Suggest suitable formulae or method to calculate the in-cylinder gas temperature in a diesel engine from the measured in-cylinder gas pressure during combustion.
The ideal gas equation is normally used to get what is called a mass-averaged temperature. You need the cylinder trapped mass, which can be estimated from the air flow, it is probably acceptable to ignore the residual gasses, which in a diesel are on the order of 4%. There could also be a problem in turbocharged engines, as some air may be blown through the engine during valve overlap if intake pressure is above exhaust pressure. The volume is obtained from the crank angle position and the slider crank formula.
Tmass ave = pV/mR
The mass based gas constant R, does not change much, since it is the universal gas constant divided by the molecular weight. In reference to a comment above, it is cp that changes, not R, and of course cv = cp - R. Most of the gasses consist of nitrogen, and if you use a gas constant of around 29 kg/mol, that will be good enough for the mass average temperatures, since it is only a representative value anyhow.
Since the diesel combustion process is heterogeneous, the mass averaged temperature is not the same as the local temperature, which varies throughout the combustion chamber between the adiabatic flame temperature and that of the surrounding air, that is, the compression temperature. Local temperatures are many times more difficult to measure, and required much more sophisticated equipment. The mass averaged temperature cannot be used for emissions calculations, but in some simpler simulations can be used to estimate instantaneous heat transfer.
I hope Ideal gas law can be used to calculate in-cylinder temperature.
PV=mRT
P is known, V is known(as theta is known), m & R are also known.
R value could change with temperature variation since cp/cv chnages with temperature.I believe there is a more accurate realtions that ideal gas equation to calculate T from cylinder data.
Theoretically, the cylinder gas temperature for a diesel engine can be expressed a function of following input variables:
- Heat release curve (relative to TDC)
- Air/fuel ratio
- Intake air temperature
- EGR flow
- Cylinder head temperature (coolant temperature)
Now, from experimental point of view, if there is a pressure sensor mounted (I guess a Kistler sensor) there should be possible to measure also the temperature. In this way an empirical model can be validated.
The ideal gas equation is normally used to get what is called a mass-averaged temperature. You need the cylinder trapped mass, which can be estimated from the air flow, it is probably acceptable to ignore the residual gasses, which in a diesel are on the order of 4%. There could also be a problem in turbocharged engines, as some air may be blown through the engine during valve overlap if intake pressure is above exhaust pressure. The volume is obtained from the crank angle position and the slider crank formula.
Tmass ave = pV/mR
The mass based gas constant R, does not change much, since it is the universal gas constant divided by the molecular weight. In reference to a comment above, it is cp that changes, not R, and of course cv = cp - R. Most of the gasses consist of nitrogen, and if you use a gas constant of around 29 kg/mol, that will be good enough for the mass average temperatures, since it is only a representative value anyhow.
Since the diesel combustion process is heterogeneous, the mass averaged temperature is not the same as the local temperature, which varies throughout the combustion chamber between the adiabatic flame temperature and that of the surrounding air, that is, the compression temperature. Local temperatures are many times more difficult to measure, and required much more sophisticated equipment. The mass averaged temperature cannot be used for emissions calculations, but in some simpler simulations can be used to estimate instantaneous heat transfer.
It can be obtained from the first law of thermodynamics together with equation of state
- Badges
- Science topic