Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step

被引:94
作者
Kaiktsis, L
Karniadakis, GEM
Orszag, SA
机构
[1] BROWN UNIV,CTR FLUID MECH,DIV APPL MATH,PROVIDENCE,RI 02912
[2] PRINCETON UNIV,FLUID DYNAM RES CTR,PRINCETON,NJ 08544
关键词
D O I
10.1017/S0022112096007689
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
A systematic study of the stability of the two-dimensional flow over a backward-facing step with a nominal expansion ratio of 2 is presented up to Reynolds number Re = 2500 using direct numerical simulation as well as local and global stability analysis. Three different spectral element computer codes are used for the simulations. The stability analysis is performed both locally (at a number of streamwise locations) and globally (on the entire field) by computing the leading eigenvalues of a base flow state. The distinction is made between convectively and absolutely unstable mean flow. In two dimensions, it is shown that all the asymptotic flow states up to Re = 2500 are time-independent in the absence of any external excitation, whereas the flow is convectively unstable, in a large portion of the flow domain, for Reynolds numbers in the range 700 less than or equal to Re less than or equal to 2500. Consequently, upstream generated small disturbances propagate downstream at exponentially amplified amplitude with a space-dependent speed. For small excitation disturbances, the amplitude of the resulting waveform is proportional to the disturbance amplitude. However, selective sustained external excitation (even at small amplitudes) can alter the behaviour of the system and lead to time-dependent flow. Two different types of excitation are imposed at the inflow: (i) monochromatic waves with frequency chosen to be either close to or very far from the shear layer frequency; and (ii) random noise. It is found that for small-amplitude monochromatic excitation the flow acquires a time-periodic behaviour if perturbed close to the shear layer frequency, whereas the flow remains unaffected for high values of the excitation frequency. On the other hand, for the random noise as input, an unsteady behaviour is obtained with a fundamental frequency close to the shear layer frequency.
引用
收藏
页码:157 / 187
页数:31
相关论文
共 31 条
[1]   EXPERIMENTAL AND THEORETICAL INVESTIGATION OF BACKWARD-FACING STEP FLOW [J].
ARMALY, BF ;
DURST, F ;
PEREIRA, JCF ;
SCHONUNG, B .
JOURNAL OF FLUID MECHANICS, 1983, 127 (FEB) :473-496
[2]   Three-dimensional Floquet stability analysis of the wake of a circular cylinder [J].
Barkley, D ;
Henderson, RD .
JOURNAL OF FLUID MECHANICS, 1996, 322 :215-241
[3]  
BERS A, 1975, PHYSIQUE PLASMAS, P117
[4]  
CHOMAZ JM, 1990, NEW TRENDS NONLINEAR, P259, DOI DOI 10.1007/978-1-4684-7479-4_36
[5]   SPATIALLY GROWING WAVES, INTERMITTENCY, AND CONVECTIVE CHAOS IN AN OPEN-FLOW SYSTEM [J].
DEISSLER, RJ .
PHYSICA D, 1987, 25 (1-3) :233-260
[6]  
Dubiner M., 1991, Journal of Scientific Computing, V6, P345, DOI 10.1007/BF01060030
[7]   AN ITERATIVE PROCEDURE WITH INTERFACE RELAXATION FOR DOMAIN DECOMPOSITION METHODS [J].
FUNARO, D ;
QUARTERONI, A ;
ZANOLLI, P .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1988, 25 (06) :1213-1236
[9]   IS THE STEADY VISCOUS INCOMPRESSIBLE 2-DIMENSIONAL FLOW OVER A BACKWARD-FACING STEP AT RE=800 STABLE [J].
GRESHO, PM ;
GARTLING, DK ;
TORCZYNSKI, JR ;
CLIFFE, KA ;
WINTERS, KH ;
GARRATT, TJ ;
SPENCE, A ;
GOODRICH, JW .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 1993, 17 (06) :501-541
[10]   INTRODUCING 4 BENCHMARK SOLUTIONS [J].
GRESHO, PM ;
SANI, RL .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 1990, 11 (07) :951-951