Khaled

Khaled Chetehouna
email: khaled.chetehouna@insa-cvl.fr

Eddy El Tabach

Loubna Bouazaoui

Nicolas Gascoin

Predicting the flame characteristics and rate of spread in fires propagating in a bed of Pinus pinaster using Artificial Neural Networks

Keywords: Forest fires, Rate of spread, Flame geometrical characteristics, Simulation metamodelling, Artificial neural networks, Backpropagation

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Predicting the flame characteristics and rate of spread in fires propagating in a bed of Pinus pinaster using Artificial Neural Networks

Introduction

Forest fires have always existed and nowadays, due to climate changes, they are becoming a growing threat for human life and ecosystems in the world. Every year, the average areas of forest destroyed by fire in the world and in Europe are about 28 and 1.6 million hectares respectively. Moreover, in Europe the burnt area increases annually, a trend likely to continue as the World Health Organization identified fire as a growing threat for the coming years because of global warming. Despite the dramatic rise of forest fires all around the world, currently, 11 hectares per second burn in the whole world, it is noticeable that forest managers have always tried to increase their efforts towards fighting forest fires, but in many cases the main problem comes from determining the current state of the fire front. This valuable information can be described by the geometrical characteristics of the flame (position, height and tilt angle) and rate of spread. Some authors have measured these physical and geometrical characteristics of the flame using thermal and/or image processing techniques [START_REF] Zhou | Experimental measurements and numerical modeling of marginal burning in live chaparral fuel beds[END_REF][START_REF] Pastor | Computing the rate of spread of linear flame fronts by thermal image processing[END_REF][START_REF] Ononye | Automated extraction of fire line parameters from multispectral infrared images[END_REF][START_REF] Chetehouna | On the experimental determination of flame front positions and of propagation parameters for a fire[END_REF][START_REF] Martinez-De Dios | Computer vision techniques for forest fire perception[END_REF][START_REF] Rudz | Metrological Tool for the Characterization of Flame Fronts Based on the Coupling of a Heat Flux Approach with Image Processing Data[END_REF]. In addition, it was shown that these parameters depend on wind velocity, fuel moisture content and slope of ground surface [START_REF] Viegas | Slope and wind effect on fire propagation[END_REF][START_REF] Boboulos | Wind and slope effects on ROS during the fire propagation in East-Mediterranean pine forest litter[END_REF].

Studies of the effects of these factors are carried out in laboratory conditions [START_REF] Anderson | Fire spread and flame shape[END_REF][START_REF] Adkins | Flame characteristics of wind-driven surface fires[END_REF][START_REF] Bradstock | Fire in semi arid, mallee shrublands-size of flame from discrete fuel arrays and their role in spread rate[END_REF][START_REF] Dupuy | Slope and fuel load effects on fire behavior: laboratory experiments in pine needle fuel beds[END_REF][START_REF] Morandini | Fire front width effects on fire spread across a laboratory scale sloping fuel bed[END_REF][START_REF] Santoni | Measurement of fluctuating temperatures in a continuous flame spreading across a fuel bed using a double thermocouple probe[END_REF][START_REF] Dupuy | Fires from a cylindrical forest fuel burner: combustion dynamics and flame properties[END_REF][START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF][START_REF] Bartoli | Determination of the main parameters influencing forest fuel combustion dynamics[END_REF][START_REF] Fuentes | Experimental study of the burning rate of small-scale forest fuel layers[END_REF][START_REF] Morandini | Radiant, convective and heat release characterization of vegetation fire[END_REF] or under controlled fires in real vegetation beds [START_REF] Marsdden-Smedley | Fire behaviour modelling in Tasmanian buttongrass moorlands. II fire behaviour[END_REF][START_REF] Burrows | Fire behavior in jarrah forest fuels, Field experiments[END_REF][START_REF] Butler | Measurement of radiant emissive power and temperatures in crown fires[END_REF]. One of the largest database found in the literature about flame characteristics and rate of spread is presented by Mendes-Lopes et al. [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF]. Their experiments were performed in a dedicated burning tray, where wind velocity, fuel moisture content and slope were varied to study fire propagation in beds of Pinus pinaster needles. However, the main drawback is that their experimental tests are costly and they do not cover the entire range of test conditions. Therefore, it is extremely difficult and sometimes impossible to predict the flame characteristics and the rate of spread for new cases which are not included in the database. Thus, having a tool for generalization of new cases is of practical interest for saving time and money.

Other literature sources have focused on the determination of these flame characteristics using physics-based computational fire models [START_REF] Dupuy | Modeling of fire spread through a forest fuel bed using a multiphase formulation[END_REF][START_REF] Morvan | Modeling of one dimensional fire spread in pine needles flame with opposing air flow[END_REF][START_REF] Simeoni | Proposal for theoretical improvement of semi-physical forest fire spread models thanks to a multiphase approach: application to a flame fire spread model across a fuel bed[END_REF][START_REF] Simeoni | Reduction of a multiphase formulation to include a simplified flow in a semi-physical model of fire spread across a fuel bed[END_REF][START_REF] Balbi | A 3D Physical Real-Time Model of Surface Fires Across Fuel Beds[END_REF][START_REF] Morvan | Physical modelling of fire spread in Grasslands[END_REF][START_REF] Balbi | Physical Modeling of Surface fire under Nonparallel Wind and Slope Conditions[END_REF][START_REF] Menage | Numerical simulations of fire spread in a Pinus pinaster needles fuel bed[END_REF]. These valuable approaches are useful to improve the understanding of the mechanisms that are responsible for fire behaviour. On the other hand they need a large amount of computational resources [START_REF] Nmira | Numerical study of wind effects on the characteristics of flames from non-propagation vegetation fires[END_REF] and several input parameters (e.g. heat transfer coefficient, characteristics of thermal degradation, turbulent kinetic energy and its dissipation rate) which are hard to measure or not available in many cases. It is also not possible to integrate observed data directly at desired locations to improve model results. Simplified or reduced propagation models have therefore been developed [START_REF] Margerit | Modelling forest fires. Part II: reduction of twodimensional models and simulation of propagation[END_REF][START_REF] Koo | A simple model for forest fire spread rate[END_REF]. These models generally require input parameters, which depend on the fire itself, such as flame length and tilt angle [START_REF] Nmira | Numerical study of wind effects on the characteristics of flames from non-propagation vegetation fires[END_REF]. Empirical models based on experimental results have been also developped to create relationships between variations in fire behaviour factors and characteristics [START_REF] Pastor | Mathematical models and calculation systems for the study of wildland fire behaviour[END_REF]. For the ability to simulate quickly and accurately, the geometrical characteristics of the flame and rate of spread are of crucial importance in fire forecasting operations.

Here an approach is proposed based on artificial neural networks (ANNs) for simulating the rate of spread (ROS), flame height (H f ) and flame angle (α f ). The ANN provides a quick and flexible approach for data integration and model development. Over the last two decades, ANNs have been successfully used by many researchers for a wide range of engineering applications [START_REF] El Tabach | Use of artificial neural network simulation metamodelling to assess groundwater contamination in a road project[END_REF]. An ANN is based on the substitution of the complex simulation model by an approximation of the input-output relationship. The ANN has the advantage over regression that the form of the model needs not to be pre-determined [START_REF] Kleijnen | Kriging metamodeling in simulation: A review[END_REF]. In addition, the ANN can theoretically approximate any function to any level of accuracy, which is very interesting when the governing physical mechanisms are non-linear like in forest fire propagation behaviour research. The experimental results found in the literature [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF] are used to construct, to optimize and to validate the ANN model. The performance of the proposed ANN model is compared with a multilinear regression approximation method.

Construction of ANN models

Artificial neural networks

In this study, an artificial neural network (ANN) was used to predict the flame height (H f ), flame angle (α f ) and rate of spread (ROS) of a bed of Pinus pinaster needles. An ANN is a powerful mathematical tool used to model non-linear relationships between inputs and outputs without any a priori knowledge of the model. ANN models learn the relationship between the input and the output parameters as a result of training with previously recorded data.

Construction of the database

The database was built using experimental data which were collected from the literature [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF] with input parameters: slope (S), fuel moisture content (FMC) and wind velocity (W) varying in a range of representative values: -15°, -10°, -5°, 0°, 5°, 10° and 15° for S; (101)% and (181)% for FMC and -3, -2, -1, 0, 1, 2 and 3 m/s for W. The fuel bed used in the experiments [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF] is composed of Pinus pinaster needles with a depth of 4 cm and a load of 0.5 kg/m 2 . It should be noted that the negative values of W refer to backing fires and the negative value for S corresponds to down-slope orientation. More information about the experimental procedure can be found in Mendes-Lopes et al. [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF]. Totally, the database contains an appreciable size of 64 experimental test points.

The present database was subdivided in three subsets. A first subset (30 experimental tests) was used to train the network. A second one (16 experimental tests) was used to test the 6/25 ANN models to determine when to stop the training stage. The third subset (18 experimental tests) was used to validate the performance of the selected model on unseen cases.

Each input or output parameter was normalized relative to its minimum and maximum values observed in the data (according to Eq. ( 1)) to make the training procedure more efficient.

    min max min norm X X X X X    (1)
where X is an arbitrary parameter, X norm is the normalized value, and X max and X min are the maximum and minimum values of X respectively.

