Direct and Large-Eddy Simulation VIII

Direct simulations have become indispensable tools in turbulence research, and, in the last two decades, especially so for the study of wall-bounded turbulence. Early simulations dealt mostly with the viscous and buffer layers near the wall, because their Reynolds numbers had to be necessarily limited (Kim et al.,

1987

). They led very soon to a fairly complete description of the kinematics of this part of the flow (Robinson,

1991

), and, later, to the qualitative understanding of their dynamics (Jiménez et al.,

2005

). While most of those studies were carried out in turbulent channels, the results are generally believed to apply to all attached wall-bounded turbulent flows, because the time scales of the near-wall region are too fast to interact strongly with the slower processes of the non-universal outer layers.

Turbulent boundary layers constitute one of the basic building blocks for understanding turbulence, particularly relevant for industrial applications. Although the geometries in technical but also geophysical applications are complicated and usually feature curved surfaces, the flow case of a canonical boundary layer developing on a flat surface has emerged as an important setup for studying wall turbulence, both via experimental and numerical studies. However, only recently spatially developing turbulent boundary layers have become accessible via direct numerical simulations (DNS). The difficulties of such setups are mainly related to the specification of proper inflow conditions, the triggering of turbulence and a careful control of the free-stream pressure gradient. In addition, the numerical cost of such spatial simulations is high due to the long, wide and high domains necessary for the full development of all relevant turbulent scales. We consider a canonical turbulent boundary layer under zero-pressure-gradient via large-scale DNS. The boundary layer is allowed to develop and grow in space. The inflow is a laminar Blasius boundary layer, in which laminar-turbulent transition is triggered by a random volume force shortly downstream of the inflow. This trip force, similar to a disturbance strip in an experiment (Schlatter and Örlü,

2010

; Schlatter et al.,

2009

), is located at a low Reynolds number to allow the flow to develop over a long distance. The simulation covers thus a long, wide and high domain starting at

Re

θ

=180 extending up to the (numerically high) value of

Re

θ

=4300, based on momentum thickness

θ

and free-stream velocity

U

∞

. Fully turbulent flow is obtained from

Re

θ

≈500. The numerical resolution for the fully spectral numerical method (Chevalier et al.,

2007

) is in the wall-parallel directions Δ

x

+

=9 and Δ

z

+

=4, resolving the relevant scales of motion. The simulation domain requires a total of 8⋅10

9

grid points in physical space, and was thus run massively parallel with 4096 processors.

The fundamental assumption underlying large-eddy simulations (LES) is that the large, energy-carrying, eddies are resolved, while only the smaller eddies are modeled. An implication of this assumption is that the filter-width Δ, the length scale that separates the resolved from the unresolved eddies, should be a fraction of the integral scale, which is characteristic of the large eddies. In practice, however, the filter width is taken to be proportional to the grid size,

h

. This approach is generally legitimate, since the grid is usually refined where the important turbulence scales are smaller; it presents, however, two problems. First, rapid variations of the mesh (especially in methods that use local mesh refinement) may cause commutation and aliasing errors, and unphysical results (Vanella et al.,

2008

). Second, it requires knowledge, on the part of the user, on the characteristics of turbulence; in complex flows it may not be possible to predict the turbulence behavior

a priori

.

Since direct numerical simulations (DNS) of buoyancy-driven flows cannot be computed at high Rayleigh numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the nonlinear convective term. The first outstanding approach in this direction goes back to Leray (

1934

); the Navier-Stokes-

α

model also forms an example of regularization modeling (see (Geurts and Holm,

2003

), for instance). The regularization methods basically alter the convective terms to reduce the production of small scales of motion. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yields a family of

symmetry-preserving regularization

models (Verstappen,

2008

; Trias et al.,

2010

): a novel class of regularizations that restrain the convective production of smaller and smaller scales of motion in an unconditional stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). In this work, a method to dynamically determine the regularization parameter (local filter length) from the requirement that the vortex-stretching must be stopped at the scale set by the grid is also proposed and tested. The numerical algorithm used to solve the governing equations preserves the conservation properties too (Verstappen, and Veldman,

2003

) and is therefore well-suited to test the proposed simulation model. Here, the performance of the method is tested for a turbulent differentially heated cavity (DHC). Due to the complex behavior exhibit (Trias et al. in International Journal of Heat and Mass Transfer, 53:665,

2010

; Trias et al. in International Journal of Heat and Mass Transfer, 53:674,

2010

) an accurate turbulence modeling of this configuration is as a great challenge.

Large Eddy Simulation (LES) is based on a separation between large resolved, and small unresolved Sub-Grid Scales (SGS), obtained by applying a low-pass filtering operator on the governing equations. Actually, such filtering operation is often nothing but a formalism while writing the LES equations in continuous form. Indeed, in the so-called

implicit filtering approach

the discretization of both domain and differential operators is practically used as built-in filtering, e.g. see (Sagaut,

2006

). The characteristic filter length Δ is implicitly linked to the computational grid size step

h

(the only user-defined parameter) by the so-called

sub-filter resolution parameter

Q

=Δ/

h

. Hence, numerical representation of the filtered variables is associated with a finite number of resolved scales and marginal resolution.

LES is the study of turbulent flows obtained by resolving only the largest scales of Navier-Stokes equations. The restriction to the largest scales is equivalent to the application of a low pass filter, denoted by the overbar symbol

$\overline{\dots}$

, on the equations. We solve the equations for the filtered incompressible velocity field

$\overline{u}_{i}$

:

where

ν

is the kinematic viscosity of the fluid. The difference between the original and the LES Navier-Stokes equations comes from the so-called subgrid-scale stress tensor:

$\tau_{ij} =\overline{u_{i}u_{j}}-\overline{\overline{u}_{i}\overline{u}_{j}}$

acting only via the gradient of its traceless tensor

$h_{i}=\partial_{j}\tau^{\star}_{ij}$

. Its exact value cannot be computed, it is needed to approximate the exact tensor

$\tau^{\star}_{ij}$

by a subgrid-scale model tensor

$\tau^{\star}_{ij}\approx \tau^{\textrm{\tiny M}}_{ij}(\overline{u}_{l}) $

. The present study proposes a new framework to assess the LES models. So far, the assessment of subgrid-scale model relies either on a priori or a posteriori methods.

The last two decades have seen the emergence of a large number of new subgrid models, and it is the authors’ opinion that the turbulence community must devote more efforts in developing consensual criteria than in increasing the number of models. The purpose of the present letter is to investigate one possible criterion, which is the time-reversibility of a subgrid model, when the sign of the velocity is inverse,

i.e.

, under the transformation

u

→−

u

. We report the results of Eddy-Damping Quasi-Normal (EDQN) simulations in which the velocity is reversed in all, or part, of the scales of the flow. These results are then compared to results from LES in which the velocity is reversed, to assess the quality of the predictions of the models and to check whether time-reversibility is a valid criterion to assess subgrid models.

