Scour around various structures obstructing flow in an open channel is a common problem; therefore a better understanding of how turbulent flow affects sediment transport is needed. Additionally, is it the mean flow or the turbulence properties that are more important in contributing to bed shear stress? To this end, an experimental study was conducted in a fixed-bed flume containing a series of dikes. Turbulence intensities and Reynold's stresses were calculated from 3-D velocity measurements gathered with a microADV. Results showed that the maximum shear stress was nearly 12-20 times that of the approach flow, while maximum turbulence intensities were about 3-5 times those of the incoming flow. Highest magnitudes of both were seen at the tip of the second dike in the three-dike series. The mean velocity appeared to have no relation to the formation of scour near the tips of the dikes but the turbulence intensities did.

Recent research has revealed that quasi-instantaneous turbulent Reynolds stresses (RS, -u’w’) and decomposed ‘quadrant’ activity (e.g., ejections and sweeps) over dunes in fluvial and wind tunnel studies has shown that turbulent stresses at the toe of a dune often exceed time-averaged, streamwise shear stress (u*2) estimates. It is believed that semi-coherent turbulent structures are conveyed toward the bed along concave streamlines in this region, and these activities cause fluctuations in local surface stresses that assist in grain entrainment. This study focuses on event-based landform scale interactions between turbulent airflow and sediment transport over a vegetated foredune through the assessment of two different experiments that took place at Greenwich Dunes, Prince Edward Island National Park, P.E.I., Canada. Reynolds decomposition of quasi-instantaneous fluctuating u’ and w’ signals into quadrant (Q) activity (i.e., Q1 outward interactions: u’>0, w’>0; Q2 ejections: u’<0, w’>0; Q3 inward interactions: u’<0, w’<0; Q4 sweeps: u’>0, w’<0) is explored to identify patterns of Reynolds stress signal distributions over the dune. Over flat surfaces, Q2 ejections and Q4 sweeps often dominate RS signals, whereas Q1 outward and Q3 inward interactions are less frequent and contribute negatively to RS generation. Over dunes, however, topographically forced streamline curvature effects alter quadrant activity distributions and, hence, near-surface RS generation by enhancing (at the toe) or inhibiting (at the crest) turbulent motions. This results in Q2 ejection and Q4 sweep activity dominating stress generation on the beach, dune toe, and lower stoss slope, whereas, toward the crest, there is a shift toward Q1 outward and Q3 inward interactions. A flow 'exuberance effect' was identified that explains the contribution of positive to negative contributing activities that varies over the dune and helps explain the spatial pattern in RS. RS generation and sand transport depend on location over the dune (via topographic forcing effects on streamline curvature and flow stagnation/acceleration) and on incident flow direction via topographic steering effects that alter the apparent ‘steepness’ of the dune to flow streamlines. Transport on the lower portion of the dune was driven predominantly by ejection and sweep activity, while toward the crest it became dominated by outward and inward interactions, likely due to increased frequency of streamwise gusts (+u’) and vertical lift (+w’) in topographically compressed flow. / Graduate

