Development of improved turbulence closure models for compressible fluid flow simulations requires better understanding of the effects of compressibility on various underlying processes of turbulence. Fundamental studies of turbulent velocity gradients hold the key to understanding several non-linear processes like material element deformation, energy cascading, intermittency and mixing. Experiments, direct numerical simulation (DNS) and simple mathematical models are three approaches to study velocity gradients. With the goal of furthering our understanding of the effects of compressibility on turbulent velocity gradients, this dissertation (i) employs DNS results to characterize some of the effects of compressibility on turbulent velocity gradients, and (ii) develops simple mathematical models for velocity gradient dynamics in compressible turbulence. In the first part of the dissertation, effects of compressibility on velocity gradient invariants and the local topology of compressible turbulence are characterized employing DNS results of compressible decaying isotropic turbulence. Joint statistics of second and third invariants of velocity gradient tensor and the exact probability of occurrence of associated topologies conditioned upon dilatation (degree of compression/expansion of fluid) are computed. These statistics are found to be (i) highly dependent on dilatation and (ii) substantially different from the statistics observed in incompressible turbulence. These dilatation-conditioned statistics of compressible turbulence, however, are found to be fairly independent of Mach number and Reynolds number. In the second part of the dissertation, two mathematical models for compressible velocity gradient dynamics are developed. To take into account the significant aero-thermodynamic coupling that exists in compressible flows, the models are derived explicitly using the continuity, energy and state equations, along with the momentum equation. The modeling challenge involved in the development of these models lies in capturing the inherently non-local nature of pressure and viscous effects as a function of local terms to derive a closed set of ordinary differential equations. The models developed in this dissertation are evaluated in a variety of flow regimes - incompressible limit (low Mach number); pressure-released limit (extremely high Mach number); and intermediate (sub-sonic Mach numbers) - and are shown to recover a range of known compressibility effects.

High Mach-number compressible flows with heat release are inherently more complicated than incompressible flows due to, among other reasons, the activation of the thermal energy mode. Such flow fields can experience significant fluctuations in density, temperature, viscosity, conductivity and specific heat, which affect velocity and pressure fluctuations. Furthermore, the flow field cannot be assumed to be dilatation-free in high Mach numbers and even in low Mach-number flows involving combustion, or in boundary layers on heated walls. The main issue in these high-speed and highly-compressible flows is the effect of thermal gradients and fluctuations on turbulence. The thermal field has various routes through which it affects flow structures of compressible turbulence. First, it has direct influence through pressure, which affects turbulence via pressure-strain correlation. The indirect effects of thermal fields on compressible turbulence are through the changes in flow properties. The high temperature gradients alter the transport coefficient and compressibility of the flow. The objective of this work is to answer the following questions: How do temperature fluctuations change the compressible flow structure and energetics? How does compressibility in the flow affect the non-linear pressure redistribution process? What is the main effect of spatial transport-coefficient variation? We perform direct numerical simulations (DNS) to answer the above questions. The investigations are categorized into four parts: 1) Turbulent energy cascade and kinetic-internal energy interactions under the influence of temperature fluctuations; 2) Return-to-isotropy of anisotropic turbulence under the influence of large temperature fluctuations; 3) The effect of turbulent Mach number and dilatation level on small-scale (velocity-gradient) dynamics; 4) The effect of variable transport-coefficients (viscosity and diffusivity) on cascade and dissipation processes of turbulence. The findings lead to a better understanding of temperature fluctuation effects on non-linear processes in compressible turbulence. This improved understanding is expected to provide direction for improving second-order closure models of compressible turbulence.

Rapid distortion theory (RDT) is applied to compressible ideal-gas turbulence subjected to homogeneous shear flow. The study examines the linear or rapid processes present in turbulence evolution. Specific areas of investigation include:(i) characterization of the multi-stage flow behavior,(ii) changing role of pressure in the three-regime evolution and (iii) influence of thermodynamic fluctuations on the different regimes. Preliminary investigations utilizing the more accurate Favre-averaged RDT approach show promise however, this approach requires careful validation and testing. In this study the Favre-averaged RDT approach is validated against Direct Numerical Simulation (DNS) and Reynolds-averaged RDT results. The three-stage growth of the flow field statistics is first confirmed. The three regime evolution of turbulence is then examined in three different timescales and the physics associated with each regime is discussed in depth. The changing role of pressure in compressible turbulence evolution shows three distinct stages. The physics of each stage is clearly explained. Next, the influence of initial velocity and thermodynamic fluctuations on the flow field are investigated. The evolution of turbulence is shown to be strongly dependent on the initial gradient Mach number and initial temperature fluctuations which tend to delay the onset of the second regime of evolution. The initial turbulent Mach number, which quantifies velocity fluctuations in the flow, influences turbulence evolution only weakly. Comparison of Reynolds-averaged RDT against Favre-averaged RDT for simulations of nonzero initial flow field fluctuations shows the higher fidelity of the latter approach.

