Thermodynamic Cycle Question

  • #1
soofking
Poster warned about not using the homework template

Homework Statement


[/B]
A four-stroke petrol engine with a compression ratio of 9 has a total swept volume of 2.71 litres distributed over 4 cylinders.

Assume the corresponding ideal thermodynamic cycle and the following conditions to calculate the maximum amount of fuel which can be safely added to the air in one cylinder.

  • CV of air: 0.718 kJ/ (kg K)
  • Cp of air: 1.005 kJ/ (kg K)
  • pressure at intake: 0.91 bar
  • Temperature at intake: 279 K
  • Maximum temperature in cylinder: 1,365 K
  • Calorific value of fuel: 48 MJ/kg
Where necessary, assume that the mass of fluid contained in the cylinder can be calculated using dry air (and neglecting the mass of the added fuel).



Homework Equations



V2=V1/(P1/P2)^(1/γ).
possible other equations such as ideal gas equation etc


The Attempt at a Solution


[/B]
So far I have only managed to work out the output power from V2=V1/(P1/P2)^(1/γ). which comes out as 8.19 bar.

any help would be greatly appreciated.
 
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Answers and Replies

  • #2
Andrew Mason
Science Advisor
Homework Helper
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Homework Statement


[/B]
A four-stroke petrol engine with a compression ratio of 9 has a total swept volume of 2.71 litres distributed over 4 cylinders.

Assume the corresponding ideal thermodynamic cycle and the following conditions to calculate the maximum amount of fuel which can be safely added to the air in one cylinder.

  • CV of air: 0.718 kJ/ (kg K)
  • Cp of air: 1.005 kJ/ (kg K)
  • pressure at intake: 0.91 bar
  • Temperature at intake: 279 K
  • Maximum temperature in cylinder: 1,365 K
  • Calorific value of fuel: 48 MJ/kg
Where necessary, assume that the mass of fluid contained in the cylinder can be calculated using dry air (and neglecting the mass of the added fuel).



Homework Equations



V2=V1/(P1/P2)^(1/γ).
possible other equations such as ideal gas equation etc


The Attempt at a Solution


[/B]
So far I have only managed to work out the output power from V2=V1/(P1/P2)^(1/γ). which comes out as 8.19 bar.

any help would be greatly appreciated.
Welcome to PF soofking!

I would then use the adiabatic condition expressed in terms of temperature: ##T_2V_2^{(\gamma-1)} = T_1V_1^{(\gamma-1)}##. That will give you the temperature of the compressed air in the cylinder before injection of fuel. The ignition of the fuel will then provide heat flow into the compressed air at constant volume, raising the temperature. The amount of heat flow is limited by the maximum temperature allowed, which limits the amount of fuel that can be burned.

From what you have provided, there appears to be no consideration of the amount of O2 needed for combustion, so assume there is more than needed for complete combustion.

AM
 

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