EP2108802B1 - Method for determining the amount of fuel to be injected when starting an engine with external injection - Google Patents

Description

The present invention relates to a method for determining the amount of fuel to be injected at the start of an indirect injection engine.

The combustion by engines mounted in motor vehicles produces polluting emissions. These pollutants are likely to be released into the atmosphere and degrade the environment. Increasingly stringent anti-pollution standards are being put in place, particularly for spark ignition and indirect injection engines. In order to meet the standards, exhaust aftertreatment systems have been developed on the vehicles. Catalytic post-treatment systems are based primarily on the use of precious metals and reduce the emission of pollutants from the vehicle.

However, the proper functioning of the catalysts is ensured only for temperatures above a priming temperature. Therefore, when starting the cold engine, the treatment of pollutants is not optimum. Thus, 80% of the vehicle's polluting emissions are emitted during the first 40 to 80 seconds after starting the engine.

Under these conditions, it appears interesting to reduce the amount of pollutants emitted at the start of the vehicle. One of the ways is to use as little fuel as possible for starting the engine.

But, determining the minimum amount of fuel to be injected to start the engine is tricky. This evaluation depends in fact a lot on the characteristics of the fuel. In particular, one of the difficulties stems from the significant variation in the chemical composition of fuel from one country to another and according to the season in question.

Currently, to ensure an engine start for all fuels, the amount of fuel injected is greater than the amount just needed which should ideally be injected. Once the start has been made, probes located in the vehicle's exhaust line can detect that too much fuel is injected into the vehicle. engine. This defect is corrected by progressively decreasing the quantity of fuel injected until the detection of the fault by the probes disappears.

This technique, described as "a posteriori", implies an over-consumption of fuel at start-up compared to an optimized situation. This over-consumption generates an emission of a larger quantity of pollutants compared to the optimal situation.

There are also "a priori" determination procedures for the amount of fuel required for starting. These methods are based on fuel volatility parameters such as the points of the distillation curve or any linear combination of these parameters. These latter methods are commonly referred to as "driveability index" or "driveability index".

However, existing models using fuel volatility information do not take into account the interactions between species. Existing models are not able to correctly determine the amount of fuel needed to start. This is especially true for fuels containing polar compounds such as alcohols. Given the variability of fuels in the world, this causes problems of robustness of the provision of starting and engine actuation: no-start, bad start, stall, approval driving degraded after startup.

There is therefore a need for a process that ensures the start-up of an indirect injection controlled ignition engine by using the most accurate amount of fuel possible.

The subject of the present invention is therefore a method for determining the quantity of fuel to be injected at the start of an indirect injection engine, a mixture of an air and fuel gas phase and a liquid fuel phase. being injected into the engine, the method comprising calculating the chemical composition of the gas phase and the liquid phase at the interface between the gas phase and the liquid phase, using a model and, with the aid of the chemical composition of the gas phase, the calculation of the transport rate of the gas phase, using a model.

In a variant, associated with an engine comprising a combustion chamber and an intake duct in the engine of the mixture, the liquid phase being deposited on the walls of the intake duct.

In a variant, the model for calculating the chemical composition of the gas phase and the liquid phase takes into account the chemical composition of the fuel previously determined. The number of fuel species for determining the chemical composition of the fuel is reduced, preferably to fifteen. The chemical composition of the fuel is preferably determined by a laboratory analysis member or by an on-board analysis unit on board a vehicle, preferably an on-board sensor type of on-board sensor using near-field spectroscopy. infrared.

In a variant, the model for calculating the chemical composition of the gas phase and the liquid phase is based on the ideal gas hypothesis and Raoult's law.

In a variant, the model for calculating the chemical composition of the gas phase and of the liquid phase takes into account the fugacity coefficient of each of the fuel species, the fugacity coefficient being calculated or obtained in tables.

In a variant, the method further comprises calculating the richness of the mixture obtained by the ratio between the value of the integral of the transport rate of the gas phase and the value of the volume of air injected. Preferably, the transport rate calculation model takes into account the mass of fuel to be injected, the method further comprising determining the amount of fuel to be injected at startup in the engine to achieve a predetermined richness of the mixture by use of tables or by iteration of the mass of fuel to be injected.

