# Parametric Analysis of a Two-Shaft Aeroderivate Gas Turbine of 11.86 MW

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

_{4}, as the main parameters, whose studied values are taken from the manufacturer operational recommendations. This analysis considers the existence of pressure drops in the combustion chamber as well as in the LPT and is carried out for compressor and turbine isoentropic efficiencies of 0.85 and 0.80, respectively.

_{2}, and the compressor suction pressure, P

_{1},

_{1}, and the technological parameters ${\pi}_{C}$ and ${\eta}_{C}$.

_{4}and P

_{4}, can be found from the LPT pressure ratio, π

_{LPT}; and the useful output specific work generated by the power turbine can then be written as follows

## 3. Exergetic Analysis

_{r}, the maximum rate of conversion from thermal energy to work is

_{0}is used as the other thermal energy reservoir, and it can be expressed as

_{3}.

#### 3.1. Gas Turbine

_{HPT}, is the frictional reheat, which is defined as ${r}_{HPT}={h}_{4}-{h}_{4s}$.

#### 3.2. Compressor

_{C}is the frictional reheat of the compression process, which is defines as ${r}_{C}={h}_{2}-{h}_{2s}$.

_{C}/i

_{C}increases as the compressor efficiency decreases due the increase of the irreversibilities in the compressor and the frictional reheat; likewise, by decreasing the compressor efficiencies and also decreasing r

_{HPT}/i

_{HPT}, since the increase of the irreversibilities is higher than the increase the frictional reheat. For a compressor efficiency of 0.86, the value of r

_{C}/i

_{C}is of 2.27 and the value exergetic efficiency of the compressor of 0.938. Indeed, a 0.84% reduction in the compressor efficiency can be observed that the r

_{C}/i

_{C}is increased 0.98%, due that the frictional reheat increase 17.01% and the irreversibilities only 15.8%; nevertheless, the exergetic efficiency of the high pressure turbine is not affected in great measure. As result of an increase of 7% of the irreversibilities in the high pressure turbine, the r

_{HPT}/i

_{HPT}decreases 1.1%.

_{LPT}/i

_{LPT}increases as the compressor efficiency decreases due to the increase of the irreversibilities in the low pressure turbine and the frictional reheat; likewise, by decreasing the turbine efficiencies and also decreasing r

_{HPT}/i

_{HPT}, since the increase of the irreversibilities (i

_{HPT}) is higher than the increase the frictional reheat (r

_{HPT}). For a turbine efficiency of 88%, the value of r

_{LPT}/i

_{LPT}is of 2.5795 and the value exergetic efficiency of the low pressure turbine of 0.9498. Indeed, reducing the turbine efficiency from 88% to 86% the r

_{LPT}/i

_{LPT}increases 1.07%, due that the frictional reheat increase 13.98% and the irreversibilities 12.77%. Nevertheless, the exergetic efficiency of the high pressure turbine decreases 0.73% and the r

_{HPT}/i

_{HPT}decreases 1.209%, a result of the increase of 20.84% in the irreversibility in the high pressure turbine.

**Figure 4.**Variation of exergetic efficiencies of compressor and low and high pressure turbines as function of ratio of reheat degree and irreversibility for different compressor and turbine efficiencies.

Engine Components | Energy | Irreversibility | Exergetic Efficiency |
---|---|---|---|

Compressor | ${w}_{C}=\frac{{c}_{pa}{T}_{1}}{{\eta}_{C}}\left({\pi}_{C}^{x}-1\right)$ | ${i}_{C}={\epsilon}_{1}-{\epsilon}_{2}+{w}_{C}$ | ${\phi}_{C}=\frac{{\epsilon}_{2}-{\epsilon}_{1}}{{w}_{C}}$ |

Combustion chamber | ${q}_{in}={c}_{Pg}{T}_{1}\left[y-1-\frac{1}{{\eta}_{C}}\left({\pi}_{C}^{x}-1\right)\right]$ | ${i}_{cc}={\epsilon}_{2}-{\epsilon}_{3}+{\epsilon}_{f}$ | ${\phi}_{cc}=\frac{{\epsilon}_{3}}{{\epsilon}_{2}-{\epsilon}_{f}}$ |

High pressure turbine | ${w}_{HPT}{\eta}_{m}={w}_{C}$ | ${i}_{HPT}={\epsilon}_{3}-{\epsilon}_{4}-{w}_{HPT}$ | ${\phi}_{HPT}=\frac{{w}_{HPT}}{{\epsilon}_{3}-{\epsilon}_{4}}$ |

Low pressure turbine | ${w}_{LPT}={c}_{Pg}{\eta}_{LPT}{T}_{4}\left(1-\frac{1}{{\pi}_{LPT}^{x}}\right)$ | ${i}_{LPT}={\epsilon}_{4}-{\epsilon}_{5}-{w}_{LPT}$ | ${\phi}_{LPT}=\frac{{w}_{LPT}}{{\epsilon}_{4}-{\epsilon}_{5}}$ |

## 4. Results and Discussion

_{f}/s) with respect to point b. It shows that by decreasing the high pressure turbine inlet temperature to 1100 °C keeping constant pressure ratio, the fuel flow rate increases to the 0.577 kg

_{f}/s, supplying 10% more fuel to maintain the same power on Mars 100.

_{3}. The behavior of the Figure 7 is similar to the Figure 6b due to the relationship that there is with the fuel. For the operation conditions of the turbine Mars 100, the heat rate is 12,200 kJ/kW-h (point a); with respect to π

_{C}for maximum thermal efficiency (point b), there is a variation lower to 100 kJ/kW-h.

