Ex. 11a

A gas turbine drives an air-compressor and an electricity-generator. The compressed air flows from the compressor to an isobaric combustion chamber. The temperature of the exhaust gases behind the combustion chamber is 900 °C. The hot exhaust gases flow into the turbine and expand to the ambient pressure. The other parameters of the system are as below:

p_a=1 bar

t_a=15 °C

V_air=27000 m³/h - at the ambient conditions !!!

p_{combustion chamber} =8 bar

HHV=40 MJ/kg

η_iC=0,83

η_mC =0,91

η_iT =0,88

η_mTt=0,95

η_CC =0,95

η_G =0,98

R= 287 J/kgK for the air

- for the air

c_pair=1,0045 kJ/kg - the average specific heat for the air

- for the exhaust gases

c_ps=1,08 kJ/kg - the average specific heat for the exhaust gases

Calculate:

A) Electric power P_e

B) The air flow at the standard conditions if P_Gel= 100 MW; standard conditions: 1013 hPa, 273,15 K

Paliwo: fuel

Powietrze: airEx. 13a

The air is compressed from the ambient conditions (t_a=15 °C, p_a=950 hPa) up to p₂=12 bar with the internal adiabatic efficiency of the compressor η_iC=0,8. The air flow into the combustion chamber where a gaseous fuel of HHV=48 MJ/kg and LHV ≈44 MJ/kg is combusted. The temperature of the exhaust gases after the compressor chamber is T₃=1200 K. The gases expand at the gas-turbine to the ambient pressure. The temperature of the exhaust gases behind yhe turbine is 720 K and the flow is directed into a heat exchanger to generate hot water. The mechanical efficiency of the compressor is η_mC=0,99 and of the turbine η_mT=0,992. The electricity generator efficiency is η_G=0,97. Neglect energy losses at the combustion chamber. Assume: the average specific heat of the air c_paur av=1,005 kJ/kgK and of the exhaust gases c_{peg av}= 1,08 kJ/kgK. The isentropic exponent for the air is k=1,4 and assume k=1,38 for the exhaust gases.

Obliczyć:

1. Estimate a polytrophic efficiency of the compressor

2. Calculate:

1. Mechanical power at the shaft of the gas-turbine if the mas flow of the air at the compressor is m₁=150 kg/s

2. The flow of the air at the compressor m₁ if the power output from the generator is P_e=50 MW

3. For both cases: 2(a) and 2(b) estimate amount of the heat exchanged with the water if the temperature of the exhaust gases after the heat exchanger is 85 °C.

4. For both cases: 2(a) and 2(b) calculate electric efficiency of the plant and the overall efficiency of the plant as the CHP system.

Ex. 22 - (remark : I have not checked if the below data are correct)

The gas turbine drives the compressor and the generator. The compressed air is heated at the isobaric regenerator and directed into the isobaric combustion chamber. The temperature of the exhaust gases after the combustion chamber is 930 °C. The exhaust gases expanded at the turbine flow into the regenerator to heat the compressed air. The following data are available:

- ambient pressure 1 bar

- ambient temperature 15 °C

- air flow into the compressor 7,774 m³/s (at standard conditions 1013 hPa, 273,15 K)

- compressed air pressure 8 bar

- fuel consumption 574 kg/h

- HHV 40 MJ/kg

- internal adiabatic efficiency of the compressor η_iC=0,83

- mechanical efficiency of the compressor η_mC=0,98

- internal efficiency of the turbine η_iT=0,88

- mechanical efficiency of the turbine η_mT=0,99

- average specific heat of the air and the exhaust gases (estimation) c_pair = c_peg = 1005 J/(kg K)

- regenerator efficiency 0,98

- combustion chamber efficiency 0,95

Calculate:

1) Outlet temperature of the exhaust gases and the Δt_ln for the counter-flow structure of the heat exchanger

2) the system efficiency (as a power plant)

Ex. 20

The piston engine of the jump volume V_sk=0,05 m³ and compression factor ε=V₁/V₂=6. works with the frequency of C=2 cycles/s. The engine operates according to an Otto cycle, working fliud is an ideal diatomic gas, and the minimum and the maximum temperatures of the ccle are T₁=300 K, T₃=2100 K. The lowest pressure at the engine is p₁=0,10 MPa.

Calculate:

1) theoretical power output

2) theroretical efficiency of the engine.

Ex. 20a

The piston engine of the jump volume V_sk=0,05 m³ and compression factor ε=V₁/V₂=6. works with the frequency of C=2 cycles/s. The engine operates according to a Sabathe cycle, working fluid is an ideal gas of k=1,35, and the minimum and the maximum temperatures of the ccle are T₁=300 K, T₃=2400 K. The lowest pressure at the engine is p₁=0,10 MPa and the load factor is ϕ=V₄/V₃=2.

Calculate:

1) theoretical power output

2) theoretical efficiency of the engine.

Ex. 54

A rocket engine is fired with ethyl alcohol, the gas constant for the exhaust gases is R_eg=305 J/kgK and isentropic exponent is k=1,2. The parameters at the combustion chamber are: p₀=20 bar, T₀=3000K. The exhaust gases outflow is
=125 kg/s. The maximum speed of the flight is c=1500 m/s. Calculate the maximum power output of the rocket.

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