Direct numerical simulations

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a 0 -C continuous expansion. Computationally and theoretically, by increasing the polynomial order p , high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.

is a graduate student supported by internal institutional funds. He is relatively new in the project and has been mainly spending time learning to use the various software tools available. He is also working with researchers from France who would like to use our simulation data for purposes of wavelet analyses and Coherent Vortex Simulation.

Dynamical behavior of the turbulent channel flow separation induced by a wall-mounted two-dimensional bump is studied, with an emphasis on unsteadiness characteristics of vortical motions evolving in the separated flow. The present investigations are based on an experimental approach and Direct Numerical Simulation (Dns). The main interests are devoted to give further insight on mean flow properties, characteristic scales and physical mechanisms of low-frequencies unsteadiness. The study also aims to clarify the Reynolds number effects. Results are presented for turbulent flows at moderate Reynolds-number Re τ ranging from 125 to 730 where Re τ is based on friction velocity and channel half-height. A large database of time-resolved two-dimensional Piv measurements is used to obtain the velocity distributions in a region covering the entire shear layer and the flow surrounding the bump. An examination of both high resolved velocity and wallshear stress measurements showed that for moderate Reynolds numbers, a separated region exists until a critical value. Under this conditions, a thin region of reverse flow is formed above the bump and a large-scale vortical activity is clearly observed and analyzed. Three distinct self-sustained oscillations are identified in the separated zone. The investigation showed that the flow exhibits the shear-layer instability and vortexshedding type instability of the bubble. A low-frequency self-sustained oscillations associated with a flapping phenomenon is also identified. The experimental results are further emphasized using post-processed data from Direct Numerical Simulations, such as flow statistics and Dynamic Mode Decomposition. Physical mechanisms associated with observed self-sustained oscillations are then suggested and results are discussed in the light of instabilities observed in a laminar regime for the same flow configuration.

During the last decade, many approaches for resolved-particle simulation (RPS) have been developed for numerical studies of finitesize particle-laden turbulent flows. In this paper, three RPS approaches are compared for a particle-laden decaying turbulence case. These methods are, the Volume-of-Fluid Lagrangian method, based on the viscosity penalty method (VoF-Lag); a direct forcing Immersed Boundary Method, based on a regularized delta-function approach for the fluid/solid coupling (IBM); and the Bounce Back scheme developed for Lattice Boltzmann method (LBM-BB). The physics and the numerical performances of the methods are analyzed. Modulation of turbulence is observed for all the methods, with a faster decay of turbulent kinetic energy compared to the single-phase case. Lagrangian particle statistics, such as the velocity probability density function and the velocity autocorrelation function, show minor differences among the three methods. However, major differences between the codes are observed in the evolution of the particle kinetic energy. These differences are related to the treatment of the initial condition when the particles are inserted in an initially single-phase turbulence. The averaged particle/fluid slip velocity is also analyzed, showing similar behavior as compared to the results referred in the literature. The computational performances of the different methods differ significantly. The VoF-Lag method appears to be computationally most expensive. Indeed, this method is not adapted to turbulent cases. The IBM and LBM-BB implementations show very good scaling.

Polymer additives are commonly utilized to manipulate bubbly flows in various applications. Here, we investigate the effects of clean and contaminated bubbles driven upwards (upflow) in Newtonian and viscoelastic turbulent channel flows. Interface-resolved direct numerical simulations are performed to examine sole and combined effects of soluble surfactant and viscoelasticity using an efficient 3D finite-difference/front-tracking method. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant concentrations. The latter coupling is accomplished by a non-linear equation of state that relates the surface tension to the surfactant concentration. For Newtonian turbulent bubbly flows, the effects of Triton X-100 and 1-Pentanol surfactant are examined. It is observed that the sorption kinetics highly affect the dynamics of bubbly flow. A minute amount of Triton X-100 is found to be sufficient to prevent the formation of bubble clusters restoring the singlephase behavior while even two orders of magnitude more 1-Pentanol surfactant is not adequate to prevent the formation of layers. For viscoelastic turbulent flows, it is found that the viscoelasticity promotes formation of the bubble-wall layers and thus the polymer drag reduction is completely lost for the surfactant-free bubbly flows, while the addition of small amount of surfactant (Triton X-100) in this system restores the polymer drag reduction resulting in 25% drag reduction for the W i = 4 case.

