THERMODYNAMIC ANALYSIS OF GAS TURBINE
INTRODUCTION
The gas turbine is also the most powerful turbomachinery on the market today. In critical industries such as power generation, oil and gas, process plants, transportation, as well as domestic and smaller associated industries, it can be used in a variety of modes.
A gas turbine combines air, which it compresses in its compressor module, with gasoline, which is then ignited. The gases that result are extended using a turbine. The turbine’s shaft begins to spin, moving the compressor on another shaft, and the process begins. The first rotor motion is generated by a separate starter unit before the turbine’s Irotation achieves design speed and can hold the whole unit going.
Solar turbines has developed the Mercury 50 PG recuperated gas turbine as part of its contribution to the US Department of Energy’s Advanced Turbine Systems (ATS) program (Solar Turbines Incorporated, 2020).
This gas turbine has a 10 stage axial compressor with variable inlet guidance vanes, an annular type combustor that runs on Natural Gas (you can approximate this as pure Methane), a 2 stage reaction turbine, and a Main Surface type recuperator that runs on Natural Gas (you can approximate this as pure Methane).
Figure 1 Section View of Mercury 50 PG recuperated gas turbine (Solar Turbines Incorporated, 2020)
THEORY
Compressor, rotor, and combustion chamber make up a gas turbine. Two isentropic and two isobaric cycles make up the basic gas turbine cycle. However, there are certain differences between the real gas turbine cycle and the perfect Brayton cycle. The deviations will be shown in the diagram below. The reasons for the anomalies are also attributed to irreversibilities.
Figure 2 Basic cycle of gas turbine
Figure 3 TS diagram of the basic cycle
In a gas turbine, reheating is used to improve the turbine work without increasing the compressor work or melting the turbine components. A reheater can be used efficiently when a gas turbine plant has both a high and low pressure turbine. Reheating will boost productivity by as much as 3%. The movement between the high and low pressure turbines is reheated by a reheater, which is a combustor. A heat exchanger is used in intercooling to cool the compressor gases during the compression process. When the compressor has both a high and low pressure unit, an intercooler can be placed between them to cool the flow. The work required for compression in the high-pressure unit would be reduced as a result of this cooling procedure. Water or air should be used as a cooling fluid. Sea water is used to cool the fluid in marine gas turbines. It has been discovered that a good intercooler installation will raise gas turbine performance.
Figure 4 Gas turbine cycle with reheat
Figure 5 TS DIAGRAM OF REHEAT CYCLE
GIVEN DATA
Power output (100% Load) | 4600 kWe |
Ambient Temperature | 15°C |
Ambient Pressure | 101.325 kPa |
Compressor Pressure Ratio | 9.9: 1 |
Compressor Isentropic Efficiency (overall) | 87% |
Combustor Pressure Loss (AP/P_in) | 0.03 |
Fuel Lower Heating Value | 50 MJ/kg |
Turbine Inlet Temperature | 1275 K |
Turbine Isentropic Efficiency (per stage) | 89% |
Exhaust (to atmosphere) Temperature | 365°C |
Table 1 Operating parameters and key component performance (Solar Turbines Incorporated, 2018)
THERMODYNAMIC ANALYSIS
1. BASIC CYCLE
A basic cycle analysis of the Mercury 50 gas turbine using the data supplied below (Solar Turbines Incorporated, 2018) to calculate:
- Inlet mass flow rate of air required to give the rated power output
Power Output = 4600 Kwe
Pressure ratio = 9.9
