Direct and Large-Eddy Simulation IX

Since the larger eddies in turbulent flow cannot reach a near equilibrium between the rate at which energy is supplied and the rate at which energy is dissipated (by the action of viscosity), they break up, transferring their energy to somewhat smaller scales.

In the present work we introduce an LES framework which does not require any commutation property between filtering and derivative operators. A consistent redefinition of the SGS tensor in the new framework introduces several differences in the classical modeling strategies, including a modified, cheaper, form of Germano dynamic procedure. This dynamic procedure is exploited trough a new form of mixed model, whose scale-similar part is derived by a Taylor series analysis of the SGS tensor. The model is implemented in a commercial unstructured finite volume solver and numerical tests are performed on the turbulent channel flow at

$$\mathrm {Re}_\tau = 590$$

Re

τ

=

590

, showing the flexibility and accuracy of the proposed modeling strategy.

In practical turbulent flow applications exhibiting extreme geometrical complexity and a broad range of length and time scales direct numerical simulation (DNS) is prohibitively expensive and dependable large scale predictions of highly nonlinear processes must be typically achieved with under-resolved computer simulation models.

We consider the numerical simulation of the incompressible Navier-Stokes (NS) equations.

Space transportation systems predominantly rely on cryogenic rocket combustion engines, which have successfully been used for decades. However, satisfying the increasing requirements in terms of rocket performance and reliability is very challenging due to decreasing budgets and the request for short development cycles. Therefore, the importance of computational methods in the development process increases steadily, raising the demand for computational fluid dynamics (CFD) tools that are able to simulate the flow at rocket combustor conditions.

A primary mainstay of difficulty when working with problems of very high Reynolds numbers is the lack of computational resources; this implies that numerical simulations in this realm are, in general, always under-resolved.

The integral conservation laws for mass, momentum and energy of a flow field are universally valid for arbitrary control volumes. Thus, if the associated fluxes across its bounding surfaces are determined exactly, the equations capture the underlying physics of conservation correctly and guarantee an accurate prediction of the time evolution of the integral mean values.

Flow control of ground vehicles has recently attracted large interest in both industry and academia. The potential in energy savings seems to be considerable and at the moment both passive and active control strategies are explored.

The characterization of the relationship between the base pressure of bluff bodies and the geometrical and fluid dynamical parameters defining a certain configuration is a complex and still open problem, of interest for both fundamental research and practical applications.

This work is motivated by the need of the automotive industry to manufacture vehicles that progressively reduce and ultimately eliminate both their negative environmental impact and dependence upon oil.

Large-Eddy Simulation (LES) and Direct Numerical Simulation (DNS) are increasingly popular modeling tools for the understanding and the prediction of turbulent flows.

The discontinuous Galerkin (DG) method is a particular class of finite element methods which was first introduced by Reed and Hill in 1973 [

1

] for the treatment of the neutron transport equations.

This paper presents the second step of the validation of a compressible discontinuous Galerkin method (DGM) for the direct numerical simulation (DNS) and the large eddy simulation (LES) of turbomachinery flows.

Due to the broad range of spatial and temporal structures of turbulent flows, the resolution requirements for a fully resolved representation of all scales are prohibitively expensive and make Direct Numerical Simulations (DNS) impossible in all but a very limited number of cases.

Volume penalization is a subclass of immersed boundary methods for modeling complex geometry flows, which introduces the effects of obstacles by modifying the governing equations.

The direct numerical simulation (DNS) of unsteady flow past a square-cylinder has a very high computational cost, even at moderately.

In the current context of steady computational power increase, high-resolved unsteady simulations such as Large Eddy Simulation (LES) or Direct Numerical Simulation (DNS) are no longer restricted to academic usage, and becoming tools of interest for the industry.

A new high-order method for the accurate simulation of incompressible wall-bounded flows is presented. In stream- and spanwise direction the discretisation is performed by standard Fourier series, while in wall-normal direction the method combines high-order collocated compact finite differences with the influence matrix method to calculate the pressure boundary conditions that render the velocity field divergence-free. The main advantage over Chebyshev collocation is that in wall-normal direction, the grid can be chosen freely and thus excessive clustering near the wall is avoided. Both explicit and implicit discretisations of the viscous terms are described, with the implicit method being more complex, but also having a wider range of applications. The method is validated by simulating fully turbulent channel flow at friction Reynolds number

$$Re_\tau = 395$$

R

e

τ

=

395

, and comparing our data with existing numerical results. The results show excellent agreement proving that the method simulates all physical processes correctly.

Subgrid stress modelling plays an important role in the quality of LES results, and a number of different closure methods exist.