With the aim to get a better insight of wall-turbulence interaction, we designed an original configuration where a random forcing replace usual shear-related mechanisms of turbulence production. The synthesized turbulence diffuses by itself from a central plane layer, and continuously feeds on both sides a

solid

-wall or

free-slip

-surface with a shearless agitation. This specific situation allows to understand the blocking effect induced by the normal velocity cancelation at the surface, and is particularly relevant to quantify the intercomponent energy transfer occurring in this region. The configuration, extensively described in (Bodart et al.,

2010

), can be seen as the numerical counterpart of the oscillating grid experiment (see

e.g.

(De Silva and Fernando,

1994

)).

The most important contribution to the description of the energy transfer mechanism in the space of scales of turbulent flows is Kolmogorov theory. Under the assumption of isotropy, this theory asserts that the energy cascade in the inertial range is from large to small scales and proportional to the rate of energy dissipation. This picture is claimed to be universal since it is commonly assumed that isotropy recovery takes place at small scales of any flow for sufficiently high Reynolds number. This assumption fails to hold in wall-turbulence, where the interaction between anisotropic production and inhomogeneous spatial fluxes strongly modifies the classical energy cascade up to a reverse cascade (Marati et al.,

2004

).

High Reynolds numbers cavity flows are characterized by both broadband small-scales typical of turbulent shear layers, and discrete self-sustained oscillations due to a complex feedback phenomenon between the two corners of the cavity. Intermittency of the shear-layer turbulence may lead to multiple modes which apparently coexist. The self-sustained oscillations may then exist in more than one stable state, jumping between the different modes. This complex phenomenon is often greatly simplified to build lumped models such as the Rossiter formula.

Compact finite difference methods are nowadays very popular for the simulation of compressible turbulent flows, see for instance (Lele,

1992

) and (Boersma,

2005

). Due to the low dissipation and dispersion errors of the compact finite difference schemes, they can be used for various type of problems including large eddy and direct numerical simulation of turbulent flow and laminar turbulent transition. However due to the low numerical dissipation compact finite difference have the tendency to be numerically quite unstable. In practice this instability issue is solved by applying a spatial filter to the calculated solution or by using a staggered layout of the flow variables. The latter is of course more appealing. In this paper we will extend the staggered formulation we have developed for compressible flow, see (Boersma,

2005

) to the incompressible flow case.

Numerical simulation of turbulent flows in complex geometries is one of the most investigated fields in computer science in the last decades. But even though the power of supercomputers has regularly increased for many years, it has been understood that the numerical simulation of realistic flows at high Reynolds number would require too many efforts in term of memory and CPU time if one discretizes directly the Navier-Stokes equation.

Using large eddy simulation (LES) instead of DNS potentially introduces modeling errors and discretization errors both depending on the step size of the grid. Hence it seems promising to optimize the grid in an LES via adaptation to minimize this effect. In contrast to classical grid adaptation, the LES equations depend on the grid via the subgrid-scale term and therefore change whenever the grid is changed, so that criteria for adaptation need to be LES-specific. The present work uses

r

-adaptive refinement, defined by redistribution of a given number of grid points in the computational domain.

Turbulence can generally not be computed directly from the Navier-Stokes equations, because the flow possess far too many scales of motion. Therefore numerical simulations of turbulence have to resort to models of the small scales of motion for which numerical resolution is not available. Large-eddy simulation (LES) seeks to predict the dynamics of spatially filtered flows. If a spatial filter

$u \mapsto \overline{u}$

is applied to the (incompressible) Navier-Stokes equations an expression depending on both full velocity field

u

and the filtered field

$\overline{u}$

results, due to the nonlinearity. The dependence on

u

can be removed by adopting an eddy-viscosity model, for instance (Sagaut,

2001

). The governing equation is then given by

$$\partial_t v + (v\cdot\nabla)v +\nabla p = 2\nabla \cdot \left( (\nu+\nu_e)\,S(v)\right)$$

where

ν

and

ν

e

denote the fluid viscosity and the eddy viscosity, respectively;

S

(

v

) is the symmetric part of the velocity gradient (the rate-of-strain tensor). The solution

v

is supposed to approximate the filtered Navier-Stokes solution

$\overline{u}$

.

The Ahmed body car is a semi-rectangular vehicle with a rounded front part and a slant back. Flow over this generic body reproduce the basic fluid-dynamics features of real cars with a typical fastback geometry and its simplified topology allows easy comparisons between experimental and numerical works.

The properties of wavelet transform, viz. the ability to identify and efficiently represent temporal/spatial coherent flow structures, self-adaptiveness, and de-noising, have made them attractive candidates for constructing multi-resolution variable fidelity schemes for simulations of turbulence (Schneider and Vasilyev,

2010

). Stochastic Coherent Adaptive Large Eddy Simulation (SCALES) (Goldstein and Vasilyev,

2004

) is the most recent wavelet-based methodology for numerical simulations of turbulent flows that resolves energy containing turbulent motions using wavelet multi-resolution decomposition and self-adaptivity. In this technique, the extraction of the most energetic structures is achieved using wavelet thresholding filter with a priori prescribed threshold level.

With the recent development of wavelet-based techniques for computational fluid dynamics, adaptive numerical simulations of turbulent flows have become feasible (Schneider and Vasilyev,

2010

). Adaptive wavelet methods are based on wavelet threshold filtering that makes it possible to separate coherent energetic eddies, which are numerically simulated, from residual background flow structures that are filtered out. By varying the filter thresholding level different approaches with different fidelity are obtained: from the highly accurate wavelet-based direct numerical simulation (WDNS) that does not involve any model to the stochastic coherent adaptive large eddy simulation (SCALES) that needs a closure modeling procedure,

i.e.

(De Stefano et al.,

2008

).

The scale similarity (SS) idea was first introduced by Bardina et al. (

1980

). Following this idea the subgrid-scale stress tensor can be modeled through the modified Leonard tensor, which can be computed as a function of the variables resolved in LES by means of the application of an additional explicit filter. In the original idea, this filter should be the same as the grid one. It has been shown in a priori tests in the literature (see (Meneveau and Katz,

2000

) for a review) that the SS model correlates very well with the exact SGS stress tensor and represents quite well energy backscatter from the unresolved to the resolved scales. However, when the scale-similarity SGS model is used alone in actual large-eddy simulations, it does not provide enough SGS dissipation and the simulations may undergo numerical instability. Therefore, the modified Leonard tensor (or SS term) is always used in combination with an eddy-viscosity term, leading to the so-called

mixed models

(Meneveau and Katz,

2000

).

