then consist of disturbance components satisfying the relations 4) and will have an infinite gradient at the singular point where another condition…”

Stability Analysis of Rotating-Disk Flows with Uniform Suction

“…A comparison of the neutral curves of the parallel-flow theory 15) and those in this figure confirms again that the existence of curvature terms in the stability equations makes it possible to describe the S-C mode belonging to centrifugal instability.…”

“…6 as 258 and 50.6, respectively, which are slightly lower than the values R c ¼ 290, 282 and 284 for C-F mode given by Lingwood, 11) Itoh 12) and Pier, 13) and R c ¼ 69, 64 and 63 for the S-C mode by Faller,8) Balakumar and Malik 16) and Itoh,12) respectively, as well as the experimentally observed lower limits of C-F mode listed by Malik et al 17) However, the Orr-Sommerfeld equation gives R c ¼ 177 for the C-F mode, 15) which is much lower than the above non-parallel estimations. Since the present study restricts non-parallel terms only to those of the most fundamental activity in the multiple instabilities, it is reasonable that the equations proposed give a critical value midway between the parallel approach and the non-parallel attempts.…”

Transition to turbulence of the Batchelor flow in a rotor/stator device

“…More recently, and following the pioneer work of Lingwood [9], Serre et al [11] studied theoretically and numerically the transition from convective to absolute instability of these flows. Experimentally, Savas [12,13] followed by Itoh [14,15] were the first to visualize the different waves occurring in a rotor/stator system. The complete transition diagram was then built by Schouveiler, Le Gal & Chauve [16] as function of the ratio h/δ of the cavity and of the Reynolds number Re = ΩR 2 /ν (R being the radius of the disk).…”