T Boushaki

S Guessasma
email: sofiane.guessasma@nantes.inra.fr

J C Sautet

Predictive analysis of combined burner parameter effects on oxy-fuel flames

Keywords: Oxy-fuel combustion, Separated jet burners, lifted flame, neural computation

The present paper aims at studying the influence of burner parameters with a separated jet configuration, namely nozzles diameters and separation distance between the jets, on the flame characteristics (lift-off positions of flame and flame length). The experimental layout considers the use of OH-chemilumenescence to measure the flame characteristics for different combinations of processing conditions. The predictive analysis is based on a neural computation that considers the correlations between the inputs and the outputs of a combustion system using a configuration of separated jet. The predictive analysis show that a good agreement is found between numerical and experimental results in the case where the predictions are within the process window. The exploration of other process parameter combinations beyond that window gives less convincing results. This is mainly attributed to the fact that steady state characteristics are predicted numerically whereas it is expected experimentally that some of burner parameter combinations can lead to an increase of the parameters characterizing the flame.

Introduction

Oxy-fuel burners are widely used in high-temperature industrial furnaces to improve productivity and fuel efficiency, to reduce emissions of pollutants, and to eliminate the capital and maintenance costs of an air preheater. Indeed, the substitute oxygen by air provides a high flame temperature, a less consumption of fuel and a low NOx production since we eliminate the nitrogen of air [1,2]. This makes it possible to have a better thermal efficiency and a better stabilization of flame. Furthermore, the use of oxy-combustion in separated jet burners open interesting possibilities in the pollutant reduction such the NOx and the modularity of flame properties (stabilization, topology, flame length, etc.) [3,4]. For separated jet burners, the principle is based on the geometrical separation of its nozzles. This design gives a high dilution of the reactants by the combustion products, a large and plate flame and a homogeneous temperature in all volume of flame [4,5].

Flames from burner with multiple jets have many practical situations. Several studies have been published on the structure and development of non-reacting multiple jets [6][7][8][9].

However, the studies of multiple jet flames are mostly limited, for example, flame developing in still air without confinement [10] or in a wind tunnel with cross flow [11]. Recently, Lee et al. (2004) [12] studied the blowout limit considering the interaction of multiple nonpremixed jet flames and giving a number of variables such as distance between the jets, the number of jets and their arrangements.

The burner configuration used in this work is composed of three round jets, one central jet of natural gas and two lateral jets of pure oxygen. The power of burner is 25 kW and the flames develop inside combustion chamber with 1-m high. The OH chemiluminescence technique has been used to indicate the instantaneous flame reaction zone and thereby characterize features of the stabilization region. The lift-off positions and the flame lengths for several configurations of burner are measured.

Various parameters govern the flow from burner with multiple jets such as the number of jets, the form of nozzles, the spacing between the jets, the exit velocities, etc. Consequently, these geometrical and dynamical parameters of burner have important effects on the behaviour of flame. Considering the number of parameters, many configurations of burner are possible however it is experimentally difficult to study all possible cases. In a previous paper [4], several configurations have been tested experimentally to highlight the influence of tubes diameters, distance between the jets and the deflection of jets on the characteristics of the flame. Based on these experimental results we study in the present paper the behaviour of stabilization point (height and radius) as well as the flame length using a numerical method based on the artificial neural network (ANN). The methodology is an advanced statistical of data analysis [13]. It is particularly used when the correlations between the inputs and outputs of a given problem are difficult to capture using standard fitting routines. Typical examples of complex correlations can be found in the case of input interdependencies, several outputs attached to a set of inputs, a large number of parameter combinations, among others. The neural computation was already applied to different situations related to engineering processes [14,15]. In this paper, we are concerned by the study of the interactions between the burner parameters and their influence on the flame characteristics in a set-up that uses separate jets. This work is actually an extension of a previously published experimental study [4] and it aims at predicting the flame behaviour within and outside the operating window. The operating window represents here the range of the burner parameters used in the experimental investigation. We have used neural computation instead of standard fitting tools because of the nonlinear correlation between burner characteristics and the burner parameters as pointed out by several authors [16][START_REF] Baukal | Industrial Burners Handbook[END_REF]. In addition, simple preliminary analysis of the experimental data detailed hereafter have shown a significant burner parameters interdependencies [3][4].

Experimental layout

The experimental system consisted of a burner and operating conditions, a furnace, and OH Chemiluminescence setup. Fig. 1 shows a schematic diagram of the separated-jet burner apparatus. The burner is composed of three round tubes, one central of natural gas and two side tubes of pure oxygen. The fuel is a mixture of natural gas (85.2% CH 4 , 9.1% C 2 H 6 , 2.44% C 3 H 8 , 1.97 %N 2 , 0.75 %CO 2, plus traces of higher hydrocarbon species) with a density ). The internal diameters ( ng d and ox d ) range from 4 to 10 mm, and the separation distance between the jets (S) varies from 7 to 30 mm. Table 1 summarizes the operating conditions of burner parameters including the central and side jet characteristics (diameter, exit velocity and Reynolds number). The burner is located on the bottom wall of the furnace, which is a 1-m-high vertical tunnel with square cross section (60 × 60 cm). The lateral walls are refractory lined on the inside and water cooled on the outside.

Optical access is provided through quartz windows.

OH* chemiluminescence technique is used (Fig. 2) to describe the flame front and therefore to measure liftoff positions and flame lengths. The radical OH* characterizes the reaction zone, and is present in sufficiently high proportion giving a good quality signal, in particular for the oxy-fuel combustion [4,[START_REF] Ditaranto | [END_REF]. However, the chemiluminescence of other radicals (CH* at 430.5 nm or C 2 * at 516.5 nm) representative of the reaction zone can also be considered, although the use of an interferential filter is necessary, inducing a signal with a very low intensity. Furthermore, the presence of pure oxygen as oxidizer leads to a higher rate of OH radical compared to other radicals such as C 2 and CH. The radical OH* is located in the reaction zone where it has been created. OH* is not very sensitive to the turbulent convection, as well as its life time in an electronic excited state is very short (~1µm), allowing an accurate location where the radical is created. Emission of OH* radical is located in the wavelength range from 280 to 310 nm. The molecule excited OH* is formed by the following reactions [19] To extract the lift-off heights and the flame lengths, classical image processing (binarization, average, rms, thresholding) was used on all the images for each configuration. To determine the lift-off position of flame, it is necessary to perform a binarization then a detection of contour. The choice of threshold of binarization is delicate since we have to eliminate the noise from the images without affecting the signal. The method used here consists in locating the region of interest where the flame is stabilized and then to make a profile of the signal along the axis of object. Threshold value is taken at the inflection point of the intensity profile. Lift-off height is determined as the closest point to the burner where the signal appears. Fig. 3 shows an example of image processing for OH chemiluminescence in the stabilization region.

