<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>

This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.

This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.

A new method to perform direct numerical simulations of wall-bounded flows has been developed and implemented. The method uses high-order compact finite differences in wall-normal (for channel flow) or radial direction (for pipe flow) on a collocated grid, which gives high-accuracy results without the effectfof filtering caused by frequent interpolation as required on a staggered grid. The use of compact finite differences means that extreme clustering near the wall leading to small time steps in high-Reynolds number simulations is avoided. The influence matrix method is used to ensure a completely divergence-freesolution and all systems of equations are solved in banded form, which ensures an effcient solution procedure with low requirements for data storage. The method is unique in the sense that exactly divergence-free solutions on collocated meshes are calculated using arbitrary dffierence matrices. The code is validated for two flow cases, i.e. turbulent channel and turbulent pipe flow at relatively low Reynolds number. All tests show excellent agreement with analytical and existing results, confirming the accuracy and robustness ofthe method. The next step is to eciently parallelise the code so that high-Reynolds number simulations at high resolution can be performed. We furthermore investigated rare events occurring in the near-wall region of turbulent wall-bounded flows. We find that negative streamwise velocities and extreme wall-normal velocity uctuations are found rarely (on the order of 0:01%), and that they occur more frequently at higher Reynolds number. These events are caused by strong vortices lying further away from the wall and it appears that these events are universal for wall-bounded flows. / <p>QC 20150303</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.

Generating an adverse pressure gradient (APG), using a rotating cylinder in the proximity of a plane wall under a laminar freestream flow, is studied numerically in this work. The magnitude of the generated APG is a function of the gap, G, between the cylinder and the wall, and the rotational speed of the cylinder, Ω. The flow in such a configuration is characterized by periodic transient vortex shedding at high Reynolds number. A numerical model for the computation of the transient flow for this configuration is developed using the ANSYS CFD simulation tool. The model is validated against published experimental and numerical data for similar flow configurations and excellent agreement is observed. A parametric study is carried out for different combinations of G and Ω for two different Reynolds numbers of 200 and 1000 to examine the development of the resulting separation bubble due to the generated APG. The mechanism of the boundary layer separation over the plane wall and the corresponding wake dynamics is investigated. Results are presented in terms of the distribution of the pressure coefficient as well as skin friction coefficient along the wall and flow patterns around and downstream of the cylinder in the proximity of the wall. The results of these computations confirm that using a rotating cylinder over a plane wall in a freestream flow is an effective technique to generate a controlled range of adverse pressure gradients.

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

It is well known that most fluid flows observed in nature or encountered in engineering applications are turbulent and involve separation. Fluid flows in turbines, diffusers and channels with sudden expansions are among the widely observed areas where separation substantially alters the flow field and gives rise to complex flow dynamics. Such types of flows are referred to as internal flows since they are confined within solid surfaces and predominantly involve the generation or utilization of mechanical power. However, there is also a vast variety of engineering applications where the fluid flows past solid structures, such as the flow of air around an airplane or that of water around a submarine. These are called external flows and as in the former case the downstream evolution of the flow field is crucially influenced by separation. The present doctoral thesis addresses both internal and external separated flows by means of direct numerical simulations of the incompressible Navier-Stokes equations. For internal flows, the wall-driven flow in a onesided expansion channel and the pressure-driven flow in a plane channel with a single thin-plate obstruction have been studied in the fully developed turbulent state. Since such geometrical configurations involve spatially developing turbulent flows, proper inflow conditions are to be employed in order to provide a realistic fully turbulent flow at the input. For this purpose, a newly developed technique has been used in order to mimic an infinitely long channel section upstream of the expansion and the obstruction, respectively. With this approach, we are able to gather accurate mean flow and turbulence statistics throughout each flow domain and to explore in detail the instantaneous flow topology in the separated shear layers, recirculation regions as well as the recovery zones. For external flows, on the other hand, the flow past a prolate spheroid has been studied. Here, a wide range of Reynolds numbers is taken into consideration. Based on the characteristics of the vortical structures in the wake, the flow past a prolate spheroid is classified as laminar (steady or unsteady), transitional or turbulent. In each flow regime, the characteristic features of the flow are investigated by means of detailed frequency analysis, instantaneous vortex topology and three-dimensional flow visualizations.

This thesis is focused on direct numerical simulation (DNS) of compressible and incompressible fully developed and developing turbulent flows between isothermal walls using a discontinuous Galerkin method (DGM). Three cases (Ma = 0.2, 0.7 and 1.5) of DNS of turbulent channel flows between isothermal walls with Re ~ 2800, based on bulk velocity and half channel width, have been carried out. It is found that a power law seems to scale mean streamwise velocity with Ma slightly better than the more usual log-law. Inner and outer scaling of second-order and higher-order statistics have been analyzed. The linkage between the pressure gradient and vorticity flux on the wall has been theoretically derived and confirmed and they are highly correlated very close to the wall. The correlation coefficients are influenced by Ma, and viscosity when Ma is high. The near-wall spanwise streak spacing increases with Ma. Isosurfaces of the second invariant of the velocity gradient tensor are more sparsely distributed and elongated as Ma increases. DNS of turbulent isothermal-wall bounded flow subjected to favourable and adverse pressure gradient (FPG, APG) at Ma ~ 0.2 and Reref ~ 428000, based on the inlet bulk velocity and the streamwise length of the bottom wall, is also investigated. The FPG/APG is obtained by imposing a concave/convex curvature on the top wall of a plane channel. The flows on the bottom and top walls are tripped turbulent and laminar boundary layers, respectively. It is observed that the first and second order statistics are strongly influenced by the pressure gradients. The cross-correlation coefficients of the pressure gradients and vorticity flux remain constant across the FPG/APG regions of the flat wall. High correlations between the streamwise/wallnormal pressure gradient and the spanwise vorticity are found near the separation region close to the curved top wall. The angle of inclined hairpin structure to streamwise direction of the bottom wall is smaller (flatter) in the FPG region than the APG region. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2009-12-21 13:59:53.084

A new hybrid approach to model high Reynolds number wall-bounded turbulent flows is developed based on coupling the two-level simulation (TLS) approach in the inner region with conventional large eddy simulation (LES) away from the wall. This new approach is significantly different from previous near-wall approaches for LES. In this hybrid TLS-LES approach, a very fine small-scale (SS) mesh is embedded inside the coarse LES mesh in the near-wall region. The SS equations capture fine-scale temporal and spatial variations in all three cartesian directions for all three velocity components near the wall. The TLS-LES equations are derived based on defining a new scale separation operator. The TLS-LES equations in the transition region are obtained by blending the TLS large-scale and LES equations. A new incompressible parallel flow solver is developed that accurately and reliably predicts turbulent flows using TLS-LES. The solver uses a primitive variable formulation based on an artificial compressibility approach and a dual time stepping method. The advective terms are discretized using fourth-order energy conservative finite differences. The SS equations are also integrated in parallel, which reduces the overall cost of the TLS-LES approach. The TLS-LES approach is validated and investigated for canonical channel flows, channel flow with adverse pressure gradient and asymmetric plane diffuser flow. The results suggest that the TLS-LES approach yields very reasonable predictions of most of the crucial flow features in spite of using relatively coarse grids.