In this study for the first time we generalize streamline models to compressible flow using a rigorous formulation while retaining most of its computational advantages. Our new formulation is based on three major elements and requires only minor modifications to existing streamline models. First, we introduce a relative density for the total fluids along the streamlines. This density captures the changes in the fluid volume with pressure and can be conveniently and efficiently traced along streamlines. Thus, we simultaneously compute time of flight and volume changes along streamlines. Second, we incorporate a density-dependent source term in the streamline saturation/composition conservation equation to account for compressibility effects. Third, the relative density, fluid volumes and the time-of-flight information are used to incorporate cross-streamline effects via pressure updates and remapping of saturations. Our proposed approach preserves the 1-D nature of the conservation calculations and all the associated advantages of the streamline approach. The conservation calculations are fully decoupled from the underlying grid and can be carried out using large time steps without gridbased stability limits. We also extend the streamline simulation to compositional modeling including compressibility effects. Given the favorable computational scaling properties of streamline models, the potential advantage for compositional simulation can be even more compelling. Although several papers have discussed compositional simulation formulation, they all suffer from a major limitation, particularly for compressible flow. All of the previous works assume, either explicitly or implicitly, that the divergence of total flux along streamlines is negligible. This is not only incorrect for compressible flow but also introduces inconsistency between the pressure and conservation equations. We examine the implications of these assumptions on the accuracy of compositional streamline simulation using a novel and rigorous treatment of compressibility. We demonstrated the validity and practical utility of our approach using synthetic and field examples and comparison with a finite difference simulator. Throughout the validation for compositional model, we found out the importance of finer segments discretizations along streamlines. We introduce optimal coarsening of segments to minimize flash calculations on each segment while keeping the accuracy of finer segments.

Cette Thèse de Doctorat est consacrée à l'étude des écoulements cisaillés réactifs supersoniques et plus particulièrement à la dynamique des jets compressibles fortement sous détendus. Ce type d'écoulement est rencontré dans un certain nombre d'applications relatives, par exemple, à l'injection d'hydrogène dans les superstatoréacteurs ou bien à l'allumage de moteurs fusées. Il est aussi représentatif du percement de réservoirs à haute pression. Ce travail s'appuie sur l'emploi d'un outil de simulation numérique haute fidélité: CREAMS (Compressible REActive Multi-species Solver). Ce code de calcul met en oeuvre des schémas numériques d'ordre élevé: schéma d' intégration d'ordre 3 en temps et d'ordre 7 et 8 en espace. Il s'appuie sur une description des termes de transport moléculaire et des termes sources chimiques la plus précise possible (transport détaillé et chimie complexe). Les simulations réalisées dans des conditions inertes permettent de caractériser l'importance des interactions choc/turbulence avec une attention particulière accordée au mélange turbulent à petite échelle. Les simulations réactives de jets fortement sous détendus d' hydrogène montrent les difficultés d'allumage et de stabilisation de la combustion pour ce type de conditions, même en présence d'un apport externe d' énergie. Enfin, l'analyse d'un jet représentatif d'un allumeur de moteur fusée révèle certaines spécificités de l'auto-allumage dans ces conditions non-prémélangées rapides. / This dissertation is devoted to the study of sheared supersonic reactive flows and more specifically the dynamics of highly underexpanded jets. Such complex compressible turbulent flow conditions are of praclical interest for scramjets as well as rocket engines applications. Similar condit ions may also be found during the accidentai releases of flammable substances into the atmosphere during high pressure vessel rupture or venting. This work is conducted with a high fidelity computational solver: CREAMS (Compressible Multi-reactive species Solver). It uses high precision numerical schemes third-order Runge Kutta scheme for time integration, plus a combination of seventh and eighth-order centered and WENO schemes for spatial integration. The molecular transport terms and chemical sources terms are handled with the most accurate descriptions, i. e., including detailed transport and chemistry. Inert flow simulations allow to characterize the importance of shock/turbulence interactions with a special emphasis placed on the small-scale scalar mixing. Highly under-expanded reactive hydrogen jet simulations underline the specific difficulties associated to ignition and combustion stabilization even in the presence of an external deposit of energy. Finally, the analysis of the rocket engine igniter jet reveals some specific features of self-ignition phenomena in such non-premixed conditions.