A Large-Eddy Simulation (LES) methodology adapted to the resolution of high Reynolds number turbulent flows in supersonic conditions was proposed and developed. A novel numerical scheme was designed, that switches from a low-dissipation central scheme for turbulence resolution to a flux difference splitting scheme in regions of discontinuities. Furthermore, a state-of-the-art closure model was extended in order to take compressibility effects and the action of shock / turbulence interaction into account. The proposed method was validated against fundamental studies of high speed flows and shock / turbulence interaction studies. This new LES approach was employed for the study of shock / turbulent shear layer interaction as a mixing-augmentation technique, and highlighted the efficiency in mixing improvement after the interaction, but also the limited spatial extent of this turbulent enhancement. A second practical study was conducted by simulating the injection of a sonic jet normally to a supersonic crossflow. The validity of the simulation was assessed by comparison with experimental data, and the dynamics of the interaction was examined. The sources of vortical structures were identified, with a particular emphasis on the impact of the flow speed onto the vortical evolution.

The requirement for reduced jet noise in order to meet stringent noise legislation (civil aviation), and low infra-red observability and the use of unconventional exhaust nozzle configurations to improve aircraft survivability and performance (military aviation) is driving research to develop a better understanding of jet development and mixing mechanisms. One option open to the engineer is the use of small-scale model testing to investigate jets flows and provide valuable data for the validation of numerical models. Although more economical than large/full scale testing, additional factors that influence jet development may be present which would not be present at full scale and whose influence needs to be fully understood in order to allow small scale–large scale read-across. One such factor is the nozzle exit boundary layer. Although considerable data exist on the influence of nozzle exit boundary layers on low speed jet flows, current information on high speed jet flows is limited. It was, therefore, the aim of this thesis to extend the current understanding of nozzle exit boundary layers and their influence on the jet development for high speed jet flows through a combination of experimental and computational techniques. A combination of pneumatic probe measurements and Laser Doppler Anemometry (LDA) was used to investigate nozzle inlet and exit boundary layers of simple conical nozzles and the influence of adding a parallel extension piece. The measurements showed that the rapid acceleration of the boundary layer within the nozzle significantly reduced its momentum thickness Reynolds number and changed the state of the boundary layer from turbulent to laminar-like. The addition of a parallel extension to the nozzle exit returned the boundary layer to a fully turbulent state. A low Reynolds number RANS CFD approach was used to investigate the flow within the nozzle. Simulations using the Launder-Sharma low Reynolds number k–ε model revealed that the magnitude of the acceleration within the conical nozzles resulted in the boundary layer beginning to relaminarise. Full relaminarisation was not achieved due to the short axial distance over which the acceleration was sustained. The addition of a parallel extension provided a relaxation region in which the boundary layer could recover from the acceleration to become fully turbulent. Measurements of the jet plume originating from nozzles with laminar-like and turbulent boundary layers showed little influence of the boundary layer shape and thickness on shear layer spreading and jet centreline development.

