Rozprawy doktorskie na temat „Transitional channel flow”

Thesis (MTech (Chemical Engineering))--Cape Technikon, 2004
When designing the open channels to transport the homogenous non-Newtonian slurries, the effect of channel shape is one of the parameters that should be checked and very little research has been conducted to address this matter. Open channels are commonly applied in the mining industry where mine tailings have to be transported to the disposal dams at high concentrations to save water consumption. This thesis addresses the effect of the cross-sectional shape of the channel with emphasis on laminar and transitional flow of non-Newtonian fluids. The literature review on the flow of Newtonian and non-Newtonian fluids has been presented. The most relevant one to this topic is the work done by Straub et al (1958) for Newtonian fluids and the analytical work presented by Kozicki and Tiu (1967) for non-Newtonian fluids. Authors like Coussot (1994) and Haldenwang (2003) referred to their work but did not comprehensively verified it experimentally. Three flume shapes were designed to investigate this problem namely, rectangular, semi circular, and trapezoidal flume shape. The test rig consisted of a 10 m long by 300mm wide tilting flume that can be partitioned into two sections to form a 150 mm wide channel. All three flume shapes were tested in both the 150 mm and 300 mm wide flumes. This flume is linked to the in-line tube viscometer with three tube diameters namely, 13 mm; 28 mm; and 80 mm. The experimental investigation covered a wide range of flow rates (0.1-45l/s), and flume slopes (1-5 degrees). The fluids tested were kaolin suspension (5.4 - 9% v/v), CMC solution (1 - 4% m/m), and bentonite suspension (4.6 and 6.2% mlm). The models found in the literature were evaluated with the large database compiled from the test results to predict the laminar and transitional flow of these fluids with the aim of checking the effect of the cross-sectional shape of these channels selected in these flow regimes. For all the flume shapes and non-Newtonian fluids selected in this thesis it was found that in predicting the laminar flow, the effect of shape is adequately accounted for by the use of hydraulic radius. In predicting the transitional flow, it was found that the effect of shape does not have to be included.

The present study is concerned with the stability of a flow of viscous conducting liquid driven by a pressure gradient between two parallel walls in the presence of a transverse magnetic field, which is investigated using a Chebyshev collocation method. This magnetohydrodynamic counterpart of the classic plane Poiseuille flow is generally known as Hartmann flow. Although the magnetic field has a strong stabilizing effect, the turbulence is known to set in this flow similarly to its hydrodynamic counterpart well below the threshold predicted by the linear stability theory. Such a nonlinear transition to turbulence is thought to be mediated by unstable equilibrium flow states which may exist in addition to the base flow. Firstly, the weakly nonlinear stability analysis carried out in this study shows that Hartmann flow is subcritically unstable to small finite-amplitude disturbances regardless of the magnetic field strength. Secondly, two-dimensional nonlinear travelling wave states are found to exist in Hartmann flow at substantially subcritical Reynolds numbers starting from Ren = 2939 without the magnetic field and from Ren ∼ 6.50 × 103Ha in a sufficiently strong magnetic field defined by the Hartmann number Ha. Although the latter value is by a factor of seven lower than the linear stability threshold Rel ∼ 4.83×104Ha and by almost a factor of two lower than the value predicted by the mean-field (monoharmonic) approximation, it is still more than an order of magnitude higher than the experimentally observed value for the onset of turbulence in this flow. Three-dimensional disturbances are expected to bifurcate from these two-dimensional travelling waves or infinity and to extend to significantly lower Reynolds numbers. The by-product of this study are two developments of numerical techniques for linear and weakly nonlinear stability analysis. Firstly, a simple technique for avoiding spurious eigenvalues is developed for the solution of the Orr-Sommerfeld equation. Secondly, an efficient numerical method for evaluating Landau coefficients which describe small amplitude states in the vicinity of the linear stability threshold is introduced. The method differs from the standard approach by applying the solvability condition to the discretised rather than the continuous problem.

Thesis submitted in fulfilment of the requirements for the degree Master of Technology: Chemical Engineering in the Faculty of Engineering at the Cape Peninsula University of Technology
Open channels are widely used in the mining industries where homogeneous non-Newtonian slurries have to be transported around plants (Sanders et al., 2002). As water becomes scarcer and more costly due to legislative limitations, higher concentrations of slurries have to be transported. Very little work had been done to predict the laminar-turbulent transition flow of non-Newtonian fluids in open-channels. The effect of open channel on flow of non-Newtonian fluids in the transition region is not well understood. A systematic study on the effect of open channel shape on transitional flow for different non-Newtonian fluids has as far as can be ascertained not been conducted to date. This work investigated the effect of the channel cross-sectional shape on transitional flow of non-Newtonian fluids. There are a number of analytical and empirical methods available for the prediction of transitional flow in open channels. However, there are no conclusive guidelines in the literature that would predict the transitional flow for different shapes. A large experimental database for non-Newtonian flow produced by the Flow Process Research Centre at the Cape Peninsula University of Technology in rectangular, trapezoidal, semi-circular and triangular channels at slopes varying from 1° to 5° was used to achieve the objective. The test fluids consisted of bentonite and kaolin clay suspensions, and solutions of carboxymethyl cellulose (CMC) of various concentrations. The shear stress - shear rate behaviour of each test fluid was measured using in-line tube viscometry. To evaluate predictive models of transitional flow in various channel shapes, a comparison of critical actual velocities with models velocities was conducted for power law, Bingham plastic and yield-shear thinning fluids. After comparison of various models in different flume shapes, Haldenwang‟s critical Reynolds number for rectangular channels was deemed to be the best predictive model. To improve Haldenwang‟s critical Reynolds number, new correlations based on Haldenwang‟s (2003) method were developed for each shape studied and their corresponding critical velocities were compared. By combining all the transition data for the four shapes a new correlation “combined model” was developed for onset of transition and onset of full turbulence which can adequately accommodate the four different channel shapes for all fluids tested.

This thesis deals with the stability of particle laden flows. Both modal and non-modal linear analyses have been performed on two-way coupled particleladen flows, where particles are considered spherical, solid and either heavy or light. When heavy particles are considered, only Stokes drag is used as interaction term. Light particles cannot be modeled with Stokes drag alone, therefore added mass and fluid acceleration are used as additional interaction forces. The modal analysis investigates the asymptotic behavior of disturbances on a base flow, in this thesis a pressure-driven plane channel flow. A critical Reynolds number is found for particle laden flows: heavy particles increase the critical Reynolds number compared to a clean fluid, when particles are not too small or too large. Neutrally buoyant particles, on the other hand, have no influence on the critical Reynolds number. Non-modal analysis investigates the transient growth of disturbances, before the subsequent exponential behavior takes over. We investigate the kinetic energy growth of a disturbance, which can grow two to three orders of magnitude for clean fluid channel flows. This transient growth is usually the phenomenon that causes transition to turbulence: the energy can grow such that secondary instabilities and turbulence occurs. The total kinetic energy of a flow increases when particles are added to the flow as a function of the particle mass fraction. But instead of only investigating the total energy growth, the non-modal analysis is expanded such that we can differentiate between fluid and particle energy growth. When only the fluid is considered in a particle-laden flow, the transient growth is equal to the transient growth of a clean fluid. Besides thes Stokes drag, added mass and fluid acceleration, this thesis also discusses the influence of the Basset history term. This term is often neglected in stability analyses due to its arguably weak effect, but also due to difficulties in implementation. To implement the term correctly, the history of the particle has to be known. To overcome this and obtain a tractable problem, the square root in the history term is approximated by an exponential. It is found that the history force as a small effect on the transient growth. Finally, Direct numerical simulations are performed for flows with heavy particles to investigate the influence of particles on secondary instabilities. The threshold energy for two routes to turbulence is considered to investigate whether the threshold energy changes when particles are included. We show that particles influence secondary instabilities and particles may delay transition.
QC 20111013