Subgrid-scale (SGS) modeling and resolution are two important issues that can affect the quality of large eddy simulation (LES) to a large extent. Many SGS models are based on an isotropic description of the SGS motions. However, SGS turbulence is not always isotropic. Near-wall SGS motions in wall-bounded turbulent flows is an example of such. In that case, the quality of LES largely depend on the grid resolution and the SGS modeling used. On the other hand, one could speculate that dependence of LES results on the resolution would be less if the SGS model is able to properly take into account the anisotropy of SGS stresses. In this paper, the influence of resolution on LES is investigated. Three SGS models are used, namely: the standard dynamic Smagorinsky model (DS) based on (Germano et al.,

1991

) and modifications of (Lilly,

1992

) which is an isotropic eddy viscosity model, the high-pass filtered dynamic Smagorinsky (HPF) model of (Stolz et al.,

2005

) which is based on the variational multiscale method and the recent explicit algebraic (EA) model of (Marstorp et al.,

2009

) which is capable of properly modeling the anisotropy of the SGS stresses. LES of channel flow is carried out using these SGS models at

Re

τ

=934, based on friction velocity and channel half width, and the results are compared to DNS data.

Complex geometries can be investigated with a non-structured solver. Another approach retained in this paper is to keep a structured mesh with the addition of an immersed boundary concept. Immersed Boundary Methods employ cartesian meshes that do not conform to the shape of the body in the flow and modify the governing equations to incorporate the boundary conditions. First introduced by Peskin (

1972

), IBMs involve either continuous or discrete forcing approaches. Only discrete forcing approach preserves good performance at high Reynolds number. The ghost-cell method (discrete forcing approach) utilizes a sharp boundary with a modification of the computational stencil and an extrapolation scheme to deduce the state variables in the border cells.

Coexisting laminar and turbulent regions have been observed in several types of wall bounded flows. In Taylor Couette flow, for example, alternating helical shaped laminar and turbulent regions have been observed within a limited Reynolds number range (Prigent et al.,

2002

) and oblique laminar and turbulent bands have been seen in experiments (Prigent et al.,

2002

) and simulations (Barkley and Tuckerman,

2005

), (Duguet et al.,

2010

) of plane Couette flow for Reynolds numbers

Re

=

U

w

h

/

ν

between about 320 and 380. Here ±

U

w

is the velocity of the two walls,

h

is the half width of the wall gap and

ν

is the viscosity. In this Reynolds number range the turbulent-laminar patterns seem to sustain while at lower

Re

the flow becomes fully laminar and at higher

Re

no clear laminar patterns can be distinguished and the flow eventually becomes fully turbulent. Similar oblique laminar-turbulent bands appeared as well in direct numerical simulations (DNS) of plane channel flow for friction Reynolds numbers

Re

τ

=

u

τ

h

/

ν

=60 and 80 (Fukudome et al.,

2009

), (Tsukahara,

2010

), where

u

τ

is the friction velocity and

h

is again the gap half width.

In many industrial applications, there is a need to understand scalar mixing, e.g. in gas turbine combustion systems. In such combustion systems, the majority of momentum transport and scalar mixing is driven by the large-scale structures, therefore LES becomes a natural choice. During the last years, promising results are obtained with LES, however, as opposed to LES modeling of the velocities, only a limited body of literature is devoted to scalar modeling, especially in wall-bounded flows. The most commonly used model is the so-called eddy-diffusivity model requiring the predetermination of the turbulent Prandtl number (model coefficient), usually assumed to be a constant. In turbulent channel flow, Moin

et al.

(

1991

) extended the dynamic Smagorinsky model to compressible turbulence and scalar transport. Later, Calmet & Magnaudet (

1997

) performed simulation with three different Schmidt numbers: 1, 100 and 200 using the dynamic mixed model. The mass transfer coefficient is found to agree very well with previous experimental results. Recently, You & Moin (

2009

) generalised their previous SGS model You & Moin (

2007

) to account for scalar transport. The model does not require any spatial nor temporal average of the coefficient and thus can be used to simulate flows in complex geometry. However the results are similar to those obtained with dynamic Smagorinsky model.

In environmental flows where the Reynolds numbers are very high it is not possible to solve directly the near-wall region because of the still-limited computer power. Furthermore, the presence of irregular wall-roughness in practical high Reynolds flows would make the direct resolution of the near wall viscous layer somewhat useless. When using Large-eddy simulations (LES), many efforts have been made in the last decades to develop LES wall-layer models (LWM) designed to skip the resolution of the near-wall layer (Piomelli,

2008

). One of the common approaches used both in channel flows and planetary boundary layers, is to derive the stress to be used as boundary condition by the assumption that the instantaneous near-wall velocity belongs to a logarithmic profile (see among the others (Mason et al.,

1986

), (Temmerman et al.,

2003

)). We propose a modification to this kind of approach in which an analytically derived correction to the evaluation of the near wall Smagorinsky eddy viscosity and diffusivity is made. This correction, which is a simplified version of the two part model first proposed by (Schumann,

1975

) and then adapted by (Sullivan et al.,

1994

) for planetary boundary layers, is computationally simple to implement and does not require homogeneity, thus being a good candidate to simulate complex-terrain configurations typical of environmental flows of practical interest. The quality of the resulting velocity prediction as well as of the temperature profiles is significantly improved. The proposed LWM is validated reproducing with a very coarse mesh a plane channel flow at two Reynolds numbers,

Re

∗

=4000 and

Re

∗

=20000 for a case of forced convection.

The evolution of a mixing layer is very sensitive to upstream flow conditions (Moser and Rogers,

1993

). We optimize the initial flow conditions of a temporal mixing layer. We use this case as a substitute experiment to study how long flow control can affect the evolution of the mixing layer solution. In earlier work, we showed that optimization of the initial condition can be used to, e.g. increase the rate of kinetic energy dissipation at the end of a selected optimization time window significantly (Delport et al.,

2009

). The current paper focusses on longer time windows and addresses the robustness of the optima in presence of white noise.

The modeling of turbulent two-phase flows is a subject of interest both to those who wish to understand and predict natural phenomena (e.g. clouds, tornadoes, volcanic clast dispersion, etc.) and those who wish to design and optimize engineered products (combustion devices based on fuel-spray injection such as gas turbine engines or spark ignition engines, augmenters in military aircraft, spray coating whether for painting or for protection against pests, consumer-product sprays such as those dispensed in cans, medical sprays, etc.). Despite the considerable range of applications and the substantial monetary advantages of successful prediction of turbulent two-phase flows, and despite numerous studies addressing modeling of these flows, there is still a lack of consensus for simulating these flows. The results described below are in the context of volumetrically dilute two-phase flows in which the volume of the condensed phase is negligible with respect to that of the carrier gas (e.g.

O

(10

−3

)) although the ratio of the condensed-phase mass to that of the carrier gas mass can be a substantial fraction (e.g.

O

(10

−1

)) because the density of the condensed phase is larger by a factor of

O

(10

3

) than that of the gas.

Particle-laden channel flows are found in a variety of natural settings and are also of great practical importance due to their frequent occurrence in engineering applications. Numerous experimental and computational studies related to particle transport in turbulent flows were reported in the literature. There have been a few applications of Direct Numerical Simulations to particle-laden channel flows, such as in (Li et al.,

2001

) and (Soltani and Ahmadi,

1995

). Those studies necessarily focus on rather low Reynolds numbers. Kulick

et al.

