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1
- #1
FireLover
Automotive
- Jun 21, 2001
- 27
Background: I am trying to calculate the mass flow of exhaust gases from an IC engine versus engine position during the exhaust event. Engine conditions are steady state (fixed speed, fixed total mass flow, fixed exhaust gas composition, fixed coolant temperature)
Given: The exhaust gas composition and properties, trapped mass of exhaust in cylinder prior to exhaust valve open, total mass flow of exhaust during exhaust event, cylinder pressure and cylinder volume as a function of engine position, engine position for exhaust valve open and close, coolant temperature.
Assumptions: Exhaust gas behaves close to ideal at the pressures and temperatures during this exhaust process.
Solution: Ideal gas equation of state (IGE) can be used at any engine position during exhaust event to calculate mass in the cylinder. Since the exhaust valve is the only point for mass transfer, the change in mass between any two engine positions will give the exhaust mass flow rate (not so true near exhaust valve closing due to intake valve overlap, but I can deal with that).
The only unknown in the above solution is gas temperature versus engine position. Knowing trapped mass prior to exhaust valve open, the IGE can be used to compute gas temperature at exhaust valve opening. If I assume isentropic (NO heat transfer), I can use the following equation derived from the 2nd law to incrementally calculate in cylinder gas temperature versus engine position:
T2 = T1 * (P2/P1)^(k-1/k)
This solution overpredicts the total mass flow during the exhaust event, since heat transfer is neglected. Since I know the total mass flow, I want to add a heat transfer term to my equation to determine in cylinder gas temperature. Something like:
(Tcoolant - T1) *Cht = Q
where Cht is the coefficient of heat transfer. I can then trim Cht until I get the correct total mass flow during the exhaust event!
My question is where does the heat transfer term fit in? I can't figure how to get an equation such as T2 = f(Q, T1, P1, P2, etc.). Anybody have any ideas or hints?
Given: The exhaust gas composition and properties, trapped mass of exhaust in cylinder prior to exhaust valve open, total mass flow of exhaust during exhaust event, cylinder pressure and cylinder volume as a function of engine position, engine position for exhaust valve open and close, coolant temperature.
Assumptions: Exhaust gas behaves close to ideal at the pressures and temperatures during this exhaust process.
Solution: Ideal gas equation of state (IGE) can be used at any engine position during exhaust event to calculate mass in the cylinder. Since the exhaust valve is the only point for mass transfer, the change in mass between any two engine positions will give the exhaust mass flow rate (not so true near exhaust valve closing due to intake valve overlap, but I can deal with that).
The only unknown in the above solution is gas temperature versus engine position. Knowing trapped mass prior to exhaust valve open, the IGE can be used to compute gas temperature at exhaust valve opening. If I assume isentropic (NO heat transfer), I can use the following equation derived from the 2nd law to incrementally calculate in cylinder gas temperature versus engine position:
T2 = T1 * (P2/P1)^(k-1/k)
This solution overpredicts the total mass flow during the exhaust event, since heat transfer is neglected. Since I know the total mass flow, I want to add a heat transfer term to my equation to determine in cylinder gas temperature. Something like:
(Tcoolant - T1) *Cht = Q
where Cht is the coefficient of heat transfer. I can then trim Cht until I get the correct total mass flow during the exhaust event!
My question is where does the heat transfer term fit in? I can't figure how to get an equation such as T2 = f(Q, T1, P1, P2, etc.). Anybody have any ideas or hints?
