Nathanaël Machicoane

Romain Volk

Lagrangian velocity and acceleration correlations of large inertial particles in a closed turbulent flow

We investigate the response of large inertial particle to turbulent fluctuations in a inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters are comparable to the flow integral scale. Both velocity and acceleration correlation functions are analyzed to compute the Lagrangian integral time and the acceleration time scale of such particles. The knowledge of how size and density affect these time scales is crucial in understanding partical dynamics and may permit stochastic process modelization using two-time models (for instance Sawford's). As particles are tracked over long times in the quasi totality of a closed flow, the mean flow influences their behaviour and also biases the velocity time statistics, in particular the velocity correlation functions. By using a method that allows for the computation of turbulent velocity trajectories, we can obtain unbiased Lagrangian integral time. This is particularly useful in accessing the scale separation for such particles and to comparing it to the case of fluid particles in a similar configuration.

I. INTRODUCTION

The dynamics of particles freely suspended in a turbulent flow is a multi scale problem with a wide range of applications such as meteorology, oceanography, and engineering. Among these domains, particle dispersion has been widely studied and still remains an open question concerning large "material particles" (i. e. of diameter larger than a portion of flow scales), with a density that can be different from that of the fluid. This stands naturally as a Lagrangian problem where (time) correlation functions are an appropriate tool, being easily accessed and offering direct interpretation. When measuring velocity or acceleration correlation functions over particle trajectories, one can estimate the particle characteristic times, which are typically used in stochastic modelization to achieve prediction of particle dynamics. While only one characteristic time can be enough to simulate the dynamics of an inertial point-like particle immersed in a known flow (in the framework of 1,2 ), modeling material particles is often more demanding. A limiting cost can be achieved in direct numerical simulation by use of a corrected Faxen model 3 , but the fastest way lies in stochastical two-time models in the spirit of Sawford's 4 . These models make it pertinent to study both the velocity and acceleration time scales of such particles.

In homogenous and isotropic turbulence, the velocity correlations of fluid particles were found to be nearly exponential for time lags larger than the dissipative time of the turbulent flow 5,6,7 . Some studies have also focused on Lagrangian velocity power spectra as such analysis may provide insight into inertial particle response to velocity fluctuations 8,9 . Since the pioneering works using large weather balloons released in the atmosphere 10 , or ocean floats 11 , modern and controlled experiments have confirmed the presence of an inertial regime in Lagrangian velocity spectra 12 , and found flow anisotropy existing at the very smallest scales 13 .

These experiments and simulations consider tracer particles in unconfined and homogeneous turbulence in the absence of any significant mean flow, thus ignoring the influence of the flow topology on particle dynamics. On top of a possible impact of a mean flow on particle dynamics, its presence biases Lagrangian correlation functions and disentangling the signature of turbulence from the mean flow statistics is an important problem in turbulence research, in the general context of close flows.

The purpose of the present work is to address the dynamics of very large particles freely advected in a confined turbulent flow presenting a large scale structure. These particles, known to become less and less sensitive to the flow fluctuations as compared to the mean flow 14,15 , preferentially sample the low pressure regions of the flow when their diameter approaches the flow integral scale 16 . Complementing these previous works, we investigate Lagrangian velocity and acceleration correlations while tracking the particles for times much larger than the large eddy turnover time of the flow. Our motivation stems from the possibility that particle dynamics may be influenced by the flow topology from the very lowest frequencies down to the frequency cutoff due to the particle size. We investigate the effect of particle size and density on their dynamics, by extracting the particle response times to turbulent fluctuations.

The experiment is performed in a counter rotating von Kármán flow (briefly described in section II), where particles are tracked optically in the main part of the flow volume. We discuss in section III the possibility to i) define a turbulent a) romain.volk@ens-lyon.fr velocity correlation function by removing the mean flow contribution, ii) estimate a Lagrangian integral time. The very high frequency range of the dynamics (i. e. acceleration) and its cutoff due to particle size is then investigated in section IV. Finally, the scale separation, which is given by the ratio of the velocity and acceleration time scales, for such large particles is discussed in section V, before a final summary in section VI.

II. EXPERIMENTAL SETUP

We investigate the dynamics of large inertial particles in a water-filled von Kármán flow, using the same setup as detailed in 16,17 . We chose this system as it presents a well known mean flow with a magnitude of the same order of the turbulent fluctuations. We also note that it shares similarities with industrial mixers and that several previous Lagrangian studies of particles dynamics have been conducted in the center of such vessel 12,18,19 . The flow is produced by means of two counter rotating disks of radius R = 9.5 cm located at z = ±10 cm which generate an intense turbulence in a cubic domain of length H = 20 cm ≃ 2R. As depicted in Figure 1(a), the resulting flow has a mean spatial structure composed of a strong azimutal motion near the disks plus a meridian recirculation flow whose origin lies in the pumping motion imposed by the disks. This setup produces non homogeneous and non isotropic turbulence 13,20 , with flow fluctuations stronger near the mid plane (z = 0).

The particles are polyamide and polypropylene spheres with diameters D = [6, 10, 18, 24] mm (accuracy 0.01 mm, Marteau & Lemarié, France) and densities ρ PA = 1.14 g.cm -3 and ρ PP = 0.9 g.cm -3 respectively. All experiments are performed with pure water (kinematic viscosity ν = 10 -6 m 2 .s -1 ) maintained at constant temperature Θ = 20 °C. The particles are inertial, and have diameters of the order of the integral length scale L of the flow, much larger than the Kolmogorov length scale (see Table I for the flow parameters obtained with tracer particles).

Particles are tracked in a very large volume 20 × 20 × 15 cm 3 using 2 high-speed video cameras (Phantom V.12, Vision Research, 1Mpix@6kHz) placed at 90 • as shown in Figure 1(a). Both cameras observe the measurement volume with a resolution 800 x 768 pixels, limiting the maximum length of trajectories to 13900 frames. We performed experiment with a moderate sampling frequency adjusted in the range f sampling ∈ [1600, 3000] Hz (depending on the disks velocity) to obtain trajectories with mean duration ∆t ≃ 0.5/Ω (Figure 1(b)). We can then obtain velocity and acceleration trajectories by convolution of a filtering-differentiating Gaussian kernel (as was done in 16 ) allowing for the computation of velocity/acceleration correlation functions over meaningful times.

III. ESTIMATING TURBULENT VELOCITY CORRELATIONS

The aim of this section is to compute the characteristic time of particle velocity fluctuations. The next session will consider the response time to high frequency fluctuation, linked to acceleration. Studying how both times change with the particle characteristics yield then an understanding of size and density effect on particle dynamics. In

Ω u ′ [m.s -1 ] εpower[W.kg -1 ] η[µm] τη[ms] Re R λ L[cm]
= ((u ′ x ) 2 + (u ′ y ) 2 + (u ′ z ) 2
)/3: fluctuating velocity averaged over components measured from tracer dynamics in a large volume around the geometrical center. ε: energy dissipation estimated from the electrical power consumption of the motors (see 16 for more details). τη ≡ (ν/ε) 1/2 : Kolmogorov time scale. η ≡ (ν 3 /ε) 1/4 : Kolmogorov length scale. Re ≡ (2πR 2 Ω)/ν: Reynolds number computed using the disk tip velocity. R λ = 15u ′4 /εν: Reynolds number based on the Taylor micro scale. L = u ′3 /ε: the estimated integral length scale.