Architecture and learning process of ANN models

An artificial neural network model is composed of interconnected groups of artificial neurons or nodes. The most frequently utilized network is the multilayer backpropagation neural network (BPNN) which is used in the present study. The BPNN structure consists of three layers, an input layer which receives data; an output layer which sends computed information; and one or more hidden layers to link the input and output layer. All the neurons (nodes) in a layer are connected with all the neurons of the previous and the next layer. In general, the number of the nodes in the input and output layer are determined by the nature of the problem. The architecture of a typical 3-layer backpropagation neural network is shown in Fig. 1. Mathematically, a 3-layer BPNN with n, m, and p the number of input, hidden and output neurons respectively, can be formulated as follows:

                      ∑ ∑ 1 1 m j jk n i i ij j k k W X W b f b f O (2)
where X i are the input values of the network and O k are the output values; b j , the hidden unit biases; b k , output nodes biases; W ij , the connection weights between the input layer and the hidden layer; W jk , the connection weights between the hidden layer and the output layer and f is a transfer function. The sigmoid transfer function (Eq. ( 3)) is represented as:

x e x f    1 1 ) ( ( 3
)
Where x is the excitation.

The learning process of the BPNN is based on a series of connection weight adjustments in order to minimize the gap (global error) between the outputs of the BPNN and the target values [START_REF] Najjar | Computational neural networks for predictive microbiology: I. Methodology[END_REF]. Initially, all biases and connection weights are initialized to random values in the range of [-1, +1]. Inputs are first propagated forward through each layer of the ANN. Errors between outputs and target values are then propagated backwards and the connection weights are modified according to a specific learning algorithm (delta rule) to reduce the overall error.

This process (forward-backward) is repeated until predicted outputs and target answers coincide within a given tolerance [START_REF] Duda | Pattern Classification[END_REF].

The most common convergence criterion is the average squared error (ASE) defined as:

  2 s 1 q p 1 k qk qk O t s 1 p 1 ASE         (4)
where t qk and O qk are the target and predicted value of the output node k for the pattern q respectively, p is the number of output nodes, and s is the number of patterns. It should be noted that any level of agreement between predicted and target vectors can be achieved by providing a sufficient number of training cycles. Such an overtraining is, however, detrimental to the capacity of the network to generalize from unseen data (a network that can accurately predict the output of the testing patterns is said to have generalized). It is thus preferable to calculate the ASE both on training and testing patterns during training cycles for optimum convergence: this process is called cross-validation (Fig. 2). Fig. 2 Convergence criterion and optimum network architecture.

Results and Discussion

Optimum artificial neural network architecture

The determination of the ANN architecture constitutes one of the major tasks in the use of the ANN. The overall performance of an ANN is dependent on the number of hidden layers and hidden nodes. In the usual case of a 3-layer BPNN, the optimum number of hidden nodes can be determined by cross-validation in the same way as for the optimum number of training cycles (Fig. 2).

In the present article, a neural network relating inputs {X 1 , X 2 , …, X n } to outputs {O 1 , O 2 , …, O p } and containing one hidden layer with m hidden nodes is noted as:

{O 1 , O 2 , …, O p } = ANN n m p {X 1 , X 2 , …, X n } (5)
In our case, ROS, H f and α f are sought as a function of S, FMC and W. So, it is possible to compute ROS, Hf and α f by using a BPNN model with three nodes in the output layer (Eq. ( 6)).

Training Testing

Optimum number of cycles (Stop training here)

Average squared error (ASE)

Number of hidden nodes or training cycles

As can be observed in Fig. 3 the optimal value of ASE was calculated while using 5 nodes in the hidden layer of the model.

{ROS, H f , α

f } = ANN 3-5-3 {S, FMC, W} (6)
The ASE values for the training, testing and validation phases for the optimal artificial neural network model (ANN 3-5-3 ) are 1.37E-3, 2.39E-3 and 6.28E-3 respectively. Fig. 3 Average squared error (ASE) variations with the number of hidden nodes for the testing data subset.

Discussion of the performance of the models

The performance of the ANN model is evaluated by comparing target (Y i ) and predicted

(  i Y ) values.

ASE Number of hidden nodes

A basis of comparison for BPNN performance is usually sought in multiple linear regression [START_REF] Tabachnick | Using multivariate statistics[END_REF], a more ubiquitous prediction tool in fires propagating research. Least square parameter fitting for three different linear models (models 2 through 4) expressing ROS, H f and α f as a function of S, FMC and W (Eq. (7-9)) are performed on the same training database subset as for BPNN model.

W FMC S ROS       5275 . 0 0605 . 0 011 . 0 (Model 2) (7) W FMC S H f       9664 . 4 5661 . 1 3938 . 0 (Model 3) (8) W FMC S f        3092 . 22 8 . 6 9399 . 0  (Model 4) (9)
These models were tested to predict the never-seen data from the BPNN validation database subset. The lowest R 2 value is obtained for multiple linear regression models. It is also noted that the trend line deviates somewhat from the 1:1 line in case of models 2 through 4. The coefficients of determination for models 1 through 4 for all training, testing and validation phases are given in Table 1. The multiple linear regression models seem to be less efficient than model 1, the ANN model, for predicting the variations of ROS, H f and α f . This result is expected: the physical phenomena captured in the database are complex and nonlinear. In an ANN non-linearity is accounted for by the use of transfer functions (Eq. ( 3)), while complexity can be controlled by varying the number of hidden nodes. In the present case, the artificial neural network provides good and realistic predictions.

H f (cm) H f target value (cm) Model 1 predicted H f (cm) H f target value (cm) Model 3 predicted H f (cm) H f target value (cm) Model 3 predicted H f (cm) H f target value (cm) Model 3 predicted H f (cm) H f target value (cm)
α f (°) α f target value (°) Model 1 predicted α f (°) α f target value (°) α f target value (°) Model 4 predicted α f (°) α f target value (°) Model 4 predicted α f (°) α f target value (°)

Comparison to models and experimental data from literature

A comparison is made with models from literature describing flame propagation in fuel beds of Pinus needles [START_REF] Rothermel | Influence of moisture and wind upon the characteristics of free-burning fires[END_REF][START_REF] Porterie | Fire spread through fuel beds: Modelling of the wind-aided fires and induced hydrodynamics[END_REF][START_REF] Morandini | A model for the spread of fire across a fuel bed incorporating the effects of wind and slope[END_REF]. The model of Anderson and Rothermel [START_REF] Rothermel | Influence of moisture and wind upon the characteristics of free-burning fires[END_REF] is a semiempirical one where rates of spread are predicted as a function of fuel particle size, fuel bed compactness with fuel moisture content and wind velocity. The model of Porterie et al. [START_REF] Porterie | Fire spread through fuel beds: Modelling of the wind-aided fires and induced hydrodynamics[END_REF] is a physical one, e.g., a detailed description of the heat and mass transfer mechanisms, combustion and turbulence is given. As this model is computationally intensive, the approach of Porterie et al. [START_REF] Porterie | Fire spread through fuel beds: Modelling of the wind-aided fires and induced hydrodynamics[END_REF] is limited up to now to line fires for which a 2D approximation in a plane defined by the direction of propagation is applied. The model of Morandini et al. [START_REF] Morandini | A model for the spread of fire across a fuel bed incorporating the effects of wind and slope[END_REF] is also a physical model. This model incorporates a reaction-diffusion equation for the thermal balance and a simplified one-dimensional formulation represents the flow in the fuel layer.

The predicted rates of spread and some experimental data of Mendes-Lopes et al. [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF] are provided in Fig. 7 for a horizontal spread (S=0), FMC =10% and wind velocity ranging from 0 to 3m/s. These experimental values are selected from the third subset of 18 experimental tests which are not used to calibrate the developed model as described in subsection 2.2. Fig. 7 gives also two experimental sets of data from literature [START_REF] Boboulos | Wind and slope effects on ROS during the fire propagation in East-Mediterranean pine forest litter[END_REF][START_REF] Fernandes | Models for the sustained ignition and behaviour of low-to-moderately intense fires in maritime pine stands[END_REF] and predicted rates of spread Measured Mendes-Lopes et al. [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF]. Measured Fernandes et al. [START_REF] Fernandes | Models for the sustained ignition and behaviour of low-to-moderately intense fires in maritime pine stands[END_REF]. Measured Boboulos and Purvis [START_REF] Boboulos | Wind and slope effects on ROS during the fire propagation in East-Mediterranean pine forest litter[END_REF]. Predicted present model. Predicted Morandini et al. [START_REF] Morandini | A model for the spread of fire across a fuel bed incorporating the effects of wind and slope[END_REF]. Predicted Porterie et al. [START_REF] Porterie | Fire spread through fuel beds: Modelling of the wind-aided fires and induced hydrodynamics[END_REF]. Predicted Anderson and Rothermel [START_REF] Rothermel | Influence of moisture and wind upon the characteristics of free-burning fires[END_REF].

Fig. 7 Comparison between some predicted models and experimental data [START_REF] Boboulos | Wind and slope effects on ROS during the fire propagation in East-Mediterranean pine forest litter[END_REF][START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF][START_REF] Fernandes | Models for the sustained ignition and behaviour of low-to-moderately intense fires in maritime pine stands[END_REF] for windblown fire spread across a fuel bed of Pinus pinaster needles (FMC = 10% and S=0).

Application of the BPNN model to predict fire behaviour

An application of ANN is now proposed in the following part. Considering a constant slope (S) of 7%, it is now possible to simulate the variation of ROS, H f and α f within the range of [-2.5m/s,+2.5m/s]. The evolution of the rate of spread (ROS) using the BPNN as a function of fuel moisture content (FMC) yields a decrease in ROS when the fuel moisture content increases (Fig. 8). It can also be observed also that the predicted ROS increases steeply with wind velocity for wind-driven fires (W>0) but does not depend on wind speed for backing fire spread rates (W<0). The results obtained agree with the observations reported in literature [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF]. It is thus very important to note that the BPNN approach is able to reproduce physical variations.

ROS (cm/s)

Wind velocity (m/s)

18/25 Fig. 8 BPNN model predicted ROS variations with fuel moisture content for S=7%.