The advent of advanced vehicle concepts involving Urban Air Mobility (UAM) and small Unmanned Aerial Systems (sUAS) has brought about a new class of rotorcraft technology which operate predominantly in low-Reynolds ($Re$) number regimes. In such regimes, the flow experiences complex boundary layer phenomena like laminar separation, flow transition and reattachment. These effects are known to greatly alter the flow at and near the rotor wall, influencing its aerodynamic performance as well as the noise generated. Capturing these effects in our computational models is necessary to further our understanding of rotor aerodynamics and acoustics. The current study has introduced a novel RANS transition turbulence model, SSG/LRR-$\omega$-$\gamma$, that is capable of modeling different modes of transition involving natural, bypass, separation-induced and crossflow transition. The model framework uses a Reynolds stress transport model, SSG/LRR-$\omega$, as the base turbulence formulation and is coupled with Menter's $\gamma$ transition model. It was validated using a number of canonical cases that exhibited different transition mechanisms and the model performed equivalently or better than existing state-of-the-art transition models. It is worthy to note that the proposed model was able to perform well in three-dimensional flows, demonstrated using the case of a prolate spheroid. This underscores the capability of Reynolds stress models to accurately capture complex flow curvatures, improving upon the capabilities of linear eddy viscosity models. The transition model, integrated into OpenFOAM, was then employed to analyze two different UAV propellers. The rotor flow was examined using a URANS simulation with an overset grid. The objective was twofold: firstly, to validate the predictions generated by the proposed model for low-Reynolds number (low-$Re$) rotors, and secondly, to evaluate its effectiveness across a range of operating conditions. Comparisons were drawn against established fully turbulent and transition models. The analysis showed that transition models in general tended to be consistent in their predictions and less sensitive to changing operating conditions when compared to fully turbulent models. They also demonstrated the ability to accurately predict the mechanisms leading to separation and transition. Further, the proposed transition model demonstrated superior capability in capturing detailed flow features, particularly in the wake, compared to other fully turbulent and transition models, which is attributed to its Galilean invariant framework. To leverage the boundary layer information obtained from the proposed model, a semi-empirical broadband noise prediction method was implemented. This method utilized boundary layer data predicted by URANS simulations to estimate blade self-noise. An evaluation of the fully turbulent $k$-$\omega$ SST model and the proposed transition model revealed that both exhibited reasonable accuracy at lower rotor advance ratios. However, the transition model performed better at higher advance ratios. It was also observed that CFD-based approaches provided superior prediction accuracy compared to lower-fidelity aerodynamic models in the context of blade self-noise prediction Finally, the proposed aerodynamic and acoustic computational framework was applied to a design case study of swept propellers to understand the advantages of blade sweep on rotor aerodynamics and noise. A qualitative analysis of the flow suggested that the swept rotor exhibited lower levels of blade wake interaction compared to the unswept geometry, in line with the experimental observations. / Doctor of Philosophy / Advanced vehicle concepts such as air taxis for Urban Air Mobility (UAM) and other multi-copter applications like drone delivery, reconnaissance, etc. are emerging sectors in aviation that have garnered great industrial as well as academic interest. However, since these vehicles are expected to fly at low altitudes within urban settings, noise mitigation is of particular interest to improve their public acceptance. The vehicle configurations in these applications predominantly comprise of rotorcraft which operate at low Reynolds ($Re$) numbers and tip speeds. These operating conditions introduce complex phenomena like flow transition and separation within the boundary layer that significantly alter their aerodynamic as well as aeroacoustic performance. The current work proposes a novel transition turbulence model that improves prediction of these complex boundary layer mechanisms in low-$Re$ propellers compared to the state-of-the-art. Furthermore, this work establishes a fast broadband noise prediction method by leveraging the detailed flow data from the transition model. The focus of this method is on modeling those propeller noise sources that are directly influenced by the aforementioned boundary layer phenomena (blade self-noise). The noise prediction study revealed that transition models yield consistent predictions across different operating conditions. Finally, a brief design study is conducted using the proposed aerodynamic and acoustic framework to assess the flow dynamics and possible noise mitigation capabilities of a swept propeller.

Turbulent flows affected by buoyancy lie at the basis of many applications, both within engineering and the atmospheric sciences. A prominent example of such an application is the atmospheric boundary layer, the lowest layer of the atmosphere, in which many physical processes are heavily influenced by both stably stratified and convective turbulent transport. Modelling these turbulent flows correctly, especially in the presence of stable stratification, has proven to be a great challenge and forms an important problem in the context of climate models. In this thesis, we address this issue considering an advanced class of turbulence models, the so-called explicit algebraic models.In the presence of buoyancy forces, a mutual coupling between the Reynolds stresses and the turbulent heat flux exists, which makes it difficult to derive a fully explicit turbulence model. A method to overcome this problem is presented based on earlier studies for cases without buoyancy. Fully explicit and robust models are derived for turbulence in two-dimensional mean flows with buoyancy and shown to give good predictions compared with various data from direct numerical simulations (DNS), most notably in the case of stably stratified turbulent channel flow. Special attention is given to the problem of determining the production-to-dissipation ratio of turbulent kinetic energy, for which the exact equation cannot be solved analytically. A robust approximative method is presented to calculate this quantity, which is important for obtaining a consistent formulation of the model.The turbulence model derived in this way is applied to the atmospheric boundary layer in the form of two idealized test cases. First, we consider a purely stably stratified boundary layer in the context of the well-known GABLS1 study. The model is shown to give good predictions in this case compared to data from large-eddy simulation (LES). The second test case represents a full diurnal cycle containing both stable stratification and convective motions. In this case, the current model yields interesting dynamical features that cannot be captured by simpler models. These results are meant as a first step towards a more thorough investigation of the pros and cons of explicit algebraic models in the context of the atmospheric boundary layer, for which additional LES data are required. / <p>QC 20150522</p>