The method according to the invention is more particularly used in a control member of an engine or in a tool for assisting the development of a motor.

Other features and advantages of the invention will appear on reading the following description of the embodiments of the invention, given by way of example and with reference to the appended figure which shows figure 1 an example flowchart of the method.

A method for determining the amount of fuel to be injected at startup is proposed. This method applies to an indirect injection engine in which a mixture of air and fuel gas phase and a liquid fuel phase is injected into the engine. The method comprises calculating the chemical composition of the gas phase and the liquid phase at the interface between the gas phase and the liquid phase, using a model. In addition, using From the chemical composition of the gas phase, the process calculates the transport rate of the gas phase, using a model.

The method thus makes it possible, from the detailed chemical composition of a fuel, to determine the chemical composition of the gas phase that is injected into the combustion chamber of the indirect injection controlled ignition engine. As a result, the amount of fuel required to start an indirect injection controlled ignition engine can be determined.

The quantity of fuel injected at startup can therefore be optimized. As a result, the process makes it possible to reduce the polluting emissions of the car, which reduces the precious metal charge of the catalytic post-treatment. The cost of manufacturing the car is reduced.

In addition, the quality and robustness of the start-up and activation service is improved, in particular because this service does not depend on the country or the season in question.

The method may comprise a number of steps as shown in figure 1 . The figure 1 is an example of a flowchart of the method for determining the amount of fuel to be injected at startup.

Prior to step 6 of calculating the chemical composition of the gas phase and the liquid phase, the method may comprise a step 2 of determining the detailed chemical composition of the fuel. The detailed chemical composition gives access to the different species of fuel as well as their proportion in the fuel.

The detailed chemical composition can come from an analysis carried out for example at the level of the vehicle fuel tank by one or any combination of the following techniques: gas chromatography, mass spectrometry, nuclear magnetic resonance (NMR), ultraviolet spectroscopy or infrared spectroscopy.

The fuel analysis can be performed by a laboratory analysis unit. Chromatography and mass spectrometry can be used in the laboratory. Such instruments make it possible to obtain a very precise chemical composition of the fuel for the development of the engines.

The chemical composition of the fuel can also be determined by an onboard analysis unit on board a vehicle. This makes it possible to obtain the composition of the gasoline in the vehicle. In particular, an opto-electronic sensor that exploits near-infrared spectroscopy ("near infrared spectroscopy" or "NIR spectroscopy") can be used. Such a sensor has the advantage of being compact.

The detailed chemical composition thus obtained serves as input data for the calculation of the composition in the gas phase which is described below.

In some cases, the detailed chemical composition of the fuel may involve a calculation time too important to perform the calculation of the composition in the gas phase. In order to reduce the calculation time, it may thus be advantageous to proceed to a step 4 of using a reduced number of fuel species found in step 2.

By way of example, to represent a commercial essence without European lead 95, a chemical composition reduced to 15 species can be used: 12 hydrocarbons and 3 oxygenated compounds. The following table gives the 15 species classified by increasing boiling temperature (T ° eb): Chemical species T ° eb (K) n -Butane 273 isopentane 301 n -Pentane 310 methylbutene 312 MTBE (Methyltertiobutyl ether) 328 2-methylpentane 334 hexene 337 ETBE (Ethyltertiobutyl ether) 346 Ethanol 351 cyclohexane 354 n- Heptane 372 2,2,4-Trimethylpentane 372 Toluene 384 m -Xylene 412 1,2,4-trimethylbenzene 443

Moreover, the composition of the air can also be simplified and be reduced to two species: di-oxygen (02), di-nitrogen (N2).

The reduced or detailed chemical composition thus obtained in step 2 or 4 is used in particular for a step 6 of the process. Step 6 is a step in which the chemical composition of the gaseous phase of the fuel is calculated at any time.

The calculation is done using a model. The model is a thermodynamic model and more precisely a model of chemical thermodynamic equilibrium. The thermodynamic model makes it possible both to determine the compositions of the liquid phase and of the gaseous phase of the fuel at thermodynamic equilibrium.

The thermodynamic model is based on the use of a thermodynamic equilibrium condition and uses thermodynamic data (temperature, pressure, etc.) as well as the chemical composition of the mixture between air and fuel produced in the duct. engine intake.

