论文标题
两个不同速度流的界面中的方形圆柱体
Square cylinder in the interface of two different-velocity streams
论文作者
论文摘要
我们研究了不可压缩的流，经过一个平方缸，在附近的上游分离板板上浸入了两个不同速度的流。底部流reynolds编号，基于正方形，$ re_b = 56 $保持恒定，而自上而下的reynolds编号比率$ r \ equiv re_t/re_b $在$ r \ in [1,6.5] $中增加了，与Bulk Reynolds编号的变化相对应$ re \ equiv（re_t+re_b）/2 \ in [56,210] $和a {\ it等价} nondiformentional剪切参数$ k \ equiv2（r-1）/（r+1）\在[0,1.4667] $中。涡旋开发的发作，$ r = 2.1 \ pm0.1 $（对应于$ re = 86.8 \ pm2.8 $，$ k = 0.71 \ pm0.04 $），被推向与经典配置中的方形缸相比，将其推向更高的$ re $。三维的出现是由$ r \ r \ simeq3.1 $（$ re \ simeq115 $，$ k \ simeq1.02 $）的模式-C型不稳定性触发的，其波长$λ_z\ simeq2.4 $，据报道，据报道，据报道，开放的圆环和正方形的圆环和正方形的圆环。所得的溶液是周期的两倍，并表现出三合一的跨度对称性：镜像反射和两个时空对称性，涉及进化的一半（两个涡流隔离周期），然后是侧面反射或半波长的移位。此后，在$ r \ in（3.4,3.8）$的$ r \ in（3.4,3.8）$的情况下，启动了时空混乱的路径，也使跨度周期性翻了一番。随后的非线性溶液仅在四个涡旋脱落周期后才重复，并且仅保留一个时空不变性，该时空不变性由进化的一半（两个涡流式循环）组成（两个涡流式循环），然后对流向跨流平面进行镜面反射。在$ r \ geq4 $的高价值的情况下，流量已成为时空混乱，但模式C的主要特征仍然可以明显区分。
We investigate the incompressible flow past a square cylinder immersed in the wake of an upstream nearby splitter plate separating two streams of different velocity. The bottom stream Reynolds number, based on the square side, $Re_B=56$ is kept constant while the top-to-bottom Reynolds numbers ratio $R\equiv Re_T/Re_B$ is increased in the range $R\in[1,6.5]$, corresponding to a coupled variation of the bulk Reynolds number $Re\equiv(Re_T+Re_B)/2\in[56,210]$ and an {\it equivalent} nondimensional shear parameter $K\equiv2(R-1)/(R+1)\in[0,1.4667]$. The onset of vortex-shedding, at $R=2.1\pm0.1$ (corresponding to $Re=86.8\pm2.8$, $K=0.71\pm0.04$), is pushed to higher $Re$ as compared to the square cylinder in the classic configuration. The advent of three-dimensionality is triggered by a mode-C-type instability at $R\simeq3.1$ ($Re\simeq115$, $K\simeq1.02$) with wavelength $λ_z\simeq2.4$, much as reported for open circular rings and square cylinders placed at an incidence. The resulting solution is period-doubled and exhibits a triad of spanwise symmetries: a mirror reflection and two spatiotemporal symmetries involving the evolution by half a period (two vortex-shedding cycles) followed by either specular reflection or a half-wavelength shift. The path towards spatio-temporal chaos is initiated thereafter with a modulational period-doubling tertiary bifurcation at $R\in(3.4,3.8)$ that also doubles the spanwise periodicity. The ensuing nonlinear solution repeats only after four vortex shedding periods and retains only a spatiotemporal invariance consisting in the evolution by half a period (two vortex-shedding cycles) followed by mirror reflection about a streamwise-cross-stream plane. At slighlty higher values of $R\geq4$, the flow has become spatio-temporally chaotic, but the main features of mode C are still clearly distinguishable.