Compressibility profoundly affects many aspects of turbulence in high-speed flows - most notably stability characteristics, anisotropy, kinetic-potential energy interchange and spectral cascade rate. Many of the features observed in compressible flows are due to the changing nature of pressure. Whereas for incompressible flows pressure merely serves to enforce incompressibility, in compressible flows pressure becomes a thermodynamic variable that introduces a strong coupling between energy, state, and momentum equations. Closure models that attempt to address compressibility effects must begin their development from sound first-principles related to the changing nature of pressure as a flow goes from incompressible to compressible regime. In this thesis, a unified framework is developed for modeling pressure-related compressibility effects by characterizing the role and action of pressure at different speed regimes. Rapid distortion theory is used to examine the physical connection between the various compressibility effects leading to model form suggestions for the pressure-strain correlation, pressure-dilatation and dissipation evolution equation. The pressure-strain correlation closure coefficients are established using fixed point analysis by requiring consistency between model and direct numerical simulation asymptotic behavior in compressible homogeneous shear flow. The closure models are employed to compute high-speed mixing-layers and boundary layers in a differential Reynolds stress modeling solver. The self-similar mixing-layer profile, increased Reynolds stress anisotropy and diminished mixing-layer growth rates with increasing relative Mach number are all well captured. High-speed boundary layer results are also adequately replicated even without the use of advanced thermal-flux models or low Reynolds number corrections. To reduce the computational burden required for differential Reynolds stress calculations, the present compressible pressure-strain correlation model is incorporated into the algebraic modeling framework. The resulting closure is fully explicit, physically realizable, and is a function of mean flow strain rate, rotation rate, turbulent kinetic energy, dissipation rate, and gradient Mach number. The new algebraic model is validated with direct numerical simulations of homogeneous shear flow and experimental data of high-speed mixing-layers. Homogeneous shear flow calculations show that the model captures the asymptotic behavior of direct numerical simulations quite well. Calculations of plane supersonic mixing-layers are performed and comparison with experimental data shows good agreement. Therefore the algebraic model may serve as a surrogate for the more computationally expensive differential Reynolds stress model for flows that permit the weak-equilibrium simplification.

The present work presents a framework for multiscale modeling of multimaterial flows using surrogate modeling techniques in the particular context of shocks interacting with clusters of particles. The work builds a framework for bridging scales in shock-particle interaction by using ensembles of resolved mesoscale computations of shocked particle laden flows. The information from mesoscale models is “lifted” by constructing metamodels of the closure terms - the thesis analyzes several issues pertaining to surrogate-based multiscale modeling frameworks. First, to create surrogate models, the effectiveness of several metamodeling techniques, viz. the Polynomial Stochastic Collocation method, Adaptive Stochastic Collocation method, a Radial Basis Function Neural Network, a Kriging Method and a Dynamic Kriging Method is evaluated. The rate of convergence of the error when used to reconstruct hypersurfaces of known functions is studied. For sufficiently large number of training points, Stochastic Collocation methods generally converge faster than the other metamodeling techniques, while the DKG method converges faster when the number of input points is less than 100 in a two-dimensional parameter space. Because the input points correspond to computationally expensive micro/meso-scale computations, the DKG is favored for bridging scales in a multi-scale solver. After this, closure laws for drag are constructed in the form of surrogate models derived from real-time resolved mesoscale computations of shock-particle interactions. The mesoscale computations are performed to calculate the drag force on a cluster of particles for different values of Mach Number and particle volume fraction. Two Kriging-based methods, viz. the Dynamic Kriging Method (DKG) and the Modified Bayesian Kriging Method (MBKG) are evaluated for their ability to construct surrogate models with sparse data; i.e. using the least number of mesoscale simulations. It is shown that unlike the DKG method, the MBKG method converges monotonically even with noisy input data and is therefore more suitable for surrogate model construction from numerical experiments. In macroscale models for shock-particle interactions, Subgrid Particle Reynolds’ Stress Equivalent (SPARSE) terms arise because of velocity fluctuations due to fluid-particle interaction in the subgrid/meso scales. Mesoscale computations are performed to calculate the SPARSE terms and the kinetic energy of the fluctuations for different values of Mach Number and particle volume fraction. Closure laws for SPARSE terms are constructed using the MBKG method. It is found that the directions normal and parallel to those of shock propagation are the principal directions of the SPARSE tensor. It is also found that the kinetic energy of the fluctuations is independent of the particle volume fraction and is 12-15% of the incoming shock kinetic energy for higher Mach Numbers. Finally, the thesis addresses the cost of performing large ensembles of resolved mesoscale computations for constructing surrogates. Variable fidelity techniques are used to construct an initial surrogate from ensembles of coarse-grid, relative inexpensive computations, while the use of resolved high-fidelity simulations is limited to the correction of initial surrogate. Different variable-fidelity techniques, viz the Space Mapping Method, RBFs and the MBKG methods are evaluated based on their ability to correct the initial surrogate. It is found that the MBKG method uses the least number of resolved mesoscale computations to correct the low-fidelity metamodel. Instead of using 56 high-fidelity computations for obtaining a surrogate, the MBKG method constructs surrogates from only 15 resolved computations, resulting in drastic reduction of computational cost.