The flame length estimation is based on the visualization at the flame top. Fig. 4a shows an example of instantaneous images of the flame top. After binarization, the flame length can be measured for each configuration as shown in Fig. 4b. To do so, the pixel corresponding to the end of flame (highest position) is extracted and the average of these maximum values on all acquired images is calculated, following the expression:

n Z Z L n i 1 i i 0 f ∑ = = + = (2)
where Z 0 is the exit burner -base flame distance, Zi is the height of the flame in the image i and n is the number of instantaneous images used for the processing (Fig. 4b).

The experimental results related to the flame characteristics for several configurations of burner are summarized in Table 2.

Modelling technique

Neural computation requires several steps to allow the predictions of the correlations between the input and output of the present problem. The basic mechanism behind ANN is the neuron activity. The neuron is a mathematical processing unit that receives an input (a number), transforms it (by simple mathematical operations) and forward it to other neurons.

Details about the methodology can be found in [13,20]. In the following, we will stick to a concise description of the technique.

Step1 Indeed, since the parameter range can influence the quality of the predictions, all variables are expressed in the range 0-1, using the upper and lower limits available for each variable. Such pre-processing assumes the following conversion scheme, which is detailed in previous

studies i min i max min x x y x x - = - (3)
where y i is the dimensionless form of the variable x i . x min and x max represent the window range of variable x i . These limits are summarized in Table 3 for all studied parameters.

Each neuron is connected the other neurons following a feed-forward scheme. This writes

i ij j I W O = ( 4
)
where I i is the input of neuron i belonging to the forward layer, Oj is the output of a given neuron j from the backward layer W ij is the weight parameter that relates neurons i and j.

A typical sketch of the neuron connectivity can be found in [13] The output of a given neuron is related to its input using the expression [21] ( )

i i 1 O 1 exp I = + -
where the sigmoid function is used to nonlinearly transform the input of each neuron in the network structure. The output is thus bounded between 0 and +1.

Step2: building the database

As the number of experimental sets is limited (29 experiments as shown in Table 2), small ANN structures are used. A typical structure comprises the input and output patterns plus hidden units (neurons) organised in intermediate layers. The more units in the hidden layers, the more experimental sets needed for the optimisation of the ANN structure. Thus, it is decided to keep one intermediate layer for which the number of neurons is varied between 1 and 6. Following the correlation between weight population and database size, we are slightly below the lower bound when 6 neurons are used in the hidden layer (see for example [13]).

We vary the neuron number between the abovementioned bounds to demonstrate where the robustness of neural network is applicable. We know that a unique neuron in the hidden layer is insufficient to give reliable prediction and we know also that 6 neurons is larger than the weight population. Thus, optimal neural network have to be searched between these bounds.

The database is organised in two main categories: training and test categories. The training set data are picked out randomly and varied between 0% to 100%, where the percentage is expressed with respect to the whole database.

Step3: performing the analysis

Training category is used to tune the neuron connections, i.e., weights [20]. In the test procedure, experimental sets are used without correcting any weight. The convergence of the procedure is obtained if the error evolution of the training and test steps stabilise. The procedure is robust if these quantities are close to each other and small enough. The error is obtained by comparing the experimental and numerical response for a given input condition.

Results and discussion

Fig. 5 shows a typical optimisation procedure of the ANN structure. The convergence criteria are two average and two maximum errors. The evolution of training errors as function of iteration level up to 1000 itrs well depicts the stabilisation of the convergence criteria beyond 300 cycles (Fig. 5a). We have selected a small iteration number compared to what is reported in the literature because we have used an efficient training algorithm that can lead to significant overtraining. The final iteration number is large enough to obtain a steady state asymptotic error evolution (significant changes are within the first 300 iterations). The maximum iteration number is lower than 10 000 to avoid overtraining. Fig. 5a well shows that overtraining is not attained since the maximum error is higher than the average error. When increasing the number of neurons from 1 to 6, the final training error decreases. Such a decrease is explained by the increase of the weight number (increase of connections between neurons). This has the consequence to give more variables to the system to find the best weight configuration with respect to a given set of submitted samples. However, when the weight number is too large, the prediction beyond the operating window becomes less evident to trust because a proper prediction requires more experimental sets. In our case, we do not need to have a large neuron number as suggested in Fig. 5a because even in the worst case (one unique neuron in the hidden layer), the maximum error is still less than 5%. Fig. 5b shows the evolution of the test criterion for a training database size of 70%. Convergence of the criterion is obtained irrespective of the neuron number. In particular, with two neurons in the hidden layer, the test errors are the smallest ones. The difference between the maximum and the average error seems more significant compared to the training procedure. is sufficient to enforce the convergence whatever is the neuron number. It seems that at

Tr=50%, the error decreases with the decrease of neuron number. Two optimal configurations are found corresponding to (NN=2, Tr=70%) and (NN=6, Tr=50%).

In the case of test procedure, the predicted map contains discriminating information (Fig. 6b)

as we can see clearly that the decrease of training samples (i.e., the decrease of test database size) predicts the minimum error. The influence of the neuron number is minor. Thus, it makes sense to choose the configuration (NN=2, Tr=70%) as being the optimal condition.

Our selection is based on the fact with 2 neurons the weight population is reduced so that the predictions are more reliable. This situation is comparable to searching optimal function with few parameters to fit the experimental data. Of course, selecting the optimal neural structure based on a smaller training set would be also reasonable. The result of the optimisation procedure described above is still valid for the two other outputs. In the following, the exploitation of the ANN predictions is detailed. This exploitation considers the optimal ANN structure for which the weight parameters are fixed.

