17 research outputs found

    Transition in Particle-laden Flows

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    This thesis presents the study of laminar to turbulent transition of particle laden flows. When a flow becomes turbulent, the drag increases one order of magnitude compared to a laminar flow, therefore, much research is devoted to understand and influence the transition. Previous research at the Linne Flow Centre at KTH has concentrated on the understanding of the bypass transition process of single-phase fluids. Though there are still questions, the principles of this process are now, more or less, known. However, little is known of the influence of particles on transition. While experiments in the 1960s already showed that particles can reduce the friction in turbulent channel flows significantly. The question explored in this thesis is whether this can be attributed to their influence on transition. The initial onset of transition has been investigated with both modal and non-modal linear stability analysis in a Poiseuille flow between two parallel plates. Particles are introduced as a second fluid and they are considered to be solid, spherical and homogeneously distributed. When the fluid density is much smaller than the particle density, ξ (≡ ρf/ρp) &lt;&lt; 1, an increase of the critical Reynolds number is observed. However, transient growth of streamwise vortices resulting in streaks is not affected by inclusion of particles. Particles with ξ ∼ 1 hardly seem to have an effect on stability. Although linear analysis shows that particles hardly influence the transient growth of disturbances, they might affect other (non-linear) stages of transition. To investigate such effects, the full Navier-Stokes equations for 3D Poiseuille flow between two parallel plates are numerically solved and particles are introduced as points with two-way coupling. For particles in a channel flow with ξ&lt;&lt;1, results show that the transition to turbulence is delayed for mass fractions ƒ (=mp N / ρf) larger than 0.1. For a mass fraction of ƒ=0.4 the initial disturbance energy needed to get a turbulent flow increases with a factor of four. Even if lower particle mass fractions ƒ are used, locally there could be large particle mass fractions. Therefore, the next step is to investigate the generation of local large particle mass fractions ƒ. Such particle clusters can be as large as the typical flow structures in the flow, like streak width and vortex size. Then they might change the flow field and (in)stability mechanisms. Numerical simulations of bypass transition in a boundary layer flow are used to determine whether particles cluster and where they tend to cluster. It is found that point particles with ξ&lt;&lt;1 and a large particle relaxation time tend to move in the low speed regions of the flow. In case of streaks, the low speed streaks are most favourable. For smaller particle relaxation times, particles act as tracers and do not have a preferential position and are homogeneously distributed. For particles with ξ∼1 the linear stability analysis showed no transition effect at any ƒ. However, one effect neglected until now is that of particle size. For particles with dimensions of the same order of magnitude of the flow disturbance, particles might influence the flow field. To investigate whether such particles migrate towards positions where they can affect transition some exploratory numerical simulations and experiments are performed. Numerically, the lateral migration of large particles (H/d=5) with ξ=1 in a 3D Poiseuille flow between two parallel plates is investigated. In laminar channel flow, large particles tend to move laterally due to shear to an equilibrium position. For a single large particle some key parameters for migration are identified: the size of the particle and the velocity of the fluid. When multiple particles are present, they tend to form particle trains. If particles are close, they influence each other and the equilibrium position shifts towards the wall, where the final position is dependent on the inter particle spacing. Also, not one steady equilibrium position is present, but particles move around an equilibrium position. Experimentally, migration of particles in bypass transition with ξ=1 is investigated to find out whether neutrally buoyant particles have a preferential position within streaks. The first results with tracer particles (d∼50μm) and few large particles (d∼200μm) do not show detectable preferential positioning.QC 20131030</p

