On the laminar-turbulent transition of the rotating-disk flow: the role of absolute instability

被引:37
作者
Imayama, Shintaro [1 ]
Alfredsson, P. Henrik [1 ]
Lingwood, R. J. [1 ,2 ]
机构
[1] KTH Mech, Linne Flow Ctr, SE-10044 Stockholm, Sweden
[2] Univ Cambridge, Inst Continuing Educ, Cambridge CB23 8AQ, England
基金
瑞典研究理事会;
关键词
absolute/convective instability; boundary layer stability; transition to turbulence; BOUNDARY-LAYER-TRANSITION; SECONDARY INSTABILITY; GLOBAL-MODES; VORTICES; STABILITY;
D O I
10.1017/jfm.2014.80
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
This paper describes a detailed experimental study using hot-wire anemometry of the laminar-turbulent transition region of a rotating-disk boundary-layer flow without any imposed excitation of the boundary layer. The measured data are separated into stationary and unsteady disturbance fields in order to elaborate on the roles that the stationary and the travelling modes have in the transition process. We show the onset of nonlinearity consistently at Reynolds numbers, R, of similar to 510, i.e. at the onset of Lingwood's (J. Fluid Mech., vol. 299, 1995, pp. 17-33) local absolute instability, and the growth of stationary vortices saturates at a Reynolds number of similar to 550. The nonlinear saturation and subsequent turbulent breakdown of individual stationary vortices independently of their amplitudes, which vary azimuthally, seem to be determined by well-defined Reynolds numbers. We identify unstable travelling disturbances in our power spectra, which continue to grow, saturating at around R = 585, whereupon turbulent breakdown of the boundary layer ensues. The nonlinear saturation amplitude of the total disturbance field is approximately constant for all considered cases, i.e. different rotation rates and edge Reynolds numbers. We also identify a travelling secondary instability. Our results suggest that it is the travelling disturbances that are fundamentally important to the transition to turbulence for a clean disk, rather than the stationary vortices. Here, the results appear to show a primary nonlinear steep-fronted (travelling) global mode at the boundary between the local convectively and absolutely unstable regions, which develops nonlinearly interacting with the stationary vortices and which saturates and is unstable to a secondary instability. This leads to a rapid transition to turbulence outward of the primary front from approximately R = 565 to 590 and to a fully turbulent boundary layer above 650.
引用
收藏
页码:132 / 163
页数:32
相关论文
共 38 条
[1]   SECONDARY INSTABILITY IN ROTATING-DISK FLOW [J].
BALACHANDAR, S ;
STREETT, CL ;
MALIK, MR .
JOURNAL OF FLUID MECHANICS, 1992, 242 :323-347
[2]   TURBULENT BOUNDARY-LAYER FLOW ON A ROTATING DISK [J].
CHAM, TS ;
HEAD, MR .
JOURNAL OF FLUID MECHANICS, 1969, 37 :129-&
[3]   Experiments on secondary instability of streamwise vortices in a swept-wing boundary layer [J].
Chernoray, VG ;
Dovgal, AV ;
Kozlov, VV ;
Löfdahl, L .
JOURNAL OF FLUID MECHANICS, 2005, 534 :295-325
[4]   Global instabilities in spatially developing flows: Non-normality and nonlinearity [J].
Chomaz, JM .
ANNUAL REVIEW OF FLUID MECHANICS, 2005, 37 (37) :357-392
[5]   Stationary travelling cross-flow mode interactions on a rotating disk [J].
Corke, TC ;
Knasiak, KF .
JOURNAL OF FLUID MECHANICS, 1998, 355 :285-315
[6]  
DAGENHART J. R., 1999, NASA TECH PUB
[7]   Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer [J].
Davies, C ;
Carpenter, PW .
JOURNAL OF FLUID MECHANICS, 2003, 486 :287-329
[8]   INSTABILITY AND TRANSITION OF DISTURBED FLOW OVER A ROTATING-DISK [J].
FALLER, AJ .
JOURNAL OF FLUID MECHANICS, 1991, 230 :245-269
[9]  
GARRETT S. J., 2012, P 28 ICAS C 2012 BRI, P1
[10]   ON THE STABILITY OF 3-DIMENSIONAL BOUNDARY LAYERS WITH APPLICATION TO THE FLOW DUE TO A ROTATING DISK [J].
GREGORY, N ;
STUART, JT ;
WALKER, WS .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1955, 248 (943) :155-199