Problem_Sheet_on_GaS_Power_CyCle

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Assignment on ‘GaS Power CyCle’ 
Q.1] An Otto cycle operates between maximum and minimum pressures of 600 kPa and 100 
kPa. The minimum and maximum temperatures in the cycle are 27ºC and 1600 K. Determine 
thermal efficiency of cycle and also show it on T-s and P-V diagram. 
Q.2] In a Diesel engine during the compression process, pressure is seen to be 138 kPa at 1/8th 
of stroke and 1.38 MPa at 7/8th of stroke. The cut-off occurs at 1/15th of stroke. Calculate air 
standard efficiency and compression ratio assuming indicated thermal efficiency to be half of 
ideal efficiency, mechanical efficiency as 0.8, calorific value of fuel = 41800 kJ/kg and γ = 1.4. 
Also find fuel consumption@ 1 bhp/hr. 
Q.3] In an IC engine using air as working fluid, total 1700 kJ/kg of heat is added during 
combustion and maximum pressure in cylinder does not exceed 5 MPa. Compare the efficiency 
of following two cycles used by engine: (a) Cycle in which combustion takes place iso-
chorically. (b) Cycle in which half of heat is added at constant volume and half at constant 
pressure. Temperature and pressure at the beginning of compression are 100ºC and 103 kPa. 
Compression and expansion processes are adiabatic. Specific heat at constant pressure and 
volume are 1.003 kJ/kg · K and 0.71 kJ/kgK. 
Q.4] In an air standard Brayton cycle the minimum and maximum temperature are 300 K and 
1200 K, respectively. The pressure ratio is that which maximizes the net work developed by 
the cycle per unit mass of air flow. Calculate the compressor and turbine work, each in kJ/kg 
air, and thermal efficiency of the cycle. 
Q.5] A gas turbine unit receives air at 1 bar, 300 K and compresses it adiabatically to 6.2 bar. 
The compressor efficiency is 88%. The fuel has a heating value of 44186 kJ/kg and the fuel-
air ratio is 0.017 kg fuel/kg of air. The turbine internal efficiency is 90%. Calculate the work 
of turbine and compressor per kg of air compressed and thermal efficiency. For products of 
combustion cp = 1.147 kJ/kg K, γ = 1.33. 
Q.6] In a Brayton cycle gas turbine power plant the minimum and maximum temperature of 
the cycle are 300 K and 1200 K. The compression is carried out in two stages of equal pressure 
ratio with intercooling of the working fluid to the maximum temperature of the cycle after the 
first-stage of compression. The entire expansion is carried out in one stage only. The isentropic 
efficiency of the both compressors is 0.85 and that of the turbine is 0.9. Determine the overall 
pressure ratio that would give the maximum net work per kg working fluid. Take γ = 1.4. 
Q.7] In a gas turbine installation air is supplied at 1 bar, 27ºC into compressor having 
compression ratio of 8. The air leaving combustion chamber is heated upto 1100 K and 
expanded upto 1 bar. A heat exchanger having effectiveness of 0.8 is fitted at exit of turbine 
for heating the air before its inlet into combustion chamber. Assuming polytropic efficiency of 
the compressor and turbine as 0.85 and 0.90. Determine cycle efficiency, work ratio and 
specific work output of plant. Take cp = 1.0032 kJ/kgK for air. 
Q.8] A gas turbine plant has air being supplied at 1 bar, 27ºC to compressor for getting 
compressed upto 5 bar with isentropic efficiency of 85%. Compressed air is heated upto 1000 
K in combustion chamber where also occurs a pressure drop of 0.2 bar. Subsequently expansion 
occurs to 1 bar in turbine. Determine isentropic efficiency of turbine, if thermal efficiency of 
plant is 20%. 
Q.9] A gas turbine plant has air supplied at 1 bar, 27ºC for being compressed through pressure 
ratio of 10. Compression of air is achieved in two stages with perfect intercooling in between 
at optimum pressure. The maximum temperature in cycle is 1000 K and compressed air at this 
temperature is sent for expansion in two stages of gas turbine. First stage expansion occurs 
upto 3 bar and is subsequently reheated upto 995 K before being sent to second stage. Fuel 
used for heating in combustion chamber has calorific value of 42,000 kJ/kg. Considering cp = 
1.0032 kJ/kg. K throughout cycle determine, net output, thermal efficiency and air fuel ratio 
when air flows into compressor at 30 kg/s. Take isentropic efficiency of compression and 
expansion to be 85% and 90% respectively. 
Q.10] A regenerative-reheat cycle has air entering at 1 bar, 300 K into compressor having 
intercooling in between the two stages of compression. Air leaving first stage of compression 
is cooled upto 290 K at 4 bar pressure in intercooler and subsequently compressed upto 8 bar. 
Compressed air leaving second stage compressor is passed through a regenerator having 
effectiveness of 0.80. Subsequent combustion chamber yields 1300 K at inlet to turbine having 
expansion upto 4 bar and then reheated upto 1300 K before being expanded upto 1 bar. Exhaust 
from turbine is passed through regenerator before discharged out of cycle. For the fuel having 
heating value of 42000 kJ/kg determine fuel-air ratio in each combustion chamber, total turbine 
work and thermal efficiency. Consider compression and expansion to be isentropic and air as 
working fluid throughout the cycle. 
Q.11] A gas turbine installation operates with fixed maximum and minimum temperatures T3 
and T1 respectively. Show that the optimum specific work output shall be obtained at same 
overall pressure ratio for each of following arrangement. Also give expression for this pressure 
ratio for air as working fluid throughout. (i) There is single stage compression followed by two 
stages of expansion in turbine. The expansion ratio in two stages is equal and reheating is done 
upto the maximum temperature at inlet of second stage of expansion. (ii) There occurs 
compression in two stages of equal compression ratio with intercooling upto the minimum 
cycle temperature at inlet to second stage of compression followed by single stage expansion 
in turbine. Take isentropic efficiency of compressor and turbine stages as ηc and ηT 
respectively. 
Q.12] In an I.C. engine operating on the dual cycle (limited pressure cycle), the temperature of 
the working fluid (air) at the beginning of compression is 27ºC. The ratio of the maximum and 
minimum pressures of the cycle is 70 and the compression ratio is 15. The amount of heat 
added at constant volume and at constant pressure are equal. Compute the air standard thermal 
efficiency of the cycle. State three main reasons why the actual thermal efficiency is different 
from the theoretical value. 
Q.13] An engine operates on Dual cycle with a compression ratio of 15. At the end of suction 
the air is available at 1 atm and 27ºC. Total heat added is 430 kJ/kg. Heat supply is in ratio of 
(0.536:1) for heat supply at constant volume and constant pressure. Determine cycle efficiency 
and mean effective pressure. 
Q.14] A diesel engine operating an air standard diesel cycle has 20cm bore and 30cmstroke. 
The clearance volume is 420cm3.if the fuel is injected at 5% of the stroke, find the air standard 
efficiency. 
q.15] An Engine working on Otto cycle has a volume of 0.45 m3, pressure 1 bar and 
Temperature 30OC, at the beginning of compression stroke. At the end of Compression stroke, 
the pressure is 11 bar and 210 KJ of heat is added at constant Volume. Determine i) Pressure, 
temperature and volumes at salient points in the cycle. ii.) Efficiency.