I Zdanevitch

O Bour

QUALITY OF COMPOSTS FROM MUNICIPAL BIODEGRADABLE WASTE OF DIFFERENT ORIGINS

Keywords:

mechanical biological treatment of municipal solid waste is increasing rapidly in France as well as in other European countries. One of the outputs of this treatment is a compost prepared from the organic matter of the waste. This organic matter can be either collected selectively from the customers as biowaste, or separated from the total MSW in the plant. Unlike in Germany or Austria, where only the compost from selective collection of biowaste is allowed to serve as an amendment, in France the use of the compost is based on its compliance to a quality Standard. We present here the first results on an enquiry concerning the quality of composts from the two processes, determined on 5 French plants, between 2008 and now. All the composts fulfill to the prescriptions of the Standard and can be used as soil amendments.

INTRODUCTION

Biologic pretreatment of municipal waste: composting, anaerobic digestion (AD) is rapidly increasing nowadays in Europe and in France. Aims are the reduction and the stabilisation of landfilled waste to fulfill the Landfill Directive, the production of renewable energy (through AD), the valorisation of organic matter as a soil fertilizer. To be efficient, these biological treatments include a separation of the organic matter which undergoes the biological treatment. This separation can be done either by separate collection of biowaste, or sorting prior to the biological treatment in the treatment plant (mechanical biological treatment or MBT).

In France, there are now several installations of both types, composting and anaerobic digestion, with either separate collection of biowaste or mechanical sorting in the plant. Some intallations are only stabilizing waste prior to landfilling, but most of the plants produce composts which are used as soil amendments. For this use, the quality of the compost (e.g. agronomic quality and innocuity) must be assessed. The French standard NF U 44-051: 2006 (NF U 44-095 for composts from sewage sludges) describes both the agronomic quality (minimum carbon content, C/N ratio etc.) and the maximum values for a number of contaminant and inert compounds to which composts much comply before being used on fields. The French regulation states that all the values described by the standard shall be respected, nevertherless the origin of the compost (from separated biowaste collection or raw waste with optimized sorting).

INERIS has started an enquiry on the quality of composts from MBT and biological treatment plants, in order to evaluate the influence of a) the collective selection of biowaste or not, b) the pre-treatment, on the quality of the final product.

PARAMETERS FOR THE QUALITY OF COMPOSTS

The composts which are put onto the market in France must comply with the French standard on the quality for organic amendments, NFU 44051. This standard specifies the waste which are allowed for composting, the agronomic parameters, limit values for contaminants (with a maximum flux on soils per 10 years period for metals and organic trace compounds) and microbiology. Compliance with this standard is mandatory for use on soil. Limit values are completed for some parameters by maximum fluxes per 10 years period, in g/ha (ha: surface unit, one "hectare": 10,000 square meters). Prescribed values for the different parameters are given in Table 1 to 5

ORIGINS OF THE COMPOSTS

Composts on which the quality and contaminants content are discussed come from 5 French plants, representative of the different technologies which are presently operational. All the composts studied are prepared from the biodegradable fraction of municipal solid waste. Four of the composts come from an anaerobic digestion (AD) of the organic fraction of the waste; the last one was directly prepared by aerobic degradation (composting) of the organic matter, after the sorting of the waste. Two sites (with AD) treat organic fraction with a selective collection of biowaste, green waste and oils from food manufacturing, the 3 other sites treat municipal waste collected mixed, the organic fraction is sorted within the plant. All composts from these 5 sites comply with the standard NF U 44-051.

Processes are:

• Plant A: anaerobic digestion of biowaste collected separately, mixed with municipal green waste, garden waste, food waste; no preparation before anaerobic digestion (thermophilic, 25 days); post-treatment comprises an active composting step in tunnels (3 weeks), a sorting and a maturation step (another 3 weeks) in an open building.

Analytical results cover the year 2010 (12 analysis) and are reported as "Site A".

• Plant B: anaerobic digestion of biowaste collected separately, mixed with municipal green waste, garden waste, food waste (cooking grease), paper and cardboard collected in the urban area; no preparation before anaerobic digestion (thermophilic, 3 weeks); post-treatment comprises drying (36 hours), active composting 15 days, passive composting 15 days. The compost is sieved at 12 mm.

Analysis are performed on a quaterly basis; 10 analytical sets are available over 2009-2010; they are reported here as "Site B".

• Plant C: anaerobic digestion of MSW, following a separated collection of recyclables.

There is no crushing of the raw waste; the first step is a pre-biological degradation in a rotating tube (3 days) in which garbage bags are opened. During this step, paper and carboard are reduced to small pieces. This step is followed by several separation steps. The smaller fraction (smaller than 10 mm, composed to more than 95% of organic matter) is introduced in the digestors for 1 month. The digestate is then dried, mixed with wood, and sent to the composting plant for 2 weeks of active composting (2 weeks with forced aeration and returns). The compost is then kept for 1 month of maturation. Analyses are performed each month (e.g. on each lot of compost).

Analytical results were available for 2 years (2009)(2010), giving a 24-values set. They are reported here as "Site C".

• Plant D: anaerobic digestion of MSW, following a separated collection of recyclables. A crushing of the raw waste is performed as a first step. The crushed matter undergoes anaerobic digestion for 3 weeks. The digestate is pressed, and then filtered. The solid fraction of the filtering step goes to composting, mixed with wood pieces to structure the compost.

Composting is performed outside of the plant.

Analysis are performed on a 6 months basis, since March 2010. 2 to 4 results (depending on the parameter) were available. They are reported as "Site D".

• Plant E: composting process on MSW (with a separated collection of recyclables); no crushing; first biological step in a rotating tube (3-4 days); several separation steps; the smaller fraction (smaller than 10 mm) is sent to a composting hall and deposited in windrows.

Windrows are turned with an automatic turner twice a week (1 month); compost is then matured for 2-3 months.

Analysis are performed on a more or less quaterly basis (except for trace organic compounds, once or twice a year). A set of 12 results cover 2009-2011. They are reported as "Site E".

RESULTS: AGRONOMIC QUALITY AND CONTAMINANTS

Agronomic quality

Although the contaminants are the major problem which could arise from the use of composts from organic municipal waste, these products are sold as amendments. Therefore, in order to be valorized, they must comply with agronomic qualities of amendments, prescribed as dry matter content, organic matter content etc. Figures 1 to 4 plot all the available results for the 5 composts. The limit values prescribed by the Standard for each parameter are reported on the graphs when possible.

• All composts content enough dry matter: from 50 to 70 % in weight, while the prescription of the Standard is at least 30 % (see Figure 1). The two composts obtained from the selective collection of biowaste show the more scattered results; the dry matter contents of composts from organic matter of MSW (OMMSW) are closer: 55 to 60 %.

• The organic matter contents of the composts are more scattered than the dry matter contents: see Figure 2. One of the composts from the selective collection of biowaste has a content of 20 % (on total weight), which is the minimum value prescribed by the standard. The compost from site E (OMMSW without anaerobic digestion) show scattered values. On this site, organic matter content of the compost was low until early 2010. Since then, the process has changed a little, and the organic content rose up to between 27 and 39 %.

• All the composts have a C/N ratio which fulfills the Standard (> 8): see Figure 3. Values are scattered from 8 to 20. There is no evidence that the selective collection of biowaste give better results for this criterion.

• The sums of the fertilizing compounds (nitrogen, phosphorus and potassium) fall well below the maximum value of 7 % for all the composts, as shown on Figure 4 (the limit value is not represented on the graph as it falls well above the values for 4 composts). This parameter was not determined for Site D and is therefore not reported. Once again, there is no obvious difference between composts from selective collection of biowaste and OMMSW.

As a summary, after optimization of the process (e. G. Site E), all the composts fulfill the agronomic specifications stated by the French Standard to be considered as organic amendments, with no obvious difference due to the collection or treatment processes.

Contaminants and impurities

As we have seen in paragraph 2, the French Standard NFU 44051 prescribes limit values for several inorganic, organic and biological contaminants, as well as for impurities. These parameters are discussed here. • All the composts fulfil the limit values stated by the Standard for plastics (either films, polystyrene or other plastics, see figures 5 and 6). Surprisingly, the compost from site D, where total MSW is crushed before entering the digestor, presents the lower content for plastics. This comes from the fact that the digestate is pressed; the liquid fraction of the pressing process is then filtered. The solid residue of the pressing process contains all the "large" impurities (bigger than 2 mm) and is discarded. Only the solid part of the filtering process undergoes the composting process (the liquid fraction is reinjected in the process). This solid fraction contains very few large particles.

Inerts (plastics, glass and metal pieces)

• All the composts nearly fulfil the Standard limit value for inert materials (glass and metal pieces larger than 5 mm). There are only 2 analytical values (out of 24) for the compost from site C which slightly exceed this value. These analyses were done in 2009 and 2010. At the beginning of 2011, the city which sends its waste to site C set a separate collection for glass, door-to-door, for all the customers. It is expected that the glass content of the compost should be lowered and could then always fulfil the criteria of the Standard.

Heavy metals

Analytical results for heavy metals are numerous and therefore are not represented by graphs. Table 6 presents the mean values for all the metals cited by the Standard, for the 5 composts. The higher value for each compound is bolded. For all the composts, heavy metal contents are well below the limit values: the mean values are half of the limit value or less. Maximum values for all the composts are not presented here, but there is no value exceeding the limit values, for each metal, over the 60 analysis. As for the metals, all the data gathered for all the composts fall well below the limit values for the 3 compounds. It should be noticed that, except for the compost of site E, for which the quantification limit on BbF and BaP are 0.5 mg/kg, the composts from the OMMSW present a lower organic content than the composts from selective collection of biowaste.

Microbiology

All the analytical results for all the samples, for which we received analytical data, showed a lack of both viable Helminth eggs and Salmonella in respectively 1.5 and 1 g of the samples. Thus, these composts are correctly hygienized by the processes and can be used as amendments in cultures without biological contamination problems.

