Turbulence and Interactions

The paper considers low swirl turbulent number jets. Swirling jets are used to stabilize premixed flames in gas turbines. Normally, the swirl number is large enough to allow vortex break-down and thereby flame stabilization along the upstream edge of the back-flowbubble.With decreasing swirl the vortex-breakdown may disappear altogether. However, it has been found that under certain conditions the flame may be kept at a certain (mean) distance away from the nozzle even without vortex break-down. The mechanism for the flame holding under such conditions is discussed. The discussion is based upon LES results and some experimental data. We discuss also the precession of the central core both under non-reacting and reacting condition. LES and experimental results show that the precession of the central core is normally in the same direction as the swirl. However, for certain range of swirl numbers and at some axial distances one may find precession in the counter direction. The mechanism for this effect is discussed.

This paper deals with some of the features that distinguish wall-bounded sheared turbulence from that in free-shear flows. It concerns itself mostly with the largest structures at each wall distance, because they are where energy is fed into the fluctuations, and therefore the ones that differ most between the different flows. Because of the geometric limitations imposed by the wall, the largest scales roughly coincide with the smallest ones in the viscous buffer layer, but the rest of the flow is characterised, as in most turbulent cases, by a wide range of scales.

This article reviews the planetary-boundary-layer (PBL) turbulence and its interactions with atmospheric processes. We show three examples: turbulence response to surface heating and cooling over lands, effects of ocean waves, and interactions with radiation and cloud microphysics.We also show how computational fluid dynamics methods are used to gain fundamental understanding of these interactions mostly under idealized environments. For certain practical applications in which idealized conditions may not apply, a brute-force method may be needed to explicitly simulate the turbulence interaction. One way is to nest a large-eddy simulation domain inside a weather forecast model, and to allow for turbulence feedback to other physical processes. This numerical method sounds straightforward but poses two major problems. We suggest a systematic approach to examine the problems.

Flows driven by a pressure gradient that oscillates periodically around a non-zero mean (pulsating flows) are found in a variety of geophysical, engineering and biomedical settings. Moreover, aside from their practical importance, they are a useful model to understand the more general problem of how unsteadiness affects the properties of a boundary layer. In this paper, we consider examples of pulsating flows over smooth and wavy surfaces studied with the aid of LES. For the smooth case, the surprising result is that the time averaged statistics are marginally if at all affected by the presence of oscillations (at least in the regime considered of current dominated flows), whereas the oscillating part is influenced by the underlying steady turbulence. Introducing waviness of sufficient amplitude to induce flow separation, at least during part of the cycle, couples the mean to oscillating component much more tightly, resulting in an increased drag felt by the mean flow. Such enhanced drag is due to the ejection of large, coherent spanwise vortices that form in the lee of the ripples, and it has a strong and non trivial dependence on the frequency of the oscillation.

We develop numerical capabilities of direct numerical simulation and large-eddy simulation for turbulent flows with waving boundaries, which can be coupled with nonlinear surface wave simulation, to study the mechanism of turbulence-wave interaction. Simulation of turbulence in the vicinity of surface waves with various wave conditions reveals strong dependence of the statistics, structures, and dynamics of the turbulent flow on wave characteristics including wave phase, wave age, and wave nonlinearity. Simulation of nonlinear wave evolution provides wave growth quantification in a phase-resolving context, which is valuable for deterministic wavefield prediction. The results obtained in this study suggest the importance of two-way coupling between turbulence and waves in their dynamic evolution.

We propose a model for turbulent wall-bounded flows based on new understanding of the turbulent structure. Specifically, we identify three basic eddy motions: (1) the Large-Scale Motions (LSMs) which are related to the vortex packets defined by Head and Bandyopadhyay (1981) and Adrian et al. (2000); (2) the Very Large-Scale Motions (VLSMs) interpreted by Liu et al. (2001) and Balakumar and Adrian (2007) in terms of a concatenation of the outer layer bulges and by Monty et al. (2007) in terms of the meandering “superstructures” observed in pipe, channel and boundary layers; and (3) the streaks associated with longitudinal vortex-like structures in the near-wall region, as identified by Kline et al. (1967). The new model maps the attributes of each eddy type in physical space to wavenumber space. Experimental data are then used to determine the scaling behavior of the three basic eddy motions in wavenumber space, and the scaling behavior of the Reynolds stress behavior is recovered b! y integrating over all wavenumbers.