It considers also different combinations of input parameters varied in a continuous way and for which the outputs are calculated for each input combination.

Fig. 8a shows the effect of varying separation distance and the oxygen jet diameter on the value of lift-off height of flame for a given value of ng d . Z lo is found to be the highest one for a large S and a small ox d values. The tendency seems to be polynomial rather than linear. The increase of S delays the mixing of reactants and consequently the combustion starts later at larger distances from burner. This obvious result is well reported in the literature [11][12]. The decrease of ox d leads to the increase of the oxygen jet velocity because a fixed flow rate is used. Thus, the flame base is moved far away from the nozzles exits [11,[22][23][START_REF] Schefer | Proc. Int. 22 th Symposium on Combustion/The Combustion Institute[END_REF][START_REF] Cessou | [END_REF]. Fig. 8b shows the same evolution map for a larger ng d value. Despite the similar tendency obtained using the combination of S and ox d (i.e., the increase of Z lo is correlated to the increase of S/ ox d ), a smaller domain where this effect prevails is noticed. Indeed, as illustrated in Fig. 8b, the region below the solid line exhibits the smallest Z lo values. In fact, a small natural gas jet diameter increases the jet velocity because of the constant flow rate. Thus, when increasing The effect of the burner parameters on horizontal position of flame base is shown in Fig. 9.

When combining S and ox d for a fixed value of ng d , it is predicted that X lo increases non- linearly only with the increase of S for any particular value of ox d (Fig. 9a). In fact, the horizontal position of the stabilisation point is fully dependent on the spacing between the jets due to geometrical considerations [4]. When increasing ng d , no major change in X lo is observed either in magnitude nor in trend, which means that the unique control parameter is the spacing between the jets.

The combined effect of separation distance between the jets and the natural gas jet diameter on horizontal position of the stabilisation point is shown in Fig. 9b. The trend is different from the first case. Despite that S is the first control parameter (X lo increases when S increases), The analysis of the third output (the flame length) as function of studied parameters reveals the following ideas summarized in Fig. 10. When combining S and ox d (Fig. 10a), it is predicted that the evolution of L f is positively correlated to the evolution of the product S x ox d . This actually represents the unique combination of burner parameters where an interaction effect is highlighted. Indeed, when comparing this result to that corresponding for example to the combination (S, ng d ), it is found that only S has an effect on L f (Fig. 10b). This is also confirmed by the last trend (Fig. 10c) where the increase of L f is only attributed to the increase of ox d . The prevailing effect of S can be deduced from the mixing process of natural gas and oxygen for which the increase of S means a delay of the combustion start and an increase of the flame length [3].

In order to quantify all the previously mentioned correlations, fitting routine is applied on the predicted data. Table 4 summarizes the coefficients of a simple regression applied for all studied outputs ( )

3 3 3 3 2 j i i i j ij 1 2 3 i 1 i 1 i 1 j i y a x x x x 1 x x x = = = > = + + + -δ + ∑ ∑ ∑ ∑ (4)
where a is a constant value, y j is one of the output responses (L f , X lo, Z lo ) and x i is one of the inputs (S, ox d , ng d ), δ is the Kronecker operator.

Conclusions

The combined effect of burner parameters (S: separation distance between the jets, ox d and ng d : the jet diameters of oxygen and natural gas, respectively) on the studied flame characteristics suggests the following correlations:

• Lift-off height of flame is dependent on all burner parameter interactions in the sense • The flame length is predicted to depend positively on all parameters. Combining S and ox d allows better results (in this case, the interaction term is 0.64). S and ox d represent here the most influential parameters to vary L f .

Figure captions

  calorific value (NCV) is 45 MJ/kg. Fuel and oxidizer flow rates are constant for all experiments to ensure constant power flames of 25 kW (

  The lift-off positions (vertical position, Z lo and horizontal position, X lo ) and the flame lengths L f are given as a function of nozzle diameters ( ng d and ox d ) and the separation distance between the jets (S). The horizontal position of flame lift-off (or radius) has a zero value at the centre of the central jet of the natural gas.

  : definition of the input/output sets Three burner parameters (the internal diameters ng d , ox d and the separation distance between the jets S) are attributed each one neuron. This set of neurons represents the input pattern. The output pattern represents the flame characteristics (the vertical and horizontal lift-off positions Z lo , X lo and the flame lengths L f ). All variables are expressed in a dimensionless form.

Fig. 6

 6 Fig.6shows the training and test error maps after an optimisation procedure performed on the

Fig. 7

 7 Fig. 7 compares the experimental and predicted responses at the final iteration level in the

  ng d , smaller Z lo values are expected for a given combination of S and ox d .

Fig. 8c depicts

  Fig. 8c depicts the effect of S and ng d on Z lo for a given value of ox d . It is clearly shown here

  ng d plays a secondary role as predicted in Fig. 9b (slightly higher levels of X lo are predicted when increasing ng d ). In Fig. 9c is presented the evolution of X lo as function of ng d and ox d . Again, the effect of ng d is predominant compared to ox d . The higher is ng d value, the larger is X lo response. This last trend confirms the previous results (Figs. 9a, 9b) in the sense that a classification of the influential effects can be deduced based on the analysis of all maps shown in Fig. 9. In fact, S is the major control factor, ng d is the intermediate one and ox d has the smallest effect. The interaction effects are more subtle except when combining S and ng d .

that larger heights are proportional to single terms: - 8 •

 8 The horizontal position of the flame lift-off is dependent on a unique burner parameter interaction 0.01(S ng d ). If we exclude the former interaction term, a simple linear correlation (R²=0.92) is sufficient to represent truly the correlations. This correlation highlights the prevailing role of S and ng d compared to ox d : X lo ∝ 0.3

Fig. 1 .Fig. 2 .

 12 Fig. 1. Schematic diagram of separated-jet burner.

Fig. 3 .

 3 Fig. 3. Example of image processing of the lift-off zone of a flame issued from an oxy-fuel

Fig. 4 .Fig. 5 .

 45 Fig. 4. (a) Examples of OH instantaneous images at the flame top and (b) their corresponding

Fig. 6 .Fig. 7 .

