Les écoulements cisaillés en rotation sont fréquents en ingénierie — par exemple en turbo- machines et dans la production d’énergie hydraulique — et en géophysique et astrophysique. L’étude de leurs propriétés de stabilité en lien avec la production de turbulence est donc essentielle. Dans la présente étude, nous ne considérons pas d’éventuels effets inhomogènes, et nous nous concentrons sur la complexité de la dynamique anisotrope, qui ne peut se représenter facilement par les seuls modèles statistiques en un point. La thèse porte donc sur l’étude des propriétés de la turbulence homogène anisotrope (HAT) avec champ moyen uniforme et effet Coriolis, à l’aide de modèles statistiques en deux points. Un modèle orig- inal est proposé qui permet de prédire la dynamique de la turbulence cisaillée en rotation, et sépare les effets de déformation linéaire de la dynamique turbulente non linéaire, afin de proposer un traitement adapté pour chaque contribution. Le modèle proposé porte sur les équations qui régissent l’évolution du tenseur spectral du second ordre des corrélations de vitesse en deux points. Il permet d’aborder les gradients de vitesse moyenne arbitraires, avec ou sans rotation d’ensemble du système. L’effet direct linéaire des gradients moyens est exact dans le modèle, alors que les effets non linéaires con- stitués des corrélations d’ordre trois en deux points sont fermés par un modèle anisotrope de type EDQNM. Dans ce modèle de fermeture, l’anisotropie est restreinte à un développe- ment tronqué en termes d’harmoniques angulaires d’ordre bas Mons et al. (2016). Notre nouveau modèle est validé pour le régime linéaire par comparaison à une solution trés pré- cise de distorsion rapide visqueuse (vRDT) dans plusieurs cas de cisaillement: stabilisant, déstabilisant ou neutre. Le modèle diffère des approches de simulation numérique directe (DNS) pseudo-spectrale pour les écoulements cisaillés proposées par Rogallo (1981) en ingénierie et par Lesur & Longaretti (2005) en astrophysique, en ce que l’opérateur de convection n’est pas résolu en suivant les courbes caractéristiques moyennes spectrales ou physiques, mais grâce à un schéma original de type différences finies d’ordre élevé qui permet de calculer les dérivées ∂ i iv par rapport au vecteur d’onde k. On évite ainsi la déformation du maillage et l’obligation de remailler, ce qui autorise l’obtention aisée des harmoniques angulaires à chaque instant, grâce au fait que l’espace physique ou spectral n’est pas déformé. La capacité de prédiction de cette nouvelle approche est significativement améliorée par rapport au modèle de Mons et al. (2016), pour lequel la solution linéaire peut être remise en cause à grand temps d’évolution, particulièrement pour le cas non tournant. Le nouveau modèle est suffisamment universel puisqu’il est implémenté pour plusieurs cas de gradients de vitesse moyenne compatibles avec l’approximation homogène. Les validations ont notamment été réalisées dans des cas de déformation plane. Pour la turbulence cisaillée, dont la modélisation est demeurée jusqu’à présent un point dur des approches en un point et aussi de l’approche en deux points de Mons, nous proposons une version adaptée de notre modèle en deux points, en l’hybridant avec un modèle de retour à l’isotropie proposé par Weinstock (2013). Ce nouveau modèle hybride pour la turbulence cisaillée fournit des résultats extrêmement satisfaisants. / Stability and turbulence in rotating shear flows is essential in many contexts ranging from engineering—as in e.g. turbomachinery or hydraulic energy production—to geophysics and astrophysics. Apart from inhomogeneous effects which we discard in the present study, these flows are complex because they involve an anisotropic dynamics which is difficult to represent at the level of one-point statistics. In this context, the properties of these flows, such as scale-by-scale anisotropy or turbulent cascade can be studied via two-point statistical models of Homogeneous Anisotropic Turbulence (HAT), in which the distorting mean flow is represented by uniform mean velocity and density gradients, and by body forces as the Coriolis one. The context of HAT can be relevant for flows in a plane channel with spanwise rotation, or for a Taylor-Couette flow. We propose a new model for predicting the dynamics of homogeneous sheared rotating turbulence. The model separates linear distortion effects from nonlinear turbulent dynamics, so that each contribution can be treated with an adapted model. Our model deals with equations governing the spectral tensor of two-point second-order velocity correlations, and is developed for arbitrary mean velocity gradients with or with- out system rotation. The direct linear effect of mean gradients is exact in our model, whereas nonlinear effects come from two-point third-order correlations which are closed by an anisotropic EDQNM model. In the closure, the anisotropy is restricted to an expansion in terms of low-degree angular harmonics (Mons et al., 2016). The present model has been validated in the linear regime, by comparison to the accurate solution of viscous Rapid Distortion Theory (vRDT), in several cases, stabilizing, destabilizing or neutral. In contrast with pseudo-spectral DNS adapted to shear flow by Rogallo (1981) in en- gineering and by Lesur & Longaretti (2005) in astrophysics, the advection operator is not solved by following characteristic lines in spectral or physical space, but by an original high- order finite-difference scheme for calculating derivatives ∂ i with respect to the wave vector k. One thus avoids mesh deformation and remeshing, thus one can easily extract angular ii harmonics at any time since physical or spectral space are not distorted. With this new approach, we are able to improve the prediction of the previous model by Mons et al. (2016), in which the linear resolution is questioned at large time, especially in the case without rotation. The proposed new model is versatile since it is implemented for several cases of mean velocity gradients consistent with the homogeneity approximation. Validations have been done for several cases of plane deformations. In the case of sheared turbulence, whose modelling resists most one-point approaches and even the two-point model by Mons, we propose an adaptation of our two-point model in a new hybrid model, in which return-to- isotropy is explicitly introduced in the guise of Weinstock (2013)’s model. Predictions of the new hybrid model are extremely good.