In thermodynamics, two phases (for example liquid, gas or solid) are in equilibrium when the free enthalpy noted G of the system composed of the two phases reaches its minimum, or when the differential of the free enthalpy noted dG is zero.

où n désigne le nombre de moles, l'indice i l'espèce considérée, l'indice gaz la phase gazeuse, l'indice liq désigne la phase liquide et µ le potentiel chimique.Now, at fixed pressure and temperature, the differential of free enthalpy is written in our particular case of a gas-liquid binary mixture: $$\mathit{dG}\square \Sigma {\mathit{\square }}_{i,\mathit{gas}}{\mathit{dn}}_{i,\mathit{gas}}\square \Sigma {\mathit{\square }}_{i,\mathit{liq}}{\mathit{dn}}_{i,\mathit{liq}}$$

where n denotes the number of moles, the index i the species considered, the gas index the gaseous phase, the index liq designates the liquid phase and μ the chemical potential.

In addition, when the system is closed and no chemical reaction takes place, the preservation of the material implies that: $${\mathit{dn}}_{i,\mathit{gas}}\square {\mathit{dn}}_{i,\mathit{liq}}\square 0$$

The conditions of equation E ₂ can be considered as fulfilled in the case of the fuel contained in the fuel tank of the vehicle.

It can be deduced from the two equations E ₁ and E ₂ that the thermodynamic equilibrium condition of the thermodynamic model becomes: $$\Sigma [{\mathit{\square }}_{i,\mathit{gas}}\square {\mathit{\square }}_{i,\mathit{liq}}[{\mathit{dn}}_{i,\mathit{gas}}\square 0$$

As a result, the thermodynamic model can result in the equality of the chemical potentials of each species i in each of the liquid or gaseous phases.

où T est la température, P_i est la pression de l'espèce considérée, R la constante des gaz parfaits, l'exposant «°» désigne les conditions standard soit une pression de 1 bar et une température de 0°C et enfin f_i est la fugacité de l'espèce i dans une phase donnée.However, for any phase (gaseous or liquid), the chemical potential is defined by the relation E ₄ : $${\mu }_i\left(T,P_i\right)=\mu °\left(T,P_i°\right)+\mathit{RT}\ln \left(\frac{f_i}{f_i°}\right)$$

where T is the temperature, P _i is the pressure of the considered species, R is the constant of the perfect gases, the exponent "°" designates the standard conditions of a pressure of 1 bar and a temperature of 0 ° C and finally f _i is the fugacity of species i in a given phase.

Thus, the thermodynamic equilibrium condition of the thermodynamic model results in the equality of the fugacities of each species i in each of the phases. The equilibrium condition between the phases is therefore for each species i: $$f_{i,\mathit{gas}}=f_{i,\mathit{liq}}$$

avec ϕ_i,x le coefficient de fugacité de l'espèce i dans la phase x (gaz pour gazeux, liq pour liquide), X_i la fraction molaire de l'espèce i dans la phase x (gaz pour gazeux, liq pour liquide) et P la pression dans le conduit d'admission du moteur.The fugacity expressing itself by definition as: $$f_{i,x}={\phi }_{i,x}\mathrm{.}P\mathrm{.}{X}_{i,x}$$

with φ _{i, x} the fugacity coefficient of species i in phase x (gaseous gas, liq for liquid), X _i the molar fraction of species i in phase x (gas for gaseous, liq for liquid ) and P the pressure in the engine intake duct.

The thermodynamic model is thus expressed by the equality E ₇ for each species i: $${\phi }_{i,\mathit{gas}}\mathrm{.}{X}_{i,\mathit{gas}}={\phi }_{i,\mathit{liq}}\mathrm{.}{X}_{i,\mathit{liq}}$$

The resolution of the equation E ₇ for all the species under consideration makes it possible to obtain the chemical composition of the gaseous and liquid phases at the interface between the gas phase and the liquid phase. The resolution of equation E ₇ can be done in several different ways.