 67 Fig. 6. (a) training and (b) test error maps relative to the output Z lo as function of neuron

Fig. 8 .

 8 Fig. 8. Predicted maps of Z lo as function of studied parameters. (a) ng d =4, (b) ng d =11, (c)

Fig. 9 .Fig. 10 .

 910 Fig. 9. Predicted maps of X lo as function of studied parameters (a) ng d =5.8, (b) ox d =13 (c)

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .

 1234 Fig. 1. Schematic diagram of separated-jet burner.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Evolution of the average and maximum convergence criteria as function of iteration

Fig. 8 .Fig. 9 .Fig. 10 . 1 Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .Fig. 10 .

 8910112345678910 Fig. 8. Predicted maps of Z lo as function of studied parameters. (a) ng d =4, (b) ng d =11, (c)

Table 1 .

 1 Operating conditions of the burner parameters.

	Table(s)
	Central natural gas jet	One lateral oxygen jet
	d ng (mm)	0 ng U (m/s)	Re ng	d ox (mm)	0 ox U (m/s)	Re ox
				6	25.4	10792
	4	53.3	16152	8	14.3	8101
				10	9.1	6444
				6	25.4	10792
	6	23.6	10727	8	14.3	8101
				10	9.1	6444
	8	13.4	8121	6 8	25.4 14.3	10792 8101

Table 2 .

 2 Experimental database used to assess lift-off positions of flame (Z lo and X lo ) and flame length (L f ) as a function of nozzles diameters (for the natural-gas ng and the oxygen jet, ox d ) and the separation distance between the jets (S).

			Inputs			Outputs
	Exp. #	ng d (mm)	ox d (mm)	S (mm)	Z lo (mm)	X lo (mm)	L f (mm)
	1	4	6	7	56.14	3.31	463
	2	4	8	8	14.43	3.19	527
	3	4	8	12	44.27	4.91	568
	4	4	8	16	77.90	6.31	-
	5	4	10	9	10.54	3.26	-
	6	4	10	12	27.30	4.53	-
	7	4	10	16	39.96	5.83	-
	8	6	6	8	19.03	3.94	461
	9	6	6	12	46.08	6.55	520
	10	6	6	16	61.78	8.52	548
	11	6	6	20	74.71	10.47	593
	12	6	6	30	92.08	13.90
	13	6	8	9	11.84	4.17	564
	14	6	8	12	23.77	5.54	580
	15	6	8	16	38.39	7.36	611
	16	6	8	20	49.12	9.14	656
	17	6	8	30	75.16	12.38	-
	18	6	10	10	-	-	-
	19	6	10	12	18.35	5.41	-
	20	6	10	16	28.64	6.80	-
	21	6	10	20	43.34	8.53	-
	22	8	6	9	11.69	4.93	452
	23	8	6	12	16.62	6.64	517
	24	8	6	16	33.19	8.65	507
	25	8	6	20	47.48	11.19	592
	26	8	8	10	-	-	568
	27	8	8	12	17.48	6.00	582
	28	8	8	16	28.82	7.95	608
	29	8	8	20	45.92	9.90	672

Table 3 .

 3 Window range of the studied parameters.

			Inputs			Outputs
	Limit	ng d (mm)	ox d (mm)	S (mm)	Z lo (mm)	X lo (mm)	L f (mm)
	x Min	4	4	7	0	0	0
	x max	20	20	50	-	-	-

Table 4 .

 4 Regression coefficients based on ANN predicted results and using different approximations.

		a	d	ox	d	ng	S	ox d ²	ng d ²	S ²	ng d x ox d	ox d xS	ng d xS	ng d x ox d xS	R²
		109 -8.1 -8.3 -0.26 0.029 0.033	0.014	0.515	0.143	0.138	-0.016	0.92
	Z lo	43 -2.6 -2.8 2.0 69 -3.3 -3.6 0.82 0.03 0.03	0.03 0.03	0.01 0.01	0.06	-0.05	-0.05		0.89 0.86
		53 -2.6 -2.8 1.6								0.85
		-4.4 -0.13 0.67 0.68 0.0010 -0.0031 -0.0048 0.0040	0.0022	-0.0092	-0.0001	0.99
	X lo	-4.7 -0.11 0.69 0.69 0.0010 -0.0030 -0.0048 0.0017 -2.1 -0.04 0.44 0.59 0.0004 -0.0036 -0.0048	0.0012	-0.0102		0.99 0.97
		1.3 -0.03 0.35 0.31								0.94
		-76 76 0.85 18	-1.2 -0.0004 -0.0586 -0.0002 -0.6230	0.0099	-0.0016	0.99
	L f	-82 77 1.40 18 147 58 0.58 11	-1.22 -0.0004 -0.059 -1.22 -0.0004 -0.06	-0.05	-0.64	-0.0094		0.99 0.93
		328 29 0.58	7								0.90

Two main convergence criteria are studied: the average and maximum errors calculated with respect to the submitted cases. The average quantity is expressed as a mean square error.

Step4: solving the problem of equivalent ANN structures

The ANN structures (obtained by varying the neuron number) are classified based on the smallest training and testing errors and also on the basis of the lowest percentage of the data in the training set used for the optimisation. Table 1. Operating conditions of the burner parameters. Table 2. Experimental database used to assess lift-off positions of flame (Z lo and X lo ) and flame length (L f ) as a function of nozzles diameters (for the natural-gas jet, ng d and the oxygen jet, ox d ) and the separation distance between the jets (S).

List of Tables


Hazar Ben Barka

Sarah Mokaddem

Nature of the Director's profile and Knowledge Transfer in Corporate Social Responsibility: A Literature-based Approach

Keywords: Profile of the director, Knowledge Transfer, Board of Directors' Network. Behavioral Governance, CSR Profil de l'administrateur, Transfert de connaissances, Réseaux du conseil, Gouvernance comportementale, RSE

Board Interlocks could have a positive effect on the adoption of governance practices and especially on the Corporate Social Responsibility (CSR). We surpass the predictions of the agency theory by proposing a cognitive-behavioral approach of governance to define the role of director. Given the lack of previous researches, a literature-based approach comes as a necessity. We study the connection between the nature of the director's profile and the knowledge transfer in CSR practices; and this could be beneficiary for the boards of directors. We underline the importance of individual director characteristics such as identification, recognition or motivation in the success of this transfer.