order to compute velocity correlations, one must track particles for durations longer than the large eddy turnover time of the flow T = 1/Ω. Particles will then explore a significant part of the flow during one track and may be lost for small durations when hidden by other particles, cutting the tracks in an ensemble of smaller trajectories. Though this is a severe limitation when computing Lagrangian spectra, this does not introduce any bias in the estimation of the correlation functions providing the particles can be identified before and after being lost. We thus run the experiments with one particle per diameter in the flow volume so that we reduce the number of experiments while being able to identify all particles. Figures 2(a,b) display the resulting normalized auto-correlation functions, These figures show the particle size has a weak impact on velocity correlation functions for all the velocity components. All curves have a very similar shape at short times, and it is very difficult to differentiate them for particles larger than 10 mm (D/L = 0.33) as all auto-correlation functions become negative when τ Ω ∼ 0.4. After crossing zero, the functions then tend towards zero on a longer time scale (with eventual oscillations), which is not shown here as the statistics are less converged for large time lags τ . This zero-crossing behavior is not due to any finite volume bias as discussed for Lagrangian measurements performed in the homogeneous central region of von Kármán flows 12 . It is due to the fact that particles are tracked in a very large portion of a bounded flow. Indeed, in this case, the Lagrangian integral time, T L = ∞ 0 R v (τ )dτ , must be zero for a bounded flow [START_REF] Tennekes | A first course in turbulence[END_REF] . This result means one must disentangle the contributions of the mean flow from the turbulent fluctuations in order to estimate turbulent velocity To achieve this, we compute the stationary Eulerian flow for each particle type as the ensemble average v E (x, y, z) = v x , v y , v z , and define the particle velocity components as the sum of the local mean flow value at the particle location x(t) and the fluctuating velocity:

R vi (τ ) = v i (t)v i (t + τ ) / v 2 i (i = x, z),
0 0.2 0.4 0.6 0 0.1 0.2 τΩ C u x v x C vxvx C v ′ x v ′ x C vxvx C v ′ x vx C vxv ′ x 0 0.2 0.4 0.6 0 0.1 τΩ C u x v x C vz vz C v ′ z v ′ z C vz vz C v ′ z vz C vz v ′ z b) a) 0 0.2 0.4 0.6 0 0.5 1 τΩ R v'
v i (t) = v ′ i (t) + v i (x(t))
. More details about this Eulerian Lagrangian conditioning can be found in 16 . The auto-correlation function of v i is then the sum of four terms :

v i (t)v i (t + τ ) = v ′ i (t)v ′ i (t + τ ) + v i (x(t))v i (x(t + τ )) + v i (x(t))v ′ i (t + τ ) + v ′ i (t)v i (x(t + τ )) , (1)
which can be rewritten as

C vivi = C v ′ i v ′ i + C vivi + C viv ′ i + C v ′ i vi , (2)
where C uivi stands for the covariance of u i and v i (i.e. non normalized correlation function). We compute the five covariances for all particle types, and display the results for the transverse and axial velocity components of a polyamide particle with size D/L = 0.6 in Figures 3(a,b) respectively. Whatever the component, we observe that the cross correlations C vv ′ and C v ′ v are much smaller than C vv and C v ′ v ′ . This property, valid whatever the particle size and density ratio, implies that fluctuations experienced by particles can be considered to be uncorrelated with their dynamics due to the mean flow even if particles do not sample the flow homogeneously. For the transverse component, we also find that C v ′ v ′ and C vv are of the same order of magnitude. The particles dynamics is reflecting a key property of the counter rotating von Kármán flow by which mean velocity and transverse fluctuations are of the same order of magnitude. The result concerning the axial component is more surprising because we observe the total velocity correlation is dominated by the turbulent contribution C v ′ z v ′ z . This result also holds for other particle sizes although less apparent for smaller particles which are not trapped in regions of small mean axial velocity (i. e. toroidal regions close to the disks).

As the proposed decomposition is valid whatever the particle size, we display in Figure 3(c) the resulting autocorrelation functions of the turbulent transverse velocity, R v ′

x , for all particle diameters. As opposed to the total velocity, the curves have similar shapes but a clear ordering appears for different particle diameters. The functions time scales indeed increase with particle size, but they no longer cross zero (up to statistical convergence) as if the dynamics were unbounded. The result is different for the axial component where we find that the shape of R v ′ z strongly evolves with the particle size as demonstrated in Figure 3(d). The functions become more and more curved as the particle size increases and it becomes evident that no rescaling can put theses functions on a single master curve. Indeed, while the functions are quite ordered at small times, the changes of shape lead to a point where all functions cross each other (around τ Ω = 0.25), resulting in a reversal of the order. The functions shape for larger particles yields a zero crossing and eventual oscillations, as was observed before for the total velocity (figure 2). Through the method seems to work well for the smallest particle considered, it appears not to be sufficient for larger particles for which another bias is present. This component is indeed more sensitive to preferential sampling, which explains that R v ′ z oscillates when particles are large enough to experience coming and going motions between trapping regions of small axial mean flow with high gradient in fluctuating velocity. x, ρ p /ρ f = 0.9 z, ρ p /ρ f = 0.9 x, ρ p /ρ f = 1.14 z, ρ p /ρ f = 1.14 As it is difficult to achieve statistical convergence of velocity correlations for large time lags we define a Lagrangian integral time, T v = τ95 0 R v ′ (τ )dτ , where τ 95 is the time needed for R v ′ (τ ) to decrease by 95%. This ensures one can measure the integral time for all velocity components without accounting for the negative part of R v ′ (τ ). Figure 4 shows the transverse velocity time scale increases by 30% when increasing the particle size from D/L = 0.2 to 0.8, which is consistent with other results obtained using a corrected Faxen model to simulate the dynamics of isodense particles with sizes larger than the Kolmogorov scale 3 . As a result of the velocity correlation's anisotropy, we find T v is strongly anisotropic, being smaller for the axial component as compared to the transverse one. Furthermore, no substantial variation of T v with D is detected for the axial velocity because the shape of R v ′ z strongly changes at increasing particle size (which biases the measure of T v ). Up to now, only results at the highest Reynolds number have been presented. Indeed, the turbulence is fully developed, meaning that the Re dependence of time scales is fully captured by the rotation frequency Ω. This is easily checked when looking at the evolution of T v Ω with Ω (figure 4(b)). We indeed observe no significant variations whatever the component or particle diameter considered.

Concerning the influence of relative density, we find that light particles present a similar behavior to the one of heavy particles but with an integral time 10% smaller, irrespective of the velocity component. In the spirit of Tchen-Hinze theory 22 , this may be understood as an effect of the added mass force. Indeed it is in agreement with previous measurements of acceleration magnitude which show the rms value of acceleration to be proportional to β = 3ρ f /(2ρ p + ρ f ), where ρ p is the particle density 16 . In this framework, high frequency fluctuations appear to be amplified or attenuated depending on the value of β (β PP = 1.07, while β PA = 0.91) such that light particles always have smaller correlation times (as will be shown in section IV).

IV. HIGH FREQUENCY CUTOFF

In order to estimate the "dissipative time" of particle dynamics, we now focus on small time scales and investigate acceleration correlation functions. Acceleration is a short correlated quantity as compared to velocity and is only weakly affected by the mean flow, hence only results for the total particle acceleration are presented. Figure 5(a) presents the acceleration autocorrelation functions of polyamide particles for the four diameters investigated. One can clearly observe that particle acceleration decorrelates in a similar manner albeit at larger and larger time scales as the particle size increases. Indeed, normalizing the time lag axis τ by the acceleration correlation time T a (defined as the integral of the positive part of R a as introduced for small particles 18,19 ), we find that all functions almost collapse on a master curve (figure 5(b)), even when looking at the axial component.