The atomization problem of high speed viscous jets has many applications in industrial processes and machines. In all these applications, it is required that the droplets have high surface area/volume ratio meaning that the droplets should be as small as possible. This can be achieved with high rates of turbulence and mixing of the flow. In order to constitute a foresight of geometry eects on droplet size, experimental investigation and the determination of flow characteristics in near and far fields of a low-speed air jet have been performed. In order to fulfill this task, three components of instantaneous velocity are measured, using a triple sensor Constant Temperature Anemometer (CTA) system. Through these measurements, mean velocity, Reynolds stress, velocity decay, spreading rate, turbulent kinetic energy, vorticity, and mass entrainment rate values are obtained. Stress-Strain relationship is also observed. Measurements are obtained for a baseline circular nozzle (round jet) as well as for an equilateral triangular and a square nozzle. On the basis of these measurements, the equilateral triangular jet is found to be the best option in order to get highest turbulence and mixing level with smallest core length.

Thesis (M.App.Sc.) - Carleton University, 2005. / Includes bibliographical references (p. 224-244). Also available in electronic format on the Internet.

In this work the predictive capability of a number of Reynolds stress transport(RST) models was first tested in a range of non-equilibrium homogeneous flows, comparisons being drawn with existing direct numerical simulation (DNS) results and physical measurements. The cases considered include both shear and normally strained flows, in some cases with a constant applied strain rate, and in others where this varied with time. Models were generally found to perform well in homogeneous shear at low shear rates, but their performance increasingly deteriorated at higher shear rates. This was attributed mainly to weaknesses in the pressure-strain rate models, leading to over-prediction of the shear stress component of the stress anisotropy tensor at high shear rates. Performance in irrotational homogeneous strains was generally good, and was more consistent over a much wider range of strain rates. In the experimental plane strain and axisymmetric contraction cases, with time-varying strain rates, there was evidence of an accelerated dissipation rate generation. Significant improvement was achieved through the use of an alternative dissipation rate generation term, Pε , in these cases, suggesting a possible route for future modelling investigation. Subsequently, the models were also tested in the inhomogeneous case of pulsating channel flow over a wide range of frequencies, the reference for these cases being the LES of Scotti and Piomelli (2001). A particularly challenging feature in this problem set was the partial laminarisation and re-transition that occurred cyclically at low and, to a lesser extent, intermediate frequencies. None of the models tested were able to reproduce correctly all of the observed flow features, and none returned consistently superior results in all the cases examined. Finally, models were tested in the case of a plane jet interacting with a rectangular dead-end enclosure. Two geometric configurations are examined, corresponding a steady regime, and an intrinsically unsteady regime in which periodic flow oscillations are experimentally observed (Mataoui et al., 2003). In the steady case generally similar flow patterns were returned by the models tested, with some differences arising in the degree of downward deflection of the impinging jet, which in turn affected the level of turbulence energy developing in the lower part of the cavity. In the unsteady case, only two of the models tested, a two-equation k-ε model and an advanced RST model, correctly returned purely periodic solutions. The other two RST models, based on linear pressure-strain rate terms, returned unsteady flow patterns that exhibited complex oscillations with significant cycle-to-cycle variations. Unfortunately, the limited availability of reliable experimental data did not allow a detailed quantitative examination of model performance.

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