Lucia Venturelli

Paolo E Santangelo
email: paoloemilio.santangelo@unimore.it

Paolo Tartarini

FUEL CELL SYSTEMS AND TRADITIONAL TECHNOLOGIES. PART II: EXPERIMENTAL STUDY ON DYNAMIC BEHAVIOR OF PEMFC IN STATIONARY POWER GENERATION (Abbreviated title: ANALYSIS ON DYNAMIC BEHAVIOR OF PEMFC)

Keywords: stationary generation, fuel cells, PEMFC, dynamic behavior, efficiency

The present work is focused on electric generation for stationary applications. The dynamic behavior of a PEMFC-based system has been investigated at both constant and variable load conditions from an experimental point of view. An analysis of efficiency as a function of time has been proposed to summarize the dynamic performance; moreover, current intensity and voltage have been considered as main parameters of interest from the electric point of view. In addition, other energetic and thermodynamic parameters have been studied in this work.

The experimental campaign has been carried out over four test typologies: constant load; increasing and decreasing load; random load. These tests have been planned to challenge the system with a variety of load-based cycles, in frame of a thorough simulation of real load conditions.

Introduction

Fuel cells are now commonly considered a promising alternative to traditional systems in energy generation. These devices have gained a strong market appeal both for stationary (residential and industrial) and for mobile (automotive and aerospace vehicles) applications. Although the occurring physical and chemical phenomena have been strongly investigated, many researches are still conducted to understand their functioning, especially from an engineering point of view. This work is set in the broad field of heat and power generation for stationary application. Among the numerous review papers in this area, it is worthwhile to mention the one by Onovwiona and

Ugursal [START_REF] Onovwiona | Residential cogeneration systems: review of the current technology[END_REF], that describes fuel cell based systems for residential cogeneration. Likewise Wu and Wang [START_REF] Wu | Combined cooling, heating and power: A review[END_REF] have included fuel cells among the prime movers in combined cooling, heating and power, as well as turbines, internal combustion engines and Stirling engines. Many works have been also carried out with particular countries as a setting. Aki et al. [START_REF] Aki | Fuel cells and energy networks of electricity, heat, and hydrogen in residential areas[END_REF] have focused their work on residential hydrogen networks for energy generation in Japan: fuel cells obviously represent the core of such a system.

Brown et al. [START_REF] Brown | An emerging market in fuel cells? Residential combined heat and power in four countries[END_REF] have studied fuel cell market in the residential field through a comparison over four countries (Japan, Germany, USA and UK). Zabalza et al. [START_REF] Zabalza | Feasibility analysis of fuel cells for combined heat and power systems in the tertiary sector[END_REF] have performed a feasibility analysis of a fuel cell based cogeneration system, strongly referring to Spain.

The present work is related to Proton Exchange Membrane Fuel Cells (PEMFC), which are an attractive type of fuel cells because of their reliability and robustness.

PEMFC are interesting both for practical applications and for academic researches:

Hamada et al. [START_REF] Hamada | Operating results and simulations on a fuel cell for residential energy systems[END_REF] have employed a PEMFC device to run an experimental campaign about energy generation for residential units, while Chu et al. [START_REF] Chu | The development of a small PEMFC combined heat and power system[END_REF] have focused their study on the design of a PEMFC-based combined heat and power system. On the other hand, other types of fuel cells (e.g.: SOFC) have inspired similar works: among the others, it is worthwhile to mention Santangelo and Tartarini [START_REF] Santangelo | Fuel cell systems and traditional technologies. Part I: Experimental CHP approach[END_REF] and Zink et al. [START_REF] Zink | A solid oxide fuel cell system for buildings[END_REF]. In particular, the contribution by Santangelo and Tartarini [START_REF] Santangelo | Fuel cell systems and traditional technologies. Part I: Experimental CHP approach[END_REF] can be considered as an introductory work to the present paper. It dealt with the project of an experimental setup which was focused on testing high-temperature Solid Oxide Fuel Cells (SOFC).

Even if several factors led to modify that project to the present analysis of lowtemperature PEMFC, that paper can still be regarded as a Part I of a thorough study on technical and economical perspectives of fuel cells in the frame of worldwide energy problems.

A noteworthy study has been performed by Auld et al. [START_REF] Auld | Applications of one-cycle control to improve the interconnection of a solid oxide fuel cell and electric power system with a dynamic load[END_REF], who modeled a SOFCbased power system to satisfy the dynamic load of a commercial building, facing both steady state and transient conditions. Chaisantikulwat et al. [START_REF] Chaisantikulwat | Dynamic modelling and control of planar anode-supported solid oxide fuel cell[END_REF] have extensively discussed dynamic responses of SOFC systems, proposing a complete model to determine electric performance from classic thermodynamic relations.

An experimental analysis has been conducted focusing on the characterization of a PEMFC system facing different load conditions. From a practical point of view, the ultimate goal of the experimental campaign was determining how this system follows the user's electric need and how its efficiency varies thereby. Torchio et al. [START_REF] Torchio | Experimental analysis of the CHP performance of a PEMFC stack by a 2 4 factorial design[END_REF] have pursued the same aim through a statistical methodology applied to a PEMFC stack for combined heat and power. Selamo ullari et al. [START_REF] Selamo Ullari | A systems approach for sizing a stand-alone residential PEMFC power system[END_REF] have collected experimental data about response-to-load in order to propose a stochastic methodology for sizing a residential PEMFC-based power system. Entchev and Yang [START_REF] Entchev | Application of adaptive neuro-fuzzy inference system techniques and artificial neural networks to predict solid oxide fuel cell performance in residential microgeneration installation[END_REF] have followed a similar procedure to validate an adaptive model for SOFC in residential microgeneration.

The dynamic behavior of the fuel cell device has been investigated along a load-based series of tests. Different load cycles have been imposed to simulate a realistic variety of working conditions for a residential energy system. This approach has been employed in many researches, especially to determine the dynamic trend of electric parameters, like current intensity and voltage. El-Sharkh et al. [START_REF] El-Sharkh | A dynamic model for a stand-alone PEM fuel cell power plant for residential applications[END_REF] have developed a theoretical electrochemical model to predict the response capability of a PEMFC power plant for residential applications. Santarelli and Torchio [START_REF] Santarelli | Experimental analysis of the effects of the operating variables on the performance of a single PEMFC[END_REF] have conducted an experimental analysis to investigate the electric performance of a single PEMFC as a function of some thermodynamic variables. Uzunoglu et al. [START_REF] Uzunoglu | Dynamic behavior of PEM FCPPs under various load conditions and voltage stability analysis for stand-alone residential applications[END_REF] have carried both an experimental campaign and a theoretical analysis about voltage stability under different load conditions in PEMFC power plants. Chen and Zhou [START_REF] Chen | Diagnosis of PEM fuel cell stack dynamic behaviors[END_REF] have focused their work on steady-state and dynamic behavior of PEMFC at various current conditions, particularly referring to the relation between stack voltage and cathode/anode pressure drop. De Bernardinis et al. [START_REF] Bernardinis | Fuel cells multi-stack power architectures and experimental validation of 1 kW parallel twin stack PEFC generator based on high frequency magnetic coupling dedicated to on board power unit[END_REF] have developed a dynamic model for PEMFC at high perturbation frequencies; however, this model is aimed to support a multi-stack fuel cell architecture for vehicle units. Moreover, a theoretical approach to predict dynamic properties of fuel cells has been proposed in many works [START_REF] Huo | Nonlinear dynamic modeling for a SOFC stack by using a Hammerstein model[END_REF][START_REF] Mckay | Parametrization and prediction of temporal fuel cell voltage behavior during flooding and drying conditions[END_REF][START_REF] Zhi-Dan | Adaptive maximum power point tracking control of fuel cell power plants[END_REF]. It is worthwhile also to mention a numerical study about transient behavior of PEMFC at high temperature carried out by Peng et al. [START_REF] Peng | Transient response of high temperature PEM fuel cell[END_REF].

