The present work investigates the stability properties of the flow in a 90°-bend pipe with curvature $\delta =R/R_c=1/3$, with R being the radius of the cross-section of the pipe and $R_c$ the radius of curvature at the pipe centreline. Direct numerical simulations (DNS) for values of the bulk Reynolds number ${\mathit{Re}}_b=U_{b}D/\nu$ between 2000 and 3000 are performed. The bulk Reynolds number is based on the bulk velocity $U_b$, the pipe diameter D, and the kinematic viscosity $\nu$. The flow is found to be steady for ${\mathit{Re}}_b⩽2500$, with two main pairs of symmetric, counter-rotating vortices in the section of the pipe downstream of the bend. The presence of two recirculation regions is detected inside the bend: one on the outer wall and the other on the inner side. For ${\mathit{Re}}_b⩾2550$, the flow exhibits a periodic behaviour, oscillating with a fundamental non-dimensional frequency $\mathit{St}=\mathit{fD}/U_b=0.23$. A global stability analysis is performed in order to determine the cause of the transition from the steady to the periodic regime. The spectrum of the linearised Navier-Stokes operator reveals a pair of complex conjugate eigenvalues with positive real part, hence the transition is ascribed to a Hopf bifurcation occurring at ${\mathit{Re}}_{b,\mathit{cr}}\approx 2531$, a value much lower than the critical Reynolds number for the flow in a torus with the same curvature. The velocity components of the unstable direct and adjoint eigenmodes are investigated, and they display a large spatial separation, most likely due to the non-normality of the linearised Navier-Stokes operator. Thus, the core of the instability, also known in the literature as the wavemaker, is sought performing an analysis of the structural sensitivity of the unstable eigenmode to spatially localised feedbacks. The region located 15° downstream of the bend inlet, on the outer wall, is the most receptive to this kind of perturbations, and thus corresponds to where the instability originates. Since this region coincides with the outer-wall separation bubble, it is concluded that the instability is linked to the strong shear by the backflow phenomena. The present results are relevant for technical applications where bent pipes are frequently used, and their stability properties have hitherto not been studied.

本工作研究了曲率90°弯管中流体的稳定性。 $\delta =\mathrm{[R}/{\mathrm{[R}}_C=\mathrm{1个}/3$，其中R是管道横截面的半径，${\mathrm{[R}}_C$管道中心线的曲率半径。直接数值模拟（DNS），以计算雷诺数${\mathit{回覆}}_b={ü}_{b}d/\nu$在2000到3000之间执行。体积雷诺数基于体积速度${ü}_b$，管径D和运动粘度$\nu$。发现流动稳定${\mathit{回覆}}_b⩽2500$，在弯管下游的管段中有两对主要的对称，反向旋转的涡旋。在弯头内部检测到两个再循环区域的存在：一个在外壁上，另一个在内侧上。对于${\mathit{回覆}}_b⩾2550$，流表现出周期性的行为，以基本的无量纲频率振荡 $\mathit{圣}=\mathit{D}/{ü}_b=0.23$。进行全局稳定性分析，以确定从稳定状态到周期性状态过渡的原因。线性化的Navier-Stokes算子的频谱揭示了一对具有正实部的复共轭特征值，因此，该跃迁归因于在以下位置发生的Hopf分叉${\mathit{回覆}}_{b，\mathit{铬}}\approx 2531$，该值比具有相同曲率的圆环中的流的临界雷诺数低很多。研究了不稳定的直接本征模态和伴随本征模态的速度分量，它们显示了较大的空间间隔，这很可能是由于线性化的Navier-Stokes算子的非正态性所致。因此，不稳定的核心，在文献中也被称为造波器寻求对不稳定本征模式对空间局部反馈的结构敏感性进行分析。位于弯曲入口下游15°处的外壁区域最容易受到这种扰动的影响，因此对应于产生不稳定性的位置。由于该区域与外壁分离气泡重合，因此可以得出结论，不稳定性与回流现象与强剪切力有关。目前的结果与经常使用弯管且迄今尚未研究其稳定性能的技术应用有关。