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a 0-C continuous expansion. Computationally and theoretically, by increasing the polynomial order p , high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.

Dynamical behavior of the turbulent channel flow separation induced by a wall-mounted two-dimensional bump is studied, with an emphasis on unsteadiness characteristics of vortical motions evolving in the separated flow. The present investigations are based on an experimental approach and Direct Numerical Simulation (Dns). The main interests are devoted to give further insight on mean flow properties, characteristic scales and physical mechanisms of low-frequencies unsteadiness. The study also aims to clarify the Reynolds number effects. Results are presented for turbulent flows at moderate Reynolds-number Re τ ranging from 125 to 730 where Re τ is based on friction velocity and channel half-height. A large database of time-resolved two-dimensional Piv measurements is used to obtain the velocity distributions in a region covering the entire shear layer and the flow surrounding the bump. An examination of both high resolved velocity and wallshear stress measurements showed that for moderate Reynolds numbers, a separated region exists until a critical value. Under this conditions, a thin region of reverse flow is formed above the bump and a large-scale vortical activity is clearly observed and analyzed. Three distinct self-sustained oscillations are identified in the separated zone. The investigation showed that the flow exhibits the shear-layer instability and vortexshedding type instability of the bubble. A low-frequency self-sustained oscillations associated with a flapping phenomenon is also identified. The experimental results are further emphasized using post-processed data from Direct Numerical Simulations, such as flow statistics and Dynamic Mode Decomposition. Physical mechanisms associated with observed self-sustained oscillations are then suggested and results are discussed in the light of instabilities observed in a laminar regime for the same flow configuration.

A database of direct numerical simulation (DNS) of spatially evolving turbulent mixing slot jets of C7H16/O2 and C7H16/Air is developed. The formulation includes the compressible form of the governing equations, a generalized multicomponent diffusion model with Soret and Dufour effects, a cubic real gas equation of state and realistic property models. Simulations are conducted over a wide range of initial pressures (1atm < P0 < 100atm) and jet width based Reynolds numbers of 850 and 1300. High order explicit finite difference schemes in combination with low order boundary closures and Runge-Kutta time integration schemes are used to approximate the spatial and temporal derivatives. Non-reflecting inflow and outflow boundary conditions in combination with absorbing zones are applied for proper convection of flow structures and acoustic waves with minimal reflection of numerical waves. Low level disturbances are imposed on the laminar inflow near the nozzle to initiate instabili...

Fundamental numerical studies of seepage induced geotechnical instabilities and filtration processes depends on accurate prediction of the forces imparted on the soil grains by the permeating fluid. Hitherto coupled Discrete Element Method (DEM) simulations documented in geomechanics have most often simulated the fluid flow using computational fluid dynamics (CFD) models employing fluid cells that contain a number of particles. Empirical drag models are used to predict the fluid-particle interaction forces using the flow Reynolds number and fluid cell porosity. Experimental verification of the forces predicted by these models at the particle-scale is non-trivial. This contribution uses a high resolution immersed boundary method to model the fluid flow within individual voids in polydisperse samples of spheres to accurately determine the fluid-particle interaction forces. The existing drag models are shown to poorly capture the forces on individual particles in the samples for flow with low Reynolds number values. An alternative approach is proposed in which a radical Voronoi tesselation is applied to estimate a local solids volume fraction for each particle; this local solids fraction can be adopted in combination with existing expressions to estimate the drag force. This tessellation-based approach gives a more accurate prediction of the fluid particle interaction forces.

The effect of blowing through a localized slot on the wall turbulence dynamics and heat transfer process is analyzed by direct numerical simulations in a fully developed turbulent channel flow. The severity parameter is mild and there is no flow separation induced by the blowing. The shear stress transport and temperature energy budget is discussed in detail. The wall shear and flux decreases immediately downstream the slot in a similar manner but the Reynolds analogy does not hold over the slot. The physical process is governed by the production and pressure redistribution over the slot in a complex manner. The turbulent transport and especially the advection play an essential role in the heat transfer mechanism.