No. of stage = 10
Pressure ratio % = (9.9)1/10 = P2 / P1 = 1.27
Work done by compressor /stage = {ma x Cpa x [(P2/P1)(1.4-1)/1.4 – 1] x T1} / ⴄ isen
= { ma x 1.005 x [(1.27)(1.4-1)/1.4 – 1] x 288 } / 0.87
Work done by 10 stages = ma x 1.005 x 21.79 x 10 Kw
Work done by Turbine = {ma x Cpa x [T3 – (P4/P3’)(1.4-1)/1.4 – 1] x T1} x ⴄ isen
= {ma x 1.005 x [1275 – (1/9.6)(1.4-1)/1.4 – 1] x T1} x 0.87
P3 = 0.03 x 9.9 x 101.325 = 30.09 Kpa
P3’ = 973.11 Kpa
= 9.9 x 101.325 – 30.09
= 973.11 Kpa
= ma x 1.005 x [1275 – 668.13] x 0.89
= ma x 540.11 x 1.005
4600 = ma [ 540.11 – 217.9 ] x 1.005
ma = 14.2 kg/s
- The recuperator effectiveness
T5 = 365 + 273 = 638 k
T2’ = 308.35k
T4’ = 734.88k
Tx = 405.23k
ⴄ isen = (T2-T1) / (T2’-T1)
0.87 = { [(P2/P1)y-1/y – 1] x 288 } / T2’ – 288
0.87 = { [(1.27)1.4-1/1.4 – 1] x 288 } / T2’ – 288
T2’ – 288 = 20.35
T2’ = 308.38 k
0.89 = 1275 T4’ / [1275 – {[(1/9.6)1.4-1/1.4 – 1]}
T4’ = 734.88k
Tx –T2’ = T4’ –T 5
= 734.88 +308.35 – 638
= 405.23k
ᴇ = (405.23 – 308.35) / (638 – 405.23)
ᴇ = 0.41
- The cycle thermal efficiency
ⴄ = 4600 / (ma x cp x (T3- Tx)
ⴄ = 4600 / (14.22 x 1.005 x (1275- 405.23)
ⴄ = 37.05 %
2. REHEAT CYCLE
Assumptions for the Reheat cycle:-
- Inlet mass flow rate and recuperator effectiveness are the same as you calculate above
- Component efficiencies do not change
- Loss are unchanged
- Compressor pressure ratio is unchanged and the pressure ratio over the two turbine stages is equal
WT = ma x cp x [T3 – (P4/P3) y-1/2y. T3 ] x 2 x0.89
WT = 14.22 x 1.005 x 1275 [1 – (1/9.6) 1.4-1/2×1.4] x 2 x0.89
WT = 8955.09 Kw
Wc = 14.22 x 1.005 x [217.9]
= 3114.03 Kw
WT = 8955.09 Kw – 3114.03 Kw
= 5841.06 KW
Power Uplift = 5841 – 4600
Power Uplift = 1240 KW
T4’ = 961.72 k
T2’ = 308.35 k
0.89 = (T3 – T4’)/(T3 – T4)
0.89 = (T3 – T4’)/352
0.89 x 352 = T3 – T4’
T4’= 1275 – 0.89 x 352
T4’ = 961.72 k
Tx – T2’ = T4’ – T5
Tx = 961.72 – 638 + 308.3
Tx = 632.07 k
ⴄ = 5841.06/(ma x cp x (1275-632.07)+ma x cpx (1275-961.72)
= 0.427
ⴄ = 42.7%
RESULTS AND DISCUSSION
From the above calculations, for the basic cycle mass flowrate is 14.22 kg/s , recuperator effectiveness is 0.41, cycle efficiency is 37.05 %.
So as of reheat cycle the power has been uplift to the 5841KW which is 1200kw more than the basic cycle. The efficiency of the cycle becomes 42.07% which is 5% more than the basic one.
CONCLUSION
By introducing the reheat into recuperated gas turbine the efficiency has been improved by 5% and the power has been uplifted to 26%. Hence the reheat cycle has given a suitable profit to the cycle but the power consumption and area of the components has been increased. That’s the overall efficiency has not been increased much.
REFERENCES
- Solar Turbines Incorporated., 2018. Mercury 50 — Recuperated Gas Turbine Generator Set I Solar Turbines. [online] Solarturbines.com. Available at: http://s7d2.scene7.com/is/content/Caterpillar/CM20150710-52396-21070
- Solar Turbines Incorporated., 2020. Mercury 50 – Power Generation Packages I Solar Turbines. [online] Solarturbines.com. Available at: https://www.solarturbines.com/en US/products/power-generationpackaRes/mercurv-50.html
- V. Tara Chand, B. Ravi Sankar and M. Ramanjaneya Reddy (2013), First Law and Second Law Analysis of Gas Turbine Plant. International Journal of Mechanical Engineering and Research. ISSN No. 2249-0019, Volume 3, Number 4 (2013), pp. 415-420 [2]
- M.K.Pal, H.Chandra and A.Arora (2014), Second Law Analysis of Gas Based Thermal Power Plant to Improve Its Performance. International Journal of scientific research and management (IJSRM) ||Volume||2||Issue||3 ||Pages|| 688-682||2014||