摘要
用Chebyshev谱配置法求解柱坐标下线化不可压缩Navier Stokes方程 ,分析喷管出口附近粘性旋拧射流的线性稳定性 .为了研究离心不稳定对线性增长率的影响 ,本研究中基本流的周向速度可以是离心稳定的 ,也可以是离心不稳定的 .结果表明在一定参数下旋拧能增强扰动的线性增长率 ,且对于离心不稳定的剖面增长率升高更大 .对于离心稳定的速度型 ,有旋拧时轴对称模态的增长率轻微下降 ,而负周向波数扰动的增长率明显上升 ;对于离心不稳定的速度型 ,可以观察到优势模态由低波数时的Kelvin Helmholtz(K H)不稳定波转换到高波数时的离心不稳定波 .
The linearized incompressible Navier-Stokes equations in cylindrical coordinates are solved by a Chebyshev spectral collocation method, in order to study the temporal instabilities of viscous swirling jets near a nozzle exit. To investigate the roles of centrifugal instability on the linear growth rate of the flows, the azimuthal velocity of the basic flow is either centrifugally stable or unstable. Results show that the swirl enhances the maximum linear growth rates of disturbances under certain parameters, and that the increases of the growth rates for the centrifugally unstable velocity profile are more evident. For the centrifugally stable one, swirl slightly decreases the growth rate of the axisymmetric mode, and obviously increases the growth rates of negative helical modes. For a fixed swirl ratio q, there exists a critical wave number n cr <0, the growth rate will increase with azimuthal wave number decreasing when n>n cr and decrease when n<n cr . For a fixed negative azimuthal wave number, there also exists a critical q cr , the growth rate will increase with azimuthal wave number when q<q cr and vice versa. For the centrifugally unstable one, two peaks are found in the dispersion relation curve, which implies that the dominant mode switches from the Kelvin-Helmholtz unstable wave at low axial wave numbers to the centrifugally unstable one at high axial wave numbers. The influences of some parameters, such as momentum thickness of shear layer, size of vortex core, and Reynolds numbers are also outlined in the present study. The obtained results suggest that centrifugal instability does play an active role in the enhancement of mixing in swirling flows.
基金
国家自然科学基金!资助项目 (19772 0 5 2 )