The suboptimal control with the cost function directly connected to the wall shear and introduced for a while has been revisited through direct numerical simulations of high temporal and spatial resolution. Its effect on the fine structure of the wall turbulence has been analyzed in details, essentially through the spanwise vorticity transport mechanism. It is shown that only half of the viscous sublayer is mainly affected by the control. The actuation efficiency is limited in terms of the wall shear stress reduction, but is high as long as the turbulent wall activity is concerned. The wall shear stress is reduced due both to the reduction of the shear production in the viscous sublayer and to the contribution of the turbulent body force. The dissipation involving in the streamwise vorticity fluctuations transport equation increases significantly and overcomes the production in a thin layer near the wall leading to a drastic diminution of the turbulent wall shear stress fluctuations.

La mesure des profils transitoires et de la vitesse de solidification sont deux données importantes pour le contrôle de procédés industriels impliquant un changement de phase. Dans le cas de l'électrolyse de l'aluminium, ce processus de solidification assure la protection du système et influe sur la performance énergétique du procédé de fabrication. Malheureusement, ces données se révèlent, dans la plupart des cas, difficilement accessibles. Ce travail de thèse porte sur le développement de nouveaux outils permettant l'étude et la caractérisation de la solidification de matériaux à changement de phase et à haute température. L'objectif est de développer un système de mesure du front de solidification de matériaux à changement de phase non destructif et ne perturbant pas le milieu de mesure, tout en assurant une précision et une réponse suffisamment rapide pour exploiter de nouvelles stratégies de contrôle dans les cuves d'électrolyse. Ce travail couple une étude expérimentale fondamentale de la solidification de la cryolithe avec une modélisation numérique de phénomène de changement de phase solide-liquide dans des conditions proches du fonctionnement de cuves d'électrolyse.

The rich structures arising from the impingement dynamics of water drops onto solid substrates at high velocities are investigated numerically. Current methodologies in the aircraft industry estimating water collection on aircraft surfaces are based on particle trajectory calculations and empirical extensions thereof in order to approximate the complex fluid-structure interactions. We perform direct numerical simulations (DNS) using the volume-of-fluid method in three dimensions, for a collection of drop sizes and impingement angles. The high speed background air flow is coupled with the motion of the liquid in the framework of oblique stagnation-point flow. Qualitative and quantitative features are studied in both pre-and post-impact stages. One-to-one comparisons are made with experimental data available from the investigations of Sor et al. (Journal of Aircraft 52 (6), pp. 1838-1846, 2015), while the main body of results is created using parameters relevant to flight conditions with droplet sizes in the ranges from tens to several hundreds of microns, as presented by Papadakis et al. (AIAA Aerospace Sciences Meeting and Exhibit 0565, pp. 1-40, 2004). Drop deformation, collision, coalescence and microdrop ejection and dynamics, all typically neglected or empirically modelled, are accurately accounted for. In particular, we identify new morphological features in regimes below the splashing threshold in the modelled conditions. We then expand on the variation in the number and distribution of ejected microdrops as a function of the impacting drop size beyond this threshold. The presented drop impact model addresses key questions at a fundamental level, however the conclusions of the study extend towards the advancement of understanding of water dynamics on aircraft surfaces, which has important implications in terms of compliance to aircraft safety regulations. The proposed methodology may also be utilised and extended in the context of related industrial applications involving high speed drop impact such as inkjet printing and combustion.

Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/hp element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, thereby allowing them to be more readily used in a wide range of application areas. In this paper, we present the algorithmic, implementation and application developments associated with our Nektar++ version 5.0 release. We describe some of the key software and performance developments, including our strategies on parallel I/O, on in situ processing, the use of collective operations for exploiting current and emerging hardware, and interfaces to enable multi-solver coupling. Furthermore, we provide details on a newly developed Python interface that enables a more rapid introduction for new users unfamiliar with spectral/hp element methods, C++ and/or Nektar++. This release also incorporates a number of numerical method developments-in particular: the method of moving frames (MMF), which provides an additional approach for the simulation of equations on embedded curvilinear manifolds and domains; a means of handling spatially variable polynomial order; and a novel technique for quasi-3D simulations (which combine a 2D spectral element and 1D Fourier spectral method) to permit spatially-varying perturbations to the geometry in the homogeneous direction. Finally, we demonstrate the new application-level features provided in this release, namely: a facility for generating high-order curvilinear meshes called NekMesh; a novel new AcousticSolver for aeroacoustic problems; our development of a 'thick' strip model for the modelling of fluid-structure interaction (FSI) problems in the context of vortex-induced vibrations (VIV). We conclude by commenting on some lessons learned and by discussing some directions for future code development and expansion.

During the last decade numerous studies considered collisions of inertial particles in turbulent flows. A magnitude of the turbulence-induced collision rate enhancement factor reported in these studies ranges from a few percent to several hundred. The authors of the majority of the studies apply their results to explanation of rain formation in atmospheric clouds. At the same time many of these investigations were performed under the conditions quite different from those encountered in real clouds. For instance, in most analytical and direct numerical simulations (DNS) the effect of gravity-induced differential drop sedimentation was neglected. Using the collision enhancement factors obtained in these studies for cloud modeling may lead to unrealistic cloud evolution and impair research in cloud physics. In this study we present an analysis of the applicability of the results obtained in different recent studies (mainly DNS simulations) to actual clouds. We discuss the progress reached in the topic as well as unsolved problems.

It is well known that additive drag-reducing methods have broadly developing prospects, so studies on mechanisms of additive drag reduction are very necessary. We hypothesised that the main reason for bubbles induced drag reduction is the modification on liquid-phase turbulence structure by the addition of bubbles, and therefore such modification is the focus of our investigation. In this paper, effects of bubbles on liquid-phase turbulence under the circumstance of regular bubble array were investigated by using Euler-Lagrange two-way numerical simulations. The liquid-phase velocity field was solved by using direct numerical simulations (DNS) in Euler frame of reference, and the bubble motion was tracked by using Newtonian motion equations that took into account interaction forces including drag force, shear lift force, gravity force, buoyant force, and inertia force in Lagrange frame of reference. The coupling between the phases was realised by regarding the interphase forces as momentum source terms of the continuous phase. Similarities and differences for effects of bubbles and surfactants on liquid turbulent flows were also analysed. The study indicated that addition of bubbles enhances the mean streamwise velocity, greatly reduces the Reynolds stress, and shows anisotropic suppression to the velocity fluctuations. The interphase force has a great influence on budget of energy balance. It is a gain term near the wall and is a loss term in a wide range of the channel core.

The nonlinear vorticity dynamics of the Batchelor trailing vortex is presented. Direct numerical simulations of the three-dimensional, incompressible, Navier-Stokes equations by a spectral method are used. It is shown that the initial vortex core is subjected to three transformations: a twisting phase, a lateral expansion of its cross section and formation of a spiral structure. These transformations are accompanied by a gradual deceleration of axial velocity. Mean kinetic energy is then transferred to radial velocity. When the transfer is maximum a secondary instability is initiated leading to the spiral structure. These transformations are in agreement with vortex breakdown observed in recent experiments.

Based on direct numerical simulations, the paper investigates momentum fluxes and hydrodynamic stresses within and above a mobile granular bed in a turbulent open-channel flow laden with monodisperse spherical particles. Two simulation scenarios are considered: one with partially mobilized particles ("heavy" particles) and another with all particles in motion ("light" particles). The momentum fluxes were computed as temporal and spatial averages following the double-averaging methodology for rough-bed flows. The analysis, hence, allows the DNS data to be convoluted in a rigorous way to provide detailed description and quantification of the physical mechanisms involved in momentum exchanges. In particular, it was found that heavy particles create streamwise bedforms causing heterogeneity in the spanwise direction. This yields significant form-induced momentum fluxes that cannot be neglected. For both scenarios, the mobile particles take up a substantial amount of the momentum supplied, which ultimately increases the hydraulic resistance of the channel. These effects enhance and stabilize secondary flows in the channel.

