EP2100019A2

EP2100019A2 - Estimation of exhaust gas temperature at the output of the egr circuit of a combustion engine

Info

Publication number: EP2100019A2
Application number: EP07866527A
Authority: EP
Inventors: Philippe Recouvreur; Olivier Tigrine
Original assignee: Renault SAS
Current assignee: Renault SAS
Priority date: 2006-11-17
Filing date: 2007-10-31
Publication date: 2009-09-16
Also published as: WO2008059153A2; US20100043525A1; WO2008059153A3; FR2908825A1; US8037737B2; JP2010510426A; JP5079815B2; FR2908825B1

Abstract

The invention relates to a method for estimating the temperature T3 of the exhaust gases of a combustion engine at the output of a EGR circuit fitted on the engine, based on a model that takes into account the thermal energy losses of the exhaust gases at the EGR cooler or EGR circuit, characterised in that the model also takes into account the thermal exchange between the exhaust gases and the walls of a duct conveying said exhaust gases to the EGR cooler. The invention further relates to a vehicle capable of implementing such estimation.

Description

ESTIMATION OF AN EXHAUST GAS TEMPERATURE IN

The invention relates to an estimate of the temperature of the exhaust gas of a combustion engine at the output of an EGR circuit fitted to the engine. SUMMARY OF THE INVENTION In the strategies developed in the engine software about air management, the knowledge of the temperature of the exhaust gas at the exit of the EGR circuit is indeed necessary.

The measurement of the exhaust gas temperature at the outlet of the EGR circuit can be made from a thermocouple measurement. This solution is precise but expensive (including thermocouple cost, cost of the acquisition chain). It also requires to provide, in the engine compartment, the volume necessary for its integration.

This is why it is more and more preferred to estimate the exhaust gas temperature at the outlet of the EGR circuit, in place of the thermocouple. For this purpose, numerical models based on physics equations are used (e.g. conservation mass equation, energy conservation equation).

The major disadvantage is the lack of precision and reliability of the model. Indeed, to achieve a high level of precision, it is necessary to solve complex equations involving complex calculation means.

However, these calculation means must be simple enough to be integrated in the computer of the motor vehicle.

A compromise "accuracy of estimation / simplicity of calculation" must therefore be found. Such an approach is conventionally used in calculators by making assumptions about the physical phenomena governing the energy exchanges of exhaust gases in the EGR circuits and by specifying that the temperature drop of the exhaust gases in an EGR circuit is linked to the thermal performance of the cooler. EGR. Based on the actual thermal performance of the EGR cooler, However, vehicle tests have shown that the temperature of the gases leaving the EGR circuit between the estimation and the measurement could reach 200 to 300 ^° C.

By numerically adjusting the thermal performance of the chiller to try to correlate the measurements with the model, the average deviations were then reduced to about fifty degrees Celsius.

However, this inaccuracy remains important and therefore unsatisfactory. A main objective of the invention is to improve the accuracy of the temperature estimation at the output of the EGR circuit. Another object of the invention is to reduce the complexity of calculations of this temperature, while keeping a possible margin of error acceptable.

In order to achieve these objectives, the invention proposes, according to a first aspect, a method for estimating the exhaust gas temperature Ts of an engine at the output of an EGR circuit fitted to the engine, based on a model taking into account the loss of thermal energy of the exhaust gases at the EGR cooler of the EGR circuit, characterized in that the model also takes into account the heat exchange between the exhaust gases and the walls of the exhaust gas. a conduit leading the exhaust gases to the EGR cooler.

