Thermodynamics Review Problems for Mechanical Engineering Students | Series 21: Diesel Cycle For The Third Time
This is the 21st series of my "Thermodynamics Review Problems for Mechanical Engineering Students". If you've missed the previous series you may try scrolling this blog and head over to the "Curriculum". Additionally this series happens to be the 3rd that tackles the Diesel Cycle. This time around, we will be computing review problems with respect to the operating conditions of each given Diesel cycle.
Review Problem 1
In an air standard Diesel cycle, compression starts at
100 kPa and 300°K. The compression ratio is 12 to 1. The maximum cycle temperature is 2000°K. Determine the cycle efficiency.Solution
For this review problem, the first thing to obtain is the temperature at the end of isentropic compression which is
T2. T2 can be obtain since we’re provided with compression ratio which is 12 and by using the relation, we’ve found out T2 is equal to 810.58°K. Since in the isobaric heat addition process there is a cut-off ratio which is the ratio of the volumes at the end and at the start of addition process which is further simplified as the ratio of the temperatures at the end and at the start of heat addition process, and by doing so, we’ve found out that the cut-off ratio (rc) is equal to 2.47. Finally, we can now compute for the cycle efficiency by using the shortcut formula which is expressed as a function of compression ratio (rk), cut-off ratio (rc) and adiabatic index (k). And with that, we’ve found out that the cycle is 0.5421 = 54.21 % efficient.T2 |
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rc |
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e |
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Review Problem 2
A Diesel engine is operating on a
4-stroke cycle, has a heat rate of 10,000 kJ/kW-hr brake. The compression ratio is 10. The cut-off ratio is 2. Using k = 1.32, what is the brake engine efficiency.Solution
For this review problem, the first thing to obtain is the cycle efficiency of the Diesel engine which is easily obtained using the shortcut formula for and by doing so, we’ve found out that the Diesel cycle is
0.4573 = 45.73 % efficient. Next thing to obtain is the brake thermal efficiency (etb) which is expressed in the formula 3600/SHR where 3600 is the conversion of 1 hour to seconds and SHR which stands for the specific heat rate and using the mentioned formula, we’ve found out that the Diesel engine’s brake thermal efficiency is 0.36 = 36 %. Finally, the brake engine efficiency (eeb) is obtained as the ratio of the etb and ec. Using the mentioned relation, we’ve found out that the brake engine efficiency is equal to 0.7872 = 78.72 %.ec |
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etb |
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eeb |
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Curriculum
Reference
- PIPE - PROBLEM SET #3 by Alcorcon Engineering Review Center
- Sta. Maria, H. [1990] 2012. Thermodynamics 1. Mandaluyong City: National Bookstore Inc..
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