(

1994

) reported results of experiments on particle-laden flows in a vertical channel down-flow at

Re

τ

≈644 (based on friction velocity and channel half-width). Large-Eddy Simulation results for a channel flow at approximately the same Reynolds number are also available, e.g. (Fukagata et al.,

2001

).

The use of Large Eddy Simulation (LES) has emerged in recent years as a powerful simulation technique with the specific goal of achieving a good statistical accuracy while retaining a computational cost lower than Direct Numerical Simulations (DNS) (Sagaut,

2006

). In LES, only large-scale motions are directly computed (resolved on the computational grid) while small scale motions are not computed explicitly but modeled via Sub-Grid Scale (SGS) models. Due to the complex statistical properties of turbulence, many models and methodologies have been proposed in the past. Although none of the proposed models can be considered a perfect substitute to DNS, their performance can be sometimes considered fairly accurate for what concerns the most common Eulerian turbulent flow statistics. The problem of particle transport in turbulence demands much more to LES than just reproducing low order Eulerian statistics (e.g. spectra, average profiles etc) (Salazar and Collins,

2009

; Toschi and Bodenschatz,

2009

). Here we propose a way to quantify the effect of (the error due to) sub-grid modeling on particle properties.

Dispersion of particles in a turbulent wall-bounded flow is crucial in many practical applications. For numerical simulation of particle-laden turbulent flow various approaches are available. Among these, LES is perhaps the most promising because its computational cost is lower than that of DNS and its predictive capability is much higher than Reynolds-Averaged Navier-Stokes methods especially in case of particles-turbulence interaction in boundary layers. Various subgrid models are available which have proved their validity for several types of flow. However, the treatment of particles in LES is still a relatively new topic with open questions regarding e.g. Sub-Grid Scales (SGS) effects on particle behavior and the modeling of particle-particle, particle-fluid or particle-wall interactions. To address these issues, an international collaborative benchmark test has been proposed as part of the activity of the COST Action P20 LESAID. The objective is to gather a large database of results obtained with different numerical methods, SGS models and physical models in order to resolve questions about the validity of these models. In this paper the first statistics of the benchmark for a base Eulerian-Lagrangian simulation of particle-laden channel flow, are presented. The specific simulation parameters have been chosen also to allow estimate of the quality of the LES results upon comparison with available DNS results (Marchioli et al.,

2008

) for the same test case. The groups participating in the benchmark are: UUD-UPI (Marchioli, Soldati, Salvetti); TUE (Kuerten); IMFT-ASU (Konan, Fede, Simonin, Squires); TUM (Gobert, Manhart); TUK-TUD (Jaszczur, Portela). Results provided by each group refer to a statistically stationary situation in which the particle concentration has reached a steady state. The time taken to reach steady concentration is very long (up to 2⋅10

4

in wall units (Marchioli et al.,

2008

)) thus making the required computational effort quite high even for a LES-based calculation.

This contribution deals with Large-Eddy simulation (LES) of particle-laden flow. State of the art methods are capable to predict the dynamics of small particles in dilute suspensions as long as direct numerical simulation (DNS) is possible. However, as soon as the Reynolds number is too high, DNS is not an alternative and often LES is the method of choice. For LES of particle-laden flow, the effect of the unresolved subgrid scales (SGS) needs to be modeled, a least for small or moderate Stokes numbers of the particles. This means that two turbulence models are necessary. One model for SGS effects on the resolved scales of the carrier fluid flow (such as the Smagorinsky model) and another model for SGS effects on the particle dynamics. Hereinafter, the former type of models is refered to as

f

luid-LES models and the latter type as

p

article-LES models.

Turbulent jets with a dispersed phase are widely found in technological applications or in natural flows. In Plinian volcano eruptions a multiphase jet-column is produced. In this process the mixing of the entrained fresh air into the hot stream of gas is crucial in establishing the conditions for pyroclastic flows (Kaminski et al.,

2005

).

Non-isothermal turbulent flows laden with large number of particles or droplets occur in numerous situations e.g., combustion, catalytic cracking, droplet growth in clouds, etc. Due to interactions between continuous and dispersed phase the distribution of the particles and its statistical properties can be highly non-uniform (Eaton and Fessler,

1994

). This non-uniformity can have important consequences on the chemical processes affecting the efficiency of the combustion or chemical reactions. Experiments and DNS demonstrates that shear flow, mean gradient in the fluid and velocity of the particles have complex effect on the particle fluctuations.

The interaction of droplets that undergo phase transition with a turbulent flow is encountered in many areas of engineering and atmospheric science as described in (Lanotte et al.,

2008

). In the context of cloud physics the evaporation and condensation of water vapor from and to the droplets is the governing process for the growth of the droplets from sub micron size up to a size of around 20

μ

m, after which they grow mostly by coalescence until they become large enough to fall as rain drops under gravity. Much pioneering work has been done in (Luo et al.,

2008

; Lanotte et al.,

2008

; Sidin et al.,

2009

) on the theoretical and numerical investigation of the influence of turbulence on evaporation and condensation associated with aerosol droplets. In this paper we consider the situation of water droplets undergoing phase change and moving in air. Air also advects the vapor concentration field. We compute the natural size distribution of the droplets that arises as a result of the interaction between the droplets and the transporting turbulent flow. We assume the turbulent flow to be homogeneous and isotropic. We will perform DNS of the velocity field and the passively advected vapor and temperature field. The droplet trajectories are computed time-accurately in a domain with periodic boundary conditions.

Direct numerical simulation of turbulent channel flow is employed to show that two-way coupling effects in particle-laden flows leads to reduced preferential clustering and turbophoresis (Kuerten and Vreman,

2005

) even for low values of volume and mass fraction. The effect of including two-way coupling on the phenomenon of turbophoresis and preferential clustering is studied for particles of different response times at a variety of loading ratios.

Turbulent motions of a multiphase fluid are present in many natural processes and technological applications. In clouds the interactions between turbulence and dispersed droplets lead to the growth of water micro-particles by means of collisions and coalescence that may accelerate the rain. In engineering, transport and evaporation phenomena of micro-droplets in pipes are crucial in the mixing between the fuel and oxidizer in combustion chambers. A good mixing efficiency between the two phases enables smaller and lighter burners.

Mixing layers are a fundamental phenomenon that occurs in many more complex flows such as jets, counter-flows and recirculating flows. The importance of mixing layers as a building-block in fluid mechanics is evident in the large number of computational, experimental and theoretical studies devoted to the topic. With its simple configuration and easy control of flow parameters, mixing layers were one of the first flows that became amenable to direct numerical simulation (DNS). Examples of DNS of incompressible (Moser and Rogers,

1991

) and compressible (Vreman et al.,

1996

) can be found. However, these studies and most others have considered only single-species (usually air) mixing layers, in which the two streams have different flow properties but the same fluid properties. Relatively few studies by DNS have considered binary-species (Okong’o et al.,

2002

) and multi-species (Knaus and Pantano,

2009

; Echekki and Chen,

2003

; Zheng et al.,

2004

))mixing layers in which the fluid properties of different streams differ. Such binary- and multi-species mixing layers are of special importance in the process and energy (i.e. combustion) industry.