CONCLUSIONS

/As IVID I plants quickly develop in France, there are que st ions on the quality of composts from the organic fraction of IVIoVV as soil amendments.

I he present study gives first responses to those questions.

There is no obvious difference from composts produced by biological plants which receive biowaste collected separately, and composts originated from MBT plants (either aerobic or anaerobic). A specific analysis done with transmission electronic microscopy (not discussed here) shows that compost from anaerobic digestion is more stabilized than the one produced by a simple composting process. This is due to the anaerobic digestion, which lasts 1 month in this case. Therefore, the disponibility of the nutritive elements differ and should be taken into account in the amendment plan. Nevertherless, both these composts have a good agronomic quality, and a low contaminant content, which makes them suitable for all agricultural crops. As a matter of fact, they are well apreciated by the local farmers.

These compost qualities make a real improvement for the use of the MBT. These sustainable and local productions of organic matter of good quality should be more widely proposed. The quality of the MSW compost must compete with other source of organic matter. The only drawback is the need to make a study for the possible use of compost at the local scale, in order to maximize the benefits of that treatment.

Figure 2 .

 2 Figure 1. dry matter content ofthe 0 composts

Figure 4 .

 4 Figure 3. C/N ratio of the 5 composts.

Figures 5

 5 Figures 5 to 7 represent the impurities contents of the 5 composts. Limit values are shown on the graphs for each parameter.

Figure 5 .Figure 7 .

 57 Figure 5. Films and PSE content of the 5 composts.

Figure 8 .

 8 Figure 8. Fluoranthene content of the 5 composts.

I

  he results of the present study complete the data sets gathered by other French Institutes ^/\LJ L. IVI F_, r\\ l\IUr\J, and will participate to a European study on the qual i ty of c o m p osts from different origins, launched by the Joint Kesearch Lentre (^OevilleJ in IVI ay c\) I I .

Table 1 .

 1 . Agronomic parameters prescribed by the French Standard NFU

										44051	for	composts.
	Parameter	Dry matter	Organic matter	N**	P 2 O 5 ** K 2 O**		Z	C/N
										(N +	P +	JQ	ratio
	Limit value	> 30 % of total matter	< 15 to 25% of total matter*	< 1 %	< 1 %	< 1 %	<	7%	>8
	* this value depends on the category of compost, 20 %for composts from organic matter of municipal
	waste
	** otherwise the compost is soldas "amendment with fertilizer"
	Table 2. Limit values for heavy metals prescribed by the French Standard NF U 44051 (content
	and flux to the soil).
	Metal	As	Cd	Cr		Hg	Ni	Pb	Se	Cu	Zn
	Limit value, mg/kg	18		120	2	60	180	12	300	600
	DM*
	Limit value, mg/kg									600	1,200
	OM**
	Max flux per 10 years,	900	150	6,000	100	3,000	9,000	600	10,000	30,000
	g/ha***
	Max flux per year, g/ha	270	45	1,800	30	900	2,700	180	3,000	6,000
	* DM: dry matter
	** OM: organic matter
	*** ha: hectare (1 ha = 10,000 m 2 )
	Table 3. Limit values for inert materials and impurities prescribed by the French Standard
	NFU 44051.
	Inert materials and	Films+ PSE**		Other plastics > 5 mm	Glass + metal pieces
	impurities	> 5 mm							> 2 mm
	Limit values, % DM*		< 0.3				<0.8			<2.0

Table 4 .

 4 Maximum flux per 10 years and limit values for Organic Trace Compounds (O. T. C.) prescribed by the French Standard NF U 44051.

	O. T. C.	Fluoranthene	Benzo-b-	Benzo-a-pyrene
			fluoranthene
	Maximum flux, g/ha/year*	6	4	2
	Limit value, mg/kg DM**	4	2.5	1.5
	* ha: hectare
	** DM: dry matter

Table 5 .

 5 Limit values for pathogens prescribed by the French Standard NF U 44051.

	Pathogen	All cultures except	Market gardening
		market gardening
	Viable Helminth eggs	Lack in 1.5 g	Lack in 1.5 g
	Salmonella	Lack in 1 g	Lack in 25 g

Table 6 .

 6 Heavy metal content of the 5 composts, mean values, compared to the limit values (NFU 44051).

	Metal		As	Cd	Cr	Hg	Ni	Pb	Se	Cu	Zn
	Limit value, mg/kg DM*		18	3	120	2	60	180	12	300	600
	Mean value, site	A	4.17	0.75	27.51	0.13	17.76	83.6	2.63	49.67	248.1
	Mean value, site	B	3.51	0.53	24.98	0.12	16.18	61.9	1.91	74.73	229.9
	Mean value, site	C	3.06	0.99	44.27	0.49	24.01	98.6	0.57	90.11	297.6
	Mean value, site	D	1.49	0.80	35.19	0.32	14.02	118.7	0.88	75.87	243.3
	Mean value, site	E	3.12	0.44	24.78	0.24	15.19	44.6	0.63	80.07	239.7
	* DM: dry matter
	4.2.3 Trace organic compounds
	Figures 8 to 10 represent the analytical data for the trace organic compounds.

ACKNOWLEDGEMENTS

The Authors wish to thank the plant operators for providing the analytical results. This study is funded by the French Ministry of Ecology and Sustainable Development.


Agnès Janès
email: agnes.janes@ineris.fr

Douglas Carson

Experimental study of bulk storage ignition by hot points

An experimental study of ignition risk due to hot points in the storage of bulk materials is required to ensure fire safety. Many parameters are involved in this phenomenon: nature of the material, storage volume and temperature, type and size of hot point, etc. The aim of this study is to determine critical ignition temperatures of hot spots embedded in powder materials for different conditions and with several types of hot points. Materials selected for this study are pulverized coal, wood dust, cocoa powder, alfalfa, rice husks and coffee husks. Ignition tests were carried out in 1,000 and 2,700 cm 3 cubic baskets containing the combustible sample and using an inert sphere at a given initial temperature as well as a glowing cigarette butt and charcoal as ignition sources. The critical ignition temperature is defined in terms of the hot point temperature that is able to ignite the sample. Differences between the results obtained under these test conditions have been explained by the oxy-reactivity of materials tested, different basket sizes and specific heat or heat production of hot points. Data obtained need now to be compared to available theoretical modeling. These results will then allow the prediction of material behavior under other storage conditions.

Overview

Fire and explosion risk is generated by chemical or biological oxidation of combustible materials. Selfignition is a consequence of exothermic oxidation reactions and occurs when the heat produced by oxidation is greater than that dissipated to the environment at storage surfaces. Then, the temperature increase may lead to a fire, sooner or later. The self-ignition phenomenon depends essentially on three parameters: 1) material temperature, 2) ambient temperature and 3) storage size. Experimental characterization of self-ignition hazards in storage spaces is performed by thermal analysis of the material. Self-ignition tests in isothermal ovens lead to the critical storage size as a function of storage temperature, for a given shape. Test results are extrapolated to industrial scale by modelling using the Frank-Kamenetskii theory. Studies on self-heating were performed in the 1920s by Semenov. They were completed by Frank-Kamenetskii (1969). Semenov considered a homogenous temperature in the whole volume, as it appears on Figure 1. This model involves geometrical characteristics of storage spaces such as surface area and volume. However, it is not valid for large storage spaces of solids, since it does not take into account the inner and outer thermal gradients of the material. Frank-Kamenetskii theory is more accurate. It includes the heat transfer resistance in the material. It considers that heat transfer is due to conduction inside the material, and is linked to an ideal convection at the outer surface. This model involves geometrical characteristics of the storage space and the thermal conductivity of the material. Frank-Kamenetskii's theory does not take into account the surface heat resistance, unlike Thomas and Bowes's -theory [START_REF] Bowes | Self Heating: Evaluating and Controlling the Hazards[END_REF]. Indeed, Thomas and Bowes consider simultaneously the heat transfer resistance into the material and the surface heat resistance. This model is the most complete and introduces the thermal conductivity of the material, the shape and finally convection and radiation parameters at the interface, using the Biot number (). It corresponds to the ratio of conduction and convection coefficients. In the case of heating by a hot spot, the initial heat contribution is not due to self-heating. Some examples can be found in industrial situations [START_REF] Carson | Inflammation des matériaux pulvérulents par sources extérieures[END_REF][START_REF] Krause | Propagation of smouldering in dust deposits caused by glowing nests or embedded hot bodies[END_REF]: Hot spot of inert material at a given initial temperature introduced into powder storage. It may be metal particles introduced accidentally in a hot storage or mechanical sparks, Hot spot of combustible material at a given initial temperature introduced into powder storage. This can be linked to a part of the storage locally overheated because of a failure of temperature regulation of a dryer, or even a cigarette butt, Hot spot of inert material maintained at a given temperature. This corresponds to a limit case of the first two points: very high heat capacity of the inert material or reaction rate of the oxidation limited by oxygen diffusion. This could correspond to the case of surfaces heated by outside: welding or an electrical equipment. Modelling of this phenomenon was recently proposed for the specific case of metallic powders [START_REF] Chunmiao | Ignition behavior of magnesium powder layers on a plate at constant temperature[END_REF].

Experimental

A previous study performed at INERIS (Janès et al., 2011) was devoted to design and validate an experimental protocol to measure the critical ignition temperature by a hot point of bulk storage of coal dust, in baskets cube of variable size. Hot points used were a steel sphere of 30 mm diameter and heating steel cylinders of 6.5 and 10 mm diameter.

The objective of the experimental setup protocol that was developed is ultimately to show the relationship between the storage size of a bulk material and the critical temperature of a hot spot located in the center of the storage. Thus, it is necessary to test other experimental conditions, by varying the nature and the size of the hot spot and testing other materials. Tests were performed on the six materials listed in table 1. The critical ignition temperature by hot spots is determined in 1,000 and 2,700 cm3 cubic baskets. Tests are performed into a 125 L ventilated oven, regulated at 27 °C. Cubic baskets are made, except their upper face, of 10 urn wire mesh. This is sufficiently fine to avoid sieving, but does not restrain the oxygen diffusion.