The Partially-Averaged Navier-Stokes (PANS) approach is a recently proposed method which changes seamlessly from the Reynolds-Averaged Navier-Stokes (RANS) model equations to the direct numerical solution (DNS) of the Navier-Stokes equations as the unresolved-to-total ratios of kinetic energy and dissipation are varied. Two variants of the PANS model are derived up to now, one based on the k-

ε

formulation and the other based on the k-

ω

formulation.We introduce here another variant which is based on four equation eddy viscosity transport model, namely

ζ

-f turbulence model. Benefits of using such near wall model inside the PANS concept are clearly presented in this paper.

This paper reports on an experimental study of turbulent flow through model two-dimensional porous media bounded on one side by a solid plane wall and on the other side by a zone of clear fluid. The porous media comprised of square arrays of transparent circular acrylic rods that were inserted into holes drilled onto pairs of removable plates. The removable plates were then inserted into groves made in the side walls of the test channel. The rod diameter and/or center-to-center spacing between adjacent rods were varied to simulate porosities that ranged from 0.56 to 0.89. A particle image velocimetry technique was used to conduct detailed velocity measurements in the flow within the porous media and the adjacent clear zone. From these measurements, the slip velocity and profiles of the spatially averaged mean velocities and Reynolds stresses were obtained to study the effects of porosity on the velocity field.

Cascade Stochastic Differential Equation (SDE), a continuous time model for energy dissipation in turbulence, is a generalization of the Yaglom discrete cascade model. We extend this SDE to a model in random environment by assuming that its two parameters are switched by a continuous time Markov chain whose states represent the states of the environment. Moreover, a Dirichlet process is placed as a prior on the space of sample paths of this chain. We propose a Bayesian estimation method of this model which is tested both on simulated data and on real data of wind speed measured at the entrance of the mangrove ecosystem in Guadeloupe.

Both Fourier and wavelet transforms are performed on data obtained from large-eddy simulations of the turbulent flow in a lid-driven cubical cavity. The analyzed data or synthetic signals are picked at three specific points inside the cavity allowing to investigate three regimes over time: laminar, transitional and turbulent. The main objective of this study is to generate and analyze synthetic signals in order to confirm the correlation between the computed physical quantities and those expected theoretically.

The numerical simulation of the interaction between a plasma flow and a liquid jet is important for understanding and predicting the physical parameters involved in plasma spraying processes. This work proposes an original model for dealing with three-dimensional and unsteady turbulent interactions between a plasma flow and a liquid water jet. A compressible model, based on augmented Lagrangian, Large Eddy Simulation (LES) turbulence modeling and Volume of Fluid (VOF) approaches, capable of managing incompressible two-phase flows as well as turbulent compressible motions is presented.

The characterisation of fluidized beds still requires specific investigation for understanding and modelling the local coupling between the dispersed phase and the carrier fluid. The aim of this work is to simulate this type of unsteady particle laden flows via Direct Numerical Simulations in order to provide a local and instantaneous description of particle flow interactions and to extract statistical parameters useful for large scale models. A fluidized bed has been studied experimentally by Aguilar Corona ([1]). In this laboratory experiment, 3D tracking of a single bed particle provided Lagrangian properties of the discrete phase motion, while 2D PIV was used to characterize the flow of the continuum phase. This fluidized bed has been simulated during nine seconds in order to compare experimental and numerical results and to obtain some data that experimental studies can’t give.

The paper presents two novel turbulent models for LES based on a wavelet decomposition. This approach, denoted WALES, is simple and easy to implement. Tests on a number of flows using grids with different resolution near walls show that the models exhibit the same quality as the Smagorinsky model without the need of wall functions or near-wall damping. In the paper the basic wavelet framework and two such models are described in detail. Physical benefits of the models due to the use of wavelets are discussed. Results obtained with the models are compared to those using the Smagorinsky model, to experimental results and to results from Direct Numerical Simulations. The agreement achieved is generally good.

