Félicité Ondze

Jean-Henry Ferrasse

Olivier Boutin
email: olivier.boutin@univ-amu.fr

Jean-Christophe Ruiz

Frédéric Charton

Process simulation and energetic analysis of different supercritical water gasification systems for the valorisation of biomass

The energetic efficiency for the supercritical gasification of biomass is studied for three cases: hydrogen and methane production, heat and electricity cogeneration. Experimental results from the gasification of glucose are used to represent the gasifier. The other unit operations are simulated using the software ProsimPlus through thermodynamic equilibrium calculations. Simulations are conducted at different pressure, temperature and initial biomass concentration. The energetic and exergetic yields are calculated, as well as the minimum heat requirement estimated from a pinch analysis. All the results are then exploited to determine optimal conditions for two systems: adiabatic and isothermal. The optimal temperature ranges from 584 to 626 °C, whereas the optimal initial concentration ranges from 51 to 87 g L -1 . The system giving the best result in term of global energetic optimisation is methane production in isothermal conditions, followed by methane production in adiabatic conditions. The optimal energy efficiencies are 94% and 91% respectively.

Introduction

Among different processes of biomass conversion, an attractive way is gasification: the "dry" gasification, which operates at high temperature (up to 950 °C) and a pressure close to atmospheric pressure, and supercritical water gasification (SCWG) with temperature ranging from 450 to 600°C and pressure up to 40 MPa. This last one is more specifically dedicated to wet biomass as no pre-drying step is needed.

Gasification in supercritical water can be used for the production of hydrogen [START_REF] Calzavara | Evaluation of biomass gasification in supercritical water process for hydrogen production[END_REF][START_REF] Savage | Biomass gasification in supercritical water[END_REF][START_REF] Antal | Biomass gasification in supercritical water[END_REF]. However a mixture of carbon monoxide, hydrogen and methane are generally obtained depending on the operating conditions [START_REF] Van Rossum | Catalytic gasification of dry and wet biomass[END_REF][START_REF] Resende | Noncatalytic gasification of cellulose in supercritical water[END_REF][START_REF] Matsumura | Biomass gasification in near-and super-critical water: status and prospects[END_REF]. Gas compositions from experimental results for various biomass or chemical compounds are available and specific calculations have been performed to predict gas composition at thermodynamic equilibrium [START_REF] Letellier | Gasification of aqueous biomass in supercritical water: a thermodynamic equilibrium analysis[END_REF][START_REF] Tang | Supercritical water gasification of biomass: thermodynamic analysis with direct Gibbs free energy minimization[END_REF][START_REF] Feng | Biomass conversions in subcritical and supercritical water: driving force, phase equilibria, and thermodynamic analysis[END_REF]. Equilibrium predictions are in accordance with experimental data when light gas molecules are considered but are not of use when bigger molecules are presents in complex mixtures.

Regarding conventional lignocellulosic biomass, it is generally accepted that glucose is a model compound for cellulose (also sometimes for hemicellulose), aromatic compounds a model for lignin and glycine a model for protein [START_REF] Schmieder | Hydrothermal gasification of biomass and organic wastes[END_REF]. A study of many different biomass of agricultural origin shows the wide range of results and the difficulty of predicting yields regarding the composition of the initial biomass [START_REF] Szargut | Exergy Analysis of Thermal. Chemical and Metallurgical Processes[END_REF]. For residues, SCWG has been tested for industrial effluent: black liquor from paper mills, food industry or municipal in the case of sewage sludge with massic water content higher than 90%. Yakaboylu et al. [START_REF] Yakaboylu | Supercritical water gasification of biomass: a literature and technology overview[END_REF] and Casademont et al. [START_REF] Casademont | Supercritical water gasification: a patents review[END_REF] provide a complete overview on biomass gasification, from experimental approaches to modelling.

Contrary to the important quantity of experimental results for SCWG of biomass, less studies have paid attention to the use of experimental results for a global energetic analysis of the systems, from the raw biomass to the final useful product. In literature, first approaches are based on the estimation of overall energy balances. For instance, a classical and complete approach on energetic evaluation has been proposed by Marias et al. [START_REF] Marias | Energetic analysis of gasification of aqueous biomass in supercritical water[END_REF]. The same kind of work have been conducted by Guan et al. [START_REF] Guan | Energetic analysis of gasification of biomass by partial oxidation in supercritical water[END_REF] for partial oxidation of biomass. However, these works are dedicated only to the gasification reactor and not to the complete system up to the production of the final useful gas. A more complete study including other unit operations, up to the production of a syngas, is proposed by Wan [START_REF] Wan | An innovative system by integrating the gasification unit with the supercritical water unit to produce clean syngas: effects of operating parameters[END_REF]. Different operating parameters have been tested, the different stages being modelled through thermodynamic equilibrium. However, in all these studies, a systemic study of the operating conditions as well as an optimisation for the gas production are not developed.

This work presents the evaluation of three scenarios (production of hydrogen, production of methane and cogeneration) simulated using a commercial software, based on experimental data for the gasification reactor and mainly thermodynamic equilibrium for other operation units. These simulations give energy and exergy yields, and along with a Pinch analysis, the minimum energy required for each case studied. Eventually, using a numerical design approach, the influence of operating conditions on these three parameters is studied.

Process simulations

Process simulations have been carried out with the numerical simulation software ProSimPlus (version 3.5.18, France). This software allows the calculation of mass and energy balances for each unit operation. It is also a data bank for the physical properties of the different compounds considered. Except for supercritical gasification, process units are mainly calculated with thermodynamic equilibrium using Predictive Soave Redlich Kwong model. For few cases, another thermodynamic model can be used; this model being indicted in the text. Experimental data from the supercritical water gasification of glucose are used at the entering and the exit of the gasifier [START_REF] Ondze | Supercritical water gasification of beet residues: from batch to continuous reactor[END_REF]. For the three scenarios, the different unit operation are calculated either as an isothermal system or an adiabatic system. Detailed conversion systems are given bellow. A brief description of the simulation tool is given in the Supplementary materiel, Appendix A.

Gasifier

The simulation of the generation of gases from the gasification reactor is common to the three scenarios. The data correspond to the experimental results obtained from the gasification of glucose [START_REF] Ondze | Supercritical water gasification of beet residues: from batch to continuous reactor[END_REF]. The gasifier is fed by a glucose solution with a flowrate of 1 kg h -1 (Flow 1 in Fig. 1). The initial concentration of Total Organic Carbon (TOC) varies from 20 to 80 g L -1 . The incoming flow is pressurized by a high pressure pump (HP pump on Fig. 1) having an isentropic efficiency of 90%. The stream [START_REF] Savage | Biomass gasification in supercritical water[END_REF] is then preheated between 450 and 600 °C. The gasification reactor (GR) is simulated by a subroutine considering experimental conversion rates: a balance equation is written for each experimental condition tested on glucose. Indeed, as a matter of fact, equilibrium composition cannot be used due to the remaining carbon in the experimental results. All balance equations used in the gasifier module are presented in the supporting Information part (Supplementary material, Appendix B). For example, for the simulation of the production of gas at 600 °C with an initial glucose solution of 20 g L -1 , the following reaction is considered (Eq. ( 1

The last term "C 2 H 6 O" (ethanol) is added to the equation in order to complete the atom balance and to fulfil with experimental results. Indeed, for each conversion, the mass balance and the atom balance on C H and O is calculated. In order to fulfil all atom balance another compounds has to be used. The use of ethanol, in this case, allows to make atom balance correct and are consistent with the remaining TOC of liquids after conversion. Compounds in the outlet are not quantified except by TOC measurement. The heat of reaction accompanying gasification is calculated on the basis of the balance equation using the enthalpy of formation of the various compounds. The stream leaving the reactor ( 4) is fed to a two-phase separator downstream with an overflow valve and a cold heat exchanger.

