Anirudh Asuri Mukundan

Giovanni Tretola

Thibaut Ménard
email: thibaut.menard@coria.fr

Marcus Herrmann

Salvador Navarro-Martinez

Konstantina Vogiatzaki

Jorge César

C Brändle De Motta

Alain Berlemont

Jorge César Brändle De Motta

DNS and LES of primary atomization of turbulent liquid jet injection into a gaseous crossow environment

Keywords: Atomization, Crossow, Interface capture, Stochastic elds, Drop size distribution

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Introduction

With the growing number of long-haul passenger aircraft, it has become necessary to develop more ecient aircraft engines that can oer long range with reduced pollutant emissions. The amount of pollutants produced depends on the completeness of the fuel combustion which is linked to the quality of injected liquid fuel atomization. Atomization is the process of disintegration of the coherent liquid structure into droplets. In fact, small droplets promote quick evaporation and better mixing with the oxidizer, while large drops may deposit on the walls of the engine chamber thereby lowering the combustion eciency and eventually harming the engine. Hence, it is imperative to understand and gain control of the atomization process.

To that end, a commonly employed injection conguration in aero engines called liquid jet in crossow is chosen for the investigation in this study. In this conguration, the liquid fuel injected into a crossowing gaseous environment atomizes into droplets. There have been multiple experimental investigations [START_REF] Aalburg | Properties of nonturbulent round liquid jets in uniform gaseous cross ows[END_REF][START_REF] Ng | Bag breakup of nonturbulent liquid jets in crossow[END_REF] for this conguration to understand the breakup mechanisms [START_REF] Brown | Proceedings of the ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems[END_REF], to classify the breakup regimes [START_REF] Madabhushi | Proceedings of the ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems[END_REF], to characterize the jet penetration [START_REF] Wu | Breakup processes of liquid jets in subsonic crossows[END_REF][START_REF] Stenzler | Penetration of liquid jets in a cross-ow[END_REF], and to gain understanding of the jet dynamics [START_REF] Leask | Critical evaluation of momentum ux ratio relative to a liquid jet in crossow[END_REF]. For a complete review, the reader is referred to the work of Broumand and Birouk [START_REF] Broumand | Liquid jet in a subsonic gaseous crossow: Recent progress and remaining challenges[END_REF].

There have also been several numerical studies, for example, Herrmann [START_REF] Herrmann | Detailed numerical simulations of the primary atomization of a turbulent liquid jet in crossow[END_REF] performed detailed numerical simulations of primary atomization of an experimentally investigated liquid jet in crossow conguration [START_REF] Brown | Proceedings of the ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems[END_REF]. The grid dependence of the droplet diameters [START_REF] Herrmann | Detailed numerical simulations of the primary atomization of a turbulent liquid jet in crossow[END_REF], the eect of the density ratio on the atomization characteristics [START_REF] Herrmann | The inuence of density ratio on the primary atomization of a turbulent liquid jet in crossow[END_REF] and the jet dynamics [START_REF] Herrmann | The impact of density ratio on the liquid core dynamics of a turbulent liquid jet injected into a crossow[END_REF] have been investigated in the past. The eect of inow velocity proles on the atomization characteristics have been investigated by Ghods and Herrmann [START_REF] Ghods | Proceedings of the ILASS Americas, 25th Annual Conference on Liquid Atomization and Spray Systems[END_REF] using three dierent velocity proles (in-nozzle large eddy simulations (LES), fully developed turbulent velocity proles each with, and without nozzle geometry) under two dierent density ratio operating conditions. These studies found that the jet penetration was in agreement with the experimental correlation of Wu et al. [START_REF] Wu | Breakup processes of liquid jets in subsonic crossows[END_REF] for the case of turbulent inow velocities taking the injector geometry into account. Furthermore, they found that the liquid column was more deformed when using a fully developed turbulent pipe inow without nozzle geometry than when including the nozzle geometry.

The results conrm the observations of Brown and McDonell [3] that the initial velocity prole has a high impact on the atomization characteristics.

Owkes et al. [START_REF] Owkes | Proceedings of the AIAA SciTech Forum[END_REF] used LES to investigate the eect of rounded and sharp edged nozzle exits on the atomization characteristics. They found excellent agreement between the simulations and experiments of Gopala [START_REF] Gopala | Breakup characteristics of a liquid jet in subsonic crossow[END_REF] for both the nozzle geometries and reasonable match of the droplet sizes with experimental data. Recently, Li and Soteriou [START_REF] Li | High delity simulation and analysis of liquid jet atomization in a gaseous crossow at intermediate weber numbers[END_REF][START_REF] Li | Detailed numerical simulation of liquid jet atomization in crossow of increasing density[END_REF] investigated the eects of liquid fuel density, viscosity, and intermeditate Weber number on the liquid jet penetration, evolution of Sauter Mean Diameter (SMD) as a function of crossow direction, and jet dynamics of the crossow atomization.

The direct numerical simulations (DNS) approach provides a complete description of the ow dynamics, but its high computational cost limits its use to ows with moderate Reynolds and Weber numbers and liquid-gas density ratio. LES on the other hand has cheaper computational cost but requires modeling of the sub grid (or unresolved) multiphase turbulence dynamics.

Despite the numerous eorts, there has not been a direct comparison of DNS and LES for the liquid jet in crossow injection conguration. This paper presents, for the rst time, the direct comparison of results of primary atomization of turbulent liquid jet injected into a subsonic gaseous crossow. The DNS in this study is to be considered as quasi -DNS without sub-grid scale model in capturing the small droplets (due to under-resolution). However, it resolves all relevant processes [START_REF] Asuri Mukundan | Proceedings of the ILASS Americas, 30th Annual Conference on Liquid Atomization and Spray Systems[END_REF][START_REF] Asuri Mukundan | Proceedings of the AIAA SciTech Forum[END_REF] to predict drop sizes larger than the mesh spacing but does not resolve the Kolmogorov scales for both the phases in a classical sense of DNS. The operating condition chosen in this work is comparable to that of a practical aero engine. The non-dimensional numbers such as liquid-gas momentum ux ratio, Reynolds, and Weber numbers follow the experimental study of Brown and McDonell [3]. This study aims to investigate and contrast the dierent atomization and breakup characteristics, jet penetration, and drop size distributions (DSDs) between DNS and

LES.

This paper is organized as follows. The governing equations solved in DNS and LES along with the numerical methods of the respective ow solvers and phase interface capturing methods are presented in Section 2. This is followed by the presentation of the liquid jet in crossow conguration, case setup, and operating conditions in Section 3. Finally, the results obtained from the simulations are presented and discussed in Section 4 from which the conclusions are drawn in Section 5.

