管流中使turbulence不稳定的最小挡板设计
Designing a minimal baffle to destabilise turbulence in pipe flows
摘要：
受到最近实验结果的启发（Kühnen等人，Flow Turb.燃烧第100卷，2018年，pp. 919-943）中，我们考虑了设计挡板（流动的障碍物）以使管流中的湍流再分层的问题。将挡板建模为流内线性阻力$\mathbf{f}(\mathbf{x},t)=-χ(\mathbf{x})\mathbf{u}_{tot}(\mathbf{x},t)$的空间分布（$\mathbf{u}_{tot}$为总速度场，$χ\ge 0$为标量场），考虑了两个不同的优化问题，以在雷诺数$Re=3000$下设计$χ$。在第一种方法中，寻求根据$χ$的$L_1 $范数定义的最小挡板，该挡板使流的粘性耗散率最小化。在第二种方法中，处理使流动的总能量消耗最小化的挡板。这两个问题表明，挡板应轴对称和径向局部管壁附近，但努力预测最佳流向范围。手动搜索找到一个最佳的挡板一个半径长，然后用于研究如何与$Re$高达$15\,000$的振幅变化的再层化。在管壁处发现大的应力减小，但是以增加穿过挡板的压降为代价。然后对折流板下游的盈亏平衡点进行估计，在该点处，由于再层化流而引起的壁处的应力减小补偿了由折流板产生的额外阻力。
英文摘要：
Motivated by the results of recent experiments (Kühnen et al., Flow Turb. Combust., vol. 100, 2018, pp. 919-943), we consider the problem of designing a baffle (an obstacle to the flow) to relaminarise turbulence in pipe flows. Modelling the baffle as a spatial distribution of linear drag $\mathbf{f}(\mathbf{x},t)=-χ(\mathbf{x})\mathbf{u}_{tot}(\mathbf{x},t)$ within the flow ($\mathbf{u}_{tot}$ is the total velocity field and $χ\ge 0$ a scalar field), two different optimisation problems are considered to design $χ$ at a Reynolds number $Re=3000$. In the first, the smallest baffle defined in terms of a $L_1 $ norm of $χ$ is sought which minimises the viscous dissipation rate of the flow. In the second, a baffle which minimises the total energy consumption of the flow is treated. Both problems indicate that the baffle should be axisymmetric and radially localised near the pipe wall, but struggle to predict the optimal streamwise extent. A manual search finds an optimal baffle one radius long which is then used to study how the amplitude for relaminarisation varies with $Re$ up to $15\,000$. Large stress reduction is found at the pipe wall, but at the expense of an increased pressure drop across the baffle. Estimates are then made of the break even point downstream of the baffle where the stress reduction at the wall due to the relaminarised flow compensates for the extra drag produced by the baffle.
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