Figure 5(c) shows T a increases at increasing particle size in a more pronounced fashion than T v (T a is approximately multiplied by 2.5 when D increases fourfold). This increase of acceleration correlation time is not incompatible with the one found for much smaller material particles 19 (where T a /τ η increases by 2.8 when D/η increases from 10 to 40). Contrary to observations made for the velocity, transverse accelerations have time scales barely larger than axial ones due to the fact that acceleration is more isotropic, as was observed for fluid particles [START_REF] Mordant | [END_REF] . This quasi-isotropy stands whatever the particle size or density, and, as it is the case for previous results, the Reynolds number dependence is fully captured by normalizing quantities with the rotation frequency Ω (as seen on figure 5(d)).

Varying the density in the range ρ p /ρ f ∈ [0.9, 1.14], one finds light particles have a time scale approximately 10% shorter than heavier particles as was observed for the velocity (figure IV(d)). A closer analysis of the density ratio effect on particle dynamics can be made by use of the raw acceleration power spectra. Even if they are directly linked to correlation functions (by a Fourier transform), we find them more appropriate to compare light particles dynamics to the one of heavier particles through all time scales. Figure 6(a) shows indeed that whatever the particle size, acceleration power spectra are more energetic for a given light particle than for its heavy counterpart. Of course this yields higher/lower rms acceleration values for light/heavy particles (by a factor β = 3ρ f /(ρ f + 2ρ p ) as shown in 16 ), which correspond to the integral of the power spectra.

Whatever the density, spectra exhibit a sharp cutoff in the range 2 ≤ f /Ω ≤ 20 with a cutoff frequency, f c , which decreases at increasing particle size (linked to the increase of T a with D). When a power law is tested, one finds φ a (f ) ∝ f -α with an exponent α ≃ 3. The present decrease is faster than that observed for ocean floaters 11 , or as predicted by Sawford's two-times model for which acceleration spectra decrease as f -2 beyond the cutoff frequency 4 . Accordingly, spectra do not exhibit any plateau compatible with a Kolmogorov scaling as observed for small particles, likely due to a lack of scale separation between the velocity integral time T v and the acceleration time scale T a . Note that the increase in the raw acceleration power spectra for high frequencies corresponds to noise coming from position measurement.

V. DISCUSSION

Finding acceleration less sensitive to trapping effects or to the mean flow geometry can be expected as it is a small-scale quantity. However, with the small scale separation T v /T a found for these large particles, it is surprising that theses results still stand (which is confirmed by the fact that no decomposition is indeed needed to study particle acceleration). Few Lagrangian studies have measured both the velocity and acceleration time scales of fluid particles in turbulent flows and we will focus our comparison with the work of 12 which took place in a similar setup. Note that the particles considered in 12 are slightly larger than the Kolmogorov length scale. The velocity autocorrelation x, ρ p /ρ f = 0.9 z, ρ p /ρ f = 0.9 x, ρ p /ρ f = 1.14 z, ρ p /ρ f = 1.14 functions of such tracers have an exponential shape, with the Lagrangian time T L as characteristic time scale, yielding T tracer v ≃ T L . The authors indicated that the acceleration correlation functions cross zero at a value approximately 4 times larger than the value 2.2τ η commonly reported 7,19,[START_REF] Mordant | [END_REF] (an effect of the particles' finite size). Using a better estimate of the zero crossing time as 2τ η , and assuming the positive part of the acceleration function is triangular, we then have T tracer a ≃ τ η . In the range of Taylor micro scale Reynolds number 500 < R λ < 1000 explored, we can then estimate from their data 70 < T tracer v /T tracer a < 130, increasing linearly with R λ 24 , which is consistent with the fact that the inertial range (hence the scale separation) grows at increasing Reynolds number. In the case of the large particles considered in the present study, we find ratios between 1.5 and 4 depending on the particle size and acceleration component (figure 6(b)). This is indeed a much smaller scale separation for such particles, which is enlightening for modeling their dynamics, using for instance a two-time model ( 4 for instance). We note that, as both T v and T a scale with Ω in the same way, there is no Reynolds number dependence of the scale separation for large particles, in opposition to the case of fluid particles. This is in agreement with the fact that the acceleration x, ρ p /ρ f = 0.9 z, ρ p /ρ f = 0.9 x, ρ p /ρ f = 1.14 z, ρ p /ρ f = 1.14 b) a)

FIG. 6. a) Transverse raw acceleration power spectra for polyamide particles with diameters D/L = 0.2 (solid line), D/L = 0.6 (dashed line) and polypropylene particles (diamonds) with diameters D/L = 0.2 (solid line), D/L = 0.6 (dashed line), with a rotation frequency Ω = 4 Hz. b) Evolution of the ratio of the velocity and acceleration correlation time, Tv/Ta, as a function of particle size for polyamide particles with relative density 1.14 (• ax, az) and polypropylene particles (• ax, az) with relative density 0.9. magnitude of large particles does not follow the classical a rms ∼ ε 3/4 ν -1/4 (see for instance 15 ) but was found to scale with the forcing time scale a rms ∼ RΩ 216 . D/L stands then as the good parameter, as the integral length scale is approximately constant with the Reynolds number, while the Kolmogorov length scale decreases with Re. Indeed, plotting T aΩ (or just T a) as function of D/η would yield different sets of curves, while one master curve emerges when plotted against D/L.

The particle density ratio, found to increase both velocity and acceleration time scales by approximately the same factor, play indeed no role on the T v /T a ratio (figure 6(b)). The observed decrease of this ratio confirms that velocity time scales increase slower than that of acceleration, which is highlighted by the axial component where velocity time scales tend towards a constant value. The anisotropy of the scale separation is therefore attributed to velocity anisotropy, which is inherent to von Kármán flows. We believe that, the impact of the mean flow is totally removed for the transverse components, its evolution is more representative. It would be interesting to compare this decrease of the scale separation to particles of size in or below the inertial range. To our knowledge, previous studies of smaller material particles (typically in the range 1 < D/η < 50 18,19 ), only report measurements of acceleration time scales, as the velocity time scale demands much longer trajectories.

VI. SUMMARY

Using 3d particle tracking, we have studied the characteristic time scales of very large inertial particles in a non homogeneous fully turbulent flow. Lagrangian tools have shown the strong influence of particle size on their dynamics. Indeed, for these large objects, we found both acceleration and velocity time scales to be strongly increasing with the particle size. This is the signature of a modification of the particle dynamics over the whole range of frequencies, as shown by the Lagrangian power spectra of the particle acceleration. Frequencies higher than the injection frequency displayed strong cutoffs in acceleration spectra due to particle size, corresponding to the observed increase of acceleration time scales T a with the particle size. Although this is in agreement with previous measurements of finite size particle acceleration 18,19 , acceleration spectra were found to decrease much faster than f -2 as reported for ocean floats with much smaller D/η ratios 11 .

In order to separate the effects of size and density, we varied the particle relative density and compared systematically the results obtained for particles 10% lighter than the fluid to the one of particles 14% heavier. For all quantities, the role of density was found much less influential than particle size. This is a specificity of particles much larger than the Kolmogorov length scale, for which density appears only to finely tune the dynamics, whose main features (trapping and response to turbulent fluctuations) are imposed by the particle size. As a result, the observed variation in the statistics can be qualitatively explained through the action of the added mass force.