Governing Equations and Numerical Methods

DNS

To describe the multiphase ow with DNS, the pressure and velocity elds of the ow are obtained by solving the following conservative form of the incompressible Navier-Stokes equations,

∇ • u = 0, (1)
∂(ρu) ∂t + ∇ • (ρu u) = -∇P + ∇ • (2µD) + T σ , (2)
where ρ is the density, u is the velocity eld, P is the pressure eld, µ is the dynamic viscosity, D = 1 2 (∇u + ∇ T u) is the strain rate tensor and T σ is the surface tension force acting on the location of the liquid/gas interface x intf .

The interface is captured using a coupled level set volume of uid (CLSVOF) method [START_REF] Ménard | Coupling level set/VOF/ghost uid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet[END_REF] in which the location of the interface x intf is described by a scalar level set signed distance function φ proposed by Osher and Sethian [START_REF] Osher | Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations[END_REF]. The value of φ(x, t) > 0 denes the liquid phase (uid 1), φ(x, t) < 0 denes the gas phase (uid 2), and φ(x intf , t) = 0 denes the location of the interface.

The fraction of the liquid volume within a computational cell is represented by the liquid volume fraction scalar F . The advection of the interface is achieved by solving the following transport equation for Ψ = [φ, F ] T :

∂Ψ ∂t + u • ∇Ψ = 0, (3)
The physical properties of the phases α in a compuational cell is determined

using F as α(x) = α 1 F (x) + α 2 (1 -F (x))
. This expression involves an assumption that the physical properties are constant within each phase where α is either density ρ or viscosity µ with the indices 1 and 2 denoting the respective uid properties. A directionally-split advection method [START_REF] Weymouth | Conservative Volume-of-Fluid method for free-surface simulations on Cartesian-grids[END_REF] is used to solve Equation (3). This approach is implemented in the in-house ow solver ARCHER [START_REF] Ménard | Coupling level set/VOF/ghost uid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet[END_REF]22,[START_REF] Asuri Mukundan | A 3D Moment of Fluid method for simulating complex turbulent multiphase ows[END_REF] with consistent mass and momentum ux computation [22]. A staggered variable arrangement with scalar quantities stored at the cell center and vector quantities at the cell faces is employed in ARCHER. A second-order central dierence scheme is employed for discretization of the spatial derivatives and fth-order WENO scheme for convective term with second-order Runge-Kutta scheme for temporal advancement of the Navier-Stokes equations. For more details, the reader is referred to Vaudor et al.

[22]. The physics of atomization of the coherent liquid jet into droplets of varying sizes are captured by solving these equations. All the droplets are described in the Eulerian framework and no transfer to Lagrangian descriptions is employed in the DNS.

LES

In the case of LES, a Σ-Y -PDF approach is employed to solve the incompressible Navier-Stokes equations. This approach consists of solving the joint probability density function (jPDF) transport equation of liquid volume and surface density using stochastic methods [START_REF] Navarro-Martinez | Large eddy simulation of spray atomization with a probability density function method[END_REF]. A system of stochastic partial dierential equations (SPDE) is derived from the PDF transport equations using N stochastic elds, where each stochastic eld has its own liquid volume fraction F n (instead of the mass fraction Y n ) and surface density Σ n where n ∈ {1, 2, . . . N }. The advantage of this approach is that it can simulate both dense and dilute regions of the spray.

Using the Ito formulation [START_REF] Valiño | A eld monte carlo formulation for calculating the probability density function of a single scalar in a turbulent ow[END_REF], the following transport equations for the stochastic elds are obtained,

dF n dt + ūj ∂F n ∂x j = ∂ ∂x j D SGS ∂F n ∂x j + 2D SGS ∂F n ∂x j dW n j dt , (4)
dΣ n dt + ūj ∂Σ n ∂x j = ∂ ∂x j D SGS ∂Σ n ∂x j + 2D SGS ∂Σ n ∂x j dW n j dt + S ( 5
)
where S is the source term, D SGS is the sub-grid scale (SGS) diusivity which is proportional to the SGS viscosity ν SGS according to the relation

D SGS = ν SGS /Sc SGS with a SGS Schmidt number of Sc SGS = 1.
In this equation, dW n represents a Wiener process with mean 0 and variance equal to ∆t 1/2 . The solution of Equations ( 4) and ( 5) allows to obtain the moments of the PDF equations. The rst-moments are computed as

F = 1 N N n=1 F n , Σ = 1 N N n=1 Σ n . (6)
If all the moments are known, Equations ( 4) and ( 5) are equivalent to the LES ltered counterpart [START_REF] Navarro-Martinez | Large eddy simulation of spray atomization with a probability density function method[END_REF]. After the stochastic eld equations have been advanced in time, all relevant parameters can be obtained directly. For example, the characteristic fragment length per stochastic eld is the Sauter Mean Diameter (SMD) is dened as

d n 32 = 6 F n (1 -F n ) Σ n , (7)
where the corresponding ltered moment d32 can be obtained directly from Equation ( 6). The DSD (in space and time) can then be obtained directly from binning the SMD values.

The source term S is modelled as a non-linear restoration to equilibrium term as proposed by Lebas et al. [START_REF] Lebas | Numerical simulation of primary break-up and atomization: Dns and modelling study[END_REF],

S = Σ n τ 1 - Σ n Σ eq , (8)
where Σ eq is the equilibrium surface density and τ is the associated relaxation time-scale related to the ow [START_REF] Navarro-Martinez | Large eddy simulation of spray atomization with a probability density function method[END_REF]. At high Weber numbers typical of spray atomization, the time scale can be LES-scale based on the ltered strain rate,

τ ∝ || Sij || -1
, or proportional to a turbulent time scale (as in the Reynolds Averaged Navier-Stokes approach). Capillary eects in the source term are restricted to the local value of Σ eq , which can be characterized by a critical

Weber number [START_REF] Duret | Improving primary atomization modeling through DNS of two-phase ows[END_REF] as We crit = 2k SGS (ρ l + ρ g )F (1 -F )/(σΣ eq ), where k SGS is the local sub-grid scale turbulent kinetic energy and following Navarro-Martinez [START_REF] Navarro-Martinez | Large eddy simulation of spray atomization with a probability density function method[END_REF], We crit = 1 is used in this work.