Time-accurate calculations are used to investigate the three-dimensional flow structure and understand its influence on the heat transfer in a channel with concave indentations on one wall. A dimple depth to channel height ratio of 0.4 and dimple depth to imprint diameter ratio of 0.2 is used in the calculations. The Reynolds number (based on channel height) varies from Re = 25 in the laminar regime to Re = 2000 in the early turbulent regime. Fully developed flow and heat transfer conditions were assumed and a constant heat flux boundary condition was applied to the walls of the channel. In the laminar regime, the flow and heat transfer characteristics are dominated by the recirculation zones in the dimple with resulting augmentation ratios below unity. Flow transition is found to occur between Re = 1020 and 1130 after which both heat transfer and friction augmentation increase to values of 3.22 and 2.75, respectively, at Re = 2000. The presence of large scale vortical structures ejected from the dimple cavity dominate all aspects of the flow and heat transfer, not only on the dimpled surface but also on the smooth wall. In all cases the thermal efficiency using dimples was found to be significantly larger than other heat transfer augmentation techniques currently employed.
Master of Science

The growing demand for energy worldwide requires attention to the design and operating of heat exchangers and thermal devices to utilise and save thermal energy. There is a need to find new heat transport fluids with better heat transfer properties to increase convective heat transfer, and nanofluids are good alternatives to conventional heat transport fluids. Although extensive research has been done on the properties of nanofluids in recent decades, there is still a lack of research on convection heat transfer involving nanofluids, particularly in the transitional flow regime. This study focused on the application of nanofluids in heat exchangers as heat transport fluids by investigating forced convective heat transfer of alumina-water and titanium dioxide-water nanofluids prepared by using the one-step method. The particle size used was 46 nm and 42 nm for the aluminium oxide and the titanium dioxide respectively. Uniform heat flux boundary conditions were used by uniformly heating the rectangular channel electrically. Nanofluids with volume concentrations of 0.3, 0.5 and 1% were used for the alumina-water nanofluids, and volume concentrations of 0.3, 0.5, 0.7 and 1% were used for the titanium dioxide-water nanofluids. The viscosity of the nanofluids under investigation was determined experimentally, while the thermal conductivity and other properties were predicted by using suitable correlations from the literature. A Reynolds number range of 200 to 7 000 was covered, and the investigated flow rates included the laminar and turbulent flow regimes, as well as the transition regime from laminar to turbulent flow. Temperatures and pressure drops were measured to evaluate heat transfer coefficients, Nusselt numbers and pressure drop coefficients. Heat transfer and hydrodynamic characteristics in the transition flow regime were carefully studied and compared with those in the transition regime when flowing pure water in the same test section. The study also investigated another approach of enhancing heat transfer in heat exchangers by increasing the heat transfer area of the heat exchanger itself, and this was done by filling the rectangular test section with porous media to increase the heat transfer surface area and thus enhance heat transfer. Hence in this study, the effect of using porous media was also studied by filling the rectangular test section with high-porosity nickel foam. The permeability of the used nickel foam was determined by conducting pressure drop measurements through the nickel foam in the test section, and heat transfer and pressure drop parameters were measured and compared with those in the empty test section. The results showed that all the nanofluids used enhanced heat transfer, particularly in the transition flow regime. The 1.0% volume concentration alumina nanofluid showed maximum enhancement of the heat transfer coefficient, with values of 54% and 11% in the turbulent regime. The maximum enhancement of the heat transfer coefficient was 29.3% in the transition regime for the 1.0% volume concentration titanium dioxide-water nanofluid. The thermal performance factor in the transition flow regime was observed to be better than that in the turbulent and laminar flow regimes for all the nanofluids. The results of the nickel foam test section showed that the values of the friction coefficient were 24.5 times higher than the values of the empty test section, and the Nusselt number was observed to be three times higher when using nickel foam than without foam in the test section. No transition regime was observed for the foam-filled test section on either the heat transfer results or the pressure drop results; however, transition from laminar to turbulent was found for the test section without foam. The results of the thermal factor of the foam-filled test section showed a thermal performance factor higher than unity through the entire Reynolds number range of 2 000 to 6 500, with better thermal performance factor at lower Reynolds number.
Thesis (PhD (Mechanics))--University of Pretoria, 2019.
Mechanical and Aeronautical Engineering
PhD (Mechanics)
Unrestricted

The main scope of this PhD thesis is the analysis of unsteady laminar and transitional suddenly expanded flows. For this reason Implicit Large Eddy Simulation (ILES) approach was used in combination with high order, high resolution numerical methods. The numerical methods examined are a 2nd order Monotonic Upwind Scheme for Scalar Conservation Laws (MUSCL) with Van Leer limiter, a high order (3rd) interpolation and a 5th order Weighted Essentially Non-Oscillatory scheme (WENO). First the numerical data for three low (steady state) Reynolds numbers and for two unsteady ( in the form of primary frequencies) were compared to the experimental data and were found in good agreement. A grid convergence study was undertaken for two Reynolds numbers demonstrating grid convergence and justifying the selection of the grid. The three numerical methods were evaluated for two Reynolds numbers showing good agreement for Reynolds number 412 and discrepancies at Reynolds number 900 between MUSCL and WENO with the MUSCL demonstrating a very dissipative behavior. The physical behavior of the flow in a wide range of Reynolds numbers were examined. For this range the flow behavior changed from steady to unsteady laminar and finally exhibiting localized transition to turbulence. The behavior of the main recirculation areas was described and the vortex shedding that occur there and how this change with the Reynolds number. The flow was observed to change from an unsteady quasi three dimensional flow at Reynolds number 412 to an increased transitional state with three dimensional vortical structures at Reynolds number 550. Kinetic energy spectra were calculated for the aforementioned range of Reynolds numbers. The primary frequencies are increasing with Reynolds number as expected. The slopes that were calculated for the inertial subrange revealed a trend. As the Reynolds number is increasing the slopes are decreasing approaching the value given by Kolmogorov -5/3.

Cette thèse présente une étude numérique des régimes turbulents au sein d'un écoulement de Poiseuille plan forcé par un gradient de pression constant. L'effort numérique a porté principalement sur le concept d'Unité Minimale. Dans la première partie, des simulations en régime turbulent ont été conduites en géométrie périodique. Les DNS en Unité Minimale montrent que, l'activité turbulente se trouve localisée à proximité d'une des parois, et que la dynamique aux temps longs s'organise autour de renversements abrupts. Dans la seconde partie, on recherche par le calcul les états cohérents exactes en particulier les états dits frontière. Ces états frontière, obtenus par dichotomie, sont caractérisés par tourbillons longitudinaux et une paire unique de stries toujours localisées à proximité d'une seule paroi. Des représentations de la dynamique dans l'espace des phases sont reconstruites à l'aide de divers observables. La dynamique d'un renversement s'articule autour de visites transitoires vers un espace de solutions quasi-symétriques. Une onde progressive exacte, instable et quasi-symetrique a ainsi été identifiée. L'analyse de stabilité révèle que ses vecteurs propres séparent l'espace des phases en deux basins distincts. La dernière partie remet en question l'auto-similarité des différents régimes d'équilibre d'écoulement. Contrairement aux études récentes qui se concentrent sur les solutions à structure symétrique imposée, nos résultats suggèrent que les unités de parois sont également pertinentes pour les états frontière lorsqu'ils sont localisés près d'une paroi, meme si l'auto-similarité n'est pas aussi flagrante que pour les régimes turbulents
This thesis numerically investigates the dynamics of turbulence in plane Poiseuille flow driven by a fixed pressure gradient. The focus is especially on computations carried out within the minimal flow unit (M.F.U.). In the first part, turbulent simulations are carried out in spatially periodic channels. In the M.F.U. simulations, the turbulent activity appears to be localised near one wall and the long term dynamics features abrupt reversals. In the next part, we look numerically for exact coherent states in the M.F.U. system. Edge states, which are computed using bisection exhibit streamwise vortices and a single pair of streaks localised near only wall at all times. Different state space representations and phase portraits were constructed using appropriately chosen variables. The dynamics along a turbulent reversal is organised around transient visits to a subspace of (almost) symmetric flow fields. A nearly-symmetric exact travelling wave (TW) solution was found in this subspace. Stability analysis of the TW revealed that its unstable eigenvectors separate the state space into two symmetric basins. In the last part of this thesis, the self-similarity of the different non-trivial equilibrium flow regimes computed in this work, is addressed. Contrarily to most studies focusing on symmetric solutions, the present study suggests that inner scaling is relevant for the description of edge regimes as well although the self-similarity is not as satisfactory as for the turbulent regimes

Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, June 1990.
Thesis Advisor(s): Ligrani, Phillip M. ; Subramanian, Chelakara S. "June 1990." Description based on signature page. DTIC Identifier(s): Channel flow, Tollmien Schlichting waves, Klebanoff type waves, Stroubal number, Turbulence. Author(s) subject terms: Imposed oscillations, Tollmien-Schlichting waves, Klebanoff type waves, phase-averaged velocity, longitudinal velocity fluctuations, intermittency, center mode of secondary instability. Includes bibliographical references (p. 219-222). Also available online.