Hydrogen production

For hydrogen production, the different stages of enrichment and purification are based on the data from literature [START_REF] Toonssen | Exergy analysis of hydrogen production plants based on biomass gasification[END_REF][START_REF] Cohce | Energy and exergy analyses of a biomass-based hydrogen production system[END_REF][START_REF] Ruthven | Pressure Swing Adsorption[END_REF]. Fig. 1 shows the system for hydrogen production from biomass, including the gasifier reactor.

The gasification reactor outlet stream ( 6) is cooled down and is separated by a liquid flash stream (LF1) at given temperature and pressure. The temperature specification (noted "SPEC" on Fig. 1) is performed on the ratio of the flow of water necessary for the enrichment step over the flow of gaseous carbon (flux 10). It reduces both the heat needed for flux 11 and the CO 2 content in the gas mixture at the outlet of the separator. Remaining gases consist of H 2 , H 2 O, CO 2 , CO, CH 4 and C2-C4 at a pressure of 3 MPa and in varying proportions depending on the temperature of the gasification reactor. At this step, the hydrogen flow ranges from 1.5 to 8 g h -1 and represents from 5 to 30 mol% of the producted gas, for a temperature range between 450 and 600 °C in the gasification reactor.

To increase hydrogen concentration in the mixture an enrichment step consists of two hydrocarbons reforming reactors in series:

CH 4 + H 2 O ↔ CO + 3H 2 (2)
i-A reforming reactor for light hydrocarbons (R1). For instance, the reforming of methane to hydrogen is simulated by steam reforming reactions through Eq. ((2) and ( 3)).

CH 4 + H 2 O ↔ CO + 3H 2 (2) CH 4 + 2H 2 O ↔ CO 2 + 4H 2
(3) Under the conditions of temperature and pressure of 3 MPa and 700 °C, the formation of coal that may occur during the process of reforming [START_REF] Toonssen | Exergy analysis of hydrogen production plants based on biomass gasification[END_REF] is avoided. ii-A reforming reactor for CO (R2), following Eq. (4) (water gas shift reaction):

CO + H 2 O ↔ CO 2 + H 2 (4)
For other hydrocarbons, stoichiometric equations are written and the excess of initial water is used for reactions. The gaseous mixture is then cooled to separate residual water from the product gas (LF2) prior to final purification of the hydrogen stream. After this step, the gaseous mixture (flux 17) has a composition closed to 70% molar H 2 and 30% molar CO 2 .

The last step is the purification of hydrogen produced using the PSA (pressure swing adsorption) cycle: pressures between 0.3 and 3.4 MPa at temperatures between 20 and 30 °C. The PSA is set according to ref [START_REF] Cohce | Energy and exergy analyses of a biomass-based hydrogen production system[END_REF]. The process is simulated as a continuous process where both discontinuous effect are simultaneously considered. The continuity of the operation result in the implementation of two adsorbent beds with alternating operations (noted AB on Fig. 1). PSA cycle has four phases: adsorption, depressurization, regeneration or low pressure purge and recompression. The phases are simulated as follows:

• Adsorption (AB) is simulated by the separator module component in which hydrogen is separated at 3 MPa with a recovery rate of 90% [START_REF] Cohce | Energy and exergy analyses of a biomass-based hydrogen production system[END_REF].

• Depressurization and regeneration are simulated by two turbine modules in series with respective pressure loss of 2 and 0.9 MPa, to release the adsorbed gas.

• Recompression is simulated by a three-stage compressor with in- tegrated cooling systems. This module compresses the gas from 0.1 to 3 MPa.

Heat exchangers (HE 1, 2 and 3 on Fig. 1) inserted between the stages maintain the temperature of the gases at the dew point of the mixture. Mass and energy balances from these simulations allow the calculation of the different yields. The maximum flow rate of hydrogen produced is 23 gh -1 (for an input flow of 200 gh -1 of dry matter). At the end of the process, hydrogen is cooled down to ambient temperature before exiting the process. All the calculated data for hydrogen production (vapour fractions, mass flows, stream composition …) are given in Supplementary material, Appendix C.

Methane production

Several studies on the production of methane from biomass are proposed in the literature. Industrial processes of methane production are often biological processes such as fermentation. Thermochemical processes are still under investigation [START_REF] Gassner | Thermo-economic process model for thermochemical production of Synthetic Natural Gas (SNG) from lignocellulosic biomass[END_REF][START_REF] Gassner | Thermo-economic optimisation of the polygeneration of synthetic natural gas (SNG), power and heat from lignocellulosic biomass by gasification and methanation[END_REF][START_REF] Gassner | Optimal process design for the polygeneration of SNG, power and heat by hydrothermal gasification of waste biomass: thermo-economic process modelling and integration[END_REF][START_REF] Duret | Process design of Synthetic Natural Gas (SNG) production using wood gasification[END_REF][START_REF] Gassner | Optimal process design for the polygeneration of SNG, power and heat by hydrothermal gasification of waste biomass: process optimisation for selected substrates[END_REF]. Fig. 2 shows the flowsheet of the process of methane production from flux 12, the first part being the same as on Fig. 1.

Following the gasification reactor, a first separation step is proposed. The separation of gaseous and liquid effluents is different from that of H 2 production. The separation temperature and the flow rate required for the step of enrichment of the gas mixture to methane in the R1 and R3 reactors are obviously different. The supercritical mixture is expanded to 2.5 MPa to satisfy the conditions for reforming hydrocarbons, other than methane, to CO at 370 °C (R1). This is followed by the methanation reaction between CO and hydrogen in reactor R3, respecting thermochemical equilibrium, which increases the amount of methane up to 25 mol%. The mole fraction of methane produced does not exceed 50% of the gas mixture in the different conditions tested. The entire carbon is converted to methane and CO 2 .

The next step is the purification of the gas. The purification process must operate at high pressure as the pressure of the gas exiting the methanation reactor varies from 5 to 15 MPa. The removal of CO 2 in the gas mixture depends on the partial pressure of CO 2 and the purity of the final product. When the mole fraction of CO 2 is higher than 40% in the gas mixture, three techniques are identified: physical absorption, membrane processes and PSA. The first two are suitable for injection at 5 MPa, while the PSA operates at 3 MPa. Due to these specifications, the purification system is simulated by an absorption column (Scrubber on Fig. 2) of 15 plates; the gas mixture reaches the bottom of the column at 100 °C. Methane at the outlet of the scrubber is obtained with a purity up to 99% by weight. The purity is controlled by the flowrate of solvent used (water + methyl diethanolamine, represented with the thermodynamic model "amine and acid gas" in Prosim software). It reaches room temperature under a pressure of 15 MPa at the outlet. This high pressure is kept high to allow the gas to join gas pipeline. The absorbed gases are released downstream of the washing column by performing a low-pressure flash. The solvent may then be regenerated and recycled (this point is not evaluated in this study). All the calculated data for hydrogen production (vapour fractions, mass flows, stream composition …) are given in Appendix D.

Production of electricity and heat (cogeneration)

Fig. 3 shows the flowsheet of this process from flux 12, the first part being the same as on Fig. 1. The thermodynamic cycle selected for the production of electricity is a simple cycle consisting of a compressor, a combustor and a gas turbine. As previous systems, pressurization, compression and turbine are simulated with an isentropic efficiency of 90%. Air (flux 11) is compressed at the same pressure than the separator outlet (flux 12). Preheating of the air and gas mixture is performed at 120 °C if necessary. In the combustion chamber, all the gas is completely oxidised to CO 2 and water. A second specification is performed on the air supply to set the oxygen level to a normalized value of emission in the atmosphere at a molar fraction of 0.06 in the fumes. Heat available in the fumes is calculated by adding an heat exchanger cooling down the fumes to ambient temperature. In isothermal conditions, a steam utility is used to remove heat, and added to heat generation system. The adiabatic system differs from the isothermal system by specifying the outlet temperature. The outlet temperature of combustion chamber in the adiabatic system can reach 1500 °C.