Our study has investigated the dynamics of particles over the whole volume of a confined flow and tracked them for durations larger than the large eddy turnover time. As a consequence, velocity correlations were biased by contributions from the mean flow so that the Lagrangian integral time was zero. By removing the local value of the mean flow along each trajectory to estimate fluctuating velocity correlations, we were able to quantify the effects of size and density on the Lagrangian integral time. As particles above a certain size develop coming and going motions in the axial direction in such flows 16 , the autocorrelation functions of the axial velocity are more heavily biased. Indeed, the shape of the autocorrelation function of the fluctuating velocity remained strongly influenced by the particle size such that the Lagrangian integral time remained the same up to measurement errors (in the axial direction only). This shows how difficult it is to disentangle the influence of the mean flow and turbulent fluctuations in a non homogeneous turbulent flow.

FIG. 1

 1 FIG. 1. a) Flow vessel and camera arrangement for 3d particle tracking. Arrows indicate the mean flow geometry with counter rotation in the azimutal direction and meridian recirculation. b) Sample of 20 trajectories of 18 mm polyamide particles obtained with a rotation frequency Ω = 4 Hz.

FIG. 2

 2 FIG. 2. a) Normalized auto-correlation functions of the transverse velocity vx, noted Rv x , for polyamide particles with diameters D/L = 0.2 (solid line), D/L = 0.33 (dashed line), D/L = 0.6 (dashed-dotted line), D/L = 0.8 (dotted line), and a rotation frequency Ω = 4 Hz. b) Corresponding normalized auto-correlation functions of the axial velocity vz.

  FIG. 3. a) Correlation functions of the transverse velocity (see equation 2) for polyamide particles with D/L = 0.6 and a rotation frequency Ω = 4 Hz. Cv x vx (thick solid line),C v ′ x v ′ x (dashed line), Cv x v x (dashed-dotted line), C vxv ′ x (dotted line), C v ′x vx (thin solid line). b) Corresponding correlation functions for the axial velocity. c) Normalized auto-correlation functions of the fluctuating velocity v ′x , noted R v ′ x , for polyamide particles with diameters D/L = 0.2 (solid line), D/L = 0.33 (dashed line), D/L = 0.6 (dashed-dotted line), D/L = 0.8 (dotted line), and a rotation frequency Ω = 4 Hz. d) Corresponding normalized auto-correlation functions of the axial fluctuating velocity v ′ z .

FIG. 4

 4 FIG. 4. a) Evolution of the velocity integral time as a function of particle size for polyamide particles (filled symbols) with relative density 1.14 and polypropylene particles (open symbols) with relative density 0.9. • and solid line: transverse component x. and dashed line: axial component z. b) Evolution of the velocity integral time as a function of the rotation frequency for polyamide particles along the transverse component x (continuous line, filled symbols) and axial component (dotted line, empty symbols) for different diameters (colours and symbols).

FIG. 5 0 0

 50 FIG. 5. a) Axial acceleration auto-correlation functions of polyamide particles, Ra z for polyamide particles with diameters D/L = 0.2 (solid line), D/L = 0.33 (dashed line), D/L = 0.6 (dashed-dotted line), D/L = 0.8 (dotted line), and a rotation frequency Ω = 4 Hz. b) Same figure as (a) but with the time lag τ normalized by the acceleration correlation time Ta = τ 0 0 Ra(τ )dτ , where Ra(τ0) = 0. c) Evolution of the acceleration correlation time, Ta, as a function of particle size for polyamide particles with relative density 1.14 (• ax, az) and polypropylene particles (• ax, az) with relative density 0.9. d) TaΩ as a function of Ω for polyamide particles for the transverse component x (continuous line, filled symbols) and axial component (dotted line, empty symbols) for different diameters (colours and symbols).

TABLE I .

 I Experimental parameters. Ω: rotation frequency of the counter rotating disks. u ′

	2 Hz	0.25	0.48	38	1.44 1.2 10 6 350 3.2
	3 Hz	0.38	1.67	28	0.77 2.4 10 6 430 3.2
	4 Hz	0.52	4.03	22	0.5 3.6 10 6 520 3.4

correlations and a Lagrangian integral time.

Acknowledgments

The authors want to thank Peter Huck for his reading of the manuscript, and Jean-François Pinton, Mickael Bourgoin, Nicolas Mordant and Javier Burguete for stimulating discussions. This work is supported by French research program ANR-12-BS09-0011 "TEC2" and ANR-13-BS09-0009 "LTIF".


David Masclet
email: david.masclet@univ-rennes1.fr

Clemens Puppe
email: clemens.puppe@kit.edu

Keywords: Conflict, Conflict Resolution, Experiments, Conflict of interest, Social Welfare

Introduction to the special issue "Experiments on conflicts and conflict resolution"

David Masclet, Clemens Puppe

Introduction to the Special Issue "Experiments on Conflicts and Conflict

Resolution"

General presentation

Conflicts are frequent in the real world, ranging from interpersonal conflicts such as domestic violence to inter group conflicts like civil conflicts. There are probably as many definitions of conflict as there are occasions for its occurrence. According to some authors, conflicts would occur when individuals (or groups) have divergent interests in such a way that they could be negatively affected by another individual (group) [START_REF] Thomas | Conflict and negotiation processes in organizations[END_REF]. Other authors define conflicts as "a battle or clash" involving individuals or groups in opposition to each other.

This special issue presents a series of eight articles dealing with experiments on conflict and conflict resolution. The genesis of this special issue is the workshop on experiments on conflict held in Rennes, France, in May 2012. Some papers in this issue were presented during the workshop. Others were selected from the submissions in response to a call for papers. All papers of this special issue -whether they address interpersonal, intra group or inter group conflicts -share the same methodology, namely experimental economics. The aim of this special issue is threefold. First, the determinants of conflicts are investigated; second, the consequences of conflicts in term of social welfare losses are measured, and finally, attempts are made to assess the efficiency of different mechanisms in reducing and/or preventing conflicts.

The rest of this introductory paper is organized as follows. Section 2 discusses the determinants of conflicts. Section 3 investigates the collective costs of conflicts while Section 4 deals with conflict resolution. Section 5 briefly summarizes each paper presented in this special issue. Finally, Section 6 discusses the main findings and concludes.

The determinants of conflicts

There exist several sources of conflicts. A first source of conflicts is greed (Collier and Hoeffler 2004;[START_REF] Fisher | Intergroup Conflict[END_REF]. The "greed" explanation relies on the idea that, in a context of relative scarcity of resources, individuals (or groups) would act in pursuit of self-interested material gain. In other words, the greed explanation of conflict reflects competition over valuable (natural) resource rents (lands, primary commodities, etc). There are numerous examples of such situations where individuals or groups compete for scarce resources ranging from electoral competition, promotion tournaments within firms, research contests where teams of researchers compete for being the first unit to innovate, to full wars between countries to get access to natural resources or land [START_REF] Abbink | Inter-Group Conflict and Intra-Group Punishment in Experimental Contest Games[END_REF]. If greed can explain interpersonal or inter group conflicts, it may be also at the heart of social dilemmas that characterize several intra group conflicts. Social dilemmas have been formulated in mathematical terms by game theory to reflect both the existence of conflict of interest as well as the tension arising between individual and collective interests. In social dilemmas individuals may rationally choose to defect because of greed, i.e. the desire to get the highest possible outcome for oneself, which is socially suboptimal. 3 The two-person prisoner's dilemma is a good illustration of such conflict of interest where the dominant strategy is to defect while it would be socially optimal that both parties cooperate. Another example of social dilemma is the public good dilemma. A public good is a resource from which all may benefit, regardless of whether or not they have provided the good (public goods are nonexcludable). Another characteristic of public goods is that they are non-rival such that one person's use of the good does not diminish its availability to another person. Driven by greed, individuals may be rationally incited to free ride i.e. to enjoy the public good without contributing to its provision, which is also socially suboptimal. Several experiments have tested the predictions in either game and have confirmed that individual decisions converge toward the Nash equilibrium over time (see, for instance, [START_REF] Isaac | Public goods provision in an experimental environment[END_REF][START_REF] Isaac | Group size effects in public goods provision: The voluntary contributions mechanism[END_REF][START_REF] Keser | Voluntary contributions to a public good when partial contribution is a dominant strategy[END_REF], for experiments on public good games).