Empirical researches recognize two primordial roles in the board of directors. The roles are controlling the management team and protecting shareholders' interests as stipulated in the agency theory [START_REF] Fama | The Separation of Ownership and Control[END_REF]Jensen, 1983, Ferris, Jagannathan and[START_REF] Ferris | Too busy to mind the business? Monitoring by directors with multiple board appointments[END_REF]Monks andMinow, 1996, Perry andPeyer, 2005). On the other hand, the resource theory (Pfefferet and Salancik, 1978;Villiers, Naiter et Van Staden, 2011) presents the board of directors as a "co-leader" of the management team. This gives way to say that it has a role to assist and monitor the strategic choices of Management, and watch over the risk management as well (Johnson, Daily an Ellstrand, 1996;[START_REF] Charreaux | Discipline ou compétence ? L'apport des perspectives cognitives et comportementales à la compréhension des mécanismes de gouvernance d'entreprise[END_REF]Guieu and Meschi, 2008).The commitment concerning Corporate Social Responsibility (CSR) is one of the axes that a board of directors has to include in the approval of the risk map. The research of Villiers, Naiter and Van Staden (2011) validates the predictions of both theories. Consistent with agency theory, the authors find a positive relationship between environmental performance, higher board independence and lower concentrations of directors appointed after the nomination of the CEO. Furthermore, consistent with resource dependence theory, a larger board with legal experts and larger representation of active CEOs is associated with higher environmental performance.

The evaluation of the role of directors in engaging in CSR supposes first that they are aware that as there is a potential financial or operational risk, there is a CSR risk too. Plus, the CSR risk has to be integrated into the definition of the global strategy of the company. We can distinguish two research groups. The first studied the relationship between board composition and the environmental performance (Villiers, born and Van Staden, 2011) and the second focused on the study of the relationship between directors and the spreading of good governance practices, in reference to networks theory (Davis et al, 2003;Robins and Alexandre, 2004;Shropshire, 2010). As we know, the relationship between the three parameters (director's profile, knowledge transfer and adoption of CSR practices) has not been sufficiently developed. Choosing to study the profile of the director has led us to surpass the assumptions of the agency and resource dependence theories to propose a behavioral and organizational approach. The purpose is to investigate the impact of the director's profile on the success of a knowledge transfer through a dissemination of good governance practices in CSR. Although the phrasing of the objective in this paper presents a knowledge transfer process where the director's profile is the input and the adoption of CSR practices is the output, we opted for the proposal of a conceptual model that does not claim a predefined sense of relationships between the three parameters (see Figure 1, page 2). This choice is justified by the lack of researches that has already dealt with the subject and the possibility that one of the parameters could have a moderating effect in defining the relations of the two other parameters.

To clarify the role of director's profile and board interlocks on the adoption of CSR practices, a theoretical work is as important as an empirical one. Most formalistic network approaches reveal powerful effects of configurations such as the degree of connectivity or centrality of a company member's cluster. These results, based on algorithm methods, are very interesting but should not be considered as the end products of research process (Alder and Kwon, 2002, p 35). A better understanding of social network and board interlocks needs to develop, in the same time, a conceptual framework that integrates the different theoretical perspectives. In fact, the concept of social capital has been treated by a wide range of social science disciplines (sociology, economics, organization etc.) which proposes different answers to the problems exposed in their own fields. Moreover, the studies of organizational behavior interact with the individual, the corporate as well as the interfirm levels. We believe that a literature-based approach is first required as it allows identifying some of the key issues under debate before embarking in empirical approach.

Figure1-Proposed Model

The structure of our paper is as follows. First, we will present the conceptual framework that processed the issues of knowledge transfer in the board of directors. Second, we will discuss the relationship between governance and CSR by highlighting the role and the responsibility of director. We will end with concluding and presenting the limitations of this study and the possibilities for future researches. Knowledge transfer has become a central concept in the field of research in strategic management and corporate governance. Indeed, several authors consider it as fundamental explanation element of the existence of the firm itself [START_REF] Conner | A resource-based theory of the firm: knowledge versus opportunism[END_REF]Spender andGrant, 1996, Nonaka and[START_REF] Argote | Knowledge transfer in organizations: learning from experience of others[END_REF]. In addition, many other researchers who work on inter-organizational relationships refer to the knowledge transfer as a central issue [START_REF] Dyer | The relational view: cooperative strategy and sources of interorganizational competitive advantage[END_REF]Tsang, 1999, Simonin, 2004). According to Tsoukas (1996), knowledge in the organization is distributed among individuals or between units. The company will then seek to take advantage of the different expertise through the knowledge transfer [START_REF] Argote | Knowledge transfer in organizations: learning from experience of others[END_REF]. Note here that the network represents an ideal scene for learning new knowledge (Powell, 1998). Thus, the management of knowledge in network allows the company to adopt easily new knowledge but also to create a situation where it is no longer necessary for it to have an exclusive ownership of knowledge for profit (Powell, 1998). Furthermore, the management of a network for a learning objective allows the creation of common knowledge that is source of relational annuities [START_REF] Dyer | The relational view: cooperative strategy and sources of interorganizational competitive advantage[END_REF]. These are related, among other things, to the existence of complementary knowledge and modes of governance based on relational principles (trust, shared values). What is most interesting in this paper is the knowledge transfer between individuals in different organizations and this does not necessarily presume formal intentions for organizations to cooperate but rather individual initiatives moderated by various parameters [START_REF] Ben Hadj Mbarek | Influence des réseaux d'administrateurs sur la stratégie de la firme: Application au cadre des partenariats stratégiques[END_REF]Shropshire, 2010).