Adaptive methods with both mesh and polynomial order refinements have been used extensively in computational fluid dynamics to achieve optimal accuracy with the minimal computational cost.

Using an adaptive method in the context of a large eddy simulation (LES) is rarely seen in literature. A challenging aspect for this combination is the interplay between the resolution of the grid and the governing equations to be solved, since the grid spacing defines the scale separation between the resolved large-scale turbulent fluctuations and the unresolved subgrid-scale turbulence, so that whenever the grid changes in time this decomposition changes as well.

The international Benchmark on the Aerodynamics of a Rectangular 5:1 Cylinder (BARC [2]) was launched in 2008 with the support of Italian and international associations.

While many subgrid-scale (SGS) models have, over the years, been proposed (see [

6

]), the effects of various SGS models in simulations of wind turbine wakes has not been documented in great detail yet. In this study, we explore such effects in simulations of single wind turbine under laminar and turbulent inflow conditions.

Historically, industrial CFD simulations have been based on the Reynolds Averaged Navier-Stokes Equations (RANS). For many decades, the only alternative to RANS was Large-Eddy Simulation (LES), which has however failed to provide solutions for most flows of engineering relevance due to excessive computing power requirements for the simulation of wall-bounded flows.

Since wall-resolved LES suffers from very fine near-wall grid resolutions required (

$$\varDelta y_{1st}^+ < 2$$

Δ

y

1

s

t

+

<

2

,

$$\varDelta x^+$$

Δ

x

+

=

$${\fancyscript{O}}$$

O

(50–150),

$$\varDelta z^+$$

Δ

z

+

=

$${\fancyscript{O}}$$

O

(15–40)), the idea to embed a near–wall (U)RANS region within a LES represents both, a specific type of hybrid approach and an enhanced kind of wall model.

The so-called jet in cross-flow (JCF) refers to fluid that exits a nozzle and interacts with the surrounding boundary layer flowing across the nozzle.

In the present numerical study we consider a body of water with a stable temperature-induced density gradient and an unstable salinity-induced density gradient resulting in an overall density gradient that is weakly stable.

The flow around airfoils in full stall is a problem of great interest in aerodynamics and specifically for the design of turbo-machines (turbines, propellers, wind turbines, etc.).

Turbulent shallow jets discharged into ambient fluid of much larger spanwise and streamwise dimensions can be considered as a paradigm of effluent discharges into shallow lakes, rivers, and coastal waters as well as large-scale geophysical flows in the atmosphere and oceans.

From an engineering point of view turbulent pipe flow is a very important flow geometry, because of its wide range of technical applications.

Laminar as well as turbulent oscillatory pipe flows occur in many fields of biomedical science and engineering.

The jets issuing tangentially to a solid surface are called wall jets. Plane two dimensional wall jets are the simplest and have been studied extensively.

Wall-bounded turbulence emerges e.g. along the surface of moving ships and airplanes or in pipelines. The prediction of skin friction and drag is directly related to fuel consumption or the power needed to transport gases through pipelines, thereby emphasizing the practical relevance of wall turbulence.

An understanding of mixing and dispersion rates and the characterization of concentration fluctuations of a passive scalar in a turbulent flow is relevant for a broad range of scientific and engineering applications of both practical and fundamental interest.

Interior channels of gas-turbine blades are often lined with ribs, which act as turbulence promoters to enhance heat transfer between the hot blade surface and the cooling air.

The flow past a circular cylinder is associated with different types of instabilities which involve the wake, the separated shear layers and the boundary layer.

Convergent-divergent (C-D) ducts operating in supersonic flow-regimes provoke choked flow conditions in the region of the narrowest cross-section.

Jet noise reduction remains an important long-range goal in commercial and military aviation.

The phenomenon of vortex breakdown is observed in a variety of technical (vortex burners, delta wing aircraft) and environmental flows (tornadoes, hurricanes).

The Navier-Stokes equations for compressible flow can be expressed in different forms. Although the forms are mathematically equivalent, each form emphasizes different properties of compressible flow, and each form yields a different numerical discretization.

High-subsonic cavity flows have been intensively studied due to their practical importance in aeronautical applications, such as, weapon bays, measurement windows and wheel wells [

1

].

As a simplified model of a large class of convective processes, Rayleigh-Bénard convection (RBC) enables fundamental and numerical studies of convection including Direct Numerical Simulations (DNS). Although it has been investigated for more than 100 years there are still many open questions including the influence of the geometrical characteristics of the convection cell on the flow dynamics.

Natural convection heat transfer in cavities has been studied extensively in the literature due to its relevance to many engineering areas such as low temperature solar collectors, design of buildings, cooling of nuclear reactors, etc.