The BPNN predicted H f values as a function of fuel moisture content (FMC) and wind velocity (for S=7%) is shown in Fig. 9. It can be seen that the predicted H f values decrease with fuel moisture content (for a constant wind velocity). Moreover, it can be concluded physically, that the wind velocity and the fuel moisture content play an important role in the determination of the flame height.

The BPNN predicted α f values as a function of fuel moisture content (FMC) and the wind velocity (for S=7%) is shown in Fig. 10. It can be seen that the predicted α f values increase when the fuel moisture content increases (for a constant wind velocity). Moreover, it can be concluded also that the wind velocity and the fuel moisture content have almost no effect on α f for the backing fire spread rate (W<0).

Predicted ROS (cm/s) FMC (%)

19/25

Fig. 1

 1 Fig. 1 Architecture of a typical multilayer BPNN.

Fig. 4 ,

 4 Fig.5and Fig.6show the comparison between the BPNN predicted values and the target values for ROS, H f and α f on training, testing and validation data. In the same graphs the best fit through the origin is also plotted and the coefficient of determination R 2 for this line is computed. R 2 coefficients close to unity indicate a high degree of linearity between predicted and target values. Associated with a best fit slope close to unity, it indicates a high model prediction accuracy.

Fig. 4

 4 Fig. 4 Comparison between target and predicted values for ROS using BPNN (model 1) and multi-linear regression (model 2) for all data subsets.

Fig. 6

 6 Fig.[START_REF] Rudz | Metrological Tool for the Characterization of Flame Fronts Based on the Coupling of a Heat Flux Approach with Image Processing Data[END_REF] Comparison between target and predicted values for α f using BPNN (model 1) and multi-linear regression (model 4) for all data subsets.

Fig. 9

 9 Fig.9BPNN model predicted H f variations with fuel moisture content for S=7%.

Fig. 10

 10 Fig.10BPNN predicted α f variations with fuel moisture content for S=7%.

  An artificial neural network tool was used to simulate the rate of spread (ROS), flame height (H f ) and flame angle (α f ) in fires propagating in a bed of Pinus pinaster needles. Based

Table 1 :

 1 R2 values for the ANN model and the three multiple linear regression models on all datasets.

		Neural network		Multiple linear regression
	R 2	Model 1			Model 2	Model 3	Model 4
		ROS	H f	α f	ROS	H f	α f
	Training phase	0.9869 0.9881	0.9845 0.4030	0.5513	0.6782
	Testing phase	0.9913 0.9738	0.9758 0.4119	0.4744	0.6446
	Validation phase 0.9626 0.9261	0.9593 0.4826	0.4464	0.5555

obtained by the three models described above. It is clear regarding this figure that there is a discrepancy between these three experimental data. Indeed, experimental values of Boboulos and Purvis [START_REF] Boboulos | Wind and slope effects on ROS during the fire propagation in East-Mediterranean pine forest litter[END_REF] are obtained for a Pinus pinaster fuel bed with a load three times higher than the one of Mendes-Lopes et al. [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF]. In addition, experiments of Fernandes et al. [START_REF] Fernandes | Models for the sustained ignition and behaviour of low-to-moderately intense fires in maritime pine stands[END_REF] are performed at field scale where the control of wind speed, fuel load and depth are very difficult compared to laboratory experiments. The fire behaviour predicted by the present model (BPNN) is in good agreement in comparison to the three models cited above. The present model and these literature models give predicted rates of spread close to those measured by Mendes-Lopes et al. [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF] compared to the other experimental data. The models of Anderson and Rothermel [START_REF] Rothermel | Influence of moisture and wind upon the characteristics of free-burning fires[END_REF] and Porterie et al. [START_REF] Porterie | Fire spread through fuel beds: Modelling of the wind-aided fires and induced hydrodynamics[END_REF] underestimate the experimental rate of spread [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF] for the highest wind velocity (W=3m/s). This latter gives also predicted rate of spread slightly lower than the experimental value for a wind speed of 2 m/s. The model of Anderson and Rothermel [START_REF] Rothermel | Influence of moisture and wind upon the characteristics of free-burning fires[END_REF] may be very efficient for fuel and environmental conditions comparable to those of the test-fires used to tune them but the lack of a real physical description make it not applicable in other situations. Although the structure of the model of Porterie et al. [START_REF] Porterie | Fire spread through fuel beds: Modelling of the wind-aided fires and induced hydrodynamics[END_REF] is very sound, conversely it possesses a great set of submodels (thermal degradation of fuels, heat transfer in porous medium, gaseous kinetics for combustion, drag forces) used to close it. Those submodels need improvement to allow better predictions [START_REF] Balbi | A 3D Physical Real-Time Model of Surface Fires Across Fuel Beds[END_REF].

In the contrary of the models of Porterie et al. [START_REF] Porterie | Fire spread through fuel beds: Modelling of the wind-aided fires and induced hydrodynamics[END_REF] and Morandini et al. [START_REF] Morandini | A model for the spread of fire across a fuel bed incorporating the effects of wind and slope[END_REF], the developed model is not based on physical modeling. Nevertheless, the last model and the developed one match well the experimental data subset of Mendes-Lopes et al. [START_REF] Mendes-Lopes | Flame characteristics, temperature-time curves and rate of spread in fires propagating in a bed of pinus pinaster needles[END_REF] which are not handled to calibrate the proposed model. It should be noted that the flame height is an input parameter in the physical approach of Morandini et al. [START_REF] Morandini | A model for the spread of fire across a fuel bed incorporating the effects of wind and slope[END_REF] and it is computationally intensive. on experimental data found in literature, the optimum architecture of the artificial neural network was trained and validated, in order to generalise the prediction of ROS, H f and α f under different configurations not included in the database. The validation (using a set of experimental data which are not handled to calibrate the proposed model) showed good performance of this ANN model for the prediction of the flame characteristics (H f and α f ) and rate of spread (ROS) in fires propagating in a bed of Pinus pinaster needles (R²>0.92). In addition, this model has been compared to three literature models (2 physical models and 1 semi-empirical model) and the obtained results are very close. All these models (even the proposed one) have been confronted to two other sets of experimental data from literature works and the observed discrepancy has been discussed. The ANN was applied to an application, where it proved powerful and effective in the evaluation of the ROS, H f and α f by using data not included in the database.


Eddy El Tabach
email: eddy.el-tabach@univ-orleans.fr

Leyla Adishirinli

Nicolas Gascoin

Prediction of transient chemistry effect during fuel pyrolysis on the pressure drop through porous material using artificial neural networks

Keywords: Pyrolysis, Artificial neural networks, Modelling, Permeation, Coke, Porous medium

Hydrocarbon fuels appear as good candidates for cooling purpose within aerospace applications. Fuel flows through permeable structures. Thus, internal convection cooling is reinforced by chemical kinetics (endothermic effect of fuel pyrolysis). Perfectly tuned conditions may thus rapidly change due to unexpected coke formation that will clogged the pores of the material and thus strongly affect the cooling efficiency. The pressure drop is one of the indicator to monitor the modification of the through-flow and thus of the cooling.

Having a tool to predict these variations is of practical and theoretical interest for a better management of the complex chemical and physical phenomena. This paper presents a model based on artificial neural networks (ANN) for estimating the transient changes of the pressure drop of a reactive fluid (n-dodecane) under pyrolysis conditions passing through porous 2/27 metal material. The ANN is developed using experimental data obtained from an experimental bench, which assures the monitoring of fluid mass flow rate, pressure and temperature in stationary and transient conditions. For each case, the fluid pressure which crosses the metallic porous material is measured as a function of test time, inlet operating pressure, temperature and fuel mass flow rate. The optimal ANN architecture with error backpropagation (BPNN) was determined by the cross validation method. The ANN architecture having 9 hidden neurons gives the best choice. Comparing the simulated values by ANN with the experimental data indicates that the ANN model give correct results. The performance of the ANN model is compared with the multiple linear regression model. This work is expected to be used for later prediction of pressure drop under a wide range of clogging conditions.

Introduction

The development of hypersonic vehicles for future access to space or civil transport applications leads to an important heating of the engine and air frame. At flight speeds near Mach 4 and above, the air taken on board these vehicles will be too hot to cool the engines and airframe. Therefore, using fuel within regenerative cooling technique may be applicable [START_REF] Kuhn | Application of transpiration cooling for hot structures, RESPACE: Key Technologies for Reusable Space Systems[END_REF]. To do so, it will be necessary to study and develop adapted light weight and hightemperature materials whose characteristics in terms of permeability and porosity are well defined. Among the materials the composite ones made of Ceramic Matrix (e.g. silicon based matrix) with carbon fibers are particularly interesting. For the lowest speed regime, metallic materials may also be used [START_REF] Gascoin | High temperature and pressure reactive flows through porous media[END_REF]. The aero-thermal loads must be thus addressed to quantify permeability/porosity fluctuations of materials as a function of operating conditions. In the literature, different studies are found in relationship with this need, experimentally [START_REF] Langener | Experimental investigations on transpiration cooling for scramjet applications using different coolants[END_REF][START_REF] Gascoin | Comparaison of two permeation test benches and two determination methods for Darcy's and Forchheimer's permeabilities[END_REF][START_REF] Zhang | On Temperature and Strain Rate Dependent Strain Localization Behavior in Ti-6.5Al-3.5Mo-1.5Zr-0.3Si Alloy[END_REF] or numerically [START_REF] Romagnosi | Pyrolysis in Porous Media: Part 1. Numerical model and parametric study[END_REF][START_REF] Tabach | Neural-Network Metamodelling for the Prediction of the Pressure Drop of a Fluid Passing Through Metallic Porous Medium[END_REF]; even mathematically [START_REF] Zhou | Theoretical Investigation on Mechanical and Thermal Properties of a Promising Thermal Barrier Material: Yb 3 Al 5 O 12[END_REF]. Such studies are not only dedicated to the flow description but also to the heat transfers [START_REF] Ji | Effect of Temperature on Material Transfer Behavior at Different Stages of Friction Stir Welded 7075-T6 Aluminum Alloy[END_REF][START_REF] Fau | Fuel pyrolysis through porous media: Coke formation and coupled effect on permeability[END_REF][START_REF] Herbinet | Thermal decomposition of n-dodecane: Experiments and kinetic modeling[END_REF]. The flows in porous materials are widely studied under common operating conditions.