All the calculated data for heat and electricity production (vapour fractions, mass flows, stream composition …) are given in Appendix E.

Results and discussion

Pinch analysis

An approach to facilitate energy integration is the pinch method analysis [START_REF] Linnhof | Thermodynamics analysis in the design of process networks[END_REF][START_REF] Gourlia | La méthode du pincement ou exploitation des diagrammes température/enthalpie, Notions de base[END_REF]. This method analyses the possible heat exchange between the cold fluids (which require the application of heat) and the hot fluids (which can dissipate heat) in order to minimize irreversibilities in the process. On these curves, the point where hot and cold curves are close is the pinch point. These data are combined to build the cold composite curves for all common cold and hot composite curves for all the warm currents. At the pinch point, the temperature gap is set at 10 °C. This method enables the calculation of the minimum heat requirement (MER) for the system.

The pinch analysis is realised for all scenarios and for different configuration of reactors (isothermal or adiabatic) and operating conditions (temperature, inlet concentration of glucose). All the data are taken from the simulations presented in the previous part, giving the different heat flux exchanges. A result of typical composite curve (hot and cold) is drawn in Fig. 4 for hydrogen production, while the typical grand composite curve for each scenarios is proposed in Fig. 5.

In the adiabatic cogeneration system (Fig. 5), results show that it is no need to supply heat. This is due to the complete combustion of organic matter in the combustion chamber that totally compensates the energy demand for the gasification part, slightly endothermic in this case. The highest energy requirement is observed for hydrogen production and is explained by the two endothermic reactors (gasification and hydrocarbons reforming). To produce methane, the energy required is less important than that needed for hydrogen production.

A comparison of the minimum energy required in several configuration is presented in Table 1 for gas production, while net electric production and cold minimum energy is presented for the cogeneration configuration. The adiabatic or isothermal cases are considered in the gasification reactor, reforming reactors and combustion chamber reactors. Usually, the value of MER decreases as a function of the conditions of the gasification reactor, in particular the reaction temperature. The value for isothermal systems is lower than for adiabatic systems. The isothermal system presents steps for yield calculated at low temperature when the concentration of the solution increases for both hydrogen production and methane production. This means that increasing the concentration at low temperature has no influence on the amount of heat to be supplied in the system. On the other hand, at high temperature, the increase in concentration decreases the value of MER. This means that the energy intake of glucose contributes to maintain the reactions at high temperature, therefore requires less external energy. In the case of cogeneration, the net heat electricity production follows the same trend. This production is calculated by subtracting to the work delivered by the turbine, the pump work and the compressor work. The increase in temperature and for a given temperature the increase in glucose content increases this net production. This is directly linked to the net gases mass production that allows a much higher combustible gas input into the combustion chamber. In the case of adiabatic reactors, the theoretical combustion temperature is higher than the set temperature for isothermal mode (1373 K) and thus allows the production of higher power and results in the release offumes at higher temperatures.

Energy and exergy analysis

Energetic calculations have been conducted considering the data from the simulations presented in previous paragraph (mass flows, temperatures, pressure) and the data from the pinch analysis.

In the cases of gas production, the energetic efficiency for each product (Eq. ( 5)) is calculated with the different lower heating values of the entering and exiting flows, as proposed for instance in the work of Gasafi et al. [START_REF] Gasafi | Exergetic efficiency and options for improving sewage sludge gasification in supercritical water[END_REF].

= × × × η LHV Q LHV Q 100 i Gasi Gasi
Biomass Biomass [START_REF] Resende | Noncatalytic gasification of cellulose in supercritical water[END_REF] with: Q i the mass flows (kg s -1 ) and LHV i the Lower Heating Value (J kg -1 ). The energy efficiency calculated by several authors for different biomass varies from 45 to 70% [START_REF] Calzavara | Evaluation of biomass gasification in supercritical water process for hydrogen production[END_REF][START_REF] Matsumura | Biomass gasification in near-and super-critical water: status and prospects[END_REF][START_REF] Gasafi | Exergetic efficiency and options for improving sewage sludge gasification in supercritical water[END_REF].

The global energy efficiency of gas production systems is calculated by equation 6.

= × + + × × η LHV Q Δ W MER LHV Q 100 Gi Gasi Gasi Biomass Biomass (6)
With MER: minimum heat requirement and ΔW: sum of the mechanical power used.

In the case of cogeneration of heat and electricity, Eq. ( 7) is used for the global energy efficiency.

= + + + × × η P Q MER Δ W LHV Q 100 GCo Turbine Fumes Biomass Biomass (7)
Where: P Turbine and Q Fumes represent respectively the power recovered at the gas turbine and the heat recovered from the flue gases. Calculation results for global energy efficiency obtained for hydrogen and methane production are shown in Table 2.

An increase in H 2 and CH 4 energy efficiency with temperature can be observed. Increasing the concentration of the initial solution has no real effect on product yields. In the case of hydrogen, energy efficiency is the same for both systems studied. In the case of methane, the performance of adiabatic system is higher than that obtained in the isothermal system.

Exergy concept is a powerful tool to analyse the efficiency of a system. The exergy available from heat sources exchanged with the system is calculated by integrating factor Carnot heat flux (Eq. ( 8)).

= × Ex θ Q (8)
With: Q the amount of heat exchanged and θ, the Carnot factor:

= - θ 1 T T 1 2
Eq. ( 8) is used for the calculation of exergy for the fumes exiting the system, as well as for the resulting MER. For glucose or gases, the amount of incoming exergy is calculated as the product of its LHV and the flowrate.

The exergy efficiency is calculated according to the definitions in the literature [START_REF] Grassman | Zur allgemeinen definition des wirkungsgrades[END_REF][START_REF] Sorin | Thermodynamic techniques for the conceptual design of thermochemical refrigerators using two salt materials[END_REF] as the ratio between the useful and incoming exergies. In our case, systems can exchange exergy with the environment through heat generated (Q < 0), chemical exergy or through mechanical power used generated (W > 0) [START_REF] Smith | Energy integration of methane's partial-oxidation in supercritical water and exergy analysis[END_REF]. Incoming exergies are thus formed of exergy of the incoming biomass, pumps, compressors and heating (gathered in the MER). Outgoing exergies consist of exergy contained in the product gas stream, turbines, and heat. These definitions lead to Eq. ( 9) that defines the exergetic efficiency for gas production systems Eq. ( 9).

= × × + + × × η LHV Q MER θ Δ W LHV Q 100 Exi Gasi Gasi Biomass Biomass (9)
For cogeneration, exergy efficiency is given by Eq. ( 10).

= + × × + + × × η P Q θ MER θ Δ W LHV Q 100 ExCo Turbine Fumes Biomass Biomass (10)
For instance, Gasafi et al. [START_REF] Gasafi | Exergetic efficiency and options for improving sewage sludge gasification in supercritical water[END_REF] calculated the total exergy efficiency of gasification of sewage sludge in supercritical water for hydrogen production is of the order of 52% exergy efficiency. Calculations by Feng et al. [START_REF] Feng | Energy efficiency analysis of biomass-based synthetic natural gas production process using interconnected fluidized beds and fluidized bed methanation reactor[END_REF] upon the gasification of biomass in supercritical water environment indicate exergy efficiencies of the order of 40.6%. An interesting work on exergy analysis, in the case of supercritical water oxidation of coal, has been proposed by Yan et al. [START_REF] Yan | The exergy release mechanism and exergy analysis for coal oxidation in supercritical water atmosphere and a power generation system based on the new technology[END_REF].