In many industrial and natural processes turbulent dispersion of immiscible phases occur. An industrial example is the process of steel making, where bubble flotation is used to remove inclusions which downgrade the quality of steel. An example from nature is the formation of droplets in clouds, where turbulent air influences the collision-coalescence rate. To gain a better understanding of droplet dynamics and turbulence modification in the clustering regime at Stokes number

St

∼1, proper modeling of coalescence and break-up is crucial. To be able to investigate these effects the number of deformable droplets should be relatively high and the problem has to be solved in an accurate and efficient way. The goal of our research is therefore to perform Direct Numerical Simulation (DNS) of a large number (∼10

3

) of inertial droplets in a turbulent carrier fluid, where coalescence and break-up is treated in a physical way. In general such simulations are expensive in terms of CPU, but in this work we show that our code scales well with an increasing number of deformable droplets and grid sizes.

In many regions the atmospheric surface layer is affected substantially by vegetation canopies. Most previous work has focused on effects of vegetated terrain characterized by a single length scale, e.g. a single obstruction of a particular size, or canopies consisting of plants, often modeled using a prescribed leaf-area density distribution with a characteristic dominant scale. It is well known, however, that typical flow obstructions such as canopies are characterized by a wide range of length scales, branches, sub-branches, etc. Yet, it is not known how to parameterize the effects of such multi-scale objects on the lower atmospheric dynamics. This work aims to study boundary layer flow over fractal, tree-like shapes. Fractals provide convenient idealizations of the inherently multi-scale character of vegetation geometries, within certain ranges of scales. Preliminary results from a large-eddy simulation (LES) and experimental study of a fractal tree canopy in a turbulent boundary layer are reported. The LES use Renormalized Numerical Simulation (Chester et al.,

2007

, J. Comp. Phys.) to provide subgrid parameterizations of drag forces from unresolved small-scale branches. Experiments aiming at understanding drag forces acting on fractal trees are performed in a water tunnel facility. Drag force measurements are obtained on a set of “pre-fractal” trees containing 1-5 branch generations.

When wind turbines are arranged in large wind farms, their efficiency decreases significantly due to wake effects and to complex turbulence interactions with the atmospheric boundary layer (ABL) (Frandsen et al.,

2006

). For large wind farms whose length exceeds the ABL height by over an order of magnitude, a “fully developed” flow regime may be established (Frandsen et al.,

2006

; Calaf et al.,

2010

; Cal et al.,

2010

). In this asymptotic regime, the changes in the stream-wise direction are small compared to the more relevant vertical exchange mechanisms. Such a fully developed wind-turbine array boundary layer (WTABL) has recently been studied (Calaf et al.,

2010

) using Large Eddy Simulations (LES) under neutral stability conditions. The simulations showed the existence of two log-laws, one above (characterized by:

$u_{*}^{hi},\,z_{o}^{hi}$

) and one below (

$u_{*}^{lo},\,z_{o}^{lo}$

) the wind turbine region. This enabled the development of more accurate parameterizations of the effective roughness scale for a wind farm. Now, a suite of Large Eddy Simulations, in which wind turbines are modeled as in (Calaf et al.,

2010

) using the classical drag disk concept are performed, again in neutral conditions but also considering temperature. Figure 1 shows a schematic of the geometry of the simulation.

The fluid flow over rough sand beds in rivers has unique dynamics compared with the flows that occur when the bed is flat. Depending on the flow Reynolds number, the most commonly found river-bed formations are ripples and dunes. Ripples have dimensions much smaller than the river depth, while dunes may reach heights of the order of the depth. Ripples do not affect the dynamics of the whole flow depth whereas dunes influence on the turbulent flow as well as the sediment transport at the whole depth. Dune formation may affect navigation, erosion of bridge piles and other structures, as well as dispersion of contaminants (Itakura and Kishi,

1980

).

Local scour phenomena around bridge abutments and piers can induce the collapse of hydraulic structures (Cardoso and Bettess,

1999

). Understanding of the erosion process is required for the a-priori estimation of the scour-hole geometry. The problem of local erosion is particularly difficult since a complete modeling of the process needs to take into account several phenomena ranging from fluid mechanics to river geomorphology. The turbulence characteristics of the incoming flow field (Sumer,

2007

), the dynamics of the coherent structures that forms in junction flows (Simpson,

2001

) and the sediments motion which is characterized by large intermittency (Radice et al.,

2009

), are processes that have to be properly considered. The first step of the present research is aimed at the analysis of the coherent structures dynamics around the bridge abutment and how they change in different scour conditions. In fact many authors found out that the lack in understanding these processes is one of the motivation of the incapability of the models to accurately predict the scour-hole geometry and its maximum depth (Ahmed and Rajaratnam,

2000

). The second step is aimed at understanding how the coherent structures and their dynamics can influence the scouring process. It is important to know how the fluctuations and the intermittent character of the vortical structures can be involved in the sediment transport and to single out the most important forces that can destabilize the sediments since a clear view of the incipient motion is still missing. This study focuses on the analysis of the turbulent field around a 45

○

wing-wall bridge abutment at different phases of the scour phenomenon.

The scope of this paper is to analyze the performance of wall-layer model Large Eddy Simulation (WLES) in the prediction of flow separation under stable stratification. This is a fundamental problem of practical importance both in industrial and in environmental applications. We consider turbulent flow in a plane asymmetric diffuser because this simple configuration is particularly challenging for testing the performance of numerical models to reproduce flow separation. Further, this flow has been previously investigated both experimentally and numerically. A sketch of the geometry is in Fig. 1. Depending on the slope of the diffuser and on the Reynolds number (

Re

=

ul

/

ν

with

u

and

l

characteristic velocity and length scale of the problem, while

ν

is the kinematic viscosity) separation occurs.

The details of the transport of riverine sediments to the ocean are not fully understood (Geyer et al.,

2004

; McCool and Parsons,

2004

). Normally the freshwater-particle mixture is lighter than estuarine saltwater such that most river plumes are positively buoyant. Thus, the particles can be transported over relatively large distances with the freshwater current until their settling dominates over the horizontal transport. Generally, two different

settling modes

are known to increase the average particle settling speed significantly (McCool and Parsons,

2004

):

flocculation

of individual particles forming larger effective aggregates with larger Stokes settling speeds (Geyer et al.,

2004

) and the settling enhancement due to

turbulence

(McCool and Parsons,

2004

).