Other optional features of this estimation method are: said model takes into account the following heat exchanges: the internal heat exchanges between the gases and the wall of said duct; external exchanges between the wall of said tube and the external environment of the engine compartment, such as convective exchanges linked to an air flow and radiative exchanges of components external to the duct; cooling the gases through the EGR cooler; said model is based on simplified equations of conservation of thermal energy of the gases taking into account the different heat exchanges throughout the EGR circuit allowing: (a) an evaluation of the thermal exchanges between the exhaust gases and the walls of a duct bringing the exhaust gases to the EGR cooler of the EGR circuit; (b) an evaluation of the thermal exchanges of the exhaust gases with the inlet of the EGR cooler, taking into account the evaluation of step (a); (c) an evaluation of the thermal exchanges of the exhaust gases in the EGR cooler;

said equations are a system of three equations with three unknowns T _p , T ₂ and T ₃ , knowing that T _p is the estimated temperature of the walls of said duct and that T ₂ is the estimated temperature of the exhaust gas at the inlet of the cooler , the three equations corresponding respectively to the three evaluations (a), (b) and (c); the temperature T ₃ is mainly estimated from the knowledge of the temperature of the exhaust gas entering the EGR circuit, the temperature of the engine cooling water at the engine outlet, the specific heat of the EGR gas at constant pressure, the mass flow rate of the EGR gases, the specific heat of said duct, and the geometric and mass characteristics of the duct; the model is a system of first-order, linear and independent differential equations; these latter equations are found by making the following approximations: the convective external exchanges linked to a flow of air around the duct are of the same order of magnitude as the radiative exchanges by components external to the duct; the convection temperature is approximately equal to the temperature of the water; the changes of T ₂ in time are instantaneous compared with the modifications of T _p in time. According to a second aspect, the invention proposes a vehicle equipped with an electronic temperature estimator comprising calculation means and predetermined and / or measured data storage means, in order to implement said estimation method.

Other features, objects and advantages of the invention will be better understood on reading the detailed description of non-limiting embodiments. of the invention, illustrated by the following figures:

Figure 1 shows schematically the various elements of a compartment of a combustion engine equipped with an EGR circuit.

FIG. 2 schematically represents a longitudinal sectional view of an EGR cooler and a portion of its inlet and outlet ducts.

FIG. 3 represents a block diagram of a thermal assembly equivalent to the EGR cooler assembly according to FIG. 2, illustrating a first embodiment of the invention.

FIG. 4 represents a diagram showing a block diagram of a thermal assembly equivalent to the EGR cooler assembly according to FIG. 2, illustrating a second embodiment of the invention.

FIG. 5 represents a diagram illustrating large steps of an estimation method according to the invention.

FIG. 6 is a graph showing the evolution of the temperature at the outlet of the EGR circuit as a function of the EGR cycles, and whether the temperatures are measured or estimated.

The invention which will be described later presents the following two embodiments, making it possible to obtain an estimate of the exhaust gas temperature at the outlet of the EGR cooler: - development of equations close to physical phenomena, reducing them to their most strictly necessary to be able to be integrated into a motor software; a significant improvement in the accuracy of the exhaust gas temperature estimator in the EGR circuit is obtained since the model used is closer to reality. - Drastic simplification of the equations mentioned in the first embodiment. The goal is to minimize calculation time and software size.

The two proposed embodiments are easily applicable to all internal combustion engines equipped with EGR circuits (diesel engine, gasoline, etc.).

Referring to Figure 1, there is shown an example of a combustion engine compartment. This engine compartment comprises an internal combustion engine 10 supplied with air by an intake duct 11 and releasing its exhaust gas through a discharge duct 12. This engine compartment is further provided with a turbocharger 50 comprising a compressor 51 located on the intake duct 11 to compress the fluid-fuel from the track 53. Optionally, cooling means 40 and a flap 30 are provided between the compressor 51 and the engine 10. The air that reaches the engine 10 is cold. The turbine 52 of the turbocharger 50 is located at the end of the exhaust duct 12 and is coupled to the compressor 51. The exhaust gases are from the engine compartment and then exhausted via the track 54.

In addition, this assembly comprises an EGR circuit 20 whose input 28 is connected to the exhaust duct 12 and whose outlet 29 is connected to the intake circuit 11. This EGR circuit 20 comprises an EGR cooler 22 connected upstream by an inlet duct 25 and downstream by an outlet duct 27, for cooling the exhaust gases for reinjecting them into the engine 10.