Knowledge Transfer and Board Interlocks

Knowledge transfer

Director's profile CSR practices

Networking and spreading practices

The board interlocks are a privileged channel for knowledge transfer and could play an important role in the adoption of certain governance practices [START_REF] Del Vecchio | Réseaux de conseils d'administration et adoption de pratiques de gouvernance d'entreprise[END_REF]. Thus according to [START_REF] Davis | Corporate Elite Networks and Governance Changes in the 1980s[END_REF], changes in governance practices in a board of directors could be explained by a process of adaptation to observed practices in other boards in which the directors sit. Therefore, board interlocks could have a positive effect on a board's cognitive role and the adoption of governance practices (Mizruchi, 1996, Westphal andZajac, 1997). Conyon and Muldoon (2006) implement the economic model of "small worlds" founded by Jackson and Rogers (2005) in the context of corporate governance. The two researchers differ from other previous studies on "social network" by the context chosen (Davis et al, 2003;Robins and Alexander, 2004). Indeed, they demonstrate, by comparing data boards of directors in three countries (the United States, England and Germany), the importance of graph theory1 in the understanding of the boards of directors 'functioning. They investigate not only the connectivity between the boards but also the one between the directors of the boards. Conyon and Muldoon (2006) find a positive relationship between the directors who combine a high number of terms. « Big-Hitters associate with big hitters and low hitters associate with other low hitters», which is defined by sociologists as "homophily" (McPherson et al. 2001). [START_REF] Charreaux | Le point sur…les réseaux d'administrateurs et les dirigeants[END_REF] insists on the importance of socio-strategic theories2 (Mizruchi, 1996) in comparison with financial theories in the evaluation of the role of directors interlocks. He argues that they provide better understanding of the performance, the financial behavior and the distribution of certain corporate governance practices. These theories provide a supportive environment that takes into account the cognitive functions, the contingency to a strategy, and the ambiguity of defining the meaning of the relationship between the board and performance. Henceforth, the board is a place for learning and a provider of cognitive resources (Charreaux and Wirtz, 2006). Del Vecchio (2010) confirms that board interlocks are a way of acquiring knowledge and skills. She adds that the density of relations and their concentrations around an actor are the key parameters to promote the efficiency of a network.

The knowledge transfer or the adoption of best practices could be dilemma-arising terms. We refer to the Shropshire's definition of knowledge transfer which presents it as an initial action in a stepwise multilevel process of diffusion (Shropshire, 2010, p 259). A process that begins with an individual action and then gets moderated by the context (see Table 1, page 4). The spread of best practices would be then the output of this process. Indeed, understanding the organizational behavior and especially that of the board in our "case-study" assumes a multidisciplinary approach that integrates several micro-and macro-economic factors and goes beyond the scope of a single theory [START_REF] Fama | The Separation of Ownership and Control[END_REF]Hitt, Beamish, Jackson andMathieu, 2007 cited in Shropshire, 2010). However, the measurement of certain variables that allow the understanding of the operational process of a board remains perplexed. The director's knowledge transfer across board interlocks, by the diffusion of best practices is affected by the directors' individual characteristics like his competence and his profile; but it is also be affected by the structure of the board, its receptivity and by the environment in which it operates (Shropshire, 2010[START_REF] Del Vecchio | Réseaux de conseils d'administration et adoption de pratiques de gouvernance d'entreprise[END_REF]. In this paper, we focus on the individual parameters of the director.

Individual parameters of the director for a knowledge transfer

The agency theory emphasizes motivation as a factor that determines the success of the board in its monitoring role. However, the resources dependence theory is more focusing on the structure and composition of the board. Combining these two approaches in the study of the role and functioning of the board would be inevitable. Indeed, the board structure has an impact on the success of its control role and on the integration of new resources on the board but the board's motivations can also moderate these relationships (Hillman and Dalziel, 2003). Note that the role of the board cannot be reduced to the disciplinary dimension, but must rather be considered as a working group whose output is essentially cognitive and Milliken, 1999). Indeed, board directors could be associated with the concept of social capital. The definitions of this concept, provided by many researchers, are highly influenced by their fields' requirements (Burt, 1992;Coleman, 1990;Pennar, 1997;cited in Adler and Kwon;2002). One of the definitions is [START_REF] Adler | Social capital: Prospects for a new concept[END_REF], which states that the social capital is the resource available to actors as a function of their location in the structure of their social relations. [START_REF] Adler | Social capital: Prospects for a new concept[END_REF] identify three sources of social capital: opportunity, motivation and ability. This identification responds to the development that follows.

The motivation of a director to transfer his knowledge and the degree of influence that he can exert on the board to adopt its recommendations, are very crucial. The theoretical framework developed in social networks (Ashforth and Mael, 1989;[START_REF] Foreman | Members' Identification with Multiple-Identity Organizations[END_REF] marks the identification as a first parameter of the director's motivation. A director who identifies himself to the corporation in which he works is likely to be more motivated to get engaged and share experiences with the board (Harrison and al. 2002). In addition, a desire for recognition as a good director by the market and the opportunities to have other terms are other motivation's sources (Hillman and Dalziel, 2003;[START_REF] Westphal | Keeping directors in line: Social distancing as a control mechanism in the corporate elite[END_REF]. Directors could also be driven by "instrumental motivation" [START_REF] Adler | Social capital: Prospects for a new concept[END_REF]. They cultivate and exploit social capital to advance their careers. However, this motivation may be questioned by the risk of an attitude of complacency with interpersonal behaviors between different directors. [START_REF] Westphal | Flattery will get you everywhere (especially if you are a male causasian): How ingratiation, boardroom behavior, and demographic minority status affect additional board appointments at U.S. companies[END_REF] cited the example of being in favor of certain decisions in order to validate other ones or to have directorships in other companies. However, directors could also be motivated by "normative commitment" or norms of generalized reciprocity which could transform an individual from egocentric agent into member of a community with shared interests [START_REF] Adler | Social capital: Prospects for a new concept[END_REF].

