Thank you for your response AM. I appreciate it and will work through the steps.

In summary, a four-stroke petrol engine with a compression ratio of 9 and a total swept volume of 2.71 litres distributed over 4 cylinders is being examined. Using an ideal thermodynamic cycle and given conditions such as CV and Cp of air, pressure and temperature at intake, maximum temperature in the cylinder, and calorific value of fuel, the maximum amount of fuel that can be safely added to the air in one cylinder can be calculated. The calculation involves using equations such as V2=V1/(P1/P2)^(1/γ) to determine output power and the adiabatic condition to determine the temperature of the compressed air before fuel injection. The maximum temperature allowed limits the amount of fuel that can
  • #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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  • #2
soofking said:

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
 

Related to Thank you for your response AM. I appreciate it and will work through the steps.

1. How does a thermodynamic cycle work?

A thermodynamic cycle is a series of processes that a system undergoes to transfer energy or perform work. It follows the laws of thermodynamics, which state that energy cannot be created or destroyed, but can only be transferred or converted from one form to another.

2. What are the different types of thermodynamic cycles?

There are four main types of thermodynamic cycles: the Carnot cycle, Rankine cycle, Otto cycle, and Brayton cycle. Each type has its own unique set of processes and is used in various applications, such as power generation, refrigeration, and engines.

3. What is the purpose of a thermodynamic cycle?

The purpose of a thermodynamic cycle is to convert energy from one form to another in an efficient and controlled manner. This can be used to produce power, heat or cooling, or to perform mechanical work.

4. How is efficiency calculated in a thermodynamic cycle?

The efficiency of a thermodynamic cycle is calculated by dividing the output energy by the input energy and multiplying by 100%. This can vary depending on the specific type of cycle and the efficiency of the components used.

5. What are some real-world applications of thermodynamic cycles?

Thermodynamic cycles have a wide range of real-world applications, including power plants, refrigeration systems, air conditioning units, and engines in vehicles. They are also used in industrial processes, such as chemical production and oil refining.

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