A first method consists of calculating the fugacity coefficient of each fuel species. The fugacity coefficients are deduced from the system equation of the system considered by derivation with respect to the number of moles.

où R la constante des gaz parfaits.A state equation is an algebraic relation between the pressure P, the temperature T and the volume V. The equation of state is often expressed in terms of a thermodynamic quantity Z called compressibility factor and defined by the relation E ₈ : $$Z=\frac{\mathit{PV}}{\mathit{RT}}$$

where R is the constant of perfect gases.

Cubic equations of state are among the few types of state equations that exist. Strongly used in industry, the cubic equations are quite simple and can be expressed in the form of third-degree polynomials in Z. The cubic equations have the advantage of making volumetric resolution optional, which is an iterative method requiring a certain amount of time. not negligible calculation. The two most used equations in engineering are the equation of Peng and Robinson (noted equation PR in the following) and the equation of Soave, Redlich and Kwong (denoted equation SRK in the following).

où k, k', A* et B* sont des paramètres détaillés dans les paragraphes qui suivent.A cubic state equation can be expressed as a function of the compressibility factor, in the form of equation E ₉ : $$Z^3-\left(1+B*-\mathit{kB}*\right){\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">Z</figure-callout>}}^2+\left(\mathrm{AT}*+\mathit{K\text{'}B}{*}^2-\mathit{kB}*-\mathit{kB}{*}^2\right)Z-\left(\mathrm{AT}*\mathit{B}\mathit{*}+\mathit{K\text{'}B}{*}^2-\mathit{K\text{'}B}{*}^3\right)=0$$

where k, k ', A * and B * are detailed parameters in the following paragraphs.

The constants k and k 'make it possible to distinguish the different equations of state. For example, the equation PR corresponds to values of k = 2 and k '= -1 while the equation SRK is characterized by the values k = 1 and k' = 0.

où a et b sont respectivement le paramètre énergétique et le covolume. Plusieurs expressions de a et b existent dans la littérature.The parameters A * and B * are defined by the relations E ₁₀ : $$\mathrm{AT}*=\frac{\mathit{<figure-callout\; id="2"\; label="aP\; R"\; filenames="imgf0001.png"\; state="\{\{state\}\}">aP\; </figure-callout>}}{R^{}}\mathrm{and}B*=\frac{\mathit{bP}}{\mathit{RT}}$$

where a and b are respectively the energetic parameter and the covolume. Several expressions of a and b exist in the literature.

The calculation of the parameters a and b involves knowing additional physical properties of the hydrocarbon species and in particular their critical temperature noted T _c , their critical pressure noted P _c and the acentric factor of the pure body noted ω.

où les paramètres f₁ ou f₂ sont donnés par les relations E_{11 :} $$\{\begin{array}{l}{f}_1=5,92714-\frac{6,09648}{\theta }-1,28862\ln \theta +0,169347{\theta }^6\\ f_2=15,2518-\frac{15,6875}{\theta }-13,4721\ln \theta +0,43577{\theta }^6\end{array}$$

For example, it is possible to use the Lee-Kesler correlation to calculate the acentric factor ω of each species of the species. By defining the parameter θ by the relation θ = T _eb / T _c where T _eb is the boiling temperature of the species and T _c the critical temperature, Lee-Kesler's relation is written $${\mathrm{Ln\; P}}_{\mathrm{vs}}\mathrm{=}\mathrm{-}\left({\mathrm{f}}_{\mathrm{1}}\mathrm{+}\mathrm{<figure-callout\; id="2"\; label="\omega \; f"\; filenames="imgf0001.png"\; state="\{\{state\}\}">\omega \; </figure-callout>}{\mathrm{f}}_{}{\mathrm{}}_{\mathrm{2}}\right)$$

where the parameters f ₁ or f ₂ are given by the relations E _11: $$\{\begin{array}{l}{f}_1=5,92714-\frac{6,09648}{\theta }-1,28862\ln \theta +0,169347{\theta }^6\\ {\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="imgf0001.png"\; state="\{\{state\}\}">f</figure-callout>}}_2=15,2518-\frac{15,6875}{\theta }-13,4721\ln \theta +0,43577{\mathrm{<figure-callout\; id="6"\; label="\theta "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\theta </figure-callout>}}^6\end{array}$$

For example, knowing that for butane nC ₄ H ₁₀ , the critical pressure is P _c = 38.017 bar, the critical temperature T _c = 425.2 K and the boiling temperature T _eb = 272.7 K, the calculation of acentric factor by the method of Lee-Kesler gives ω = 0.197.