Hot spots used are represented on figure 2 below: An incandescent cigarette butt, An incandescent oak charcoal, A steel sphere of 10 mm diameter, preheated in an oven.

Some preliminary tests showed a surface temperature of these three hot points near 310 °C. Each test is performed using a clean and dry cubic basket. The amount of coal introduced in the basket is weighted. Then, the coal is introduced into the basket, without compaction. The K-thermocouples are placed into the basket before introduction of the sample and the hot point, preventing its cooling. Location of thermocouples in the basket is represented on Figures 3 and4.

The sphere is heated in a furnace regulated at 450°C. When the test temperature is reached, it is then moved over in the full basket. In the case of cigarette butt and oak charcoal, the heating is obtained using an ignited propane torch.

After the start of the test, the temperatures into the basket are measured as a function of time. When the temperatures strongly increase and go over the hot point for at least 50 °C, it can be considered that an ignition occurs.

When the temperatures grow up and go over hot point temperature, but stabilize in a plateau at the hot point temperature, ignition does not occur.

Some previously tests showed a +/-5 °C repeatability of this method. Note: T1 is not representative of the hot point temperature, since there is a thickness of a few mm of bulk material between the hot point and the thermocouple.

Hot point

Results

Table 2 indicates the experimental conditions associated to tests performed.

Discussion

Tests performed with cigarette butt and oak charcoal did not lead to an ignition of material tested. These hot spots were located in the center of the basket. The limited oxygen diffusion up to the combustible hot point was not enough to permit the propagation of the combustion to the material tested and the hot point was progressively cooling. Indeed, the amount of energy transmitted from the combustible hot spots to the materials tested was not sufficient to initiate their combustion, unlike the case of heated inert sphere of 10 mm diameter, at the same temperature. This is related to the fact that in the case of combustible hot spots, only a small volume was heated, comparatively to the heated sphere. Furthermore, the heat capacity of the combustible hot spots is much lower than that of the steel sphere, for which ignition were observed. These tests show that, although the material tested is very oxy-reactive, an ignition does not occur when a small combustible hot point is introduced into bulk storage. The basket size, 1,000 or 2,700 cm 3 , does not appear as an influencing parameter on test results. Indeed, coal does not ignite in both cases. However, wood dust was ignited with the two tested basket size. The induction time, which corresponds to the delay between the introduction of the hot spot and the ignition, is variable depending on the material tested and the basket size.

In the case of 2,700 cm 3 basket tests, an ignition is obtained in a few minutes for alfalfa dust. The induction delay observed for the same basket size is much higher for wood dust and cocoa powder, since it reaches up 2 to 3 h. The induction delay is related to the thermal conductivity and heat capacity of the test product, in addition to its reactivity.

Conclusion

The aim of this paper was to describe an adapted experimental protocol to determine ignition temperatures of powders under different conditions and with several types of hot points. The first results demonstrate that this protocol is relevant. Discrepancies between the results obtained under these different test conditions have been explained considering basket sizes and hot points geometry. However, other test conditions should be experimented to acquire more data. For example, the ignition using an inert hot point at a given heating flow was not tested.

These different test conditions will allow the simulation of industrial situations of incident such as the presence of an appliance power supplied or an incandescent particle in a storage space like a silo. It will then be possible to compare data obtained to available theoretical modelling.

Figure 1 :

 1 Figure 1: Shape of theoretical temperatures in Semenov (a) and Frank-Kamenetskii (b) models

Figure 2 :

 2 Figure 2: View of the three types of hot points used

Figure 3 :Figure 4 :

 34 Figure 3: Location of temperature measurement points inside the 2,700 cm3 baskets

Figure 4 :TestFigure 5 :

 45 Figure 4: Temperature measurements observed during test #2

Table 1 :

 1 List of materials selected for the tests

	Material	Particle size	Humidity
	Wood dust	33.1 % > 315 m (sieving)	0 rel. % (dried before testing)
	Lucy coal	Median: 29 m (LASER diffraction)	1.4 rel. %
	Cocoa powder	Median: 8 m (LASER diffraction)	2.9 rel. %
	Alfalfa	100 %> 315 m (sieving)	0 rel. % (dried before testing)
	Rice husks	100 %> 315 m (sieving)	9.3 rel. %
	Coffee husks	100 %> 315 m (sieving)	14.2 rel. %

Table 2 :

 2 List of tests performed

	Test # Material	Hot point	Basket Initial weight Mass loss
				size	(g)	(%)
				(cm 3 )
	1	Lucy coal	Cigarette butt 1,000	576
	2	Alfalfa	Oak charcoal 2,700 2 18
	3	Wood dust	Heated sphere 1,000	3,3
	4	Wood dust	Heated sphere 2,700	7 4
	5	Lucy coal	Heated sphere 1,000	579
	6	Lucy coal	Heated sphere 2,700	1584
	7	Cocoa powder Heated sphere 2,700	No measured >50 %
	8	Alfalfa	Heated sphere 2,700 2 4	88
	9	Rice husks	Heated sphere 2,700 2 35	0
	10	Coffee husks Heated sphere 2,700 50 6	0


Agnès Janès
email: agnes.janes@ineris.fr

Jacques Chaineaux

Experimental Determination of Flash Points of Flammable Liquid Aqueous Solutions

The flash point is considered as a determinant parameter to classify the flammable liquids, regarding the European CLP regulation, as well as the transport of dangerous goods regulation. In the case of some low concentrated flammable liquid aqueous solutions, the existence of a flash point is not very well defined, and their flammability is not precisely known. The experimental measurements of flash points are described in numerous national or international standards, which differ by their range of validity and by the specified experimental conditions. The flash point of ethanol, acetone, acetic acid and formic acid aqueous solutions was measured using Abel and Pensky-Martens in close cup methods, chosen regarding predicted values of flash point. Results obtained show that, for the most flammable products, such as acetone or ethanol, weakly concentrated aqueous solutions still remains flammable. In the case of acetic or formic acid aqueous solutions, a threshold concentration can be determined under which the solutions are considered as non flammable, regarding the European CLP regulation and the transport of dangerous goods regulation.

Principle of flash point determination

The flash point is defined as the lowest temperature at which a liquid generates flammable vapours which can be ignited in air by a flame above its surface. The flash point is determined experimentally by heating a vessel containing the tested liquid. A flame is presented at regular intervals to the liquid surface. If a flash occurs in the vessel, it indicates that the temperature of the tested liquid has reached (or exceeded) the flash point. The test vessel can be open or close. The flash point is then measured respectively in "open-cup" or in "closed-cup". The experimental determination of flash point is described in many national and international standards, which differ in their scope and in the specified experimental conditions. The value of the flash point is a key parameter for the flammable liquids classification, as defined in European CLP Regulation (EC, 2008). However, it should be noted that the flash point is not sufficient to assess the risk associated to the use or the storage of a flammable liquid in conditions of liquid-vapour equilibrium. Indeed, in a closed container, liquid-vapour equilibrium can be established. In this case, the atmosphere in the container consists of a homogeneous mixture of vapour and air and, if the vapour concentration is included in the flammability range, comprised between the lower flammability limit (LFL) and the upper flammability limit (UFL), an explosive atmosphere is present in the closed container. The lower point of explosion (LPE) of a liquid is defined as the temperature at which the concentration of vapours emitted by this liquid, in thermodynamic liquid-vapour equilibrium conditions and when mixing with air at atmospheric pressure, is equal to the lower flammability limit (LFL). As showed on Figure 1, the lower point of explosion (LPE) is only a few K below the flash point in the case of pure liquids. This difference may be one to three tens of K in the case of different volatilities liquid mixtures. Vapour concentration (vol. %)

Temperature

Figure 1: Graphical representation of the influence of temperature on the flammability of the vapour/air homogeneous mixture in a closed vessel containing a flammable liquid, under atmospheric pressure [START_REF] Chaineaux | Conditions de formation d'une atmosphère explosive lors de la mise en oeuvre d'un liquide inflammable -ND 2313-216-09[END_REF] This difference is related to the operating conditions for measuring the flash point, whatever the standard applied. Even in the case of determinations in closed-cup, the conditions of the liquid-vapour equilibrium cannot be satisfied at the time of presentation of the flame to the liquid surface. Therefore, beyond the issue of regulatory classification of flammable liquids, to assess the risk of formation of an explosive atmosphere in a flammable liquid closed container, it is wise to consider the lower point of explosion (LPE). If this information is not known, it is possible to rely on the flash point, retaining a safety margin of a few K for a pure liquid, and up to 30 K for a mixture of different volatilities liquids.

Experimental

Materials tested and methods used are described below.

Methods used for experimental measurement of flash points

The experimental determination of flash points of flammable liquid solutions was performed using two methods, depending on their scope: Abel closed-cup method: EN ISO 13736 (ECS, 2008) standard, and Pensky-Martens closed-cup method: EN ISO 2719 (ECS, 2003) standard. Abel closed-cup method is applicable to combustible liquids having flash points between -30.0 °C and 70.0 °C, inclusive. INERIS manual Abel apparatus is presented on Figure 2. Pensky-Martens closed-cup method is applicable to combustible liquids, liquids with suspended solids, liquids that tend to form a surface film under the test conditions and other liquids. It is applicable for liquids with a flash point above 30 °C. Procedure A is used for the determination of the flash point of paints and varnishes that do not form a surface film, unused lubricating oils and other petroleum products not covered by Procedure B. Procedure B is used for the determination of the flash point of residual fuel oils, cutback bitumens, used lubricating oils, liquids that tend to form a surface film, liquids with suspensions of solids and highly viscous materials such as polymeric solutions and adhesives. INERIS manual Pensky-Martens apparatus is presented on Figure 3 below.