The present study focuses on both electric (current intensity, voltage) and thermodynamic (hydrogen pressure, gas temperatures) parameters. Among these latter, there is a final discussion about efficiency, that constitutes a major issue from an engineering point of view.

Experimental apparatus

The experimental campaign has been run on the Mobixane

ACCEPTED MANUSCRIPT

The first de-compression stage reduces hydrogen pressure from 200 to 5 bar and the second from 5 to 0.3 bar. A sketch of the whole apparatus is shown in Fig. 1.

Methodology

Tests have been carried out at four nominal power values: 0.6, 1, 1.5 and 1.8 kW.

Every time the prescribed load has been applied to the system by switching a certain number of lamps on and regulating the ones provided with the dimmer. A nominal value of power is reported on the display of the device, but it does not represent the power yielded to the user. This latter has been measured by the wattmeter and shown to be lower. On the other hand, the power generated by stack can be calculated as voltage times current intensity: this value is bigger than the one reported on the display. The gap between the measured and the calculated value is discussed in the following paragraph. The results of this analysis have been obtained for both every test (Eqs. ( 1), ( 3), ( 5)) and every load value (Eqs. ( 2), ( 4), ( 6)).

The second test session has been performed at monotonic increasing and monotonic decreasing load, while the third one was characterized by random mixed load cycles.

Additional tests have been run including both the two kinds of load trend (increasing and decreasing). These tests were characterized by a certain level of regularity, unlike the mixed ones: a gradual monotonic trend has been imposed to the former, while a random load cycle has been planned for the latter. The mixed tests have been performed

to challenge the fuel-cell system with a reasonable small-scale simulation of a typical residential power request, that may be constituted by random variations of the applied load. The ultimate goal of these experiments was to understand how a PEMFC device follows the applied load and how the efficiency is affected by the load cycle.

Results

The main result of constant load session consists of the characteristic curve of the stack (Fig. 2). Mean value and percentage dispersion of current intensity and voltage are reported in Fig. 2 at each nominal load; dispersion related to current intensity is lower than 4%, while dispersion related to voltage is lower than 1%.

The PEMFC device has shown a considerably rapid response in following the applied load. The stack has been proved to respond to any load variation within the acquisition frequency (0.1 Hz). An analysis about the hydrogen volumetric flow rate at the inlet has been performed.

Fig. 4 shows the hydrogen volumetric flow rate at the inlet as a function of time at random mixed load. At non-constant time steps the hydrogen pipe system is emptied through a series of purges. Pressurized hydrogen is flown in order to drain condensed water away in the channels. Condensed water is due to humidification of hydrogen and could obstruct the ducts; therefore, purges are very common in fuel cell devices and have been extensively studied [START_REF] Corbo | Experimental analysis and management issues of a hydrogen fuel cell system for stationary and mobile application[END_REF][START_REF] Del Real | Development and experimental validation of a PEM fuel cell dynamic model[END_REF]. Purged hydrogen is diluted by the air of the cooling system; this process causes a relevant hydrogen loss.

The amount of hydrogen consumed in the stack can be prima facie evaluated through a classic electrochemical formula, that is applied to the involved reaction:

. 2F

I n = (7)
Actually, Eq. ( 7) allows to calculate the stoichiometric molar flow rate, that is effectively required to carry out the chemical reaction. The hydrogen amount consumed in the stack is slightly higher because of a certain surplus in fuel consumption. Finally, a remarkable difference arises if stoichiometric flow rate is compared with the measured flow rate: this latter is two times the former on average, because of the purges, which have been previously discussed.

Constant load tests have yielded to determine stack temperature trend as an experimental result. This parameter converges to a value close to 65 °C (Fig. 5). This is consistent with the internal air-cooling system, that keeps stack temperature below 70

°C. The aim is to prevent any degeneration for the polymer electrolyte membrane: this phenomenon occurs if the stack temperature grows beyond this limit value. Equilibrium temperature is reached after a transient time, that varies up to the applied load. Transient time is shorter at higher loads, that implies and explains stronger power losses at higher loads. The cooling system starts working earlier, dissipates more heat and needs more energy.

When a thermodynamic approach is employed to study fuel cells, the opportunity of performing CHP has to be investigated. Availability and feasibility of heat recovery has to be determined from a technical point of view. This research shows that heat recovery can be hardly realized in the present case. Water produced through the chemical reaction shows a maximum temperature of 28.5 °C occurring during tests at constant load of 1.8 kW. Moreover, its flow rate is approximately 0.8 l/h at the same value of constant load. Therefore, heat recovery appears not to be convenient, because it should be performed at such low values of temperature and flow rate. Cooling air presents a maximum temperature of 35.9 °C at constant load of 1.8 kW: for the same reason previously mentioned about the produced water, heat recovery seems not to be convenient from cooling air as well. The temperature trends for produced water and cooling air at constant load of 1.8 kW are shown in Fig. 6.

stack has been calculated as result of multiplying the instantaneous values of current intensity and voltage and final power released to user has been measured by the wattmeter. Fig. 7 shows mean value and percentage dispersion of these two parameters and of power losses, which are defined as the difference between stack power and power yielded to the user. Comparing the power generated by the stack and the one yielded to the user, a remarkable gap can be noticed. This is due to losses related to sustaining the auxiliary systems and transformation from direct to alternate current, which occurs in the inverter. Once load increases, chemical reactants are forced to increase in their concentration. Power to run the compressor, that supplies air to cathode, grows as well. Thus, heat to be dissipated is higher; therefore power to be yielded to air-refrigerating fans increases.

As far as efficiency represents the ultimate quantification of the behavior of any energy system, a discussion has been proposed about this parameter applied to PEMFC.

First of all, two kinds of instantaneous efficiency have been calculated: Instantaneous efficiency is meant as the efficiency calculated at each data acquisition.