This paper presents the application of the double-averaging methodology to actual data obtained for the mobile-bed conditions from direct numerical simulations using an immersed boundary method. The dimensions of the computational domain resemble those for open-channel flows with small relative submergence. The domain bottom is a plane covered with one layer of hexagonally packed, single-size spheres fixed to the bed. The fixed particles are covered by 2000 mobile particles of the same size that are free to move. Two simulation scenarios at distinctly different values of the Shields parameter are studied representing a fully mobilized and partially mobilized granular bed. The effects of the averaging time and the averaging domain size and shape on the double-averaged flow quantities are identified first. Then, the data analysis focuses on the detailed assessment of the key terms of the double-averaged momentum balance equation formulated for mobile-bed conditions. The paper demonstrates that the double-averaging methodology provides an efficient reduction of the massive datasets produced by the fully resolved simulations to a manageable number of physically meaningful double-averaged quantities, which should help devising closure strategies for modelling mobile-bed flows.

To simulate turbulent flows in complicated enclosed three-dimensional domains a fast finite-volume high-order method is developed. In principle, the method is based on the Chorin-Temam scheme. The Poisson solver, which is applied to compute the pressure, uses the separation of variables together with capacitance matrix technique. The developed numerical method generally allows to use hexahedral computational meshes, which are non-equidistant in all three directions and non-regular in any two directions. The method was successfully used in three-dimensional Direct Numerical Simulations of turbulent high-Rayleigh-number thermal convection in cylindrical and parallelepiped domains with obstacles.

To simulate turbulent flows in complicated enclosed three-dimensional domains a fast finite-volume high-order method is developed. In principle, the method is based on the Chorin-Temam scheme. The Poisson solver, which is applied to compute the pressure, uses the separation of variables together with capacitance matrix technique. The developed numerical method generally allows to use hexahedral computational meshes, which are non-equidistant in all three directions and non-regular in any two directions. The method was successfully used in three-dimensional Direct Numerical Simulations of turbulent high-Rayleigh-number thermal convection in cylindrical and parallelepiped domains with obstacles.

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.

The flow motion of solid particle suspensions is a fundamental issue in many problems of practical interest. The velocity field of a such system is computed by a finite element method with a multi-domain approach of two phases (namely a viscous fluid and rigid bodies), whereas the particle displacement is made by a particulate method. We focus our paper on a simple shear flow of Newtonian fluid. RÉSUMÉ. Les écoulements de fluides chargés de particules interviennent dans de nombreux procédés industriels. Le champ de vitesse dans un tel système est donné par une méthode éléments finis associée à une formulation multidomaine (le fluide visqueux et les particules solides). Puis le déplacement des particules est effectué par une méthode particulaire. Cette approche est ici testée sur un écoulement de cisaillement simple.

We use direct numerical simulations to study the dynamics of incompressible homogeneous turbulence subjected to a uniform magnetic field B (the Alfvén velocity) in a rotating frame with rotation vector Ω. We consider two cases: Ω B and Ω ⊥ B. The initial flow state is homogeneous isotropic hydrodynamic turbulence with kinetic Reynolds number Re = u l l/ν 170. The magnetic Prandtl number is Pm = ν/η = 1 and the Elsasser number Λ = B 2 /(2Ωη) = 0.5, 0.9 or 2. Both for Ω B and Ω ⊥ B, the total (kinetic + magnetic) energy E decays as ∼ t −5/7 for Λ = 0.5 and 0.9, and as ∼ t −6/7 for Λ = 2. In the spectral range 2 < k < 20, the radial (spherically averaged) spectrum of kinetic energy scales as ∼ k −p where the index p increases with time (2 ≤ p ≤ 4.2), or equivalently, with the interaction parameter N = B 2 l/(ηu l). This time-dependent scaling is similar to that observed in quasi-static MHD. The two rotating MHD flow cases differ mainly in how kinetic and magnetic fluctuations exchange energy, with a mechanism mostly driven by the dynamics of the spectral buffer layer around k Ω = |Ω•k|/Ω ≈ 0. At k Ω = 0, both the frequencies of inertial and Alfvén waves vanish when Ω B, but only the frequency of inertial waves vanishes for the case when Ω ⊥ B. When Ω B, rotation results in an increased reduction of magnetic fluctuations generation. In terms of anisotropy, we show that the elongated structures occurring in rapidly non-magnetized rotating flows are distorted or inhibited for Ω ⊥ B, and their intensity is weakened for Ω B.