Table 3 (adiabatic case) and Table 4 (isothermal case) gather respectively the results of energy efficiency and overall exergy efficiency obtained from the simulation of production processes of H 2 , CH 4 and cogeneration, in adiabatic and isothermal cases.

Tables 3 and4 show an increase in energy and exergy efficiencies with temperature and also with the initial concentration for all the scenarios. Adiabatic processes yields are higher than the yields for isothermal systems. The results obtained for the process of cogeneration indicate yields ranging from 20 to 85% and 25-75% respectively for energy efficiency and exergy in the adiabatic system. In the isothermal system, these yields are lower and they vary between 22 and 72% and 24-60% respectively for energy and exergy efficiencies. For cogeneration, as all combustible gases are burnt in the system, there are thus no losses during chemical conversion as in methane or hydrogen production where a part of the carbon is turned into CO 2 . It is shown here how the coupling of energy and exergy yields can be valuable. Indeed, when in term of energy yields cogeneration appears to be more efficient, the contrary conclusion could be done for exergy. This is due to the important amount of heat available (ranging from 1.5 to 3 times higher than the net electricity production) but at temperature quite low (from 673 to 861 K, in the case of isothermal reactors).

Influence of operating parameters through numerical design

The objective is to quantify the influence of operating parameters and search for optimal conditions. This study is performed on the Nemrod software (France) using the numerical design methodology that have been already successfully used and presented in Lefevre et al. [START_REF] Lefevre | Energetic optimization of wet air oxidation process using experimental design coupled with process simulation[END_REF] to analyse conversion systems. The shape of the computational domain is spherical and the type of model used is a quadratic model. Factors are the reaction temperature in the gasifier (three levels: 450, 500 and 600 °C) and the initial TOC concentration of the glucose solution (four levels: 20, 30, 60 and 80 gL -1 ).

Three responses are examined:

-The energy efficiency of the conversion system calculated with Eqs. ( 6) and ( 7); -The exergy efficiency of the conversion system calculated with Eqs. ( 9) and ( 10); -The MER calculated from the pinch analysis.

A multilinear regression was performed with ANOVA method and residue coefficients calculations. The coefficient of determination of the different model representing the fitting of the data varies between 97.2 and 99.8%. This shows a good correlation between the model data and the simulation data. These models can be considered as valid. Contour graphs are given in Supplementary material, Appendix F.

Analysis of the results of numerical design

The results discussed in this section are those for the production of H 2 and CH 4 in the adiabatic case. Increasing the initial concentration of the solution appears to be a good factor to improve energy efficiency as well as exergy efficiency. High temperatures can increase yields as already outlined in the experimental study [START_REF] Ondze | Supercritical water gasification of beet residues: from batch to continuous reactor[END_REF]. A minimum of heat is obtained for higher temperatures but the initial concentration of the solution has no influence on the MER. This point is very interesting because the process could be operated in very large quantities of organic materials in the same way as for solutions with lower concentrations.

In the case of methane production, the variations are substantially similar to those presented in the case of hydrogen production. Energy and exergy efficiencies are highly dependent on high temperatures but also high concentrations. The variation of MER has a dependence on the temperature. A slight effect of concentration can be observed at very high temperature values.

Energy and exergy efficiencies and heat supply for adiabatic cogeneration evolve identically to the previous scenario. The variation in MER in this case depends on the temperature and the initial concentration of the glucose solution.

In all scenarios, for adiabatic cases, the optimum range appears to be slightly decentred on the response surface. The results are interesting because the surfaces obtained for all responses indicate higher values for the two factors studied. Only the minimum heat input in the case of the production of fuel gas does not exhibit sensitivity to the initial concentration of the solution.

The response surfaces obtained for cogeneration isothermal case show an influence of the two factors. The production of methane exhibit a plateau for temperature and a more pronounced slope for the initial concentration influence. The same conclusion is obtained for H 2 production.

Study of the optimal domain

The aim of desirability study is to find an area of compromise between specifications with simultaneous optimization of multiple with no preference on the target. For the exergy efficiency, the target is set at 80%. For minimum heat input, the target is 0 W. Table 5 presents a summary of the optimum values for all conversion systems simulated in the adiabatic and isothermal cases. For hydrogen production, in the case of adiabatic conversion, the optimal area is for high initial concentrations and high temperatures. This conclusion is also observed on the response surfaces for exergy efficiency. In this example, the maximum value of desirability is 86%: this means that all the targets in the responses are not reached. More precisely, the target for optimal exergy efficiency is reached, however, that of MER is not reached. The coordinates of the maximum of desirability are a reaction temperature of 626 °C and an initial TOC concentration of 51 g L -1 . The value provided regarding the temperature is outside the scope defined.

Desirability obtained for systems are different for the same process according to whether it is adiabatic or isothermal. They are all less than 100%, meaning that all he targets cannot be reached with the same input conditions. The coordinates of the maximum are outside the boundaries for at least one of the factors. The temperature in all adiabatic simulations is slightly out of bounds. For the production of methane, the initial concentration must be high in order to get the higher value. The best results are those obtained in the case of methane production for an isothermal reactor. The temperature is slightly lower than the maximum value of the defined range and the concentration is maximum. The desirability is still not 100%. The results of the responses obtained in this case are: a minimum heat input of 66.5 W and exergy efficiency of 80%.

In the case of cogeneration, the simulation for adiabatic conversion give a low value but close to 80% and higher initial factors for concentration and lower desirability for temperature in this case than in the isothermal system. The response surfaces show remarkable results, the possibility of using solutions with very high concentrations of organic matter is noted. The reaction temperature has a very important influence on the variations of all the responses studied. In all cases, maximum temperatures favour the conversion of matter and therefore exergy efficiency.

Conclusion and prospects

Different scenarios are simulated by software modules in Prosim.

Implementing these processes is based on experimental results. The results of the analysis indicate the need to supply heat for all systems, except for cogeneration. The minimum heat requirements MER are dependent on the temperature of the gasification reactor while the initial concentration seems to have a slighter influence.

Energy yields indicate better results in adiabatic conversion systems; they differ according to the scenario and range from 30 to 90%. The best results are obtained at higher temperature.

Numerical design and desirability functions indicate a temperature and concentrations dependence.

The MER mainly depends on temperature. The study of the optimal range gives desirability ranging from 76 to 94%. All targets are not reached. Only the desirability in the case of the production of methane give values higher than 90%.

This method give very interesting results for an accurate energetic analysis of biomass valorisation and could be applied to many other types of biomass.

Fig. 1 .

 1 Fig. 1. Hydrogen production flowsheet (following the flux from the entrance, the different equipment are: High Pressure pump, Gasification Reactor, Liquid Flash 1, Reforming reactor for light hydrocarbons R1, Reforming reactor for CO R2, Liquid Flash 2, Adsorption AB simulated by a separator module, two turbine modules, Recompression with a three-stages compressor, Heat exchangers HE 1, 2 and 3).

Fig. 2 .

 2 Fig. 2. Methane production flowsheet (R1: Hydrocarbons reforming, other than methane, CO and H 2 reforming R3, absorption column Scrubber of 15 plates, Liquid Flash).

Fig. 3 .

 3 Fig. 3. Heat recovery and electricity production flowsheet (mixing flux, combustion chamber, and turbine).

Fig. 4 .

 4 Fig. 4. Example of pinch analysis. The composite hot (in red) and cold (in blue) curves for the simulation of H2 production (TOC concentration 20 g L -1 ; gasification reactor temperature 600 °C; temperature gap is set at 10 °C; P letter on the graph represents the pinch point; area R indicates the overlap area). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5 .