Eq. ( 8) reports the theoretical efficiency of the system, that is a function of net power and theoretical hydrogen volume flow rate. This latter can be easily calculated from the stoichiometric molar flow rate, that is yielded by Eq. [START_REF] Chu | The development of a small PEMFC combined heat and power system[END_REF]. Eq. ( 9) presents the net efficiency, that is a function of net power and measured flow rate. Fig. 8 reports instantaneous theoretical and net efficiency at random mixed load. The former seems to vary on average along with load variations, while the latter appears to be more constant regardless of the purges.

As a conclusive quantification of the system behavior, the final efficiency has been calculated for every test:

, LHV Q E th net th fin, ⋅ = (10)
.

LHV Q E net net net fin, ⋅ = (11)
Fig. 9 shows both theoretical and net efficiency at constant load cycles. Eqs. ( 10) and Calculations by Eq. ( 11) have been performed for every test at constant load, at monotonic load and at mixed load. Average mean values over every kind of test (at constant, monotonic and mixed load) are reported in Table 1. Moreover, Table 2 remarks a major issue related to efficiency: it appears to be practically constant varying the applied load cycle.

Conclusions

An experimental investigation on dynamic behavior of a PEMFC-based system for stationary applications has been carried out. The device has been tested over different load conditions and four kinds of load cycle have been applied. As a first goal, the characteristic curve of the stack (Voltage vs. Current Intensity) has been reconstructed.

Moreover, the device has shown a notably rapid response to load variations in terms of current intensity and voltage. Stack temperature as a transient has been analyzed: it converges more rapidly as applied load increases. Temperature trends of produced water and cooling air have been measured to investigate availability and feasibility of heat recovery. This opportunity appears to be hardly applicable because of the low values of these two parameters. The difference between stack and net power has been stressed out as a key point to evaluate electrical losses. This analysis has shown that power losses tend to increase as nominal load increases. A final analysis about efficiency has been performed as the ultimate aim of this work. A thermodynamic approach has been employed and the difference between theoretical and net efficiency has been reported for every load value. Hydrogen purges have been investigated and their influence on net efficiency has been detected through a comparison with stoichiometric fuel consumption. An optimization of purges appears to be recommended in order to improve net efficiency, especially at low values of the imposed load because their effect at these conditions is greater than at high load values. Final net efficiency appears to be practically constant varying the load typology: this represents one of the main results of the present study. All the data gained from this experimental activity have been processed through an uncertainty analysis.

As a final comment, this work has been performed in the frame of a comprehensive research on fuel cells applied to stationary power generation. A reliable collection of new experimental data is here reported as a useful contribution to the full work, that is supposed to represent a reference for comparisons between fuel-cell systems and traditional technologies especially in terms of efficiency.

NomenclatureDFx

  (x) l standard deviation of parameter x related to nominal load l D(x) kl standard deviation of parameter x related to test k l Disp(x) kl percentage dispersion of parameter x related to test k l Disp(x) l percentage dispersion of parameter x related to nominal load l E generated electrical energy [kWh] Faraday constant (= 96485.3399 C mol -1 ) I current intensity [A] LHV hydrogen lowest heat value (= 3.00 kWh Nm -3 ) M(x) kl mean value of parameter x related to test k l M(x) l mean value of parameter x related to nominal load l n molar flow rate [mol s -measured parameter (I, V, P stack , P net ) load (12 tests, 3 tests for every load value l) l nominal load (0.6, 1, 1.5, 1.8 kW) net net

TM,

  produced by Axane Fuel Cell Systems. It is a PEMFC-based electrical generator, that has shown the capability of releasing power between 0.5 and 1.8 kW. Below 0.5 kW, the stack cannot produce the minimum quantity of water vapor to obtain a sufficient humidification of the internal membrane. The upper limit of 1.8 kW is governed by the internal safety system: once this value is overtaken, the device stops working. An internal data acquisition system is provided for this device. Every 10 seconds the values of the following parameters of interest are recorded: stack current intensity, stack voltage, volumetric flow rate of the supplied hydrogen, hydrogen pressure and stack temperature. The power effectively released to the user has been measured by a wattmeter. Starting from the already mentioned values, other parameters have been a posteriori calculated: power released by the stack, losses, stack efficiency and final efficiency.This device is structured in modules, so it follows the applied load by generating only the requested power. During the experimental campaign two kinds of lamps have been employed as a load: 200 W with dimmer and 500 W. Thermocouples have been used to measure temperature of cooling air and water produced by the stack. The system is fueled by pure hydrogen. The fuel supply is constituted by a storage facility, that is placed outside the test chamber. This structure contains 8 tanks (10 Nm 3 each), has a decompression system and is connected to the fuel cell system by a stainless steel pipeline.

  The first experimental session has been conducted at constant load, in order to characterize the device and to check repeatability of tests and trends of parameters as functions of time. As a matter of fact, the characteristic curve of the stack can be obtained from constant load data and held as valid for any load cycle. In addition, these tests have proved the capability of the device to have an on average constant behavior over a prescribed time. In particular, three tests have been run at every nominal load.Many parameters related to constant load test (current intensity, voltage, stack power, net power and instantaneous efficiency) have been processed through a data analysis, aimed to stress out mean value, standard deviation and percentage dispersion. These three mathematical operators are defined as follows:

Fig. 3

 3 is related to a random mixed load cycle and shows how current intensity and voltage follow its variations. Current intensity and voltage are basically mirror image: the former has the same trend as the applied load, while the latter has the opposite trend. This result is consistent to the already mentioned characteristic curve.

( 11 )

 11 allow to perform the required calculations. Each presented value is the average of efficiency over all the tests conducted at the same load value. The reported trends are very similar: they are almost constant over the considered operative range, even if efficiency appears to be slightly lower at low values of applied load. The difference between the two presented curves emphasizes the hydrogen losses primarily due to purges and to hydrogen surplus too. Both the efficiencies take electrical losses into account, but the comparison enlightens the waste of energy due to a non-stoichiometric fuel consumption.

Figure captions:Fig. 1 -

 1 Figure captions: Fig. 1 -Sketch of the experimental facility.

Fig. 2 -

 2 Fig. 2 -Characteristic curve of the stack (Voltage vs. Current Intensity).

Fig. 3 -Fig. 4 -Fig. 5 -Fig. 6 -Fig. 7 -

 34567 Fig. 3 -Mixed Random Applied Load, Current Intensity and Voltage vs. Time.Fig. 4 -Mixed Random Applied Load and Hydrogen Volumetric Flow Rate vs. Time. Fig. 5 -Stack Temperature vs. Time at every nominal load.Fig. 6 -Water and cooling-air temperature at constant load of 1.8 kW. Fig. 7 -Stack, Net Power and Power Losses vs. Nominal Load with percentage dispersion at constant load cycle.

Fig. 8 -Fig. 9 -

 89 Fig. 8 -Mixed Random Applied Load, Theoretical and Net Efficiency vs. Time. Fig. 9 -Theoretical and Net Final Efficiency vs. Nominal Load.