This paper presents a post-Keynesian ecological macro model that combines three strands of literature: the directed technological change mechanism developed in mainstream endogenous growth theory models, the ecological economic literature which highlights the role of green innovation and material flows, and the post-Keynesian school which provides a framework to deal with the demand side of the economy, financial flows, and inter- and intra-sectoral behavioral interactions. The model is stock-flow consistent and introduces research and development (R&D) as a component of GDP funded by private firm investment and public expenditure. The economy uses three complimentary inputs - Labor, Capital, and (non-renewable) Resources. Input productivities depend on R&D expenditures, which are determined by relative changes in their respective prices. Two policy experiments are tested; a Resource tax increase, and an increase in the share of public R&D on Resources. Model results show that policy instruments that are continually increased over a long-time horizon have better chances of achieving a "green" transition than one-of climate policy shocks to the system, that primarily have a short-run affect.
Series: Ecological Economic Papers

Recently, a new kind of turbulence has been discovered in the flow of concentrated polymer melts and solutions. These flows, known as purely elastic flows, become unstable when the elastic forces are stronger than the viscous forces. This contrasts with Newtonian turbulence, a more familiar regime where the fluid inertia dominates. While there is little understanding of purely elastic turbulence, there is a well-established dynamical systems approach to the transition from laminar flow to Newtonian turbulence. In this project, I apply this approach to purely elastic flows. Laminar flows are characterised by ordered, locally-parallel streamlines of fluid, with only diffusive mixing perpendicular to the flow direction. In contrast, turbulent flows are in a state of continuous instability: tiny differences in the location of fluid elements upstream make a large difference to their later locations downstream. The emerging understanding of the transition from a laminar to turbulent flow is in terms of exact coherent structures (ECS) — patterns of the flow that occur near to the transition to turbulence. The problem I address in this thesis is how to predict when a purely elastic flow will become unstable and when it will transition to turbulence. I consider a variety of flows and examine the purely elastic instabilities that arise. This prepares the ground for the identification of a three-dimensional steady state solution to the equations, corresponding to an exact coherent structure. I have organised my research primarily around obtaining a purely elastic exact coherent structure, however, solving this problem requires a very accurate prediction of the exact solution to the equations of motion. In Chapter 2 I start from a Newtonian ECS (travelling wave solutions in two-dimensional flow) and attempt to connect it to the purely elastic regime. Although I found no such connection, the results corroborate other evidence on the effect of elasticity on travelling waves in Poiseuille flow. The Newtonian plane Couette ECS is sustained by the Kelvin-Helmholtz instability. I discover a purely elastic counterpart of this mechanism in Chapter 3, and explore the non-linear evolution of this instability in Chapter 4. In Chapter 5 I turn to a slightly different problem, a (previously unexplained) instability in a purely elastic oscillatory shear flow. My numerical analysis supports the experimental evidence for instability of this flow, and relates it to the instability described in Chapter 3. In Chapter 6 I discover a self-sustaining flow, and discuss how it may lead to a purely elastic 3D exact coherent structure.

Ce travail de thèse s'intéresse à l'effet d'une variation longitudinale de l'occupation du sol de la plaine d'inondation sur l'écoulement d'une rivière en débordement. Nous traitons le cas d'une transition entre une zone de prairie et une zone de forêt, et vice versa. Cette variation d'occupation du sol est associée à une transition de rugosité hydraulique entre une rugosité de fond (prairie fortement immergée) et des macro-rugosités émergées (arbres), modélisées respectivement par une moquette plastifiée et par un champ de cylindres. Ces écoulements sont étudiés en laboratoire dans un canal de dimension 18 m x 3 m. Dans un premier temps, nous considérons l'écoulement à travers un champ de cylindres émergents en lit simple, en étudiant l'effet du fond sur le sillage des cylindres et le phénomène de seiche (fortes oscillations de la surface libre). Dans un deuxième temps, nous nous penchons sur le développement vers l'uniformité d'un écoulement en lit composé de rugosité uniforme. La croissance asymétrique de la couche de mélange du lit composé, la propriété d'autosimilarité ainsi que l'organisation tridimensionnelle des structures turbulentes cohérentes associées à la couche de mélange sont analysées. Le troisième temps fait l'objet de la transition longitudinale de rugosité en lit composé, dont l'effet sur la couche de mélange et sur les structures cohérentes est discuté. Nous évaluons également les différentes contributions au transfert latéral de quantité de mouvement entre lit mineur et plaine d'inondation par diffusion turbulente, par échange de masse et par les courants secondaires
This PhD thesis investigates the effect of a longitudinal change in floodplain land use on an overflooding river flow. We consider a transition between a meadow and a woodland and vice versa. This change in land use is associated with a change in hydraulic roughness, between a bed roughness (highly submerged meadow) and emergent macro-roughnesses (trees), respectively modelled by a plastic artificial grass and an array of emergent cylinders. The flows are experimentally investigated in an 18 m x 3 m laboratory flume. In a first step, we investigate the flow through a cylinder array in a single channel, focusing on the effect of bed roughness on the cylinder wakes and on the seiche phenomenon (strong free surface oscillations). In a second step, we study the development towards flow uniformity of compound channel flows with a uniform hydraulic roughness on the floodplains. The asymmetrical growth of the compound channel mixing layer, the self-similarity property and the three-dimensional organisation of the turbulent coherent structures associated with the mixing layer are analysed. In a third step, we investigate the longitudinal change in roughness in compound channel configuration, which effects on mixing layer and on coherent structures are discussed. We also assess the contributions to lateral transfers of momentum between main channel and floodplain by turbulent diffusion, by mass exchange and by secondary currents

Une approche d'interface raide est présentée pour le calcul des écoulements diphasiques avec tension superficielle et changement de phase en régime à faible nombre de Mach. Pour développer un tel modèle, où de légers effets compressibles sont pris en compte ainsi que des fermetures thermodynamiques correctes, le liquide et le gaz sont considérés comme compressibles et décrits par un solveur compressible précis. Ce solveur compressible adopte une technique de décomposition appelée "décomposition du transport acoustique" qui décompose le système Euler en deux parties: acoustique et transport. Sur la base du sous-système acoustique, un solveur de Riemann approximatif qui tient compte des effets de tension superficielle et de changement de phase est développé. L'interface de l'écoulement diphasique est capturée par la méthode de Level Set et considérée comme raide. La problème de la capture d'interface de la méthode Level Set dans le cadre Eulérien est le point clé des simulations d'écoulement diphasique, et dans ce travail, nous proposons et adoptons des approches d'ordre élevé pour l'advection de l'interface, la redistanciation et l'estimation de la courbure. En régime à faible nombre de Mach, les solveurs compressibles conventionnels perdent en précision et une correction à faible Mach est alors nécessaire pour réduire la dissipation numérique. Pour une méthode d'interface raide, l'interface est traitée comme la discontinuité de contact via la méthode Ghost Fluid. Sans une région lisse à l'interface, une telle discontinuité existant à l'interface présente un énorme défi pour la conception d'un schéma numérique. La correction à faible Mach bien connue dans la littérature pourrait conduire à une erreur de troncature significative, en particulier pour les écoulements diphasiques avec de grands rapports de densité et de vitesse du son. Pour retrouver une bonne propriété de préservation asymptotique, nous proposons une nouvelle correction à faible Mach avec une analyse asymptotique rigoureuse. Plusieurs cas de test numériques ont été utilisés pour valider la présente approche numérique et montrer ses bonnes performances
A sharp interface approach is presented for computing two-phase flows with surface tension and phase change in low Mach regime. To develop such a model, where slight compressible effects are taken into account as well as correct thermodynamical closures, both the liquid and the gas are considered compressible and described by a precise compressible solver. This compressible solver adopt a splitting technique called "acoustic-transport splitting" which splits the Euler system into two parts: acoustic and transport. Based on the acoustic subsystem, an approximate Riemann solver that accounts for surface tension and phase change effects is developed. The interface between two-phase flows is captured by the Level Set method that is considered to be sharp. The interface capturing issue of the Level Set method within the Eulerian framework is the key point of the two-phase flow simulations, and in this work we propose and adopt high-order approaches for interface advection, redistancing and curvature estimation. In low Mach regime, conventional compressible solvers lose accuracy and a low Mach correction is then necessary to reduce the numerical dissipation. For a sharp interface method, the interface is treated as the shock-wave contact discontinuity via the Ghost Fluid method. Without a smooth region at the interface, such discontinuity existing at the interface presents a huge challenge to the design of a numerical scheme. The well-known low Mach fix in literature could lead to significant truncation error, especially for two-phase flows with large density and sound speed ratios. To recover a good asymptotic-preserving property, we propose a new low Mach correction with rigorous asymptotic analysis. Several numerical test cases have been employed to validate the present numerical approach and enlighten its good performance