Preferential concentration of solid inertial colliding particles suspended in homogeneous isotropic turbulence is numerically investigated using Direct Numerical Simulation (DNS) coupled with Discrete Particle Simulation (DPS). The results show that the preferential concentration is decreasing when the collision frequency increases. This effect is found enhanced for non-elastic particle-particle collisions.

Turbulence control techniques are of great economical and ecological interest. In the present work a fundamental study is carried out in which body forces are introduced in the near-wall region of a turbulent channel flow and thus modify the near-wall behavior. It is investigated how these forces, which selectively act on one of the velocity components, modify near-wall turbulence and its statistical properties with the goal to extract properties that can directly be linked to the skin friction drag. The alignment between the principal axis of the Reynolds stress tensor and the mean flow direction is identified as an interesting quantity in this respect.

The transonic buffet is an aerodynamic phenomenon that results in a large-scale self-sustained periodic motion of the shock over the surface of the airfoil. The time scale associated to this motion is much slower than the one of the wall bounded turbulence. It is then an appropriate case for URANS approaches and first attempts with these methods have been reasonably successful in reproducing the mean features of such flows. Nevertheless, as shown by Thiery and Coustols [2] results are very sensitive to the turbulence model. Moreover, with some models, it is necessary to increase the angle of attack with respect to experiment to obtain an unsteady flow.

This paper deals with the numerical simulation (using a LES approach) of the interaction between an atmospheric boundary layer (ABL) and a canopy, representing a forest cover. This problem was studied for a homogeneous configuration representing the situation encountered above a continuous forest cover, and a heterogeneous configuration representing the situation similar to an edge or a clearing in a forest. The numerical results, reproduced correctly all the main characteristics of this flow, as reported in the literature: the formation of a first generation of coherent structures aligned transversally from the wind flow direction, the reorganisation and the deformation of these vortex tubes to horse shoe structures. The results obtained, introducing a discontinuity in the canopy (reproducing a clearing or a fuel break in a forest), were compared with experimental data collected in a wind tunnel. The results confirmed the existence of a strong turbulence activity inside the canopy at a distance equal to 8 times the height of the canopy, referenced in the literature as an Enhance Gust Zone (EGZ) characterized by a local peak of the skewness factor.

Isotropic turbulence receives a continuous effort for an increasingly refined description, but complex effects modify the dynamics of turbulence, and are poorly understood. Instances of distorted turbulence by external body forces are present throughout natural and industrial flows, as in geophysical flows submitted to the Earth’s rotation, and to density or temperature stratification. We focus here on the effects of stable stratification and solid body rotation on the dynamics and structure of homogeneous turbulence.We perform high resolution Direct Numerical Simulations (DNS), to characterize the 3D structure of anisotropic turbulence and its statistical properties. Vertical structures appear in rotating turbulence, or a layering in stably stratified turbulence, depending on the rotation rate and the density gradient, parameters that are varied in our simulations (see [8]).

An interpretation to the use of deconvolution models when used in implicitly filtered large-eddy simulations as a way to approximate the projective grid filter is given. Consequently, a new category of subgrid models, the grid filter models, is defined. This approach gives a theoretical justification to the use of deconvolution models without explicit filtering of the solution and explains how the use of such models can be effective in this context.

This viewpoint also allows to consider a new way of designing the convolution filter which has to approximate the grid filter and therefore a new way of improving such subgrid models. In this framework, a general technique for the approximation of the grid filter associated with any function-based numerical method is proposed. The resulting subgrid model is parameterless, only depends on the mesh used for the large-eddy simulation which is

a

priori

known and vanishes locally if the flow is not turbulent, thereby ensuring the consistency of the model with the Navier-Stokes equations.

The present work investigates the response of a porous media to an unsteady forcing resulting from the superposition of an harmonic component to a mean one. The analysis is carried out both in terms of global parameters and local fields obtained processing data from numerical solution of the Navier-Stokes equations at pore level performed with a spectrally accurate multi-domain algorithm.