A second source of conflicts is grievance [START_REF] Gurr | People versus states: Minorities at risk in the newcentury[END_REF], Collier and Hoeffler 2004[START_REF] Cramer | Inequality and Conflict -A Review of an Age-Old Concern, United Nations Research Institute for Social Development[END_REF]. Central to grievance is the concept of (horizontal) inequalities -either in terms of land or income. While the idea of a relationship between inequality and conflict is appealing, the empirical evidence is however not clear-cut. Indeed some studies have found positive relationships between income inequality and political violence [START_REF] Binswanger | Power, distortions, revolt and reform in agricultural land relations[END_REF][START_REF] Schock | A Conjectural Model of Political Conflict: The Impact of Political Opportunities on the Relationship Between Economic Inequality and Violent Political Conflict[END_REF] while others have observed no relationship [START_REF] Weede | Income Inequality, Average Income, and Domestic Violence[END_REF], Collier et al. 2004). This absence of clear empirical evidence of a relationship between inequality and conflict may be due to the fact that it is hard to clearly disentangle inequality from other factors, and that unethical activities are hidden and therefore hardly observable directly in survey data [START_REF] Brockett | Measuring political violence and land inequality in Central America[END_REF]. Controlled laboratory experiments may thus help to investigate the role played by inequality in the occurrence of conflicts. For instance, some experimental studies have provided evidence of the existence of a positive relationship between inequality and conflicts, indicating that individuals may be willing to engage in conflicts by harming others when they suffer from disadvantageous inequality [START_REF] Zizzo | Are People Willing to Pay to Reduce Others' Incomes?[END_REF]. [START_REF] Zizzo | Are People Willing to Pay to Reduce Others' Incomes?[END_REF] designed a game where subjects can reduce (burn) other subjects' money at own costs. The authors found that despite the own cost of burning money, a large majority of participants chose to destroy some part of others' money, which is (partly) consistent with some models of inequality aversion.

A third explanation of conflicts often evoked in the literature is retaliation. However whether opportunities of retaliation will lead to more or less conflicts is also not clear-cut in the literature. Indeed on the one hand, one may reasonably expect that the opportunity to retaliate leads to the escalation of conflicts into a long-term vendetta [START_REF] Fisher | Intergroup Conflict[END_REF]. According to [START_REF] Fisher | Intergroup Conflict[END_REF] conflicts would have a tendency to escalate in the case of repeated situations. The role played by retaliation in the occurrence of conflicts has also been investigated in several previous experimental studies [START_REF] Bolle | Vendettas[END_REF][START_REF] Zizzo | Money Burning and Rank Egalitarianism with Random Dictators[END_REF]. For instance, [START_REF] Bolle | Vendettas[END_REF] studied the determinants of vendettas. The authors found that vendettas frequently occurred even when initial endowment were equal and despite the fact that vendettas were pointless. On the other hand, the opportunity of retaliation could also have a deterrent effect and therefore reduce the likelihood of conflicts if the parties anticipate and fear retaliation (Collier andHoeffler 2004, Abbink and[START_REF] Abbink | The pleasure of being nasty[END_REF]. In other words, parties may refrain from engaging in conflicts for fear of retaliation. Some studies have shown that both effects may coexist in the laboratory [START_REF] Abbink | The pleasure of being nasty[END_REF]. In a repeated money burning experiment, [START_REF] Abbink | The pleasure of being nasty[END_REF] observe significantly less destruction in a money burning game under full information as compared to a treatment where participants could hide their destruction behind random destruction. While the presence of retaliation opportunities incite individuals to burn less money, the authors observe however that in case of destruction, such acts are immediately followed by retaliation.

Finally, a fourth explanation of conflicts relies on non-monetary factors related to pure nastiness and desire for dominance. Standard microeconomic theory has traditionally ignored the role of status and desire for dominance assuming that utility is a function only of one's own absolute income. Notable exceptions include [START_REF] Duesenberry | Income, saving and the theory of consumer behavior[END_REF], [START_REF] Veblen | The Theory of the Leisure Class, George Allen and Unwin[END_REF], or [START_REF] Frank | The Demand for Unobservable and Other Nonpositional Goods[END_REF]. However recent behavioural findings have provided strong evidence that individuals may be willing to harm others in order to dominate despite the absence of immediate or future expected monetary returns [START_REF] Charness | Relative Payoffs and Happiness[END_REF][START_REF] Charness | Understanding Social Preferences with Simple Tests[END_REF][START_REF] Zizzo | Are People Willing to Pay to Reduce Others' Incomes?[END_REF][START_REF] Zizzo | Money Burning and Rank Egalitarianism with Random Dictators[END_REF][START_REF] Abbink | The pleasure of being nasty[END_REF][START_REF] Chowdhury | The Equivalence of Contests[END_REF][START_REF] Abbink | The Moral Costs Of Nastiness[END_REF][START_REF] Dohmen | Relative versus absolute income, joy of winning, and gender: Brain imaging evidence[END_REF][START_REF] Bolle | Vendettas[END_REF][START_REF] Charness | The Dark Side of Competition for Status[END_REF].

The consequences of conflicts on welfare

Conflicts are typically viewed as something negative that should be avoided. Indeed conflicts for resources may be socially wasteful because the contestants may spend too much resource to win the prize (see [START_REF] Tullock | Efficient rent seeking[END_REF]. 4 Conflicts associated with competition for scarce resources may also lead the contestants to engage in unethical activities such as destruction of resources, or sabotage against competitors in order to increase their chances of winning the contest (Lazear 1989, Harbring and[START_REF] Harbring | How many winners are good to have? On tournaments with sabotage[END_REF]. Conflicts of interest that arise from social dilemmas are also socially costly as they may result in significant social welfare losses if defection and free riding occur. Moreover, some studies have shown that conflicts may significantly reduce trust [START_REF] Lei | Competition vs. communication: An experimental study on restoring trust[END_REF]. It is for all these reasons that governments and firms spend significant amounts of resources in order to prevent or to reduce the occurrence of conflicts.

Conflict resolution

In this section, we briefly discuss a few mechanisms ranging from punishment institutions to cost sharing or compensation mechanisms that could be implemented to avoid or, at least, to limit the occurrence of conflicts. For instance in the context of public good dilemmas, several studies have shown that punishment institutions may be an efficient way to deter free riding within groups and thus to solve intra group conflicts (see, for instance, Fehr and Gächter 2000). This special issue also discusses the limitations of these mechanisms. For example, several studies have shown that punishment institutions may exhibit the following features: (i) punishment may be socially costly both for the target and for the punisher, at least in the short run; (ii) punishment itself may constitute a public good (second order free riding) due to the fact that individuals may expect others to punish free riders without themselves incurring the cost of punishment; (iii) punishment may induce retaliation (counter punishment and revenge); (iv) punishment may be antisocial, e.g. when the cooperators are punished [START_REF] Gächter | The Long-Run Benefits of Punishment[END_REF][START_REF] Herrmann | Antisocial Punishment Across Societies[END_REF].

