Perform appropriate gas turbine engine analysis data is give

Perform appropriate gas turbine engine analysis (data is given).

Use the following data to analyse the GT100s gas turbine. Source (with references including this assignment brief) any appropriate equations you needed for your analysis.

Speed

1000’s of rev/min

T₁

^oC

T₂

^oC

T₃

^oC

T₄

^oC

P₁

mbar

gauge

P₂

bar

gauge

P₃

bar

gauge

P₄

mbar

gauge

Nozzle 100%

85

22

109

524

474

22.9

0.84

0.72

53

100

22

136

570

498

34.6

1.26

1.1

87

Nozzle 85%

85

22

107

528

451

22.9

0.85

0.73

60

100

22

139

585

498

34.6

1.25

1.1

100

Speed

1000’s of

rev/min

Mass flow rate

gram / s

Air flow rate kg / s

T_2i

^oK

?_i

%

Power to drive

compressor

W

Nozzle 100%

85

2.14

0.26

100

2.95

0.33

Nozzle 85%

85

2.21

0.27

100

2.94

0.33

c_p = 1005 J/kgK

Atmospheric pressure from barometer:         p_atmos= 1.013 bar

Guidance

Isentropic efficiency of a centrifugal air compressor (GT100S gas turbine)

Centrifugal compressor

Axial compressor fitted to a gas turbine

Theory: In reversible work transfer processes, the system passes from its initial to final state through a series of equilibrium states in which the properties are equal throughout the system at any given instant. There is no heat transfer (Q = 0) and it is assumed that there is no friction. A process in which there is no heat transfer is known as an adiabatic process. A reversible adiabatic process without friction is known as an ISENTROPIC PROCESS. This is the IDEAL WORK TRANSFER PROCESS.

Real processes are never reversible, and the compression processes of centrifugal compressors in particular, involve considerable turbulence and fluid friction. This means that during an actual irreversible compression process, frictional heating of the air produces a temperature rise that is greater than that which would have been produced if the process had been carried out reversibly without friction and turbulence.

The temperature at the end of a reversible adiabatic process, i.e. an ISENTROPIC process, may be calculated for IDEAL GASES from the equation:

T_2i/ T₁= (p₂/ p₁)⁽?^{– 1)/} ? where ? = 1.4 for air.

? The temperature at the end of an isentropic compression process = T_2i = T₁(p₂ / p₁)⁽? ^{– 1)/} ?

The SFEE is:           Q – W = ?PE + ?KE + ?H                   where ?H = mc_p(T₂ – T₁)    for a perfect gas.

But Q = 0 for an adiabatic process and ?PE and ?KE can be assumed negligible in this case, hence:

The REAL WORK required to compress the air = W_real = mc_p(T₂ – T₁) / kg

where T₂ = the temperature of the air at the end of the actual compression process,

And the IDEAL WORK required to compress the air = W_isen = mc_p(T_2i – T₁) / kg

where T_2i = the temperature of the air at the end of the ideal ISENTROPIC compression process.

Note that T₂ > T_2i due to the frictional heating of the air in the actual compression process.

  

Then the isentropic efficiency ?_i = W_isen / W_real = (T_2i – T₁) / (T₂ – T₁)

Absolute pressure (p) = gauge pressure (p_g) + atmospheric pressure.    

Note that p = p_g + p_atmos                                      

Temperature at the end of an isentropic compression process = T_2i = T₁(p₂ / p₁)⁽ ? ^{– 1)/}?

The isentropic efficiency ?_i = W_isen / W_real = (T_2i – T₁) / (T₂ – T₁)

Actual Power required to drive compressor = m(dash)c_p(T₂ – T₁)                     

For the task you are recommended to examine how the isentropic efficiency and compressor power change with rev/min, and then draw key conclusions.

Speed 1000’s of rev/min	T1 oC	T2 oC	T3 oC	T4 oC	P1 mbar gauge	P2 bar gauge	P3 bar gauge	P4 mbar gauge
Nozzle 100%
85	22	109	524	474	22.9	0.84	0.72	53
100	22	136	570	498	34.6	1.26	1.1	87
Nozzle 85%
85	22	107	528	451	22.9	0.85	0.73	60
100	22	139	585	498	34.6	1.25	1.1	100

Solution

i) What material properties should an engineer focus on to cope with the high rotational speed and high blade loading?

ii) What is the expression for the \"flow coefficient\"?

iii) What is the expression for \"stage loading coefficient\"?

iv) Given a turbine row with constant axial velocity of 150m/s at 5000 rpm on a mean radius of 0.7m and an absolute flow an absolute flow angle at exit from the stator of 70°. The turbine operates with axial leaving flow and is a repeating stage. Calculate the flow coefficient and the stage loading coefficient.

Analyse your results and comment.