Direct Numerical Simulation is used to study the mechanisms underlying the production of turbulent density fluctuations in a sheared turbulent flow with uniform mean velocity gradient and non-uniform mean density and temperature gradients. The coupling between the production mechanism of the Reynolds stresses and the one of the fluctuating density is investigated through the budgets of several relevant turbulent quantities. An interaction of this kind of turbulent flow with a shock wave is then considered in order to elucidate the effect of the shock on the previous mechanisms. The influence of the sign of the upstream correlation

$\overline{u'_1T'}$

is finally reported.

A CT based simplified upper human airway model was created by preserving all critical geometrical features. The fluid flow at a normal breathing flow rate of 30 l/min is numerically studied employing RANS, DES and LES methods. The complex flow patterns with skewed velocity profiles and flow separations are discussed for the LES model. The deposition efficiency and the deposition patterns for the particle diameters 2, 4, 6, 8 and 10

μ

m are presented. For particle diameters in the respirable range, LES and DES showed considerable improvement over the RANS model, however, for the particles above 5

μ

m, RANS performs as good as LES/DES. The frozen LES method for particle tracking consistently underestimated the deposition of bigger particles.

Turbulent drag reduction in wall-bounded flows is investigated experimentally by considering the dynamic effects provoked by large variation of anisotropy in the velocity fluctuations. Deductions based on the analysis of near-wall turbulence lead to the design of the grooved surface topology, for which it is demonstrated experimentally that it can produce a maximum drag reduction of DR ≃ 25%. The drag reduction effect persisted in a narrow range of flow velocities and for the reported experimental conditions corresponds to groove dimensions of about 0.8 viscous length-scale.

In fundamentel research the geometrically simple Rayleigh-Bénard experiment is often chosen to investigate the turbulent heat exchange between a thermally driven fluid and a hot bottom and a cold top wall, respectively.

The coherent vortex extraction (CVE) is a technique based on the nonlinear filtering of the vorticity field projected onto an orthonormal wavelet basis. The coherent vortices of the flow are reconstructed from few strong wavelet coefficients, while the incoherent background flow corresponds to the majority of weak wavelet coefficients. Here CVE is applied to a lid driven cavity flow. Only 2.3% of wavelet coefficients are necessary to capture the coherent structures and contains almost all the enstrophy. The incoherent flow, which is the remaining, is structureless and noise-like. The results show that lid driven cavity flows are characterized by the presence of pronounced coherent structures.

In this paper we show that the role of kinematic relationships in the issue of nonlocality goes far beyond their use in the nonlocal interpretation of the Kolmogorov 4/5 law and applicable also to general stochastic processes, unrelated to the N-S equation.We put special emphasis on this aspect pointing to a large number of such relations for the structure functions expressed via terms all of which have the form of correlations between large- and small-scale quantities, and giving examples of their experimental verification at large Reynolds numbers in field and airborne experiments.

The turbulent flow around a high-lift configuration consisting of slat, main element and flap is simulated at a Reynolds number of 1.7 × 10

6

with an implicit finite-volume based numerical method. The 3D unsteady motion in separated flow regions is resolved on a 25 million volume mesh employing the recent Delayed Detached-Eddy Simulation (DDES) approach [12]. Compressible calculations and the use of non-reflecting boundary conditions enable sound radiation to be captured in the simulation. The presented results cover the first step in a two-step approach towards the prediction of noise emitted into the acoustic farfield and provide insight into the complex flow dynamics in the slat region. The computed pressure distributions, statistics and spectra exhibit good agreement with findings from NASA Langley Research Center (LaRC) [2, 5].

Vortex mechanism of heat transfer enhancement in a narrow channel with dimples has been investigated numerically using unsteady Reynolds averaged Navier Stokes equations (URANS SST and SAS) and Large Eddy Simulations (LES). The flow separation results in a formation of vortex structures which significantly enhance the heat transfer on dimpled surfaces conducted by a small increase of the pressure loss. The vortex structures and the flow are sufficiently unsteady. The vortex structure inside of the dimple changes steadily its orientation causing the long period oscillations with opposite-of-phase motion. The heat transfer enhancement is caused mostly by the amplification of convection. The effect of the wetted area increase is sufficiently smaller.

