Question 12.CSGP.129: Find the temperature after combustion and the specific energ......
Find the temperature after combustion and the specific energy release by combustion in Problem 12.92 using cold air properties. This is a difficult problem and it requires iterations.
The worlds largest diesel engine has displacement of 25 m³ running at 200 RPM in a two stroke cycle producing 100 000 hp. Assume an inlet state of 200 kPa, 300 K and a compression ratio of 20:1. What is the mean effective pressure?
We have 3 parameters for the cycle: T _1, P _1 and CR we need one more, so this comes from the total rate of work Eq.12.11.
Combustion and expansion volumes
v _3= v _2 \times T _3 / T _2= v _1 T _3 /\left( T _2 \times CR \right) ; \quad v _4= v _1
Expansion process, isentropic from Eq.8.32
T _4= T _3\left( v _3 / v _4\right)^{ k -1}= T _3\left[ T _3 /\left( CR \times T _2\right)\right]^{ k -1}= T _3^{ k }\left( CR \times T _2\right)^{1- k }=0.01908 T _3^{ k }
The net work is also given by the heat transfers
w _{\text {net }}= q _{ H }- q _{ L }= C _{ p }\left( T _3- T _2\right)- C _{ v }\left( T _4- T _1\right)
Substitute w _{\text {net }} \text { and } T _4 into this equation and we get
366.03=1.004\left( T _3-994.3\right)-0.717\left(0.01908 T _3^{ k }-300\right)
divide by 1.004 and combine terms to get
1144.63= T _3-0.013626 T _3^{ k }
Trial and error, guess T _3 \Rightarrow RHS _{1400}=1054.1 ; RHS _{1600}=1183
Interpolate: