This paper presents a global stability analysis of the boundary layer developed on a slender circular cone. The base flow direction is towards the apex of a cone, and the pressure gradient is positive (adverse) in the flow direction. The decelerating base flow is non-parallel and non-similar. The increased semi-cone angle increases the adverse pressure gradient in the flow direction. For a given semi-cone angle, transverse curvature increases in the flow direction. However, increased semi-cone angle reduces transverse curvature at any streamwise location. The Reynolds number of the flow is defined based on the displacement thickness at the computational domain’s inlet. The radius of the cone reduces in the flow direction, which results in the increased transverse curvature. The governing stability equations are derived in the spherical coordinates and discretized using the Chebyshev Spectral collocation method. The discretized equations, along with homogeneous boundary conditions, form a general eigenvalue problem, and it is solved using Arnoldi’s iterative algorithm. The global temporal modes have been computed for small semi-cone angles $\alpha =2$°, 4°, and 6°, azimuthal wave-numbers $N=0$, 1, 2, and 3 and $Re=283$, 416, and 610. Thus, the state of base flow is laminar at the inlet (line pq) of the domain pqrs. All the global modes computed within the range of parameters are found temporally stable. Further, the global modes are found less stable at higher semi-cone angles ($\alpha$) due to the streamwise adverse pressure gradient. The effect of transverse curvature has been found significant at higher semi-cone angles. For a given $Re$ and $\alpha$, the global modes are found least stable for the helical mode $N=1$ and most stable for $N=3$. The eigenmodes’ two-dimensional spatial structure suggests that flow is spatially unstable as the disturbances grow in the streamwise direction.

本文介绍了在细长圆锥体上形成的边界层的整体稳定性分析。基本流动方向朝向圆锥体的顶点，并且压力梯度在流动方向上为正（负）。减速的基本流量是不平行且不相似的。增加的半锥形角增加了流动方向上的不利压力梯度。对于给定的半圆锥角，横向曲率在流动方向上增加。但是，增加的半圆锥角会在任何流向位置减小横向曲率。流的雷诺数是根据计算域入口处的位移厚度定义的。圆锥的半径沿流动方向减小，这导致横向曲率增大。在球坐标系中导出控制稳定性方程，并使用Chebyshev光谱搭配方法离散化。离散方程与齐次边界条件一起形成一个一般的特征值问题，并使用Arnoldi的迭代算法进行求解。已为小半圆锥角计算了全局时间模式$\alpha =2$°，4°和6°方位波数 $ñ=0$，1、2和3以及 $\mathrm{[R}Ë=283$，416和610。因此，基本流的状态在域pqrs的入口（线pq）处是层流的。发现在参数范围内计算的所有全局模式在时间上都是稳定的。此外，发现整体模式在较高的半圆锥角下不稳定（$\alpha$）由于逆流的逆流压力梯度。已经发现，在较高的半圆锥角下，横向曲率的影响显着。对于给定$\mathrm{[R}Ë$ 和 $\alpha$，发现全局模式对于螺旋模式最不稳定 $ñ=\mathrm{1个}$ 最稳定的 $ñ=3$。本征模的二维空间结构表明，当扰动沿流向增加时，流动在空间上是不稳定的。