An extensive review was made to study the wake characteristics of a backward-facing step. Experimental and numerical studies of the backward-facing step suggest that the wake of a separated shear layer to be dependent on parameters such as: expansion ratio, aspect ratio, free stream turbulence intensity, boundary layer state and thickness at separation. The individual and combined effects of these parameters on the reattachment length are investigated and discussed in detail in this thesis. A new scaling parameter, sum of step height and boundary layer thickness at separation is proposed, which yields significant collapse of the available data. Based on the literature review, an axisymmetric model is designed for further investigating the dynamics of the flow independent of aforementioned parameters. Additionally, porous suction strips are incorporated to study the step wake characteristics independent of Reynolds number. This model has been built and will be tested extensively at UTIAS.

An extensive review was made to study the wake characteristics of a backward-facing step. Experimental and numerical studies of the backward-facing step suggest that the wake of a separated shear layer to be dependent on parameters such as: expansion ratio, aspect ratio, free stream turbulence intensity, boundary layer state and thickness at separation. The individual and combined effects of these parameters on the reattachment length are investigated and discussed in detail in this thesis. A new scaling parameter, sum of step height and boundary layer thickness at separation is proposed, which yields significant collapse of the available data. Based on the literature review, an axisymmetric model is designed for further investigating the dynamics of the flow independent of aforementioned parameters. Additionally, porous suction strips are incorporated to study the step wake characteristics independent of Reynolds number. This model has been built and will be tested extensively at UTIAS.

One of the biggest unsolved problems of modern physics is the turbulence phenomena in fluid flow. The appearance of turbulence in a flow system is regularly determined by velocity and length scales of the system. If those scales are small the motion of the fluid is laminar, but at larger scales, disturbances appear and grow, leading the flow field to transition to a fully turbulent state. The prediction of transitional flow is critical for many complex fluid flow applications, such as aeronautical, aerospace, biomedical, automotive, chemical processing, heating and cooling systems, and meteorology. For example, in some cases the flow may remain laminar throughout a significant portion of a given domain, and fully turbulent simulations may produce results that can lead to inaccurate conclusions or inefficient design, due to an inability to resolve the details of the transition process. This work aims to develop, implement, and test a new model concept for the prediction of transitional flows using a linear eddy-viscosity RANS approach. The effects of transition are included through one additional transport equation for v2 as an alternative to the Laminar Kinetic Energy (LKE) framework. Here v2 is interpreted as the energy of fully turbulent, three-dimensional velocity fluctuations. This dissertation presents two new single-point, physics-based turbulence models based on the transitional methodology mentioned above. The first one uses an existing transitional model as a baseline which is modified to accurately capture the physics of fully turbulent free shear flows. The model formulation was tested over several boundary layer and free shear flow test cases. The simulations show accurate results, qualitatively equal to the baseline model on transitional boundary layer test cases, and substantially improved over the baseline model for free shear flows. The second model uses the SST k-w fully turbulent model and again the effects of transition are included through one additional transport equation for v2. An initial version of the model is presented here. Simplicity of the formulation and ease of extension to other baseline models are two potential advantages of the new method.

This thesis investigates Stochastic Separated Flow (SSF) models for particle dispersion in turbulent shear flows. A new model is presented that accounts for anisotropy and incorporates a temporal and a spatial autocorrelation in the description of the fluctuating component of the turbulent gas-phase velocity. This model and three SSF models available in the literature are evaluated by comparing predictions with the shear layer experiments of Lazaro and Lasheras (1989), Hishida et al (1992) and the turbulent round jet experiment of Yuu et al (1978). Results are discussed and deficiencies in the models explored. The new model of Evinou and Lightstone compensates for the crossing trajectory effect with the inclusion of a spatial correlation based on the relative velocity of the particle and the time step employed. / Thesis / Master of Applied Science (MASc)