<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>

La simulation des écoulements cavitants est confrontée à des difficultés de modélisation et de résolution numérique provenant des caractéristiques particulières de ces écoulements : changement de phase, gradient de masse volumique important, variation du nombre de Mach, turbulence diphasique, instationnarités. Dans cette thèse, nous nous sommes appliqués à dériver proprement le modèle de mélange homogène 1-fluide couplé à une modélisation RANS de la turbulence. A partir des termes contenus dans ces équations et de la nature des écoulements cavitants étudiés, plusieurs modèles de turbulence basés sur la notion de viscosité turbulente ont été testés : modèles faiblement non-linéaires (corrections SST et de réalisabilité), ajout des termes de turbulence compressible, application de la correction de Reboud, modèles hybrides RANS/LES (DES, SAS). Ces modèles ont été incorporés dans un code compressible qui fait appel à une résolution implicite en pas de temps dual des équations de conservation avec une technique de pré-conditionnement bas-Mach pour traiter les zones incompressibles. Les simulations 2D et 3D ont porté sur deux géométries de type Venturi caractérisées par la présence d’une poche de cavitation instationnaire due à l’existence d’un jet rentrant liquide/vapeur le long de la paroi. Elles montrent que l’ensemble des modèles sont capables de capturer le jet rentrant. En revanche, la dynamique de la poche varie entre les modèles et le manque de données expérimentales ne permet pas de discriminer les modèles entre eux. Il apparaît à la vue des résultats que les approches avec la correction de Reboud ou les modèles SAS améliorent la simulation des écoulements. / The computation of cavitating flows is a challenging issue due to the characteristics of these flows : phase transition, large density gradient, Mach number variation, interaction between phases and turbulent flow, unsteadiness. In the present study, we performed a derivation of the one-fluid compressible homogenous model coupled with a RANS approach for the turbulent flow. From these equations and the nature of the cavitating flows, several models based on the eddy viscosity assumption have been tested : weakly non-linear models (SST and realisability corrections), compressible turbulence models, hybrid RANS/LES turbulence models (SAS, DES) and the Reboud correction. All the models are implemented in a compressible code, which solves the equations using an implicit dual-time stepping method coupling with a pre-conditionning technique for the incompressible area. 2D and 3D computations are performed on two Venturi geometries characterized by an unsteady cavitation sheet with a liquid/vapor re-entrant jet. All the models are able to capture the re-entrant jet. Nevertheless, the dynamic behaviour differs from one model to another and the lack of experimental data prevents to discriminate the models between them. From the results, the computations with the SAS model and the Reboud correction improve the prediction of the flow.

Neste trabalho, é apresentada a simulação de escoamentos compressíveis turbulentos no entorno de corpos móveis rígidos ou deformáveis empregando-se técnicas adaptativas. As simulações numéricas são conduzidas utilizando-se o método dos elementos finitos. A discretização espaço-temporal é desenvolvida através do método das linhas ou direções características (Characteristic-Based Split - CBS) e a modelagem da turbulência é feita através de um modelo de Simulação de Grandes Escalas (SGE, ou na terminologia em inglês, Large Eddy Simulation – LES) com o coeficiente de Smagorinsky variável no tempo e espaço (SGE ou LES dinâmico). A análise estrutural de corpos deformáveis imersos no fluido é realizada através de um modelo de elementos finitos triangulares para análise de placas e cascas com não linearidade geométrica, usando materiais elásticos com comportamento linear. Conjuntamente, um método de adaptação anisotrópica transiente de malhas é empregado para obter resultados com boa resolução a baixos custos computacionais. A consideração do movimento relativo de corpos imersos no escoamento é feita através de um método híbrido de movimento da malha que emprega interpolação com funções de base radial. Exemplos bidimensionais e tridimensionais são apresentados de forma a validar cada uma das metodologias desenvolvidas. Por fim, exemplos de simulações complexas são investigados, comparando-se os resultados obtidos com resultados experimentais e numéricos presentes na literatura. / In this work, the simulation of compressible turbulent flows around rigid and flexible moving bodies is presented using adaptative techniques. The numerical simulations are solved employing the finite element method. The space-time discretization is performed using the Characteristic-Based Split scheme (CBS) and turbulence is modelled with Large Eddy Simulation (LES) and a dynamic Smagorinsky sub-grid model. The structural analysis of deformable bodies immersed on the flow is performed using a triangular finite element model for the analysis of geometrically non-linear elastic plates and shells. An anisotropic mesh adaptation algorithm for transient simulations is coupled with the solver to achieve results with good resolution and low computational costs. The consideration of the relative movement of immersed bodies on the flow is performed employing an hybrid method of mesh movement based on radial basis function interpolation. Twodimensional and three-dimensional examples are presented in order to validate the proposed methodologies. Finally, complex simulations are investigated, where results are compared with experimental and numerical data available in the literature.

