Study On Stability Of The Wake Flow Downstream Of A Rectangular Cylinder

Flow around a blunt body relates to many other basic theoretical issues，suchas the flow separation, vortex generation and shedding vortex interaction.So it has animportant value in academic research. Starting from the theory, it can be made clearthat formation, development and decay of vortex, the law of interaction betweenvortex and vortex, and the law of interaction among vortex and other factors,throughthe analysis of stability of stationary and oscillating cylinder wake.The stability of wakes behind a two-dimensional rectangular cylinder of length towidth ratio L/B=3.0has been studied by experiment and numerical simulation atReynolds numbers close to the onset of vortex shedding.The experiment was carried out in a propeller-driven water channel of test section1.5m long,0.25m wide and0.2m high. The cylinder wake was steady at a Reynoldsnumber Re80, and no obvious fluctuation of the wake was found in the range ofobservation time20minutes. A vertical impulse jet disturbance was then applied to thewake at a stream-wise station, and the wake fluctuation was visualized by color liquidand the long-period evolution of the disturbed wake was recorded by a CCD camera.Results showed that persistent vortex shedding could be induced if the disturbance wasapplied at stations upstream of or in the near wake of the cylinder. At stations far downstream of the cylinder, however, the impulse disturbance could not induce persistentregular vortex shedding.Numerical simulation at the same conditions reproduces the results of experiment,and shows that the strength of disturbance, defined by jet speed (the jet width andblow time are fixed at b/B=0.04and t=1s respectively), has a strong influence on theresults. At a low jet speed u/U=15.6, the disturbance can not induce persistent vortexshedding. At u/U=31.2or even higher, persistent vortex shedding can be excited if thedisturbance is applied in the range-12<X/B<10.The above results show that, there is an absolute instability region in which theimpulse disturbance can rapidly induce vortex shedding, and strong nonlinear effect exists in the wake, the induction of vortex shedding is greatly influenced by thestrength of the disturbance.The suppression mechanism of vortex shedding from a cylinder is another issueaddressed in this paper. Linear stability analysis of time averaged velocity profiles inthe wake of a cylinder without and with suppression has been carried out. Thedisturbing stream function is expressed by Chebyshev-polynomials with a series ofunknown constants. The stream function satisfies the O-S equation at distributedmatching points, and the problem is to solve a group of algebraic equations. Thesaddle-points of the dispersion relation (k) and their corresponding complex wavenumbers and complex frequencies are obtained by a searching process of iteration. Theresults show that the absolute instability regions in the wakes with a control elementplaced at certain positions are smaller than the region of the wake without control, andthe calculated absolutely unstable frequency in the case without control is close to themeasured frequency of vortex shedding.