Le mouvement d'une bulle d'azote de Taylor dans des solutions mixtes glycérol-eau s'élevant à travers différents types d'expansions et de contractions est étudié par une approche numérique. La procédure CFD est basée sur un solveur open-source Basilisk, qui adopte la méthode du volume de fluide (VOF) pour capturer l'interface gaz-liquide. Les résultats des expansions/contractions soudaines sont comparés aux résultats expérimentaux. Les résultats montrent que les simulations sont en bon accord avec les expériences. La vitesse de la bulle augmente dans les expansions soudaines et diminue dans les contractions soudaines. Le modèle de rupture des bulles est observé dans les expansions soudaines avec de grands taux d'expansion, et un modèle de blocage des bulles est observé dans les contractions soudaines avec de petits rapports de contraction. De plus, la contrainte de cisaillement de la paroi, l'épaisseur du film liquide et la pression dans les simulations sont étudiées pour comprendre l'hydrodynamique de la bulle de Taylor montant par expansions/contractions. Le processus transitoire de la bulle de Taylor passant par une expansion/contraction soudaine est ensuite analysé pour trois singularités différentes: graduelle, parabolique convexe et parabolique concave. Une caractéristique unique de la contraction concave parabolique est que la bulle de Taylor passe par la contraction même pour de petits rapports de contraction. De plus, un modèle de changement de phase est développé dans le solveur Basilisk. Afin d'utiliser la méthode VOF géométrique existante dans Basilisk, une méthode VOF géométrique générale en deux étapes est implémentée. Le flux de masse n'est pas calculé dans les cellules interfaciales mais transféré aux cellules voisines autour de l'interface. La condition aux limites de température saturée est imposée à l'interface par une méthode de cellule fantôme. Le modèle de changement de phase est validé par évaporation de gouttelettes avec un taux de transfert de masse constant, le problème de Stefan unidimensionnel, le problème d'aspiration de l'interface et un cas d'ébullition à film plan. Les résultats montrent un bon accord avec les solutions analytiques ou les corrélations
The motion of a nitrogen Taylor bubble in glycerol-water mixed solutions rising through different types of expansions and contractions is investigated by a numerical approach. The CFD procedure is based on an open-source solver Basilisk, which adopts the volume-of-fluid (VOF) method to capture the gas-liquid interface. The results of sudden expansions/contractions are compared with experimental results. The results show that the simulations are in good agreement with experiments. The bubble velocity increases in sudden expansions and decreases in sudden contractions. The bubble break-up pattern is observed in sudden expansions with large expansion ratios, and a bubble blocking pattern is found in sudden contractions with small contraction ratios. In addition, the wall shear stress, the liquid film thickness, and pressure in the simulations are studied to understand the hydrodynamics of the Taylor bubble rising through expansions/contractions. The transient process of the Taylor bubble passing through sudden expansion/contraction is further analyzed for three different singularities: gradual, parabolic convex and parabolic concave. A unique feature in parabolic concave contraction is that the Taylor bubble passes through the contraction even for small contraction ratios. Moreover, a phase change model is developed in the Basilisk solver. In order to use the existed geometric VOF method in Basilisk, a general two-step geometric VOF method is implemented. Mass flux is calculated not in the interfacial cells but transferred to the neighboring cells around the interface. The saturated temperature boundary condition is imposed at the interface by a ghost cell method. The phase change model is validated by droplet evaporation with a constant mass transfer rate, the one-dimensional Stefan problem, the sucking interface problem, and a planar film boiling case. The results show good agreement with analytical solutions or correlations

Au sein des écosystèmes côtiers, la composition, la distribution et la dynamique phytoplanctoniques sont influencées par les variations spatio-temporelles des structures hydrologiques et des para mètres biogéochimiques, sous les pressions naturelles et anthropiques. Les suivis de référence, de par leur faible résolution spatiale et temporelle, peuvent manquer des événements-clés comme l'initiation ou la fin des efflorescences ou nuisibles (du type Harmful Algal Blooms). Pour permettre leur détection et mieux comprendre la distribution et la dynamique de ce compartiment à la base des réseaux trophiques et acteur majeur des cycles biogéochimiques, l'utilisation d'approches automatisées à haute fréquence permet de compléter les approches taxonomiques par la caractérisation fonctionnelle de l'ensemble du spectre de taille du phytoplancton. Cette thèse est consacrée à l'étude des caractéristiques morphologiques et physiologiques des groupes fonctionnels phytoplanctoniques définis à partir de leurs propriétés optiques à l'échelle de l'individu, rencontrés dans des mers épi-et intracontinentales contrastées en utilisant la cytométrie en flux automatisée de type "pulse-shape-recording". Tout d'abord, la distribution des groupes phytoplanctoniques et de leurs traits ont été explorés en Manche occidentale et centrale lors de la transition été-automne, ce qui a permis de mettre en évidence la formation de patches d'abondance et de biomasse à proximité du front d'Ouessant et une structuration à sub-mésoéchelle. En deuxième lieu, la dynamique des groupes fonctionnels phytoplanctoniques en Manche orientale et sud Mer du Nord a été étudiée pendant la période de développement des blooms printaniers de diatomées et de Phaeocystis globosa, avec l'utilisation de la LCBD et de la SCBD permettant l'observation de ségrégation spatiale entre groupes phytoplanctoniques dont leur distribution est expliquées par les paramètres de niche (marginalité et tolérance). Enfin, l'étude des paramètres conditionnant la distribution spatiale verticale le long d'un gradient de salinité en Mer Baltique a été abordée pendant la période estivale, en relation avec les propriétés biogéochimiques des masses d'eaux, qui a permis d'identifier les caractéristiques des groupes phytoplanctoniques participant à la distribution des groupes phytoplanctoniques. Les variations des traits ressortent comme étant les meilleurs prédicteurs de la distribution horizontale et verticale vis-à-vis des paramètres de niche et des descripteurs spatiaux (dispersion, paramètres physiques et biologiques). L'approche par traits fonctionnels, dérivés des mesures optiques à haute résolution, couplée à l'analyse de niche permettent d'avancer dans la compréhension des réponses des communautés aux gradients environnementaux, elles-mêmes détectées par les mesures d'indices de diversité. Ce travail a bénéficié de l'appui des projets régionaux (CPER MARCO), nationaux (convention MTES-CNRS) et européens (JERICO-NEXT)
In coastal ecosystems, phytoplankton composition, distribution and dynamics are strongly influenced by spatial and temporal variations of hydrological structures and biogeochemical parameters, consequences of natural and anthropogenic pressures. Reference monitoring, due to its low spatial and temporal resolution, may fail to detect key events as the initiation and end of phytoplankton outbursts or harmful algal blooms (HABs). By increasing the spatial and/or temporal resolution as well as completing taxonomical counting by investigating the phytoplankton whole size spectra, the use of automated sensors may allow contributing to a better understanding of the distribution and dynamics of this major player in biogeochemichal cycles, at the basis of most foof webs. This thesis consists in studying the characteristics of phytoplankton functional groups defined from their optical properties at the single-cell level, in relation to spatio-temporal variability encountered in contrasting marginal seas, applying the pulse shape-recording automated flow cytometry. This functional classification reflects the diversity of particles according to morphological and physiological properties. First of all, the distribution of phytoplankton groups and their traits where explored in the Western and Central English Channel during the summer period. Most groups formed patches of abundance and biomass near the Ushant front and were structured at the sub-mesoscale. Secondly, phytoplankton functional groups dynamics was characterized in the Eastern English Channel and Southern North Sea during the development period of diatoms and Phaeocystis globosa spring groups, by calculating LCBD and SCBD, wich allowed the observation of spatial segregation between phytoplankton groups. Their distribution was explained by the niche parameters (marginality and tolerance). Finally, the vertical distribution of phytoplankton functional groups in a salinity gradient was addressed in the Baltic Sea, in relation to the biogeochemical properties of the water masses and the characteristics of each PFGs. The variations of the traits are thus stand out as the best predictors of the horizontal and vertical distribution of phytoplankton groups with the respect to niche parameters and spatial descriptors (dispersion, physical and biological parameters). The functional approach, derived from phytoplankton optical properties addressed by automated flow cytometry, coupled to the niche analysis, make it possible to better explain and predict community responses to environmental gradients, such responses being detected in parallel by diversity indices. This work benefited from the support of local (MARCO State-Region Plan Contract), national (CNRS-MTES convention) and international European H2020 JERICO-NEXT projects