The problem becomes more difficult when the coolant can react with the materials or within the material (local coking) [START_REF] Gascoin | High temperature and pressure reactive flows through porous media[END_REF]. In case of chemical reaction, the formation of carbon deposit on the surface and inside the porosities can impact the physical properties of the material (lowering the permeability and the porosity) and thus the cooling efficiency. These reactions can be due to the thermal fluid decomposition and to the degradation of the material itself. The degree of decomposition is highly dependent on the operating conditions (temperature, pressure, type of flow, nature of reactor) [START_REF] Fau | Fuel pyrolysis through porous media: Coke formation and coupled effect on permeability[END_REF][START_REF] Billaud | Thermal coupling of methane in a tabular flow reactor: parametric study[END_REF][START_REF] Murphy | Analysis of products of high-temperature pyrolysis of various hydrocarbons[END_REF][START_REF] Liu | Supercritical thermal cracking of Ndodecane in presence of several initiative additives: products distribution and kinetics[END_REF][START_REF] Fau | Hydrocarbon pyrolysis with a methane focus: A review on the catalytic effect and the coke production[END_REF]. Thermal cracking of hydrocarbons have been widely studied in petrochemical industry [START_REF] Zhou | Thermolytic reactions of dodecane[END_REF][START_REF] Aribike | Thermal cracking of n-Butane and a light hydrocarbon mixture[END_REF][START_REF] Wauters | Computer generation of a network of elementary steps for coke formation during the thermal cracking of hydrocarbons[END_REF][START_REF] Chakraborty | High pressure pyrolysis of n-heptane[END_REF][START_REF] Sadrameli | Thermal/catalytic cracking of hydrocarbons for the production of olefins: A state-of-the-art review 1: Thermal cracking review[END_REF] and in the context of chemical vapor infiltration for the preparation of carbon/carbon composites [START_REF] Marinkovic | Carbon/carbon composites prepared by chemical vapor infiltration-15 years later[END_REF][START_REF] Li | Densification of unidirectional carbon-carbon composites by isothermal chemical vapor infiltration[END_REF][START_REF] Wu | Kinetics of thermal gradient chemical vapor infiltration of large-size carbon/carbon composites with vaporized kerosene[END_REF][START_REF] Deng | Densification behavior and microstructure of carbon/carbon composites prepared by chemical vapor infiltration from xylene at temperatures between 900 and 1250[END_REF][START_REF] Ren | Preparation of carbon/carbon composite by pyrolysis of ethanol and methane[END_REF]. It appears than the bigger the molecule, the higher the number of reactions which occur.

Considering dodecane pyrolysis, the number of reactions largely overpasses 1000 [START_REF] Herbinet | Thermal decomposition of n-dodecane: Experiments and kinetic modeling[END_REF]. This implies very complex phenomena (heat and mass transfers with chemistry).

A lot of studies, often under high pressure (up to 2MPa) are available for ambient to average temperature conditions (under 800K) [START_REF] Langener | Experimental investigations on transpiration cooling for scramjet applications using different coolants[END_REF] or for low pressure and high temperatures [START_REF] Kuhn | Application of transpiration cooling for hot structures, RESPACE: Key Technologies for Reusable Space Systems[END_REF]. But only few are dedicated to both high temperature and high pressure conditions in case of reactive fluid. Numerous equations (derived from Brinkman's equation) which relate the pressure drop (ΔP=P in -P out ) through the porous material to the through-flow velocity have been published [START_REF] Gascoin | Comparaison of two permeation test benches and two determination methods for Darcy's and Forchheimer's permeabilities[END_REF][START_REF] Romagnosi | Pyrolysis in Porous Media: Part 1. Numerical model and parametric study[END_REF]. They are based on coefficients, whose physical meaning is not evident [START_REF] Gascoin | Comparaison of two permeation test benches and two determination methods for Darcy's and Forchheimer's permeabilities[END_REF]. One of the complexities of such configuration is due to the fact that along the chemical reactor (cooling channel of the hot vehicle), the fluid is supercritical [START_REF] Gascoin | High temperature and pressure reactive flows through porous media[END_REF]. Multi-species flow is found due to fuel degradation during which heavy compounds (coke particles) are formed and produce solid particles that can block the pore within the porous medium where they are flowing [START_REF] Fau | Fuel pyrolysis through porous media: Coke formation and coupled effect on permeability[END_REF][START_REF] Gascoin | Charaterisation of coking activity during supercritical hydrocarbon pyrolysis[END_REF]. Due to these large and open difficulties, CFD calculations may not be relevant and experimental tests are costly and they cannot cover the entire range of test conditions/material variety, fluid nature.

As a consequence in this paper, we have used an approach based on the artificial neural networks (ANN) for simulating the transient changes of the pressure drop of n-dodecane (reactive fluid) passing through the porous material (Stainless Steel) by taking into account both high temperature and high pressure conditions. This work intends to indirectly predict the chemical effect of fuel pyrolysis, of coking and of clogging on the permeation process which directly controls the cooling efficiency. The description of the same numerical approach applied to another set of gas mixture (inert) and flow conditions can be found in a previous study [START_REF] Tabach | Neural-Network Metamodelling for the Prediction of the Pressure Drop of a Fluid Passing Through Metallic Porous Medium[END_REF]. Over the last two decades, ANN have been successfully used by many researchers for a wide range of engineering applications [START_REF] Tabach | Use of artificial neural network simulation metamodelling to assess groundwater contamination in a road project[END_REF][START_REF] Arumugam | Ultimate Strength Prediction of Carbon/Epoxy Tensile Specimens from Acoustic Emission Data[END_REF][START_REF] Nazari | Computer-aided Prediction of the ZrO 2 Nanoparticles Effects on Tensile Strength and Percentage of Water Absorption of Concrete Specimens[END_REF]. ANN is based on the 5/27 substitution of the complex simulation model by an approximation of the input-output relationship. ANN has the advantage over regression that the form of the model needs not to be pre-determined [START_REF] Kleijnen | Kriging metamodeling in simulation: A review[END_REF]. In addition, ANN can theoretically approximate any function to any level of accuracy, which is very interesting when the governing physical mechanisms are non-linear like in high velocity fluid flow in porous materials. The database was built with four input parameters (experiment time, inlet fuel mass flow rate, inlet operating pressure and the uniform temperature) and with the outlet fuel pressure as the output parameter. The results obtained experimentally are used to construct, to optimize and to validate the model. This artificial neural network has been trained and tested on this database using the error backpropagation algorithm and cross validation. The performance of the ANN model is compared with a multilinear regression approximation method.

Material

Experimental permeation bench

The COMPARER pyrolysis test bench (Fig. [START_REF] Kuhn | Application of transpiration cooling for hot structures, RESPACE: Key Technologies for Reusable Space Systems[END_REF]) is used to pressurize and to heat the fuel under flow conditions [START_REF] Gascoin | Comparaison of two permeation test benches and two determination methods for Darcy's and Forchheimer's permeabilities[END_REF]. Its main characteristics are the following:  Maximum operating conditions: 1800K, 8MPa, 0.0006 kg.s -1 for liquid fuel and 0.006 kg.s -1 for gas.

 Sensors: 5 pressure transducers, 5 mass flow rates, over 10 K-type and R-type thermocouples with data acquisition system (16 bits, 48 channels, 0.1 Hz).

A permeation test cell contains the porous sample (Fig. 1). This cell is inserted inside the furnace of the COMPARER bench and it is connected to the fluid supply system and to the suitable sensors. The permeable material bounds the cell in two high and low pressure chambers (upstream and downstream to the porous material respectively). An inlet pipe provides the fuel into the system. This cell is connected to a dynamic sampling system to get 6/27 hot pressurized samples at three location points in the cell. Despite its small size (external diameter of 40mm), it enables measuring the temperature, pressure and mass flow rate on each side of the porous sample.

In the present work, an isotropic stainless steel material is preferred to composite one to avoid considering complex microstructure (fibres, layers). It is characterized by a porosity around 30 %, a grain diameter of 14.1 µm and a pore diameter of 4.1 µm. Further geometrical information can be found in Gascoin et al. [START_REF] Gascoin | Comparaison of two permeation test benches and two determination methods for Darcy's and Forchheimer's permeabilities[END_REF].  The experimental protocol is achieved with constant mass flow rate and given downstream pressure (P out ). The upstream pressure (P in ) increases due to coking and clogging of the porous medium; which makes the pressure drop to increase as a function of the test time.

 Monitoring of the chemical species: transiently thanks to a FTIR spectrometer for 5 gaseous species (methane, ethane, ethylene, propane, propylene) and during the three thermal plateaus by using a dedicated sampling system [START_REF] Fau | Fuel pyrolysis through porous media: Coke formation and coupled effect on permeability[END_REF] coupled with a GC/TCD/FID/MS apparatus (more than 40 species analysed).

