# Prof. K. M. Joshi

## Head, T&P Cell Asst. Professor (MED), S.S.A.S. Inst. of Tech., Surat.

### Tutorial-2 Gas Cycle Last date of checking:13/3/14

1.         What is an air-standard cycle? What is an air-standard efficiency? State the assumptions made for analysis of air standard cycles.

2.         Explain the Otto cycle (Or What is the air-standard cycle of spark ignition engine ? What are its four processes?). Drive the equation of ideal efficiency and mean effective pressure of Otto cycle.

3.         Find out the value of compression ratio for the maximum work done in Otto cycle working betn temp. limit of Tmax and Tintake. Also find the value of intermediate temp.
Ans. r = (Tmax/Tintake)1.25

4.         Explain the mixed or dual cycle and drive the equation of efficiency.

5.         State the four processes of the Diesel cycle. Derive an expression for the efficiency of Diesel cycle in terms of the compression ratio r, the cut-off p and Y. Also drive the expression for m.e.p.

6.         Explain the Atkinson cycle and drive the equation of efficiency.

7.         Explain with p-v and t-s diagram the working of Simple gas turbine (Brayton) cycle and drive the equation of efficiency.

8.         Find out the value of pressure ratio rp  for optimum work done in Brayton cycle working betn upper limit and lower limit temp. T3 and T1. Also find the value of intermediate temp.

9.         Give the comparison between Otto Dual and Diesel cycles by considering following parameters. (i) pressure ratio, (ii) Heat added  (iii) Heat Rejected (iv) maximum pressure and (v) maximum temperature.

Examples:

1.     In a Carnot cycle, the maximum pressure and temperature are limited to 18 bar and 410°C. The ratio of isentropic compression is 6 and isothermal expansion is 1.5. Assuming the volume of the air at the beginning of isothermal expansion as 0.18 m3. Determine the temperature and pressures at main points in the cycle.

Ans   P1= 18 bar; P2=12 bar; P3=0.97 bar; P4=1.46bar; T1=T2=683K; T3= T4=333.2 K

2.     A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by 70°C, its efficiency is doubled. Find the temperature of the source and the sink.

Ans: T2= 1442°C; T1 = 1785 °C

3.     The minimum pressure and temperature in an Otto cycle are 100 kPa and 27°C. The amount of heat added to the air per cycle is 1500 kJ/kg. (i) Determine the pressures and temperatures at all points of the air standard Otto cycle. (ii) Also calculate the specific work and thermal efficiency of the cycle for a compression ratio of 8 : 1.

Take for air : cv = 0.72 kJ/kg K, and g = 1.4.

Ans: T2 = 689.1 K; p2 = 18.379 bar; T3 = 2772.4 K; P4 = 4.023 bar; Sp work = 847 kJ/kg; Thermal effi = 56.47%.

4.     An air standard Otto cycle has a volumetric compression ratio of 6, the lowest cycle pressure of 0.1 MPa and operates between temperature limits of 27°C and 1569°C.

(i) Calculate the temperature and pressure after the isentropic expansion (ratio of specific heats = 1.4).

(ii) Since it is observed that values in (i) are well above the lowest cycle operating conditions, the expansion process was allowed to continue down to a pressure of 0.1 MPa. Which process is required to complete the cycle? Name the cycle so obtained.

(iii) Determine by what percentage the cycle efficiency has been improved.

Ans: T4=900 K; P4=3 bar. Otto effi = 51.16%; Atkinson effi = 59.29%

5.     An ideal Diesel cycle with air as the working fluid has a compression ratio of 18 and a cut off ratio of 2. At the beginning of the compression process, the working fluid is at 14.7 psia, 80°F, and 117 in3. Utilizing the cold-air standard assumptions, determine (a) the temperature and pressure of air at the end of each process, (b) the net work output and the thermal efficiency.

Note: Rankine [°R] = Fahrenheit [°F]  + 460; mass, m = 0.00498 lbm;

Cv = 0.240 Btu/lbm.°R; Cp = 10.171 Btu/lbm.°R.

Ans: P1=14.7psi; T1=540°R; P2=P3841psi; T2=1716°R; T3=3432°R; P4=38.8psi; T4=1425°R; Wnet=1.297Btu; thermal effi=63.2%

6.     A perfect gas undergoes a cycle which consists of the following processes taken in order: (a) Heat rejection at constant pressure.

(b) Adiabatic compression from 1 bar and 27°C to 4 bar.

(c) Heat addition at constant volume to a final pressure of 16 bar.

(d) Adiabatic expansion to 1 bar.

Calculate: (i) Work done/kg of gas. (ii) Efficiency of the cycle.

Take : Cp = 0.92, Cv = 0.75.

Ans: 282600N.m/kg; 32.6%

7.     An isentropic air turbine is used to supply 0.1 kg/s of air at 0.1 MN/m2 and at 285 K to a cabin. The pressure at inlet to the turbine is 0.4 MN/m2. Determine the temperature at turbine inlet and the power developed by the turbine. Assume Cp= 1.0 kJ/kg K.