Optionally, there is provided a bypass circuit 24 connected on the one hand to a valve 23 located upstream of the cooler 22 and on the other hand to the outlet of the cooler 22, so that the valve 23 can pass through the cooling circuit. bypassing a certain quantity of exhaust gas according to its position. Thus, by selecting a valve position 23, a desired quantity of uncooled gas is passed through the bypass circuit 24, and the temperature of the exhaust gas at the outlet of the cooler 22 is selected. An EGR valve 21 is further provided at the output of the circuit 20 so as to regulate in time the amount of cooled exhaust gas supplied to the intake duct 11. FIG. 2 schematically represents a longitudinal sectional view of an EGR cooler 22 connected in upstream by the gas inlet duct 25 and downstream by the gas outlet duct 27. These two ducts 25 and 27 are represented here as being tubes having a wall 26. In this figure, it will also be possible to observe the differences of temperature along the circuit 20. Thus: - T _av t is the temperature of the exhaust gas measured at the inlet 28 of the circuit EGR 20;

T ₂ is the temperature of the exhaust gas at the inlet of the cooler 21;

T ₃ is the temperature of the exhaust gas at the outlet of the cooler 21;

T _p is the temperature of the wall 26 of the inlet duct 25. It will also be noted that the mass flow rate of the exhaust gases in the circuit

20 is denoted Q _egr.

The applicant has made exhaust gas temperature readings along the EGR circuit 20 showing that about 35% of the gas energy at the inlet 28 of the circuit 20 can be lost in the inlet conduit 25 and that about 65 % is lost in the cooler 22.

The temperature of the inlet gases 28 of the circuit 20 can not be confused with the temperature of the gases entering the cooler 22.

It is therefore necessary to take into account, in a model, the heat exchanges between the gases and the inlet duct 25 upstream of the cooler 22. 1 ^st embodiment: development of physical equations

To correctly estimate the heat exchanges within an EGR circuit 20, it is necessary to take into account: Internal heat exchanges between the gases and the wall of the inlet duct 25; External exchanges between the wall 26 of the inlet duct 25 and the environment of the engine compartment. Two types of exchanges are predominant in the engine compartment:

- the convective exchanges linked to the flow of air around the GMP (Powertrain), - the radiative exchanges between the various components of the under hood (cylinder head, exhaust manifold, turbocharger, apron, ski, ...) The cooling of the gases through the EGR cooler With reference to FIG. 3, an "electrical <=>thermal" analogy is shown used to draw up an energy balance of the EGR circuit 20. This method allows an equivalence between the thermal system of Figure 2 and the electrical system of Figure 3.

It should be noted that the entire wall of the EGR tube is summarized here at a global and unique temperature: T _p . The energy conservation equations for the EGR system can thus be in the form of:

Stainless steel 'stainless steel' convective _ mt erne '\ 2 p / convective _ external'X convective p / raώative _ external ^* \ radiative p /

p) ^ ^~ & egr - ^ P'egr ^• (/ avt ^~ ^ 2)

K ₃ -Cp ₃ . Sj = _egr -Cp _egl .. \ l ₁ - j ^~ K ^ ₃ _e _ro f i _d i _ _ssuer _egr

The meanings of terms in these equations can be better understood by reading the "glossary" at the end of the description. By explaining the CONDUCTIBLES (internal _con guration, External G _ra diative, G _CO nvective external), it comes then:

M _ιnox .Cp _mox . ^ = H _mt .S. (T ₂ - T _p ) + ε.σ.Sf _ιJ . (T * _Λatve - T _p ^A ) + h _ext . S (T _convectve - T _p ) (1)

^M e _g r ^^ ^ ^{k =} ^S ^ - ^(T P ^{~ T} 2) + Qegr ^'C P e ri _g avt ^T ^{~ T} 2) (2)

Here again, the meanings of different terms of this system of equations can be better understood by reading the "glossary" at the end of the description. In addition, the meanings and values of some terms of this system of differential equations are given below: The internal convective exchanges between the EGR gases and the wall 26 of the inlet duct 25 are macroscopically described by a _hen exchange _coefficient . This coefficient is obtained by using an empirical relation connecting three dimensionless coefficients: the Nusselt number (Nu), the Reynolds number (Re) and the Prandtl number (Pr).