    Transition in Particle-laden Flows

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    This thesis presents the study of laminar to turbulent transition of particle laden flows. When a flow becomes turbulent, the drag increases one order of magnitude compared to a laminar flow, therefore, much research is devoted to understand and influence the transition. Previous research at the Linne Flow Centre at KTH has concentrated on the understanding of the bypass transition process of single-phase fluids. Though there are still questions, the principles of this process are now, more or less, known. However, little is known of the influence of particles on transition. While experiments in the 1960s already showed that particles can reduce the friction in turbulent channel flows significantly. The question explored in this thesis is whether this can be attributed to their influence on transition. The initial onset of transition has been investigated with both modal and non-modal linear stability analysis in a Poiseuille flow between two parallel plates. Particles are introduced as a second fluid and they are considered to be solid, spherical and homogeneously distributed. When the fluid density is much smaller than the particle density, ξ (≡ ρf/ρp) &lt;&lt; 1, an increase of the critical Reynolds number is observed. However, transient growth of streamwise vortices resulting in streaks is not affected by inclusion of particles. Particles with ξ ∼ 1 hardly seem to have an effect on stability. Although linear analysis shows that particles hardly influence the transient growth of disturbances, they might affect other (non-linear) stages of transition. To investigate such effects, the full Navier-Stokes equations for 3D Poiseuille flow between two parallel plates are numerically solved and particles are introduced as points with two-way coupling. For particles in a channel flow with ξ&lt;&lt;1, results show that the transition to turbulence is delayed for mass fractions ƒ (=mp N / ρf) larger than 0.1. For a mass fraction of ƒ=0.4 the initial disturbance energy needed to get a turbulent flow increases with a factor of four. Even if lower particle mass fractions ƒ are used, locally there could be large particle mass fractions. Therefore, the next step is to investigate the generation of local large particle mass fractions ƒ. Such particle clusters can be as large as the typical flow structures in the flow, like streak width and vortex size. Then they might change the flow field and (in)stability mechanisms. Numerical simulations of bypass transition in a boundary layer flow are used to determine whether particles cluster and where they tend to cluster. It is found that point particles with ξ&lt;&lt;1 and a large particle relaxation time tend to move in the low speed regions of the flow. In case of streaks, the low speed streaks are most favourable. For smaller particle relaxation times, particles act as tracers and do not have a preferential position and are homogeneously distributed. For particles with ξ∼1 the linear stability analysis showed no transition effect at any ƒ. However, one effect neglected until now is that of particle size. For particles with dimensions of the same order of magnitude of the flow disturbance, particles might influence the flow field. To investigate whether such particles migrate towards positions where they can affect transition some exploratory numerical simulations and experiments are performed. Numerically, the lateral migration of large particles (H/d=5) with ξ=1 in a 3D Poiseuille flow between two parallel plates is investigated. In laminar channel flow, large particles tend to move laterally due to shear to an equilibrium position. For a single large particle some key parameters for migration are identified: the size of the particle and the velocity of the fluid. When multiple particles are present, they tend to form particle trains. If particles are close, they influence each other and the equilibrium position shifts towards the wall, where the final position is dependent on the inter particle spacing. Also, not one steady equilibrium position is present, but particles move around an equilibrium position. Experimentally, migration of particles in bypass transition with ξ=1 is investigated to find out whether neutrally buoyant particles have a preferential position within streaks. The first results with tracer particles (d∼50μm) and few large particles (d∼200μm) do not show detectable preferential positioning.QC 20131030</p

    Stability analysis of channel flow laden with small particles.

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    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 2011101

    Modal and non-modal stability analysis of a channel flow seeded with light particles

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    Both modal and non-modal stability analysis of a channel flow laden with light particles is presented. The particles are assumed spherical and solid and their presence modeled using two-way coupling, with Stokes drag, added mass and fluid acceleration as coupling terms. The Stokes drag is a function of particle relaxation time and mass fraction, while added mass and fluid acceleration are a function of mass fraction and density ratio. When the particles considered have a density ratio of order one, all three terms are important. Modal analysis shows a decrease in critical Reynolds number proportional to the mass fraction for all particle relaxation times at a density ratio of one. Lighter particles decrease the critical Reynolds number further, whereas heavier particles might increase the critical Reynolds number. Most effect is found when the stability Stokes number is of order one. Non-modal analysis shows that the transient growth of the total system is enhanced in proportion to the particle mass fraction, as observed in flows laden with heavy particles. The generation of streamwise streaks is still the most dominant disturbance-growth mechanism in particle laden flows with light particles. Thus, the presence of particles may not work to delay the transition.QS 2012031

    Modal and non-modal stability analysis of a channel flow seeded with light particles

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    Both modal and non-modal stability analysis of a channel flow laden with light particles is presented. The particles are assumed spherical and solid and their presence modeled using two-way coupling, with Stokes drag, added mass and fluid acceleration as coupling terms. The Stokes drag is a function of particle relaxation time and mass fraction, while added mass and fluid acceleration are a function of mass fraction and density ratio. When the particles considered have a density ratio of order one, all three terms are important. Modal analysis shows a decrease in critical Reynolds number proportional to the mass fraction for all particle relaxation times at a density ratio of one. Lighter particles decrease the critical Reynolds number further, whereas heavier particles might increase the critical Reynolds number. Most effect is found when the stability Stokes number is of order one. Non-modal analysis shows that the transient growth of the total system is enhanced in proportion to the particle mass fraction, as observed in flows laden with heavy particles. The generation of streamwise streaks is still the most dominant disturbance-growth mechanism in particle laden flows with light particles. Thus, the presence of particles may not work to delay the transition.QS 2012031

    Numerical Simulations of laminar-turbulent transition in particle-laden channel flow

