Superhydrophobic surfaces are able to entrap gas pockets in-between surface roughness elements when submerged in water. These entrapped gas pockets give these surfaces the potential to reduce drag due to the overlying flow being able to locally slip over the gas pockets, resulting in a mean slip at the surface. This thesis investigates the different effects that slip and the texturing of the surface have on turbulence over superhydrophobic surfaces. It is shown that, after filtering out the texture-induced flow, the background, overlying turbulence experiences the surface as a homogeneous slip boundary condition. For texture sizes, expressed in wall units, up to $L^+ \lesssim 20$ the only effect of the surface texture on the overlying flow is through this surface slip. The direct effect of slip does not modify the dynamics of the overlying turbulence, which remains canonical and smooth-wall-like. In these cases the flow is governed by the difference between two virtual origins, the virtual origin of the mean flow and the virtual origin experienced by the overlying turbulence. Streamwise slip deepens the virtual origin of the mean flow, while spanwise slip acts to deepen the virtual origin perceived by the overlying turbulence. The drag reduction is then proportional to the difference between the two virtual origins, reminiscent of drag reduction using riblets. The validity of slip-length models to represent textured superhydrophobic surfaces can resultantly be extended up to $L^+ \lesssim 20$. However, for $L^+ \gtrsim 25$ a non-linear interaction with the texture-coherent flow alters the dynamics of the background turbulence, with a reduction in coherence of large streamwise lengthscales. This non-linear interaction causes an increase in Reynolds stress up to $y^+ \lesssim 25$, and decreases the obtained drag reduction compared to that predicted from homogeneous slip-length models.

Karhunen-Lo`{e}ve decomposition is a well established tool, in areas such as signal processing, data compression and low-dimensional modeling. In computational fluid mechanics (CFD) too, KL decomposition can be used to achieve reduced storage requirements, or construction of relatively low-dimensional models. These relatively low-dimensional models, can be used to investigate the dynamics of the flow field in a qualitative manner. Employment of these reduced models is beneficial, as the they can be studied with even stringent computing resources. In addition, these models enable the identification and investigation of interactions between flowlets of different nature (the flow field is decomposed into these flowlets). However, one should not forget that, the reduced models do not necessarily capture the entire dynamics of the original flow, especially in the case of turbulent flows. In the presented study, a KL basis is used to construct reduced models of Navier-Stokes equations in the case of wall-bounded turbulent flow, using Galerkin projection. The resulting nonlinear dynamical systems are then used to investigate the dynamics of transition to turbulence in plane Poiseuille flow in a qualitative fashion. The KL basis used, is extracted from a flow filed obtained from a direct numerical simulation of plane Poiseuille flow.

<p>Laminar or turbulent flows over porous surfaces have received extensive attention in the past few decades, due to their potential to achieve passive flow controls. These surfaces either in natural exhibit roughness or are engineered in purpose, and usually entail special features such as increasing/reducing surface drags. An increasing interest has arisen in the interaction between these surfaces and high-speed compressible flows, which could inform the next-level flow control studies at supersonic and hypersonic speeds for the designs of high-speed vehicles. In this dissertation, the interaction between high-speed compressible turbulent flows and acoustically permeable surface is investigated. The surface property is modeled via the Time-Domain Impedance Boundary Condition (TDIBC), which avoids the inclusion of the geometric details in the numerical simulations.</p> <p>We first perform Large-Eddy Simulations of compressible turbulent channel flows over one impedance wall for three bulk Mach numbers:Mb = 1.5, 3.5 and 6.0. The bulk Reynolds number Reb is tuned to achieve similar viscous Reynolds number Re∗τ ≈ 220 across all Mb to ensure a nearly common state of near-wall turbulence structures over impermeable walls. The TDIBC based on the auxiliary differential equations (ADE) method is applied to bottom wall of the channel. A three-parameter complex impedance model with a resonating frequency tuned to the large-eddy turn-over frequency of the flow is adopted. With a sufficiently high permeability, a streamwise traveling instability wave that is confined in nature and that increases the surface drag, is observed in the near-wall region and changes the local turbulent events. As a result, the first and second order mean flow statistics are found to deviate from that of a flow over impermeable walls. We then perform a linear stability analysis using a turbulent background base flow and confirm that the instability wave is triggered by a sufficiently high permeability and manifests a confined nature. The critical resistance Rcr (interpreted as the inverse of the permeability), above which the instability is suppressed, is found to be sub-linearly proportional to the bulk Mach number Mb, indicating less permeability required to trigger the instability in high Mach number flows.</p> <p>Due to the extremely high computational cost in high Mach number wall-bounded flow calculations, the next-phase optimization/flow control design using the porous surface becomes unaffordable. An ’economical’ flow setup that can server the purpose of rapid flow generation would greatly benefit the planned research. For such reason, we carry out a study about the effect of the domain size on the near-wall turbulence structures in compressible turbulent channel flows, to identify such type of flow setup. Apart from the concept of minimal flow units (MFU, as in the literature) entailing a minimal domain size required for near-wall turbulence to be sustained, efforts have also been made to identify a range of the domain size that can sustain both the inner and outer layer turbulence, and lead to only small deviations in mean flow statistics from the baseline data, which herein defined as minimal turbulent channel (MTC). The motivation of proposing the concept of MTC is to provide a computationally efficient setup for the rapid generation of near-wall turbulence with minimal compromise on the fidelity of the simulated field for investigations requiring numerous simulations, such as machine learning, flow control/optimization designs. It is found that the mean flow statistics from a computational domain spanning 700 − 1100 and 230 − 280 local viscous units in streamwise and spanwise directions, respectively, agree reasonably well with the reference calculations of all three Mach numbers under investigation, and are thus identified as the range in which the MTC stays. The large scale near-wall turbulence structures observed in full scale DNS simulations, and their spatially coherent connections, are roughly preserved in MTC, indicated by the existence of the grouped streamwise aligned hairpin vortices of various sizes and the resulted patterns of uniform momentum zones and thermal zones in the instantaneous flow field. In an MTC, the energy transfer paths among the kinetic energy of the mean field, turbulent kinetic energy and mean internal energy are slightly modified, with the most significant change observed in the viscous dissipation. The mean wall-shear stress and mean wall heat flux see less than 5% error as compared to the full scale simulations. Such reduced-order flow setup requires less than 3% of the computational resource as compared to the full scale simulations.</p>