The Σ-Y -PDF approach is implemented in the nite volume open source software OpenFOAM [START_REF] Jasak | International workshop on coupled methods in numerical dynamics[END_REF]. The spatial derivatives for the momentum equation are approximated by standard second-order central dierences. The momentum equations are integrated using a second-order Crank-Nicolson temporal scheme. The WALE [START_REF] Nicoud | Subgrid-scale stress modelling based on the square of the velocity gradient tensor[END_REF] method is used to model the sub grid stress terms using ν SGS since it did not introduce excessive diusion for this conguration. The stochastic elds are solved using an operator-splitting technique with the MULES scheme [START_REF] Weller | A new approach to VOF-based interface capturing methods for incompressible and compressible ow[END_REF] for the convective step to minimise numerical diusion and central derivatives for diusive processes. The Ito formulation is retained in this work. The spatial gradient appearing in the stochastic terms of Equations ( 4) and ( 5) in the Ito formulation is approximated using central dierences. The temporal term of the Ito process is discretized using the Euler-Maruyama scheme [START_REF] Kloeden | Numerical solution of stochastic dierential equations[END_REF]. The Wiener process is modelled with a weak approximation as dW n j = η n j ∆t 1/2 , where η n i is a {-1, 1} dichotomic random vector [START_REF] Gardiner | Handbook of stochastic methods[END_REF]. The resultant scheme is weakly consistent of order ∆t 1/2 [START_REF] Kloeden | Numerical solution of stochastic dierential equations[END_REF] and the number of elds chosen in the simulations is N = 16 following Navarro-Martinez [START_REF] Navarro-Martinez | Large eddy simulation of spray atomization with a probability density function method[END_REF]. Similar to DNS, no Lagrangian transformation of droplets is performed in the LES.

Operating Condition and Computational Domain

The operating condition for the simulations (both DNS and LES) used in this work has been studied experimentally by Brown and McDonell [START_REF] Brown | Proceedings of the ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems[END_REF] and numerically by Herrmann [START_REF] Herrmann | Detailed numerical simulations of the primary atomization of a turbulent liquid jet in crossow[END_REF] previously. Table 1 summarizes the values of the physical quantities of the liquid and gas phase. It is to be remarked that although the liquid-to-gas density ratio r ρ is articially reduced in the simulations (by modifying liquid velocity, viscosity, and density), all the nondimensional numbers, i.e., liquid-gas momentum ux ratio q, Reynolds number Re, and Weber number We of the liquid and gas phases remain the same as in the experiments. It is to be noted that all the details mentioned in this section apply to both DNS and LES unless otherwise stated explicitly. Density ratio (r ρ ) 10

Momentum ux ratio (q) 6.6

Jet Weber number (We j ) 2178

Jet Reynolds number (Re j ) 14,079

Crossow Weber number (We c ) 330

Crossow Reynolds number (Re c ) 570,000

The computational domain chosen in this work is of size 40D j × 10D j × 20D j [START_REF] Asuri Mukundan | Proceedings of the ILASS Americas, 30th Annual Conference on Liquid Atomization and Spray Systems[END_REF] where D j is the diameter of the liquid jet. This domain is smaller than in the experiments [START_REF] Brown | Proceedings of the ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems[END_REF], however, as observed from previous numerical studies [911], the domain size reduction does not aect the primary breakup description.

In the case of DNS, a uniform structured Cartesian mesh containing about 262 million cells is used for discretizing the computational domain. This re-sults in a uniform mesh spacing of ∆x = ∆y = ∆z = D j /32 throughout the domain. While in the case of LES, a Cartesian mesh composed of approximately 2.5 million cells is employed. The grid is rened in the region close the liquid inlet and then stretched (at 3% cell expansion ratio) along the crossow downstream direction resulting in a computational cell size Λ in the range of D j /32 to D j /8 with Λ min = D j /32 near the injection region.

Since an implicit ltering technique with the computational mesh as lter is employed in LES, the lter width is the cubic root of the computational cell volume.

Both the DNS and LES use a fully developed turbulent pipe ow velocity prole at the inlet of the liquid jet. The liquid jet at t * = tU j /D j = 0 is initialized in the DNS as a cylinder of diameter D j and height 4∆x protruding into the crossow channel. While in LES, the initial domain is empty at t * = 0 and the injection starts from t * > 0. The reported results from the simulations in the following sections are non-dimensionlized using the jet velocity U j and jet diameter D j as reference quantities unless otherwise explicitly mentioned. The simulations are performed up to t * = 73 (in DNS) and t * = 75 (in LES) with data stored approximately every t * = 1.3.

Results and Discussion

Figure 1 shows instantaneous snapshots of the side view of the liquid jet from DNS and LES. In the DNS (Figure 1a), the interface is sharp and is indicated by the zero level iso-contour of the level set function φ. The droplets atomized from the liquid core of the jet and the instability waves formed on the liquid jet column can be clearly seen in Figure 1a. However, in the case of LES (Figure 1b), due to the diused nature of the interface, the iso-contour of F = 0.5 is an indication of where the mean interface could be but not the exact location of the interface. The droplet breakup occurs at large as well as small scales however those at large scales are not visible in the visualization (c.f. Figure 1b) since the interface is diused. Moreover, a part of the small scale breakup occurs in sub-grid scales and hence such sub-grid droplets are also not visible in the visualisations.

The DNS and LES results revealed two main simultaneous atomization mechanisms: column/bag and ligament/surface breakup. The instabilities that are formed predominantly on the windward side of the liquid jet column generate roll-ups that continue to grow along the jet nally forming bag-like structure. Such structures break, forming varying sized droplets, thus, called column/bag breakup [START_REF] Herrmann | Detailed numerical simulations of the primary atomization of a turbulent liquid jet in crossow[END_REF]. In addition, ligaments are seen stripping o the sides of the liquid column in the simulations. This phenomenon is seen as surface rupture in the literature [START_REF] Herrmann | Detailed numerical simulations of the primary atomization of a turbulent liquid jet in crossow[END_REF], thus, its name ligament/surface breakup. Such ligaments undergo further breakup into droplets due to Rayleigh-Plateau instability. These observations of the breakup mechanisms are consistent with the literature [START_REF] Herrmann | Detailed numerical simulations of the primary atomization of a turbulent liquid jet in crossow[END_REF][START_REF] Herrmann | The impact of density ratio on the liquid core dynamics of a turbulent liquid jet injected into a crossow[END_REF].

The instability waves generated on the windward side of the liquid jet column are responsible for the droplet and ligament breakup. The plots of the contour of liquid volume fraction from DNS and LES shown in Figure 2 clearly depicts these instability waves as the corrugations on the windward side of the liquid jet. These contour plots are obtained at the mid-plane location along the spanwise direction (direction perpendicular to both liquid injection and crossow) in the computational domain. In fact, the waves are profoundly visible in the DNS result (Figure 2a) due to the sharp interface capture while the diused interface capture is demonstrated in the LES result (c.f. Figure 2b). The reader is referred to the study of Asuri Mukundan et al.