Added to the director's motivation, his profile can be considered as second criterion to be adopted in the definition of knowledge transfer. We invoke three points that we consider important in defining this profile: the degrees of proximity to the CEO, the extent of professional experience and the power to veto any decisions of the CEO. In fact, belonging to a group of majority in the board enhances the contribution of the director and gives more value to his information. Researchers have identified several dimensions such as gender, race, degree, and industry expertise to distinguish this group of majority who are most influential on the board [START_REF] Westphal | The other pathway to the boardroom: interpersonal influence behavior as a substitute for elite credentials and majority status in obtaining board appointments[END_REF]. Directors who have easy access to the CEO usually have a hearing board which is more receptive to their experience and knowledge [START_REF] Golden | When will boards influence strategy? Inclination x power = strategic change[END_REF]. The CEO shares with them the same route as serving in other boards, being a member of some philanthropic associations or simply a member in the same club (Kramarz and Thesmar, 2007).The chairmen give more trust to their suggestions and experiences. These social connections and affinities between the directors of a board help promote certain standards of behavior in defining the role of an outside director and in facilitating knowledge transfer (Shropshire, 2010). Concerning the board's ability to balance the power of the CEO, empirical researches specifically highlight the ability of the board, if necessary, to initiate or inhibit the corporate strategy [START_REF] Westphal | Collaboration in the boardroom: The consequences of social ties in the CEO/board relationship[END_REF][START_REF] Golden | When will boards influence strategy? Inclination x power = strategic change[END_REF].

"With a powerful CEO, decisions are more likely to reflect the CEO's preferences and experience, rather than those of interlocking directors." (Shrophire, 2010, p 255) In addition to his motivation and the quality of his relationship with the CEO, the director's experience facilitates his ability to provide a plus to the board; For example, living the single case of renewal of the CEO, acquisitions, planning etc. [START_REF] Finkelstein | Not the usual suspects: How to use board process to make boards better[END_REF]. His aptitude to do that can be defined not only through the cumulative number of directorships in other boards but also through the function performed (Executive director, special committee member or chairman of a committee). However, does the responsiveness of the board to the director's experiences tend to decrease under their heavy presence in other boards, as the board's attention will be shared between all these directors? The composition of the board and especially the demographic diversity can make decisions-making more complex. This diversity presents both advantages and limitations in terms of speed of decision making, quality of debate and what these discussions lead to (Harrison, Price, Gavin, and Florey, 2002). Nevertheless, Guieu and Meschi (2008) found, in studying the boards of major European groups, that the cognitive function of the board is facilitated by its large size (which allows the diversity of directors) and the multiplicity of weak links between directors.

Towards a socially responsible governance

Divergence or convergence of two concepts: governance and CSR?

Following the financial scandals of large corporations such as Enron and Parmalat, the governance and the diligence of the board are becoming the concern of regulators, rating agencies, financial analysts etc. Moreover, the importance of CSR and the Socially Responsible Investment (SRI) has increased considerably in recent decades. Indeed, companies are forced to include this parameter in their overall approach. Before discussing the possible interrelationships between governance and CSR, it would be appropriate to point out the ambiguity of these two concepts.

CSR is a complex concept (Goebbels, 2001;Henderon, 2001;[START_REF] Allouche | Responsabilité sociale des entreprises : la mesure détournée ?[END_REF]). This complexity is reflected first through the conceptualization deficit [START_REF] Dupuis | La responsabilité sociale de l'entreprise: gouvernance partenariale de la firme ou gouvernance de réseau[END_REF]. Money and Schpers (2007) refer to the results of the study by KPMG in 2005 to discuss a change in the definition of CSR. Indeed, CSR is initially limited to the purely environmental issues. It reflects today's sustainability issues and the way a corporate culture is established in large listed companies. The same way, Saulquin and Schier (2005) provide the definition of CSR with the concept of "social construction of co-performance". Indeed, they present it as a process of redefining the mission and the company purpose, more in line with new environmental constraints and new expectations of stakeholders. The performance is then the result of a social co-construction between the company and its stakeholders. According to Van Marrewijk (2003), CSR is the overlap between several concepts such as sustainable development, business ethics, responsible entrepreneurship or the "Triple Botton Line" which is the evaluation of the social, environmental and economic performance.

Responsible management according to the European Commission (EC) referred in 2004 to a voluntary integration by companies of social and environmental concerns in their business operations and their relationships with stakeholders as well. In 2011, the EC presented CSR as an obligation and not as a spontaneous action of the companies. It then proposes to redefine CSR as "corporate responsibility towards the effects they have on society." It aligns with the definition of ISO 26000 and particularly emphasizes the importance of collaboration with stakeholders to perform a process that allows the integration of CSR concerns. In fact, the commitment to a CSR strategy can lead to beneficial consequences for the company in terms of cost reduction, employees' loyalty, better regulations and new knowledge acquisitions (Luetkenhorst, 2004). However, each partner of the company (workers, government agencies, management etc.) has a different interpretation of this concept. In all cases, the sustainability of the company would be the ultimate goal towards which all objectives of CSR should converge (Linnanem and Panapanaan, 2002;Van Marrewijk, 2003).

A very important issue is the kind of relationship that may exist between governance and CSR. Governance has been most often defined as the system by which companies are directed and controlled3 . The first academic works (Berle and Means 1932, Friedman 1962, Jensen and Meckling, 1976) are more shareholder-oriented approach that addresses the problems arising from a separation of capital ownership and management. Since the 80s, a new corporate governance paradigm is appearing. It marks a transfer from shareholder vision to stakeholder vision. This stakeholder approach has influenced concepts in governance and has a certain convergence with CSR [START_REF] Ayuso | Responsible corporate Governance: towards a Stakeholder board of directors?[END_REF]. As we mentioned, CSR assumes a stakeholder approach (Freeman, 1984) that exceeds the company's vision of economic profit as the only objective of any organization. Stakeholder theory could be a "regeneration" of the theory of civil society. In fact, both of them legitimize the interests of all parties [START_REF] Bonnafous-Boucher | Towards a stakeholder society: Stakeholder theory vs theory of civil society[END_REF]. The authors add that the stakeholder theory occupies an intermediate position between strategic management and political philosophy (the sovereignty of big business). Moreover, if the stakeholder theory is generally the theory of reference in dealing with CSR issues, Dupuis (2008, p 68) explains that "CSR practices are not limited to convey a stakeholder governance model. They also participate, equally and even more, to the emergence of networks governance". He emphasizes the ability of flexible firms, operating in network, to adopt CSR practices beyond a regulatory imposing framework. In addition to the theoretical framework, the concepts of governance and CSR converge at the level of obligations of a fiduciary order and the moral responsibility of companies towards stakeholders (Jamali and al., 2007). Indeed, both concepts convey transparency, ethics, and sustainability of the organization. What would be the responsibility of directors towards these new challenges?