In this work we present a Large Eddy Simulation of an aero-acoustic test case consisting of a plate located in the turbulent wake of a circular cylinder. This configuration is very attractive for the validation of low Mach number aero-acoustic codes and coupling techniques, since a high sound pressure level is present at a very low Mach number and also because its simple geometry. Further it seems to be an interesting test case for future works if besides aero-acoustics also fluid induced vibrations are of interest.

In order to identify the involved noise generation mechanisms, mean pressure fluctuations as well as frequency spectra are investigated. The numerically obtained frequencies are compared to experimental data.

Three different activation strategies for active flow control around an Ahmed body are investigated using large eddy simulations. Both the separation region on the slanted surface and the cone-like trailing vortices were influenced using different actuation strategies. However, only one of the flow regions was influenced at a time. The actuation of the separation slant region was done using either constant blowing or periodic blowing and suction through the spanwise slot near the edge between the slant and the top of the body. Another actuation strategy used blowing of constant jets into the cone-like vortices with the objective to weaken them. The latter strategy was found to produce an increased drag in agreement with previous experimental data. Only the actuation strategy using constant blowing along the spanwise slot was found to decrease the overall drag on the body.

DNS of turbulent bubble-laden channel flow has been used with one-way coupling to investigate consequences of a postulated dependence of acceleration on drag. This dependence is known to hold for converging and diverging steady streamlines, and is here postulated to also exist for the instantaneous acceleration of micro-bubbles that arises from turbulent velocity fluctuations. Bubble segregation is found to be considerably increased through this dependency of drag on acceleration, particularly for smaller bubbles.

The unsteady flowfield induced by an interaction between an impinging shock wave and a turbulent boundary layer is analysed by means of both Large-Eddy simulations and experiments relying on PIV and wall pressure measurements. A simple kinematic model is derived from these analyses and demonstrates a good ability to reproduce the main unsteady features found in the data.

An extension of the laser Doppler technique for measuring particle acceleration is presented. The basic principles of the technique follow closely those introduced in [11], although numerous improvements have been implemented in the signal processing for increasing the reliability of individual estimates of particle acceleration. The main contribution of this study is to identify and quantify the errors due to optical fringe divergence in the detection volume of the present laser Doppler system, to introduce an appropriate experiment involving a falling wire and to compare the acceleration measurements of the laser Doppler system to the results of a particle tracking system with high-speed cameras in a highly turbulent flow. Noteworthy is the fact that all measurements were performed with a commercial off-the-shelf laser Doppler system.

A novel approach to the simulation of isothermal, turbulent two-phase (liquid/vapour) flow is presented. The two-phase nature of the flow is modeled by means of a

diffuse-interface

concept and of the

Korteweg tensor

of capillary forces at the interface, so that a single system of compressible Navier-Stokes equations can be written for the whole flow domain. A Van der Waals equation of state is also included to account for the variation of pressure with density at the given value of temperature. After explanation of a stable numerical method, results of a classic benchmark problem are shown. Next,

subgrid terms

related to the nonlinear pressure and capillary terms are studied by means of an a priori analysis based on DNS results, and a subgrid model for these terms is proposed.

We present two models for turbulent flows with periodic boundary conditions and with either rotation, or a magnetic field in the magnetohydrodynamics (MHD) limit. One model, based on Lagrangian averaging, can be viewed as an invariant-preserving filter, whereas the other model, based on spectral closures, generalizes the concepts of eddy viscosity and eddy noise. These models, when used separately or in conjunction, may lead to substantial savings for modeling high Reynolds number flows when checked against high resolution direct numerical simulations (DNS), the examples given here being run on grids of up to 1536

3

points.

Direct numerical simulation (DNS) of thermally driven turbulent flows inside a fully confined eclosure is performed using state-of-the-art Chebyshev pseudo-spectral methods. The identification of turbulent coherent structures through

λ

2

method is presented as well as the direct influence of turbulent eddies on the local Nusselt number and the shear stress distribution at the active walls. Furthermore a first study of turbulent kinetic energy and temperature variance together with the respective production and dissipation terms are reported for Rayleigh number

Ra

= 10

9

.

Computations of a lean premixed methane - air flame in a lean stepped combustor are performed using a Delayed Detached Eddy Simulation approach to model turbulence. Two conditions for the outlet section are simulated and compared to an experimental database including mean velocity, mean temperature and instantaneous

OH

* emission measurements. The main objective of this study is to assess of the efficiency of DDES for a massively separated reactive flow.