[18] for a detailed analysis of these instability waves. averaging procedure is to be consistent with that employed for the shadowgraphy images from experiments. In the LES, since the interface is diused, the precise location of the interface is not clearly determined. Thus, the upper jet plume boundary is determined as the locus of points for each line in the jet injection direction where the liquid volume fraction decreases below a threshold δ% of the local maximum value. In this paper, δ = 5 is chosen to determine the jet upper boundary. This method has been suggested for experimental analysis of the trajectory [START_REF] Brown | Proceedings of the ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems[END_REF] and has been implemented numerically [START_REF] Andreini | Development of a turbulent liquid ux model for EulerianEulerian multiphase ow simulations[END_REF][START_REF] Puggelli | Proceedings of the 1st Global Power and Propulsion Forum GPPF[END_REF]. Figure 3 shows the mean jet penetration from DNS and LES compared with the experimental correlations for validation. The jet plume boundary obtained from simulations are compared with the two experimental correlations: Wu et al. [START_REF] Wu | Breakup processes of liquid jets in subsonic crossows[END_REF] (valid in near-injector regions) given as z/D j = 1.37 (q x/D j ) 1/2 and from Stenzler et al. [START_REF] Stenzler | Penetration of liquid jets in a cross-ow[END_REF] (valid in far-injector regions) given as z/D j = 2.63q 0.442 (x/D j ) 0.39 We -0.088 c µ exp j /µ H 2 O -0.027 where µ exp j correspond to the dynamic viscosity of the liquid used in the experiments. On analyzing Figure 3, we see that simulation results qualitatively agree with the experimental correlation of Stenzler et al. [START_REF] Stenzler | Penetration of liquid jets in a cross-ow[END_REF] (gray dashed line) that that of Wu et al. [START_REF] Wu | Breakup processes of liquid jets in subsonic crossows[END_REF] (green solid line). Such an agreement is consistent with the observation from the literature [START_REF] Herrmann | Detailed numerical simulations of the primary atomization of a turbulent liquid jet in crossow[END_REF]. As remarked by Herrmann et al. [START_REF] Herrmann | The impact of density ratio on the liquid core dynamics of a turbulent liquid jet injected into a crossow[END_REF], the low value of the liquid-to-gas density ratio of 10 used in this work (compared to the density ratio of 816 in experiments) is prone to under-prediction of the jet penetration and bending in the simulations for the near-injector correlation of Wu et al. [START_REF] Wu | Breakup processes of liquid jets in subsonic crossows[END_REF]. [6] ( ).

Besides the jet penetration and bending, the DSD is a vital quantity to ascertain the quality of the primary atomization. Moreover, it is useful for primary atomization modeling in which droplets are injected along a specic liquid core path with a given velocity [START_REF] Behzad | Proceedings of the ILASS Americas, 22nd Annual Conference on Liquid Atomization and Spray Systems[END_REF]. The DSDs are obtained from the DNS and LES by post-processing the data after the total mass in the and LES mesh spacings. A log-normal t (solid lines in Figures 4a and4b)

to the DSD from the DNS and LES is observed to be a good model as also observed by Herrmann [START_REF] Herrmann | Detailed numerical simulations of the primary atomization of a turbulent liquid jet in crossow[END_REF]. It is to be remarked that the tting is made based on the respective simulation data range, hence, the tting law parameters are dierent for DNS and LES. The drops with diameters d drop < 2∆x are not well resolved in the DNS while the drops larger than Λ 20 (mesh spacing at the sampling location x/D j = 20) are not found in the LES. Since the DNS captures the mesh resolved droplets and LES characterizes the sub grid droplets by construction of each simulation framework, the combined DSD would determine the physical DSD. The rationale behind this idea is that either approach (i.e., DNS and LES) is good for one range of drop sizes so a combined DSD will give a good estimate of the true measure of the range of the droplet diameters belonging to resolved as well as sub-grid scales. This resulted in a direct comparison of the DSD between DNS and LES as shown in Figure 4c. This gure revealed that there is an overlap region of nite size [0.08D j , 0.2D j ] for the droplet diameters. To get the model for the physical DSD, a log-normal distribution is found to be a reasonable t as shown by the solid line in Figure 4c capturing the large well resolved droplets from the DNS and small sub-grid droplets from the LES. (Figure 5e). Overall, it can be seen that the of the overlap region reduces downstream until the last sampling plane of x/D j = 30 which could indicate generation of a bimodal distribution of large and small droplets. On one hand, the detection of drops with d drop > 0.1D j shows the presence and importance of large drops that are not captured by the LES. On the other hand, the presence of sub-grid droplets shows the signicant pres-ence of small drops not captured by DNS. This wide range of scales needs to be considered when modeling primary atomization for liquid jet in crossow congurations. The agreement between the DNS and LES in the overlapping (or shared) range at all sampling locations (c.f. Figure 5) suggests that the sub-grid distribution observed from the LES can be reliable. The scales investigated by DNS and LES are shown in Figure 6 displaying the schematic representation of the ideal limits of the droplet sizes depicted by the hatched region. This highlights the advantage of a LES study allowing extract a wide of range of drop sizes for analyses and modeling of primary atomization processes.

Figure 1 :

 1 Figure 1: Instantaneous snapshots of the side view of the atomizing liquid jet obtained from DNS and LES.

Figure 2 :

 2 Figure 2: Instantaneous snapshots of liquid volume fraction from DNS and LES in the near-injector region.

Figure 3 :

 3 Figure 3: Averaged side view snapshot of the liquid jet in crossow from DNS with experimental curve t. DNS(averaged image), LES ( ) Wu et al. [5] ( ), and Stenzler et al.

  computational domain is stabilized to indicate statistical steady state. The droplets/liquid structures from the DNS are rst identied using a connected component labelling (CCL) liquid structure detection algorithm in which the cells belonging to each single liquid structure (i.e., droplets) are tagged and labelled forming a cluster of cells for each liquid structure. The droplets and their attributes are then collected for each structure (from all its comprising cells). The attributes include volume, surface area, volume averaged coordinates of droplet centroid, and volume averaged velocity components at centroid. An equivalent spherical diameter of each droplet is obtained from its volume. The droplets are then sampled at specic downstream locationsx/D j . The DSD is then generated by binning the drop diameters into 20 bins of equal size in terms of log(d drop /D j ) where d drop represents the drop diameter. A total of 10,282 droplets were collected over all sampled time steps from the DNS. In the case of LES, due to the diused nature of the interface, no grid reslved droplets (drops larger than mesh spacing) are captured. However, the sub-grid droplets are captured whose diameter values are determined from the Equation (7). The DSD is then generated by these diameter values using the same procedure as that of the DNS.The droplets are sampled at the locations x/D j = 5, 10, 15, 20, 25, 30 from the DNS and LES results.