Presentation of the papers of this special issue

We now provide a brief overview of the articles presented in this special issue.

The determinants of conflicts :

The role of greed grievance, reciprocity and desire for dominance.

The paper "The Impact of Relative Position and Returns on Sacrifice and Reciprocity: An Experimental Study using Individual Decisions"by Jordi Brandts, Enrique Fatas, Ernan Haruvy and Francesco Lagos (this issue) contributes to the existing literature on the determinants of conflicts by investigating whether individuals are willing to decrease/increase others' payoffs at different costs and, if so, whether such decisions are related to (anti-)social preferences. More precisely, the authors investigate whether destruction decisions depend on selfishness (greed), (dis)advantageous inequality aversion (grievance), reciprocity, competitiveness, or pure desire for dominance. These issues are investigated through a series of different binary pairwise choices between two alternative states described only by payoffs to oneself and to another person. The findings of this study reveal an important heterogeneity of types of participants. Pure selfishness is the most frequently observed behavior. Among subjects exhibiting (anti-)social preferences, social welfare maximization is the most frequent, followed by inequality aversion and by competitiveness (i.e. a desire for dominance).

The cost of inter group conflicts: Segmentation of the society and losses in term of trust and trustworthiness

The paper entitled "What Happens If You Single Out? An Experiment" by Fabio Galeotti and Daniel Zizzo 5 focuses its attention on the social cost of inter group conflicts in terms of lower trust and trustworthiness in the specific context of "singling-out" situations. More precisely, this paper investigates a specific form of inter group conflicts, namely "singling-out" situations that can be defined as inter group situations in which one individual (a singleton group) is socially identified as different from a second group that is larger in size. A subject can be singled out by others because he or she possesses undesirable qualities which may lead to social exclusion, marginalization, or stigmatization. In this paper, the authors investigate the social costs associated with singling out an individual in terms of trust and trustworthiness. For this purpose, the authors artificially induce the status of being singled out in the lab by asking participants to rank other participants according to how much they would like to be matched with them in the experiment (from the most preferred to the least preferred match). After this questionnaire, participants are matched and play a trust game. The experimental treatments differ in the ranking phase. Under a positive frame, subjects singled out the most preferred match in the experiment, whereas under a negative frame they singled out the least preferred match in the experiment. The authors find that trustworthiness declines if there is a singled out subject; non-singled out subjects discriminate against the singled out subject when they are not responsible of the distinct status of this person; under a negative frame, the singled out subject returns significantly less.

Conflicts of interest in social dilemmas within groups and conflict resolution

The three papers by Agathe Rouaix, Charles Figuières and Marc Willinger (this issue), Charles Noussair, Daan van Soest and Jan Stoop (this issue), and Dirk Engelmann and Nikos Nikiforakis (this issue) discuss the social cost associated with within-group conflicts that may arise from social dilemmas due to the fact that private and public interests are not aligned. These papers also investigate the effectiveness of mechanisms such as redistribution programs or punishment institutions that may be implemented to reduce the conflicts of interest and free riding.

The paper "The Trade-off between Welfare and Equality in a Public Good Experiment" by Agathe Rouaix, Charles Figuières and Marc Willinger investigates whether redistribution policies may help reducing free riding in a public good dilemma by introducing heterogeneity in the endowments of the group members. Public good games with endowment heterogeneity have been addressed in the literature; however, the question whether heterogeneity is positive or detrimental for efficiency has still not been answered unambiguously in the literature. Some studies have found that groups with heterogenous endowments are less successful, while other studies observed the opposite finding, namely that group heterogeneity may increase the level of contributions. In their present paper, the authors contribute to the existing literature by testing the effect of heterogeneity on efficiency in a public good context. Their results show that welfare increases with the introduction of a redistribution mechanism that induces more unequal endowments.

The paper "Punishment, Reward, and Cooperation in a Framed Field Experiment" by Charles Noussair, Daan van Soest and Jan Stoop investigates the effectiveness of punishment in sustaining cooperation in the context of a social dilemma using field experiment data. The setting of their field experiment is a recreational fishing facility where the participants are regular customers of the facility. The design consists of three treatments.

The baseline treatment is similar to a linear voluntary contributions game in which the fishermen are assigned to groups of four members. The punishment treatment is similar to the baseline except that individuals have an opportunity to punish others after having observed how many fish they catch. In the reward treatment, participants can reward others. The authors find that punishments tend to be directed at non-cooperators and rewards are assigned to those who are relatively cooperative. However, in contrast to the results typically found in laboratory experiments, the authors find that both punishments and rewards fail to increase the average level of cooperation. Several features of the game may explain these differences: (i) individuals engage in a real time activity, (ii) they can update their cooperation tendency in real time, (iii) the experiment is framed as harvesting of a resource, and (iv) the game may evoke competitive behavior which makes the norm of cooperation less salient. This paper suggests that the effectiveness of punishment institution would be strongly context dependent.

The paper "In the long-run we are all dead: On the benefits of peer punishment in rich environments" by Dirk Engelmann and Nikos Nikiforakis also investigates the effectiveness of punishment mechanisms in a public good context. Specifically, the authors shed light on the limitations of peer punishment mechanisms in order to deter free riding in a public good context. According to previous studies, the costs of peer punishment can be outweighed by the benefits of higher cooperation under certain conditions: (i) if there is a sufficiently long time horizon, and (ii) if punishment cannot be avenged. However, as mentioned by the authors, in most instances in real life these conditions are not met, which implies that punishment can be often retaliated. The authors use a design that allows participants to employ a wide range of punishment strategies including retaliation of punishment. Similar to previous studies they find that, if punishment cannot be avenged, peer punishment leads to higher earnings relative to a baseline treatment without any punishment opportunities. However, in the more general setting, they find no evidence of a significant increase in group earnings over time relative to the baseline treatment.

Conflicts of interest, negative externalities and conflict resolution

The two following papers deal with conflict of interest generated by negative externalities and mechanisms to help reducing such conflicts.

The paper "Cracking down on bribery" by Sheheryar Banuri and Catherine Eckel (this issue) also investigates the effectiveness of punishment institutions but in another context, namely the context of corruption that distorts economic decision making, induces conflicts of interests and imposes negative externalities on society. Specifically, in this paper, the authors investigate experimentally the effectiveness but also the limitation of punishment institutions to combat corruption. The experiment is based on a three-player repeated bribery game. The three players are a firm that makes a discrete choice of whether to offer a bribe to the government official, a government official that observes the firms behavior and makes a discrete choice whether to grant the firm a favor, and a third party who is negatively affected by the transaction. In this context, the authors investigate experimentally whether corruption crackdowns reduce or increase corruption in the long run. Indeed, anti-corruption reforms are costly in terms of resources and time so that they are often followed by either a partial or complete retraction. In addition, the authors investigate whether the long term effects of crackdown policies vary by culture. This is done by comparing two countries that differ significantly in overall perception of corruption and experience with bribery: the US and Pakistan. The main findings of this study show that post-crackdown behavior is not significantly different from pre-crackdown behavior, suggesting that crackdowns are completely ineffective in the long run as corruption rebounds to pre-crackdown levels. In other words, the effect of the punishment institutions is not persistent over time once it has been removed.