Neste trabalho, é apresentada a simulação de escoamentos compressíveis turbulentos no entorno de corpos móveis rígidos ou deformáveis empregando-se técnicas adaptativas. As simulações numéricas são conduzidas utilizando-se o método dos elementos finitos. A discretização espaço-temporal é desenvolvida através do método das linhas ou direções características (Characteristic-Based Split - CBS) e a modelagem da turbulência é feita através de um modelo de Simulação de Grandes Escalas (SGE, ou na terminologia em inglês, Large Eddy Simulation – LES) com o coeficiente de Smagorinsky variável no tempo e espaço (SGE ou LES dinâmico). A análise estrutural de corpos deformáveis imersos no fluido é realizada através de um modelo de elementos finitos triangulares para análise de placas e cascas com não linearidade geométrica, usando materiais elásticos com comportamento linear. Conjuntamente, um método de adaptação anisotrópica transiente de malhas é empregado para obter resultados com boa resolução a baixos custos computacionais. A consideração do movimento relativo de corpos imersos no escoamento é feita através de um método híbrido de movimento da malha que emprega interpolação com funções de base radial. Exemplos bidimensionais e tridimensionais são apresentados de forma a validar cada uma das metodologias desenvolvidas. Por fim, exemplos de simulações complexas são investigados, comparando-se os resultados obtidos com resultados experimentais e numéricos presentes na literatura. / In this work, the simulation of compressible turbulent flows around rigid and flexible moving bodies is presented using adaptative techniques. The numerical simulations are solved employing the finite element method. The space-time discretization is performed using the Characteristic-Based Split scheme (CBS) and turbulence is modelled with Large Eddy Simulation (LES) and a dynamic Smagorinsky sub-grid model. The structural analysis of deformable bodies immersed on the flow is performed using a triangular finite element model for the analysis of geometrically non-linear elastic plates and shells. An anisotropic mesh adaptation algorithm for transient simulations is coupled with the solver to achieve results with good resolution and low computational costs. The consideration of the relative movement of immersed bodies on the flow is performed employing an hybrid method of mesh movement based on radial basis function interpolation. Twodimensional and three-dimensional examples are presented in order to validate the proposed methodologies. Finally, complex simulations are investigated, where results are compared with experimental and numerical data available in the literature.

Neste trabalho, é apresentada a simulação de escoamentos compressíveis turbulentos no entorno de corpos móveis rígidos ou deformáveis empregando-se técnicas adaptativas. As simulações numéricas são conduzidas utilizando-se o método dos elementos finitos. A discretização espaço-temporal é desenvolvida através do método das linhas ou direções características (Characteristic-Based Split - CBS) e a modelagem da turbulência é feita através de um modelo de Simulação de Grandes Escalas (SGE, ou na terminologia em inglês, Large Eddy Simulation – LES) com o coeficiente de Smagorinsky variável no tempo e espaço (SGE ou LES dinâmico). A análise estrutural de corpos deformáveis imersos no fluido é realizada através de um modelo de elementos finitos triangulares para análise de placas e cascas com não linearidade geométrica, usando materiais elásticos com comportamento linear. Conjuntamente, um método de adaptação anisotrópica transiente de malhas é empregado para obter resultados com boa resolução a baixos custos computacionais. A consideração do movimento relativo de corpos imersos no escoamento é feita através de um método híbrido de movimento da malha que emprega interpolação com funções de base radial. Exemplos bidimensionais e tridimensionais são apresentados de forma a validar cada uma das metodologias desenvolvidas. Por fim, exemplos de simulações complexas são investigados, comparando-se os resultados obtidos com resultados experimentais e numéricos presentes na literatura. / In this work, the simulation of compressible turbulent flows around rigid and flexible moving bodies is presented using adaptative techniques. The numerical simulations are solved employing the finite element method. The space-time discretization is performed using the Characteristic-Based Split scheme (CBS) and turbulence is modelled with Large Eddy Simulation (LES) and a dynamic Smagorinsky sub-grid model. The structural analysis of deformable bodies immersed on the flow is performed using a triangular finite element model for the analysis of geometrically non-linear elastic plates and shells. An anisotropic mesh adaptation algorithm for transient simulations is coupled with the solver to achieve results with good resolution and low computational costs. The consideration of the relative movement of immersed bodies on the flow is performed employing an hybrid method of mesh movement based on radial basis function interpolation. Twodimensional and three-dimensional examples are presented in order to validate the proposed methodologies. Finally, complex simulations are investigated, where results are compared with experimental and numerical data available in the literature.