This thesis is a comprehensive experimental investigation of transitional and turbulent channel flow in the Reynolds number range of Reτ = 55 − 1559. Towards this objective, a new channel flow facility was designed and built, with a very high area contraction ratio of 108. This is achieved by building a channel of cross section 600 mm × 50 mm, length 7320 mm and connecting it to the downstream section of a blower wind tunnel. Two-dimensional (x-y plane along the mid-span of the channel) velocity field is measured using particle image velocimetry, hot-wire anemometry and Pitot tube. The contractions are carefully designed with optimal parameters to have minimal non-uniformity at the exit. This ultra high contraction ratio causes large reduction in the disturbance levels leading to delay in the onset of transition (at Rem = 2050, rather than the usual value of around 1500) and protraction of the extent of the transitional regime by around 4 times (ΔRem = 3150, as opposed to the usual value of around 800). Here Rem is the bulk Reynolds number. A new scaling law for velocity in the transitional region has been obtained based on the present measurements. The mean velocity in the transitional region is scaled by the centerline velocity, and displays a log law given by u/Uc = 0.13ln(y/h) + D1 with a ‘universal’ slope of 0.13. For the relatively quiet channel of the present study, this holds over a range of about 0.3 ≤ y/h ≤ 0.6. The results are compared with experimental and DNS data from literature for the configurations channel, pipe and boundary layer to confirm the universality of the slope, where they are valid over a smaller range. Using this, a relation for skin friction in the laminar-turbulent transitional flow is derived by a methodology similar to that of Prandtl for fully turbulent flow. From this, an expression for pressure drop in a channel (or pipe) as a function of bulk velocity is obtained, consistent with the well known Darcy-Weisbach relation. For the present experiments, pressure drop is given by ΔP ∝ un m, where n = 1.0, 2.5, 1.75 respectively for laminar, transitional and turbulent zones. While the results for laminar and turbulent regimes are already known, the one for the transitional regime is a new result. The scaling of mean velocity in the turbulent region, given by the long known and celebrated log law (Millikan (1938)), is an asymptotic expectation. A stringent test for the validity of the log law for finite Reynolds numbers is the constancy of the so-called diagnostic function in the inertial sublayer. However, for turbulent channel flow, the diagnostic function does not become constant till about Reτ = 5200 (?? and hence the standard log law does not accurately predict the mean velocity for Reτ < 5200. A modified version of the log law is derived from the mean flow momentum equation, which accounts for low Reτ and viscous effects. For closure Townsend (1980) is followed, wherein the turbulent kinetic energy equation is simplified to obtain a mixing-length-like relation between Reynolds shear stress and the mean velocity gradient. The resulting expression for mean velocity is seen to be consistent with the experimental and direct numerical simulation data in the inertial sublayer compared to the standard log law. This is further extended using a composite mixing length estimate for the outer layer along with the inertial sublayer and the agreement of the predicted mean velocity with experimental and direct numerical simulation data is excellent at high Reτ in the outer region. While both the modified and extended log law expressions work reasonably well in predicting the mean velocity from present experiments and DNS of Lee and Moser (2015), the prediction of diagnostic function was not satisfactory. However, when the variation of the structure parameter was accounted for, the prediction of diagnostic function was very good. Overall this vindicates a mixing length model as derived from the turbulent energy equation as proposed by Townsend (1980). Further, instantaneous uniform momentum zones (UMZs) are examined and found to exist in a turbulent channel flow at moderately high Reτ . Next, the scaling of streamwise turbulence intensity (Townsend (1980)) is examined. This scaling which yields a log law for turbulence intensity, seems to occur only at fairly high Reτ in the literature. The notion of active and inactive motions was introduced by Townsend (1961) (see also Bradshaw (1967)). It is proposed here that the non-occurrence of the log-law scaling for turbulence intensity at lower Reynolds numbers such as those of the present experiments are perhaps due to the obfuscatory effect of ‘inactive motions’. By using the so-called episodic description of wall turbulence (Narasimha et al. (2007)), the flow is split into active and inactive parts. The universal or active part of turbulence intensities so separated, display a universal logarithmic slope of -1.26 even at moderate Reynolds numbers while the log-law intercept in non-universal. This is also a vindication of the methodology to separate active and inactive parts followed herein. Conceptually, a connection between episodic descriptions and the active/ inactive description is also established. Next, the distribution of mean and fluctuating spanwise vorticities in the transitional and moderately turbulent regimes are considered. Dimensional mean vorticity profiles plotted for both transitional and turbulent regimes show that mean vorticity increases with Reynolds number close to the wall much more than away from the wall. This is well quantified by an integral quantity, akin to displacement thickness for a boundary layer, called centroid of mean vorticity. This centroid reduces monotonically with Reynolds number showing progressive migration of mean vorticity towards the wall. Likewise for fluctuating vorticity also, a centroid is defined in a similar manner. The centroid of fluctuating vorticity was also found to decrease monotonically with Reynolds number, in both transitional and turbulent regimes, showing increased concentration of fluctuating vorticity towards the wall as the Reynolds number is increased. Probability density function (PDF) of fluctuating spanwise vorticity were seen to be particularly peaky in the core region. Combined with a vanishingly small mean vorticity, a peaky PDF would signify a highly intermittent behaviour. However, we are not able to directly verify the intermittent vortical behaviour from the present study as the vorticity measurement is not time-resolved. Near the wall though, the PDF is less peaky and the mean is also nonzero. Taken together, this indicates, in outer co-ordinates, the vorticity concentration shifts towards the wall with Reynolds number. The (dimensional) vorticity fluctuation increases in the outer region also with Reynolds number, but at a much slower rate compared to the near-wall regions. We anticipate that this tendency is likely to accentuate at very high and ultra high turbulent Reynolds numbers outside the range of present studies. Further, two-point correlation with respect to the wall is measured using hotwire anemometry. Results show that the average inclination angle of the correlated structures decrease with Reynolds number, consistent with the corresponding inward vorticity migration. The next question that is addressed is that of interaction of inner and outer regions of a channel. The footprints of this activity manifest as a very large wavelength activity or very large scale motion (VLSM) in the power spectra of streamwise velocity fluctuation. We propose a scaling to relate the VLSM wavelengths (λ close to the centreline of the channel, with the time scale (T) of the corresponding low frequency activity displayed by the wall-normal velocity at the centerline. Further, the vertical velocity at the centerline has been split using kinematics into three terms. The first term (d/dx(Ucδ∗)) is instantaneous streamwise derivative of mass defect up to the centreline. The second term (hdUc/dx) is acceleration/deceleration of the freestream, is possibly due to the instantaneous response from the other side of the channel. The third term (R h0∂w∂z dy) is due to instantaneous dilation in the spanwise direction and the fourth term (vw) is due to wall transpiration (zero in the present case). The time series of the terms seems to signify a quasi-periodic see-saw like acceleration/deceleration of the streamwise centerline velocity due to the interaction between both the sides of the channel.