The large structures occurring in the fluid flow on the Sun’s outer layer, in the atmosphere and oceans of planets, including our Earth, are primarily driven by convection. The flow structure but also the efficiency of the heat transport are, however, significantly influenced by the Coriolis force due to rotation.

If flowines has been In the ideal Brayton cycle, an increase of the pressure ratio directly leads to an increase of the thermodynamic efficiency and subsequently to a decrease of the specific fuel consumption. Unfortunately, this pressure ratio growth causes a direct increase of the temperature ratio through the turbine stages, which may impact the design of turbine blades.

Wind turbines operate in the atmospheric boundary layer and their rotating mechanisms provide complicated aerodynamic phenomena within their operating environments. When the upstream wind is uniform and normal to the plane of a rotating blade, rotational effects (i.e. rotational augmentation) emerge. Rotational augmentation means that stall occurs at a higher angle of attack on the rotating blade section than it does on an analogous stationary airfoil.

Dynamic stall refers to the stall process of an airfoil which is moved around the critical stall angle of attack. It is a complex phenomenon and a well known constraining parameter for designers.

In modern low pressure turbines (LPT), reducing the number of airfoils in a turbine leads to an increase in the blade loading, which inevitably increases the possibility of laminar separation.

Laminar separation bubble (LSB) is a phenomenon that can greatly affect the performance of wings at a low Reynolds number.

Within many technical fields like aerospace and naval engineering, civil engineering and biomedical applications, fluid-structure interactions (FSI) can be observed. Moreover, most of the flows in these fields are dominated by turbulence, which can be predicted in a reasonable manner by Large-Eddy Simulation (LES).

Most of the drag on a truck is caused by the wake behind the trailer. It is caused by the sharp edges on the rear end.

Geophysical flows including stable stratification and system rotation are a special challenge for turbulence subgrid-sclae models for large-eddy simulation (LES) and hence require validation with suitable test cases. We validate different subgrid-scale models for this kind of flows using a breaking monochromatic inertia-gravity wave that has been studied before. We find that the standard Smagorinsky model cannot be recommended while the dynamic Smagorinsky model and the implicit turbulence model ALDM are suitable to simulate this complex flow with high accuracy.

The marine planetary boundary layer topped by stratocumulus clouds (STBL) is key for the planetary radiation balance [

5

]. In its simplest configuration the STBL consists of a lower moist boundary layer which is topped by a dry and warm free atmosphere. The top of the STBL is populated by stratocumulus clouds that emit long wave radiation, cooling the moist boundary layer. Radiative cooling is thought to be the main source of turbulent energy for the STBL.

With increasing sizes of wind farms, the influence of large scale wind farms on the Atmospheric Boundary Layer (ABL) has become an area of interest recently. While for a lone-standing turbine, power extraction equals to the difference between upstream and downstream kinetic energy fluxes, for a turbine in a large wind farm the kinetic energy must be entrained from the faster moving flow above [

4

]. In that case, the vertical transport of kinetic energy by turbulence is of the same order of magnitude as the power extracted by the wind turbines. Therefore, the understanding of the interaction between wind farm and the ABL becomes crucial, e.g., to maximize the extracted energy, etc.

Traffic is known to be a significant pollutant emission source in urban environments.

The problem of pollutant dispersion is a crucial issue for life quality in urban areas.

The massively developing urban areas with different buildings in proximity of each other, makes it an important topic to study wind engineering to understand the mechanism of flow-structure interactions.

The investigation of the fundamental features of the 3D separated flows of the stratified fluid around a horizontally moving blunt body is very complex problem which solved with difficulty and which give us also some insight on the real atmospheric flows around the hills and the mountains.

Large-eddy simulations (LES) of oscillating turbulent boundary layers, over a rippled bed, subjected to frame rotation are presented. This flow is archetypal of a bottom-ocean, tidally driven boundary layer developing over sand dunes. A forcing-type immersed boundary method (IBM) is used to represent the solid bed and the filtered structure function model for the sub-grid stresses. Three different rotation patterns were examined, each one corresponding to different geographic latitudes. The effect of ripples was found to significantly modify the elliptical patterns and the phase of the Ekman layers generating between the ripple crests.

Turbulent flows in an opened Taylor-Couette system with an axial throughflow is studied here by the means of large eddy simulations. The ultimate industrial application is the effective cooling of the rotor-stator gap of an electrical motor.

Recently there has been some renewed interest in the three-dimensional flow around a rotating circular cylinder at high Reynolds number, due partly to investigation into potential energy savings available for maritime propulsion.

It is the aim of this contribution to focus on the effect of thermal radiation on the turbulence structure rather than on the influence of turbulence on radiation.

Large eddy simulation (LES) gives access to unsteady flame behaviours as encountered during transient ignition.