The paper "Choice Overload, Coordination and Inequality: three hurdles to the Effectiveness of the Compensation Mechanism" by Estelle Midler, Charles Figuières and Marc Willinger (this issue) also investigates mechanisms to help reducing the conflict of interest generated by negative externalities when the decision of one agent harms someone else. Specifically, this paper discusses the effectiveness of the so-called "compensation mechanism" [START_REF] Varian | A solution to the problem of externalities when agents are well-informed[END_REF]) that allows agents who suffer from negative externalities to compensate those who reduce their production by means of transfers. In theory, such compensation mechanisms lead to a Pareto optimal outcome. However several studies have argued that this kind of mechanism may create a coordination problem that would undermine its effectiveness. In their paper, the authors investigate various factors that might affect the likelihood that subjects coordinate on a Pareto optimum. They show that the coordination problem is in fact not the only problem associated with the compensation mechanism. In addition, the authors find that the (in)effectiveness of the compensation mechanism also depends on several other factors, including (i) the size of the strategy space, (ii) the number of equilibria, and (iii) the inequality associated with the outcomes. In particular, increasing merely the number of options reduces the success of the mechanism. More importantly, allowing subjects to choose an option that provides equal payoffs to both players increases the mechanism's effectiveness.

Conflict resolution as a social dilemma

Finally, the paper "The UN in the lab" by Malcolm Kass, Enrique Fatas, Catherine Eckel and Daniel Arce (this issue) discusses the effectiveness of policies implemented to reduce the occurrence of global form of conflicts such as terrorism. Specifically, this paper discusses the limitation of anti-terrorism policies that may suffer from a free riding problem. Indeed, when combating terrorism, a country may face a choice between two strategies: preventive versus defensive actions. Preventative actions, such as destroying a terrorist training ground, benefit all governments. In sharp contrast, defensive actions reduce the attractiveness of the defending government but make other countries relatively more attractive as targets. While prevention is the most efficient choice, each country is tempted to free ride on the others' investment by using defending actions. This constitutes a prisoner's dilemma. In such context, the Nash equilibrium of the game is therefore for both countries to invest in defensive actions, which is Pareto inefficient. Countries thus face a difficult problem in coordinating on effective counterterrorist policies. This paper expands the experimental environment developed in [START_REF] Arce | Counterterror Strategies in a Lab[END_REF] to test the ability of a cost sharing institution in alleviating the collective action problem. In the experiment, treatments vary in the extent to which players share the cost of choosing the prevention strategy. The authors find that cost sharing can be a powerful policy choice, boosting the utilization of the optimal policy, but only when the level of cost sharing is sufficiently high.

Conclusion

To summarize, the papers presented in this issue shed light on the various determinants of conflict including selfishness (greed), inequality aversion (grievance), reciprocity and competitiveness (desire for dominance). Each motive alone does not seem to be sufficient to explain the occurrence of conflicts. In any case, conflicts are socially costly as they typically induce significant welfare losses. They may also destroy trust and trustworthiness and lead to the underprovision of public goods. For all these reasons, there is scope for governments to intervene and to implement institutions and mechanisms in order to prevent or reduce the occurrence of conflicts. Among these mechanisms the punishment institutions seem to represent a powerful device to deter free riding in the context of social dilemmas; punishment may also be helpful in the context of corruption. However, some of these mechanisms suffer from serious weaknesses. For instance, it has been shown that punishment institutions are not the panacea as they may induce perverse behaviors such as retaliation or anti-social punishment. Furthermore, it seems that the effects of punishment are not persistent over time after the institutions have been removed, suggesting that they fail to enforce positive norms of sustainable cooperation. Finally some studies have shed light on the fact that some policies aimed at solving conflicts may suffer from free riding problems (second order free riding). This may be the case for instance when, at the international level, governments have to coordinate on the best policies to combat terrorism. While preventative actions would benefit all countries, each country in isolation may be tempted to invest in defensive actions, which is collectively sub-optimal.

Another potential reason for defection is the fear of being a sucker, i.e., cooperating while the other party will defect.

It should be noticed however that conflicts of interest are not necessarily always bad for an organization. This may be the case for instance when conflicts rhyme with inter individual or inter group competition that provides strong incentives to innovate and to outperform (e.g.[START_REF] Lazear | Rank-Order Tournaments as Optimum Labor Contracts[END_REF]. Conflicts of interest become detrimental to an organization or a society only when such competition induces important collective welfare losses and/or when it leads the individuals (or groups) to engage in destructive and unethical activities to win the contest.

This paper has already been published in a previous issue of this journal: Galeotti and[START_REF] Bolle | Vendettas[END_REF], "What happens if you single out? An experiment," Social Choice and Welfare 43 (3), p.703-729.

Acknowledgements

We would like to thank all the anonymous reviewers of the papers considered for this special issue. We would also like to thank Marc Fleurbaey and Vincent Merlin for comments and support. Any opinions, findings, conclusions, or recommendations expressed here are those of the authors who are solely responsible for the analysis and conclusions.


Andrei Hossu
email: hossu@aii.pub.ro

Daniela Andone

RECOVERING DATA TRANSFER CONSISTENCY OF ETHERNET-BASED COMMUNICATION IN AN INDUSTRIAL ROBOTIC APPLICATION

Keywords: Industrial Robotic Application, Ethernet-based communication, data transfer consistency, Artificial Vision System, Control Management System, Routing Control System

The actual trend in automation control systems is to distribute control logic to modular and easy to connect production cells. As part of this trend is the increase of Ethernet technology for machine-machine data communication inside this modular based architecture. The paper presents a robotic handling application of moving parts located on a transport conveyor. Data representing a set of parameters of the parts to be handle form the conveyor is provided by a Routing Control System (RCS). The Control Management System (CMS), which controls a number of robotic cells is receiving this data from RCS and merge it with the information provided by an Artificial Vision System. The communication between these two Control Systems (RCS and CMS) is Ethernet-based. Ethernet technology is good, reliable and fast for large amount of data, but because of its non-deterministic character, it has a lack of tools for data synchronization. The paper includes an analysis of the experimental results of the measurements of the non-deterministic factor of the existing network. The "worst case scenario" of the maximum communication delay caused by Ethernet traffic and the minimum time between two consecutive data commands, shows that without recovering data transfer time-consistency, the application requirements can not be achieved. The paper is presenting a mechanism developed at protocol level, in order to guarantee the consistency in time, at CMS level, of the data provided from RCS with the data provided by Vision System.

THE DESCRIPTION OF THE ROBOTIC APPLICATION

The system described in the paper is dedicated for the robot-based automation of the unloading and packing stages in the flat glass industry.

In Fig 1 it is presented the architecture of the proposed automation system. This architecture is often utilized in industrial applications (in palletizing of moving objects systems).

The System Structural Architecture:

Active Elements: Control Management System (CMS), Routing Control System (RCS), Vision System and Robotic Cells.

Passive Elements: Conveyor, glass plates.

Infrastructure: Communicational Link between Vision System and CMS.

Communicational Link between CMS and Robots Controllers.

Communicational Link between CMS and RCS.

General assumptions:

The plates are connected to the conveyor (the same speed and direction).

The System Functional Architecture:

The Routing Control System has to provide for CMS the Routing Data -a description of the possible destinations (one or more of the robotic cells) of each plate in the moment the plate is passing the Decision Point of the Vision System.

The role of the Vision System is to inspect the cutting accuracy and the shape parameters of every plate. The Vision System is analyzing the information provided by a Line Scan Acquisition System (a dual line scan camera system) in conjunction with the information provided by an encoder connected to the transport conveyor. The Vision Data, containing the data resulted from the inspection process, together with the data Both sets of data (Routing Data and Vision Data) are merged by CMS. CMS will take the decision to send the pick the plate command to a certain robotic cell only if Vision Data describe the plate having cutting accuracy and shape parameters inside the accepted tolerances for a certain packing destination AND the plate is routed to that certain destination.

