Wall-bounded turbulent flows in many engineering applications are subjected to spatial and/ortemporal acceleration and deceleration and surface roughness due to factors such as corrosion. The first part of the report aims to understand: (1) the coupled effect of roughness and mean-flow acceleration on wall-bounded turbulence and (2) to how does the turbulence response depends on the roughness topography, especially for multi-scale roughness. To that end, direct numerical simulations (DNS) are performed on periodic half-channel flows subjected to an impulse acceleration of the bulk velocity. Two different roughness topographies: a semi-uniform sand grain roughness and a multiscale turbine-blade roughness are compared with a baseline smooth-wall case. The flow developed from a transitionally rough flow at the initial equilibrium state to a fully rough flow at the new equilibrium state. Comprehensive analyses are carried out for the single-point statistics of all three components of an instantaneous flow quantity in the presence of a rough wall: the space-and-phase-average, the spatial heterogeneity of the phase-averaged perturbations (i.e. form-induced/dispersive fields), and the turbulent fluctuations. It is observed that, while the smooth-wall case undergoes a reverse transition toward the quasi-laminar state as a results of the strong acceleration, on the rough walls the reverse transition process is prevented. Instead, the turbulence near a rough wall rapidly recovers the equilibrium state, owing to an instantaneous augmentation of the form-induced perturbations as a result of the acceleration. The roughness texture plays a role in determining the rate of recovery of the near-wall turbulence to the new steady state. The effect of the form-induced perturbations on turbulence production, previously thought to be negligible for equilibrium boundary layers, is found to be significant in a strongly accelerating flow. In addition, the approximate scaling of the form-induced velocity on the velocity at the edge of roughness sublayer is identified. In the second part of the report, the structures of both the turbulent and form-induced fields are characterized; the dynamic interactions between these two components are identified and quantitatively compared. A second mechanism through which the form-induced velocities and stresses indirectly affect the Reynolds stress isotropy through modifying pressure fluctuations is identified. The form-induced perturbations of the Reynolds stresses, rarely studied in the literature, are found to play an important role in preventing the reverse transition on rough walls. In addition, results showed that the structural response of turbulence to the acceleration on the multiscale roughness displayed similarities with that on a smooth wall: turbulent eddies are noticeably elongated in the streamwise direction, indicating local process of reverse transition even on a rough wall. Evidences suggested that this is due to strong form-induced shear, which linearly stretched the turbulent eddies instead of non-linearly modifying the eddies through augmented turbulence production. The findings above suggest that a key part in the dependence of non-equilibrium turbulence response on the roughness texture is the form-induced quantities, whose production is known to be attributed to the work of mean flow against the roughness pressure drag (quantified by the equivalent sandgrain height, ??). Hence, the third part of the report focuses on analyzing and modeling the dependence of the roughness-sublayer mean-velocity profile ?(?) and ?? on the roughness texture, based on data-driven machine-learning approaches. Gaussian Process Regression (GPR) and Neural Networks (NN) are trained on a comprehensive database of half-channel flows over different rough surfaces consisting of new or existing numerical/experimental datasets of mean velocity profiles or ?? . Feature sensitivity analyses using both systematic selection of rough features and principal component analyses (PCA) consistently identified an optimal (minimal) set of important features for the prediction of ?(?), including slope, magnitude and skewness of height variations, spatial correlation, and element inclination. For ?(?) prediction, the GPR model is shown capable of accurate prediction for the majority of test cases with a maximum error (across ?) less than 10% and a ?2 error less than 0.5%. For the ?? prediction, an existing NN method is extended to include two-point features (i.e. correlation lengths), which is shown to significantly improve the prediction. A PCA analysis showed that the majority of variation of the roughness topography in currently available datasets is mostly captured by three principal components, which depend on a set of singleand two-point features. In addition, the relatively small contribution from element inclination to the principal components indicates a need for more datasets with systematically varied roughness inclinations. These results suggest the importance of surface correlation lengths, which are not usually used in roughness modeling, in both ?(?) and ?? predictions. The sets of important features identified for ?(?) and ?? are found roughly consistent, due to similar physics (i.e. time-mean flow separation around roughness elements) determining the two quantities. The current work provides improved understanding of the turbulence response in non-equilibrium accelerated flows on rough walls. Scaling relations (of total drag and time-mean velocity fields) of the roughness-sublayer flow are identified, which will inform future physics-based roughness models. The flow dependency on the roughness texture is characterized with machine learning techniques and state-of-the-art numerical/experimental datasets. The important roughness features that play a role in determining non-equilibrium flows response are identified for a wide range of rough surfaces, which will provide guidance on future generation of new rough surfaces for additional datasets and improve the physical understanding of individual roughness topographical features. Findings of the modeling and topography-dependency analyses of the roughness-sublayer flows carried out herein can be extended to non-equilibrium flows according to the identified scaling of RSL mean flows. Future directions are identified to complete the understanding of non-equilibrium wall turbulence in other roughness regimes and separating flows.
Read