Figure 4

 4 shows the individual plots of the DSD from DNS and LES sampled at x/D j = 20 along with their log-normal distribution ts (solid lines in the plots). It can be seen that the DSD span over a nite range of the droplet diameters that are within the limits of DNS

10 dFigure 4 :

 104 Figure 4: Drop size distribution DNS ), LES ( ) with log-normal t ( ), ∆x ( ), 2∆x ( ), and Λ 20 ( ) limits at x/D j = 20.

10 -2 10 - 2 d 15 10 - 2 10 -1 10 0 10 - 1 2d 30 5:

 10215210130 drop /D j PDF(d (a) x/D j = 5 10 -2 10 -1 10 0 d drop x/D j = 10 10 -2 10 -1 10 0 d drop /D j (c) x/D j = drop /D drop j ) (d) x/D j = 25 10 -2 10 -1 10 0 d drop /D j (e) x/D j = Drop size distribution from DNS ) LES ( ) at dierent downstream sampling locations along with their respective log-normal ts ( ).

Figure 6 :

 6 Figure 6: Schematic of range of length scales of motion resolved by DNS and LES at x/D j = 20 with shared length scales shown in hatched region.

Table 1 :

 1 Operating conditions and non-dimensional numbers

	Quantity	Simulation
	Jet diameter (D j ) [mm]	1.3
	Jet density (ρ j ) [kg/m 3 ]	12.25
	Jet velocity (U j ) [m/s]	97.84
	Jet viscosity (µ j ) [kg/ms]	1.11 × 10 -4
	Surface tension (σ) [N/m]	0.07
	Crossow gas density (ρ c ) [kg/m 3 ]	1.225
	Crossow gas velocity (u c ) [m/s]	120.4
	Crossow viscosity (µ

c ) [kg/ms] 1.82 × 10 -5

Acknowledgments

The funding for this project from the European Union`s Horizon 2020 research and innovation programme under the Marie Skªodowska-Curie grant agreement N°675676 is gratefully acknowledged. The computing time at CRIANN (Centre Régional Informatique et d'Applications Numériques de Normandie) under the scientic project No. 2003008 and at GENCI-[TGCC/ 20 CINES/IDRIS] (Grant2019-2613) are also gratefully acknowledged. The authors also acknowledge funding by the UK's Engineering and Physical Science Research Council support through the grant EP/S001824/1 (KV, GT).


Sylvain Cherrier
email: sylvain.cherrier@univ-eiffel.fr

Rami Langar
email: rami.langar@univ-eiffel.fr

Semantic network coding for WSAN in IoT Applications

Keywords: IoT, Semantic, Network coding, WSAN

Software uses and approaches in the Internet of Things (IoT) are very varied and rich. But the data they collect is often gathered from networks of sensors. However, the constraints of Wireless Sensors and Actuators Networks (WSAN) are not always well taken into account by IoT software approaches. Thus, the massive data collection, well managed by Big Data tools in IoT applications, conflicts with the energy constraints to which the sensors are subject. Each transmission is costly for these devices and a massive stream reduces the whole WSAN lifetime.

This article presents an approach that meets the data needs in the vision of IoT users while seeking to limit the impact of the massive transmissions required. Edge computing is often used to reduce the amount of data to be treated in this research field. But the reduction is still made outside the WSAN, leaving a significant transmission load for these constrained networks. Energy-aware IoT applications get increased attention from the researchers. Network coding is an appropriate and already well-known tool for saving energy in constrained networks. Then the question is how to combine all the messages to reduce their number while maintaining their accuracy.

In this paper, we present an approach focusing on the gain obtained thanks to the semantics of data. The Semantic Network Coding leads to a reduction in the number of messages forwarded, thus leveraging the network and saving energy, while keeping a good quality to the collected data.

I. INTRODUCTION

The Internet of Things (IoT) is a major trend in network research. It combines the large installed base of public protocols for network interconnection (Internet) with recent developments in the field of sensor networks, which have become a major part of the objects of loT (Things). With strong demand from the industry, the field is very active and the angles of analysis very diversified.

The usual solutions in the proposed approaches are usually based on Cloud/Big Data. Very large amount of data are collected by objects (sensors in WSAN), and sent to the Cloud where it is stored. Then applications use BigData tools to create analysis and extract representations whose objective is to help users manage their buildings, business or cities.

In this vision, the data stream is always coming from the Things, which are mainly Wireless Sensors and Actuators, and send to the Cloud. This centralized architecture has some issues, in terms of ownership, privacy, and amount of data. Another way to handle the data stream is to distribute the treatment. As the content of each message in Things is rather small and specific, specialized in a limited or unique value, it appears that some pre-treatment can be done before transmitting the data to the central point.

The idea of distributed computing for IoT has been presented in many papers, under different names such as Edge computing, Cloudlet or Fog computing, depending on the place and the actor in charge of the treatment. In Edge computing, a trade-off is made between the computing capability of a device and its proximity to the place where the data was collected. The solution is to limit the number of hops, and to control the amount of basic information stored in the cloud. Data are treated as closely to the sensors as possible, and as soon as possible. But it is very rare that the treatment has been considered to be done directly on the nodes, because the limited processing power of IoT devices are not able to handle big processes.

In fact, WSAN devices have poor processing capabilities and small memory, because they were intend to mainly create and receive network messages. But as the main constraint of these devices is energy consumption, it appears that data transmission is one of the most costly operations they offer. And even with its limited processing capabilities, we assume that the device has enough to manipulate, adapt the data and then limit the need for transmission. We also assume that the treatments are not that complex, because the nature of the data manipulated is simple (in size, value and type) and the computation easy.

In this paper, we present our proposition to use the semantics of the collected data, assuming that it is fairly well defined and not very variable within a given WSAN. In Section II, we present the energy issue in WSAN/IoT, the contribution of network coding and the interest for semantic in IoT. Section III describes our approach with its pros and cons, while Section IV gives details on our experimentation. Finally, we conclude and give some propositions for the evolution of this work.

II. RELATED WORK

In the IoT field, precisely in Massive IoT, there are two important issues to solve. On one side, the huge amount of data to be treated by Big-Data solutions, and on the other side, the difficulty to send these data from the very constrained devices used in IoT. With a large number of devices, the pricing leads the manufacturers to design them with low processing power, memory size, low network range and throughput to reduce the total cost of the installed hardware. These devices must be very cheap (because of the number to be used), the energy consumption very low (because the maintenance must be reduced to the minimum). On the other hand, users want them to send a lot of information, which goes against the previous constraints.