Particle dispersion in turbulent channel flow is investigated through Lagrangian tracking of inertial pointwise particles one-way coupled to the fluid. First, the results obtained in direct numerical simulations at two different shear Reynolds numbers,

$Re^l_{\tau}$

= 150 and

$Re^h_{\tau}$

= 300, for particles having different inertia are briefly summarized and the Reynolds number effects are discussed. Then, particle dispersion in LES flow fields at

$Re^h_{\tau}$

is compared to reference DNS data. Comparison is made with and without approximate deconvolution of the LES fluid velocity field in the particle motion equations. It is found that particle segregation and, consequently, near wall accumulation are underestimated in LES, although approximate deconvolution improves the agreement with DNS. These findings confirm those of analogous previous studies at

$Re^l_{\tau}$

.

Turbulence models often involve Reynolds averaging, with a closure providing the Reynolds stress

$\overline{u'v'}$

as function of mean velocity gradient dū/dy, through a turbulence constitutive equation (Eq. 1). The main limitation of this linear closure is that it rests on an analogy with the kinetic theory. For this analogy to be valid there has to be scale separation. The aim of this work is to better understand this hypothesis from a microscopic point of view. Therefore, fluid elements are tracked in a turbulent channel flow. The flow is resolved by direct numerical simulation (DNS). Statistics on particle trajectories are computed leading to estimations of the turbulent mixing length scale and the Knudsen number. Comparing the computed values to the values in the case of scale separation we may know where and to what extent Eq. (1) is not verified. Finally, a new non-local formulation for predicting the Reynolds stress is proposed.

Supersonic jets with a complex shock pattern appear in numerous technical applications. Most supersonic jets, especially in modern military or civil aircraft, are not perfectly expanded. Thereby, shocks are appearing in the jet core and interacting with the turbulent mixing-layers and emanating shock induced noise. Under certain conditions this upstream traveling noise can be amplified due to a closed feedback loop. These so called

screech tones

can reach sound pressure levels of up to 160 dB [11] and hence lead to immense noise pollution and even structural fatigue.

The focus of this research project lies in the numerical simulation of supersonic jet noise and finally the minimization of screech tones with an adjoint shape optimization approach of the nozzle geometry. To this end the nozzle geometry, based on a complex shape, has to be included in the computational domain. In the present paper the method of overset grid techniques is presented for the simulation of supersonic jet noise. Direct numerical simulations with a modeled nozzle inlet showed a good agreement of the screech frequency to a semi-empirical low found by Powell in 1953 [6].

Implicit Large Eddy Simulation (ILES) in conjunction with high resolution and high order computational modelling was applied to a turbulent mixing jet of a fuel injector in gas turbine combustors. In the ILES calculation, the governing equations for three dimensional, single phase, nonreactive multi-species compressible flow were solved using a finite volume Godunov method. A fifth-order accurate methods was used to achieve high order spatial accuracy and a second order explicit scheme was applied for time integration. Comparison of mean and fluctuating velocity components and mixture fraction with experiment and conventional LES demonstrated that the ILES successfully captured the turbulent flow structures without explicit subgrid scale modelling.

The flow around a complete model wind turbine is computed using LES and the immersed boundary method. The influence of inlet velocity profile and turbulence level is evaluated. The inlet velocity profile was found to have major influence in the upper regions of the flow field. The imposed turbulence level had no major influence on the turbulent spectra but it’s effect is clearly seen on the generated vortices.

Instantaneous amplitude and phase concept emerging from analytical signal formulation is applied to the wavelet coefficients of streamwise velocity fluctuations in the buffer layer of a near wall turbulent flow. Experiments and direct numerical simulations show both the existence of long periods of inert zones wherein the local phase is constant. These regions are separated by random phase jumps. These behaviours are reminiscent of phase synchronization phenomena observed in stochastic chaotic systems. The lengths of the constant phase inert (laminar) zones reveal a type-I intermittency behaviour. The observed phenomena are related to the footprint of coherent structures convecting in the low buffer layer that synchronizes the wall turbulence.