Figure 3: View of INERIS manual Pensky-Martens closed-cup flash point apparatus

The experimental parameters prescribed are the following:

Heating rate of the test portion in the cup: up 5 to 6°C/min, Stirring speed: up 90 to 120 r/min, in a clockwise rotation, The temperature read at the time the test flame application caused a distinct flash in the interior of the test cup must be recorded as the observed flash point.

When the temperature of the test portion reaches 23 °C below the expected flash point, the test flame must be applied for the first time, The test flame must be applied every 1 °C rise in temperature if the flash point is less than or equal to 110 °C and every multiples of 2 temperatures if the flash point is greater than 110 °C.

Materials tested

The flammable liquids selected for these tests are listed in Table 1. It also indicates the method used for the flash point measurement. These liquids come from chemicals suppliers. Aqueous solutions were prepared at INERIS.

Results

Table 2 below summarizes the results of experimentally determined flash points.

Impact on classification as flammable liquids of solutions tested

The classification as "flammable liquids" of aqueous solutions studied depends on the value of flash point. , 2009). This may allow the exclusion of these solutions of the flammable liquids class.

In the case of solutions of acetic and formic acids, the concentration below which the aqueous solution is no longer classified as flammable is much higher, i.e. between 75 and 80 % for acetic acid and between 90 and 100 % for formic acid.

Conclusion

This work has been devoted to the study of the flammability of aqueous solutions of some common flammable liquids, by characterizing their flash points at various concentrations. These values are necessary for the classification of flammable liquids, which is based on flash point and ebullition temperatures.

However, these values should be used with caution if they are used to assess the safety of a process in which equilibrium conditions can be reached. In this particular case, it is safer to use lower explosion point (LEP) instead of flash point.

Figure 2 :

 2 Figure 2: View of INERIS manual Abel closed-cup flash point apparatus

Table 2 :

 2 Results of flash point measurement on different aqueous solutions

Table 1 :

 1 List of liquids selected for the tests and method used

	Flammable liquid	Purity	Flash point measurement method used
	Acetone	99.5	%	EN ISO 13736 -Abel in closed cup
	Ethanol	96°/i		EN ISO 13736 -Abel in closed cup
		99.5	%	EN ISO 13736 -Abel in closed cup
	Acetic acid	99-	100%	EN ISO 2719 Method A -Pensky-Martens in closed cup
	Formic acid	99°/i 3	EN ISO 2719 Method A -Pensky-Martens in closed cup

Table 3

 3 indicates classification criteria, according to current regulations.

Table 3 :

 3 Classification criteria for flammable liquids used in current regulations, based on ebullition temperature and flash point value

	Flash point	<0°C	< 23 °C < 55 °C < 60 °C < 100	°C
	CLP Regulation			Not considered
	(EC,2008)			as a « Flamable
				liquid »
		lfTeb<35°C: Cat. 1 -Danger -H224 V	-Flammable liquid	Flammable liquid Cat. 3-
		If Teb > 35°C: no pictogram -Flammable	Warning -H226
		liquid Cat. 2 -Danger -H225
	European
	Dangerous
	substances (EC, 1967)and	lfTeb<35°C:
	preparation (EC, Extremely flammable -
	1999) Directives R12
		IfTeb>35°C:
		Flammable -R11

  The results obtained show that, for the most flammable products such as acetone and ethanol, flash points of aqueous solutions containing only a few % flammable liquid remain below the classification as flammable liquid threshold. Nevertheless, it is specified in the CLP regulation (EC, 2008) that liquids with a flash point of more than 35°C need not be classified in Category 3 if negative results have been obtained in the sustained combustibility test L.2, Part III, section 32 of the UN Recommendations on the Transport of Dangerous Goods, Manual of Tests and Criteria (UNO

	Flammable -R10 ê No pictogram -Easily	Not considered as a « Flamable liquid »
	flammable -
	R11
	Teb: ebullition temperature
	Hazard statements:
	R12: Extremely flammable	H224: Very highly flammable liquid and vapour
	R11: Easily flammable	H225: Highly flammable liquid and vapour
	R10: Flammable	H226: Flammable liquid and vapour


A O Diallo

G Marlair
email: guy.marlair@ineris.fr

An Insight of Combustibility Induced Safety Issues Pertaining to Ionic Liquids

Keywords: Explosion hazard, flammability, ionic liquids, toxicity issues

This study is a consolidated overview on explosion and fire safety issues pertaining to ionic liquids. Indeed safety performance of ionic liquids relating to physico-chemical hazards is very rarely investigated as it is often perceived as a non-existing issue due to the lack of traditional flashpoint for these liquids. It focuses on the experimental evaluation of the fire hazard of imidazolium, phosphonium and pyrrolidinium-based ionic liquids by use of the Fire Propagation Apparatus. It provides experimental data that can quantify the flammability of ionic liquids in all its aspects (ease of ignition, mass burning rate, heat release rate, fire-induced toxicity data...). A case study featuring a major failure in a process unit leading to a given fire scenario is also illustrated. This case study is examined in terms of fire induced toxicity by use of CFD modeling of fire product releases dispersion and using the concept of fractional effective concentration.

INTRODUCTION

Ionic liquids (ILs) are in the focus of recent research and more and more considered for use in emerging industrial applications. Because of their unique physical properties (e.g., high thermal stability, large liquid range, negligible vapor pressure), these chemicals are used in many domains, such as energy conversion and storage [START_REF] Sakaebe | Application of Room Temperature Ionic Liquids to Li Batteries[END_REF], biomass pre-treatment [START_REF] Zhu | Dissolution of Cellulose with Ionic Liquids and Its Application: a Minireview[END_REF], metal processing [START_REF] Abbott | Processing of Metals and Metal Oxides Using Ionic Liquids[END_REF], engineering fluids [START_REF] Predel | Ionic Liquids as Operating Fluids in High Pressure Applications[END_REF], and polymer additives [START_REF] Lu | Advanced Applications of Ionic Liquids in Polymer Science[END_REF]. They are made by association of large organic cations (e.g. imidazolium, phosphonium, pyrrolidinium, pyridinium, ammonium, guanidinium...) with a variety of counter-anions (halogens, BF 4 , PF 6 and many others) that are liquids under 100°C. Many of them are already liquid below room temperature (and in such a case designated as Room Temperature ILs (RTILs)).

The growing interest in ILs in the early 2000s was partly due to the generic assumption that these materials were implicitly highly stable, non-flammable, or safe to use in any process [START_REF] Ngo | Thermal Properties of Imidazolium Ionic Liquids[END_REF][START_REF] Bonhôte | Hydrophobic, Highly Conductive Ambient-Temperature Molten Salts[END_REF][START_REF] Mcewen | Electrochemical Properties of Imidazolium Salt Electrolytes for Electrochemical Capacitor Applications[END_REF]. Owing to infinite combinations of cations and anions, potentially billions of such materials are in existence. Surprisingly, some of them are considered as promising energetic materials for application as propellants [START_REF] Schneider | Ionic Liquids as Hypergolic Fuels[END_REF], showing that combustibility in such case is perceived as a technical advantage. Even if there is practically no study about toxicity of ILs to humans, many are moderately or very toxic to aquatic organisms and non-biodegradable. The general assumption that prevailed for a long time that ILs were green chemicals per se has to be revised, which is no longer questionable, due to their toxic potency. In addition, recent findings have shown that safety assessments of ILs must not only encompass toxicity and ecotoxicity issues, but also the full range of physico-chemical hazards including combustibility. Therefore, sustainable use of such materials must be studied on a case by case basis, considering adequate analysis of physicochemical and health safety, disposal and potential environmental impacts of them.

As a continuation of our previous research on the actual fire hazards of ILs, the paper gives a short literature review on flammability and explosivity hazards of ILs. It mostly focuses on the experimental evaluation of the fire hazard of imidazolium, phosphonium and pyrrolidiniumbased ionic liquids, including a case study featuring a major failure in a process unit leading to a given fire scenario (pool burning). This case study is examined in terms of fire induced toxicity by use of CFD modeling of fire product releases dispersion and using the concept of fractional effective concentration (FEC), as defined in ISO 13571 [START_REF]Life-threatening Components of Fire -Guidelines for the Estimation of Time Available for Escape Using Fire Data[END_REF].

REVIEW ON FLAMMABILITY AND EXPLOSIVITY HAZARDS OF IONIC LIQUIDS

ILs have long been labeled and described as "not flammable" due to their low vapor pressure and measured flash point. Although so far no industrial accident involving an IL has been listed, two recently informally reported laboratory incidents during and just after synthesis of ILs containing nitrate anion (e.g. ethyl-ammonium nitrate) have taken place in the EU. Both these incidents have resulted in explosion events that are confirming that the explosion hazard of ILs must not be neglected in some cases.

More frequently, self-sustained or piloted combustion of some ILs have been shown as a potential incidental scenario in some experiments. In most cases, rapid exothermic decomposition occurs when ILs with high nitrogen content are taken to high temperature and the subsequent decomposition products are sensitive to ignition and combustion. The combustion may tend to be explosive even under vacuum as shown by Smiglak et al. [START_REF] Smiglak | Combustible Ionic Liquids by Design: Is Laboratory Safety Another Ionic Liquid Myth?[END_REF] for imidazoliumbased ILs or hydrazinium-based ILs tested in their work.

In addition, burning tests performed on 4-amino-1-methyl-1,2,4-triazolium nitrate by Schaller [START_REF] Schaller | Synthesis, Characterization and Combustion of Triazolium Based Salts[END_REF] have led to a flame temperature of 2200 K. In some cases ILs are even combustible by design where intended for use as propellants as alternatives to hydrazine [START_REF] Shamshina | Catalytic Ignition of Ionic Liquids for Propellant Applications[END_REF]. Ultimately, once the various molecular bonds reach their thermal decomposition temperature in these carbonbased ILs, smaller and more flammable molecules could be released leading to combustion similarly to polymer combustion.

