On the virtual origin determined from momentum equation analysis using experimental data within the roughness sublayer
On the virtual origin determined from momentum equation analysis using experimental data within the roughness sublayer
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DOI：
10.1007/s00348-018-2600-6
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发表时间：
2018-09
影响因子：
2.4
通讯作者：
T. Kameda;S. Mochizuki;H. Osaka
中科院分区：
文献类型：
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作者：
T. Kameda;S. Mochizuki;H. Osaka
摘要讨论了粗糙度比PR为4的方形肋粗糙表面上的壁面有界湍流的分布阻力质心，该质心被解释为离壁面距离的来源。利用一维激光多普勒测速仪测量了波动速度分量的一阶矩和二阶矩，估算了粗糙亚层的空间平均量。沿流平均速度和雷诺剪切应力的空间平均剖面可以用粗糙度元后观测到的混合层的代表性尺度进行标度；其中，为空腔内流动驱动力的速度标度，为作用在粗糙度元件上的形式阻力，为流体密度，为空腔宽度。空间平均剖面的解析解可以用指数形式表示，与现有的实验数据吻合较好。位移高度，即分布阻力质心到粗糙度峰的距离，可以通过空间平均雷诺剪应力剖面近似估计。在4≤PR≤8时，驱替高度的预测与实验和直接数值模拟数据的预测结果吻合较好。方形肋状粗糙表面上湍流边界层空腔内的空间平均雷诺剪应力分布可以用粗糙度单元后混合层的代表性尺度进行标度，4≤PR≤8，其中PR为粗糙度节距比。位移高度对应于壁面规律的起源，可以使用缩放的空间平均雷诺剪切应力剖面来预测，并且随着混合层在空腔上的发展，位移高度随着PR的增加而增加。
AbstractThe centroid of distributed drag acting on a roughness element, which is interpreted as the origin of the distance from the wall, is discussed for a wall-bounded turbulent flow over a rough surface with square ribs arranged with a roughness pitch ratio, PR, of 4. The first and second moments of fluctuating velocity components were measured by one-dimensional laser Doppler velocimetry to estimate spatially averaged quantities in the roughness sublayer. The spatially averaged profiles of the streamwise mean velocity and Reynolds shear stress can be scaled with the representative scales of the mixing layer observed behind a roughness element; these areandb, whereupis the velocity scale of the driven force for the flow in a cavity,Dpis the form drag acting on a roughness element,is the fluid density, andbis the cavity width. The analytical solutions of the spatially averaged profiles can be formulated in exponential form, and are in good agreement with available experimental data. The displacement height, which is the distance from the centroid of the distributed drag to the roughness crest, can be approximately estimated by the spatially averaged Reynolds shear stress profile. The prediction of the displacement height well represents that of the experimental and direct numerical simulation data for 4 ≤ PR ≤ 8.Graphical abstractThe spatially averaged Reynolds shear stress profiles in the cavity of turbulent boundary layers over square-ribbed rough surfaces can be scaled with the representative scales of the mixing layer behind a roughness element for 4 ≤ PR ≤ 8, where PR is the roughness pitch ratio. The displacement height, which corresponds to the origin of the law of the wall, can be predicted using the scaled spatially averaged Reynolds shear stress profile and increases with the PR as the mixing layer develops over the cavity.