粗糙壁湍流广泛存在于自然界和工程应用中，粗糙壁面解析和壁面模化的湍流数值模拟都是研究和工程中的重要工具。

本文首先使用清晰界面浸没边界方法计算了解析粗糙元的槽道湍流直接数值模拟，以及多个不同粗糙壁面小槽道解析壁面的直接数值模拟，并分析了粗糙元尾迹对流动的影响。通过计算不同雷诺数和带有不同粗糙元大小的粗糙壁面的周期山状流，发现了粗糙壁参数影响湍流分离流动的规律并分析了其原因。随后使用粗糙元解析的槽道湍流直接数值模拟系统评估了大涡模拟粗糙壁壁模型，并利用小槽道算例数据库训练了预测等效粗糙高度的深度神经网络模型。

论文主要成果和创新点如下：

（1）本文利用粗糙元解析的直接数值模拟计算了粗糙壁面上的湍流流动，其中粗糙壁面通过清晰界面的曲线浸没边界方法来解析，能较为准确地捕捉粗糙元形状。为了更好的理解粗糙壁表面几何特征对湍流的影响，我们分别进行了椭球和立方体粗糙元的粗糙壁面槽道湍流直接数值模拟，通过改变粗糙元间距和粗糙元取向以及对齐排列和交错排列，对粗糙壁影响湍流统计特性的机理进行研究。此工作系统分析了不同壁面参数对湍流统计量的影响，建立了粗糙壁小槽道湍流数据库。

（2）通过不同粗糙壁面的不同雷诺数的周期山状流大涡模拟，发现周期山状流中的分离泡随着粗糙度的增加而增加，以及雷诺数在粗糙壁面周期山状流中的无关性。且发现了不同算例之间的分离泡具有相似性：分离泡在流向上对分离泡有拉伸作用，在垂向上有抬升作用。我们定义了其特征长度，并且发现不同算例的湍流统计量通过坐标变换后也具有相似性。通过对分离点之前的边界层动量平衡分析，我们认为粗糙壁面具有减少可用动量和减小山体曲率引起的逆压梯度的双重作用。这种双重作用改变了流动分离机理，当表面粗糙度较大时，逆压梯度对流动分离的影响较小。

（3）粗糙壁模化的大涡模拟可以有效模拟粗糙壁湍流，不需要解析粗糙度尺度的流动，但其预测湍流的能力还没有被系统评估。我们通过与解析粗糙壁面的直接数值模拟槽道结果的比较，系统评估了壁面模化的大涡模拟的预测能力。对数律粗糙壁模型可以较为准确预测平均速度和外区雷诺应力，但是不能准确预测流场结构的特征尺度与速度脉动的时空关联。

（4）使用粗糙壁的大涡模拟壁模型需要事先提供不同粗糙壁面的等效砂粒粗糙度。经检验，目前预测等效粗糙高度的经验模型均不能适用本文所有的算例。基于本文建立的数据集和文献中已有的数据，我们利用深度学习方法，以不同粗糙壁面的几何特征为输入，以等效砂粒粗糙度高度为输出，改进输入参数和神经网络结构，发展了数据驱动的预测模型。结果显示，该数据驱动模型具有较好的预测能力，平均误差在5%以内，好于所检验的经验模型。

 Turbulent flows bounded by rough walls widely exist in nature and engineering applications. Numerical simulations with  resolving flow of scale rough elements  and wall-modeled simulation is  effective approach for research and engineering.

    In this thesis, direct numerical simulation (DNS) of a channel flow over resolved rough walls is first performed using the immersed boundary method with sharp interface.  To further investigate the mechanisms of how surface roughness affects turbulent statistics, DNS of minimal channels with various resolved rough surfaces are conducted and the wakes of rough elements on the flow are analyzed. Then, large-eddy simulation (LES) of flows over rough walls in periodic hills reveals the effects of roughness on separating turbulent flows and the underlying mechanisms are discussed. Subsequently, the predictive capability of WMLES with log-law wall modeling for rough walls is assessed by comparison with the rough wall DNS. Based on the minimal channel cases, a data-driven deep neural network model is developed to predict equivalent sandgrain roughness heights.

The primary contributions and innovations of this thesis introduced below:

(1)This study performs DNS of turbulence over rough surfaces with resolved rough elements, where the rough surface is represented using an immersed boundary method with sharp interface, which resolves the shape of rough elements more accurately.To better understand how different roughness parameters affect turbulence, DNS of minimal channels with ellipsoidal and cubic rough elements are performed by varying element spacing, orientation, and staggered/aligned arrangements. This work systematically analyzes the effects of roughness element orientation, spacing, and arrangement on turbulent statistics, establishing a database of rough wall channel turbulence.

(2)Large-eddy simulations of periodic hill flows with rough wall at high Reynolds numbers reveal that the separated bubble increases with roughness, and the separation point moves upstream. However, similarity is observed between different cases after proper scaling. The roughness elements induce a lift-up effect of $1.5r$ in the $y$ direction and streamwise stretching determined by the recirculation zone length. Reynolds stresses collapsed for different cases after scaling. The decrease in the available momentum promotes flow separation. The decrease in the pressure gradient magnitude, on the other hand, is beneficial for the flow to remain attached. The reductions in the available momentum are greater than those in the magnitude of the pressure gradient term explains the increase of the separation bubble's length. This work investigates the effects of rough walls on turbulent separating flows and explains the mechanisms.

(3)Wall-modeled Large eddy simulation (WMLES) employing equilibrium wall model can effectively simulate rough wall turbulence without resolving roughness scales, but its predictive capabilities have not been systematically assessed before. WMLES is evaluated  by comparing with resolved rough wall DNS. Overall, the log-law rough wall model can predict mean velocity and outer-layer Reynolds stresses reasonably accurately, but fails to accurately predict the characteristic scales of flow structures and space-time correlations of velocity fluctuations.

(4)The wall models for rough wall LES requires prior provision of equivalent sand roughness. Empirical models to predict k_s from roughness geometry are evaluated, but all models evaluated can't work for all cases.

Based on the current dataset and additional data from literature, a data-driven model using deep learning is developed to predict equivalent sandgrain roughness k_s from roughness geometry parameters. This model demonstrates good predictive performance with average errors within 5%, better than the empirical models evaluated.