Direct and large-eddy simulations of wall-bounded turbulent flows in complex geometries are presented in the thesis. To avoid the challenging resolution requirements of the near-wall region, we develop a virtual wall model in generalized curvilinear coordinates and incorporate the non-equilibrium effects via proper treatment of the momentum equations. The wall-modeled large-eddy simulation (WMLES) framework is formulated based on the wall model, accomplished via the stretched-vortex subgrid scale (SGS) model for the LES region. Based on this, we develop high-resolution in-house CFD codes, including direct numerical simulation (DNS), wall-resolved simulation (WRLES) and WMLES for wall-bounded turbulence simulations in complex geometries. First, we present LES of flow past different airfoils with Rec, based on the free-stream velocity and airfoil chord length, ranging from 104 to 2.1106. The numerical results are verified with DNS at low Rec, and validated with experimental data at higher Rec, including typical aerodynamic properties such as pressure coefficient distributions, velocity components, and also more challenging measurements such as skin-friction coefficient and Reynolds stresses. The unsteady separation behavior is investigated with skin friction portraits, which reveal a monotonic shrinking of the near wall structure scale. Second, we present LES of turbulent flow in a channel constricted by streamwise periodically distributed hill-shaped protrusions. Two Reynolds number cases, i.e. Reh=10595 and 33000 (based on the hill height and bulk mean velocity through the hill crest), are utilized to verify and validate our WMLES results. All comparisons show reasonable agreement, which enables us to further probe simulation results at higher Reynolds number (Reh=105). The Reynolds number effects are investigated, with emphasis on the mean skin-friction coefficients, separation bubble size and pressure fluctuations. The flow field at the top wall is evaluated with the empirical friction law and log-law as in planar channel flows. Finally, we present DNS of flow past the NACA0012 airfoil (Rec=104, AoA=10) with wavy roughness elements located near the leading edge. The effects of 2D surface roughness on the aerodynamic performance are investigated. For k8, massive separation occurs and almost covers the suction side of the airfoil dominating the airfoil aerodynamic performance.

Most flows in nature and engineering are turbulent, and many are wall-bounded. Further, in turbulent flows, the turbulence generally has a large impact on the behavior of the flow. It is therefore important to be able to predict the effects of turbulence in such flows. The Navier-Stokes equations are known to be an excellent model of the turbulence phenomenon. In simple geometries and low Reynolds numbers, very accurate numerical solutions of the Navier-Stokes equations (direct numerical simulation, or DNS) have been used to study the details of turbulent flows. However, DNS of high Reynolds number turbulent flows in complex geometries is impractical because of the escalation of computational cost with Reynolds number, due to the increasing range of spatial and temporal scales. In Large Eddy Simulation (LES), only the large-scale turbulence is simulated, while the effects of the small scales are modeled (subgrid models). LES therefore reduces computational expense, allowing flows of higher Reynolds number and more complexity to be simulated. However, this is at the cost of the subgrid modeling problem. The goal of the current research is then to develop new subgrid models consistent with the statistical properties of turbulence. The modeling approach pursued here is that of "Optimal LES". Optimal LES is a framework for constructing models with minimum error relative to an ideal LES model. The multi-point statistics used as input to the optimal LES procedure can be gathered from DNS of the same flow. However, for an optimal LES to be truly predictive, we must free ourselves from dependence on existing DNS data. We have done this by obtaining the required statistics from theoretical models which we have developed. We derived a theoretical model for the three-point third-order velocity correlation for homogeneous, isotropic turbulence in the inertial range. This model is shown be a good representation of DNS data, and it is used to construct optimal quadratic subgrid models for LES of forced isotropic turbulence with results which agree well with theory and DNS. The model can also be filtered to determine the filtered two-point third-order correlation, which describes energy transfer among filtered (large) scales in LES. LES of wall-bounded flows with unresolved wall layers commonly exhibit good prediction of mean velocities and significant over-prediction of streamwise component energies in the near-wall region. We developed improved models for the nonlinear term in the filtered Navier-Stokes equation which result in better predicted streamwise component energies. These models involve (1) Reynolds decomposition of the nonlinear term and (2) evaluation of the pressure term, which removes the divergent part of the nonlinear models. These considerations significantly improved the performance of our optimal models, and we expect them to apply to other subgrid models as well. / text