 5 Fig. 5. Grand composite curves obtained for the three studied systems at isothermal and adiabatic conditions (TOC 20 gL -1 ; gasification reactor temperature 600 °C).

  )).

	C 6 H 12 O 6 + 2.04 H 2 O → 3.65 CO 2 + 0.33C 2 H 6 + 5.06H 2 + 0.88
	CH 4 + 0.66 CO + 0.08 C 2 H 6 O

Table 1

 1 Minimum energy requirement (MER) in W for gases production, net electricity production and minimum cooling requirement for cogeneration.

	Exp. number		1	2	3	4	5	6	7	8	9
	GR temperature °C			450		500			600
	COT concentration g L -1	20	30	60	80	20	20	30	60	80
	Adiabatic	H 2	432 422 412 408 339 205 188 167 199
		CH 4	430 425 397 419 337 202 178 144 118
		Cogeneration	53	94	203 237 60	85	138 269 413
		(Q cold )
		P elec	15	38	56	147 20	37	72	166 264
	Isothermal H 2	405 384 356 309 273 174 150 127 198
		CH 4	382 349 282 242 277 161 123 63	67
		Cogeneration	64	114 256 297 40	102 166 326 509
		(Q cold )
		P elec	5	18	63	87	7	20	44	111 169

Table 2

 2 Energetic yields (from Eq. (6)).

	Temperature	450 °C	450 °C	450 °C	450 °C	500 °C	600 °C	600 °C	600 °C	600 °C
	TOC concentration (g L -1 )	2 0	3 0	6 0	8 0	2 0	2 0	3 0	6 0	8 0
	η GH2 adiabatic (%)	54.6	57.3	57.5	51.1	74.6	78.8	80.7	77.7	89.6
	η GH2 isothermal (%)	54.6	57.3	57.5	51.1	74.6	78.8	80.7	77.7	89.6
	η GCH4 adiabatic (%)	60.5	53.9	52.1	71.0	71.0	71.5	73.0	74.7	81.2
	η GCH4 isothermal (%)	59.5	52.8	51.1	69.9	69.6	70.3	71.8	73.4	79.8

Table 3

 3 Energetic and exergetic yields for the adiabatic cases (calculated from Eqs. (5), (9) and (10)).

	Temperature °C		450		500			600
	TOC concentration g L -1	20	30	60	80	20	20	30	60	80
	η i (%)	H 2	25	28	45	41	33	43	53	68	80
		CH 4	28	27	42	56	32	39	49	67	79
		Cogeneration	21	28	40	40	34	48	58	72	85
	η EXi (%)	H 2	31	34	51	46	40	50	60	72	85
		CH 4	38	35	50	64	41	46	55	72	82
		Cogeneration	25	32	41	39	38	48	56	64	75

Table 4

 4 Energetic and exergetic yields for the isothermal cases (calculated from equations 5, 9 and 10). The basic desirability function is built to combine the individual needs of each response. It is minimal or zero, when it is out of specification limits, and it is maximal if it fulfils all the desired conditions. To build this function, it is necessary to specify the objectives for each response by setting the basic desires. The characteristics of the overall objective can be altered by adjusting the relative weight of the responses. Once the specified desirability function is calculated, the objective is to find the point that maximizes this function. The initiation of basic desires is done by considering a Derringer transformation unilateral left for targets with positive values and unilateral right for those who have negative or zero values. Energy efficiency is considered

	Temperature °C		450		500			600
	TOC concentration g L -1	20	30	60	80	20	20	30	60	80
	η i (%)	H 2	26	30	46	43	35	42	51	61	68
		CH 4	28	28	44	59	32	39	49	64	71
		Cogeneration	22	29	41	41	36	49	61	65	71
	η EXi (%)	H 2	32	36	52	48	43	49	58	67	75
		CH 4	38	36	51	66	41	46	55	69	76
		Cogeneration	24	30	39	38	37	46	54	57	62

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.supflu.2017.10.002


Jean-Charles Mare

Garance Vinson

Thomas Prado

Michel Combacau

MODELLING AND SIMULATING THE PUMP OF AN AEROSPACE ELECTRO-HYDROSTATIC MODULE FOR FAULT DETECTION AND IDENTIFICATION PURPOSES

This communication deals with the modelling and simulation of a fixed-displacement axial-piston pump used in aerospace electro-hydrostatic actuators. The pump model is developed in the LMS-AMESim simulation environment to support the development of fault detection and identification features. The model-based fault diagnosis method is introduced first and the modelling needs are addressed. Then, a systemlevel pump model is proposed with special considerations to model architecture. The different ways to improve the model's realism are reviewed, in particular concerning energy losses (bearing friction, leakages in gaps), barrel force balance, piston back pumping, piston eccentricity and pump loading for tests. Finally, directions of research in system-level modelling of hydraulic effects are suggested.

INTRODUCTION

Flight control and landing gear actuators are major secondary -i.e. not propulsive-power consumers in aircrafts. Servo-hydraulic actuators (SHA) supplied at a constant pressure from centralized hydraulic pumps are a well established standard since the sixties. However, they require hydraulic power networks that are heavy, difficult to integrate within the airframe and that offer poor power management capabilities. Towards greener, cheaper and safer aerospace, a high effort is placed today to develop power-by-wire (PbW) systems that only involve electrical power networks. For this reason, electro-hydrostatic actuators (EHA) offer an attractive design because they combine the advantages of both electrical and hydraulic technologies:

-easiness of control and efficiency of permanent magnet synchronous machines associated with high power inverters, -efficiency, high power to mass ratio, easiness of passive mode and overload load protection of hydraulic cylinders equipped with piloted bypass and pressure relief valves.

Although EHAs have been introduced massively by Airbus on its A380, A400M and A350, they are still not sufficiently mature to be operated in front line. Therefore, they only serve as backup actuators. On their side, electro-mechanical actuators (EMA) also suffer from lack of maturity for safety critical applications, in particular regarding jamming, back-drivability, reflected inertia, nut-screw efficiency and overload protection. This is why EHAs can be considered as the most promising PbW actuators at medium term. To move EHA to service in front line for primary flight controls, costs have to be cut while reliability and availability have to be increased for long-life (typically 100 000 flight hours) applications. EHAs' costs can be significantly cut through modularization and standardization by developing electro-hydrostatic modules (EHM). These modules typically combine the electric motor and the hydraulic pump in a single unit [SAE ARP6154][Arnaud (2001)]. They play in EHAs the same role as servovalves do in SHAs. Health monitoring (HM) is considered as a convenient and efficient mean to meet the reliability and availability targets of front-line EHAs. However, most of the research and development efforts in HM are related to the electrical domain, focusing essentially on power electronics and electrical machines.

The present communication deals with the EHA pump fault detection and identification. The first section is dedicated to the health monitoring algorithms. A survey of candidate methods is proposed and justifies selecting the model-based approach. The Health-Monitoring module needs fault signatures, built from observable signals, to detect and identify the faults. The principle is to observe the system and to compare it with models outputs in order to determine which health state may have led to the observed behaviour. This method requires a complete model of the equipment, in nominal and faulty modes, represented into a formalism that suits the proposed diagnosis algorithms. The second section addresses in details the modelling and simulation of the EHA pump. The model is developed in order to serve as a virtual prototype. This prototype is used to investigate the richness of measured signals, to determine the best location and to specify the performance of sensors and finally to point out the fault signatures.

I. FAULTS DETECTION AND DIAGNOSIS OF HYDRAULIC PUMPS

Diagnosis methods

The objectives of fault detection and diagnosis are the diminution of the equipment interruption rate (improving the aircraft availability) and the minimization of the maintenance costs by improving fault localization and so decreasing aircraft down time. Implementing mature health monitoring features cannot be achieved without significantly improving the knowledge of the components wear and failures to enable proposing solutions for early fault detection and diagnosis.