avec ${\delta }_i=\frac{2\sqrt{a_i}}{a_m}{\displaystyle \sum _j}{X}_j\sqrt{a_j}\left(1-k_{\mathit{ij}}\right)$

où k_i,j désigne les coefficients d'interaction binaire dans cette expression ; a_i et b_i le paramètre énergétique et le covolume de l'espèce i, a_m et b_m du mélangeThe fugacity coefficients of each compound in each of the phases are calculated by the relation E ₁₂ : $$\mathit{Ln}\left({\phi }_i\right)=\frac{b_i}{b_m}\left(Z-1\right)-\mathit{Ln}\left(Z-B*\right)+\frac{\mathrm{AT}*}{B*\sqrt{k^2-4\mathit{k\; \text{'}}}}\left(\frac{b_i}{b_m}-{\delta }_i\right)\mathit{Ln}\left(\frac{2Z+B*\left(k+\sqrt{k^2-4\mathit{k\; \text{'}}}\right)}{2Z-B*\left(k+\sqrt{k^2-4\mathit{k\; \text{'}}}\right)}\right)$$

with ${\delta }_i=\frac{2\sqrt{{\mathrm{at}}_i}}{{\mathrm{at}}_m}{\displaystyle \underset{j}{\Sigma }}{X}_j\sqrt{{\mathrm{at}}_j}\left(1-k_{\mathit{ij}}\right)$

where k _{i, j} denotes the binary interaction coefficients in this expression; a _i and b _i the energy parameter and the covolume of the species i, a _m and b _m of the mixture

With the knowledge of the coefficients of fugacity, it becomes then possible to solve the equation E ₇ and to determine the fraction of the species i in each of the phases.

The method by calculating the fugacity coefficients of each species of the fuel is relatively precise since this method makes it possible to take into account the gas dissolution phenomenon in the liquid phase.

In return, the calculation of the fugacity coefficients requires a lot of computation time and the knowledge of many different coefficients for each species. Thus, for each species i, the calculation of the fugacity coefficient implies the knowledge of the critical temperature, the critical pressure and if possible the binary interaction coefficient with each of the other gaseous species.

As a result, the method of calculating the fugacity coefficients may prove inconvenient to implement directly on a computer on board a vehicle. To overcome this drawback, other methods to solve the equation E ₇ can be envisaged.

In particular, it may be advantageous to calculate previously the coefficients of fugacity by the previous calculation method in order to tabulate them. It is then sufficient to solve E ₇ with the tabulated coefficients. The calculation time is thus reduced. It is thus possible to use a less powerful calculator to implement the method. The tabulation method of the fugacity coefficients is thus more easily implemented in an on-board computer than the calculation method.

Another example of a simpler method to implement than the method of calculating the coefficients of fugacity is a method where two hypotheses are previously performed. The two hypotheses are the perfect gas hypothesis and the ideal mixing hypothesis in the liquid phase. These assumptions return to consider the fugacity coefficients as unitary, which makes it possible not to calculate the fugacity coefficients for each fuel species.

où P_i,sat est la pression de vapeur saturante et P est la pression du système.The use of Raoult's law then makes it possible to obtain saturation phase gas phase molar fractions, by the relationship E ₁₃ : $$X_{i,\mathit{gas}}=X_{i,\mathit{liq}}\mathrm{.}\frac{P_{i,\mathit{sat}}}{P}$$

where P _{i, sat} is the saturation vapor pressure and P is the system pressure.

où A_i, B_i et Ci sont les coefficients d'Antoine et T_surface est la température de la surface de l'interface entre la phase gaz et la phase liquide. Les coefficients A_i, B_i et C_i sont spécifiques de l'hydrocarbure i considéré et s'obtiennent par des corrélations.The saturation vapor pressure can be calculated by Antoine's relation: $$P_{i,\mathit{sat}}={10}^{\left({\mathrm{AT}}_i\frac{B_i}{{\mathrm{VS}}_i+T_{\mathit{area}}}\right)}$$

where A _i , B _i and Ci are the Antoine coefficients and T _surface is the _surface temperature of the interface between the gas phase and the liquid phase. The coefficients A _i , B _i and C _i are specific for the hydrocarbon i considered and are obtained by correlations.