One idea that we have already explored in previous papers [7] [8] is to limit energy consumption by computing data right in place, within the device. As IoT devices offer some computing capabilities, our proposition is to try to maximize the use of the processing power instead of transmission, as the energy cost of computing is often less than sending/receiving data (see Tables I andII). In this approach, the discrete values sensed by the device are lost. Depending on the use-case, it can make sense. Some IoT applications propose to react to events and not to store data for a asynchronous post-analysis (event-centric approach instead of data-centric). Y. Sun et al. use a similar idea with a rule-engine on the devices filtering a "majority of the unused atomic event" [START_REF] Sun | Efficient rule engine for smart building systems[END_REF].

F. Xhafa et al. have explained in [START_REF] Xhafa | Evaluation of iot stream processing at edge computing layer for semantic data enrichment[END_REF] that "processing and aggregating large data generated at IoT layer before sending" give good results for IoT applications. The authors argue that this solution "achiev[es] low latency", and "enhanc[es] privacy, security". We also invoked the same argument in a previous paper [START_REF] Cherrier | Services Collaboration in Wireless Sensor and Actuator Networks: Orchestration versus Choreography[END_REF].

H. Nasiri et al. show in [START_REF] Nasiri | Evaluation of distributed stream processing frameworks for iot applications in smart cities[END_REF] that ("Internet of Things (IoT) technologies enable cities to obtain valuable intelligence from a large amount of real-time produced data"). Smart city is one of the domain of the IoT which is main concerned with this solution. In fact, there is a main difference between the network flow of the Internet of Data1 . The data stream in the Internet of Data is more versatile, irregular and diversified. In the Internet of Things (and more precisely, from the devices of a WSAN that feeds the IoT), the kind of data is less different, less complex, and more repetitive. These are specificities that can be useful from this "Continuous streams of unstructured data" [START_REF] Nasiri | Evaluation of distributed stream processing frameworks for iot applications in smart cities[END_REF] with a "lack of semantic interoperable standard" [START_REF] Balakrishna | Semantics and clustering techniques for iot sensor data analysis: A comprehensive survey[END_REF].

T. Li et al. also present Network coding in the IoT in [START_REF] Li | A homomorphic network coding signature scheme for multiple sources and its application in iot[END_REF] "Network Coding (NC) can increase the robustness and throughput of wireless networks", but their purpose is mainly based on encryption and security.

G. Peralta et al. argue [START_REF] Peralta | Homomorphic encryption and network coding in iot architectures: Advantages and future challenges[END_REF] in the same direction on security. They also show the reduction in terms of delay in the network, and the improvement on the energy consumption. On the other hand, the authors warn against "The non-negligible increase in packet size and computational cost" of this kind of solutions. However, it seems that the way IoT applications work focuses mainly on the network capabilities of IoT devices, and not the contribution of their processors which remains underused.

There is a need for a better management of the network load. F. Safara et al. argue [START_REF] Safara | Prinergy: a priority-based energy-efficient routing method for iot systems[END_REF] that "Most IoT applications focus on monitoring discrete events that generate an excessive amount of data". In their survey about network coding and reliability in WSAN [START_REF] Al-Hawri | Design of network coding based reliable sensor networks[END_REF], E. Al-Hawri et al. explain that "Energy efficiency is the main concern rather than bandwidth, since nodes typically produce small volumes of data". Increasing reliability means to work primary on energy. To reach that goal, the authors present different solutions based on the nodes placement, and on network coding. C.HS. Oliveira et al. from our lab have also presented a proposal for network coding in wireless network [START_REF] Oliveira | Optimal network coding-based in-network data storage and data retrieval for iot/wsns[END_REF], but the implementation of their solution is too much a burden for the limited processing capabilities of our devices (as shown above by G. Peralta et al. in [START_REF] Peralta | Homomorphic encryption and network coding in iot architectures: Advantages and future challenges[END_REF]).

There are multiple solutions to select inside the network the set of elements that will be mixed. One approach is to define clusters. S. Balakrishna et al. describe different types of clusters [START_REF] Balakrishna | Semantics and clustering techniques for iot sensor data analysis: A comprehensive survey[END_REF] : Centroid base, connectivity based et density based, depending on the constraints the solution tries to solve. The idea of semantic network coding was presented by F. Xhafa et al. in [START_REF] Xhafa | Evaluation of iot stream processing at edge computing layer for semantic data enrichment[END_REF]. In their paper, they describe a experiment in which the sensors generate raw data. Semantics (metainformation such as the "geo-location information, timestamp, actor (device)") will be added to these data. The network coding is made at the Edge level. In this paper, we propose to code at the node level, to avoid energy consumption on upper nodes in the tree.

S. Balakrishna et al. have also classified the information inside the network in different classes: "Raw Data, Structured data, Perception data and Executive Data" [START_REF] Balakrishna | Semantics and clustering techniques for iot sensor data analysis: A comprehensive survey[END_REF]. Raw data are gathered by the sensors (sound, temp, humidity). They are then structured (date, format, unit, source) in Structured data. The next Level (Perception data) adds the semantic (Context, concept). The highest level (Executive Data) is the application reasoning, with analysis, predictive and actions.

The idea of a Semantic IoT was described by A. Palavalli et al. in [START_REF] Palavalli | Semantic internet of things[END_REF]. For the authors, the conception of an Ontology is mandatory to describe and to request in the large amount of data, once associated to concepts. They focus on the improvements from the application point-of-view, and the definition of their model. They didn't study the impact of the place where the metadata are added, neither the gain in energy consumption from the devices side, as their solution is mainly centralized, which is the common practice.. Our idea in this paper is to create semantic clusters, mapped on the network topology. In a given WSAN, the nodes sense the same kind of physical values, and all the nodes are known. The content format is known in advance, and the network organization too. WSAN devices are able to measure some data such as temperature, luminance, movement. Often, the list is short. We assume that there are not so much different kinds of data, so the semantics are limited. Within the WSAN, the device are quite similar (even if at the IoT application level, multiple and various WSAN and other Things are included).