Flow separation is a common phenomenon in decelerated subcritical flows as in open channel expansions. A highly distorted velocity and shear stress distribution due to flow separation can lead to a continuous reduction of energy and trigger an adverse pressure gradient resulting in flow separation. This causes loss of energy and hydraulic efficiency of the systems. An experimental investigation was conducted with the use of a gradual rising hump on the bed of an expansion in a rectangular open channel. Besides the hump, split vanes in the flow field were also used to reduce the expansion angle and in turn reduce the adverse effect of flow separation. These modifications resulted in a relatively more uniform velocity and shear stress distribution in the transition and in the channel downstream of the expansion. A laboratory model of rectangular open channel transition expanding was constructed with Plexiglas plates. It facilitated the measurement of the flow velocity and turbulence characteristics with the aid of Laser Doppler Anemometer (LDA). The total divergent angle of the transition was 19.78 degrees. Velocities were measured along the x, y and z directions, positioning the LDA from both the bottom and the side of the channel. Two humps with gradual linear rises of 12.5 mm and 25 mm were used. A second device included the use of a single vane and a three vane splitter plates system formed with thin Plexiglas plates. Mainly velocity distributions, with and without humps and the splitter vanes were the results sought. The variations of energy and momentum coefficients were analyzed to find the effectiveness of the devices used in the transition to control flow separation. As a small addition to the study, the use of computational fluid dynamics (CFD) to predict the flow characteristics of open channel was also undertaken. Due to their lower time demand and lower cost, these numerical methods are preferred to experimental methods after they are properly validated. In the present study, the CFD solution is validated by experimental results. A limited number of CFD simulations were completed using the commercial Software ANSYS-CFX. In particular, mean velocity distributions for the rectangular open channel transitions were used for model validation. To this end, the three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations and the two equations k-[varepsilon] models were used. The validation of the model using test data was reasonable.

In this present research work, a detailed study conducted on the transition channel and the variation of specific energy in open channel flow. An empirical model equation formulated for the kinetic energy correction coefficients and moment correction coefficients between the different dependent and independent flow parameters, this model equation applicable only for the gradual expansion simple channel under the subcritical flow. The data set of expansion channel collected from previous researchers and on the basis of data sets the calculated value of the kinetic energy and momentum correction coefficients for expansion channels. Their expansion ratio is considered such as 1:1, 2:3, 1:3 & 1:6 for the observation and the calculated value. From that analysis, the kinetic energy and momentum correction coefficients varied from 1.1041 to 1.3948 and 1.039 to 1.082. The kinetic energy and momentum correction coefficients are depending on some influencing parameters such as diverging angle, width ratio, aspect ratio, cross-sectional ratio, Reynold’s number and Froude’s number and the energy head loss. On consideration of these parameters developed a mathematical model which predict kinetic energy and momentum correction coefficients. This mathematical model also validates by previous investigators. And also calculate the error analysis models are Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE). For the kinetic energy correction coefficients error analysis shows MAE(-0.0419), MAPE(6.4367), MSE(0.0335) and RMSE(0.1016) and MAE(0.0208), MAPE(4.8748), MSE(0.0129) and RMSE(0.1139) for momentum correction coefficents .

In comparison to the flow in a rigid channel, there is a multi-fold reduction in the transition Reynolds number for the flow in a micro channel when one of the walls is made sufficiently soft, due to a dynamical instability induced by the fluid-wall coupling. The flow after transition is characterized using Particle Image Velocimetry (PIV) in the x − y plane where x is the stream-wise direction and y is the cross-stream co-ordinate along the small dimension of the channel of height 0.2 − 0.3mm. For the two different soft walls of shear modulus 18 kPa and 2.19 kPaused here, the transition Reynolds number is about 250 and 330 respectively. The deformation of the microchannel due to the applied pressure gradient is measured in the experiments, and is used to predict the laminar mean velocity profiles for comparison with the experimental results. The mean velocity profiles in the microchannel are in quantitative agreement with those predicted for the laminar flow before transition, but are flatter near the centerline and have higher gradients at the wall after transition. The flow after transition is characterized by a mean velocity profile that is flatter at the center and steeper at the walls in comparison to that for a laminar flow. The root mean square of the stream-wise fluctuating velocity shows the characteristic sharp increase from the wall and a maximum close to the wall, as observed in turbulent flows in rigid-walled channels. However, the profile is asymmetric with a significantly higher maximum close to the soft wall in comparison to that close to the hard wall, and the Reynolds stress is found to be non-zero at the soft wall, indicating that there is a stress exerted by fluid velocity fluctuations on the wall. The turbulent energy production profile has a maximum at the soft wall, in contrast to the flow at a rigid surface where the turbulent energy production is zero at the wall (due to the zero Reynolds stress). The maximum of the root mean square of the velocity fluctuations and the Reynolds stress (divided by the fluid density) in the soft-walled microchannel for Reynolds numbers in the range 250-400, when scaled by suitable powers of the maximum velocity, are comparable to those in a rigid channel at Reynolds numbers in the range 5000-20000. The near-wall velocity profile shows no evidence of a viscous sub-layer for (yv∗/ν) as low as 2, but there is a logarithmic layer for (yv∗/ν) up to about 30, where the von Karman constants are very deferent from those for a rigid-walled channel. Here, v∗ is the friction velocity, ν is the kinematic viscosity and y is the distance from the soft surface. . The surface of the soft wall in contact with the fluid is marked with dye spots to monitor the deformation and motion along the fluid-wall interface. The measured displacement of the surface in the stream-wise direction, which is of the order of 5 − 12µm, is consistent with that calculated on the basis of linear elasticity. Low-frequency oscillations in the displacement of the surface are observed after transition in both the stream-wise and span-wise directions, indicating that the turbulent velocity fluctuations are dynamically coupled to motion in the solid. Modification of soft-wall turbulence in a micro channel due to the addition of small amounts of polymer The modification of soft-wall turbulence in a microchannel due to the addition of small amounts of polymer is experimentally studied using Particle Image Velocimetry (PIV) to measure the mean and the fluctuating velocities. The micro channels are of rectangular cross-section with height about 160 µm, width about 1.5 mm and length about 3 cm, with three walls made of hard Poly-dimethylsiloxane (PDMS) gel, and one wall made of soft PDMS gel with an elasticity modulus of about 18 kPa. A dynamical instabilty of the laminar flow due to the fluid-wall coupling, and a transition to turbulence, is observed at a Reynolds number of about 290 for the flow of pure water in the soft-walled microchannel (Verma and Kumaran, J. Fluid Mech., 727, 407-455, 2013). Solutions of polyacrylamide of molecular weight 5 × 106 and mass fraction up to 50 ppm, and of molecular weight 4 × 104 and mass fraction up to 1500 ppm, are used in the experiments. In all cases, the solutions are in the dilute limit be-low the critical concentration where the interactions between polymer molecules become important. The modification of the fluid viscosity due to addition of polymer molecules is small; the viscosity of the solutions with the highest polymer concentration exceed those for pure water by about 10% for the polymer with molecular weight 5 × 106, and by about 5% for the polymer with molecular weight 4 × 104. Two distinct types of flow modifications below and above a threshold mass fraction for the polymer, cTHRESHOLD , which is about 1 ppm for the polyacrylamide with molecular weight 5 × 106, and about 500 ppm for the polyacrylamide with molecular weight 4 × 104. As the polymer mass fraction increases up to the threshold value, there is no change in the transition Reynolds number, but there is significant turbulence attenuation the root mean square velocities in the stream wise and cross-stream directions decrease by a factor of 2, and the Reynolds stress decreases by a factor of 4 in comparison to that for pure water. When the polymer concentration increases beyond the threshold value, there is a decrease in the decrease in the transition Reynolds number by nearly one order of magnitude, and a further decrease in the intensity of the turbulent fluctuations. The lowest transition Reynolds number of about 35 for the solution of polyacrylamide with molecular weight 5 × 106 and mass fraction 50 ppm. For the polymer solutions with the highest concentrations, the fluctuating velocities in the stream wise and cross-stream direction are lower by a factor of 5, and the Reynolds stress is lower by a factor of 10, in comparison to pure water. Despite the significant turbulence attenuation, a sharp increase in the intensity of the fluctuating velocities is evident at transition for all polymer concentrations. Transitions to deferent kinds of turbulence in a channel with soft walls The flow in a rectangular channel with walls made of soft polyacrylamide gel is studied to examine the effect of soft walls on transition and turbulence. The width of the channel is much larger than the height, so that the flow can be considered approximately two-dimensional, the wall thickness is much larger than the channel height (smallest dimension), the bottom wall is fixed to a substrate and the top wall is unrestrained. The fluid velocity is measured using Particle Image Velocimetry, while the wall motion is studied by embedding beads in the soft wall, and measuring the time-variation of the displacement both parallel and perpendicular to the surface. As the Reynolds number increases, two different flow regimes are observed in sequence. The first is the ‘soft-wall turbulence’ resulting from a dynamical instability of the base flow due to the fluid-wall coupling. The flow in this case exhibits many of the features of the turbulent flow in a rigid channel, including the departure of the velocity profile from the parabolic profile, and the near-wall maxima in the stream-wise root mean square fluctuating velocity. However, there are also significant differences. The turbulence intensities, when scaled by suitable powers of the mean velocity, are much larger than those after the hard-wall laminar-turbulent transition at a Reynolds number of about 1000. The Reynolds stress profiles do not decrease to zero at the walls, indicating that the wall motion plays a role in the generation of turbulent fluctuations. There is no evidence of a viscous sub-layer close to the wall to within the experimental resolution. The mean velocity profile does satisfy a logarithmic law close to the surface within a region between 2-30 wall units from the surface, but the von Karman constants are very different from those for the hard-wall turbulence. The wall displacement measurements indicate that there is no observable motion perpendicular to the surface, but displacement fluctuations parallel to the surface are observed after transition, coinciding with the onset of velocity fluctuations in the fluid. The fluid velocity fluctuations are symmetric about the center line of the channel, and they show relatively little downstream variation after a flow development length of about 5 cm. As the Reynolds number is further increased, there is a second ‘wall flutter’ transition, which involves visible downstream traveling waves in the top (unrestrained) wall alone. Wall displacement fluctuations of low frequency (less than about 500 rad/s) are observed both parallel and perpendicular to the wall. The mean velocity profiles and turbulence intensities are asymmetric, with much larger turbulence intensities near the top wall. There is no evident logarithmic profile close to either the top or bottom wall. Fluctuations are initiated at the entrance of the test section, and the fluctuation intensities decrease with downstream distance, the fluctuation intensities first rapidly increase and then decrease as the Reynolds number is increased. For a channel with relatively small height (0.6 mm), the transition Reynolds number for the soft-wall instability is lower the hard-wall transition Reynolds number of about 1000, and the laminar flow becomes unstable to the soft-wall instability leading to soft-wall turbulence and then to wall flutter as the Reynolds number is increased. For a channel with relatively large height (1.8 mm), the transition Reynolds number for the soft-wall instability is higher than 1000, the flow first undergoes the hard-wall laminar-turbulent transition at a Reynolds number of about 1000, the turbulent flow undergoes the soft-wall transition leading to soft-wall turbulence, and then to wall flutter.