Experimental results

We present in this section an experimental test result obtained for T=725K. As shown in Fig. 2, the measured pressure drop (Measured P in -P out ) varies as a function of experimental time (t) and the measured fuel mass flow rate (q in ) when the fuel (dodecane) temperature is kept constant (T=725K). Other obtained experimental results [START_REF] Fau | Fuel pyrolysis through porous media: Coke formation and coupled effect on permeability[END_REF] showed that the temperature has a major effect on the measured pressure drop. Further details on the experimental results can be found in previous work [START_REF] Fau | Fuel pyrolysis through porous media: Coke formation and coupled effect on permeability[END_REF]. Globally, based on the overall obtained experimental results, we can conclude that there are three parameters (t, q in and T) that have a great influence on the measurements of the pressure drop. ANN models learn the relationship between the input and the output parameters as a result of training with previously recorded data. The database was built using experimental data which are obtained from the developed experimental bench with input parameters: test time (t), operating inlet pressure (P in ), inlet fuel mass flow rate (q in ) and temperature (T) varying in a range of representative values: between 0 and 858s for t; between 3.3MPa and 3.8MPa for 8/27 P in ; between 0.000033 kg/s and 0.0001 kg/s for q in and 725K, 765K and 810K for T. Totally, the database contains an appreciable size of 979 experimental test points. Each input or output parameter has been normalized relative to its minimum and maximum values observed in the data (according to Eq. ( 1)) to make the training procedure more efficient.

    min max min norm X X X X X    (1)
where X is an arbitrary parameter, X norm is the normalized value, and X max and X min are the maximum and minimum values of X.

Architecture and learning process of ANN models

An artifial neural network model is composed of interconnected group of artificial neurons or nodes. The most frequently utilized network is the multilayer backpropagation neural network (BPNN) which is used in the present study. The BPNN structure consists of three layers, an input layer which receive data; an output layer which sends computed information; and one or more hidden layers to link input and output layer. All the neurons (nodes) in a layer are connected with all the neurons of the previous and the next layer. In general, the number of the nodes in the input and output layer are determined by the nature of the problem. The architecture of a typical 3-layer backpropagation neural network is shown in Fig. 3. Mathematically, a 3-layer BPNN with n, m, and p the number of input, hidden and output neurons respectively, can be formulated as in the following:

                      ∑ ∑ 1 1 m j jk n i i ij j k k W X W b f b f O (2)
where X i the input values of the network and O k are the output values; b j , the hidden unit biases; b k , output nodes biases; W ij , the connection weights between the input layer and the hidden layer; W jk , the connection weights between the hidden layer and the output layer; f is a transfer function. The sigmoid transfer function (Eq. ( 3)) was used in the present study.

x e x f    1 1 ) ( (3)
Where x is the excitation.

The learning process of BPNN is based on a series of connection weight adjustments in order to minimize the gap (global error) between the outputs of the BPNN and the target values [START_REF] Najjar | Computational neural networks for predictive microbiology: i. Methodology[END_REF]. Initially, all biases and connection weights are initialized to random values in the range of [-1, +1]. Inputs are first propagated forward through each layer of the ANN. Errors between outputs and target values are then propagated backwards and the connection weights are modified according to a specific learning algorithm (delta rule) to reduce the overall error.

This process (forward-backward) is repeated until predicted outputs and target answers coincide within a given tolerance [START_REF] Duda | Pattern Classification[END_REF].

The commonest convergence criterion is the average squared error (ASE) defined as:

  2 s 1 q p 1 k qk qk O t s 1 p 1 ASE         (4) 10/27
where t qk and O qk are respectively the target and predicted value of the output node k for the pattern q, p is the number of output nodes, and s is the number of patterns. It should be noted that any level of agreement between predicted and target vectors can be achieved by providing a sufficient number of training cycles to be carried out. Such an overtraining is however detrimental to the capacity of the network to generalize from unseen data (a network that can accurately predict the output of the testing patterns is said to have generalized). It is thus preferable to calculate the ASE both on training and testing patterns during training cycles for optimum convergence: this process is called cross-validation (Fig. 4).

Figure 4 should be placed here

Results and Discussion

Optimum artificial neural network architecture

The determination of the ANN architecture constitutes one of the major tasks in the use of the ANN. The overall performance of an ANN is dependent on the numbers of hidden layers and hidden nodes. In the usual case of a 3-layer BPNN, the optimum number of hidden nodes can be determined by cross-validation in the same way as the optimum number of training cycles (Fig. 4).

In the present article, a neural network relating inputs {X 1 , X 2 , …, X n } to outputs {O 1 , O 2 , …, O p } and containing one hidden layer with m hidden nodes will be noted:

{O 1 , O 2 , …, O p } = ANN n m p {X 1 , X 2 , …, X n } ( 5
)
In our case, the outlet operating pressure (P out ) is sought as a function of t, P in , q in and T. So, it is possible to compute P out by using a BPNN model with one node in the output layer (Eq. ( 6)). It could be noticed that usually the pressure drop through the porous medium is investigated as a function of the through-flow rate.

11/27

In this present study, the choice of the outlet pressure is preferred to limit the impact of experimental uncertainties due to the two pressure transducers (which are generally multiplied if compared to a single transducer). In addition, since the upstream pressure is an inlet parameter, looking at the pressure drop or at the pressure outlet is equivalent when focusing on the behaviour of the ANN model. As can be observed in Fig. 5, the optimal value of ASE was calculated while using 9 nodes in the hidden layer for our model.

{P out } = ANN 4-9-1 {t, P in , q in , T} (6)
The ASE values for the training, testing and validation phases for the optimal artificial neural network model (ANN 4-9-1 ) are respectively 0.000114, 0.000101 and 0.000132. through the origin is also plotted and the coefficient of determination R 2 for this line is computed according to Eq. ( 7):

                  N i i i N i i i Y Y N Y Y N R 1 2 1 2 2 1 1 1 1 ( 7
)
where N is the number of data, Y i is the target value, 1. The model 2 seems to be less efficient than model 1 for predicting the variations of P out . This result is expected::the physical phenomena captured in the database are complex and non linear. In ANN non-linearity is accounted for by the use of transfer functions (Eq. ( 3)), while complexity can be controlled by varying the number of hidden nodes. In the present case, the artificial neural networks provide good and realistic predictions. porous medium is given in Fig. 7. It is found with model 1 that the predicted outlet pressure decreases as a function of time. This expected result is due to the formation of carbon deposit (coke) on the surface and inside the porosities of the studied material. We can observe also that the model 1 predicted outlet pressure decreases when the temperature inside the porous medium increases. The density decreases due to the thermal rise and since the mass flow rate inside the medium is kept constant, the mean reactive fluid velocity increases. Thus, the outlet pressure decreases; which means that the pressure drop increases. This is clearly understandable when paying attention to the Brinkman equation. It is thus very important to note that the BPNN approach is able to reproduce physical variations. In particular, it is clear that the chemical effect strongly increases at 760 K and is clear at 770K.

 i Y is

Figure 7 should be placed here

The result of Fig. 7 can be not only related to thermal effect on density and velocity but also to the chemical effect. Indeed, the reactive fluid outlet pressure decreases as a function of time due to the formation of the coke on the surface and inside the studied material. The thermal effect may increase the fluid velocity within the porous material by enhancing coke formation and pore clogging (the lower the cross-section area, the higher the fluid velocity and the higher the pressure in case of constant mass flowrate configuration).

Measuring the pressure drop through porous material could be a way to get information of phenomena within the porous material where no direct microscopic measure seems to be possible for the fluid properties. In addition, these results should drive the engineering study of material cooling because ensuring constant cooling efficiency, thus constant fluid flow through the porous medium, clearly requires compensating higher pressure drop depending on the temperature seen by the solid materials. As a consequence, performance of pumping 14/27 system should be designed to furnish this increasing need for upstream pressure if outlet pressure should remain constant.

Conclusion

In this article, an artificial neural networks tool has been used to simulate the transient pressure drop of n-dodecane under pyrolysis conditions and crossing a metallic porous material (Stainless steel). Based on experimental data, the optimum architecture of artificial neural network was trained and validated, in order to generalise the prediction of the pressure drop under clogging configurations not included in the database for difficult access reasons.

The validation showed excellent performance of this ANN model for the prediction of dodecane transfer in the porous material (R²>0.983). An example of application was presented to detect the temperature at which chemistry starts to strongly impact the fluid flow within the porous medium. It was found that a turning point around 760 K-770K has to be expected in terms of clogging when using n-dodecane at 3.6 MPa in stainless steel medium.

This study is a contribution to the growing evidence of the benefits of ANN models in Aeronautical engineering. This important result may be applied to automate pressure drop estimations, which are used in space flight applications, without prior knowledge of material parameters and particularly for materials with transient changing properties.

Figure 1 should be placed here 2 . 2 

 122 Figure 1 should be placed here

  These experimental results are necessary to construct, to optimize and to validate a model based on ANN for predicting the transient changes of the pressure drop of a reactive fluid (n-dodecane) passing through porous metal material (stainless steel). The construction of the developed ANN model is discussed in the following section.

Figure 2 should be placed here 4 .

 24 Figure 2 should be placed here

  The present database was subdivided in three subsets. A first subset (490 experimental tests) is used to train the networks. A second one (245 experimental tests) is used to test the ANN models to determine when to stop the training stage. The third subset (244 experimental tests) is used to validate the performance of the selected model on unseen cases.

Figure 3

 3 Figure 3 should be placed here

Figure 5 should be placed here 5 . 2

 52 Figure 5 should be placed here

Figure 6

 6 Figure 6 should be placed here

Fig. 1

 1 Fig. 1 Schematic of the permeation test cell with porous material and associated measures.

Fig. 2

 2 Fig. 2 Measured pressure drop variations with the measured fuel mass flow rate and experiment time for T=725K.

Fig. 3

 3 Fig. 3 Architecture of a typical multilayer BPNN.

Fig. 4

 4 Fig.[START_REF] Gascoin | Comparaison of two permeation test benches and two determination methods for Darcy's and Forchheimer's permeabilities[END_REF] Convergence criterion and optimum network architecture.