THE DESCRIPTION OF THE INFORMATIONAL SYSTEM ARCHITECTURE

The communication between Vision System and CMS is a dedicated connection. Some of the reasons for choosing this type of communication is the geographical neighborhood of these two systems and the fact the structure of the data transferred between Vision System and CMS could be very tight specified (no need for using a general type of protocol).

Another reason is the concept that Vision System is an intelligent sensor of the Robotic Application, which means the Vision System will not be "visible" on the higher automation level, but only on the Robotic Automation Level (the Vision System is "visible" only for CMS).

This communication channel has a serial support. This type of connection is providing a deterministic character of the Vision System -CMS communication.

For the communication between CMS and RCS it was adopted an Ethernet-based topology.

The main reason of choosing this type of topology is the fact CMS is an automation entity visible on the high automation level (CMS includes all the automated stacking capabilities of the whole production line).

Industrial Protocol on Ethernet is a very good and reliable support for modern configurations on industrial automations, but because it's nondeterministic character, it is poor in data timesynchronization [START_REF] Marshall | Industrial Ethernet (2 nd Edition)[END_REF].

The time-synchronization between the Routing Data (data coming from RCS) and the Vision Data (data coming from Vision) in the merging process in CMS it is a key factor of achieving the requirements of the automation application.

EXPERIMENTAL RESULTS

In The Ethernet Delays are estimated as the differences between the CPU time of receiving Routing Data (sent over a non-deterministic communication channel) and the CPU time of receiving Vision Data (sent over a deterministic communication channel).

A lost in synchronization will occur only if the variation of the Ethernet Delay value from the average value of the Ethernet Delay is greater than the minimum time between two consecutive sets of Routing Data.

Analyzing the manufacturing process we can identify what is the minimum time between two consecutive sets of Routing Data. This is the minimum time between two glass plates coming on the conveyor (this is called "snapping period").

The actual glass manufacturing process has the minimum snapping period of 1.44 seconds.

Analyzing the experimental results we could see the necessity of implementing a method for recovering data transfer time-consistency.

RECOVERING DATA TRANSFER TIME-CONSISTENCY

A few solutions were analyzed in order to solve this problem [START_REF] Marshall | Industrial Ethernet (2 nd Edition)[END_REF], [START_REF] Rslinx | User Manual[END_REF]: -Use a more powerful Ethernet board (instead of using 10MB/s type of board, to use a 100BT Ethernet module) -Replace the communication software support (RSLinx) with another one with a better response time (a software module dedicated only for a specific protocol would provide a better response time related to a general software package like RSLinx, which is coming with a large CPU overhead). The above two solutions could improve the Ethernet behavior, but the non-deterministic character of this type of communication is not eliminated.

-Install another dedicated Ethernet module in the RCS and an additional dedicated Ethernet module in the CMS PC. These modules would be connected to a separate isolated Ethernet switch. In this case, most of the delays experienced on the current Ethernet link would be eliminated since the only traffic on the link would be between the routing system and the CMS cell PC.

-Use an ASCII serial (RS-232, RS-485, etc.) connection rather than using Ethernet. This would make the communication time between the Routing and CMS systems deterministic. -Use a dedicated digital signal from RCS to the CMS in addition of the Ethernet connection in order be used to re-synchronize the Routing Data in CMS. This would be implemented by energizing a digital output that would indicate to the CMS cell in the moment of sending current Routing Data. When the input was seen by the CMS system, the CMS system would capture its own internal time and it will use this time value in the moment the Routing Data is received over Ethernet. These last three solutions could solve the timesynchronization problem, but the solution wouldn't be accepted because of a dramatic aggression on the network topology previously agreed on the design time of the application [START_REF] Mackay | Practical Industrial Data Networks[END_REF], [START_REF] Stenerson | Industrial Automation and Process Control[END_REF].

The solution proposed in the paper is based on inserting a "timestamp parameter" in any set of Routing Data transmitted from the Routing System to the Control Management System.

This timestamp parameter will be the Routing System CPU time in millisecond representation. This timestamp parameter value will be a wraparound counter representing the least significant two bytes (one Word) of the CPU time (in milliseconds).

This timestamp parameter will be used by CMS to estimate with a "good enough" approximation of the offset between the CPU time values of the producer of the message (RCS) and the consumer of the message (CMS). This estimated offset would be used for time synchronization of the current message. It means CMS will add the estimated CPU time values offset to the current timestamp parameter value contained in the current received message.

In order to provide a "good enough" approximation of the offset between the CPU time values of the producer (RCS) and the consumer (CMS) the algorithm has to estimate the minimum value of the statistical population containing all the offsets estimated for a large number of transmitted/received messages.

This minimum is a "moving minimum" (it will be estimated from a statistical population collected on a certain time window) because we expect a slippage between the clocks of the two CPU (this slippage is accumulative and will become significant in time).

For the support of building this statistical population of offset values is used an existing message from RCS to CMS, called "Request Status Message". This message is sent by RCS every half a second in order to check the communication with CMS and also to obtain from the CMS the status of the availability of each possible plate destination stations (of each Robotic Cell).

The proposed solution requires the Routing System to move the CMS cell data hand-off point (the point where it is transmitting the Routing Data to CMS) more upstream the conveyor. The CMS has to receive the Routing Data message of a plate before the Vision Systems ends the process of analyzing that plate (even on the highest Ethernet traffic). But the method is not anymore affected by receiving Routing Data in advance. CMS will build a buffer of all the Routing Data received from the RCS describing plates will come in time, and it will be able to recover the consistency in time of these data on the merging process with the Vision Data.

CONCLUSION

The paper presented an algorithm developed at protocol level, in order to guarantee the recovering of data transfer consistency in time, at CMS level, for merging of the data provided from RCS over an Ethernet communication channel with the data provided by the Vision System over a deterministic communication channel. This solution proposed in this paper is based on the following assumptions: -The actual slippage of the clocks on either the RCS or the CMS processors would be very minimal. This assumption is not a restrictive one, being normal to accumulate a significant slippage value around one second in much more that days or even weeks. -In the time the slippage value of the clocks would become significant, the network connection would have a period of relative low traffic. This assumption is also not restrictive one, because in those days or weeks that the slippage value of the clocks is becoming significant, it is more likely a relative calm moment to occur in the net traffic. -The number of collected transmitted by the producer/received by the consumer messages (till the slippage of the CPU clocks will accumulate a significant value) will be large enough to build a statistical population. This assumption is also not a restrictive one because the statistical population main support is the "Request Status Message" which is set to be transmitted every half second (most of the statistical population members are coming from collecting the estimated offsets for this type of message)

Fig. 1 .

 1 Fig. 1. The robot-based automation system for handling glass plates from a moving conveyor describing the location of the plate, are transmitted to CMS in the moment the Vision System processing time ended. The moment (time-based) is called Vision Decision Point.Both sets of data (Routing Data and Vision Data) are merged by CMS. CMS will take the decision to send the pick the plate command to a certain robotic cell only if Vision Data describe the plate having cutting accuracy and shape parameters inside the accepted tolerances for a certain packing destination AND the plate is routed to that certain destination.

  Fig 2 are presented the experimental results of recording Ethernet Delays over around 10 minutes on the analyzed network.

Fig. 2 .

 2 Fig. 2. The experimental results of recording Ethernet Delays over around 10 minutes on the analyzed network.

Proceedings of RAAD'05, 14th International Workshop on Robotics in Alpe-Adria-Danube Region Bucharest May 26-28, 2005