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    Direct Numerical Simulation of a particle-laden channel flow is performed, with particles assumed solid, spherical and heavy. Two-way coupling between fluidand particles is modeled with Stokes drag. The equations describing the fluid flow are solved with an Eulerian mesh and those describing particles are solved in a Lagrangian frame. The numerical code is validated with results from linear optimal growth from previous studies; the optimal growth of streamwise vortices resulting in streamwise streaks is still the most efficient mechanism for disturbance amplification at subcritical conditions as for the case of a single phase fluid. We consider transition initiated by two initial disturbances well-known in literature, streamwise vortices and oblique waves. The threshold energy for transition is computed for both cases. It is observed that streamwise vortices in combination with an oblique wave as additional initial disturbance, result ina small increase of threshold energy compared to a clean fluid. In addition, the time at which transition occurs clearly increases for disturbances of equal initial energy. The threshold energy in the case of the so-called oblique scenario, increases by a factor about 4 in the presence of particles. The results are explained by considering the reduced amplification of oblique modes in the presence of particles. The results from these two classical scenarios indicate that, although stability analysis shows hardly any effect on optimal growth, particles do influence secondary instabilities and streak breakdown, thus the non-linear stages of transition, in two different ways. The presence of particles introduced threedimensional, streamwise-dependent modulations, especially at low concentrations, that may trigger and enhance secondary instabilities of streamwiseindependent streaks. On the other hand, particles decrease the amplitude ofoblique modes thus delaying transition initiated by their nonlinear interactions as in the oblique scenario.QC 2011101

    Numerical Simulations of laminar-turbulent transition in particle-laden channel flow

    No full text
    Direct Numerical Simulation of a particle-laden channel flow is performed, with particles assumed solid, spherical and heavy. Two-way coupling between fluidand particles is modeled with Stokes drag. The equations describing the fluid flow are solved with an Eulerian mesh and those describing particles are solved in a Lagrangian frame. The numerical code is validated with results from linear optimal growth from previous studies; the optimal growth of streamwise vortices resulting in streamwise streaks is still the most efficient mechanism for disturbance amplification at subcritical conditions as for the case of a single phase fluid. We consider transition initiated by two initial disturbances well-known in literature, streamwise vortices and oblique waves. The threshold energy for transition is computed for both cases. It is observed that streamwise vortices in combination with an oblique wave as additional initial disturbance, result ina small increase of threshold energy compared to a clean fluid. In addition, the time at which transition occurs clearly increases for disturbances of equal initial energy. The threshold energy in the case of the so-called oblique scenario, increases by a factor about 4 in the presence of particles. The results are explained by considering the reduced amplification of oblique modes in the presence of particles. The results from these two classical scenarios indicate that, although stability analysis shows hardly any effect on optimal growth, particles do influence secondary instabilities and streak breakdown, thus the non-linear stages of transition, in two different ways. The presence of particles introduced threedimensional, streamwise-dependent modulations, especially at low concentrations, that may trigger and enhance secondary instabilities of streamwiseindependent streaks. On the other hand, particles decrease the amplitude ofoblique modes thus delaying transition initiated by their nonlinear interactions as in the oblique scenario.QC 2011101

    Chopin in Britain : Chopin's visits to England and Scotland in 1837 and 1848 : people, places, and activities

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    Academically, Chopin's two visits to Britain in 1837 and 1848 remain unexplored. This thesis aims to rectify this, using extensive published and manuscript material in Edinburgh, London, Paris, Cracow and Warsaw, and topographical and other illustrations. On the first of Chopin's visits, in July 1837, he travelled from Paris to London with Camille Pleyel, whose family firm of Pleyel et Cie manufactured Chopin's favourite pianos. In London for only eleven days, Chopin visited the Broadwoods at No 46 Bryanston Square, went to the opera, and signed contracts with Wessel. On his second visit, in 1848, the year before he died, Chopin spent seven months in England and Scotland at the prompting of his aristocratic Scots pupil, Jane Stirling. In London, he gave recitals for the Duke and Duchess of Sutherland, Mrs Adelaide Sartoris, the Earl of Falmouth, and the Countess of Blessington. On 5 August, accompanied by John Muir Wood, Chopin took the train from Euston to Edinburgh, where he was met by the Stirlings' Polish physician, Dr Adam Lyschifiski. Subsequently, Chopin was a guest at Scottish country seats - notably Calder, Johnstone, Strachur, Wishaw, Keir, and Hamilton Palace. Aside from playing privately for his hosts, Chopin gave public concerts in the Gentlemen's Concert Hall in Manchester, the Merchants' Hall in Glasgow, and the Hopetoun Rooms in Edinburgh. Returning to London on 31 October, Chopin performed in Guildhall, the last concert of his life. On 23 November he left London for Paris, dying there on 17 October the next year. His funeral in the Madeleine was partly financed by Jane Stirling, who later published a seven-volume edition of his music, preserved Chopin memorabilia, studied with his former pupil Thomas Tellefsen, and cherished the composer's memory until her own death in 1859.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
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