Directors and CSR

National and international 4 regulations impose more and more, especially for large listed companies, rigor in extra-financial information disclosure. In France, listed companies have to disclose about the company's commitment to sustainable development and social information (NRE, 2001). They have to improve the quality of the information provided in the annual and the sustainability reports (the law called Grenelle II, 2010). These include verifying the information, giving retrospective and prospective visions that would best assess and measure. Societal data provided in these documents has become enforceable and directors' liability may be incurred 5 . Indeed, the Chairman should be responsible for the nomination of an organism accredited of data Grenelle II by the French Accreditation Committee (COFRAC). At the end of the audit, a report certifying the accuracy of the information and describing the procedures implemented as part of the mission, should be delivered. The information which deals with the commitment and CSR is no longer embedded in the report of the external auditor. Henceforth, it is the subject of a specific report.

Beyond the regulations compelling, CSR has become a priority and the board must integrate this dimension in its agenda. However, the priorities may vary depending on the status of the director. Furthermore, a survey conducted by PriceWaterhousCoopers PwC (2007) with the directors of the CAC 40, shows that the employed directors are the most sensitive to different CSR issues that refer to internal environment (working conditions, relations with NGOs, solidarity actions etc.). The chairmen pay more attention to the economic development component of long-term business. As for independent directors, the highest priorities are the policy of the company ethics and the respect for the environment. Note that the evolution of the conceptual framework of governance has led to more expectations and to greater commitment of the board in CSR [START_REF] Ayuso | Responsible corporate Governance: towards a Stakeholder board of directors?[END_REF]. In fact, the approach to shareholder governance stops at the monitoring role of the board of directors. It presents them as defendant shareholders. The stakeholder theory deals with the composition of the board into two levels [START_REF] Ayuso | Responsible corporate Governance: towards a Stakeholder board of directors?[END_REF]. The first is the normative approach which deals with ethical and moral questions. This approach proposes a board composition which represents the various stakeholders and their different interests. The Companies with securities traded on regulated market and the companies which have more than 5000 employees with total assets or sales tax-free over a billion euros, have to verified non-financial information provided in regulated reports from 31/12/2011. A phased implementation schedule is set for other types of companies. second is the instrumental approach which focuses on the increased performance and business value where the board is presented as a human and social capital (Hillman and Dalziel, 2003). This brings us to the role of the boards' networks in a successful transfer of knowledge on CSR together with the impact of the individual criteria such as experience, expertise and profile of the director. Most researches are more focused on ethical issues such as executive compensation, board structure or board composition that would allow more responsible governance to take place (Villiers, Naiter and Van Staden, 2011). In the recent years, the cognitive approach has been adopted in the treatment of the boards' role. It considers the inclusion of CSR by the board as an enrichment of the role of the director rather than an additional responsibility. Moreover, it is a contribution to value creation. That is to say, ensuring the ethics of the team management helps the board to increase the team flexibility and managerial opportunities for value creation. To best meet these new responsibilities, directors are encouraged to learn and train on specific issues and evolving businesses. The transfer of knowledge in this area, that board interlocks can guarantee, is one of the parameters of a continuous training and a conscious commitment of directors.

Conclusion

Evaluating the success of directors in fulfilling their duties within the board, should not be restricted to the study of a simple relationship with the financial or social performance. Also, if they may be held liable for the information disclosed in the reference documents, a simple regulatory compliance to CSR is not enough to assess their contribution to the dissemination of these practices. The inter-organizational approach overcomes the institutional approach in assessing the contribution of a director on the board [START_REF] Charreaux | Le point sur…les réseaux d'administrateurs et les dirigeants[END_REF]. Indeed, the interorganizational strategies, based solely on individuals, not on the organizations that are in these social networks of boards, have an impact on the behavior of different individuals belonging to these networks and on the practices of the organizations in which they operate (McPherson and al, 2001). Individual parameters such as attitudes, personality, demographic differences of the directors (gender, training, social status, proximity to the CEO) allow to measure the integration level of the director on the board and the possibility of a collaboration [START_REF] Harrison | Beyond relational demography: Time and the effects of sur-face-and deep-level diversity on work group cohe-sion[END_REF]al. 1994, Harrison andal. 2002). Even if we focused in this paper on the director's profile that is about the knowledge transfer and dissemination practices, other contingency or contextual parameters can act as the turbulence of the environment or the degree of compliance of the organization (Shropshire. 2010). Additionally, an exploratory empirical research would allow the investigation of the most significant criteria of the profile of the director in the definition of knowledge transfer in CSR, through a case study or a quantitative research.

4

  Tripartite Declaration of the International Labour Office (1977), Green Paper (2001) by the European Union, new economic regulations NRE (2001) and Authorities of the Financial Markets AMF in France, etc. 5 In France, section 225 of the Act which became article 2 Grenelle 225-102-1 of the commercial code, called for the serious of the disclosure of extra financial information.

Table 1 -The role of interlocking director and Board receptivity in the diffusion of practices Levels Summary Factors That INCREASE the Likelihood of Diffusion Summary Factors That DECREASE the Likelihood of Diffusion The role of the interlocking director in knowledge transfer

 1

		Organizational identification	Ingratiatory behavior
		Access to CEO	Breadth of board experience
		Minority experience
		Focal board committee membership
		Depth of focal board experience
		Breath of experience
		Interlocking director status
	Board receptivity	Board power Board diversity Focal firm centrality Interlocked/focal firm status	Strategic conformity Environmental turbulence Focal firm centrality
		Interlocked/focal firm age
	Source: Shropshire, C. 2010. "The role of the interlocking director and board receptivity in the diffusion of
	practices", Academy of Management Review, V 35, N° 2, p 258.

Graph theory (1735) is a computer and a mathematical theory. It's used in several areas, including those related to the concept of social network. According to the vocabulary of this theory, a graph is a set of points; some pairs are directly connected by a link. These links can be oriented or not.

The theories offer explanations of social networks based relative to strategies. Networks can meet the interests of organizations or individual connected. The links are not established on a voluntary basis as is recommended in the inter-organizational theories.

The Cadbury code definition, 1992.

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