This study combines observations, large-eddy simulations (LES), and direct numerical simulations (DNS) in order to analyze entrainment and mixing in shallow cumulus clouds at all relevant spatial scales and, additionally, to verify the results by the multiple methods used. The observations are based on three flights of the CARRIBA campaign which are similar to the classical BOMEX case used for LES. Virtual flights in the LES data are used to validate the observational method of line measurements. It is shown that line measurements overrepresent the cloud core, and it is quantified how derived statistics depend on small perturbations of the flight track, which has to be taken in account for the interpretation of airborne observations. A linear relation between fluctuations of temperature and liquid water content has been found in both LES and observations in a good quantitative agreement. However, the constant of proportionality deviates from purely adiabatic estimates, which can be attributed to cloud edge mixing. The cloud edge is compared in detail in observations and LES, which agree qualitatively although the LES cloud edge is smoother due to the model's resolution. The resulting typical amplitudes of the turbulence fields from this comparison are compared with the large-scale forcing model which is used in a series of DNS which study the mixing below the meter scale, which show that LES does not resolve the intermittency of small-scale turbulence.

The theoretical derivations were done in close cooperation between the authors, both of them contributing in an equal amount. The author of this thesis had the main responsibility for the computer implementations and wrote section 5 in the report. Malin Siklosi had the main responsibility for the literature studies and wrote sections 1-4 in the report. This paper is also part of the licentiate thesis [1].

Direct Numerical Simulations of expanding flame kernels following localized ignition in decaying turbulence with the fuel in the form of a fine mist have been performed to identify the effects of the spray parameters on the possibility of self-sustained combustion. Simulations show that the flame kernel may quench due to fuel starvation in the gaseous phase if the droplets are large or if their number is insufficient to result in significant heat release to allow for self-sustained flame propagation for the given turbulent environment. The reaction proceeds in a large range of equivalence ratios due to the random location of the droplets relative to the igniter location that causes a wide range of mixture fractions to develop through pre-evaporation in the unreacted gas and through evaporation in the preheat zone of the propagating flame. The resulting flame exhibits both premixed and non-premixed characteristics.

To simulate turbulent flows in complicated enclosed three-dimensional domains a fast finite-volume high-order method is developed. In principle, the method is based on the Chorin-Temam scheme. The Poisson solver, which is applied to compute the pressure, uses the separation of variables together with capacitance matrix technique. The developed numerical method generally allows to use hexahedral computational meshes, which are non-equidistant in all three directions and non-regular in any two directions. The method was successfully used in three-dimensional Direct Numerical Simulations of turbulent high-Rayleigh-number thermal convection in cylindrical and parallelepiped domains with obstacles.

We present results from direct numerical simulations of two types of technologically important phase change processes: directional solidification of a binary alloy and film boiling. We use a two-dimensional finite-difference/front-tracking method which allows us to accurately follow the evolution of the interface between the phases. The method is general in the sense that discontinuities in material properties between the phases as well as topological changes are easily handled. In the directional solidification problem the fully coupled solute and energy equations for a dilute binary alloy without fluid flow are solved. The effects of latent heat, unequal material properties between liquid and solid and unsteady effects are completely taken into account. We demonstrate the evolution of a cellular interface with rejection of solute ahead of the advancing interface and in the intercellular grooves. The numerical results for the transition from a planar to a cellular interface are in excellent agreement with linear stability theory. The film boiling problem couples the phase change with fluid flow. This requires the solution of the Navier-Stokes and energy equations with interphase mass transfer. We study the growth and dynamics of a vapor layer adjacent to an upward facing, flat, heated surface. Vaporization of the liquid at the liquid-vapor interface continually replenishes the vapor lost due to bubble departure from the interface. 1. Introduction Phase change plays a central role in energy systems and materials processes. However it is usually the combination of phase change with fluid flow and heat transfer that determines, for exam

