
Summer 2018 ECII Complete Solutions 9

Lecture1.1

Lecture1.2

Lecture1.3

Lecture1.4

Lecture1.5

Lecture1.6

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Lecture1.8

Lecture1.9

Lecture1.10

Lecture1.11

Lecture1.12


Winter 2017 ECII Complete Solutions 11

Lecture2.1

Lecture2.2

Lecture2.3

Lecture2.4

Lecture2.5

Lecture2.6

Lecture2.7

Lecture2.8

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Summer 2017 ECII Complete Solutions 12

Lecture3.1

Lecture3.2

Lecture3.3

Lecture3.4

Lecture3.5

Lecture3.6

Lecture3.7

Lecture3.8

Lecture3.9

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Winter 2016 ECII Complete Solutions 12

Lecture4.1

Lecture4.2

Lecture4.3

Lecture4.4

Lecture4.5

Lecture4.6

Lecture4.7

Lecture4.8

Lecture4.9

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Lecture4.12

Summer 2018 – Q.2 [Preview]
Q. 2 a) Explain multistage compression. What are the advantages of multistage compression over a single stage compression for same pressure ratio? Why intercooling is necessary in multistage compression? [5]
Answer: The pressure ratio for single stage compressor is limited to 7 bar. Increase in pressure ratio with single stage compressor causes following undesirable effects;
1) With high delivery pressure, the delivery temperature increases. It increases specific volume of air in the cylinder, thus more compression work is required.
2) Greater expansion of clearance air in the cylinder hence decreases effective swept volume and therefore there is decrease in fresh air induction.
3) For high pressure ratio, the cylinder size would have to be large, strong and heavy working parts are to be needed. It will increase balancing problems and high torque fluctuation will require a heavier flywheel.
All the above problems can be reduced to the minimum level by compressing the air in more than one cylinder with intercooling between stages for the same pressure ratio. The compression of air in two or more cylinders in series is called multistage compression. Air cooling between stages provides the means to achieving an appreciable reduction in compression work and maintaining the air temperature within safe operating limits.
The necessity of intercooling in multistage compression
1) The air can be compressed to a sufficiently high pressure.
2) By cooling the air between the stages of compression, the compression can be brought to isothermal and power input to the compressor can be reduced considerably.
3) The lowpressure ratio in a cylinder improves volumetric efficiency.
4) A low working temperature in each stage helps to sustain better lubrication.
5) More uniform torque and better mechanical balance can be achieved.
Q. 2 b) A twostage single acting reciprocating air compressor delivers air at 20 bar. The pressure and temperature of air before the compression in L.P. cylinder are 1 bar and 27^{0}C. The discharge pressure of L.P. cylinder is 4.7 bar. The pressure of air leaving the intercooler is 4.5 bar and the air is cooled to 27^{0}C. The diameter and stroke of L.P. cylinder are 40 cm and 50 cm respectively. The clearance volume is 4% of the stroke in both cylinders. The speed of the compressor is 200 rpm. Assuming the index of compression and expansion in both cylinders as 1.3.
Determine:
i) I.P. required to run the compressor
ii) Heat rejected in the intercooler per minute. [8]
Answer:
Given: Assuming Cp_{air} = 1.005, n = 1.3
P_{1} = 1 bar, T_{1} = 27^{0}C = 300 K, T_{5} = 27^{0}C = 300 K, P_{2} = P_{3} = 4.7 bar, P_{5} = P_{8} = 4.5 bar, P_{6} = P_{7} = 20 bar, C = 0.04, D_{L.P.} = 40 cm = 0.4 m, L_{L.P.} = 50 cm = 0.5 m, N = 200 rpm.
The swept volume of L.P. cylinder V_{s} = 12.566 m^{3}/min.
The volumetric efficiency is calculated as,
Effective swept volume of L.P. cylinder (V_{1} – V_{4}) = n_{vol} x swept volume = 0.90846 x 12.566 = 11.415 m^{3}/min.
T_{2} = 428.766 K
i) Heat rejected in intercooler:
Heat rejected in the intercooler = Mass of air/min x Cp_{air} x (T_{2} – T_{1}) = 13.258 x 1.005 x (428.766 – 300) = 1715.72 kJ/min
Heat rejected in intercooler = 1715.715 kJ/min.
ii) I.P. required to run the compressor:
For two stage compressor, The total work done = W.D._{L.P.} + W.D._{H.P.}
W.D. = 4946.56 x 0.84 = 4155.11 kJ/min
I.P. = W.D./60 = 4155.11/60 = 69.25 kW.
Power required to run the compressor = 69.25 kW