Nu = 0.021.Re ⁰ '*. Vv ⁰ ' ⁶ = ^h '"'- ^D ' ^rm '"" ^e

Where:

λ is the thermal conductivity of the EGR gas, which is a constant for the exhaust gas under consideration; Pr is a constant ≈ 0.7; there o.Vr - D ^is _charac _t stιque . . . . r- _JJ • _j. - ₁

- Re = = - see the glossary at the end of description for the μ μ.Tl .L ^J _é character teristic meaning of different terms.

Characteristic diameter. In the case of an EGR duct, it can be taken as equal to the internal diameter of the duct (D _egr ); * h _ext :

The convective exchanges related to the flow of air around the circuit 20 are described macroscopically by a convective exchange coefficient h _ext . This coefficient is considered constant and is adjusted in order to recalibrate the model with respect to tests carried out. The average temperature of the air passing through the engine compartment (T _convectlve ) generally follows an evolution close to that of the cooling water temperature at the output of the engine 10. In fact, the water temperature at the outlet of the engine compartment is a good indicator of the temperature in the engine compartment. This simplifies by writing:

¹ convective T = ¹ T water

* σ: Boltzmann constant (= 5,67.10 ^"8 ) to describe the radiative exchanges between the various components of the undercap. Radiative under-hood exchanges are of the same order of magnitude as convective exchanges. They can not be neglected. Energy exchanges of radiative origin are described by T ⁴ relations.

The form factor (f _v ) which is defined as "the way the inlet duct 25 sees the rest of the underhood" is imposed here at 1.

The inlet duct 25 upstream of the cooler 22 generally has emissivities (ε) of the order of 0.8.

The average temperature of the elements in the engine compartment {T _m dmtιve) generally follows an evolution close to that of the water temperature at the engine outlet. We can write:

• * radiative • * water

£ 3

Thermal power extracted by the cooler 22 are frequently translated as an efficiency: 6 ₃

T ₂ - T ₃ ε, =

¹ 2 ^'1 water

These can be identified on a body bench. The efficiency of the EGR cooler depends on the order of the EGR flow (Q _eg r) - * Other values of equations (1), (2) and (3):

M _e is the mass of gas enclosed in the inlet duct 25. It is so small compared to the other terms of the equations that it can be considered as zero.

- Cpegr is the specific heat of EGR gases at constant pressure. This value depends on the nature of the gases. It is typically close to 1150 J / kg.K.

- Cp stainless steel is the specific heat of the EGR gases in walls 26 of the inlet duct 25, value depending on the nature of the material (eg stainless steel here). - Q _eg r is the EGR flow through the inlet duct 25. It is not measured, but it is estimated by calculating a difference between a measurement of Qf _ra is (flow measured at the output of the compressor 51) and a measure of Q _word (flow entering the engine). Other existing techniques, known to those _skilled in the art, may alternatively be used to estimate Q _egr . These chosen techniques are typically specific to each engine ECU used or to each planned software.

We thus have three equations with three unknowns (T _p , T ₂ , T ₃ ), resolvable by first finding T _p , then T ₂ and finally T ₃ .

An estimate of the temperature at the outlet of the cooler 22 is then obtained by taking into account the heat dissipation at the inlet duct 25, thus making the estimate accurate because true to reality.

2 ^nd embodiment: drastic simplification of the equations

The previously developed physical equations are integrable in a calculator but can remain relatively complicated (equations 1,2 and 3). It is indeed a system of nonlinear differential equations (presence of T ⁴ terms), strongly coupled.

A simplification of this system would therefore be desirable in order to obtain a system of first-order, linear and independent differential equations. For this purpose, with reference to FIG. 4, the EGR circuit 20 is considered to be a combination of two heat exchangers 100 and 200 in series.