Flammability issues may also arise from specific behavior of hypergolic ILs. When in contact with the dinitrogen tetroxide (N 2 O4) or white fuming nitric acid (WFNA) those hypergolic materials can spontaneously ignite due to the highly exothermic reaction that takes place. It was shown that ILs with the dicyanamide or nitrocyanamide anion in particular are hypergolic [START_REF] Joo | Inorganic or Organic Azide-Containing Hypergolic Ionic Liquids[END_REF][START_REF] Zhang | Hypergolic Dimethylhydrazinium Ionic Liquids[END_REF][START_REF] He | Nitrocyanamide-Based Ionic Liquids and Their Potential Applications as Hypergolic Fuels[END_REF]. Also, 2,2-dimethyltriazanium nitrate and 2,2-dimethyltriazanium chloride are hypergolic prone materials [START_REF] Gao | Hypergolic Ionic Liquids with the 2,2-Dialkyltriazanium Cation[END_REF], suggesting that also the nature of the cation of the IL can modify hypergolic properties.

These examples show again that the traditional flashpoint type tests are certainly not adequate in most cases to properly characterize the fire hazard, as reported by Liaw et al. [START_REF] Liaw | Relationship between Flash Point of Ionic Liquids and Their Thermal Decomposition[END_REF]. This is related to our findings that ILs do not behave as traditional flammable liquids where the fire results from the combustion of the vapor phase of the concerned chemical. Our analysis [START_REF] Diallo | Revisiting Physico-Chemical Hazards of Ionic Liquids[END_REF] confirms therefore that the flammability hazard of ILs must be revisited, as those liquids show a burning behavior closely comparable to that of polymers rather than that of flammable solvents.

BRIEF DESCRIPTION OF THE MAIN EXPERIMENTAL RESULTS

The Fire Propagation Apparatus (FPA)

The fire behavior of ILs was determined using the FPA (standard ISO 12136), also called Tewarson calorimeter. This bench-scale fire calorimeter implemented at INERIS some 15 years ago has been described in detail in many studies [START_REF] Brohez | Fire Calorimetry Relying on the Use of the Fire Propagation Apparatus. Part I: Early Learning from Use in Europe[END_REF][START_REF] Brohez | Fire Calorimetry Relying on the Use of the Fire Propagation Apparatus. Part II: Burning Characteristics of Selected Chemical Substances Under Fuel Rich Conditions[END_REF][START_REF] Ribière | Investigation on the Fire-Induced Hazards of Li-ion Battery Cells by Fire Calorimetry[END_REF]. It belongs to the family of fire calorimeters that are bench-scale multipurpose testing apparatuses focusing on the characterization of burning behavior of materials and products in fire conditions. Figure 1 represents a schematic drawing of the FPA installed in the INERIS fire lab. Testing capability of the equipment encompasses ignitability, fire propagation potential, thermal and chemical characteristics in fire conditions. Repeatability and reproducibility of data count among the major advantages of the equipment together with its capacity for revealing atypical fire phenomena, like-liquid phase decomposition process of organophosphorous pesticides. In particular, parametric tests on product samples of about 25-50 g under controlled air intake allow for characterizing the fire behavior of the studied material or product (liquid, solid, gas) on the full spectrum of fire conditions (fuel rich or fuel lean). Scientific-sound diagnosis of the fire behavior of materials is achieved thanks to the access to key measures such as mass loss, Heat Release Rate (HRR) by application of fire calorimetry laws based on the assessment of oxygen consumption (OC) and carbon dioxide generation (CDG), measurements of fire effluent concentrations and related emission yields allowing for an evaluation of pollutants and fire toxicity issues. ILs samples and the mixture were tested in the FPA without any further purification step under an external heat flux of 50 kW/m 2 until ignition was observed, in order to achieve ignition in reasonably short time considering observed good to fairly good resistance to ignition in most cases. Sustained combustion following ignition requires conditions that may highly differ according to studied ILs. In this study, the external heat flux maintained after ignition was 25 kW/m 2 in all cases. Smoke analysis was performed by use of an online Fourier Transform Infrared (FTIR) spectrometer calibrated over 20 gases for derivation of CO 2 , CO, SO 2 , NOx, HCN, HCl, and HF concentrations and mass release rate versus time. An overview of the results obtained from the combustion of ILs in the FPA is summarized in Table 1. In addition, the theoretical energy of combustion of those materials measured in an oxygen bomb calorimeter following ASTM D240 protocol were given. The data and the observations made during the tests confirm generally good resistance to ignition of the ILs, based on the ignition time required under the applied external heat flux in the initial phase of the tests (50 kW/m 2 ). However, once ignition was obtained, sustained and flaming combustion phases were observed and characterized, confirming the real combustibility of all the ILs tested. Products emission factors reveal that high conversion rates of hetero-atoms in parent toxic effluents are obtained in several cases. The combustion of ILs having fluorine elements leads to the formation of HF. Whereas the presence of fluorine in organo-halogenated materials generally contributes to good flame retardancy of such materials, its conversion into HF in fire environments triggers unique hazards to exposed people and fire fighters and even equipment. This fact may justify careful evaluations before the practical use of ILs in laboratory and industrial settings.

Fire Propagation Apparatus (FPA) Tests

FROM SMALL-SCALE EXPERIMENTS TO REAL CONFIGURATION MODELLING

The FPA fire tests carried out on the different ILs led to the production of significant yields of toxic compounds. Of course, this implies a potential concern, depending on quantities involved over the toxic effects in case of a fire in a realistic configuration. Because of the important cost of ILs, it is unrealistic to perform large-scale pool fires, so the only way to evaluate real scale toxicity is dependent on the ability to carry out numerical simulations.

The starting point of a fire numerical model is in the ability of describing the fire behavior both in terms of power and toxic gases production. Being able to describe the heat release rate of an IL fire depends on the knowledge of the product properties and mainly the mass loss rate and the heat of combustion. As described in our previous paper [START_REF] Diallo | An Innovative Experimental Approach Aiming to Understand and Quantify the Actual Fire Hazards of Ionic Liquids[END_REF], and mentioned earlier in the present one, those two physical characteristics were measured during the FPA fire tests. These data can be used to build a realistic HRR.

Concerning the toxic gas production rate, the source term was built based on the smoke gas measurements done during the FPA tests coupled with the FTIR spectroscopy system. Induced reduction in visibility was not taken into consideration here due to atypical nature (mostly inorganic) of particulate emissions.

The Numerical Modeling

The FDS (Fire Dynamic Simulator) CFD (Computational Fluid Dynamics) code was used for toxicity prediction in a realistic geometry. This code was especially developed for fire consequences prediction [START_REF] Mcgrattan | Fire Dynamics Simulator (Version 5) User's guide[END_REF]. As all CFD codes, if the validations available in the literature are crucial, specific validation cases by users are also highly important. This code was evaluated by INERIS on its specific application, including toxic gases dispersion associated with [START_REF] Truchot | Numerical Analysis of Smoke Layer Stability[END_REF] or without a fire scenario [START_REF] Truchot | Are the Tunnel Ventilation Systems Adapted for the Different Risk Situations?[END_REF].

This code is based on a LES (Large Eddy Simulation) turbulence modeling concept that enables to predict with a quite great precision the toxic gas dispersion.

In the present case, the CFD approach was mainly used to give an illustration of the possible toxic impact in case of fire of an IL. While homogeneous approaches can give first evaluation of such toxicity, it is important to evaluate whether or not the energy released by the fire is sufficient for maintaining toxic gases stratification.

Toxicity

The large variety of gases produced in the IL fire suggests that taking into account their potential cumulative effects as described in ISO 13571 [START_REF]Life-threatening Components of Fire -Guidelines for the Estimation of Time Available for Escape Using Fire Data[END_REF] is actually here a requirement. This standard defines the FEC (Fractional Effective Concentration) relating to concentration-dependent toxic potency of irritant species that are found in fire gases. The concept integrates additive effect of each irritant gas present. A value of FEC higher than 1 is critical towards self evacuation of concerned people, that in such a case are considered incapacitated and therefore need to be rescued. Using this criterion in the numerical modeling generates a clear view of the toxicity area, but it also requires that the numerical model be modified to support the approach.

The FEC concept integration in our modeling work has been based on the assumption that the relative concentrations between the different toxic gases are kept constant. This means more physically that we validate that the proportions between the toxic products generated are not significantly modified by species transport.

In order to illustrate the fire induced toxicity potential concern presented by ILs in case of a fire, a case study comparing same pool fire scenario (same pool size) of two ILs was considered integrating appropriate input data from our experiments. The comparison is based on the FEC distribution in the computed domain. This domain was chosen to have realistic size but small enough to limit the computation time. The domain was then design as a room of 10 x 10 m 2 area and 5 m height with homogeneous cell size of 0.1 m in each direction. The fire size that was considered was on-purpose chosen as quite small given that current applications in chemical processing rely on use of very limited quantities of ILs as solvent and/or catalysts. Accordingly, the pool that would result from a leak in that reactor may be assumed actually quite limited in surface. In our calculations, the pool area was fixed to 0.04 m 2 . This configuration has as its main advantage to be close enough to the FPA tests to make the measured values be representative. A standard ventilation system was modeled in this building with a flow rate of 3 times the building volumes each hour.

The methodology used for integrating the FEC calculation routines was identical for all considered liquids. It is here detailed for the PYR 14 TFSI product. First the emission factors of the different products for the PYR 14 TFSI FPA test are taken from Table 2. This table also gives the individual threshold for building the critical FEC value and couples it with the individual concentration.

% _ VHCI ! VlïBr ! VHF I ( PsO1 | ( PNO2 | Çacrolein | Vformaldehyde | -y ÇjrriizRt FEC F F F F F F + 2 + 1 HCl F HBr F HF F SO2 F NO2 F acrolein F formaldehyde F Ct
In this formula, Ç represents the local concentration of the given gaseous substance while F give the threshold as indicated in above table. In the present case, considering that NO can be assimilated to NO 2 , formula can be reduced to:

X = <PHF + <PSO 2 + (P N Q 2 FEC F F F 1 HF F SO2 F NO2
It is obvious that the contribution of NO 2 in the present case is very limited. As described previously, this value must stay under 1 to ensure safety conditions for people during the evacuation phase.

