Friction factor decomposition for rough-wall flows: theoretical background and application to open-channel flows
Friction factor decomposition for rough-wall flows: theoretical background and application to open-channel flows
复制标题
DOI：
10.1017/jfm.2019.344
复制
发表时间：
2019-06
影响因子：
3.7
通讯作者：
V. Nikora;T. Stoesser;S. Cameron;Michael Stewart;K. Papadopoulos;P. Ouro;R. McSherry;A. Zampiron
中科院分区：
文献类型：
--
作者：
V. Nikora;T. Stoesser;S. Cameron;Michael Stewart;K. Papadopoulos;P. Ouro;R. McSherry;A. Zampiron
达西-韦斯巴赫摩擦系数f$粗糙床明渠流动的理论基础的关系推导和讨论。推导过程基于Navier-Stokes方程的双重平均（在时间和空间上），然后在整个流动中重复积分。所获得的关系明确地表明，摩擦系数可以被分成至少五个附加分量，由于：（i）粘性应力;（ii）湍流应力;（iii）分散应力（这又可以细分为两个部分，由于床粗糙度和二次流）;（iv）流动不稳定性和非均匀性;和（v）在床平行平面的流体应力的空间异质性。这些组成部分占粗糙度的几何效应，并突出了湍流和分散应力的意义，在近床区域，它们的值是最大的。为了探索所提出的关系的潜力，广泛的数据集已组装采用专门设计的大涡模拟和实验室实验的雷诺数范围很广。流动自仿射粗糙边界，这是自然和人造表面的代表，被认为是。数据分析的重点粗糙度几何形状（即光谱斜率在床高程谱）的影响，粗糙度元素和流量和粗糙度雷诺数，所有这些都被发现是实质性的相对淹没。据透露，在足够高的雷诺数的粗糙度引起的和二次流引起的分散应力可能会发挥重要作用，在产生床摩擦，补充占主导地位的湍流应力的贡献。
A theoretically based relationship for the Darcy–Weisbach friction factor $f$ for rough-bed open-channel flows is derived and discussed. The derivation procedure is based on the double averaging (in time and space) of the Navier–Stokes equation followed by repeated integration across the flow. The obtained relationship explicitly shows that the friction factor can be split into at least five additive components, due to: (i) viscous stress; (ii) turbulent stress; (iii) dispersive stress (which in turn can be subdivided into two parts, due to bed roughness and secondary currents); (iv) flow unsteadiness and non-uniformity; and (v) spatial heterogeneity of fluid stresses in a bed-parallel plane. These constitutive components account for the roughness geometry effect and highlight the significance of the turbulent and dispersive stresses in the near-bed region where their values are largest. To explore the potential of the proposed relationship, an extensive data set has been assembled by employing specially designed large-eddy simulations and laboratory experiments for a wide range of Reynolds numbers. Flows over self-affine rough boundaries, which are representative of natural and man-made surfaces, are considered. The data analysis focuses on the effects of roughness geometry (i.e. spectral slope in the bed elevation spectra), relative submergence of roughness elements and flow and roughness Reynolds numbers, all of which are found to be substantial. It is revealed that at sufficiently high Reynolds numbers the roughness-induced and secondary-currents-induced dispersive stresses may play significant roles in generating bed friction, complementing the dominant turbulent stress contribution.