In comparison to the flow in a rigid channel, there is a multi-fold reduction in the transition Reynolds number for the flow in a micro channel when one of the walls is made sufficiently soft, due to a dynamical instability induced by the fluid-wall coupling. The flow after transition is characterized using Particle Image Velocimetry (PIV) in the x − y plane where x is the stream-wise direction and y is the cross-stream co-ordinate along the small dimension of the channel of height 0.2 − 0.3mm. For the two different soft walls of shear modulus 18 kPa and 2.19 kPaused here, the transition Reynolds number is about 250 and 330 respectively. The deformation of the microchannel due to the applied pressure gradient is measured in the experiments, and is used to predict the laminar mean velocity profiles for comparison with the experimental results. The mean velocity profiles in the microchannel are in quantitative agreement with those predicted for the laminar flow before transition, but are flatter near the centerline and have higher gradients at the wall after transition. The flow after transition is characterized by a mean velocity profile that is flatter at the center and steeper at the walls in comparison to that for a laminar flow. The root mean square of the stream-wise fluctuating velocity shows the characteristic sharp increase from the wall and a maximum close to the wall, as observed in turbulent flows in rigid-walled channels. However, the profile is asymmetric with a significantly higher maximum close to the soft wall in comparison to that close to the hard wall, and the Reynolds stress is found to be non-zero at the soft wall, indicating that there is a stress exerted by fluid velocity fluctuations on the wall. The turbulent energy production profile has a maximum at the soft wall, in contrast to the flow at a rigid surface where the turbulent energy production is zero at the wall (due to the zero Reynolds stress). The maximum of the root mean square of the velocity fluctuations and the Reynolds stress (divided by the fluid density) in the soft-walled microchannel for Reynolds numbers in the range 250-400, when scaled by suitable powers of the maximum velocity, are comparable to those in a rigid channel at Reynolds numbers in the range 5000-20000. The near-wall velocity profile shows no evidence of a viscous sub-layer for (yv∗/ν) as low as 2, but there is a logarithmic layer for (yv∗/ν) up to about 30, where the von Karman constants are very deferent from those for a rigid-walled channel. Here, v∗ is the friction velocity, ν is the kinematic viscosity and y is the distance from the soft surface. . The surface of the soft wall in contact with the fluid is marked with dye spots to monitor the deformation and motion along the fluid-wall interface. The measured displacement of the surface in the stream-wise direction, which is of the order of 5 − 12µm, is consistent with that calculated on the basis of linear elasticity. Low-frequency oscillations in the displacement of the surface are observed after transition in both the stream-wise and span-wise directions, indicating that the turbulent velocity fluctuations are dynamically coupled to motion in the solid. Modification of soft-wall turbulence in a micro channel due to the addition of small amounts of polymer The modification of soft-wall turbulence in a microchannel due to the addition of small amounts of polymer is experimentally studied using Particle Image Velocimetry (PIV) to measure the mean and the fluctuating velocities. The micro channels are of rectangular cross-section with height about 160 µm, width about 1.5 mm and length about 3 cm, with three walls made of hard Poly-dimethylsiloxane (PDMS) gel, and one wall made of soft PDMS gel with an elasticity modulus of about 18 kPa. A dynamical instabilty of the laminar flow due to the fluid-wall coupling, and a transition to turbulence, is observed at a Reynolds number of about 290 for the flow of pure water in the soft-walled microchannel (Verma and Kumaran, J. Fluid Mech., 727, 407-455, 2013). Solutions of polyacrylamide of molecular weight 5 × 106 and mass fraction up to 50 ppm, and of molecular weight 4 × 104 and mass fraction up to 1500 ppm, are used in the experiments. In all cases, the solutions are in the dilute limit be-low the critical concentration where the interactions between polymer molecules become important. The modification of the fluid viscosity due to addition of polymer molecules is small; the viscosity of the solutions with the highest polymer concentration exceed those for pure water by about 10% for the polymer with molecular weight 5 × 106, and by about 5% for the polymer with molecular weight 4 × 104. Two distinct types of flow modifications below and above a threshold mass fraction for the polymer, cTHRESHOLD , which is about 1 ppm for the polyacrylamide with molecular weight 5 × 106, and about 500 ppm for the polyacrylamide with molecular weight 4 × 104. As the polymer mass fraction increases up to the threshold value, there is no change in the transition Reynolds number, but there is significant turbulence attenuation the root mean square velocities in the stream wise and cross-stream directions decrease by a factor of 2, and the Reynolds stress decreases by a factor of 4 in comparison to that for pure water. When the polymer concentration increases beyond the threshold value, there is a decrease in the decrease in the transition Reynolds number by nearly one order of magnitude, and a further decrease in the intensity of the turbulent fluctuations. The lowest transition Reynolds number of about 35 for the solution of polyacrylamide with molecular weight 5 × 106 and mass fraction 50 ppm. For the polymer solutions with the highest concentrations, the fluctuating velocities in the stream wise and cross-stream direction are lower by a factor of 5, and the Reynolds stress is lower by a factor of 10, in comparison to pure water. Despite the significant turbulence attenuation, a sharp increase in the intensity of the fluctuating velocities is evident at transition for all polymer concentrations. Transitions to deferent kinds of turbulence in a channel with soft walls The flow in a rectangular channel with walls made of soft polyacrylamide gel is studied to examine the effect of soft walls on transition and turbulence. The width of the channel is much larger than the height, so that the flow can be considered approximately two-dimensional, the wall thickness is much larger than the channel height (smallest dimension), the bottom wall is fixed to a substrate and the top wall is unrestrained. The fluid velocity is measured using Particle Image Velocimetry, while the wall motion is studied by embedding beads in the soft wall, and measuring the time-variation of the displacement both parallel and perpendicular to the surface. As the Reynolds number increases, two different flow regimes are observed in sequence. The first is the ‘soft-wall turbulence’ resulting from a dynamical instability of the base flow due to the fluid-wall coupling. The flow in this case exhibits many of the features of the turbulent flow in a rigid channel, including the departure of the velocity profile from the parabolic profile, and the near-wall maxima in the stream-wise root mean square fluctuating velocity. However, there are also significant differences. The turbulence intensities, when scaled by suitable powers of the mean velocity, are much larger than those after the hard-wall laminar-turbulent transition at a Reynolds number of about 1000. The Reynolds stress profiles do not decrease to zero at the walls, indicating that the wall motion plays a role in the generation of turbulent fluctuations. There is no evidence of a viscous sub-layer close to the wall to within the experimental resolution. The mean velocity profile does satisfy a logarithmic law close to the surface within a region between 2-30 wall units from the surface, but the von Karman constants are very different from those for the hard-wall turbulence. The wall displacement measurements indicate that there is no observable motion perpendicular to the surface, but displacement fluctuations parallel to the surface are observed after transition, coinciding with the onset of velocity fluctuations in the fluid. The fluid velocity fluctuations are symmetric about the center line of the channel, and they show relatively little downstream variation after a flow development length of about 5 cm. As the Reynolds number is further increased, there is a second ‘wall flutter’ transition, which involves visible downstream traveling waves in the top (unrestrained) wall alone. Wall displacement fluctuations of low frequency (less than about 500 rad/s) are observed both parallel and perpendicular to the wall. The mean velocity profiles and turbulence intensities are asymmetric, with much larger turbulence intensities near the top wall. There is no evident logarithmic profile close to either the top or bottom wall. Fluctuations are initiated at the entrance of the test section, and the fluctuation intensities decrease with downstream distance, the fluctuation intensities first rapidly increase and then decrease as the Reynolds number is increased. For a channel with relatively small height (0.6 mm), the transition Reynolds number for the soft-wall instability is lower the hard-wall transition Reynolds number of about 1000, and the laminar flow becomes unstable to the soft-wall instability leading to soft-wall turbulence and then to wall flutter as the Reynolds number is increased. For a channel with relatively large height (1.8 mm), the transition Reynolds number for the soft-wall instability is higher than 1000, the flow first undergoes the hard-wall laminar-turbulent transition at a Reynolds number of about 1000, the turbulent flow undergoes the soft-wall transition leading to soft-wall turbulence, and then to wall flutter.