Numerical Results

Before going any further in the toxicity evaluation, it is important to evaluate the thermal consequences of the fire. Among the considered product, the lowest HRR is 266 kW/m 2 , generated by the PYR 14 TFSI, the highest one is 1416 kW/m 2 , the variety of total power generated by the small fire size stay limited as presented in Fig. 2. Those values must clearly be kept in mind in the toxicity results analysis because of the direct linked with the potential stratification. This analysis is presented on Fig. 3 to Fig. 5 for the different considered ILs through the FEC distribution in the central plane of the room. Those pictures correspond to a steady state reached after about two minutes. The legend is identical between the different pictures. These values show that, for such a very small fire, the toxicity remains low enough in the lower part of the building during people evacuation. It must be kept in mind, however, that this situation corresponds to a very small fire. The associated temperature for that case stay limited as shown on Fig. 6. Despite the low level of temperature reached in the domain, a certain thermal stratification is observed in the building. This, of course, favors the toxic stratification observed in previous pictures.

The first simulations correspond to a very small fire; the case of a larger fire, 1 m 2 , with the [P4,4,4,1][MeOSO 3 ] product generates a different conclusion as shown in Fig. 7. The blue rectangle on this picture corresponds to one of the obstacle. As shown in these pictures, the FEC becomes larger than 1 in the lower part of the room after only 1 minute, meaning that evacuation will become highly dangerous for people located inside the enclosure. While this duration can appear highly short, the infinitely quick fire growth considered in this simplified case lets indicates that some additional seconds should be offered to people for the evacuation.

On top of this toxicity effect, the temperature increase inside the building is more important because of the higher heat release rate due to the larger size of the fire. The temperature distribution is shown in Fig. 8.

For that size of fire, temperatures quickly increase and can also generate some thermal effects on people before or during evacuation.

CONCLUSION

ILs are more and more used in different industrial applications because of some highly specific properties that make them highly tunable according to desired functionalities. The specific atomic composition of many ILs raises concerns about the consequences in case of fire, particularly with regards to toxicity. Estimating toxic consequences in case of fire, requires being able to predict the smoke composition. Because of the high complexity of the ILs molecules, predicting this composition imposes an experimental approach. As detailed in this paper, this was previously done using the FPA coupled with an FTIR spectrometer.

The approach presented in this paper consists in coupling these small-scale FPA measurements with a CFD approach to predict toxic consequences in case of an IL fire in a realistic industrial configuration. Because of the large variety of toxic compounds, their relative impact on the total toxic effects must be considered using fractional effective concentration (FEC) and/or dose (FED) approaches (as developed in ISO 13 571 for incapacitation) or other adverse effects of fire toxic components. Such an approach was developed thanks to the FDS fire code that enables modeling of thermal consequences of a fire but also the toxic gas dispersion inside an enclosed.

While the fire size considered in this paper is small, 0.04 m 2 , simulations for IL fires shows that the toxicity inside the building quickly increase. In case of a larger fire, the toxic gas concentration near the ground quickly becomes high enough, by having a FEC larger than 1, which means that toxic effects on people must be considered.

Of course, the results shown in this paper were obtained based on a first quite simplified approach to be improved. This, however clearly shows that the toxic consequences in case of IL fires cannot be neglected and keep highly scenario dependent.

Figure 1 .

 1 Figure 1. Schematic view of the FPA.

Figure 2 .

 2 Figure 2. Heat Release Rate developed for the different products.

Figure 3 .Figure 4 .Figure 5 .

 345 Figure 3. Iso-surface of FEC = 1 for BMIM TFSI

Figure 6 .

 6 Figure 6. Temperature distribution in the central plane of the room after having reached the steady state.

Figure 7 .

 7 Figure 7. Time evolution of the FEC = 1 iso-surface in case of [P 444 !][MeOSO 3 ] product 1 m 2 pool fire.

Figure 8 .

 8 Figure 8. Temperature distribution in the central plane of the room 60 s after the fire ignition.

Table 1 .

 1 Burning behavior of ILs in the FPA

	Ionic Liquid	[P4,4,4,1][ MeOS O3]	[BMIM][TFSI] 1MLiTFSI	[PYR 14 ][TFSI]
	Initial mass [g]	32.5	61.9	51.3
	Char residue [%]	6.5	14.9	5.7
	Time to ignition [s]	200	294	280
	Average mass lost rate [g/m 2 /s]	33	46.6	24
		Heat of combustion [MJ/kg]
	Theoretical heat of combustion	28.3	10.8	14.8
	OC method	24.6	7.5	12.0
	CDG method	26.4	7.9	13.2
	Average heat release	25.5	7.7	12.6
	Combustion efficiency [%]	90	71	85
		Emission factor [mg/g]
	CO 2	1654	552	765
	CO	36	21.6	29.6
	Soot	48.8	11	43.9
	SO 2	184	352.6	310
	NO	0	4.9	5.1
	N 2 O	0	1.9	2.2
	HF	0	268.6	221.6
	HCN	0	6.9	6.7

Table 2 .

 2 Toxic results for the FPA test with PYR 14 TFSI ionic liquid.

	Toxic Product	CO 2	CO	SO 2	NO	N 2 O	HF	HCN
	Emission factor [mg/g]	765	29.6	315.4	5.1	2 2	221.6	6.7
	Relative proportion	49.6	3	14.1	0.5	0.1	31.6	1
	FEC threshold [ppm] [10]	-	-	150	250	-	500

-Keeping in mind that the FEC is representing the cumulative effects of the different irritant gas, it consists in the following sum:


Valerie Pommier-Budinger

Marc Budinger
email: valerie.budinger@isae.fr

Sizing optimization of piezoelectric smart structures with meta-modeling techniques for dynamic applications

Keywords: Sizing, meta-model, dynamic reduced model, Finite Element, piezoelectric smart structures

This article shows an efficient method with a high industrial applicability to design piezoelectric smart structures for dynamic applications. This method allows sizing structures with requirements of dynamic displacements. The first step of this method consists in extracting dynamic reduced models from Finite Element simulations which will enable us to obtain a model for any structure, whatever its complexity, as opposed to analytical modeling methods. These models are computed for a set of design parameters. Then a meta-model, which is a simplified descriptive model of other models, is computed as a surface response model that expresses the design objectives and constraints as a function of the design variables. The combination of the results stemming from the meta-model allows working out the optimal values of the design parameters. The main advantage of the proposed method is to enable the quick design exploration of structures. As an example, the method is applied to a flexible structure whose dynamic displacements need to be controlled in bending and twisting. The theoretical results are validated in the end by experiments.

INTRODUCTION

Piezoelectric smart structures, the association of structures with piezoelectric devices (ceramics, PVDF or piezocomposite), are the subject of a very large number of studies. One of the issues these studies present lies in the design of such structures to improve performance or to obtain the required specifications. This design can be seen as a succession of several steps:

-The optimization of the piezoelectric actuators (types, sizes, locations on the structures…) -The model of the structure to control -The design of the control law In this paper, we will deal with the first step only, and even with this restriction, the number of studies remains really high. For the state of the art, we mainly refer to articles published these last ten years. The readers who would like to get an overview of previous articles can refer to Frecker [START_REF] Frecker | Recent Advances in Optimization of Smart Structures and Actuators[END_REF] who has conducted a review on the optimization of smart structures and actuators and to Chee et al. [START_REF] Chee | A Review on the Modelling of Piezoelectric Sensors and Actuators Incorporated in Intelligent Structures[END_REF] who have studied the modelling of piezoelectric sensors and actuators incorporated in intelligent structures. In order to help the analysis of the papers regarding optimization, we have chosen to classify them according to several criteria which are defined as follows:

-the optimization methodology: sizing optimization (the shape of the actuators is set and the design variables are sizes (e.g. the length and the width for a rectangular piezoelectric ceramic), shape optimization (the shape can change but not the number of boundaries) or topology design (the number of boundaries and the shape of the actuators can change).

-the objectives and constraints of the optimization: required displacements, maximum electromechanical coupling factors (EMCC), maximum controllability, maximum observability, minimum weight, required supply voltage… -the type of applications: static or dynamic -the type of analysis used to solve the problem: analytical or Finite Element analysis

The first set of studies we have analyzed deals with sizing and shape optimization. In 2002, Mukherjee et al. [START_REF] Mukherjee | Piezoelectric sensor and actuator spatial design for shape control of piezolaminated plates[END_REF] offered a method to optimize piezoelectric structures based on the minimization of the global displacement residual error between the desired and current structural configuration. The structure was discretized but all the computations were analytical and the case studies dealt with a beam in static and dynamic configurations. In 2003, Irschick et al. [START_REF] Irschik | Dynamic shape control of beam-type structures by piezoelectric actuation and sensing[END_REF] achieved dynamic shape control with a method to compute the spatial distribution of piezoelectric actuators that allows getting a structural displacement field. This analytical method was applied to composite beam-type structures. Then, Sun et al. [START_REF] Sun | Design optimization of piezoelectric actuator patterns for static shape control of smart plates[END_REF] used an energy optimization based method to find the optimal control voltages which can actuate a structure close to the desired shape within a given error. They applied the method on a static case for the shape control of composite plates. Nguyen et al. [START_REF] Nguyen | Voltage and evolutionary piezoelectric actuator design optimisation for static shape control of smart plate structures[END_REF] also proposed a design method for static cases. They studied the shape control of plates by using a method based on a multi-criteria optimization. Later, Donoso et al. [START_REF] Donoso | Optimization of piezoelectric bimorph actuators with active damping for static and dynamic loads[END_REF] considered optimal design problems in the context of active damping, more specifically to control the deflection of a structure subjected to static and dynamic loads. The optimal thicknesses or widths of the piezoelectric ceramics minimizing the deflection were computed thanks to an analytical analysis. The method was thus applied to a simple cantilever beam. Another study of Donoso et al. [START_REF] Donoso | Systematic design of distributed piezoelectric modal sensors/actuators for rectangular plates by optimizing the polarization profile[END_REF] extended the same analytical method to rectangular plates. At the same time, Zhang J. et al. [START_REF] Zhang | Study of the Optimal Location and Size of Piezoelectric Actuator in Smart Structures[END_REF] computed the optimal locations and sizes of piezoelectric actuators to produce the maximum controllability and observability of modes in smart structures. In their paper, the model of piezoelectric smart structures is built by the application of Finite Element software and the study is performed on a dynamic case but with no specification on the displacement amplitudes whatsoever. Zhang R. et al. [START_REF] Zhang | Optimal placement of piezo actuators on a beam: a dynamic problem from stochastic to deterministic[END_REF] also studied the optimal location of piezoelectric actuators in case of uncertainties. Recently, Brusa [START_REF] Brusa | Optimisation of a Hybrid Energy Scavenger with Piezoelectric/Magnetic Coupling for Sensor-Bearing Units[END_REF] proposed the optimization of a hybrid energy scavenger. Although, once again, concerning the shaping of the surface of the cantilever, the optimization was based on an analytical expression of the normal stress.

