The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation
The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation
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对数定律对压力梯度的恢复力：来自直接数值模拟的证据
DOI：
10.1017/s0022112009992333
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发表时间：
2009
影响因子：
3.7
通讯作者：
P. Spalart
中科院分区：
文献类型：
--
作者：
R. Johnstone;G. Coleman;P. Spalart
使用库埃特-泊肃叶流的直接数值模拟 (DNS) 研究压力梯度中的壁界湍流。其动机是包括不利的压力梯度，以补充经过充分研究的泊肃叶流中存在的有利压力梯度，核心问题是缩放定律如何对总剪切应力的梯度或等效的压力梯度做出反应。在此考虑的情况下，“壁区域”中局部应力与壁应力之比（即 τ+）的范围约为 2/3 到 3/2。我们的意思是，该层被认为不受对面墙的影响，因此对简单、通用的行为开放。两壁处的归一化压力梯度 p+ ≡ dτ+/dy+ 分别为 -0.00057 和 +0.0037。结果与 Galbraith, Sjolander & Head（Aeronaut. Quart. vol. 27, 1977, pp. 229–242）关于边界层（基于测量剖面）的发现大体一致：对数速度剖面比其他两个同样合理的假设（即混合长度 ℓ = κy 的普遍性和涡流粘度 νt = 的普遍性）更有弹性。 uτκy。在压力梯度中，τ+ ≠ 1，这三者发生冲突，我们的主要目的是对它们进行比较。我们认为卡门常数 κ 是唯一的，但允许范围为 0.38 到 0.41，这与当前的争论一致。它在解释上略有不同。这一弹性发现作为 DNS 结果显得很新，并且不受皮肤摩擦实验不确定性的影响。它在（相当强的）不利梯度中不如在有利梯度中那么明显；例如，y+ = 50 处的速度 U+ 在逆梯度侧低 3%。一个可能的原因是壁面剪切应力很小，并且在一定程度上被大部分流动中的应力和动能所淹没。研究了纯粹基于 p+ 修正“墙定律”的潜力，结果好坏参半。我们认为对对数定律的偏好有些违反直觉，因为标度定律是非局部的，但也已被确立并且与湍流建模高度相关。
Wall-bounded turbulence in pressure gradients is studied using direct numerical simulation (DNS) of a Couette–Poiseuille flow. The motivation is to include adverse pressure gradients, to complement the favourable ones present in the well-studied Poiseuille flow, and the central question is how the scaling laws react to a gradient in the total shear stress or equivalently to a pressure gradient. In the case considered here, the ratio of local stress to wall stress, namely τ+, ranges from roughly 2/3 to 3/2 in the ‘wall region’. By this we mean the layer believed not to be influenced by the opposite wall and therefore open to simple, universal behaviour. The normalized pressure gradients p+ ≡ dτ+/dy+ at the two walls are −0.00057 and +0.0037. The outcome is in broad agreement with the findings of Galbraith, Sjolander & Head (Aeronaut. Quart. vol. 27, 1977, pp. 229–242) relating to boundary layers (based on measured profiles): the logarithmic velocity profile is much more resilient than two other, equally plausible assumptions, namely universality of the mixing length ℓ = κy and that of the eddy viscosity νt = uτκy. In pressure gradients, with τ+ ≠ 1, these three come into conflict, and our primary purpose is to compare them. We consider that the Kármán constant κ is unique but allow a range from 0.38 to 0.41, consistent with the current debates. It makes a minor difference in the interpretation. This finding of resilience appears new as a DNS result and is free of the experimental uncertainty over skin friction. It is not as distinct in the (rather strong) adverse gradient as it is in the favourable one; for instance the velocity U+ at y+ = 50 is lower by 3% on the adverse gradient side. A plausible cause is that the wall shear stress is small and somewhat overwhelmed by the stress and kinetic energy in the bulk of the flow. The potential of a correction to the ‘law of the wall’ based purely on p+ is examined, with mixed results. We view the preference for the log law as somewhat counter-intuitive in that the scaling law is non-local but also as becoming established and as highly relevant to turbulence modelling.