Soot particles are formed during rich combustion of fossil fuels in technical devices such as internal combustion

For conventional combustion processes one of the most common oxidizers is air, mainly because it is cheap and readily available compared to other oxidizers.

A predominant part of the world energy demand is obtained by the combustion of fossil fuels. In this framework, gas turbine combustion is the most important energy conversion method today.

The energy requested to obtain a stable ignition in a turbulent gas mixture has been investigated extensively during many decades [

1

], mostly through experiments or reduced (zero- or one-dimensional) simulation models [

2

].

Sequential combustion is a promising concept for stationary gas turbines to achieve high thermodynamic efficiency and low NOx emission levels over wide load ranges [

1

].

Environmental issues and new regulations for pollutant emissions lead to consider alternative fuels for the new generation of power generators such as hydrogen, syngas, green diesel, or biodiesel.

Perhaps because turbulence is central to a variety of applications for atmospheric and oceanic flows, as well as engineering, and yet remains largely unsolved, high-performance computing plays a central role, on par with observations and experiments, for progressing in our detailed understanding of such flows.

Direct numerical simulation (DNS) is normally used to study turbulent flows.

The study of duct flow for electrically conducting liquid metal fluids exposed to an externally applied magnetic field is acknowledged to be a good approach for a better understanding of the fundamental properties of magnetohydrodynamic (MHD) turbulence.

The flow of electrically conducting fluids with an internal blockage, can be divided into two major categories: flows past solid internal obstacles (bluff bodies) subjected to an external uniform magnetic field

Liquid metal batteries, i.e. batteries in which both electrodes as well as the electrolyte are in the liquid state (Fig.

1

) are usable for grid-scale energy storage and have received considerable attention recently [

4

,

5

].

We report on the numerical modeling and simulations of compressible two-phase flows that involve phase transition between the liquid and gaseous state of the fluid.

Turbulent disperse multiphase flows play an important role in many technical applications such as the transport of powders in pneumatic conveying systems. The transport of particles is governed by many physical effects.

Biomass is important for co-firing in coal power plants thereby reducing CO

$$_{{2}}$$

2

emissions. Modeling the combustion of biomass involves various physical and chemical processes, which take place successively and even simultaneously.

The main objective of the current study is to investigate the effect of either non-resolved (point particles) or fully resolved particles on a field of isotropic, either stationary or decaying turbulence using direct numerical simulation (DNS), clarifying how those different settings influence the turbulence statistics.

In recent years numerical simulation methods have been developed for the study of particle-laden turbulent flows.

This work is part of a long-term project concerning modeling, simulation and analysis of particle-laden turbulent plumes, motivated by the study of the injection of ash plumes in the atmosphere during explosive volcanic eruptions. Ash plumes represent indeed one of the major volcanic hazards, since they can produce widespread pyroclastic fallout in the surrounding inhabited regions, endanger aviation and convect fine particles in the stratosphere, potentially affecting climate.

Turbulent bubbly and droplet-laden flows are abundant in industry and nature. Examples are bubble column reactors [

1

], spray combustion systems [

2

] and rain clouds [

3

]. The interaction between the bubbles/droplets and the surrounding turbulent carrier flow is complex and still not well understood, in particular when the bubbles/droplets have a finite-size (relative to the Kolmogorov scale) and when the bubble/droplet volume concentration is not dilute [

4

,

5

].

Turbulent flows transporting a dispersed-phase are found in many environmental applications and engineering devices. Particle-laden flows are characterized by several peculiar phenomenologies such as preferential particle concentration and turbulence modulation of the carrier-phase due to the presence of the inertial particles [

1

].

Bed-load transport in particle-laden flows is an important process in many environmental, civil engineering, and industrial applications. The particle transport mechanisms are complex and often involve highly organised structures such as multi-scale 2D and 3D bedforms moving with different speeds. The predictive capabilities for bed-load, currently available to engineers and researchers, are very limited due to lack of fundamental knowledge of these mechanisms.

Turbulent flows with small particles are of interest both for physicists and engineers: the dispersed phase is involved in a range of phenomena (including preferential concentration, agglomeration, and wall deposition) that are important in particle separators, combustion chambers, etc.

The Ranque-Hilsch vortex tube (RHVT) is a device without any moving parts in which pressurized inlet gas is separated into a hot peripheral and a cold inner stream [

1

].

Study of heat and mass transfer in droplets is of importance in a range of industrial applications; modeling fuel droplets in internal combustion engines and cavitation are examples of such applications.

The modeling of flow control is generally applied as a time-varying boundary condition at the slot position. In vehicle aerodynamics, the flow is assumed to be incompressible; however active flow control produces pressure waves that propagate instantly throughout the computational domain.