Another trend for the design of piezoelectric smart structures is the use of topology optimization based on finite element analysis and optimization techniques such as the method of moving asymptotes, genetic algorithms, optimality criteria method, … It allows computing the topology of piezoelectric patches in order to maximize or minimize a physical quantity such as compliance (external work), stress, electromechanical coupling factor, etc... Kögl et al. [START_REF] Kögl | Topology optimization of smart structures: design of piezoelectric plate and shell actuators[END_REF] used topology to design piezoelectric plates and shell actuators in static applications. Carbonari et al. [START_REF] Carbonari | Topology optimization design of functionally graded bimorph-type piezoelectric actuators[END_REF] applied topology optimization to find the optimum gradation and polarization sign variation in piezoceramic domains in order to improve bimorphtype actuators. In this study, the performance was measured in terms of static output displacements. Drenckham et al. [START_REF] Drenckhan | Topology Optimization of a Piezoelectric Actuator on an Elastic Beam[END_REF] investigated the optimal topology of a piezoelectric actuator to reduce the tip deflection of a static cantilever beam under a concentrated tip load. Rupp et al. [START_REF] Rupp | Design of Piezoelectric Energy Harvesting Systems: A Topology Optimization Approach Based on Multilayer Plates and Shells[END_REF] used topology optimization to design the layout of a multilayer structure to maximize the harvested power. The particularity of this work was to design the layout of piezoelectric and structural materials on layered plate structures as well as the harvesting circuit to which it is connected. Zheng et al. [START_REF] Zheng | Topology optimization of energy harvesting devices using piezoelectric materials[END_REF] designed energy harvesting devices in static cases by considering both the locations of piezoelectric patches and the elastic layout of the structures. The more recent works address the design of piezoelectric actuators, sensors and energy harvesters on static structural problems (Kim et al. [START_REF] Kim | Multi-physics interpolation for the topology optimization of piezoelectric systems[END_REF]), the dynamic design of piezoelectric laminated sensors and actuators to obtain specified resonance frequencies, modes and electromechanical coupling factor (Nakasone et al [START_REF] Nakasone | Dynamic Design of Piezoelectric Laminated Sensors and Actuators using Topology Optimization[END_REF]), the static shape control of piezoelectric plates (Kang et al. [START_REF] Kang | Topology Optimization for Static Shape Control of Piezoelectric Plates With Penalization on Intermediate Actuation Voltage[END_REF]), strain energy-based finite element approach (Bachmann et al. [START_REF] Bachmann | Optimum piezoelectric patch positioning: A strain energy-based finite element approach[END_REF]) and the design of piezoelectric energy harvester using stress norm constraints (Wein et al [START_REF] Wein | Topology optimization of a cantilevered piezoelectric energy harvester using stress norm constraints[END_REF]).

Our work tackles the sizing optimization of piezoelectric smart structures for dynamic applications and the method that we propose is based on the response surface methodology (Park et al. [START_REF] Park | Optimal design of rotor bars of a written-pole motor by using response surface method for improving the pole-writing performance[END_REF], Choi et al. [START_REF] Choi | Approximate optimization for minimum torque ripple of three phase switched reluctance motor using response surface modeling[END_REF]) and on the analysis of a meta-model consisting in an analytical model derived from reduced dynamic models obtained from Finite Element results. In our study, the sizing aims at getting required displacements with a minimal volume of piezoelectric patches. The meta-model is thus composed of polynomial functions expressing the dynamic displacements of the structure as a function of the piezoelectric actuators' dimensions. These displacements are worked out from a set of reduced dynamic models selected by a Design of Experiment (DoE) and obtained by Finite Element software which allow us to study more complex structures than beams or plates. The main advantage of meta-modeling techniques is that they enable to compute a design model from a finite and limited number of Finite Element simulations that are time-consuming. As a consequence, they enable quick design exploration of structures.

The above cited articles proposed studies with some similarities but neither with the same objectives nor the same methodology as the one we are developing here. As far as we know, the examples of studies using meta-modeling techniques to design piezoelectric structures (Cappelleri et al. [START_REF] Cappelleri | Design of a PZT Bimorph Actuator Using a Metamodel-Based Approach[END_REF] and Paternoster et al. [START_REF] Paternoster | Geometrical optimization of a hingeless deployment system for an active rotor blade[END_REF]) only addressed optimization of static forces and deflections. For dynamic applications, the objective functions or constraints of the common methods which tackle the design issue are the required resonance frequencies, modes or enhanced electromechanical coupling factors because these values are easy to compute. We have chosen to use the dynamic displacements, even if their computation is not immediate and requires intermediate calculations, because they are significant values in dynamics problems. Furthermore, let's also point out that vibrations control can be achieved by the use of semipassive (Guyomar et al. [START_REF] Guyomar | Damping Behavior of Semi-passive Vibration Control using Shunted Piezoelectric Materials[END_REF]) or passive (Irschik et al. [START_REF] Irschik | Dynamic shape control of beam-type structures by piezoelectric actuation and sensing[END_REF], Porfiri et al. [START_REF] Porfiri | Circuit analog of a beam and its application to multimodal vibration damping, using piezoelectric transducers[END_REF][START_REF] Porfiri | Modeling and design of passive electric networks interconnecting piezoelectric transducers for distributed vibration control[END_REF], Shen et al. [START_REF] Shen | A semi-passive vibration damping system powered by harvested energy[END_REF]) solutions and that our method relates to active solutions. Therefore, in addition to vibration control, it can be used for the generation of vibrations (e.g. for ultrasonics transducers).

The novelty of our article is to combine Finite Element simulations, computations of reduced dynamic models and meta-modeling techniques to design actively controlled smart piezoelectric structures which meet requirements in terms of dynamic displacements.

Section 2 presents the smart piezoelectric structure under study with the design variables, the reduced dynamic model computed from Finite Element simulations and its use to compute the dynamic displacements of the structure. Section 3 deals with the meta-modeling techniques. Section 4 gives the meta-model obtained from the responses (output variables) and the results of the sizing. Experimental tests validate the study.

THE STRUCTURE UNDER STUDY AND ITS REDUCED DYNAMIC MODEL

Description of the structure

The structure under study (Fig. 1) is made of a plate in aluminum alloy and a cylindrical tank in PVC whose characteristics are given in table 1. The plate is clamped at one extremity and free at the other, where the tank is attached to the plate thanks to a metallic ring. The structure has been designed to have low resonance frequencies as an aircraft wing and to study robust control laws to attenuate vibrations in bending and twisting, whatever the filling of the tank. The design study is carried out in this article for the case of an empty tank, not to deal with sloshing phenomena which would introduce other resonance frequencies than the frequencies of the single plate. However, even if it is not developed here, our method is also valid for the cases with liquid in the tank.

A Finite Element Analysis is performed to compute the first resonance frequencies of the structure and a modal testing allows measuring the damping ratio associated to these frequencies. The results are given in Table 2 for the first three modes of the structure. The objective of the control is to attenuate the vibrations 6 due to these first modes which are preponderant because of their very low frequencies and damping ratios. The requirements are to design a smart piezoelectric structure to control vibrations of 130mm peak to peak for the first bending mode, of 6mm peak to peak for the second bending mode and of 6mm peak to peak for the first twisting mode at the tip of the beam.

Design variables

Two sets of piezoelectric ceramics will be used in order to attenuate the vibrations. The piezoelectric ceramics are made of PIC151®PI. They will be bonded at the clamped side of the structure and in the middle of the beam, on each side of the symmetry axis of the beam large side (Fig. 2). These locations are chosen to get the maximal strain in the structure for the modes to be controlled and to ensure maximal efficiency of the piezoelectric actuators (Crawley et al. [START_REF] Crawley | Use of piezoelectric actuators as elements of intelligent structures[END_REF]). The design parameters of the study will be the lengths and the widths of the piezoelectric patches (Fig. 2). As the problem is symmetric, it is assumed that both patches will have the same length and width. Lengths of the patches L can vary from 30 to 300mm and widths W from 10 to 80mm. The thickness of the patches is not considered as a design parameter because it is imposed by the supply voltage and the maximal electrical field. For this application, the supply voltage is ±120V and as the maximal electrical field is ±400V/mm for dynamic applications, the minimal thickness is 0.3mm. At the end, the patches will be 0.5mm-thick due to supply constraints.