Fig. 5

 5 Fig. 5 Average squared error (ASE) variations with the number of hidden nodes for the testing data subset.

Fig. 6

 6 Fig.[START_REF] Romagnosi | Pyrolysis in Porous Media: Part 1. Numerical model and parametric study[END_REF] Comparison between target and predicted values for P out using BPNN (model 1) and multi-linear regression (model 2) for all data subset.

Fig. 7

 7 Fig.[START_REF] Tabach | Neural-Network Metamodelling for the Prediction of the Pressure Drop of a Fluid Passing Through Metallic Porous Medium[END_REF] Model 1 predicted transient P out variations with the temperature for q in = 0.04g/s and P in = 3.6MPa.

  the value predicted by the model and i Y is the mean of the N target values. R 2 coefficients close to unity indicate a high degree 12/27 of linearity between predicted and target values. Associated with a best fit line slope close to unity, it indicates a high model prediction accuracy. A basis of comparison for BPNN performance is usually sought in multiple linear regression [33], a more ubiquitous prediction tool in fluid flow through porous material research. Least square parameter fitting for a linear model expressing P out as a function of t, P in , q in , and T (model 2) is performed on the same training database subset as for BPNN model. This model is tested to predict the never-seen data from the BPNN validation database subset. The lowest R 2 value is obtained for multiple linear regression model. It is also noted that the trend line deviates somewhat from the 1:1 line in the case of model 2. The coefficients of determination (R 2 ) for model 1 and model 2 are given in Table

Table 1 should be placed here

 1 An application of ANN is now proposed in the following part. Considering a constant inlet pressure at 3.6 MPa, it is now possible to investigate the chemical effect within the range of 725K-810K. It should be noticed that fixing arbitrarily the inlet pressure imposes the outlet pressure to decrease, which simulate the pressure drop increase. The evolution of the predicted outlet pressure (P out ) using BPNN as a function of time and temperature inside the

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Table 1

 1 R 2 values between target and predicted outputs for all models.

R 2

Neural network (model


Hussain Najmi

Eddy El Tabach

Khaled Chetehouna

Nicolas Gascoin

François Falempin

EFFECT OF FLOW CONFIGURATION ON DARCIAN AND FORCHHEIMER PERMEABILITIES DETERMINATION IN A POROUS COMPOSITE TUBE

Using Fuel Cell on board of aircraft imposes to extract light species (such as Hydrogen and light hydrocarbons) from the liquid fuel which is stored and used, possibly at temperatures where a fuel pyrolysis occurs. Natural porosity of composite material could be used to filtrate the selected species. Hence the permeability of the porous media becomes one of the key parameter to be accurately measured. It is often determined experimentally in laboratory with disc samples (outlet of the flow is achieved through the porous material) and normal flow. However, this configuration is far from the realistic one consisting of tubes (a main flow is found additionally to the one through the material, tangential permeability). Therefore, the effect of a second outlet on the Darcy's and Forchheimer's permeabilities characterization should be studied (despite the permeability is an intrinsic property of the material itself and it should not be dependent on the test apparatus). This paper focuses on a new way of using an existing test bench for the determination of Darcy's and Forchheimer '

I. Introduction

Using Fuel Cell on board of aircraft could be useful in the coming years for local energy production. The Solid Oxide Fuel Cell (SOFC) for example could be used, mostly if species like hydrogen and light hydrocarbons are available onboard. In the meantime, liquid fuel (stored for propulsion application when burned in the combustion chamber) may encounter temperature that pyrolyses it and that produces light species [START_REF] Wang | An experimental investigation on transpiration cooling of wedge shaped nose cone with liquid coolant[END_REF][START_REF] Gascoin | High temperature and pressure reactive flows through porous media[END_REF][3][START_REF] Dahm | Experimental and modelling investigation of the thermal decomposition of n-dodecane[END_REF][START_REF] Fau | Fuel pyrolysis through porous media: Coke formation and coupled effect on permeability[END_REF] . Since the higher the H 2 or light hydrocarbons content, the longer the life time of the fuel cell, using heavy fuel would decrease the life time of the fuel cell. Thus, a separation of light/heavy species is required. To do so, the natural porosity of the composite materials which are used onboard may be used to separate light from heavy species and thus to increase the H 2 or light hydrocarbons concentration by filtration process.

Ceramic Matrix Composites (CMC) are usually used as a porous material with controlled permeability [START_REF] Steinhauser | A new concept for thermal protection of all-mullite composites in combustion chambers[END_REF][START_REF] François | Current MBDA R&T Effort on Ram/Scramjet and Detonation Wave Engine[END_REF][START_REF] Langener | Experimental investigations of transpiration cooling applied to C/C material[END_REF][START_REF] Dahmen | Numerical boundary layer investigations of transpiration-cooled turbulent channel flow[END_REF] to sustain large heat load compared to metallic materials, while operating at much higher temperatures.

The species like H 2 , C 2 H 2 and C 2 H 4 can even get separated from CH 4 by means of the selective permeation property of the CMC porous media [START_REF] Gilbert | Transport properties of a mixture of permanent gases and light hydrocarbons through the polytetrafluoroethylene capillary tubes of a GP-100 gas extractor[END_REF] . Therefore, the fuel could get enriched with low ignition delay species in order to have a more efficient combustion. In the meantime, the filtrated film inside the combustion chamber would be generated with CH 4 mostly which is characterized by a high auto ignition delay compared to H 2 , C 2 H 2 and C 2 H 4 [START_REF] Abe | Progress in aircraft gas turbine engine development[END_REF][START_REF] Spadaccini | Ignition delay characteristics of methane fuels[END_REF] . Previous work shows that as the methane content increases there is increase in absorbance value which is clearly seen in IR spectrum around 3100 cm -1 13 . Hence the generated film would thus play a positive role of an additional wall protection by absorbing a maximum of Infrared Radiation from the flame.

This selectivity property of CMC depends upon the permeability of the material or of the porous medium [START_REF] Pinnaua | Pure-and mixed-gas permeation properties of a microporous spirobisindanebased ladder polymer (PIM-1)[END_REF][START_REF] Baker | Permeability, permeance and selectivity: A preferred way of reporting pervaporation performance data[END_REF] . Over the last decade, it has been recognized that the separation factor for gas pairs varies inversely with the permeability of the more permeable gas of the specific pair. Indeed, an analysis of the literature data for binary gas mixtures from the list of He, H 2 , O 2 , N 2 , CH 4 , and CO 2 reveals this relationship for these mixtures [START_REF] Robeson | Correlation of separation factor versus permeability for polymeric membranes[END_REF][START_REF] Chenara | Gas permeation properties of commercial polyphenylene oxide and Cardo-type polyimide hollow fiber membranes[END_REF] . Hence the determination of the permeability and studying the factor affecting it is of prime importance. Performance criteria for the filtration media are high flux rate, stability at variable temperature, pressure and high selectivity even in the presence of other gases and contaminants (e.g. CO, CO 2 , CH 4 , H 2 O, H 2 S, etc.).

The filtration process in aerospace sector can be found in other fields of application such as geology [START_REF] Luquot | Hydro-dynamically controlled alteration of fractured Portland cements flowed by CO2-rich brine[END_REF][START_REF] Abdulgader | Hybrid ion exchange -Pressure driven membrane processes in water treatment: A review[END_REF] , petrochemical [START_REF] Tanakaa | Preparation of palladium and silver alloy membrane on a porous α-alumina tube via simultaneous electroless plating[END_REF][START_REF] Shamsabadi | Role of critical concentration of PEI in NMP solutions on gas permeation characteristics of PEI gas separation membranes[END_REF] or fuel cell. For the fuel cell application, several literature works show that filtration process through membranes is a simple technique which is characterised by a low cost and by a low energy consumption as well as a high purity of hydrogen separation [START_REF] Spillman | Economics of gas separation membranes[END_REF][START_REF] Lu | Nanoporous materials: science and engineering[END_REF][START_REF] Phair | Materials for separation membranes in hydrogen and oxygen production and future power generation[END_REF][START_REF] Chi | Transient dynamic of hydrogen permeation through a palladium membrane[END_REF][START_REF] Chi | Preparation of thin Pd membrane on porous stainless steel tubes modified by a twostep method[END_REF] . But in current fuel cells, the temperature remains relatively low or moderate.