Hazardous chemical, biological, or radioactive releases from leaks, spills, fires, or blasts, may occur (intentionally or accidentally) in urban environments during warfare or as part of terrorist attacks on military bases or other facilities. The associated contaminant dispersion is complex and semi-chaotic. Urban predictive simulation capabilities can have direct impact in many threat-reduction areas of interest, including, urban sensor placement and threat analysis, contaminant transport (CT) effects on surrounding civilian population (dosages, evacuation, shelter-in-place), education and training of rescue teams and services. Detailed simulations for the various processes involved are in principle possible, but generally not fast. Predicting urban airflow accompanied by CT presents extremely challenging requirements (Britter and Hanna,

2003

; Patnaik et al.,

2007

; Grinstein et al.,

2009

).

Urbanization modifies the bottom of the atmospheric boundary layer (ABL) leading to elevated air pollutant concentrations. Over 50% of the world population lives in cities nowadays (United Nations,

2008

). Urban air quality is thus a problem of major concern.

We review recent simulations of shock-induced separation of boundary layers and then consider in detail some properties of the detached shear layer that forms after separation of a turbulent boundary layer at Mach 2.3. Whilst still challenging in terms of numerical methods, due to the simultaneous presence of shock waves and turbulence, both direct numerical simulation and large eddy simulations (LES) are useful tools to investigate fundamental issues of shock-wave/boundary-layer interaction. In particular with LES it is feasible to calculate the long run times and wide domains necessary to study low frequency motions that occur under the reflected shock foot. We show here that a simplified model based on growth rate of the separated shear layer leads to predictions of frequency that are significantly higher than the low-frequency peak seen in LES and experiment.

Simulations of subsonic free jets can only compute noise contributions from sources connected with the large-scale structures occurring close to the potential core region and their breakdown to fine-scale turbulence (Freund,

2001

). To account for additional noise sources associated with fine-scale turbulence in the initial shear layers and the interaction of flow with the nozzle lip, the nozzle must be included in the simulation and, moreover, the flow inside the nozzle must be fully turbulent. Previous work including realistic nozzle geometries in the simulation failed to achieve fully turbulent flow at the nozzle exit (e.g. (Uzun and Hussaini,

2009

)). To overcome the difficulties encountered when using realistic geometries, the problem can be simplified by using a canonical nozzle with well defined turbulent exit conditions. The ultimate goal of this ongoing study is to use a round pipe with sufficient length as a canonical nozzle for direct noise computations of jets. This paper focuses on whether the flow conditions at the pipe exit can be used as well defined turbulent upstream conditions for such calculations. From this perspective the following issues are of interest: (i) the effect of the inflow boundary conditions on the length of the pipe required to obtain fully developed turbulent pipe flow (development length); and (ii) the effect of compressibility on the temperature field. The former is needed to specify the length of the nozzle for full jet calculations, while the latter is related to the correct prescription of the ambient temperature. The spatially developing pipe flow using a turbulent inflow generation was chosen for this study instead of the alternative recycling or precursor simulation techniques because it avoids introducing an undesired artificial recycling frequency, the need to impose a pressure gradient, and minimizes the computational cost and memory requirements.

Over the last decades, there has been considerable interest in supersonic axisymmetric wakes, or

base flows

. Initially, the motivation of the research was to gain a better understanding of the dynamics of supersonic turbulent flows, and to devise methods for drag reduction. Later, base flows were frequently chosen as a challenging test case for numerical simulations, mainly due to the availability of reliable data from carefully conducted base flow experiments (e.g. Herrin & Dutton, (

1989

)), and the fact that a complex flow is generated by a relatively simple geometry, facilitating grid generation. Furthermore, the failure of early RANS calculations to capture some of the characteristic properties of the flow, e.g. a flat base pressure distribution (Sahu et al.,

1985

), motivated studies employing various RANS and hybrid RANS/LES turbulence models.

Cryogenic rocket engines, advanced gas turbines and diesel engines are characterized by the injection of a liquid fuel into a high temperature and pressure chamber. Typically the fuel is injected at high enough pressure to be close or above the critical pressure. In these conditions the behavior of the fluid differs strongly from that of a perfect gas. It exhibits large variations of thermodynamic and transport properties also for small temperature changes, with significant effects on mixing and combustion processes. In this context an appropriate numerical simulation should take into account such thermodynamic phenomena via suitable equation of state and transport properties relations.

Studies of curved channel flows are clearly important since the flow over curvatures is related to various applications such as turbines, heat exchangers and combustors. Since Wattendorf (

1935

), many works have been made for the flow instability near the concave wall, and it was pointed out that the organized flow called Taylor-Görtler vortex grew due to the centrifugal force.

The numerical modeling of combustion systems is a very challenging task. The interaction of turbulence, chemical reactions and thermodynamics in reacting flows is of exceptional complexity. Computing power is too limited to solve practical problems in detail. This problem asks for special treatments in the modeling of flames.

In this paper the effectiveness of LES for modeling premixed methane combustion will be investigated in the context of gas turbine modeling. The required reduction of the chemistry is provided by the flamelet generated manifold (FGM) approach of van Oijen (

2002

). For turbulence-chemistry interactions an algebraic model is used to calculate variations which are used to invoke a pre-assumed pdf, Vreman et al. (

2009

). The algebraic model has a tunable parameter.

The last century has witnessed soaring gas prices, deteriorating air quality and alarming global climate changes. In recent years, increasing concerns have been raised with respect to the environmental impacts of energy consumption via the combustion of fossil fuels, for instance in stationary power generation and transportation, emitting greenhouse gases and air pollutants. As a result, governments now set more and more stringent standards. Hence, it is essential to understand and improve combustion processes, in order to reduce fuel consumption and pollutant emissions as much as possible.

Characterizing the inflow conditions, especially of droplet distribution at the computational inlet is one of the challenging aspects for a successful multiphase Large Eddy Simulation (LES). Here, we investigate spray modeling by simulating the experiments of acetone spray mixing by Chen et al. (

2006

). In the experiments, the turbulent spray is generated by a shear driven nebulizer and is carried through a 7

L

/

D

circular pipe into a mixing chamber [see Fig. 1(a)]. Two separate simulation campaigns are performed. In the first set of simulations, only the internal-flow within the injector is studied using breakup modeling. These breakup simulations are used to assess a new multi-scale breakup procedure by comparing the predicted droplet profiles at the injector exit plane with data. Experimental data at the injector exit plane is shown to be dilute and therefore, in the next set of simulations, this dilute spray exiting into the mixing chamber is simulated using different inflow profiles. Comparison with data using two different subgrid mixing models is used to highlight key features of the far field development of the spray and the gaseous flow.

In this work, an unsteady flamelet/progress variable (UFPV) model is applied in large-eddy simulation of a lifted methane/air flame in a vitiated co-flow. In this burner configuration, the flame is stabilized by autoignition. This ignition mode is of particular relevance to a number of practical applications, including furnaces, internal combustion engines, and flame stabilization in augmentors.