This dissertation considers the genesis and dynamics of interfacial instability in vertical laminar gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory by means of Orr-Sommerfeld analysis together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. The influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream, is investigated. To make contact with existing studies in the literature, the effect of various density and viscosity contrasts as well as surface tension is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low and intermediate density contrast. Furthermore, high viscosity contrast and increases in surface tension lead to some amount of mode competition for thin film. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. These regions are extended at intermediate density contrast and exhibit only small changes with increased viscosity contrast or surface tension. Direct numerical simulations of the system with low density contrast show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. Furthermore, linear stability theory also predicts when the direction of travel of the waves changes - from downwards to upwards. The practical implications of this change in terms of loading and flooding is discussed. The change in direction of the wave propagation is represented graphically for each investigated system in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation. Besides the semi-analytical and numerical analyses, experiments with an practically relevant setup and flow system have been carried out to benchmark and validate the models developed in this work.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第15371号 / 工博第3250号 / 新制||工||1489(附属図書館) / 27849 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 中部 主敬, 教授 小寺 秀俊, 教授 田畑 修 / 学位規則第4条第1項該当

We develop a viscoelastic version of the volume of fluid algorithm for tracking deformable interfaces. The code uses the piecewise linear interface calculation method to reconstruct the interface, the continuous surface force formulation to model interfacial tension forces and utilizes the semi-implicit Stokes solver (enabling computations at low Reynolds numbers). The algorithm is primarily designed to simulate the flow of superposed fluids and the drop in a flow problem in 2D shear flows of viscoelastic and/or Newtonian fluids. The code is validated against linear stability theory for the two-layer flow case and against experimental and other documented numerical investigations for the droplet-matrix case. / Ph. D.

Axisymmetric and swirling jets are generic flows that characterize many natural and man-made flows. These include cylindrical shear layer/mixing layer flows, aircraft jets and wakes, shedding of leading edge and wing tip vortices, tornadoes, astrophysical plasma flows and flows in mechanical devices such as supersonic combustion chambers and cyclone separators. These and other applications have resulted in a high level of interest in the stability of axisymmetric and swirling jets. To date, the majority of studies on stability of axisymmetric and swirling jets have been completed under the assumption of steady flow in both axial and azimuthal (swirl) directions. Yet, flows such as the ones mentioned above can have an inherent unsteadiness. Moreover, such unsteadiness can be used to control stability and thus flow characteristics in axisymmetric and swirling jets. In this work effects of periodic variations on the temporal stability of axisymmetric and swirling jets is examined. The unsteadiness is introduced in the former as a periodic variation of the axial velocity component of the flow, and in the latter as a periodic variation of the azimuthal (swirl) velocity component of the flow. The temporal linear hydrodynamic stability of both steady inviscid axisymmetric and swirling jets is reviewed. An analytical dispersion relation is obtained in both cases and solved numerically. In the case of the steady axisymmetric jet, growth rate and celerity of unstable axisymmetric and helicalmodes are determined as functions of axial wavenumber. Results show that the inviscid axisymmetric jet is unstable to all values of axisymmetric and helical modes. In the case of the steady swirling jet, growth rate and celerity of axisymmetric modes are determined as functions of the axial wavenumber and swirl number. Results show that the inviscid swirling jet is unstable to all values of axial and azimuthal wavenumber, however, it is shown that increasing the swirl decreases the growth rate and increases the celerity of axisymmetric disturbances. The effects of periodic variations on the stability of a mixing layer is also reviewed. Results show that when the instability time scale is much smaller than the mean time scale a transformation of the time variable may be taken that, when the quasi-steady approach works, will reduce the unsteady field to that of the corresponding steady field in the new time scale. The price paid for this transformation, however, is a modulation of the amplitude and phase of the unsteady modes. Extending the results from the unsteady mixing layer, the stability of a periodically unsteady inviscid axisymmetric jet is considered. An analytical dispersion relation is obtained and results show that for the unsteady inviscid axisymmetric jet, the quasi-steady approach works. Following this, the stability of a periodically unsteady swirling jet is considered and an analytical dispersion relation is obtained. It is shown that for the unsteady inviscid swirling jet, the quasi-steady approach does not work. Resulting modulations of unsteady modes are shown via a numerical solution to the unsteady dispersion relation. In both cases, using established results for unsteady mixing layers, these results are substantiated analytically by showing that the unsteady axisymmetric jet can be reduced the the exact equational form of the steady axisymmetric jet in a new time scale, whereas the unsteady swirling jet cannot. / Master of Science

Neural networks were applied to the estimation problem consisting of identifying both nearfield and quasi-farfield flow structures of a jet undergoing spatial mode excitation. The evolution of disturbances introduced by a spatially excited jet spans a linear and nonlinear regime in the downstream flow field. For the linear portion, the neural network was trained to identify critical flow field parameters using numerical data generated from linear stability analysis code. It was shown that the neural network could function as a multiple-input adaptive linear combiner over the linear nearfield of the jet flowfield. Beyond the nearfield (2.0 ≤ z/D ≤ 6.0), a back propagation neural network was trained using experimental data captured during different modal excitation patterns. Constant velocity contours for mode 0, mode 1, mode ±1, and mode ±2 jet excitations were accurately estimated using a low-order neural network filter with conditioned inputs. Moderate success was also demonstrated when the network was used to extrapolate flow field parameters outside the initial training set. This demonstration of using neural networks to predict flowfield structure in non-reacting flows is expected to be directly applicable to estimation and control of reacting flows in combustors. / Master of Science