There are three families of diagnosis methods: the experience based methods, the data driven methods, and the model based methods. For these three kinds of methods the principle is the same: the system is observed and its behaviour is compared with a data base in order to determine which health state may have led to the observed behaviour. Depending on the method, the data base is either statistical (i.e. a set of faults and consequences obtained from experience), or data recordings (obtained in service or during tests), or physical models outputs. The main reasons pumps fail are insufficient lubrication, fatigue, improper installation or contamination (fluid pollution for instance). In hydraulic pumps, cavitation leads to erosion, which leads to an increase of fluid leakage and a reduction in performance. Hydraulic pump wear reduces machine performance, causes secondary damage, and may be a precursor for catastrophic failure. Hydraulic pumps are not very much studied concerning Health Monitoring. Among literature only a few papers are found. They mostly use data driven methods.

The pressure ripples can be a good indicator of health degradation. For instance [START_REF] Johnston | Condition Monitoring of Aircrafts Fuel Pumps using Pressure Ripples Measurements[END_REF]] studies the wear of gear pumps used for delivery of high pressure fuel to aircraft engine. Tests show more and more pressure ripples, measured with piezoresistive pressure transducers, at the high pressure outlet port with the wear of the pump. [Chinniah (2004)] develops a monitoring strategy for Electro-Hydrostatic Actuators. According to these studies gears wear in gear pumps can be deduced from the observation of pressure ripples, leakage flow, or with the use of a thermograph. [START_REF] Hancock | Maintenance and fault diagnostic tools for hydraulic pumps[END_REF]]use pressure signals for one piston pump fault detection. They compare power spectral analysis using FFT to wavelet packet analysis with neural networks.

Besides pump pressure, [START_REF] Amin | Fuzzy Inference and Fusion for Health State Diagnosis of Hydraulic Pumps and Motors[END_REF]] uses case drain flow, and case drain temperature as the three indicators of pumps failures. Results are presented using pump degradation data from accelerated endurance tests provided by the Air Force Research Laboratory.

Another indicator of damage comes from vibration signals.

In [START_REF] Pawelski | Vibration based pump health monitoring[END_REF]], a non-invasive diagnosis can determine the level of pump wear. Wear that changes the vibration characteristics of the pump can be observed with an accelerometer attached to the pump's case. A series of tests were performed. In [START_REF] Mollazade | Vibration-Based Fault Diagnosis of Hydraulic Pump of Tractor Steering System by Using Energy Technique[END_REF]], the vibration signal from a piezoelectric transducer was captured for normal and worn external gear hydraulic pumps used in the tractor steering system. The Power Spectral Density of vibration spectra is calculated to perform the diagnosis.

Sometimes data are available in service. For instance in [START_REF] Gomes | A Hybrid Approach to Hydraulic Vane Pump Health Monitoring and Fault Detection[END_REF]], data are field-data collected from two aircrafts that presented pump failures. When no degradation data are available in service, it is possible to perform dedicated accelerated life tests to obtain fault data, for instance in [START_REF] Hancock | Maintenance and fault diagnostic tools for hydraulic pumps[END_REF]], to accelerate pump wear and performance degradation by adding silica sand to the hydraulic reservoir to create contaminated hydraulic fluid. The pump performance is given by the output flow that decreases when the pump is damaged. Vibration signals were decomposed using wavelet packet analysis in order to establish the health state of the pumps.

Another possibility to obtain data is to model the faults. For instance in [START_REF] Hancock | Maintenance and fault diagnostic tools for hydraulic pumps[END_REF]], the faults on piston or swash plates are modelled as leakage flows. Moreover two pumps were tested, a healthy one and a one with a worn swash plate, to compare the results with the models. Wavelet analysis is then used to detect failures in hydraulic piston pump pressure discharge signals.

There are several problems with the implementation of sensors such as accelerometers. In aerospace applications, the pump environment is very noisy, with a lot of vibration generated by other equipment for instance. Moreover any sensor addition increases the weight and required space of the equipment, and decreases its reliability. This makes it difficult to obtain relevant in-service degradation data since the number of sensors is limited. It is also complicated to perform some degradation tests since they are destructive, costly and time consuming. Since the design of pumps is already based on models, a good idea is to model the pump nominal and faulty behaviour, in order to obtain a set of nominal and faulty data. This also allows the different possible sensors to be compared for choosing the more interesting one.

Model-based diagnosis method

The choice of the method between the three kinds of diagnosis methods depends on the nature of the degradation and fault data. In our case the experience based method is not chosen since the considered hydraulic pumps are too recent to have a sufficient amount of faults experience feedback.

Moreover there is no in-service pumps data available for now, and performing ageing tests, or tests with faulty pumps, to build a signals data base would be highly costly. That is why the data driven method is not chosen neither.

It is then the model based approach that is chosen. The advantages of this method are that it gives more specific results on the degradation mechanisms and on the physics of faults than the other methods, and it is more generic since once models are built for one kind of hydraulic pump, they can easily be tuned to be adapted to other kinds of pumps (with a greater number of pistons for instance).

More precisely, the model based diagnosis method requires building the model of the equipment in nominal behaviour, and also all the models of every fault that need to be monitored. Models can be analytical or numerical, depending on the knowledge on the fault mechanism considered. Faults to monitor are chosen assessing their frequency and consequences on the pump behaviour thanks to a Failure Mode Effect and Criticality Analysis (FMECA). They are characterized, and their models are incorporated into the nominal model. Some fault indicators are built. They are combination of observable parameters. The principle is that they take specific values for at least one fault. The best indicators are the one that change most during one fault, and do not change for every other fault. A fault signature is the set of indicators values when the fault occurs. Simulations enable all the faults signatures to be built.

In the best case, the model is supplied with the same inputs as the monitored equipment/system, including environment, to be able to compare the outputs of the model with the real equipment ones. In the present application, the environment is partially unknown. For instance, ambient temperature or the load applied on the flight control actuator (that depends on aircraft speed, turbulence and flight phase) are neither controlled nor monitored. The idea is then to perform the diagnosis under well-known and repeatable conditions, for instance during pre-flight checks, post-flight checks, or preland tests. Thus, the simulations do not have to be run at every diagnosis time; the faults' consequences will always be the same in a given environment.

The use of the model-based method can also allow the different configurations of the actuator to be studied in order to define how to load the actuator and what the more suitable environment is. This enables choosing the most adapted configuration in order to obtain the best indicators. Another advantage with models is that all signals are observable with virtual sensors (no cost). Moreover, analysing the signal richness in case of faults allow sensors that give the best indicators to be selected for implementation.

Model for diagnosis

A model-based diagnosis method was proposed in [START_REF] Vinson | A Generic Diagnosis and Prognosis Framework: Application to Permanent Magnets Synchronous Machines[END_REF]]. It requires a model of the equipment describing all the components, the exchanged parameters between components and with the environment, and the component private parameters, that are then used to model the damage of a component i.e. the faults on the hydraulic pump. Such a model is presented on Fig. 1. The model structure reflects the functional architecture of the pump with associated interactions and couplings: driveshaft, bevel gear, pushrods at mechanical level, piston chambers, distribution plate, pump housing at hydraulic level.

Critical faults

The FMECA performed on the hydraulic pump shows that the more critical faults are due to mechanical wear appearing at moving parts contacts level in the pump body, possibly made worst by hydraulic fluid pollution. The chosen faults are the increase of the clearance between the pistons and the barrel bores, and the wear of the part of the connecting plate facing the barrel.