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Faculty of Engineering and Biult Enviroment School of Mechanical,Industrial And Aeronautical Engineering 9807537d efunemarc@hotmail.com / Drag over a wide range of shapes is well established for steady flow conditions. Drag in unsteady flow, however, is for the most part not well understood. The research presented herein examines the drag over cones in unsteady compressible flow. This was achieved by constraining cones, with half-vertex angles ranging from 15° to 30°, in a shock tube and passing shock waves over them. The resulting drag was measured directly using a stress wave drag balance (SWDB). Tests were run at shock Mach numbers between 1.12 and 1.31 with corresponding post-shock Reynolds numbers between 2 × 105 and 6 × 105. The drag on the four cone geometries as well as one sphere geometry was modelled numerically. Density contours of the flow fields, obtained from the numerical simulations were used to visualise the shock/model interactions and deduce the causes of any variations in drag. It was thus proved that post-shock fluctuations are due to shock wave reflections off the shock tube walls and the model support. The maximum unsteady drag values measured experimentally ranged from 53.5 N for the 15° cone at a Mach number of 1.14 to 148.6 N for the 30° cone at a Mach number of 1.29. The drag obtained numerically agreed well with experimental results, showing a maximum deviation in peak drag of 9.6%. The drag forces on the conical models peaked as the shock wave reached the base of the cone whereas the drag on the sphere peaked just before the shock reached the equator of the sphere. The negative drag and large post-shock drag fluctuations on a sphere measured by Bredin (2002) were present in the numerical results and thus confirm that these features were not due to balance error. The large post-shock drag fluctuations were also present on the cones. The unsteady drag was shown to increase as both the shock wave Mach number and the cone angle were increased. The ratio of the maximum unsteady drag to the compressible steady state drag varied from v 4.4:1 to 9.8:1, while the ratio of the maximum unsteady drag to the incompressible steady state drag varied from 8.3:1 to 22.2:1. The steady state drag values were shown to be of the same order of magnitude as the post shock unsteady drag. Further numerical work is recommended to confirm that drag fluctuations are in fact due to shock reflections and to better establish the relationship between the unsteady drag and the cone angle.

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.

The purpose of this study is to experimentally and numerically investigate flame acceleration in an obstructed channel. The motivation for this research is for the development of Pulse Detonation Engines (PDEs), which are unsteady propulsion devices that utilize the detonative mode of combustion. A literature survey on flame acceleration in the context of PDEs is presented, which covers a wide range of combustion regimes including laminar combustion, turbulent combustion, and finally detonation. An overview of current numerical modeling strategies is also presented along with a selection of recent numerical studies focused on flame acceleration in obstructed channels. Experimentally, the effect of obstacle blockage ratio on flame acceleration was investigated in a modular channel. The channel had a square cross-section and obstacles were mounted onto the top and bottom surfaces. Schlieren images were used to study the flame shape and the centerline flame velocity. A novel visualization technique has been developed to study the unburned gas flow ahead of the flame front. Flame propagation at speeds above the speed of sound in the reactants was also studied as compression waves formed in the unburned gas. It was found that shock reflection from obstacle surfaces and subsequent flame interaction dominates flame acceleration at these higher flame speeds. The unburned gas flow field ahead of the flame front was simulated using Large Eddy Simulation (LES) and was compared to the visualization technique developed experimentally. The detailed unsteady calculation was used to further study the development of recirculation zones behind the obstacle surfaces and the generation of turbulence in the shear layers. The unburned gas flow field was investigated to give insight into the speed and shape of the flame as it propagates into these regions. Flame propagation was modeled using a flame surface density combustion model and simulations showed flame interactions with the turbulent flow field and how three-dimensional vortical structures augmented the flame shape and increase total area. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2009-09-21 10:10:36.38