In previous works, a high pressure test bench with one inlet and one outlet configuration has been developed [START_REF] Gascoin | High temperature and pressure reactive flows through porous media[END_REF][START_REF] Fau | Fuel pyrolysis through porous media: Coke formation and coupled effect on permeability[END_REF] . It has been tested on different type of metal and composite disks to determine the Darcian's and Forchheimer's permeabilities with inert and reactive fluids at high temperature and pressure. Similar experimental setup has been used by several authors to determine the permeability of same type of sample geometry or of bar type specimens [START_REF] Ilias | Preparation and characterization of composite membrane for high temperature gas separation[END_REF][START_REF] Tremblay | Gas permeability, diffusivity and solubility of nitrogen, helium, methane, carbon dioxide and formaldehyde in dense polymeric membranes using a new on-line permeation apparatus[END_REF][START_REF] Papaioannou | Uphill' permeation of carbon dioxide across a composite molten salt-ceramic membrane[END_REF] . Ilias et al. (1997) investigated the permeability and selectivity of hydrogen through a palladium membrane at high temperature and low pressure. Tremblay et al. (2006) determined the permeability, diffusivity and solubility of polydimethylsiloxane, polyisoprene, polyoctenamer, and polyurethane membranes for pure nitrogen, helium, carbon dioxide, methane and formaldehyde. Papaioannou et al. (2015) evaluated carbon dioxide permeability for sintered supports with molten carbonate dual-phase membranes and its performances were found to be stable for more than 200 h of operation. Instead of so many researches on the porous media, still we face a lack in evaluating the correct flow through porous media. Permeability of the material is mostly determined through experiments using disk sample in laboratory, with normal flow. The outflow through the porous media is measured to determine the permeability of the material. Nevertheless, when using experimentally measured values to numerically simulate realistic engineering configurations, a major disagreement is found regarding the estimation of through flow. Hence, several hypothesis are possible, among which: thermal heterogeneity in the system and particularly in the porous material, material heterogeneity at macroscale, estimation of porous medium properties. Since the lab configuration (the porous disc is inserted into a tube which imposes the entire fluid to flow through the porous medium) is not exactly similar to a realistic one, a dedicated work appears necessary. In real engine, a perpendicular flow to the main one occurs in the cooling tube (cf. Figure 1) and the through flow (secondary outlet) is only a small percentage of the fluid that flows into the pipe from the inlet to the main outlet. Hence, it makes necessary to study the effect of a second flow outlet on the determination of Darcian's and Forchheimer's permeabilities (despite the fact that permeability is often considered as a characteristic of the material itself [START_REF] Allaby | A Dictionary of Earth Sciences[END_REF] ). The aim of this paper is to determine Darcian's and Forchheimer's permeabilities of a permeable medium in a realistic configuration. Therefore, a porous tube made up of generic C/SiC composite is used as a porous medium and the effect of a second outlet on the Darcian's and Forchheimer's permeabilities is investigated. The next section is dedicated to the description of the experimental setup where different "Primary over Secondary flowrates" ratios (noticed PO/SO ratios) and three values of openings of the second outlet are studied. Two analytical methods for the determination of Darcian's and Forchheimer's permeabilities are given. The results of the porous composite tube permeabilities are presented and discussed in the third section of this paper.

II. Material and Methods

Permeation experiments and test methodology

The bench used here is composed of a porous tube connected to gas injection system. Porous tube is made up of C/SiC composite [START_REF] Charles | Analysis of Generalized Pattern Searches[END_REF] having a square cross section area of 1 cm 2 and a length of 1 m. This tube has one inlet and two outlets (the main outlet "outlet-1" is noticed as Primary Outlet -P.O-and the one through the permeable medium "outlet-2" is called Secondary Outlet -S.O-, as seen on Figure 1). The pressure and the mass flow rate are measured on each end of the porous tube. The inlet is located at the left and the outlet-2 is all along the tube although outlet-1 is at extreme right. The injection system is capable of handling liquid as well as gaseous fuels with a high pressure pump (80 bar, 0.5 g.s -1 ). In this study, nitrogen gas is used as fluid. Four sensors to monitor transient variations of mass flowrates, pressure and temperature are connected to a data acquisition system (Keithley 2700, 1 Hz, 16 bits, 48 channels). The mass flowmeter with a range of 0 to 3 g/s is placed at inlet in order to measure mass flowrate of fluid entering into the porous media. An additional Low flow-Brooks glass tube variable area flowmeter is used at P.O to estimate the through flowrate of S.O by substracting the P.O flowrate from the inlet one. This Brooks flowmeter is calibrated for maximum flow of 25 mg/s for the nitrogen. Pressure transducer with a range of 0 to 60 bar is placed at inlet side after the mass flowmeter in order to measure the pressure of fluid (Pinlet) whereas both outlets (P.O and S.O) are kept at atmospheric pressure (1 bar). Flow from the primary outlet is controlled by manually operated valve where three opening percentage values (0%, 50% and 100%) are selected. Hence, this imposes different PO/SO ratios depending on the pressure conditions. Figures 2 and3 illustrate respectively a photograph of the developed permeation experimental setup and a schematic overview of the porous composite tube. ISO 4022 and P 2 methods for the determination of fluid permeabilities are followed for all the tests which are performed at room temperature and repeated at least three times.

Mathematical procedures of Darcian's and Forchheimer's permeabilities determination

Accurate description of fluid flow behavior in the porous media is essential and is described in several ways in various literature studies [START_REF] Hassanizadeh | General conservation equations for multi-phase systems: 3. Constitutive theory for porous media flow[END_REF][START_REF] Martins | The effects of non-Darcy flow in propped hydraulic fractures, SPE 20790[END_REF][START_REF] Zeng | A Criterion for Non-Darcy Flow in Porous Media[END_REF] . Usually, Darcy's law depicts fluid flow behavior in porous media [START_REF] Garanzha | Validation of non-Darcy well models using direct numerical simulation[END_REF] . According to Darcy's law, the pressure gradient is linearly proportional to the fluid velocity in the porous material. This linear relationship is valid only for very small flow velocities or low pressure gradients, typically for pore Reynolds number lower than one [START_REF] Hassanizadeh | High velocity flow in porous media[END_REF] . As the Reynolds number (Re) approaches to a critical value (i.e. turbulent regime), the relationship becomes nonlinear but it gets quadratic due to inertial force. The one-dimensional Darcy equation can be written as:

D dP V dx K    ( 1
)
where P is the pressure, x is the direction of fluid flow, µ is the fluid viscosity, V is the superficial velocity, and K D is the darcian permeability. The transient behavior in porous media is described by Navier-Stokes equations whereas Brinkman's equation below is used to describe the macroscopic fluid flow in large range flow regimes:

2 D F P V V L K K      (2)
where inlet outlet P P P    is the pressure drop through the porous medium, L is the external mean sample thickness, ρ is the inlet density (with respect to inlet pressure), K D and K F are the Darcy's and Forchheimer's terms. The right term of Eq. ( 2) is composed of two parts, one related to the Darcy's law for low velocity regime filtration (Darcian flows) and the quadratic one is related to the Stokes's law (non-Darcian flows) which takes into account the inertial effects related with flow resistance.

The Stokes equation is also called as Forchheimer's equation [START_REF] Tully | Fluid Flow and Heat Transfer in a Liquid Rocket Fuel Injector[END_REF][START_REF] Murthy | Thermal Dispersion Effects on Non-Darcy Convection over a Cone[END_REF] . Numerous other formulations of the Brinkman's equation can be found [START_REF] Kim | Fully discrete mixed finite element approximations for non-darcy flows in porous media[END_REF][START_REF] Choi | Permeability modeling of fibrous media in composite processing[END_REF][START_REF] Martin | Simulation of pyrolysis gas within a thermal protection system[END_REF][START_REF] Valdes-Parada | On the effective viscosity for the Darcy-Brinkman equation[END_REF] . Large range of flow regimes through porous media can also be described by using power laws [START_REF] Rathish | Free convection in a non-Darcian wavy porous enclosure[END_REF] and cubic laws [START_REF] Aulisa | Geometric framework for modeling nonlinear flows in porous media, and its applications in engineering[END_REF][START_REF] Nguyen | Mapping of foam mobility in porous media[END_REF][START_REF] Pazos | Compan Calculation of Klinkenberg permeability, slip factor and turbulence factor of core plugs via nonlinear regression[END_REF] .

In order to compute Darcian's and Forchheimer's permeabilities from the measured parameters on the experimental bench, the ISO 4022 norm urges to use the modified form of the above equation: 11

D F P V L V K K       (3)
The dynamic viscosity, the density and the fluid velocity in the model given by Eq. ( 3) are calculated at the mean value of the inlet and the outlet pressures. This linear model (called ISO model) can be easily used for the experiments but not in case of Computational Fluid Dynamics codes or engineering which mostly rely on welldefined upstream conditions. It make necessary to use another method based only on inlet condition. To overcome this shortcoming, another method [START_REF] Langener | Experimental investigation of transpiration cooling with subsonic and supersonic flows at moderate temperature levels[END_REF] which based on the use of a quadratic model (called P 2 model) is considered as a second method for the determination of Darcian's and Forchheimer's permeabilities. The P² model is written as:

2 2 2 2 inlet outlet inlet inlet inlet inlet D F P P V V P L P L K K        (4)
with inlet inlet m V A   and inlet inlet P rT  
where r is the gas constant and T is room temperature.

Using both models, the determination procedure considered here can be stated as the following bound constrained minimization problem:

      exp exp minimize subject to with l u th J J              (5) where   , D F K K
  is the decision variables vector that will be identified, l  , u  are respectively the lower and the upper bounds of these variables,  denotes the usual Euclidean norm, th  is the theoretical pressure loss given by ISO model (Eq. 3) or P² model (Eq. 4) and exp  is the experimental one.

A direct search algorithm provided by the ''Global Optimization'' Toolbox of Matlab® is used to solve the bound constrained optimization problem of relation (5). Unlike traditional optimization methods which need gradient or higher derivatives information to search for an optimal point, this optimization algorithm does not require any information about the gradient of the objective function. This direct search algorithm can be used to solve problems with no differentiable objective function or not even continuous, it searches a set of points around the current point, looking for a point where the objective function value is lower than the one at the current point [START_REF] Kolda | Optimization by direct search: new perspectives on some classical and modern methods[END_REF][START_REF] Charles | Analysis of Generalized Pattern Searches[END_REF] .