In our proposal, the data will be semantically network coded directly inside the WSAN. This approach is not adapted to all IoT applications. Depending on the use-case, merging the values collected in the global result can be accepted, as in fact the goal of IoT applications can be real time reactions to events that are detected. However, in a smart city application monitoring traffic for example, the precise value of the number of cars on each specific road at a specific time may be required. But IoT applications are very varied, and this precision is not always useful. Y. Sun et al. argue that "In real application scenario, [...] many messages may include the same event signal" [START_REF] Sun | Efficient rule engine for smart building systems[END_REF]. The cost of storing such detailed information must be justified by the treatment that the application will make of it. Y. Sun et al. assume that "In a smart building system, sensors report data periodically" [START_REF] Sun | Efficient rule engine for smart building systems[END_REF] and their solution in which "transmission messages [...] are the aggregated results" "reduce[s] the throughput of data transmission, thus saving energy effectively". In [START_REF] Cherrier | Services Collaboration in Wireless Sensor and Actuator Networks: Orchestration versus Choreography[END_REF], we already have studied the impact on energy according to the design of the software architecture. As the WSAN devices are very constrained in energy, network usage must be taken into account. Our lab uses two kinds of devices based on Texas Instruments CC2420 [START_REF]Texas instruments[END_REF] or cc2538 [START_REF]Texas instruments cc2538[END_REF] chips. Tables I and II show the energy consumption on these two chips for different functions, from computation compared to the reception/transmission of the data. It shows that the cost of transmission is greater than processing. However, the computing capabilities of these nodes are limited, the clock is slow, and the memory small. But it is still possible to make some operations.

III. DISCUSSION

In our lab, we mainly use Contiki [START_REF] Dunkels | Contiki-a lightweight and flexible operating system for tiny networked sensors. local computer networks[END_REF] to create IoT applications. The interest for Contiki is that it offers 6LowPan, RPL [START_REF] Tsiftes | Low-power wireless ipv6 routing with contikirpl[END_REF] and CoAP. It is then possible to mimic a REST architecture to exchange data between the WSAN and the outside world, forming the IoT application, while hiding from outside the characteristics of a IEEE 802.15.4 network.

In order to give the IPv6 access to each node, Contiki organizes the mesh WSAN network using the RPL routing protocol. With RPL (see Fig. 3), each node has its own IPv6 address, and is accessible from outside the network. RPL builds a tree inside the WSAN to give the illusion of a direct access to each node, while in fact there are multi-hops from the sink to the given node. Fig. 1. In a RPL tree, the sink is the root of the tree and the node routing data outside the network. Nodes are accessible from the Internet with their IPv6 address (i.e. From outside, all nodes seem to be at the same level, but inside the WSAN, a message from R7 will be forward by R2. It is also not visible from outside that the node R7 is in charge of relaying messages to/from nodes N13 and N14)

From the IoT application point-of-view, the WSAN is flat and all nodes are directly connected and accessible in IPv6. In fact, the WSAN is a multi-hop mesh network. Some nodes act as routers, forwarding data to others 1. Transmitting data has a cost for the node itself, but also for each node that is on the path to the sink. As the energy is one of the main concern for the researchers in WSAN, S.A. Alvi et al. have proposed in [START_REF] Alvi | On the energy efficiency and stability of rpl routing protocol[END_REF] some improvements in RPL for a better stability of the tree and a reduction of energy consumption. In our paper, we concentrate on the way the RPL tree can be used, and the impact of the data transmission by the nodes. In the tree T (such as the RPL tree presented Fig. 1) where each node n ∈ T :

• the root of the tree is n 0 .

• The level of a node n is the distance from the sink n 0 (The sink n 0 is at level 0) • the height η(T ) is the longest path found in T • the size |T | is the number of nodes of the tree • the pathlength π(T ) is the sum of the levels of each of the nodes in T • the subtree T k is the tree having n k as root. When a node n x sends data, the message is forwarded by all the nodes on the path to the sink. Each node n x sends data, and forwards all the messages from each node of its sub-tree T x . When all the nodes send data in a tree T , a total of π(T ) messages are transmitted within the network.

In our network presented Fig. 1, when the 16 nodes send one message each, there are 34 transmissions. The node N 2 sends its own data, and is in charge of forwarding all the data from its sub-tree (5 nodes).

Each transmission/reception consumes energy (Table I and II), and the 4 nodes at level 1 represent 47% of the global consumption (Table III) (but only 25% of the total number of nodes). Looking at Fig. 1, we can see that node R2 has 6 nodes in charge. This node has a risk of consuming all its energy quickly, because of all the forward to do. As RPL is dynamic, the tree can change after a while (as an important router node runs out of energy), i.e. R7 attaches to R1 and N 8 and N9 to R3. But in that case, R1 will have 7 nodes to deal with, and will consume 7 times more energy than, for example, N 4. The issue here is that the most important nodes (from the routing point-of-view) will be the first to run out of energy, stopping or endangering the network operation.

One idea to protect the network from this issue is to reduce the number of transmissions, with semantic network coding. Instead of transmitting its own data, and forward all the data coming from the sub-tree, the node mixes its own data with the upcoming message, reducing the number of transmission to a single one. At the end-point, the receiver has a unique message with a global value.

In our solution, nodes limit the number of messages they are forwarding. We assume that in this WSAN, the devices senses a unique, or a limited set of physical values (temperature, humidity, presence, luminance, etc). The semantics of the content are similar, or chosen in a small list. And in a multihop mesh network, we can consider than nodes in the same sub-tree are not far from each other.

As said above, the network tree is never very far from the real topology: I.e. in a smart city, the devices counting the number of cars on the road transmit the value to a router in the bock of buildings, that will forward the data to another router in the same neighborhood, and so on. So it makes sense to add the number of cars counted on each router to get the global traffic information in these city's district. Adding all the results of the different routers gives a global view of the traffic of this part of the city. The similarity in the collected data, and the proximity of the network organization compared to the topological position of the nodes argue for the use of a data computation to obtain a reduction of the number of transmissions.

This can be organized in multiple ways. With a unique kind of sensing (let's say temperature), each node can average its value with the values received from its children (see Fig. 2), and send this to its father (the average value, and the number of measures, as the weight of this average). At each level, the average is computed, and a unique message is transmitted to the upper level. The semantic network coding function here is average, but our solution proposes also to sum up or count values. This can be useful with traffic surveillance, or to count people in a smart building, a museum, etc.

If there are multiple kinds of measures, a vector of different values is transmitted, each node filling its part of interest. Here also, at each level of the tree, a computation is made, using average or sum of the different vectors received to create a Fig. 2. In this example, the semantic network coding uses a simple vector containing the cardinality and the average temperature value. The leaves at the bottom of the tree send their sensed values. The first router mixes these value with its own and send the result to its router, and so on. The sensed and the calculated values may be stored on the node if necessary. new one to send to the upper level. Data computing costs less energy than sending it. The CC2420 or CC2538 devices offers enough computation power (CPU speed, memory space) to get the result.