Work has been performed to characterise filtration systems according to their fractal properties and to construct agglomerates to mimic the filtration systems under scrutiny. The first objective was achieved by carrying out experiments examining the dead-end filtration of two separate mineral suspensions, namely calcite and talc. These minerals were chosen to represent typical incompressible (calcite) and compressible (talc) filtration systems, undergoing filtration using a range of pressures. The experimental apparatus produced filter cakes that could be sampled, sectioned and examined under high magnification. The second objective was met by developing a computer application that could construct simulated particle agglomerates in both two and three dimensions, using a seed agglomeration model as well as simulating filtration by means of a virtua1 filter cell. A large number of simulations were completed to mimic both the dead-end filtration and other agglomerate models. The computer application was also capable of characterising the fractal and Euclidean spatial nature of both the simulated and experimental particulate systems, using a variety of techniques. Euclidean spatial attributes such as porosity as well as fractal properties including surface roughness and a number of density fractal dimensions have been measured for both types of system and demonstrate that the conditions under which the trials were performed have a bearing on the final configuration of the structures. Results from both experimental and simulation work show that fractal dimensions offer a valid method of measuring the properties of filtration systems. Experimental results showed that as the filtering pressure was increased, the density fractal dimension for the system appeared to increase. This change in fractal dimension was also accompanied by a decrease in the porosity of the system (more so for talc than the calcite), confirming the compressibility of the materials under scrutiny. The characterisation of the sampled cakes also showed that the spatial characteristics vary within the individual slices of the sample,in agreement with modem filtration theory. Results from the simulations show that both the physical and fractal properties of the resulting structures varied with the parameters used to construct them. As a rule, as the particles in the simulations were able to move in a more diffusive manner (akin to Brownian motion), the agglomerates they formed had a more open, rugged structure. The simulation of filtration systems also showed a variation within the individual cake structures. In the case of the filtration simulations, the probability assigned to the particles' sticking to the growing agglomerate was the controlling factor. In addition, it was found that the simulated cakes had similar spatial properties to the experimental systems they were designed to replicate.

This thesis presents the numerical and analytical study of the aerodynamic and heat transfer in laminar subsonic cascades along with the development of design guidelines and procedures to improve the design of microfabricated multistage radial turbines operating at low Reynolds number. Numerical analysis was performed on 24 cascade geometries using 2D computational fluid dynamics (CFD) for over 100 flow conditions for each cascade. Two dimensional correlations were extracted from CFD for profile and mixing losses, deviation and heat transfer. These correlations include Reynolds number and compressibility effects, and take into account incidence and various geometrical parameters (solidity, stagger, blade angles, thickness and mean-line distribution). Adaptation of losses to account for three dimensional effects and correlation for blockage were derived from analytical relationships. A turbomachinery simulation software based on mean-line analysis and conservation of rothalpy incorporating the developed correlations was programmed. The software can be adapted as for the physic it uses and the turbine configuration it analyses (axial, radial inward or outward, single or multi stage). The pressure profiles obtained from simulation were found to be in good agreement with experimental data for cold turbine tests. Design guidelines and charts are provided as well as cycle analysis considering microfabrication limitations. A considerable increase in stage isentropic efficiency compared to previous devices can result from the use of slender blades, lower solidity cascades and aspect ratios of 0.5, suggesting efficiencies as high as 85% for Re > 700. The study shows that higher power density and multistage matching can be achieved through the radial outward configuration. Two designs are presented, a single stage turbine for the next generation of microturbopump prototype and a turbine configuration with four rotors and 10 stages for closed Rankine cycle providing 50.7 W of net mechanical power.

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