The main objective of this thesis is to study the fundamental behaviour of multi-component gas mixture flows in micro/nano-channels undergoing catalytic chemical reactions on the walls. This work is primarily focused on nano-scale reacting flows seen in related applications; especially, miniaturized energy sources such as micro-fuel cells and batteries. At these geometries, the order of the characteristic length is close to the mean free path of the flowing gas, making the flow highly rarefied. As a result, non-equilibrium conditions prevail even the bulk flow and therefore, continuum assumptions are not held anymore. Hence, discrete methods should be adopted to simulate molecular movements and interactions described by the Boltzmann equation. The Direct Simulation Monte Carlo (DSMC) method was employed for the present research due to its natural ability for simulating a broad range of rarefied gas flows, and its flexibility to incorporate surface chemical reactions. In the first step, fluid dynamics and the heat transfer of H₂/N₂ and H₂/N₂/CO₂ gas mixture slip flows in a plain micro-channel are simulated. The obtained results are compared to the corresponding data achieved from Navier-Stokes equations with slip/jump boundary conditions. Generally, very good agreements are observed between the two methods. It proves the ability of DSMC in replicating the fluid properties of multi-component gas mixtures even when high mass discrepancies exist among the species. Based on this comparison, the proper parameters are set for the prepared DSMC code, and the appropriate intermolecular collision model is identified. It is also found that stream variables should be calculated more accurately at flow boundaries in order to simulate the intense upstream diffusion emerging at low velocity flows frequently seen in micro/nano-applications. Therefore, in the second step, a novel pressure boundary condition is introduced for gas mixture flows by substituting the commonly used Maxwell velocity distribution with the Chapman-Enskog distribution function. It is shown that this new method yields better results for lower velocity and higher rarefaction level cases. In the last step, a new method is proposed for coupling the flow field simulated by DSMC and surface reactions modelled by the species conservation ODE system derived from the reaction mechanism. First, a lean H₂/air slip flow subjected to oxidation on platinum coated walls in a flat micro-channel 4μm in height is simulated as a verification test case. The results obtained are validated against the solutions of the Navier-Stokes equations with slip/jump boundary conditions and very good conformity is achieved. Next, several cases undergoing the same reaction with Reynolds numbers ranging from 0.2 to 3.6 and Knudsen numbers ranging from 0.025 to 0.375, are simulated using the verified code to investigate the effects of the channel height ranging from 0.5μm to 2μm , the inlet mass flow rate ranging from 5 kg/m².s to 25 kg/m².s, the inlet temperature ranging from 300K to 700K, the wall temperature ranging from 300K to 1000K, and the fuel/air equivalence ratio ranging from 0.28 to 1.5. Some of the findings are as follows: (1) increasing the surface temperature from 600K to 1000K and/or the inlet temperature from 300K to 700K results in negligible enhancement of the conversion rate, (2) the optimum value of the equivalence ratio is on the fuel lean side (around 0.5), (3) the efficiency of the reactor is higher for smaller channel heights, and (4) increasing the inlet mass flux elevates the reaction rate especially for the smaller channels; this effect is not linear and is more magnified for lower mass fluxes.

Turbulent boundary layers approximating those found on the NASA Orion Multi-Purpose Crew Vehicle (MPCV) thermal protection system during atmospheric reentry from the International Space Station have been studied by direct numerical simulation, with the ultimate goal of reducing aerothermodynamic heating prediction uncertainty. Simulations were performed using a new, well-verified, openly available Fourier/B-spline pseudospectral code called Suzerain equipped with a ``slow growth'' spatiotemporal homogenization approximation recently developed by Topalian et al. A first study aimed to reduce turbulence-driven heating prediction uncertainty by providing high-quality data suitable for calibrating Reynolds-averaged Navier--Stokes turbulence models to address the atypical boundary layer characteristics found in such reentry problems. The two data sets generated were Ma[approximate symbol] 0.9 and 1.15 homogenized boundary layers possessing Re[subscript theta, approximate symbol] 382 and 531, respectively. Edge-to-wall temperature ratios, T[subscript e]/T[subscript w], were close to 4.15 and wall blowing velocities, v[subscript w, superscript plus symbol]= v[subscript w]/u[subscript tau], were about 8 x 10-3 . The favorable pressure gradients had Pohlhausen parameters between 25 and 42. Skin frictions coefficients around 6 x10-3 and Nusselt numbers under 22 were observed. Near-wall vorticity fluctuations show qualitatively different profiles than observed by Spalart (J. Fluid Mech. 187 (1988)) or Guarini et al. (J. Fluid Mech. 414 (2000)). Small or negative displacement effects are evident. Uncertainty estimates and Favre-averaged equation budgets are provided. A second study aimed to reduce transition-driven uncertainty by determining where on the thermal protection system surface the boundary layer could sustain turbulence. Local boundary layer conditions were extracted from a laminar flow solution over the MPCV which included the bow shock, aerothermochemistry, heat shield surface curvature, and ablation. That information, as a function of leeward distance from the stagnation point, was approximated by Re[subscript theta], Ma[subscript e], [mathematical equation], v[subscript w, superscript plus sign], and T[subscript e]/T[subscript w] along with perfect gas assumptions. Homogenized turbulent boundary layers were initialized at those local conditions and evolved until either stationarity, implying the conditions could sustain turbulence, or relaminarization, implying the conditions could not. Fully turbulent fields relaminarized subject to conditions 4.134 m and 3.199 m leeward of the stagnation point. However, different initial conditions produced long-lived fluctuations at leeward position 2.299 m. Locations more than 1.389 m leeward of the stagnation point are predicted to sustain turbulence in this scenario.
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