The method is valid for hydrocarbon mixtures. This method based on the ideal gas hypothesis and Raoult's law is simpler than the method of calculating the fugacity coefficients. As a result, the method is particularly suitable for use in onboard car computers.

But, the method is not applicable in all cases. In particular, the method is no longer correct since the different molecules of the mixture have strong interactions with each other. A mixture comprising polar species such as alcohols is an example of a mixture to which the method based on the ideal gas assumption and Raoult's law can not be applied.

Whatever the method chosen to carry out the calculation of step 6, step 6 makes it possible to obtain the chemical composition of the liquid phase at the interface of the gas phase and the liquid phase at step 8 as well as the chemical composition of the gas phase at the interface of the gas phase and the liquid phase at step 10. The information of the chemical composition is not a physicochemical parameter that is too reducing like the vapor pressure. The knowledge of the chemical composition in the two phases makes it possible to know the essential characteristics of the system.

By way of example, the following table presents the chemical compositions of the gaseous and liquid phases obtained in steps 8 and 10 of the process for a commercial gasoline. Current European lead 95, at a pressure of 1 atm and a temperature of 20 ° C. The calculation of step 6 is performed by the method of calculating the fugacity coefficients. Chemical species Liquid phase (molar fraction) Gaseous phase (molar fraction) n -Butane 0078 0160 isopentane 0136 0108 n -Pentane 0040 0023 methylbutene 0095 0049 MTBE (methyltertiobutyl ether) 0054 0015 2-methylpentane 0060 0014 hexene 0043 0009 ETBE (ethyltertiobutyl ether) 0.000 0.000 Ethanol 0.000 0.000 cyclohexane 0025 0003 n- Heptane 0063 0003 2,2,4-Trimethylpentane 0073 0004 Toluene 0101 0004 m -Xylene 0109 0001 1,2,4-trimethylbenzene 0119 0.000 diNitrogen 0001 0.472 oxygen 0.000 0133

The table shows that some species have started to evaporate, such as n-Butane or n-Pentane, while other species such as m-Xylene or 1,2,4-Trimethylbenzene have a molar fraction in phase. gaseous zero or almost zero.

The chemical composition of the gaseous and liquid phases at the interface between the gas phase and the liquid phase corresponds to the chemical composition at the intake duct of the engine. However, it is not the chemical composition of the mixture between the fuel and the air that is burned at the level of the candle of the combustion chamber. Indeed, the passage of the gaseous phase of the interface between the gas phase and the liquid phase towards the core of the intake duct and towards the heart of the combustion chamber modifies the chemical composition of the mixture because the species do not have the same speed of movement in the gas phase. As a result, the amount of species present at the interface between the gas phase and the liquid phase is not the same in the combustion chamber.

As a result, the method further comprises a step 12 wherein the gas phase transport is studied. This analysis consists of calculating the transport rate of the gas phase using the chemical composition of the gas phase at the interface between the gas phase and the liquid phase.

The calculation is done using a model. The model is a transport model that is valid for engines with indirect injection ie engines where the fuel / air mixture is made before admission into the combustion chamber. This means that the fuel / air mixture is produced before an intake valve of one of the engine cylinders. The transport model is based on several hypotheses successively presented in the following paragraphs.

It is initially assumed that at startup, the fuel is deposited in the form of a liquid film on the cold walls of the engine intake duct. It is then admitted that all the evaporation comes from the evaporation of the liquid film. The evaporation in the cylinder at the end of compression as well as the evaporation related to tearing drops of the liquid film during the opening of the inlet valve are therefore neglected.

In addition, it is accepted that evaporation takes place during the intake phase (during a piston go of 180 ° V), that is to say the time during which the valve is open. The evaporation before the opening of the valve, more precisely between the injection and the opening of the valve, is not taken into account.

Due to the very large heat capacity difference between the intake duct metal and the liquid fuel, the temperature of the liquid film is assumed to be the temperature of the intake duct during the first cycle of the engine.