III. Results and Discussion

As mentioned in previous sections, the Darcian's and Forchheimer's permeabilities of porous composite tube are determined by two different approaches (ISO method and P 2 method) and the influence of different secondary outlet openings is investigated. To achieve this determination, ISO method considers the evolution of the term

P L V   as a function of V  
whereas the P 2 method considers the evolution of P L  versus inlet V . Figure 5 presents these experimental evolutions for three different P.O openings (0%, 50% and 100%). The curves are typical and very different because in case of turbulent flow the ISO method gives a linear trend while for P² method quadratic one is observed. However in case of a purely laminar flow (Darcian regime), the ISO method gives a horizontal line and a linear trend is observed for the P² method. In Figure 4 (left), it can be easily seen that for maintaining the same mass flow rate through the porous media the required inlet pressure increases slightly as the P.O opening increases. It is obviously because of the fact that as the P.O opens it creates a new pressure drop along the tube leading to a diminution in driving force. To overcome this, the pressure at inlet side should be increased. However, in order to have the same pressure drop across the tube for all three cases (0%, 50% and 100%) the inlet fluid velocity required is to be slightly lower in later case than the former which can be clearly observed in Figure 4 (right). It is also noted that as pressure drop over material thickness ratio reaches the value of 5×10 7 Pa.m -1 there is no much change in inlet fluid velocity which shows the existence of the turbulent regime expressed by the Forchheimer term. This stagnation regime due to turbulent flow (slight velocity increase for major pressure drop increase) can be illustrated by the permeation images given as example in Figure 5 for fully closed P.O case. Initially at atmospheric pressure, there is no permeation as there is no driving force. Then having vaporised water and soap on the outer surface of the tube, when the inlet pressure increases, the soap bubble formation on the tube surfaces increases along the length of the porous tube. Bubbles appear near the inlet first and the inlet pressure increases, bubbles are found further along the tube. In addition, once inlet pressure reaches the value of 3 bar, the permeation occurs from all the four faces of the tube and become more uniform as it reaches a value of 4 bar. A semi-quantitative post-treatment of the images of the bubbles formation is proposed in Figure 6 where the locally estimated S.O flowrate is divided by the entire S.O flowrate. Hence permeation distribution is given in percentage of locally permeating flow in order to express how the through flow is distributed over the entire tube length. It is seen that the central part presents a deficit in permeation which is due to the production process of the tube itself which required some structural parts (around 0.15 m, 0.30 m to 0.60 m and around 0.75 m). These structural additional parts are in the same material but the higher local thickness impacts the permeation locally. For pressure of about 4 bar, the permeation tends to be uniform while a major part of the through flow is found upstream for lower inlet pressure. As described in earlier section, a direct search algorithm is used to minimize quadratic errors between experimental data and the functions of Eq. (3) and Eq. ( 4). ISO method (related to Eq. 3) and P 2 method (related to Eq. 4) are used to determine the Darcian's and Forchheimer's permeabilities for different P.Oopenings (0%, 50% and 100%) which are given in Table 1. A comparison between the two methods (ISO and P 2 ) shows that Darcian's permeabilities determined by P 2 method for three different P.O openings (0%, 50% and 100%) are slightly higher than Darcian's permeabilities determined by ISO method. The Forchheimer's permeabilities are very close to each other for both the methods in all three P.O openings. Determination of K D by ISO method leads to a discrepancies of 2.2% and 17.2% for respectively 50% and 100% open cases. However for K F coefficients, relative gaps of 10.8% and 6.9% is found respectively for 50% and 100% P.O opening. On the other hand, K D determination by P 2 method leads to relative errors of 13% and 31% for respectively 50% and 100% open cases whereas relative changes of 7% and 10.9% are observed for K F terms. The permeability levels obtained in this paper are in quite agreement with those of literature for this kind of composite material (C/SiC). Indeed, Gascoin et al. (2013) [START_REF] Gascoin | Comparison of Two Permeation Test Benches and of Two Determination Methods for Darcy's and Forchheimer's Permeabilities[END_REF] Even if measuring accurately these permeability levels is not so easy, we can see a small increase of the Darcy permeability while the tangential flow increase.

It may depend on the way of computing the density (here taken at entry conditions, the pressure drop can increase between the different PO levels, changing the local density to be theoretically taken into account).

In order to have better understanding of above statement and deeper insight of P.O influence on Darcian's and Forchheimer's term contributions on pressure losses, Figure 7 presents the evolutions of these contribution as well as their ratio as functions of pore Reynolds number. The pore Reynolds number is computed for metallic samples by using the relation /

IV. Conclusion

In many applications from aerospace to fuel cell, the permeability of materials is a key parameter that is generally determined experimentally. Lab test conditions (1 inlet/1outlet) are not always exactly those of realistic conditions of use of these materials (1 inlet/2outlets). Consequently, the present work intended to investigate how realistic configuration plays a role on Darcian and Forchheimer permeabilities determination. Additionally, two different procedures (ISO method and P 2 method) of permeability determination were compared. A C/SiC composite tube is used as a porous medium in this paper. It is found that determination procedures (ISO method and P 2 method) gives almost same results when the primary outlet is fully closed for both Darcian's and Forchheimer's permeabilities. After performing the tests for different P.O openings, it is observed that there is no much change in Forchheimer's permeability but there is a slight increase in the Darcian's one as the P.O opening increases. In order to understand more clearly the above statement, pore Reynolds number has been estimated and Darcian's and Forchheimer's contributions are plotted with respect to Reynolds number. It shows that the Darcian's contribution decreases whereas the Forchheimer's contribution remains more or less the same as P.O opening increases. These slight variations are mostly related to the experimental accuracies and further studies will be necessary to conclude on the best way to use the Brinkman equation in case of tangential permeation on a long tube, first under ambient temperature conditions and then in presence of temperature gradients. These experimental values obtained under realistic test conditions (2 outlets) are in agreement with existing data obtained under lab test conditions (1 outlet).

In future works, mathematical backgrounds will be developed to correlate Darcian's and Forchheimer's permeabilities to the selectivity of the porous materials since this would play a role in the fuel enrichment by separating H 2 from CH 4 for example. After that, the spatial selectivity distribution of several binary mixtures will be investigated for different variable parameters such as the type of porous media, the fluid temperature, the pressure and the time.

  s permeabilities of C/SiC porous composite tube by taking two outlets into account. Operating parameters (temperature, pressure and mass flow rate) are measured for three different configurations: i) secondary outlet (S.O) is 0% open ii) S.O is 50% open and iii) S.O is 100% open. Then Darcy's and Forchheimer's permeabilities are computed by ISO and P 2 methods using a direct search algorithm. Obtained results from different methods are compared and discussed. They are in agreement with the literature data which guarantees the reliability of the test bench and of related measures. Nomenclature Acronym CMC = Ceramic Matrix Composite PO/SO ratio = ratio of the flowrate from the Primary Outlet over the one from the Secondary Outlet P

Figure 1 :

 1 Figure 1: Overview of realistic flows through porous medium in transpiration cooling system (tangential permeation).

Figure 2 :

 2 Figure 2: Photograph of the permeation test bench.

Figure 3 :

 3 Figure 3: A schematic overview of the C/SiC porous composite tube.

Figure 4 .

 4 Figure 4. Evolutions of pressure loss in terms of ρV/µ (left) and inlet fluid velocity (right).

Figure 5 .

 5 Figure 5. Step wise permeation images with respect to change in pressure and mass flowrate.

Figure 6 .

 6 Figure 6. Permeation profile of the composite tube for 0% open case.

  area and g d is the grain diameter. Let us notice that the grain diameter 3material is computed from a correlation between thickness, overall porosity and grain diameter deduced from the literature data (Gascoin 2011). It is observed from the set of plotted data that for porous composite tube, Darcian's term is always lower than the Forchheimer's term for the three different P.O openings (0%, 50% and 100%) showing that the flow is always in a turbulent regime. There is a decrease in Darcian's contribution as P.O opening increases and a relatively very low change is observed for Forchheimer's contribution. The Darcy's pressure term reaches its limit around unity for all cases (0%, 50% and 100% open) as seen in a previous work for different porous media(Gascoin 2011).

Figure 7 .

 7 Figure 7. Permeation contributions plotted versus pore Reynolds number for different secondary outlet openings in porous composite tube.

Table 1 . Darcian's and Forchheimer's permeability values by two methods at different secondary outlet openings for C/SiC composite material.

 1 estimated Forchheimer's permeabilities between 10 -10 and 10 -14 m.

	Primary outlet	ISO method	P 2 method
	opening
	percentage	K D ± ΔK D (m 2 )	K F ± ΔK F (m)	K D ± ΔK D (m 2 )	K F ± ΔK F (m)
	0%	(1.35± 0.3)×10 -14	(1.23± 0.01)×10 -12	(1.40± 0.3)×10 -14	(1.22± 0.009)×10 -12
	50%	(1.38± 0.1)×10 -14	(1.11± 0.006)×10 -12	(1.61± 0.2)×10 -14	(1.14± 0.006)×10 -12
	100%	(1.63± 0.4)×10 -14	(1.15± 0.03)×10 -12	(2.04± 0.6)×10 -14	(1.10± 0.03)×10 -12

PhD student, CE Group, PRISME Laboratory, hussain.najmi@insa-cvl.fr.

Associate Professor, DMS Group, PRISME Laboratory, eddy.el-tabach@univ-orleans.fr.

Tenure Professor, CE Group PRISME Laboratory, khaled.chetehouna@insa-cvl.fr.

Full Professor, CE Group, PRISME Laboratory, nicolas.gascoin@insa-cvl.fr, Senior AIAA Member.

Chief Engineer, Hypersonic Programs MBDA, francois.falempin@mbda-systems.com, Senior AIAA Member.

Zhao, L., Wang, J., Ma, J., Lin, J., Peng, J., Qu, D., Chen, L., An experimental investigation on transpiration cooling under supersonic condition using a nose cone model, International Journal of Thermal Sciences, Vol. 84, pp. 207-213, 2014.

Acknowledgments

This work as been performed under the support of Airbus Group and MBDA.


Experimental study on

  Combustion modes and thrust performance of a staged-combustor of the scramjet with dual-strut, Qingchun Yang, Khaled Chetehouna, Nicolas Gascoin, Wen Bao To cite this version: Qingchun Yang, Khaled Chetehouna, Nicolas Gascoin, Wen Bao. Experimental study on Combustion modes and thrust performance of a staged-combustor of the scramjet with dual-strut,. Acta Astronautica, 2016. hal-01253275