II. VIRTUAL PROTOTYPE OF THE EHM PUMP

This section deals with the modelling and simulation of the MBD fixed-displacement, axial-piston, bent-axis EHA pump. This symmetrical 7-pistons pump, Fig. 2, is declined in different ranges depending on requirements. E.g., the Airbus A380 flies 12 pumps that serve in backup flight control actuators [Todeschi (07)] or in backup local hydraulic power generation for landing gears steering and braking [Dellac (04)]. When used in EHAs, the pump is part of a closed hydraulic circuit making a hydrostatic transmission than can operate dynamically in the 4 power quadrants. It runs typically up to 350 bars, 15000 rpm, 40 l/mn with a service life greater than 50000 flight hours demonstrated at present.

Modelling need

In the field of actuation for aerospace, health monitoring is most of the time addressed considering failures at electrical motor, e.g. [START_REF] Vinson | Permanent magnets synchronous machines faults detection and identification[END_REF]] or at signal/power electronics, e.g. [START_REF] Vohnout | Prognostic Enabling of an Electrohydrostatic Actuator (EHA) System[END_REF]]. At a more mechanical or hydraulic level, Johnston [START_REF] Johnston | Condition Monitoring of Aircrafts Fuel Pumps using Pressure Ripples Measurements[END_REF]] pointed out the interest of using the pressure ripple at high pressure port as a good observable for aerospace fuel pumps. In that way, early degradation of bearings can potentially be detected before pump flow performance reduces. On basis of a simple model of the EHA, Chinniah [START_REF] Chinniah | Fault Detection in the Electrohydraulic Actuator using Extended Kalman Filter[END_REF]] showed the interest of an extended Kalman filter to identify the fluid Bulk modulus, the gear pump viscous friction coefficient and the cylinder friction. However, only a global pump model was used (no piston level) to identify global parameters at EHA level, imposing a sine position demand for a known load. A little attention was paid to the pump itself. Oppositely, Palazzolo [START_REF] Palazzolo | Leakage Fault Detection Method for Axial-Piston Variable Displacement Pumps[END_REF]] focussed his work on 3 types of leakages in a variabledisplacement axial-piston pump: barrel chamber to drain, adjacent chamber to chamber through valve plate, delivery port to drain through valve plate. The flow models were quite simple: Poiseuille flow or equivalent turbulent leakage flow through fixed orifice. However, it was shown that using the output pressure signal was promising to discriminate the source of the leakage in a faulty pump. Fault signatures were generated combining time and frequency domains.

The common modelling and simulation of hydraulic pumps generally serve the main engineering needs. Distributedparameters (3-D) models enable the local effects to be studied in order to support the detailed design of the pump, e.g. for hydrostatic or hydrodynamic bearing, force balancing or reduction of pressure ripple. On their side, lumped parameters (0-D) models are used to establish a global and a more systemlevel view of the pump, e.g. for simulating a whole EHA. Unfortunately, these latest models are generally obtained at the sacrifice of severe assumptions that remove the spatial effects to get algebraic or differential equations and that do not reflect the evolution and the influence of variable gaps within the pump.

Model architecture

The present pump model is developed in the LMS-AMESim simulation environment to serve as a virtual prototype for supporting the design of a fault detection and identification module. In this attempt, an important activity consists in defining its architecture to ensure consistency with the model involved by the fault detection and identification module. The proposed model architecture is presented on Fig. 3. The model interfaces are the drive shaft and the three hydraulic ports: two power ports connected to the EHA cylinder and one drain port that collects the internal leakages of the pump to the EHA charge accumulator. Average ambient conditions are set by modifying the fluid temperature. The pump model is split into different submodels (numbers below refer to Fig. 3):  piston/chamber model,  flow at slots through distribution plate,  chamber leakage to drain at barrel / distribution plate interface,  kinematics from drive shaft to piston,  leakage between power ports and drain at barrel / distribution plate interface,  hydrostatic and hydrodynamic forces on barrel at barrel / distribution plate interface,  viscous and pressure forces from chambers to barrel.

Model advances

According to the most critical faults to be detected, measuring pressure, estimating flow from cylinder rod velocity and estimating motor torque from windings current is considered as the most mature and efficient way to monitor the pump condition. For this reason, the pump model is developed with the main intention to increase the realism of the simulated driving torque and pressures or flow at hydraulic ports. This is mainly achieved by improving the simulation of energy losses (friction and leakage). In this attempt, the pump model has been developed with particular focus on friction at bearings level, piston/barrel wear and eccentricity, axial motion of barrel and pump characterisation process.

Friction in barrel ball bearings

The structure of friction model in bearings is well established with the new formulation proposed by SKF [SKF (06)]. In case of hydraulic machines, friction at bearing comes from two major contributors that are both load dependent:

-the speed dependent friction torque M r associated with hydrodynamic lubrication conditions during rolling (fluid kinetic viscosity  times rotating speed N):

6 . 0 ) ( N k M r r   (1)
where coefficient k r introduces the influence of type and size of bearing and load applied to the bearing.

-the speed independent friction torque M s due to sliding with friction coefficient :

  s s k M (2)
where coefficient k s introduces again the influence of type and size of bearing and load applied to the bearing.

Finally, from the mechanical point of view, the model of bearings for system simulation can be structured extending the proposition given in [START_REF] Maré | 2-D lumped-parameters modelling of EMAs for advanced virtual prototyping[END_REF]]:

-a 2 times 1D model with 4 mechanical power ports (axial and radial motion, for inner and outer ring).

n-1 piston models

       
-one thermal port enabling the model to input the actual operating temperature and to output the heat flux generated by friction losses.

In that way, the bearing model is fully balanced, mechanically as well as thermally.

Calculating the bearing friction requires determining the axial and radial forces it has to hold. On one hand, the contribution of the bevel gear drive can be modelled quite easily using common gear mechanics. On the other hand, the contribution of the barrel through the axial preload spring is quite difficult (see dedicated paragraph). The significant influence of combined velocity and temperature for a given load is illustrated on Figure 4 which displays the shape of friction torque at rated operating pressure. It is interesting to note the change of rolling friction torque: the maximum value is quite unchanged but appears for an increasing speed versus temperature. Excepted at very low temperature, the sliding friction torque contributes in the same manner as the sliding friction torque at very low velocity. This situation is particularly important, e.g. for aileron actuators in cruise conditions: averagely, the flow demand is null while the pressure difference is high to hold a constant aileron steering in the presence of constant air load.

It must be remarked that the well established friction model in rolling bearing applies to permanently rotating application without speed reversal (e.g. engines or hydro power plants). There is lack of (published) information concerning the modelling of friction for bearings operating around null velocities with high acceleration: during a step response of an aerospace EHA, the pump runs from quasi null to 10000 rpm and returns to quasi null in 0.3 s.

Piston / barrel eccentricity and wear

At system level, modelling the friction force and leakage flow with a 0-D approach does not allow 3D dynamics of the piston to be considered. Indeed, piston's motion is excited by the driving force applied by the pushrod and by centrifuge effects. Solid models are two complex and fluid-structure interaction models cannot yet be extracted from distributedparameters models. For this reason, friction and leakage are modelled using the conventional gap theory, with the assumption that piston and chamber axes keep parallel. The influence of shaft velocity can be introduced through the change of piston eccentricity in response to centrifugal force. Assuming a laminar flow in the annular gap enables the Hagen-Poiseuille theory to be used for linking the power variables according to the causal case used for simulation: flow rate Q l and viscous friction force F v are a linear function of the pressure difference P and the piston/barrel relative velocity v

                                             P v rh h e h L r h e L rh rh F Q v l 0 2 0 0 2 0 3 0 0 ) / ( 1 2 / 5 . 1 1 6 (3)
with r piston radius, h 0 radial clearance, e eccentricity, L piston length,  fluid dynamic viscosity. As an illustration, Figure 5 points out the huge influence of eccentricity on axial friction force F v . Shaft speed (rpm)

M r , -55°C M r , 0°C Mr , 40°C M s , 40°C M s , 0°C M s , -55°C
In practice, at high angular velocities, pistons are submitted to significant centrifugal forces that tend to increase eccentricity which will increase leakage and friction. Unfortunately, although the annular gap model with eccentricity is available in the hydraulic component design library of the simulation software, simulating this effect requires further model development to express the radial hydraulic force that applies to the piston as a function of eccentricity, pressure and velocity.