In addition, it is assumed, according to a conventional hypothesis in the literature, that the height of the liquid film denoted h _film is proportional to the injected mass noted m _inj of fuel at a certain power noted β: $$h_{\mathit{movie}}\alpha {\left(m_{\mathit{inj}}\right)}^{\beta }$$

The same relation can be written between the mass injected and the surface of the liquid film denoted S _film : $$S_{\mathit{movie}}\alpha {\left(m_{\mathit{inj}}\right)}^{1-\beta }$$

It is common in the literature to attribute to this coefficient β a value close to 0.5. However, this is only an example since the coefficient β depends on various characteristics of the engine and in particular the shape of the intake duct, the injector ... This parameter β can thus be used to calibrate the model for each engine.

It is also assumed that the height and the surface of the liquid film do not depend on the temperature and that there is a maximum wet surface for each intake duct.

Finally, it is assumed that the diffusion of species is infinitely fast in the liquid film. In other words, the mole fractions of the species are homogeneous in the liquid film.

où $m_{\mathit{évap},i}^{•},$

α, Re, D_FA et Y_i,GAZ sont des paramètres détaillés dans les paragraphes suivants.The transport model then models the transport of species i in the gaseous phase by a relation derived from the theory of fluid mechanics. In particular, it is possible to use the relationship E ₁₅ from the literature: $$m_{\mathit{Evaporation},i}^{•}=\alpha *\left(0,552*{\mathrm{Re}}^{0,5}\right)*{\left(m_{\mathit{inj}}\right)}^{1-\beta }*D_{\mathit{FA}}*\ln \left(1+\frac{Y_{i,\mathit{GAS}}}{1-Y_{i,\mathit{GAS}}}\right)$$

or $m_{\mathit{Evaporation},i}^{•},$

α , Re, D _FA and Y _{i, GAS} are parameters detailed in the following paragraphs.

est la dérivée temporelle de la masse de l'espèce i et représente le taux de transport de l'espèce i dans la phase gazeuse, depuis l'interface entre la phase gaz et la phase liquide vers le coeur du mélange gazeux.The parameter $m_{\mathit{Evaporation},i}^{•}$

is the time derivative of the mass of species i and represents the transport rate of species i in the gas phase, from the interface between the gas phase and the liquid phase to the core of the gas mixture.

The coefficient α is a coefficient to adjust to calibrate the model on the engine considered.

The constant Re is the Reynolds number. The constant Re is calculated with the average speed in the intake duct.

D _FA is the binary diffusion coefficient between fuel and air. It is possible to consider an overall coefficient D _FA for the fuel or a coefficient D _{FA, i} by species.

Finally, Y _{i, GAZ} is the mass fraction of species i in the gas phase at the interface between the gas phase and the liquid phase. The mass fraction of species i is linked to the molar fraction calculated previously by applying the thermodynamic model of step 6.

de chaque espèce i dans la phase gazeuse, depuis l'interface entre la phase gaz et la phase liquide vers le coeur du mélange gazeux.As a result, given the assumptions previously described, step 12 makes it possible to determine, from the mass of fuel injected, the transport rate $m_{\mathit{Evaporation},i}^{•}$

each species i in the gaseous phase, from the interface between the gas phase and the liquid phase to the core of the gas mixture.

An additional step 14 of the method may further allow to deduce the richness of the air / fuel mixture obtained using a calculation.

sur 180°V et la valeur du volume d'air introduit.The richness of the fuel mixture in the cylinder is obtained by the ratio between the value of the integral of the sum of the transport rates in the gas phase. $m_{\mathit{Evaporation},i}^{•}$

at 180 ° V and the value of the volume of air introduced.

The fuel mixture in the cylinder being considered homogeneous, the wealth obtained in step 14 corresponds to the wealth at the ignition point. The method thus makes it possible to determine the richness at the ignition point from given pressure conditions, given temperature and a given injected fuel mass.

The method may further comprise a step 16 of determining the amount of fuel to be injected.

To achieve the determination, the wealth obtained in step 14 is compared with a predetermined value of wealth to be achieved. The value of the wealth to achieve to ensure a good start of the vehicle depends in particular on the engine and the power of the candle. For example, the literature usually agrees around a richness of 0.75 to 0.8 to allow the first combustion.

