
Summer 2018 ECII Complete Solutions 9

Lecture1.1

Lecture1.2

Lecture1.3

Lecture1.4

Lecture1.5

Lecture1.6

Lecture1.7

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

Lecture2.9

Lecture2.10

Lecture2.11

Lecture2.12


Summer 2017 ECII Complete Solutions 12

Lecture3.1

Lecture3.2

Lecture3.3

Lecture3.4

Lecture3.5

Lecture3.6

Lecture3.7

Lecture3.8

Lecture3.9

Lecture3.10

Lecture3.11

Lecture3.12


Winter 2016 ECII Complete Solutions 12

Lecture4.1

Lecture4.2

Lecture4.3

Lecture4.4

Lecture4.5

Lecture4.6

Lecture4.7

Lecture4.8

Lecture4.9

Lecture4.10

Lecture4.11

Lecture4.12

Summer 2018 – Q.3 [Preview]
Q. 3 a) Explain the phenomenon of surging and choking in centrifugal compressors [5]
Answer:
Surging and choking
Surging Surging is defined as a selfoscillation of the discharge pressure and flow rate, including a flow reversal. Every centrifugal and axial compressor has a characteristic combination of maximum head and minimum flow. Beyond this point, surging will occur. During surging, a flow reversal is often accompanied by a pressure drop.
Surging is caused when mass flow rate of air is reduced to a value which is less than the predetermined value. Thus, the flow becomes unsteady, periodic reversal.
Choking When the velocity of air in the compressor reaches sonic velocity, the mass flow rate through the compressor reaches a maximum value. This situation is called choking. At choking condition, the pressure ratio in the compressor becomes unity i.e., there is no compression.
Choking means constant mass flow irrespective of pressure ratio.
At constant impeller speed, the decrease in pressure ratio leads to an increase in the mass flow rate and hence density of compressed air is decreased. Consequently the radial velocity of air increases, which increases the absolute velocity of air at impeller exit and incidence angle at diffuser vane tip. The slope of the performance curve decreases and finally the point A is reached as shown in figure. The mass flow rate of air can not be increased beyond the point A. This point is called choking state.
Q. 3 b) In an eight stage axial flow compressor, the overall pressure ratio achieved is 5:1 with an overall isentropic efficiency of 90%. The temperature and pressure at inlet are 20^{0}C and 1 bar. The work is divided equally between the stages. The mean blade speed is 175 m/s and 50% reaction design is used. The axial velocity through the compressor is constant and is equal to 100 m/s. Calculate The power required and blade angles. [8]
Answer:
Given: Number of stages = 8, n_{isentropic} = 90%, C_{f} = 100 m/s, C_{bl} = 175 m/s, P_{2} = 5 bar, P_{1} = 1 bar, T_{1} = 293 K, For 50% reaction blading,
n_{isentropic} = (T_{2}^{I} – T_{1})/(T_{2} – T_{1})
Therefore, T_{2} = 483.06 K.
Work Input = C_{p}(T_{2}T_{1})= 1.005(483.06293)= 191.017 kJ/kg
Power required = 191.017 kJ/kg
Now, work done/kg = Number of stages x C_{bl} x (Cw_{2} – Cw_{1})
—[1]
—[2]
from [1] and [2],
Q. 3 a) Explain the phenomenon of surging and choking in centrifugal compressors [5]
Answer:
Surging and choking
Surging Surging is defined as a selfoscillation of the discharge pressure and flow rate, including a flow reversal. Every centrifugal and axial compressor has a characteristic combination of maximum head and minimum flow. Beyond this point, surging will occur. During surging, a flow reversal is often accompanied by a pressure drop.
Surging is caused when mass flow rate of air is reduced to a value which is less than the predetermined value. Thus, the flow becomes unsteady, periodic reversal.
Choking When the velocity of air in the compressor reaches sonic velocity, the mass flow rate through the compressor reaches a maximum value. This situation is called choking. At choking condition, the pressure ratio in the compressor becomes unity i.e., there is no compression.
Choking means constant mass flow irrespective of pressure ratio.
At constant impeller speed, the decrease in pressure ratio leads to an increase in the mass flow rate and hence density of compressed air is decreased. Consequently the radial velocity of air increases, which increases the absolute velocity of air at impeller exit and incidence angle at diffuser vane tip. The slope of the performance curve decreases and finally the point A is reached as shown in figure. The mass flow rate of air can not be increased beyond the point A. This point is called choking state.
Q. 3 b) In an eight stage axial flow compressor, the overall pressure ratio achieved is 5:1 with an overall isentropic efficiency of 90%. The temperature and pressure at inlet are 20^{0}C and 1 bar. The work is divided equally between the stages. The mean blade speed is 175 m/s and 50% reaction design is used. The axial velocity through the compressor is constant and is equal to 100 m/s. Calculate The power required and blade angles. [8]
Answer:
Given: Number of stages = 8, n_{isentropic} = 90%, C_{f} = 100 m/s, C_{bl} = 175 m/s, P_{2} = 5 bar, P_{1} = 1 bar, T_{1} = 293 K, For 50% reaction blading,
n_{isentropic} = (T_{2}^{I} – T_{1})/(T_{2} – T_{1})
Therefore, T_{2} = 483.06 K.
Work Input = C_{p}(T_{2}T_{1})= 1.005(483.06293)= 191.017 kJ/kg
Power required = 191.017 kJ/kg
Now, work done/kg = Number of stages x C_{bl} x (Cw_{2} – Cw_{1})
—[1]
—[2]
from [1] and [2],