The turbulent wall-jet includes a number of interesting fluid mechanics phenomena with close resemblance to many mixing and combustion applications. During the last decades, both DNS (Ahlman et al.,

2007

; Ahlman et al.,

2009

), and LES (Dejoan & Leschziner,

2005

) have been used to study the turbulent wall-jet. Ahlman et al. (2009) performed DNS of nonisothermal turbulent wall jets. Earlier in 2007, Ahlman et al. investigated turbulent statistics and mixing of a passive scalar for an isothermal case by means of DNS. The first three-dimensional DNS of a reacting turbulent flow was performed by Riley et al. (1986) who simulated a single reaction of two scalars, without heat release, for a mixing layer. Recently, Knaus et al. (2009) studied the effect of heat release in non-premixed reacting shear layers (Knaus & Pantano,

2009

).

In this article, recent progress in the development of large eddy simulation (LES) for the study of compressible magnetohydrodynamic (MHD) turbulence of space plasma (Chernyshov et al.,

2007

,

2008

) is given (for LES applications in hydrodynamics of neutral gas see (Garnier et al.,

2009

) and for incompressible MHD turbulence see (Müller and Carati,

2002

)). The proper subgrid-scale (SGS) model relevant for space and astrophysical turbulence is selected based on this development, and the efficiency of LES for the investigation of the local interstellar gas turbulence is shown. In particular, the developed LES allows to explain observed data about the Kolmogorov-like spectrum of density fluctuations on the basis of three-dimensional modeling and, thus, to confirm a hypothesis that the weakly compressible regime of MHD turbulence in the local interstellar medium is fulfilled and density fluctuation are a passive scalar.

The Rayleigh-Bénard (RB) system is relevant to astro- and geophysical phenomena, including convection in the ocean, the Earth’s outer core, and the outer layer of the Sun. The dimensionless heat transfer (the Nusselt number

Nu

) in the system depends on the Rayleigh number

Ra

=

βg

Δ

L

3

/(

νκ

) and the Prandtl number

Pr

=

ν

/

κ

. Here,

β

is the thermal expansion coefficient,

g

the gravitational acceleration, Δ the temperature difference between the bottom and top, and

ν

and

κ

the kinematic viscosity and the thermal diffusivity, respectively. The rotation rate

H

is used in the form of the Rossby number

Ro

=(

βg

Δ/

L

)/(2

H

). The key question is: How does the heat transfer depend on rotation and the other two control parameters:

Nu

(

Ra

,

Pr

,

Ro

)? Here we will answer this question by giving a summary of our results presented in (Zhong et al.,

2009

; Stevens et al.,

2009

; Stevens et al.,

2010

).

Over the past years, turbulent convection has been the subject of extensive studies (see e.g. Ahlers et al.,

2009

; Kunnen et al.,

2008

; Lohse and Xia,

2010

), which attempted to determine the main flow features and the contribution of different parameters to the heat transfer in various geometries, but only few of them focused on Lagrangian statistics. Lagrangian tracking can put some light on the local properties of the flow by gathering information on the temperature and velocity fields along the particle trajectory (Schumacher,

2009

; van Aartrijk and Clercx

2008

). This, in particular, has direct relevance for many industrial and environmental applications where the fluid heat transfer is modified by the presence and deposition of particles on the walls (e.g. nuclear power plants, petrochemical multiphase reactors, cooling systems for electronic devices, pollutant dispersion in the atmospheric boundary layer, aerosol deposition etc.).

Turbulent Rayleigh-Bénard convection (RBC) is one of the classical problems of fluid dynamics. In spite of the great effort made in the past to understand the complex physical mechanisms in this type of flow, there are still many open questions which must be answered. In order to understand the effect of conductive horizontal plates on the flow structure in a Rayleigh-Bénard cell the differences between finite and infinite conductivity of the horizontal plates were the aim of many experimental and numerical studies, see (Brown et al.,

2005

; Johnston and Doering,

2009

; Verzicco and Sreenivasan,

2008

). Actually, the horizontal plates are assumed to be isothermal in most numerical simulations while they are conductive in experiments. Even more, the finite conductivity of the plates is one explanation for discrepancies between results obtained in experiments and numerical simulations. A fixed temperature boundary condition corresponds to infinite thermal conductivity of the plates while an imposed heat flux models poorly conducting plates. The effect of these two boundary conditions was recently compared by (Verzicco and Sreenivasan,

2008

). Their studies indicated that the heat transfer is suppressed for

Ra

>10

9

in simulations with plates of finite conductivity whereas for lower Ra the two cases leed to similar flows which agree with observations by (Johnston and Doering,

2009

). They concluded that below

Ra

≈10

10

the plate conductivity plays no significant role in the

Nu

∼

Ra

2/7

scaling. Nevertheless, the results of (Verzicco and Sreenivasan,

2008

) as well as those of (Johnston and Doering,

2009

) refer to a cell with infinitely thin plates while the finite thickness of the plates is considered in our simulations. In the present study the scaling exponent

β

in the Nusselt-Rayleigh relation, i.e.

Nu

∼

Ra

β

obtained for the cell with highly conducting aluminium plates is similar as those obtained by (Kaczorowski and Wagner,

2007

), who studied RBC in the same convection cell and for the same Pr and similar Ra. However, the scaling exponent obtained for the cell with poorly conducting plexiglas plates is found to be slightly lower than those obtained by (Kaczorowski and Wagner,

2007

).

To study the classical problem of Rayleigh-Bénard convection, i.e. a fluid layer confined between a heating-plate at the bottom and a cooling-plate at the top, a common assumption is that all material properties are temperature independent, except for the density

ρ

within the buoyancy part, that changes like

$$\rho(T) = \rho_0 \left(1 - \alpha \cdot (T-T_0)\right),$$

with a constant isobaric expansion coefficient

α

. In combination with the condition of an incompressible fluid this is the so-called Oberbeck-Boussinesq (OB) approximation (Boussinesq,

1903

; Oberbeck,

1879

).

Rayleigh-Bénard convection (RBC) is a phenomenon occurring in fluids heated and cooled by a wall from below and above, respectively. The vertical heat transfer through the fluid is primarily defined by the Rayleigh number

, the Prandtl number

and the aspect ratio Γ=

W

/

H

of the convection cell, where the fluid is characterized through the thermal expansion coefficient

α

, the kinematic viscosity

ν

and the thermal diffusivity

κ

. The geometry is characterized by the height

H

and the width

W

of the cell and the temperature difference between the horizontal plates is Δ

T

.