The first exchanger 100 consists of the inlet duct 25 upstream of the cooler 22. In this exchanger 100, circulate the EGR gas cooled by the ambient environment 150 prevailing in the engine compartment (T _radιatíve and T _convectíve explained above). The temperature of the gases at the outlet of this first exchanger 100 is the temperature T ₂ .

The second heat exchanger 200 consists of the EGR cooler 22. In this exchanger 200 circulates the EGR gas (at the temperature T ₂ ) which are cooled by the water of the cooling circuit 250 engine (T _water ). The temperature of the gases at the outlet of this second exchanger 200 is the temperature T3. 1. The first exchanger 100

By defining the inlet duct 25 upstream of the cooler as an exchanger 100, macroscopically an efficiency is introduced:

T - T ^~ ε -

T - T sous_capot

This efficiency summarizes the thermal performance of the inlet duct 25, that is to say the way the EGR gases are cooled in contact with the wall 26 of the duct 25 which itself is cooled by the environment of the undercap. The concept of efficiency is generally used in steady state. However, the mass of the inlet duct 25 being large (several hundred grams), the temperature (T _p ) of the wall 26 of the duct 25 is not reached for several minutes and therefore, the notion of efficiency n ' is more exploitable simply, that is to say, without involving differential equations easily integrable in a calculator.

It therefore becomes necessary to define intermediate efficiencies by involving: the temperature of the wall 26 of the inlet duct 25 when the stabilized regime is reached (T _p∞ ); the coolant inlet gas temperature when the steady state is reached (T _2∞ ). This efficiency is then broken down into two parts:

T T T - T avt p °° avt under _ hood

Approximately: εi describes how the exhaust gases heat the walls 26 of the conduit 25; - 8 ₂ describes how the exhaust gases cool in contact with the wall 26 of the conduit 25.

1 .1. Simplification of the equation (1)

The energy conservation equation (1) can be complicated to solve, in particular because of the T ⁴ term linked to the radiative exchanges under the hood. In the engine compartment, the convective exchanges linked to the flow of air around the inlet duct 25 are of the same order of magnitude as the set of radiative exchanges between the inlet duct 25 and the various components of the sub duct 25. -capot (cylinder head, exhaust manifold, turbocharger, apron, ski, ..). We then simplify the equation above by writing: dT _p

H _mox _Pιnox .C ^ -.. ≈h _ιnt .S (T ₂ -T _p) + 2.h _ext .S (T _p -T _{convectιve).}

The _water water temperature T in engine output is usually a good indicator of the thermal environment in the engine compartment, which further simplifies to:.. DT _p ^ M _mox .C _Pmox ≈h _ιnt .S (T ₂ -T _p ) + 2.h _ext . (T _water -T _p ) (5)

The time scale that governs the wall temperature of the inlet duct 25 upstream of the cooler is of the order of one hundred seconds. The time scale that governs the temperature of the EGR gas at the cooling inlet 22 is of the order of one second. T2 changes over time are therefore almost instantaneous compared with changes in T _p over time. Thus: dT, dT,

^M _srcp _egr - - d7t - <" _m ^~ _m ^" _o ^∞ _χ . -C _P * - _m ^" _o <^" _χ - _dt

Equation (2), related to the conservation of energy, can then be simplified by:

_{Mgr .C} _Pe, h _mt .S. (T -T ₂ ) + Q _egr .Cp _egr . (T _avt -T ₂ ) ≈ 0 Or :

KST _p + Q _egr .Cp _egr .T _avt h _m .S + Q _egr _{.C Pegr} ^K '

By integrating equation (6) into equation (5), we obtain:

M _1110x - Cp _1110x . - ≈. (T _avt -T _p ) + Lh ^ .S. (T _water - T _p ) (7)

We are now looking for a simple equation describing the evolution of the temperature of the wall 26 in the form: Moreover, from the definition of εi given above in equation (4) and an approximation of T _sub . _hood to T _water we can write T _p∞ in the form:

Tp ₀₀ = T _avt . (l-Sl) + Sl. teau

By identification of equations (7) and (8), it comes then:

1.2. Simplification of equation 2

The time scale that governs the temperature of the EGR gas at the cooler inlet is of the order of one second. At this scale, the wall temperature of the EGR duct upstream of the cooler changes little.