The low-frequency motions found in two large-eddy simulations of the same oblique-shock/turbulent-boundary-layer interaction with significantly different domain widths are investigated. The narrow domain artificially confines the shock-induced separation bubble, which is seen to grow significantly. In addition, the low-frequency/large-amplitude shock oscillations are found to be enhanced, therefore suggesting that they originate from an intrinsic two-dimensional mechanism. By reducing the spanwise confinement, large coherent structures as wide as one separation-bubble length are found to develop inside the interaction. Those structures can move sideways and survive for extended periods of time. Their proper resolution is therefore challenging in terms of computational cost and their meandering motions can significantly bias the interpretation of a spectral analysis performed at a fixed point.

Since direct numerical simulations of natural convection flows cannot be performed at high

Ra

-numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the nonlinearity. The regularization method basically alters the convective terms to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yields a novel class of regularizations that restrain the convective production of smaller and smaller scales of motion by means of vortex stretching in an unconditional stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. The regularization model is successfully tested for a 3D natural convection flow in air-filled (

Pr

= 0.71) differentially heated cavity of height aspect ratio 4 at

Ra

= 10

10

and 10

11

. Moreover, a method to dynamically determine the regularization parameter (local filter length) is also proposed and tested.

In the framework of turbulent interfacial multiphase flows, an

a priori

study is performed in the case of the turbulence/interface interaction. Density and viscosity ratios are set to 1 to perform a parametric study on surface tension forces. When using the ghost-fluid method, subgrid-scale terms deriving from jump conditions appear in the pressure gradient and viscous terms. A model is tested for advective SGS terms deriving from both the momentum equation and the advection of the interface.

The flow inside a three-dimensional diffuser is computed with a two-velocity hybrid RANS/LES model that ensues the separation of dissipative effects of the mean and fluctuating fields to be treated individually; by extracting a running average velocity field from instantaneous quantities. The averaged field is then used to calculate the contribution of the mean shear which is larger than that from the fluctuating one over the near wall region. Results with the hybrid model are presented and compared to those from a DES on the same grid. RANS results obtained with models upon which both these approaches are based are also reported. The RANS results are unable to capture essential characteristics of the flow whereas the hybrid method produces results which generally agree well with the experiment.

The present work focuses on the intrinsic properties of an axisymmetric separating/reattaching flow. A numerical simulation of a compressible flow over a cylinder extended by another cylinder of smaller diameter is performed at a Reynolds number based on the diameter of the larger cylinder of 1.2 × 10

6

. Statistical and fluctuating properties are compared with the available experimental data and those of two additional configurations. First the plane counterpart of the axisymmetric case allows us to assess the influence of three-dimensionality. Then a double backward facing step designed from the half upper part of the plane case permits us to survey the flow interactions. Finally a linear stability analysis is coupled with two-point correlations unveiling the importance of the highest coherent modes in the flow behaviour.

A comparative parameter study is performed in order to analyze the influence of turbulence on the rate of droplet coalescence. Therefore, Direct Numerical Simulations (DNS) of the fluid turbulence are coupled with a Lagrangian tracking of the particle phase (DPS) accounting for collisions leading to coalescence and to a broad droplet size distribution. In addition the accuracy of stochastic collision models is evaluated by comparison of Monte-Carlo predictions with the obtained results from the DNS/DPS simulations and statistical collision models are evaluated.

Droplet evaporation is usually modelled as a subgrid process and induces local inhomogeneities in the mixture fraction probability density function (PDF) and its scalar dissipation. These inhomogeneities are usually neglected, however, they can be significant and determine the combustion regime. In the present work, Direct Numerical Simulations (DNS) of fully resolved evaporating methanol droplets are analysed, assessing fuel vapour mixing in laminar and turbulent flows. The results show that scalar probability distributions and scalar dissipation vary greatly depending on the position relative to the droplet position, on droplet loading and on flow conditions. The

β

-PDF seems to capture the global behaviour for laminar flows around droplet arrays with low droplet density, however, mixing characteristics for higher droplet densities in stagnant and turbulent flows cannot be approximated by a

β

-PDF, and modelling approaches based on cell mean values will lead to erroneous results.