Table 2 :

 2 Final net efficiency for every typology of load cycle.

	Test Typology	final,net
	Constant Load	0.400
	Monotonic Load	0.400
	Mixed Load	0.411

Acknowledgements

The authors wish to thank Sonia Lauria and Dr. Luca Tarozzi for their invaluable help during the experimental campaign. This work has been supported by Regione Emilia-Romagna, Italkero S.r.l. and ProMo S.c.ar.l. (Italy).


R Palacios
email: rafael.palacios@iit.upcomillas.es

A Arenas

R Rodríguez-Pecharromán

F L Pagola

Analytical procedure to obtain internal parameters from performance curves of commercial thermoelectric modules

Keywords: Thermoelectricity, internal parameter estimation, performance simulation, basic equations

Manufacturers of commercial thermoelectric modules provide datasheets of the modules including information and graphs about the performance attained at several working conditions. Details about internal parameters are not made available to customers, because in the broad majority of the cases they are not necessary. However, when developing non-standard applications or conducting research projects it is sometimes necessary to make the modules work in different conditions than those shown in the performance curves. This paper shows a methodology to extract thermoelectric internal parameters from the information provided by performance curves, hence allowing scientists to predict the performance of the module at any working condition. The method is based on the basic equations that link thermal and electrical dynamics in which some parameters must be estimated. As a result it is possible to predict the behavior of the modules if they are operated in a non-standard way. One good example is to simulate how a module designed for cooling applications will behave if used as a Seebeck module for power generation. The proposed methodology has been successfully applied to a commercial Peltier module for which the behavior as a thermoelectric generator was simulated and then tested experimentally, attaining very similar results.

Introduction

Nowadays thermoelectric modules are so specialized that every manufacturer offers a set of modules for each kind of application. Modules within the same series are intended to be used in the same kind of application, and the set comprises modules with diverse external dimensions, while separate series differ mostly in the internal parameters such as number of pellets, pellet dimensions and geometry, and assembling procedure. The information contained in the datasheets of themoelectric modules mainly describes external dimensions and maximum performance values. Each family of TE modules is optimized in performance and manufacturing costs for a given application: cooling applications, power generation at low temperature, power generation at high temperature, etc. For a standard application it is not difficult to select the correct module looking at the performance values of the appropriate family of modules, then it is possible to estimate the final behavior of the application by using the performance curves (provided that the temperatures can be estimated accurately).

However, for non-standard applications it can be necessary to make the modules work at an atypical condition, graphically located outside of the boundaries of the performance curves. In this case it is very helpful to use an analytical model able to predict the behavior of the module. An extreme example is to use a Peltier module, originally designed for cooling applications, to generate electricity as if it were a TEG or Seebeck module. A good reason for such an abnormal use of a TE module is to obtain electrical power at higher voltages that with standard TEG, hence avoiding DC-DC amplifiers in some applications. Most TEG modules are designed for low thermal resistance by using big active elements with small height, hence allowing for higher heat transfers through the module which yields to higher electrical power. Nevertheless, this design also produces lower output voltage that, for some applications, may require a DC-DC amplifier or mounting several modules connected in electrical series. On the other hand, Peltier modules are typically designed for 12V operation and use more pellets with larger height, as a consequence if they are used for power generation, they produce lower electrical power but higher voltage than TEG modules operated at the same conditions. As a summary it can be said that Seebeck modules generate mV at low temperatures while Peltier modules may generate volts at the same operating conditions. Due to increasing number of portable devices (including phones, mp3 players, and digital cameras) with the associated problem of eventually running out of batteries, there is active research in the field of low-power electric generation from sources such as movement, heat or sun. Thermoelectricity plays an important role in the conversion of heat into electricity. However, since Seebeck modules are typically designed for temperatures in the range of 250ºC, they do not perform well in domestic or office environment where potential heat sources for producing electricity have lower temperatures. On the other hand, internal design of Peltier modules is more appropriate for this kind of application if used as thermoelectric generator, but performance curves of Peltier modules operating as thermoelectric generators are not provided.

In order to obtain the internal parameters of a given module, there are two possible approaches: obtaining the properties experimentally, or estimating parameters from the information available in the vendor datasheet. From the small number of publications related to this topic, the most significant are the experimental procedure described by Huang [START_REF] Huang | A Design Method of Thermoelectric Cooler[END_REF] and the mathematical methods described by Luo [START_REF] Luo | A simple method to estimate the physical characteristics of a thermoelectric cooler from vendor datasheets[END_REF].

Obtaining the parameters experimentally is interesting, especially before building a prototype application, because the parameters obtained represent the actual behavior of the module in a working condition which is very close to that of the final application.

Nevertheless, the experimental approach is not useful for selecting a module from the broad vendor's catalogs during the design stage. In contrast, the mathematical approach based on information available on product datasheets is more valuable for designing applications. Luo proposed two methods for computing internal parameters based on the values Vmax, Imax, Qmax and ˜Tmax, available in datasheets. Since those four values are obtained at different working conditions (and also at extreme operation) they are inconsistent and do not match the basic thermoelectric equations altogether. Hence, two methods are proposed in [START_REF] Luo | A simple method to estimate the physical characteristics of a thermoelectric cooler from vendor datasheets[END_REF]: method I uses Vmax, Imax, and ˜Tmax while method II uses Imax, Qmax and ˜Tmax, obtaining different sets of parameters with up to 5% discrepancy in the modules analyzed.

The procedure presented in this paper falls in the category of analytical methods, but instead of using three single outmost values it uses several points and minimizes the error by linear regression or curve fitting. In the proposed procedure many values are extracted form the performance graphs provided by the manufacturer in typical datasheets, in contrast with just two or three extreme numerical values used in the method proposed in [START_REF] Luo | A simple method to estimate the physical characteristics of a thermoelectric cooler from vendor datasheets[END_REF]. Although significantly more complicated to implement, the procedure presented in this paper is more accurate and can be used to simulate the behavior in a wider range of working conditions, including the simulation of Peltier modules working as thermoelectric generators.

Analytical procedure to obtain Peltier parameters

Beginning with a module typically designed for cooling applications, the performance graphs provided by the manufacturer show the maximum temperature difference (˜T) for different values of current supplied and heat transfer. However, it is not possible to know from these curves how much electrical energy could be obtained if the module is used as an electric generator for a given heat flow. The proposed method makes use of the basic thermoelectric equations [START_REF] Rowe | CRC Handbook of Thermoelectrics[END_REF] to estimate internal parameter (α, , and ) that can be used subsequently to estimate the behavior in any working condition, including the behavior as electric generator. Assuming that internal material properties (α and ) are constants that do not depend on the temperature, the equation for the heat power taken at the cold sink is:

Basic Peltier equations

E T EI IT Q c c ∆ - - = λ ρ α 2 2 1 (1)
where E [m/m 2 ] is a geometric property of the pellets defined as height divided by the cross section. Defining = /E [W/K] (thermal conductance) and = E [ ] (electrical resistance) the following equation for a given value of E is obtained:

T I IT Q c c ∆ - - = γ β α 2 2 1 (2)
Similar equations can be used for the heat power given at the hot sink, where only the sign of the middle term is changed from negative to positive:

E T EI IT Q h h ∆ - + = λ ρ α 2 2 1 (3) T I IT Q h h ∆ - + = γ β α 2 2 1 (4)
The electrical power supplied to the system is simply the product of the current and voltage. These magnitudes are not linked by a constant resistor value like in other electronic circuits, because for a given current the required voltage depends on the temperature of the system given that depends on the temperature.