Turbulent natural convection of a fluid inside an enclosure heated from below (Rayleigh-Bénard convection), has been object of many theoretical and experimental investigations (Grötzbach,

1983

; Niemela et al.,

2000

). Over the past decades numerical simulations have become a powerful tool for providing extensive data in turbulence structures and flow dynamics, but flow statistics for DNS at relative high Ra numbers are still limited by insufficient time integration (Amati et al.,

2005

). In this sense, LES can be an attractive alternative for the resolution of natural convection problems at high Ra numbers. As LES models the smallest scales of the fluid their results are not only dependent on the grid resolution and the spatial and temporal discretization but also on the choice of the appropriate subgrid scale stress (SGS) model for describing the flow behavior. There are scarce long-term first and second order statistics results in literature for comparing LES results. Furthermore, time integration for most of the statistical data available does not guarantee their independence with the LSC reversals. Thus, the objective of this work is twofold: i) to provide useful long-term accurate statistical data by means of DNS of a cylindrical enclosure of aspect ratio (Γ=

D

/

H

) 0.5 at

Ra

=2×10

9

and

Pr

=0.7 and, ii) to assess the behavior of different LES models by direct comparison with our DNS results.

At the end of the last decade it was shown that predictions by means of Direct Numerical Simulations (DNS) agree well with experimental results obtained with Laser Doppler Anemometry and Particle Image Velocimetry (see for example Eggels et al. (

1994

)) if weakly turbulent flows, i.e. low Reynolds numbers, are considered. In spite of the widely accepted merit of DNS for fundamental flow studies until now the technique could not shake off the prejudice that it is of little use for solving industrial flow problems. The reason might be that the required computational resources increase with approximately the third power of the Reynolds number and most of the industrially relevant flows, and in particular aircraft or vehicle aerodynamics, are characterized by very high Reynolds numbers. In this regard Spalart (

1999

) estimated in the year 1999, that it will take until 2080 for DNS to be applicable to such flows. However, in the last years we performed a number DNS-studies which are relevant for various industrial branches. The common objective of these incompressible flow simulations was to produce a reliable and comprehensive flow data base for the validation and improvement of corresponding Reynolds-averaged Navier-Stokes simulations (RANS). The latter rely on turbulence models which are known to perform well for simple shear flows but not in general.

The simulation of rotating cavities flows is a major issue in computational fluid dynamics and engineering applications such as disk drives used for digital disk storage in computers, automotive disk brakes, and especially in turbomachinery (see a review in (Owen and Rogers,

1995

)).

All solid surfaces in practice can be considered rough to a certain degree and this surface roughness is known to affect the fluid flow to a considerable extent. It is also known from the literature that system rotation affects both the mean fluid motion and the turbulence. Fluid flows involving both the surface roughness and the system rotation are therefore of major concern in industrial, geophysical and astrophysical applications.

A rod bundle is a key constitutive element of a wide range of nuclear reactor designs. It is composed by a set of long thin rods containing the nuclear fuel and fluid-flow between them and generally parallel to the rods. As experiments in a such densely packed geometries are difficult, thermal-hydraulics simulations are valuable to study heat transfer, fluid-forces, homogeneity of temperatures and flow rates and their fluctuations for current or and future reactor designs.

As wind power grows as an important contributor to the worldwide overall energy portfolio, wind farms will cover increasingly larger surface areas. With the characteristic height of the atmospheric boundary layer (ABL) of about 1 km, wind farms with horizontal extents exceeding 10–20 km may therefore approach the asymptotic limit of ‘infinite’ wind farms, and the boundary layer flow may approach the fully developed regime. Envisioning such large-scale implementations calls for advancements in our understanding of the detailed interactions between wind turbines and the atmospheric surface layer. In the past, a number of studies have focussed on the effect wind-turbine arrays on the WTABL using elements of momentum theory, potential flow, and the superposition of wakes of individual turbines (cf. Lissaman

1979

, and Frandsen

1992

). Several recent studies have focused on such dynamics of Wind Turbine Array Boundary Layers (WTABL) (Calaf et al.,

2010

; Meyers and Meneveau,

2010

; Cal et al.,

2010

).

Gas turbines used in the aerospace industry are subject to extremely high temperatures from the combustor. Efficient cooling systems are required to avoid damage to the turbine blades and stators. There are two approaches mainly used in the cooling and protection of the turbine blades and stators, which are external and internal cooling. External cooling is achieved by jets in the exterior of the blade that creates a thin relative cold air film around the blade. The film prevents that the incoming hot air enters in direct contact with the turbine blade. Internal cooling is obtained by the use of internal channels with turbulators and pin fins exposed to a coolant fluid flow. At the trailing edge of the blade, pin fins are placed to increase the heat transfer while providing structural support to the blade itself (Metzger

et al.

,

1984

). Metzger

et al.

(

1984

) estimated that the pin heat transfer surface coefficients doubles the end-wall coefficients. They also showed how the orientation with respect to the mean flow affects the heat transfer and the pressure drop for pin fin arrays. On the other hand, Chyu

et al.

(

1999

) concluded that the heat transfer in the pin fins is 10 to 20 percent higher than the end-wall.

Drag-reduction can be achieved by delaying of the onset of a turbulent flow as well as quenching turbulence itself. Due to the highly local nature of turbulent events and the rapid nature of breakdown a sensor-less (open-loop) strategy is highly preferable, since it prevents the necessity of large numbers of fast sensor/actuator combinations. Thus far, the success of the control strategies for boundary layer flows is limited and for bypass-transition none of the strategies has been successful. However, recent investigations indicate that sensorless (open-loop) control of transition to turbulence and drag reduction in turbulent flows is a feasible option.

The flow in two three-dimensional (3D) asymmetric diffusers with the same expansion but different aspect ratios was recently measured (Cherry et al.,

2008

). The results revealed complex 3D separation patterns with a severe sensitivity to the geometric variation. The setup served as a test case for two ERCOFTAC workshops (Jakirlić et al.,

2010

) that aimed at assessing the predictive capabilities of various turbulence modeling approaches. Reynolds-Averaged Navier–Stokes (RANS) models based on the eddy-viscosity assumption yielded qualitatively wrong results. These models cannot reproduce secondary vortices (SV) in the inlet duct. Methods that account for SV or even resolve these structures fared better. In particular Large-Eddy Simulation (LES) was able to compute the flow in both diffuser geometries within measurement uncertainty (Schneider et al.,

2010

). The hypothesis that SV have a strong impact on the separation dynamics was further corroborated by recent experiments (Grundmann et al.,

2010

). At the inlet of one of the diffusers, localized (steady and unsteady) perturbations were introduced. The authors conjectured that the forcing generated streamwise vortices and that these SV were responsible for the observed change in pressure recovery by up to 14%. In the present paper, the hypothesis is tested by controlled numerical experiments using LES and manipulation of (mean) SV in the inlet duct for both diffuser geometries.

A structure placed in a fluid flow is always affected by the pressure and shear forces acting on the surface leading to structural deformations or deflections. Partially these can be neglected and such a rigid body assumption strongly reduces the complexity of a numerical simulation setup. However, in many circumstances this assumption does not hold and fluid–structure interaction (FSI) becomes of major interest. Technical applications are numerous such as artificial heart valves, lightweight roofage or tents. Therefore, a need for appropriate numerical simulation tools exists for such coupled problems and this is the objective of the present study.