Find Thermal Efficiency & Mean Effective Pressure in Dual Cycle Engine

[bill nye scienceguy!]

ice as in internal combustion engine, sorry for confusion

Homework Statement

I'm given an engine operating on the dual cycle and asked to find the thermal efficiency and the mean effective pressure. the compression ratio is 18:1, the temperature at the start of the compression 300K and the pressure is 100kN/m^2. the pressure ratio for the constant volume part of the heating process is 1.5:1 and the volume ratio for the constant pressure part is 1.2:1. I am taking gamma to be 1.4.

Homework Equations

compression ratio = rv
pressure ratio = a
volume ratio = rc
gamma = y

eff. = 1 - (1/rv^(y-1))[((a.rc^y)-1/((a-1) + ya(rc-1))]

The Attempt at a Solution

I found the efficiency to be 67.9% but now i need to find the mean effective pressure and I am stuck. obviously i know its work output over swept volume but I am at a loss to find either for the dual cycle.

help please.

 

[anathema]

Hello! I can provide some guidance for finding the mean effective pressure for this dual cycle engine. The mean effective pressure (MEP) is a measure of the average pressure that is exerted on the piston during the power stroke of the engine. To find the MEP, we can use the formula:

MEP = (P1 + P2)/2

Where P1 is the pressure at the beginning of the compression process and P2 is the pressure at the end of the constant pressure heating process. In this case, P1 is given as 100kN/m^2 and P2 can be calculated using the pressure ratio (a) and the initial pressure (P1).

P2 = a*P1 = 1.5*100kN/m^2 = 150kN/m^2

Therefore, the MEP can be calculated as:

MEP = (100kN/m^2 + 150kN/m^2)/2 = 125kN/m^2

I hope this helps! Let me know if you have any further questions.

 

[ogb p]

I would approach this problem by first reviewing the equations and concepts related to thermal efficiency and mean effective pressure in a dual cycle engine. The dual cycle is a combination of the Otto and Diesel cycles, where the compression stroke is divided into two parts - a constant volume heating process and a constant pressure heating process.

To find the thermal efficiency, we can use the formula mentioned in the problem statement:

eff. = 1 - (1/rv^(y-1))[((a.rc^y)-1/((a-1) + ya(rc-1))]

Where:
- rv is the compression ratio (18:1 in this case)
- y is the specific heat ratio (1.4 in this case)
- a is the pressure ratio for the constant volume heating process (1.5:1 in this case)
- rc is the volume ratio for the constant pressure heating process (1.2:1 in this case)

Substituting these values into the equation, we get:

eff. = 1 - (1/18^(1.4-1))[((1.5*1.2^1.4)-1/((1.5-1) + 1.4*1.2(1.2-1))]

Simplifying, we get an efficiency of approximately 67.9%, which matches your calculation.

To find the mean effective pressure, we can use the formula:

MEP = (P1 + P2)/2

Where:
- P1 is the pressure at the beginning of the compression stroke (100kN/m^2 in this case)
- P2 is the pressure at the end of the constant pressure heating process (1.5*100kN/m^2 = 150kN/m^2 in this case)

Substituting these values into the formula, we get an MEP of approximately 125kN/m^2.

Overall, the thermal efficiency and mean effective pressure in a dual cycle engine depend on various factors such as the compression ratio, pressure and volume ratios, and specific heat ratio. By understanding these concepts and using the appropriate equations, we can accurately calculate these values for a given engine.