I V W ⋅ = (5)
Hence the power balance equation will be given by equations 2, 4 and 5

W Q Q c h = - I V T I IT T I IT c h ⋅ = ∆ + + - ∆ - + γ β α γ β α 2 2 1 2 2 1 I V I I T T c h ⋅ = + - 2 ) ( β α (6)
Therefore the following simplified equation is obtained:

I T V β α + ∆ = (7)
The important advantage of equation 7 is that it contains just two parameters that can be easily estimated from the performance curves provided by the manufacturer. After obtaining α and , the other properties , and can be derived directly.

Estimating parameters from performance curves

In this section we take as an example the performance curves of the thermoelectric module Marlow DT 12-6 which are shown in Figure 1. This particular module has 127 thermoelements connected in series in module measuring 40x40mm designed for working temperatures up to 150ºC. The next step in the proposed procedure is aimed to obtain the value of parameter , which is the parameter directly related to the thermoelectric effect. Knowing the value of it is possible to apply equation 2 also for T=0, hence The method to estimate these parameters based on Imax, Vmax, Qmax and Tmax [START_REF] Huang | A Design Method of Thermoelectric Cooler[END_REF] differ from these values 18,5% in the worst case. The main reason for a better accuracy of the method presented in this paper is the use of several data point read from the datasheet graphs instead of using just the values corresponding to the most extreme condition.

Simulating Peltier behavior

Once the internal parameters of the module have been obtained, it is possible to analytically simulate the behavior of the module at any working condition by using the basic equations described in section 2. Simulation within the space of working conditions used for estimating the internal parameters is expected to be accurate after using any system identification procedure.

The accuracy while simulating new working conditions is difficult to predict, but assuming the correctness of the basic thermoelectric equations and using precise parameters such simulations are expected to be acceptable. The following section describes the process to simulate probably the most extreme situation, which is the behavior of the Peltier module being used as a thermoelectric generator.

Simulating Seebeck performance

After obtaining the internal parameters of the module, it is possible to apply the fundamental equations to predict its behavior under different working conditions. It is even possible to simulate the behavior of a Peltier module working as a Seebeck electrical generator since both Peltier and Seebeck equations share the same internal parameters.

Basic Seebeck equations

In the case of Seebeck effect, equations 1 and 2 become the following expressions in which the signs of the last two terms have changed [START_REF] Rowe | CRC Handbook of Thermoelectrics[END_REF]:

E T EI IT Q c c ∆ + + = λ ρ α 2 2 1 (12) T I IT Q c c ∆ + + = γ β α 2 2 1 (13)
In the same way, equations for the heat dissipated at the hot sink are:

E T EI IT Q h h ∆ + - = λ ρ α 2 2 1 (14) T I IT Q h h ∆ + - = γ β α 2 2 1 (15)
Hence, from the power balance equations, we obtain:

W Q Q c h = - I V T I IT T I IT c h ⋅ = ∆ - - - ∆ + - γ β α γ β α 2 2 1 2 2 1 I V I I T T c h ⋅ = + - 2 ) ( β α (16)
Finally, the general expression derived from the balance of power is also similar to equation 7 but with one sign changed:

I T V β α - ∆ = ( 17
)
Equation 17 becomes the most significant expression to estimate the behavior of the module working as an electrical power generator, since it computes the voltage provided by the module as a function of the current and the temperatures.

This expression shows that for a given difference of temperatures, the output voltage decays in a proportional way with the current that the module supplies to an external load, in the same way as any DC source. For open circuit, the voltage attains its maximum value given in this case by α˜T. However as the value of the current increases the output voltage decreases linearly, being the slope. Therefore α˜T plays the role of the fixed internal voltage of any DC source and is equivalent to the internal output resistance.

Estimating Seebeck performance curves

Assuming the same value of the internal parameters of the module: α, , (or α, , )

for Peltier and Seebeck effects, the performance curves can be estimated from equation 17. Therefore, taking the values for α and from Table I, equation 17 becomes:

C T for I T V C T for I T V h h º 50 769 . 2 055 . 0 º 27 431 . 2 054 . 0 = ⋅ - ∆ ⋅ = = ⋅ - ∆ ⋅ = (18)
Consequently, equation 18 is the mathematical model of thermoelectric module Marlow DT 12-6 when used as an electric generator, and the characteristic V-I curve is represented in Figure 3.

For lower values of the temperature at the hot sink, it is more accurate to use the set of parameters found in the first column of Table I, which were obtained for T h =27ºC, while for higher values of the temperature it is more accurate to use the second set of parameters. However, the sensitivity with T h is not as remarkable as with ˜T. In Figure 3 the set of response curves are represented for T h =27ºC and T h =50ºC simultaneously.

The largest difference can be found for high currents, and it is a consequence of larger for higher temperatures. Marlow DT12-6 as power generator: T h =27ºC (dashed), T h =50ºC (dotted) ∆T=10ºC ∆T=20ºC ∆T=30ºC ∆T=40ºC ∆T=50ºC

Figure 3: Estimated response for T h =27ºC and T h =50ºC

Comparing the performance of this module with one module specifically designed for thermoelectric generation, it can be concluded that Peltier modules produce higher voltage and lower current for the same working condition. For example, for ˜T=40ºC the Peltier module generates up to 2.25V (

T ∆ ⋅ α ) or up to 0.8A ( β α T ∆ ⋅
), with a maximum power of less than 0.5W. On the other hand, the module HiZ-14 with a bigger size (63.9x63.9mm) but less TE elements (49) generates up to 0.75V or up to 4.5A, with a maximum power of 1.75W, as tested in [START_REF] Vázquez | Test bench for measuring the electrical properties of commercial thermoelectric modules[END_REF]. As expected, the TEG module can generate more electrical power for the same temperature conditions; however it delivers that power at a lower voltage.

Experimental verification

In order to validate the proposed analytical procedure, several experimental tests have been carried out using a module Marlow DT 12-6. The module was mounted in between cupper plates and was heated on one side, using a controlled gas burner, while the other side was refrigerated using a water heat exchanger. Once the steady state was reached and a given temperature difference becomes stable, two working points of current and voltage were measured by changing the load resistance of the circuit.

The experimental results obtained for a measured ˜T of 35ºC are shown in Figure 4 in thick line compared to the analytical estimations. Although the experimental values are slightly higher than the analytical line corresponding to ˜T=30ºC, the actual internal voltage is a bit lower than the value predicted by the model. The experimental voltage decreases with the current faster than expected so the actual internal resistance is somewhat higher. The internal resistances obtained analytically and experimentally, are in the same order of magnitude as typical values obtained in previous experiments with TE modules, which are significantly higher than those in other DC sources [START_REF] Palacios | Electrical Properties of Commercial Thermoelectric Modules[END_REF].

