Benha University Subject: Turbo- Machine

Faculty of Engineering- Shoubra Year : fourth Mech. Power

Mech. Power Department 2007/2008

Sheet No (2)

  1. An ideal, basic, air standard gas turbine engine has a compressor inlet temperature of 288 K and a turbine inlet temperature 1400 K. Calculate, assuming that Cp = 1.005 kJ/kg K, k =1.4 and that air enters the compressor at the rate of 1 kg/s,:

a- the pressure ratio that gives the maximum net work

b-  the compressor work, turbine work, heat added, and thermal efficiency for the pressure ratio found in (a)

c-  the power, in kilowatts, developed by this engine.

2- A n ideal, basic, air standard gas turbine engine has a compressor inlet temperature of 288 K and a

turbine inlet temperature 1400 K. Assuming variable specific heats and that air enters the compressor at the rate of 1 kg/s, calculate the compressor work, net work, heat added, thermal efficiency and power develop by this engine for

(a)  a compressor the pressure ratio of 15.9

(b)  a compressor the pressure ratio of 12.0

(c)  a compressor the pressure ratio of 4.0

  1. An ideal, basic, air standard gas turbine engine has a compressor inlet temperature of 288 K, a compressor efficiency of 87%, a gas generator turbine efficiency of 89%, and a power turbine efficiency of 89%. The compressor pressure ratio is 12.0. Assuming variable specific heats, a turbine inlet temperature 1400 K, a compressor inlet pressure 101.3 kPa, and that air enters the compressor, at the rate of 1 kg/s, calculate:

a- the pressure and temperature leaving the gas generator turbine

b- the net power, rate at which heat is added, and cycle thermal efficiency assuming no pressure drop during the addition process and that the pressure at the power turbine exit is 101.3 kPa.

d-  the net power, rate which heat is added, and cycle thermal efficiency if there is a 3% pressure drop in the combustion chamber and the power turbine exit pressure is 1 % above the compressor inlet pressure.

4- A gas turbine engine operating on the basic cycle has a compressor inlet pressure of 101.3 kPa, temperature of 288 K , the compressor exit and turbine pressure of 1215.6 kPa, a turbine inlet temperature of 1400K a turbine exit pressure of 101.3 kPa, a compressor efficiency of 87% and gas generator turbine and power turbine each with an efficiency of 89%.The fuel, supplied as a liquid at 298K, is n-octane,C8H18. If the air enters the compressor at the rate of 1.0 kg/s, calculate, considering the actual product gas expanding through the turbine.

a-  the percent excess air supplied

b-  the net work developed per kg of air entering the compressor

c-  the thermal efficiency based on the lower heating value

d-  the power developed in horsepower and kilowatts.

e-  The specific fuel consumption

f-  The heat rate.

5- Solve problem 4 using an air-equivalent technique. Assume when determining the mass of fuel added, that the fuel is liquid C8H18 supplied at 298 K and that the fuel has lower heating value of 44 400 kJ/kg.

6-An air standard gas turbine engine operates on the regenerative cycle. The compressor inlet temperature is 288K, compressor efficiency is 87%, turbine inlet temperature is 1400K, gas generator turbine efficiency is 89%, and power turbine efficiency is 89%. Calculate, assuming that p1=p5=p5.5=101.3 kPa, p2=p2.5=p3=405.2kPa, and air enters the compressor at the rate of 1 kg/s, the net work, heat added, thermal efficiency, and power developed in kW if the regenerator effectiveness is 75%. Compare with the results for a cycle without a regenerator. Neglect the mass of the fuel added.

7- An air standard gas turbine engine operates on the regenerative cycle. The compressor inlet temperature is 288K, compressor efficiency is 87%, turbine inlet temperature is 1400K, gas generator turbine efficiency is 89%, and power turbine efficiency is 89%. Assuming that 2.0% of air leaving the compressor leaks to state 5.5 from state 2. Assume that no energy is transferred to this air; that is, it leaks from state 2 to the pressure at state 5.5 with no change in temperature. Calculate assuming p1=p5=p5.5=101.3 kPa, p2=p2.5=p3=405.2kPa, and air enters the compressor at the rate of 1 kg/s, the net work, heat added, thermal efficiency, and power developed in kW if the regenerator effectiveness is 85%. Neglect the mass of the fuel added. Compare with the answers with those of problem 6.

8-An air standard gas turbine operates on the cycle of a gas turbine with intercooling. Known values are :

T1 =288K hc1 =87% p1 =p5 =101.3 kPa

T1.5=288K hc2 =87% p2 =p3 =1215.6kPa

T3 =1400K hcGT=87% p1.1=p1.5=350.9 kPa

hcPT=87%

Calculate, on a basis of 1 kg/s of air entering the first compressor and neglecting the fuel added:

a-  the optimum intercooler pressure

b-  the total compressor work

c-  the net power

d-  the cycle thermal efficiency

e-  compare the results with a basic gas turbine operating with the same overall pressure ratio, compressor and turbine inlet temperatures, and efficiencies.

9- An air standard gas turbine operates on the cycle of a gas turbine with reheat. Known values are :

T1 =288K hc =87% p1 =p5 =101.3 kPa

T3 =1400K hcGT =89% p2 =p3 =1215.6kPa

T4.5 =1400K hcPT=89%

Calculate, on a basis of 1 kg/s of air entering the compressor and neglecting the fuel added:

a-  the optimum reheat pressure

b-  the net power

c-  the cycle thermal efficiency

d-  compare the results with a basic gas turbine operating with the same overall pressure ratio, compressor and turbine inlet temperatures, and efficiencies.

10- An air standard gas turbine operates on the cycle of a gas turbine with intercooling and reheat. Known values are:

T1 =288K hc1 =87% p1 = p5 = p6 =101.3 kPa

T1.5 =288K hc2 =87% p1.1 =p1.5 =350.9kPa

T3 =1400K hcT2=89% p2 =p2.5 = p3 =1215.6kPa

T3.5 =1400K hcT2=89% p3.1 =p3.5

hcPT=89%

Calculate, on a basis of 1 kg/s of air entering the first compressor and neglecting the mass of fuel added:

a-  the total compressor work

b-  the net power

c-  the specific power developed by this engine

d-  the cycle thermal efficiency

e-  compare the results with a basic gas turbine operating with the same overall pressre ratio, compressor and turbine inlet temperatures, and efficiencies.