Axial motion of barrel

In the patented pump design, the barrel is linked to the driver (reference 8 on Fig. 2) by a prism pair joint type and is axially spring loaded. This enables the barrel to float axially within the driver and determines the axial gap height between the barrel and the distribution plate. In order to simulate this degree of freedom, it is of particular importance to calculate the pressure forces that apply on the barrel. However, getting a 1-D model of the hydraulic force is not easy because the fluid velocity in the gap is at least 2-dimensional in laminar conditions (introducing the variation of the gap height would add a third dimension). This results from the combination of a radial flow in the gap from high pressure to low pressure domains and a tangent flow in the gap due to viscous entrainment under relative velocity between the barrel and the distribution plate.

The first one can be seen as the hydrostatic bearing force F h that is calculated by integration of the Navier-Stokes equation in polar coordinates within the considered domain [START_REF] Bergada | Pressure, flow, force, and torque between the barrel and port plate in an axial piston pump[END_REF]]. As a result, fluid viscosity and gap height do not appear in the integrated equation that only involves:

-4 time variables (pressures P 1 and P 2 at power ports and P 0 at drain, barrel angular position  relative to plate), number of pistons k, area A of holes in the barrel for connection to chambers, geometry of the kidney slots (angle width , inner and outer radii R 2 and R 3 ), geometry of the barrel (inner and outer radii R 1 and R 4 ) ) , , , , , , , , (

4 3 2 1 2 1 , 0 R R R R A P P P f F hs   
The second one can be seen as the hydrodynamic force F hs that come from the tangential shear rate in the gap, which in its turn introduces the influence of height and fluid viscosity. This force is often neglected in axial piston pumps because they never run in the vicinity of null velocity in conventional applications. As mentioned above, this is not the case in EHAs that are used for position control. For this reason, it should be important to get a model of hydraulic forces that covers the whole domain of operation. However, getting an algebraic model from formal integration of the Navier-Stokes equations is not feasible, as mentioned in [START_REF] Bergada | Pressure, flow, force, and torque between the barrel and port plate in an axial piston pump[END_REF]]. Although the pump model currently considers the hydrostatic axial force only, it has still to be improved in order to include the hydrodynamic effect.

On its side, the frictional moment transmitted by the driver to the barrel is commonly estimated assuming a linear velocity distribution under pure tangential shear [START_REF] Ivantysyn | Hydrostatic pumps and motors[END_REF]].

  2 1 2 2 2 3 2 4 2 R R R R h M b       (4)
Once again, this model has to be improved to be applicable at very low velocity (from 10 to 100 rpm) when the flow in gap becomes more radial than tangential. The same remark applies to the modelling and simulation of the leakage flow in the gap.

III. APPLICATION: FAULT DIAGNOSIS FOR AN AXIAL PISTON PUMP OF AN ELECTRO-HYDROSTATIC ACTUATOR

Sensors and observable signals

On the electrical actuator used for flight control, steering, and extension/retraction of landing gears, there are a few sensors. Monitored signals are:

the differential pressure, the accumulator pressure, the hydraulic jack position (only for flight control and steering), the fluid temperature, the motor windings temperature, the motor position, from which can be deduced the motor rotation speed, Although there is no flow-meter, the pump output flow rate can be identified from the motor speed and the jack position measured signals.

These signals are available without any sensor addition, so they are natural candidates to use in priority for the design of fault indicators.

It is interesting to emphasize the following effect that has already been mentioned in [Maré (2006)]. In real operation, the pump housing is connected to a charge accumulator which aims at compensating the change of fluid volume versus pressure and temperature, the external leakages and the deformation of walls under pressure. The accumulator is connected to each hydraulic power line by a re-feeding check valve. When the pump output pressure reduces, the fluid expands and the walls retract. The corresponding fluid flow cannot pass through the re-feeding valves that are closed. Therefore, the fluid flows from power lines to the accumulator through the pump internal gaps and housing. Pressures in the power lines become equal and decay to the charge pressure with a first order dynamics. This dynamics comes from the combination of a resistance effect (overall hydraulic resistance of pump gaps) and a capacitance effect (fluid and walls compliance). In the test simulated on Fig. 6, the pump is driven at a variable speed between -8000 and 8000 rpm and is loaded by a fixed hydraulic resistance (1.5 mm 2 ) connecting the two power ports A and B. Charge pressure is 50 bar. It is clearly observed that when the pump is unloaded (as a consequence of speed reduction at t = 1.2 s), the pressures at power ports become equal and decay at a rate that depends on the pump leakage. This rate appears as an interesting candidate to get a good signature of the pump leakage even if there is a very little change in the pressures themselves.

Faults signatures

Simulations were run with the virtual prototype, in order to identify candidates fault indicators. In the following example, the clearance between one piston and the barrel is progressively increased from 12 to 60 m to simulate the wear of one piston. The differential pressure is set to 103 bars, the gap between the barrel and the distribution plate is 16 µm. Mechanical speed is 10366 rpm. The output flow Q A at hydraulic port A, the input flow Q B at hydraulic port B and the leakage flow Q F at drain port D are observed. Figure 7 displays the magnitude spectrum as a function of clearance. The conclusion is that new harmonics appear in case of one piston unexpected wear. Since the pump has 7 pistons, it is not surprising that the new harmonics numbers are multiple of 7. The frequency analysis of the hydraulic flow can then be an indicator of wear.

CONCLUSION

The different ways of improving the model's realism of an EHA pump has been reviewed with respect to the needs induced by the development of fault detection and identification features. A structured architecture of the pump model has been firstly proposed for fault diagnosis and for virtual prototyping. Then, the virtual prototype has been improved using a step-by-step process. When developing the models, it has clearly appeared that there is a need for advanced parameters of 0-D models, in particular for friction in bearings operating around null velocity at high angular acceleration and for flow and hydraulic forces invariable gaps. Referring to basic geometries where models can be expressed formal induce severe assumptions that generate unacceptable inaccuracy. Flow and forces models have to be established from distributed models in order to better reproduce the effect of pressure, velocity and gap height, e.g. using scaling-law based meta-models as proposed in [START_REF] Budinger | Scaling-law-based Metamodels for the Sizing of Actuation Systems[END_REF]]. Model improvement requires also the thermal effects to be considered. Although thermal-hydraulic models are available in today's software libraries, the same need appears to support model parameterization.

Figure 1 .

 1 Figure 1. Architecture of the pump model used by the fault detection and identification algorithm

Figure 2 .

 2 Figure 2. EHA pump image (top) and schematic cut view (bottom) [Bucheton (2001)]

Figure 3 .

 3 Figure 3. Structure of the pump model, focused on hydraulics (rotational dynamics not displayed)

Figure 4 .

 4 Figure 4. Influence of speed and temperature on bearing friction (at rated output pressure)

Figure

  Figure 5. Simulated peak friction force (103 bar, 10300 rpm, 40°C)

Figure 6 .

 6 Figure 6. Pump speed and pressures with gap at distribution plate 12 m (upper) and 17 m (lower)

Figure 7 .

 7 Figure 7. Magnitude spectrum of hydraulic flows vs. angular frequency for different piston/barrel clearance cd (simulation results)