Conclusions

This paper describes an analytical procedure to estimate internal parameters of commercial thermoelectric modules from the performance curves provided by the manufacturers. After these parameters have been obtained, it is possible to estimate the response of the module under any working condition. Even if the module is designed for cooling applications and only cooling performance curves are provided, the proposed methodology allows researchers to estimate the behavior when the module is used for power generation applications. While the experimental measurements do not perfectly match the results estimated analytically, they can be considered rather precise considering the difficulties for attaining accurate experimental measurements in a standard laboratory. The error of the analytical procedure estimating TEG behavior can be considered on the same level as the error of experimental measurements that try to reproduce the performance curves provided by the manufacturer.

Captions

  If a thermoelectric module is supplied with a direct current I [A], a certain amount of heat c Q [W] is absorbed in the cold side and pumped to the hot side. Because of the Peltier effect the heat pumped is proportional to the value of the current and the temperature at the cold side c T [K], being α [V/K] the Peltier coefficient. However, in a real thermoelectric module, the heat absorbed in the cold side is not just the Peltier term, because it is diminished by the power due to electrical resistance and heat transfer due to thermal conductivity. As a consequence of the electrical current going through the module there is heat generated internally (Joule effect), which is proportional to the electrical resistance E ρ [ ] and the square of the current. The power generated by Joule effect is considered to heat the hot and cold sinks in the same amount. The last term in the equation for computing the heat at the cold sink (equation 1) [1] computes the amount of heat transferred from the hot sink to the cold sink due to internal thermal resistance. In this case the amount of power is proportional to the conductivity [W/m/K] and the temperature difference

Figure 1 : 2 ]

 12 Figure 1: Performance curves of Marlow DT 12-6 [2] It can be seen that two sets of curves are provided, one set for T c =27ºC (T c =300K) and another for T c =50ºC (T c =323K). On each set there are curves to obtain T as a function of the electrical current for different values of Q c , and also curves to obtain required voltage as a function of the current. In the later case only two extreme situations are represented T=0 and Q c =0, since all other situations lay in between these curves.

  So the value of will be obtained with the following expression:By setting T=0 we have T c = T h , and the value of is already known, so equation 9 has Q c and I as the only independent variables. Consequently, the value of can be obtained with any pair of values (Q c , I) obtained from the upper set of curves for T=0 (this is at the x-axis). Instead of using Qmax and Imax, our suggestion is to compute as the average of several pair of values (Q c , I) to minimize the error. Note that Q c and I are not linearly related in equation 9 so the curves for constant Q do not cut the axis evenly spaced. Finally, the last characteristic of the module materials is the parameter , related with the thermal conductivity. In this case, equation 2 for Q c =0 will be used. value of can be obtained with any pair of values (I, T) extracted from the curve corresponding to Q c =0 in the upper graphs of Figure 1. Again, it is recommended to average several estimations of obtained with different pairs of I and T. The values of , and obtained for the Thermoelectric module Marlow DT 12-6, used as an example are shown in the following table:

1 .

 1 For example, equation 2 can be rewritten to obtain T as a function of I as: Using equation 11 for T h =27ºC and Q c =10W, 20W and 30W, three of the characteristic curves for constant heat power are obtained. Figure 2 includes dots representing the values simulated using equation 11, over the experimental curves from the manufacturer datasheet. This graph shows good precision of the simulated data and therefore confirms the accuracy of the proposed parameter estimation procedure.

Figure 2 :

 2 Figure 2: Simulated dots in a layer over the original Performance Curves of Marlow DT 12-6 [2]

Figure 4 :

 4 Figure 4: Estimated response for ˜T=35ºC

Figure 1 :Figure 2 :

 12 Figure 1: Performance curves of Marlow DT 12-6 [2]

Figure 3 :Figure 4 :

 34 Figure 3: Estimated response for T h =27ºC and T h =50ºC

Table I : Internal parameters determined from the performance curves

 I

		T h = 27 ºC	T h = 50 ºC
		(300 K)	(323 K)
	[V/K]	0.0543	0.055
	[ ]	2.431	2.769
	[W/K]	0.528	0.494

Acknowledgements

This work has been partially supported by the Spanish government through project no.

BIA2004-06001


Ernesto Benini
email: ernesto.benini@unipd.it

Sergio Pandolfo

Serena Zoppellari

Reduction of NO emissions in a turbojet combustor by direct water/steam injection: numerical and experimental assessment

Numerical and experimental investigations are conducted to assess the benefits and drawbacks of both water (mist) and steam direct injection within the combustion chamber of a 200N static thrust turbojet. For this purpose, a three-dimensional CFD model of the combustion process is implemented where pollutant emissions are calculated; in parallel, a test campaign on the turbojet at sea level static conditions is carried out. In both cases the refrigerant flow is injected directly into the combustor, outside the liner. The aim of the investigations is to evaluate the impact of increasing water and steam flows (ranging from 0 to 200% of the fuel mass flow) onto the emissions levels (NO and CO) of the engine.

Introduction and Background

Pollutant emissions arising from oxidation processes in aeronautical combustion chambers have recently become of great concern due to their environmental impact. Emissions of nitrogen oxides from aircrafts, which affect men's health and contribute to the formation of ozone, have been of particular interest to many airport operators as a result of increasing air traffic.

Since the end of World War II water injection in aero-engines has been quite extensively studied [START_REF] Ingebo | Effect of Primary-Zone Water Injection on Pollutants form a Combustor Burning Liquid ASTM A-1 and Vaporized Propane Fuels[END_REF]- [START_REF] Hilt | Nitric Oxide Abatement in Heavy Duty Gas Turbine Combustors by Means of Aerodynamics and Water Injection[END_REF], and was implemented mainly for thrust augmentation [START_REF] Wilcox | Analysis of Thrust Augmentation of Turbojet Engines by Water Injection at Compressor Inlet Including Charts for Calculating Compression Processes With Water Injection[END_REF] even at supersonic flight conditions [START_REF] Woodworth | The Significance of Major Cycle Variables on Turbojet Engine Performance at Mach 3.0[END_REF], [START_REF] Beke | Analytical investigation of the effect of water injection on supersonic turbojetengine-inlet matching and thrust augmentation[END_REF]. Such "old-style" water injection systems used on early Boeing 707 and 747 aircraft were unpopular with airlines because little benefit was readily seen while the drawbacks of servicing the system with water were observed every day. Since those times, interest regarding water injection in aero engines has dropped down until the beginning of the new century.