In our example Fig. 1, the semantic network coding reduces the number of messages from 34 to 16 (from π(T ) to |T |). If we assume that messages are short (only a value gathered by the sensors, or a vector with some values) and that the semantic network coded data still fits in one message, the global transmission reduction ratio R of the tree T can be calculated by the following formula: R t = |T | π(T ) .

IV. EXPERIMENTATION

To test the feasibility of our proposal, we programmed an experiment for a 6LowPAN network. For this purpose, we chose Contiki-3.0 [START_REF] Dunkels | Contiki-a lightweight and flexible operating system for tiny networked sensors. local computer networks[END_REF]. This free operating system runs on several devices that use the IEEE 802.15.4 protocol for wireless network. It implements 6LowPAN 2 to have IPv6 on these devices. With the routing protocol RPL, the IEEE 802.15.4 network is then organized in a cluster tree, making each node accessible with its IPv6 address without knowing the tree organization.

The Figure 3 shows the tree being build during experiment startup. Each node discovers its neighborhood and participates to the elaboration of the DODAG (Destination-Oriented Directed Acyclic Graph). The construction of this tree has a convergence time of few minutes. There are few restrictions to note. The tree may not match the topology of the environment, as each node choose its preferred parent according to a metric called LQL (Link Quality Level). Depending on the interference, a node can choose a different parent than the obvious one. Another characteristic of RPL is that the DoDAG is dynamic, and can change over times. But as mentioned above, we can assume that the network topology will be close to the geographical one. For this experiment, we used Zolertia Z1 devices. They are equipped with a CC2420 radio chip(see Table I). The micro processor is a MSP430f2617, consuming less that 10mA at 16MHz, and 0.5mA when running at 1MHz. The CC2420 consumes between 17 and 18mA in Rx/Tx mode. It has 92kB of ROM (to store the operating system, 6LowPAN stack, RPL protocol plus the soft we created) and 10kB of RAM to manipulate data (see Table IV).

For our simulation, we used Cooja, the network simulation/device emulator provided with Contiki-OS. It gives the programmer the ability to test the code in real conditions (as the device emulator strictly respects the constraints of each device) in a simulated network. The only difference is the software execution time in the devices emulated (depends on the server processor power, the number of node to emulate, and the soft complexity). For our experiment, this speed varies from 10% to 1000% of the real software speed. The other difference is the quality of the simulated radio network, which is flawless (which is not always realistic). Nevertheless, Cooja is a powerful tool for performing experiments.

In this experiment, we have one sink and 36 nodes (See Fig. 3 and Table IV) that sense physical data, and send them to the sink. Two versions of the experiment are proposed. In As each router computes data and reduces traffic, activity at the higher levels of the tree decreases. Fig 5 shows the impact on each node in terms of data volume received. For example, the Node 9, very close to the Sink, receives from the sub-tree 13 times its own data volume. In the Semantic Network coding version, the same node sees its traffic load received reduced to 4 times its own. Fig. 6. Since the Semantic Network Coding reduces traffic, there is less packet loss. The router nodes still achieves a good transmission quality (Node 9 for example has a better loss ratio in normal organization, but with 4 times more packets to transmit). Node 19 has a important loss rate in the normal version, but is at the edge of the network, with only one child. However, the Semantic Network Coding has also some reception issues (e.g. Node 21). V. CONCLUSION Data collection in data-oriented IoT applications can lead to significant consumption of the yet limited resources of connected objects. Often, for a sensor, calculating a result right in place, costs less in terms of energy consumption than transmitting data. We saw that In IoT applications, priority is mainly given to the transmission of data to the Cloud, where it is then processed and reduced. However, processing the data in the device can provide a gain in network longevity at the cost of a loss of data accuracy, which can be accepted depending on the use case.

In this paper, we have presented an analysis to reduce data transmissions, by applying network coding techniques which focus on the semantics of the data to be transmitted. The experiment was conducted on the Contiki operating system which offers end-to-end IPv6 connectivity. Our approach significantly decreases power consumption within the network, limiting data forwarding at each hop for each node, especially for the most important ones for the sustainability of the network's existence. The possible evolution of this work consists in being able to dynamically adapt the network coding function used, or in proposing a passive network mode, triggering network coded measures only with a granularity adapted to the demand.

VI. ACKNOWLEGMENT

Fig. 3 .

 3 Fig. 3. State of the RPL DODAG in our Cooja simulation at 02:05. Node 1 (in green) is the sink in the centre of the figure. The tree is visible, and nodes 19, 17, 43 and 26 are in charge of forwarding messages to the sink. Each square represents 100m 2 .

Fig. 4 .

 4 Fig. 4. this figure represents the number of packets received and transmitted for each node (the 18 first only) after a 4 hours experiment. The number of transmitted packets is the some for each node in the case of Semantic Network coding. On the contrary, in the standard organization, the router nodes are far more stressed.

Fig. 5 .

 5 Fig. 5. With the Semantic Network Coding, each router reduces the number of forwarded packets. The traffic generated by its children decreases. In this Figure, Node 9 has less traffic to handle in the Semantic Network Coding version because its own children have reduced the number of packets to forward. The higher the router is in the tree, the more visible the reduction.

Fig. 4

 4 Fig. 4 represents the traffic load of each node after a 4 hours experiment. With the Semantic Network Coding version, the outgoing traffic is equal for each node, saving energy for the router nodes (reception and transmission). In the standard version, nodes 9 or 16 are more heavily used for routing subtree messages. The loss rate analysis in Fig 6 indicates the gain of the Semantic Network Coding version. This result is very dependent on the activity inside the network. In our experiment, traffic reduction of Semantic Network Coding version has a good effect on transmission error rates. The router nodes keep a good ratio in both experiments, but some nodes far in the tree have difficulties receiving/transmitting data where there is heavy traffic load in the standard version (e.g. node 19).

TABLE III MESSAGES

 III BY LEVEL IN TREE FIG. 1

	Level Nb of msg Nb of forward Total	%
	1	4	12	16	47%
	2	6	6	12	35%
	3	6	0	6	17%

TABLE IV EXPERIMENTAL

 IV SETUP(SEE FIG. 3)

	Parameter	Value
	Radio range of the node	25 m
	Network dimensions	130 × 130 m
	node type	Zolertia Z1
	radio chip	TI CC2420
	Sink (RPL root)	1
	Normal node	50

As the opposite of Internet of Things.

Acronym of IPv6 over Low -Power Wireless Personal Area Networks.

This work was supported by the FUI SCORPION project (Grant no. 17/00464) and CNRS PRESS project (Grant no. 239953).