Thus, using the definition of ε ₂ given in equation (4), we write:

T - T T - T

_ ^J avt ^J 2∞ _^ ^J avt ^J 2∞

2 j _ j j _ j avt p∞ with p

Let: T _2∞ ≈ T _avt (\ - ε ₂ ) + ε ₂ .T _p

We search for a simple equation describing the evolution of the temperature of the EGR gases at the cooling inlet in a form:

(9) dt ^~ τ ₂ ^{K l∞ l}} By identification of the equations 9 and 2, it comes: h _mt .S _^ M _egr _{.C Pegr} h _m , S + Q _egr _{.C Pegr} h _mi .S + Q _egr _{.C Pegr}

1.3. Summary of the simplification of the first interchange 100

The energy conservation equations governing the energy exchanges of energy gas in the EGR duct upstream of the cooler were initially written

M _mox _{.C Pmox} .- ^ = h _mt .S. (T ₂ -T _p ) + ε.σ.Sf. (T _r ⁴ _admittance -T ") + h _ext . S (T _convectve -T) ( 1) dt

^M z _e _r -C _PEGR .- ± h = _mt JS. (T -T ₂ ) + Q _egr £ p _egr (T _avt - T ₂ ) dt (2)

After simplification, these two equations are now written in the form:

Simplified equation (1) Equation (2) simplified With:

2 \ _xt .S 2 \ _xt .S

S ₁ ≈ either ε KS

Q _egr -Cp _egr KvS ¹ 2.h _ext .S + Q _egr _.C _Pegr _.ε ₂ ² h _mt .S + Q _{egr .C} _Peg

2A _t .S + -

Q _egr -Cp _egr + h _mt .S ie ^M _m o o _X - ^c P _mox ^M _egr -Cp _egr

T ₀

^ K _n -S + Q _egr -C _{Pegr .ε} ₂ h _mt .S + Q _egr _{.C Pegr}

In the first order, S ₁ and ε ₂ depend only on the flow EGR (Q _eg r) - Indeed,

"for ε ₂ : h _mt , convective exchange coefficient between the EGR gases and the wall of the EGR duct, is a Reynolds function ° ' ^8. At first order, the Reynolds number is a function of the EGR flow (Q _e r ) -

S ₂ can then be written as follows: K ₇

S ₇ = - no κ ₂ + c _P n: 0 _g ,; 2 with K? = Constant

for S ₁ : S ₁ is directly linked to ε ₂ by the relation: ε ² - ^h _^ s

h _ext being, as a reminder, the convective exchange coefficient considered constant. S ₁ can then be written as follows:

K _t ει =

K _x + Cp _esr .Q _esr .ε with Ki = Constant

At first order, the time constants, τ _p and τ ₂ also depend only on the flow EGR (Q _egr ). But

"for T ₂ : the EGR mass in the EGR duct is small, the time constant T ₂ will only show small variations, and will therefore be considered constant, but other possibilities for describing this time constant may be be expected, such as a description based on a more complex model or mathematical rule managed by a program.

"For τ _p : for the sake of simplicity, an average EGR flow can be used to determine a single time constant, but other possibilities for describing this time constant can be provided, such as description based on a more complex model or mathematical rule managed by a program.

After simplification, equations (1) and (2) are written:

^T ^ = ^T avf (\ - ^ε i) ^{+ ε} V ^T water T _2∞ = T _avt . (\ - ε ₂ ) + ε ₂ .T _p dT _n dt L p∞ pi ^ dt = - T ₂ [T ₁ . -T ₁ ]

Simplified equation (1) Equation (2) simplified

With

K, K _n

* i = ε ₇ =

K ₁ + Cp ^. Q ^ e ₂ K ₂ + Cp .QJ ⁰

K] - Constant K ₇ = Constant T - Constant T ₂ -Constant

The constants Ki, K2, τ _p and T2 are known (see calculation methods above), knowing the orders of magnitude assigned to M _mox , Q _egr , h _ext and h _нnt and based on measurements and / or estimates. .