Recently, the use of water injection has been again proposed as an effective tool to reduce emission levels, particularly NOx, during taxiing and take-off operations [START_REF] Daggett | Water Misting and Injection of Commercial Aircraft Engines to Reduce Airport NOx[END_REF]- [START_REF] Saravanamuttoo | Gas Turbine Theory[END_REF]. The most comprehensive study was carried out at NASA Glenn Research Center to estimate the effects of water injection on a commercial turbofan engine to reduce specific fuel consumption (SFC), NOx emissions, and engine hot-section temperatures while maintaining constant thrust [START_REF] Daggett | Water Misting and Injection of Commercial Aircraft Engines to Reduce Airport NOx[END_REF]. According to these results, the subsequent reduction in hot-section temperatures could increase engine life and reduce maintenance costs. Water injection technique is very similar to the one employed in industrial gas turbine combustors, where water injection is currently used for power augmentation, turbine life saving and NOx reduction during the hot seasons [START_REF] Saravanamuttoo | Gas Turbine Theory[END_REF], [START_REF] Lefebvre | Gas turbine combustion[END_REF]. It consists basically in injecting finely atomized (misted) water into the engine's low pressure compressor or directly in the combustion chamber [START_REF] Soares | Gas Turbines: A Handbook of Air, Land, and Sea Applications[END_REF]. Water misting evaporates purified water to reduce the temperature of the engine inlet air and makes for a denser mixture. As opposed to old style water injection schemes, this approach has additional potential benefits of reduced Specific Fuel Consumption (SFC) and emissions, as well as greatly reduced turbine inlet temperature.

ACCEPTED MANUSCRIPT

In an aircraft engine, the water can be conveniently carried on board in an appropriate tank and delivered only during the taxiing and take-off without paying too much in terms of extra weight for the overall aircraft. This is a consequence of the relative small mass necessary, which are of the same order of magnitude of the fuel needed during take-off. In the case of steam, some of the heat produced by the engine combustion could be employed in specific heat exchangers to generate the required amount of steam. As a matter of fact, almost all the engines could take advantage from this technique, from small to high by-pass turbofans and open rotor engines.

On the other hand, based on some experiments conducted in the past [START_REF] Smith | Combustion in advanced gas turbine systems[END_REF], Benini and Mistè have recently modelled the effect of steam injection directly within an aeronautical combustor in order to study its effect on both the liner cooling and combustion efficiency [START_REF] Benini | Validation of a Two-Dimensional Numerical Model for the Simulation of Steam Injection in Aeronautical Combustors[END_REF]. They also In this paper, numerical and experimental studies are conducted to assess the potentialities of both water and steam injection in a small turbojet combustion chamber as far as NO reduction and cooling effect are concerned.

Mathematical model

A numerical model is applied to solve for the thermo-fluid dynamic flow field inside a generic combustor, where compressible and reactive phenomena, including heat transfer, occur. For this

ACCEPTED MANUSCRIPT

purpose, the ANSYS CFX© package is used. Equations implemented in the software are the following:

Conservation of mass (continuity):

(1.1)

Transport of chemical species:

(1.2)
Conservation of momentum:

(1.3)
Conservation of specific enthalpy:

(1.4)

The partial pressure of each species is calculated using Dalton's law for ideal gases:

(1.5) while the viscous stress tensor is expressed using Newton's equation:

(1.6)
and the diffusive flux of chemical species z is expressed by the Fick's law:

ACCEPTED MANUSCRIPT

(1.7)
where is the Schmidt number.

The generic source term is modeled as:

(1.8)

being Pr the Prandtl Number.

To solve for the turbulent flow, the Favre Averaged Navier-Stokes (FANS) assumption has been considered [START_REF] Hoffmann | Computational Fluid Dynamics[END_REF]. This is particularly suitable for reacting flows, where high density variations take place. In this approach, the general quantity is split into two components: its time-densityaveraged value over a period of time T' and a component that fluctuates with time:

(1.9)

Rewriting the equations of conservation, we obtain:

(1.10)

The viscous Reynolds stresses are modeled using the standard k-ε model [START_REF] Launder | The Numerical Computation of Turbulent Flow[END_REF].

The turbulent mass and heat fluxes are modeled using the gradient transport hypothesis:

(1.11)

The rate of production/consumption for the generic species has to be expressed by a combustion model, being a highly non linear function of temperature. In a generic combustion reaction that can be described in terms of z elementary reactions involving N c components , where is the stoichiometric coefficient for species I in the elementary reaction z, the rate of production/consumption for I can be computed as the sum of the rate of progress for all the elementary reactions in which component I participates , being R z the elementary reaction rate of progress for reaction z, which can be calculated using the Eddy Dissipation model [START_REF] Magnussen | On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion[END_REF], which is fully integrated in the software package, that was developed for a wide range of turbulent reacting flows. Such model is based on the assumption that chemical reactions are fast relative to the transport processes in the flow; it is valid for high values of Reynolds and Damköhler numbers, the latter relating the mixing efficiency of the reactants and their kinetic reaction .

When reactants mix at the molecular level, they instantaneously form products and the rate of combustion is determined by the rate of intermixing on a molecular scale of fuel and oxygen eddies.

The model assumes that the reaction rate may be related directly to the time required to mix reactants at the molecular level. In turbulent flows, this mixing time is dominated by the eddy properties and, therefore, the rate is proportional to a mixing time defined by the turbulent kinetic energy, k, and turbulent dissipation rate . In particular, the rate of progress of elementary reaction z is determined by the minimum of the following expression: In order to model the radiation intensity source term , a P-1 model (also known as the Gibb's model or Spherical Harmonics model) is chosen [START_REF] Warnatz | Combustion[END_REF] which assumes that the radiation intensity is isotropic or direction-independent at a given location in space.

NO Formation Model

The NO formation model is fully integrated into the software's reaction and combustion module and accounts for the following NO formation mechanisms: thermal NO, prompt NO, Fuel Nitrogen, N 2 O and reburn (destruction of NO) [START_REF] Raithby | Equations of motion for reacting, particle-laden flows[END_REF].

Case Study

The numerical model outlined above was implemented and applied to study the behavior of a small direct-flow annular-type combustor mounted in a research turbojet engine developed at the

ACCEPTED MANUSCRIPT

University of Padova and described in [START_REF] Benini | Design, Manufacturing and Operation of a Small Turbojet Engine for Research Purposes[END_REF], see Figure 1. The reader is referred to [START_REF] Benini | Design, Manufacturing and Operation of a Small Turbojet Engine for Research Purposes[END_REF] for a complete and detailed description of both the engine and the combustion chamber.

