Global mode analysis of axisymmetric bluff-body wakes: Stabilization by base bleed

The flow around a slender body with a blunt trailing edge is unstable in most situations of interest. Usually the flow instabilities are generated within the wake behind the bluff body, inducing fluctuating forces and introducing the possibility of resonance mechanisms with modes of the structure. Base bleed is a simple and well-known means of stabilizing the wake. In the present research, we investigate the global instability properties of the laminar-incompressible flow that develops behind a cylinder with sharp edges and axis aligned with the free stream using a spectral domain decomposition method. In particular, we describe the flow instability characteristics as a function of the Reynolds number, $\text{Re}=\rho W_{\infty }D/\mu$ , and the bleed coefficient, defined as the bleed-to-free-stream velocity ratio, $C_b=W_b/W_{\infty }$ , where $D$ is the diameter of the body and $\rho$ and $\mu$ the density and viscosity of the free stream, respectively. For a truncated cylinder of aspect ratio $L/D=5$ , where $L$ is the length of the body, our calculations reveal the presence of a first steady bifurcation in the wake at $\text{Re}\simeq 391$ , as well as a second oscillatory one at $\text{Re}\simeq 715$ with an associated Strouhal number $\text{St}\simeq 0.0905$ for the most unstable azimuthal mode $\left|m\right|=1$ . In addition, we report the existence of two critical values of the bleed coefficient $C_{b1}^{\ast }\left(\text{Re},\left|m\right|\right)$ and $C_{b2}^{\ast }\left(\text{Re},\left|m\right|\right)<C_{b1}^{\ast }$ , which vary with the aspect ratio of the body, needed to stabilize both the first and second bifurcations in the range of Reynolds numbers under study, $0\le \text{Re}\le 2200$ . Finally, the numerical results for the oscillatory mode obtained for a bulletlike body of aspect ratio $L/D=2$ without base bleed are compared with experiments performed in a wind tunnel using hot-wire anemometry, showing the limitations of using an axisymmetric basic flow at Reynolds numbers higher than the critical one corresponding to the first steady bifurcation in the global stability analysis.