This study combines observations, large-eddy simulations (LES), and direct numerical simulations (DNS) in order to analyze entrainment and mixing in shallow cumulus clouds at all relevant spatial scales and, additionally, to verify the results by the multiple methods used. The observations are based on three flights of the CARRIBA campaign which are similar to the classical BOMEX case used for LES. Virtual flights in the LES data are used to validate the observational method of line measurements. It is shown that line measurements overrepresent the cloud core, and it is quantified how derived statistics depend on small perturbations of the flight track, which has to be taken in account for the interpretation of airborne observations. A linear relation between fluctuations of temperature and liquid water content has been found in both LES and observations in a good quantitative agreement. However, the constant of proportionality deviates from purely adiabatic estimates, which can be attributed to cloud edge mixing. The cloud edge is compared in detail in observations and LES, which agree qualitatively although the LES cloud edge is smoother due to the model's resolution. The resulting typical amplitudes of the turbulence fields from this comparison are compared with the large-scale forcing model which is used in a series of DNS which study the mixing below the meter scale, which show that LES does not resolve the intermittency of small-scale turbulence.

During the last decade numerous studies considered collisions of inertial particles in turbulent flows. A magnitude of the turbulence-induced collision rate enhancement factor reported in these studies ranges from a few percent to several hundred. The authors of the majority of the studies apply their results to explanation of rain formation in atmospheric clouds. At the same time many of these investigations were performed under the conditions quite different from those encountered in real clouds. For instance, in most analytical and direct numerical simulations (DNS) the effect of gravity-induced differential drop sedimentation was neglected. Using the collision enhancement factors obtained in these studies for cloud modeling may lead to unrealistic cloud evolution and impair research in cloud physics. In this study we present an analysis of the applicability of the results obtained in different recent studies (mainly DNS simulations) to actual clouds. We discuss the progress reached in the topic as well as unsolved problems.

We investigate the influence of the temperature boundary conditions at the sidewall
on the heat transport in Rayleigh–Bénard (RB) convection using direct numerical
simulations. For relatively low Rayleigh numbers Ra the heat transport is higher
when the sidewall is isothermal, kept at a temperature Tc C 1=2 (where 1 is the
temperature difference between the horizontal plates and Tc the temperature of the
cold plate), than when the sidewall is adiabatic. The reason is that in the former
case part of the heat current avoids the thermal resistance of the fluid layer by
escaping through the sidewall that acts as a short-circuit. For higher Ra the bulk
becomes more isothermal and this reduces the heat current through the sidewall.
Therefore the heat flux in a cell with an isothermal sidewall converges to the value
obtained with an adiabatic sidewall for high enough Ra ('1010). However, when the
sidewall temperature deviates from Tc C 1=2 the heat transport at the bottom and
top plates is different from the value obtained using an adiabatic sidewall. In this
case the difference does not decrease with increasing Ra thus indicating that the
ambient temperature of the experimental apparatus can influence the heat transfer.
A similar behaviour is observed when only a very small sidewall region close to
the horizontal plates is kept isothermal, while the rest of the sidewall is adiabatic.
The reason is that in the region closest to the horizontal plates the temperature
difference between the fluid and the sidewall is highest. This suggests that one
should be careful with the placement of thermal shields outside the fluid sample to
minimize spurious heat currents. When the physical sidewall properties (thickness,
thermal conductivity and heat capacity) are considered the problem becomes one
of conjugate heat transfer and different behaviours are possible depending on the
sidewall properties and the temperature boundary condition on the ‘dry’ side. The
problem becomes even more complicated when the sidewall is shielded with additional
insulation or temperature-controlled surfaces; some particular examples are illustrated
and discussed. It has been observed that the sidewall temperature dynamics not only
affects the heat transfer but can also trigger a different mean flow state or change
the temperature fluctuations in the flow and this could explain some of the observed
differences between similar but not fully identical experiments.