In order to analyze the influence of water and/or steam injection, a supplementary pump is used which conveys the above fluids directly in the chamber by using copper pipes. These are insulated when the effect of water injection is investigated, and insulation-free when the steam is to be produced. In the latter case, a part of the heat developed during the combustion is used to evaporate the water. To reach an efficient combustion and to exploit an effective refrigerating effect, the steam/water injection point is put far away from the reaction zone and near the chamber walls. If a direct interaction with the reagents was achieved, the oxidation reaction could fail; in fact, in the best case the combustion would be incomplete featuring a lot of by-product and unburned fuel emissions, or, at worst, no reaction would take place. In this study, the refrigerant inlet is positioned under the air main inlet region to satisfy these needs (i.e. much closer to the engine axis of rotation). The engine combustor is operated as follows: at engine start-up, electric power from the auxiliary motor is used to accelerate the core-assy to approximately 10,000 rpm. At this point the ignition is turned on, and a natural-gas-fuel is used to light up the combustion process. Next, further acceleration of the engine to its minimum idle speed of approximately 20,000 rpm occurs. From this point, the electric motor is disconnected and the engine is self-operated. The thrust then produced can be quite easily controlled by acting on the fuel flow rate, which in turn determine the instantaneous rotational velocity of the turbojet. A changeover from natural-gas to Jet A is accomplished using the same fuel manifold system, by simultaneously closing the gas-fuel valve and opening the liquid-fuel valve. During changeover, the turbojet engine runs on a mixture of gas fuel and Jet A for a few seconds. Further acceleration to the engine's maximum continuous speed of 60,000 rpm can then be initiated. When the engine operation is stable, the water/steam injection can eventually be started and its effects analyzed.

Numerical Simulations and experimental campaign

Due to the axial symmetry of the combustor, only a 30 degrees sector was simulated in the numerical model, as represented in Figure 2, where a tetrahedral mesh is created inside the flow domain. The grid features a minimum edge length of 0.123 mm and a maximum of 3 mm, about 240,000 nodes and 1,252,000 elements.

Table 1 shows the boundary conditions applied to the domain inlet and outlet stations, as well as the fuel properties.

As far as the water/steam injection are concerned, two types of simulations are conducted: in the former, the effects of steam injection are evaluated by considering three steam flows equivalent to 0%, 100% and 200% of Jet A flow; in the latter, water injection (at 25°C) is investigated for the same mass flow ratio relative to Jet A and a comparison between steam and water injection is conducted.

The same operating points of the combustor, including water/steam injection, were analyzed experimentally. The turbine inlet temperature was measured, along with pollutant emissions (CO, NO).

Results and discussions

The results obtained after the simulations and the experimental assessment show how the principal emissions of the combustor can be reduced with the introduction of steam or demineralized water in the combustion chamber.

Figure 3 shows the effect of the refrigerant on the turbine inlet temperature as a result of both the calculation and the experimental acquisitions. Outlet temperature from the combustion chamber presents in fact almost a linear decrease with the refrigerant flow. From this point of view, an augmented cooling effect is registered with water injection, as expected.

The most important consequence of this effect is the related decrease in thermal NO emissions and, when steam is used, the appearance of a minimum in the amount of CO. Figure 4 displays a comparison between computed and measured emissions using steam injection. Figure 5 shows the same dependence obtained using water.

From Figure 4, a NO reduction of about 16% can be appreciated when the steam flow doubles the fuel flow. On the other hand, the temperature drop triggers the rise of CO and unburned fuel due to incomplete oxidation. However, this phenomenon is registered only at relatively high values of the steam flow: in fact, when the steam flow equals the fuel flow a small decrease in the CO emission is found both numerically and experimentally. This can be explained by the fact that, at relatively small quantities, steam promotes turbulent mixing of fuel and air, thus resulting in zones where the mixture strength is enhanced with respect to the baseline case (where no steam is injected).

As far as the water injection is concerned, the following considerations can be drawn. A less effective NO reduction, compared to steam injection, is registered both numerically and experimentally (Figure 5). Moreover, a substantial increase in the CO production can be appreciated. This is due to the inadequate burning rated in the primary zone of the combustion chamber, where the water tends to withstand fuel/air mixing. As a consequence, steam injection is preferred to water injection when a reduction in the NO emissions is to be pursued while maintaining relatively low CO emissions.

Conclusions

Experimental and numerical analyses show that, in this particular turbojet, steam and water injections permit a reduction in NO emission and confirm their effectiveness as refrigerants of the combustion gases. From this point of view, steam injection reduces the NO emissions up to 16% (in terms of mass fraction) when a steam flow which doubles the fuel flow is introduced, whereas a reduction of about 8% is found using water injection in the same proportions to fuel flow. On the other hand, a much higher cooling effect on outlet combustion gases is produced by water instead of steam (due to the much higher thermal capacity of water). However, a significant difference in the amount of CO produced is registered. While the CO levels reduces slightly with steam injection, their value tends to increase more and more as higher quantities of water are injected.

Tables

NO mass fraction CO [ppmv]

Water Flow/Fuel flow

  species, Molar concentration of species I Diffusive flux of chemical species z Turbulent kinetic energy per unit mass of generic quantity Random fluctuation of generic variable Stoichiometric coefficient for component I in the elementary reaction z

  observed a significant shift toward lower values in the temperature distribution within the combustor, a phenomenon which could be conveniently exploited to reduce the thermal NOx. More recently, Molnar and Marek[START_REF] Molnar | New reduced two-time step method for calculating combustion and emission rates of Jet-A and methane fuel with and without water injection[END_REF] developed a mathematical model for the simulation of Jet-A and methane fuels including water injection to be used in numerical combustion codes, and ended up in a correlation that gives the chemical kinetic time of the fuels investigated. Although the main scope of their work was to develop a numerical tool to better describe the kinetics of the burned fuels, they demonstrated how significant is the water injection in modifying the nature of the chemical reaction involved in the combustion and in reducing NOx formation. Other relevant results on modelling combustion including water injection are given in[START_REF] Brankovic | Emissions prediction and measurement for liquid-fueled TVC combustor with and without water injection[END_REF]-[START_REF] Xia | Direct numerical simulation of diluted combustion by evaporating droplets[END_REF] .

  ] is the molar concentration of species I and includes only the reactant components; A and B are two constants of the model. Previous equation is assumed to be applicable to diffusion as well as to premixed flames; the term that gives the lowest value is the one that determines the local rate of combustion. Assuming that the problem is the one in which a stable flame must be established, to start and maintain a stable flame an initial specification of product within the calculation domain is sufficient.

Figure 2

 2 better clarifies the location of the refrigerant inlet. As a matter of fact, this was the position for which the most effective NO reduction was achieved without paying too much in terms of both flame stability and combustion efficiency. At nominal conditions, the engine is fed using Jet A, a kerosene grade of fuel suitable for most turbine civil aircraft having has a flash point above 38°C and a freeze point maximum of -47°C. Jet A meets the requirements of British specification DEF STAN 91-91 (Jet A-1), (formerly DERD 2494 (AVTUR)), ASTM specification D1655 (Jet A-1) and IATA Guidance Material (Kerosene Type), NATO Code F-35.

FiguresFigure 1 -Figure 3 -Figure 4 -

 134 Figures

Figure 5 -

 5 Figure 5 -Comparison between computed (solid lines) and measured (dashed lines) emissions using water injection.

Table 1 -

 1 Boundary conditions of the simulations (30° sector).

	Air Inlet	air flow (kg/s)	0.044
		total temperature (K)	407
	Fuel Inlet	fuel flow (kg/s)	3.69*10 -4
		total temperature (K)	300