Dynamic reduced model

For the structure under study, the reduced dynamic mode is established for the first three modes. The reduced-model of a structure with k piezoelectric actuators can be modeled for n modes in the modal base with a mechanical equation and an electrical equation as shown in (Hagood et al. [START_REF] Hagood | Modeling of Piezoelectric Actuator Dynamics for Active Structural Control[END_REF]) and (Hatch [START_REF] Hatch | Vibration simulation using Matlab and ANSYS[END_REF]):

+ = + = + + V C q q F V Kq q D q M o T C s e (1)
where:

q is the modal displacement vector (nx1) q c is the electrical chargevector (kx1) -V is the voltage vector (kx1) -M is the modal mass matrix (nxn) -D is the modal damping matrix (nxn) -K is the modal stiffness matrix (nxn) -θ θ θ θ is the modal electromechanical coupling matrix (nxk) -C o is the modal turned-off capacity matrix (kxk)

-F e is the external forces vector (nx1)

This model can be computed with multiphysics Finite Element software (such as ANSYS© or ABAQUS©) that allows calculations with piezoelectric elements.

The computation of the modal matrices M and K is classical and is achieved through a modal analysis. If the modal base is normalized to the mass matrix, we have:

nxn I M = (2) (3)
where i ω are the free vibration angular frequencies.

The computation of the matrix is not so common and will be detailed thereafter. We note u(t) the vector composed of the m physical displacements (physical displacement means real displacement on the structure as opposed to modal displacement). Therefore, we can write:

q u = ( 4
)
where the matrix (mxn) is a matrix of change of basis. can be expressed as:

(

We construct the matrix such that each column is composed of the m physical displacements computed for each mode j, with j=1..n. With such a matrix and if the piezoelectric patches are short-circuited (potential null on all electrodes, V=0), the electrical equation of system (1) enables to write: [START_REF] Nguyen | Voltage and evolutionary piezoelectric actuator design optimisation for static shape control of smart plate structures[END_REF] where is composed of the k electrical charges computed for each mode j, with j=1..n .

With this method, the matrix can thus be computed through the same modal analysis as the one used for the computation of the mass and stiffness matrices provided that the modal analysis is performed with short-circuited piezoelectric patches. The advantage of this method is that you can get the model of piezoelectric structures by executing a single modal analysis.

With regards to the modal damping matrix, it is formulated as (Hasselman [START_REF] Hasselman | Modal coupling in lightly damped structures[END_REF]):

KM D ) 2 ( diag i ε = (7)
where ε i is the damping ratio of each mode. The damping ratio is generally quite difficult to calculate because it depends on too many experimental parameters and it is preferable to measure it.

For the future developments, the modal damping matrix is written as:

! (8)
By implementing the modeling method that has just been exposed, the model of the structure under study is computed with the geometric data of Table 1 and the measured damping ratios of Table 2 and in a manner to be able to get the physical displacements of the points A and B for the first three modes of the structure.

Responses: dynamic displacements

In our design, the requirements are not expressed in terms of compliance, stress or electromechanical coupling factor but in terms of displacements. The responses for the design are the peak to peak displacements in bending and twisting for the first three modes.

The peak to peak displacement " # $%&$% for the first bending mode corresponds to the peak to peak displacement of the point A or B. This displacement is computed from the model of the previous section implemented in the following conditions:

-both actuators are supplied by in phase AC voltages of magnitude V and of resonance pulsation # .

-the effect of the other modes is assumed to be negligible.

-no external force.

Then, the mechanical equation of (1) expressed at the resonance pulsation # . and combined with equations ( 4) to (8) leads to:

( )

1 11 21 11 11 1 2 D V q q u c c pk pk + = - (9)
The peak to peak displacement " $%&$% for the second bending mode is computed in the same way by considering both actuators supplied by in phase AC voltages of magnitude V and of resonance pulsation . Then, " $%&$% is expressed by: ( )

2 22 22 12 12 2 2 D V q q u c c pk pk + = - (10)
The peak to peak displacement " ' $%&$% for the first twisting mode corresponds to the peak to peak displacement between the point A (or B) and the neutral axis. It is computed from the mechanical equation of (1) combined with equations ( 4) to [START_REF] Donoso | Systematic design of distributed piezoelectric modal sensors/actuators for rectangular plates by optimizing the polarization profile[END_REF] while considering the actuators supplied by opposite AC voltages of magnitude V and of pulsation ' , in case of no external force and while neglecting the effect of the other modes. It is expressed by: ( )

3 33 23 13 13 3 2 D V q q u c c pk pk - = - (11)

META-MODELS OF THE STRUCTURE UNDER STUDY

A meta-model (Simpson et al [START_REF] Simpson | Metamodels for Computer-Based Engineering Design: Survey and Recommendations[END_REF]) is a simplified or approximated descriptive model of another model. Meta-models are also called surrogate models (Forrester et al. [START_REF] Forrester | Engineering design via surrogate modelling: a practical guide[END_REF]) or response surface approximations (Raymond et al. [START_REF] Raymond | Response surface methodology : process and product optimization using designed experiments[END_REF]). The surrogate model can be used during design and optimization tasks to evaluate design objectives and constraint functions as a function of design variables. To develop these metamodels, different Design of Experiments (DoE) and different forms of regressions can be chosen. As mentioned by (Simpson et al. [START_REF] Simpson | Metamodels for Computer-Based Engineering Design: Survey and Recommendations[END_REF]), when the errors come mainly from the variability of experiments (in case of models for physical experiments), traditional DoE are used and when the errors come mainly from the choice of the model (in the case of models for computer experiments), Design and Analysis of Computer Experiments (DACE) are used.

Several meta-models can be computed for the same structure, depending on the input parameters and on the outputs. In the case under study, the meta-models consist in 3 functions which give the displacement amplitudes of the first two bending modes and of the first twisting mode as a function of the length and the width of the piezoelectric patches. As our case is based on deterministic numerical simulations, a Latin Hyper Cube (LHC) DoE with 16 experiments (16 modal analyses performed for different widths and lengths and the computation of the displacements for each analysis) has been selected to have samples which are optimally filling the design space. This selection allows a better assessment of the error distribution and a better choice of the meta-model. Fig. 3 shows the 16 experiments and the displacement amplitudes for the first two bending modes (Fig. 3 The choice of the meta-model forms depends on the nature of the surfaces to be approximated. As the experiment values of Fig. 3 do not show many peaks and valleys, high flexibility forms such as Radial Basis Functions (Jin et al. [START_REF] Jin | Comparative studies of metamodelling techniques under multiple modelling criteria[END_REF]) and Kriging functions (Stein,[START_REF] Stein | Interpolation of Spatial Data: Some Theory for Kriging[END_REF]) (Kleijnen,[START_REF] Kleijnen | Kriging metamodeling in simulation: A review[END_REF]) are not necessary.

Thus, polynomial functions are selected as meta-model forms for the case under study.

Two polynomial function of third order (equ. 12 and equ. 13) are sufficient to represent the response surfaces of the peak to peak displacements in bending for the first two bending modes (Fig. 4(a) and 5(b)) with a coefficient of regression R 2 over 99% and another polynomial function of third order (equ. 14) allows representing the response surface of the peak to peak displacement in twisting for the first twisting mode (Fig. 4(c)) with a coefficient of regression R 2 of 98%.

" ()*() +. 7. . of the specifications is met, the grey zone to the area where a single constraint is verified and the white zone represents the possible design space. In this zone, the dimensions of the piezoelectric ceramics which minimize the volume of ceramic (optimal point of length 144mm and width 75mm) are selected but, for supply reasons, patches of length 140mm and width 75mm are bonded on the structures with rigid glue. A final simulation of the experimental device with these piezoelectric actuators is run to check that the displacements are very close to the requirements.

Then experimental tests are performed three times by supplying the actuators with:

-in phase AC voltages of magnitude 120V at the first bending frequency, -in phase AC voltages of magnitude 120V at the second bending frequency, -opposite AC voltages of magnitude 120V at the first twisting frequency.

For each voltage, the displacements at points A and B are measured by a laser vibrometer to compute the displacements due to bending and twisting. Table 3 gives the required, computed and measured displacements for the three modes under study. The errors between the required and measured displacements are inferior to 1.6%, 1.7% and to 3.4% for the first two bending modes and the first twisting mode respectively. The accuracy validates the design method of piezoelectric smart structures with meta-modeling techniques for dynamic applications. This method can be extended to other types of requirements such as accelerations.

Fig. 1 .

 1 Fig.1. Structure under study (beam with the tank at its tip): (a) picture (b) diagram

Fig. 2 .

 2 Fig.2. Design parameters: length and width of the piezoelectric actuators.

  (a) and (b)) and for the first twisting mode (Fig.3(c)) computed as explained in Section 2 with supply voltage of 120V.

Fig. 3 .

 3 Fig.3. DoE with 16 experiments and the corresponding computed displacement amplitudes (in m) (a) for the first bending mode (b) for the second bending mode (c) for the first twisting mode

"

  # ()*() +, -. *' / . 0112 / . 345 / 0 1-25 + 6 72 + . 43,5 + 3, 632 5 + 7 63725 + 7 2 ' / . ,, 5'

Fig. 4 .

 4 Fig.4. Surface responses of the displacement amplitudes as a function of the width and the length of piezoelectric actuators (a) for the first bending mode (b) for the second bending mode (c) for the first twisting mode

Fig. 5 .Table 3 .

 53 Fig.5. Feasible design space meeting the requirements (white zone)

Table 1 . Material and geometric characteristics of the structure

 1

		Beam		Tank	Fixation ring
	Length (mm)	1360	Ext. Diameter (mm)	110	144.5
	Width (mm)	160	Int. Diameter (mm)	100	110

Table 2 . Dynamic characteristics of the structure

 2

  8 + . .732 / . . 75 / . ,4025 / 1,12 + . 3 75 + 3 ,4 2 5 + 3 .625 + 1 4732 ' / . -.35'

	*' / . .642 / . ..15 / . -7,25 + . 0 32 + . .605 + . 36 2 5 + . 1,-25 / . , 32 ' / . .405 '	(13)

and 14 " ' ()*() +. ., . *


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