Systems and methods for modelling aftertreatment temperature of a vehicle

1. A method for model-based determination of a temperature distribution of an exhaust aftertreatment system of a vehicle, the method comprising:

measuring a power demand from a first component of the aftertreatment system; calculating a heat transfer into the first component of the aftertreatment system based on power demand of the first component and a configurable emissivity value of the exhaust gas;

calculating the temperature of the first component based on the calculated heat transfer;

estimating a volumetric flow rate of exhaust gas through the aftertreatment system, wherein the calculation of the heat transfer into the first component of the aftertreatment system is based on the volumetric flow rate of the exhaust gas;

determining if an internal combustion engine, ICE, of the vehicle is off; and

in response to determining that the ICE is off, configuring the emissivity value of the exhaust gas based on an emissivity value of air corrected for pressure and temperature of the aftertreatment system.

2. The method of claim 1 , further comprising configuring the emissivity value of the exhaust gas based on at least one of:

air-mass ratio;

air-fuel ratio;

fuel type;

temperature;

pressure; or

emissions output.

3. The method of claim 1 , further comprising:

determining if an internal combustion engine, ICE, of the vehicle is on and a secondary airflow is on; and

in response to determining that the ICE and secondary airflow is on, configuring the emissivity value of the exhaust gas based on air-mass ratio, air-fuel ratio, corrected for pressure and temperature of the aftertreatment system.

4. The method of claim 1 , further comprising:

determining if an internal combustion engine, ICE, of the vehicle is on and a secondary airflow is off; and

in response to determining that the ICE is on and secondary airflow is off, configuring the emissivity value of the exhaust gas based on air-fuel ratio, corrected for pressure and temperature of the aftertreatment system.

5. The method of claim 1 , wherein:

the first component of the aftertreatment system is an electrically heated catalyst, eCAT; and

the method further comprises:

determining if the eCAT is on or off; and

in response to determining the eCAT is on, selecting a first radiation heat transfer equation.

6. The method of claim 5 , further comprising:

in response to determining the eCAT is off, selecting a convection heat transfer equation, a second radiation heat transfer equation, or a combination of the convection heat transfer equation and second radiation heat transfer equations.

7. The method of claim 1 , further comprising:

monitoring an ambient temperature of the vehicle, wherein the calculation of the heat transfer is further based on the ambient temperature of the vehicle.

8. The method of claim 1 , wherein:

the aftertreatment system is divided into segments in an axial direction and the first component is located in a first segment; and

the method further comprises:

calculating the temperature of a second segment, disposed upstream of the first segment, wherein the calculation of the heat transfer is further based on an input heat from the second segment; and

calculating the temperature of a third segment, disposed downstream of the first segment, wherein the calculation of the heat transfer is further based on an output heat to the third segment.

9. A non-transitory computer-readable medium having instructions encoded thereon for model-based determination of a temperature distribution of an exhaust aftertreatment system of a vehicle which, when executed, carry out the method of claim 1 .

10. An after-treatment system of a vehicle comprising:

an electrically heated catalyst, eCAT, electrically coupled to a power source; and

a controller, communicatively coupled to the eCAT and the power source, the controller configured to:

measure a power demand of the eCAT from the power source;

calculate a heat transfer into the eCAT of the aftertreatment system based on the power demand of the eCAT and a configurable emissivity value of the exhaust gas;

calculate the temperature of the eCAT based on the calculated heat transfer;

estimate a volumetric flow rate of exhaust gas through the aftertreatment system, wherein the calculation of the heat transfer into the eCAT of the aftertreatment system is based on the volumetric flow rate of the exhaust gas;

determine if an internal combustion engine, ICE, of the vehicle is off; and

in response to determining that the ICE is off, configure the emissivity value of the exhaust gas based on an emissivity value of air corrected for pressure and temperature of the aftertreatment system.

11. The aftertreatment system of claim 10 , wherein the controller is adapted to configure the emissivity value of the exhaust gas based on at least one of:

air-mass ratio;

air-fuel ratio;

fuel type;

temperature;

pressure; or

emissions output.

12. The aftertreatment system of claim 10 , the controller further configured to:

determine if an internal combustion engine, ICE, of the vehicle is on and a secondary air pump is on; and

in response to determining that the ICE and secondary air pump is on, configure the emissivity value of the exhaust gas based on exhaust-air ratio or air-fuel ratio, corrected for pressure and temperature of the aftertreatment system.

13. The aftertreatment system of claim 10 , the controller further configured to:

determine if an internal combustion engine, ICE, of the vehicle is on and a secondary air pump is off; and

in response to determining that the ICE is on and secondary air pump is off, configure the emissivity value of the exhaust gas based on air-fuel ratio, corrected for pressure and temperature of the aftertreatment system.

14. The aftertreatment system of claim 10 , the controller further configured to:

determine if the eCAT is on or off; and

in response to determining the eCAT is on, select a first radiation heat transfer equation.

15. The aftertreatment system of claim 14 , the controller further configured to:

in response to determining the eCAT is off, select a convection heat transfer equation, a second radiation heat transfer equation, or a combination of the convection heat transfer equation and second radiation heat transfer equations.

16. A vehicle comprising the aftertreatment system of claim 10 .