These constants can then be adjusted in order to recalibrate the model compared to previous tests on the engine compartment.

2. The second heat exchanger 200

Equation (3) is retained here.

The time constant (13) is then introduced into the EGR temperature estimator to take into account the thermal inertia of the cooler 22. This constant can be measured on engine benches or be estimated from data received from a manufacturer. cooler.

This constant can be adjusted in order to readjust the model compared to tests previously carried out on an engine compartment.

The estimated temperature T ₃ is then deduced at the outlet of the cooler 22. With reference to FIG. 6, different curves of the temperature of the gases T 3 at the outlet of the cooler 22 allow comparisons between:

- a measurement made (curve 1);

an estimate according to the first embodiment of the invention (curve 2);

an estimate according to the second embodiment of the invention (curve 3). The estimation methods have been integrated in an automotive calculator.

In addition, the curve 4 gives the result of an estimate of T3 in the case where the heat dissipation is not taken into account by the inlet duct 25.

It is clear from reading the graph that taking into account in the modeling of the heat exchanges between the gases and the walls 26 of the inlet duct 25 upstream of the cooler 22 considerably improves the accuracy of the temperature estimation. EGR gases at the outlet of the cooler 22.

Thus, the average deviations between the estimation of the temperature of the EGR gas at the cooling outlet 22 according to the invention and the measurements are from 8 to 12 ° C. In addition, it should be noted that this new estimator makes it possible to correctly follow the evolutions of the gas temperatures all along the EGR circuit.

Furthermore, the simplification of the second embodiment with respect to the first embodiment of the invention leads to differences of only 2%. We will therefore use the second embodiment in the case where it is desired to minimize the means and the calculation times, and the first embodiment in the case where it is desired to maximize the accuracy of the estimate.

In addition, the estimation according to the invention has the advantage of being very simple and therefore easy to integrate into a computer. The proposal to simplify the description of heat exchange in the EGR circuit 20 is therefore entirely satisfactory.

With reference to FIG. 5, one or the other of the simplified formulations is extremely simple to solve for a computer. The estimation of the exhaust gas temperature at the outlet of the EGR circuit 20 is thus done in three successive steps:

In a first step, the wall temperature 26 of the inlet duct 25 upstream of the cooler 22 is estimated (T _p );

In a second step, the temperature of the EGR gas at the inlet of the cooler 22 is estimated (T ₂ ): Finally, the temperature of the EGR gas at the outlet of the cooler 22 is estimated (Zj).

Some modeling variants may also be provided, such as the decomposition of the inlet duct 25 upstream of the cooler 22 into several small "sections" each having its own wall temperature T _p . The invention also relates to a vehicle equipped with an electronic temperature estimator comprising calculating means or computer and storage means or data storage predetermined and / or measured, in order to implement the method of estimating temperature according to the invention. It will be possible in particular to provide an algorithm defining the temperature estimate at the output of the EGR circuit 20, the execution of which requires little computing means and few resources, given the simplicity of the process that it implements. It is therefore an ideal system to be integrated in a computer on board.

The construction of such a precise EGR temperature estimator opens up a wide variety of perspectives, such as the design of new strategies for detecting the level of fouling of the EGR circuit 20 by the exhaust gases.

Glossary

Claims

1. Method for estimating the exhaust gas temperature Zj of a combustion engine at the output of an EGR circuit fitted to the engine, based on a model taking into account the loss of thermal energy of the exhaust gases at the EGR cooler EGR circuit, characterized in that the model also takes into account the heat exchange between the exhaust gas and the walls of a conduit leading the exhaust gas to the EGR cooler.

2. Method according to the preceding claim, characterized in that said model takes into account the following heat exchanges:

Internal heat exchanges between the gases and the wall of said duct;

External heat exchanges between the wall of said duct and the external environment of the engine compartment, such as convective exchanges linked to an air flow and radiative exchanges of components external to the duct;

- the cooling of the gases through the EGR cooler.