Ans:T3=423.5K;P=13.85KW

8.     8. Consider an air standard cycle in which the air enters the compressor at1.0 bar and 20°C. The pressure of air leaving the compressor is 3.5 bar and the temperature at turbine inlet is 600°C. Determine per kg of air: (i) Efficiency of the cycle, (ii) Heat supplied to air, (iii) Work available at the shaft, (iv) Heat rejected in the cooler, and (v) Temperature of air leaving the turbine.

For air γ = 1.4 and Cp = 1.005 kJ/kg K.

Ans:30%; Qa=456.27kJ/kg; Work = 136.87kJ/kg; Qr = 319.39kJ/kg; T4=610.5K

### Tutorial-1 Vapour Cycle     Last date of submission:27/1/14

1.   Draw the Carnot and Rankine cycle on three different usual thermodynamic planes.

2.   With suitable T- S diagram explain the method of improving efficiency of Rankine cycle.                                   Or
Discuss the temperature and entropy diagram for the effect of various operating variables on the efficiency of Rankine cycle.     Or      Explain Regenerative and Reheating in Rankine cycle with the help of suitable diagram.

3.   Right a short note on the modification in Rankine cycle.

4.
Why Carnot cycle is not considered as an ideal cycle for Power Plant ? Or Limitation of Carnot cycle.

5.   Comparision between Carnot and Rankine Cycle. Or Advantages of Rankine cycle over Carnot Cycle.

6.   How actual vapour cycle is differ from the ideal cycle ? Explain in detail.

Examples

1. In a Rankine cycle the steam at inlet to turbine is saturated at a pressure of 35 bar and the exhaust pressure is 0.2 bar. Determine (1) the pump work, (2) turbine work, (3) Rankin efficiency, (4) condenser heat flow, (5) dryness at the end of expansion. Assume flow rate of 9.5 Kg/s.
Ans: Pump work = 33.63kW Turbine work = 7486 kW, Rankine efficiency =30.78% Condenser heat flow = 1675kW

2. A Carnot cycle works on steam between the pressure limits of 7 MPa and 7kPa. Determine the efficiency turbine work and compression work par kg of steam
Ans: Turbine work =963.2 KJ/Kg Compression work =303.8 KJ/Kg Thermal efficiency =44.2%

3. Determine the cycle efficiency and steam consumption in Kg/W hr for Carnot cycle and Rankine cycle using steam between pressure of 35 bar saturated and 0.07 bar Also find the pump work required in each case.
Ans: (Carnot) Pump work = 211.85kj/kg (Carnot) efficiency = 39.39%
(Rankin) pump work =3.517 KJ/Kg (Rankin) efficiency = 34.092%
(Carnot) steam rate =5.217 Kg/kWh (Rankine) steam rate = 4.007
Kg/kWh

4. Steam at 16 bar pressure and 340°C temperature is expanded in a steam turbine to 0.07 bar pressure. It then enters to a condenser where it is condensed to saturated liquid the pump feeds back the water onto the boiler (1) Assuming ideal processe. Find per kg of steam the net work and the cycle efficiency (2) if the turbine and the pump have each 83% efficiency find the percentage reduction in the net work and cycle efficiency.
Ans: (1) Pump work =165.004 KJ/Kg turbine work 920.08kj/kg heat supplied = 2914.816 KJ/Kg cycle efficiency = 31.56% (2) reduction in work output 17.065% reduction efficiency 16.83%

5.  A Rankine cycle operates between 1 bar and 100 bar in which the pump has an isentropic efficiency of 80% what must be the isentropic efficiency of the turbine if the moisture contents in the not to exceed 10% what wiil be the thermal efficiency of the cycle
Ans: Thermal efficiency =11.26%

6.   In a thermal power plant employing ideal Rankin cycle superheated steam at 20 bar and 400°C is produced in the boiler and the condenser is operated at 0.2 bar. Calculate the quality of steam at the turbine outlet and the thermal efficiency of the cycle.                                                              Ans: Thermal efficiency =29.9%

7.   An ideal Rankine cycle producing 20MW net power is equipped with a boiler which generates steam at 50 bar and 500°C and condenser which operates at 0.1 bar. Calculate the energy added in boiler per kg of water, thermal efficiency of cycle, the mass flow rate of steam in kg/s and mass flow rate of cooling water in condenser if the cooling water enters the condenser at 30°C and leaves at 40°C.
Ans. Energy added in boiler = 3236.86 KJ/kg; Thermal efficiency =37.65%; mass flow rate of water = 16.42 kg/s; mass flow rate in cooling tower = 793.09 kg/s

8. In thermal power plant operating on a Rankine superheated steam at 50 bar and 500°C enters in turbine having isentropic efficiency of 0.8 The condenser which is operated @ 0.05 bar delivers saturated liquid to a feed pump having isentropic efficiency of 0.7. Determine the thermal efficiency of power plant and mass flow rate  of steam required for 50 MW net power generation.
Ans: efficiency =31.56 %  and mass flow rate of steam = 48.17 kg/s