The quantity of fuel to be injected at startup can be obtained by successive iteration on the mass of fuel to be injected. An initial injection mass is arbitrarily chosen. If this initial mass leads to a greater wealth than the predetermined value of wealth to be achieved, it means that the mass to be injected is too great. The calculation of step 12 is repeated with a smaller injection mass. On the contrary, if this initial mass corresponds to a lower value than the predetermined value of the wealth to be achieved, the calculation of step 12 is repeated with the increased injection mass. The process is reiterated until a satisfactory wealth is obtained.

The amount of fuel to be injected can also be obtained by using tables giving the amount of liquid fuel to be used at startup. A convenient way to implement this method computerically may be to use a database in an on-board computer of the vehicle.

The minimum amount of fuel to be injected is thus known in step 18 of the process. This reduces pollutant emissions, including CO ₂ emissions. As a result, the precious metal load of the catalyst placed in post-treatment of the exhaust line can be decreased. The cost of catalytic post-treatment is therefore reduced. The cost of manufacturing the car is thus reduced.

The quality and robustness of the start-up / start-up service is also improved. In addition, this service no longer depends on fuel, whether from one country to another or from one season to another.

In a vehicle, the method can be used in an engine control member. The information "detailed composition of the fuel" is obtained by an on-board sensor, for example a sensor using near-infrared spectroscopy, immersed in the fuel tank of the vehicle.

The output data of the modeling tool (quantity of liquid fuel to be injected at startup) is an input data of the control laws of the engine control.

The quality of the start-up benefit is improved. In addition, failures and warranty costs are reduced. All these elements contribute to increase the satisfaction of the user.

The method can also be used in a tool for assisting the development of an engine, especially in a laboratory. The debugging time of the models is thus reduced. The number of tests needed to debug can be decreased. In addition, this makes it possible to calibrate the initial mass of fuel used in step 16 of the process.

The method for determining the quantity of fuel to be injected at the start of an indirect injection engine according to the invention therefore makes it possible to determine the quantity of fuel necessary for starting an indirect injection controlled ignition engine.

Claims (11)

1. Method for determining the quantity of fuel to be injected on starting up an indirect injection engine, a mixture of a gaseous phase of air and of fuel and of a liquid phase of fuel being injected in the engine,
   the method comprising:

   - the calculation of the chemical composition of the gaseous phase and of the liquid phase at the interface between the gaseous phase and the liquid phase, by the use of a model,

   - by means of the chemical composition of the gaseous phase, the calculation of the transport rate of the gaseous phase, by the use of a model.
2. Method according to claim 1, the engine comprising a combustion chamber and an intake duct in the engine for the mixture, the liquid phase being deposited on the walls of the intake duct.
3. Method according to claim 1 or 2, in which the model for calculation of the chemical composition of the gaseous phase and of the liquid phase takes into consideration the chemical composition of the fuel which was previously determined.
4. Method according to claim 3, in which the number of types of the fuel for determining the chemical composition of the fuel is reduced, preferably to fifteen.
5. Method according to claim 3 or 4, in which the chemical composition of the fuel is determined by a laboratory analysis means or by an analysis means on board a vehicle.
6. Method according to claim 5, in which the on-board analysis means is an opto-electronic sensor using close infrared spectroscopy.
7. Method according to one of claims 1 to 6, in which the calculation model of the chemical composition of the gaseous phase and of the liquid phase is based on the hypothesis of perfect gases and Raoult's law.
8. Method according to one of claims 1 to 6, in which the calculation model of the chemical composition of the gaseous phase and of the liquid phase takes into consideration the coefficient of fugacity of each of the types of the fuel, the coefficient of fugacity being calculated or obtained in tables.
9. Method according to one of claims 1 to 8, further comprising the calculation of the richness of the mixture obtained by the ratio between the value of the integral of transport rate of the gaseous phase and the value of the volume of injected air.
10. Method according to claim 9, the calculation model of the transport rate takes into consideration the mass of fuel to be injected, the method further comprising the determining of the quantity of fuel to be injected on starting up in the engine to arrive at a predetermined richness of the mixture by the use of tables or by iteration of the mass of fuel to be injected.
11. Use of the method according to one of claims 1 to 10 in a control means of an engine or in a tool for assisting the tuning of an engine.

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