3. Method according to one of the preceding claims, characterized in that said model is based on simplified equations of thermal energy conservation of gases taking into account the various heat exchanges throughout the EGR circuit for:

(a) an evaluation of the heat exchange between the exhaust gases and the walls of a duct bringing the exhaust gases to the EGR cooler of the EGR circuit;

(b) an evaluation of the thermal exchanges of the exhaust gases with the inlet of the EGR cooler, taking into account the evaluation of step (a);

(c) an evaluation of the thermal exchanges of the exhaust gases in the EGR cooler.

4. Method according to the preceding claim, characterized in that said equations are a system of three equations with three unknowns T _p , T ₂ and T ₃ , knowing that:

• T _p is the estimated temperature of the walls of the duct;

• T ₂ is the estimated temperature of the exhaust gas at the inlet of the cooler; the three equations corresponding to the three assessments (a), (b) and (c), respectively.

5. Method according to the preceding claim, characterized in that the temperature J ¹ J is mainly estimated from the knowledge of the temperature of the exhaust gas entering the EGR circuit, the temperature of the engine cooling water output of the engine, the mass heat of the EGR gases at constant pressure, the mass flow rate of the EGR gases, the specific heat of said duct, and the geometric and mass characteristics of the duct.

6. Method according to the preceding claim, characterized in that the

dT

^M _mox - ^c P _mo , - ^ - = Kx - ^s - ( ^τ i - T _P ) + εxτ.Sf. _admittance - T ⁴ ) + h _ext .S. (T _convectve - T) dt

JT ₁

^M ^ P, = h _mt JS. (T - T ₂ ) + Q _egr .Cp _egr . (T _avt - T ₂ ) dt

^ L = λ. [T _2. (L - s ₃ ) ₊ s ₃ .T _water - T ₃ ] dt Ta

or :

and or :

• convechve • * radiative • * ea

• hmt is calculated using an empirical relationship connecting the three dimensionless coefficients of Nusselt number, Reynolds number and Prandtl number: Nu =. / (Re ⁰ ' ⁸ , Pr);

• h _ext is considered constant and is adjusted in order to readjust the model to tests;

^• Λ = i;

• ε is of the order of 0.8 or another known constant;

T ₂ - T ₃

• ε

³ T ₇ - T

7. Method according to one of claims 1 to 5, characterized in that said model comes down to a system of linear differential equations of the first order and independent.

8. Method according to the preceding claim combined with claim 2, characterized in that these equations are found by making the approximations following: the convective external exchanges linked to a flow of air around the duct are of the same order of magnitude as the radiative exchanges by components external to the duct; the convection temperature is approximately equal to the temperature of the water; the changes of T ₂ in time are instantaneous compared with the modifications of T _p in time.

9. Method according to the preceding claim, characterized in that the equations of the first order are found from the equations according to claim 6 and making all the approximations according to the preceding claim, in that the first two equations of the first order are the following:

With

K, K ₁ ει = ^S 2 =

K ₁ + Cp ^. Q ^. 0.2 κ ₂ + cp n ::

Ki = Constant K? = Constant

T _n = constant T ₁ = constant t pco Instantaneous wall temperature (with zero wall thermal inertia)

! 2α Instantaneous temperature of the inlet gas cooler wall (with zero thermal inertia)

T ₃₀ Instantaneous temperature of the gases leaving the wall cooler (with zero thermal inertia) εi External efficiency of the upstream EGR cooling duct during the simplification of the differential equations

£ 2 Internal efficiency of the upstream EGR cooler duct during the simplification of the differential equations

£ 3 Efficiency of the EGR cooler

Time constant of the EGR duct upstream of the cooler t2 Time constant of the EGR gas at the inlet of the cooler

T3 Time constant of the EGR cooler in that the third first-order equation is that relative to T ₃ in claim 6, and in that said time constant Tj is introduced into the estimate of T ₃ in order to take into account account the thermal inertia of the cooler, adjusted according to tests carried out.

10. Vehicle equipped with an electronic temperature estimator comprising calculation means and predetermined data storage means and / or measured, in order to implement a method according to one of the preceding claims.