Suppression of turbulence and travelling waves in a vertical heated pipe
Suppression of turbulence and travelling waves in a vertical heated pipe
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DOI：
10.1017/jfm.2021.371
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发表时间：
2020-08
影响因子：
3.7
通讯作者：
Elena Marensi;S. He;A. Willis
中科院分区：
文献类型：
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作者：
Elena Marensi;S. He;A. Willis
流体在管道中流动时产生的紊流可以用浮力来抑制。由于湍流的抑制导致严重的传热恶化，这在加热和冷却应用中都是重要且不期望的现象。通常考虑垂直流动，因为轴向浮力可以帮助驱动流动。与加热测量的浮力参数$C$，我们的直接数值模拟表明，剪切驱动的湍流可以完全laminarised或它过渡到一个相对静止的对流驱动状态。浮力导致底部流动轮廓变平，这在等温管流中最近已与湍流的完全抑制相关联（Kühnen等人，自然物理学，第14卷，2018年，第386-390），并且扁平的层状基部轮廓具有增强的非线性稳定性（Marensi等人，流体力学杂志，第863卷，2019年，pp. 50-875）。与这些研究结果一致，这里分析的非线性下分支行波解，这被认为是调解过渡到湍流在等温管流，被证明是由浮力抑制。在所考虑的雷诺数范围内，$C\gtrsim 4$出现相对静止的对流驱动状态是由于层流底流的线性不稳定性造成的。然而，在湍流的抑制中，即在从湍流的过渡中，我们发现与He等人的分析（J. Fluid Mech.，第809卷，2016年，pp. 31-71）比上述动力系统方法更好地描述了向湍流的转变。He等人提出的层流判据是基于由驱动压力梯度测量的流动的表观雷诺数，它能捕捉到临界C=C_{cr}（Re）$，在该临界值以上，流动将被层流化或转变为对流驱动型。我们的分析表明，这是削弱卷，而不是条纹，这似乎是关键的层流。
Abstract Turbulence in the flow of fluid through a pipe can be suppressed by buoyancy forces. As the suppression of turbulence leads to severe heat transfer deterioration, this is an important and undesirable phenomenon in both heating and cooling applications. Vertical flow is often considered, as the axial buoyancy force can help drive the flow. With heating measured by the buoyancy parameter $C$, our direct numerical simulations show that shear-driven turbulence may either be completely laminarised or it transitions to a relatively quiescent convection-driven state. Buoyancy forces cause a flattening of the base flow profile, which in isothermal pipe flow has recently been linked to complete suppression of turbulence (Kühnen et al., Nat. Phys., vol. 14, 2018, pp. 386–390), and the flattened laminar base profile has enhanced nonlinear stability (Marensi et al., J. Fluid Mech., vol. 863, 2019, pp. 50–875). In agreement with these findings, the nonlinear lower-branch travelling-wave solution analysed here, which is believed to mediate transition to turbulence in isothermal pipe flow, is shown to be suppressed by buoyancy. A linear instability of the laminar base flow is responsible for the appearance of the relatively quiescent convection driven state for $C\gtrsim 4$ across the range of Reynolds numbers considered. In the suppression of turbulence, however, i.e. in the transition from turbulence, we find clearer association with the analysis of He et al. (J. Fluid Mech., vol. 809, 2016, pp. 31–71) than with the above dynamical systems approach, which describes better the transition to turbulence. The laminarisation criterion He et al. propose, based on an apparent Reynolds number of the flow as measured by its driving pressure gradient, is found to capture the critical $C=C_{cr}(Re)$ above which the flow will be laminarised or switch to the convection-driven type. Our analysis suggests that it is the weakened rolls, rather than the streaks, which appear to be critical for laminarisation.