**Figure 7.**Heat rate and thermal efficiency against compression ratio of compressor for different high pressure turbine inlet temperatures.

_{SC}effects to all components of derivate gas turbine, the results of the exergetic analysis are presented in Table 2. From this table, an increment of ${\dot{\text{I}}}_{\text{C}}$, ${\dot{\text{I}}}_{\mathrm{CC}}$, ${\dot{\text{I}}}_{\mathrm{HPT}}$ and ${\dot{\text{I}}}_{\mathrm{LPT}}$ of 20.26%, 1,5%, 7.5% and 0.14%, respectively, and the exergetic efficiencies of the low and high pressure turbines decreases in 1%, as well as η

_{C}decreases from 86% to 84% for a turbine efficiency of 85% can be observed. The heat transferred to the aeroderivate turbine increases 26.01% when the η

_{T}decreases from 86% to 76% to generate an output of 11.86 MW.

**Table 2.**Variation of exergy of heat transfer, irreversibility rate and exergetic efficiencies of the aeroderivate gas turbine components as functions of the compressor efficiency for η

_{HPT}= η

_{LPT}= 0.85.

η_{C} | ${\dot{E}}^{Q}$ (kW) | ${\dot{\text{I}}}_{\text{C}}$ (kW) | ${\dot{\text{I}}}_{\mathrm{cc}}$ (kW) | ${\dot{\text{I}}}_{\mathrm{HPT}}$ (kW) | ${\dot{\text{I}}}_{\mathrm{LPT}}$ (kW) | φ_{C} | φ_{HPT} | φ_{LPT} |
---|---|---|---|---|---|---|---|---|

0.86 | 20,190.14 | 1,112.28 | 7,919.59 | 912.20 | 816.08 | 0.94 | 0.95 | 0.94 |

0.84 | 20,963.22 | 1,337.69 | 8,038.82 | 980.60 | 814.95 | 0.93 | 0.95 | 0.94 |

0.82 | 21,845.64 | 1,590.75 | 8,178.14 | 1,059.22 | 813.73 | 0.92 | 0.95 | 0.94 |

0.80 | 22,862.27 | 1,877.49 | 8,342.24 | 1,150.43 | 812.39 | 0.91 | 0.95 | 0.94 |

0.78 | 24,046.11 | 2,205.87 | 8,537.40 | 1,257.41 | 810.91 | 0.91 | 0.95 | 0.94 |

0.76 | 25,441.93 | 2,586.66 | 8,772.14 | 1,384.46 | 809.29 | 0.90 | 0.95 | 0.94 |

_{T}decreases from 88% to 86% for a compressor efficiency of 80% can be observed. The heat transferred to the aeroderivate turbine is increased by 26.01% when the η

_{T}decreases from 88% to 86% to generate an output of 11.86 MW.

**Table 3.**Change of the exergy rate of the heat transfer, irreversibilities rate and exergetic efficiencies of components of the aeroderivate gas turbine as functions of the turbine efficiency for η

_{C}= 0.80.

η_{T} | ${\dot{E}}^{Q}$ (kW) | ${\dot{\text{I}}}_{\text{C}}$ (kW) | ${\dot{\text{I}}}_{\mathrm{cc}}$ (kW) | ${\dot{\text{I}}}_{\mathrm{HPT}}$ (kW) | ${\dot{\text{I}}}_{\mathrm{LPT}}$ (kW) | φ_{C} | φ_{HPT} | φ_{LPT} |
---|---|---|---|---|---|---|---|---|

0.88 | 17,783.42 | 1,002.16 | 7,314.01 | 611.30 | 632.66 | 0.94 | 0.96 | 0.95 |

0.86 | 19,186.12 | 1,049.58 | 7,624.87 | 773.91 | 747.49 | 0.94 | 0.96 | 0.94 |

0.84 | 20,747.46 | 1,102.37 | 7,970.88 | 961.71 | 864.47 | 0.94 | 0.95 | 0.93 |

0.82 | 22,497.97 | 1,161.54 | 8,358.82 | 1,179.99 | 983.70 | 0.94 | 0.94 | 0.92 |

0.80 | 24,476.83 | 1,228.44 | 8,797.37 | 1,435.55 | 1,105.28 | 0.94 | 0.93 | 0.92 |

**Figure 8.**Exergetic efficiency of compressor and high pressure gas turbines on irreversibility rates for different high pressure turbine inlet temperatures and pressure ratios of the compressor.

**Figure 9.**Thermal efficiency on the irreversibility rate for different high pressure turbine inlet temperatures and pressure ratios of the compressor.

**Figure 10.**Thermal efficiency on the irreversibility rate for different high pressure turbine inlet temperatures and pressure ratios of the compressor.

## 5. Conclusions

## Acknowledgements

## Author Contributions

## Conflicts of Interest

## Nomenclature

c_{p} | specific heat capacity, at constant pressure; [kJ/kgK] |

$\dot{E}$ | exergy rate; [kW] |

g | Gibbs free energy; [kJ/kg] |

h | specific enthalpy; [kJ/kg] |

HR | heat rate; [kJ/ kW h] |

i | specific irreversibility; [kJ/kg] |

$\dot{\text{I}}$ | irreversibility rate; [kW] |

$\dot{m}$ | mass flow rate; [kg/s] |

n | polytropic index; [-] |

P | pressure; [bar] |

LHV | low heating value of fuel; [kJ/kg] |

q | specific heat supplied or rejected; [kJ/kg] |

$\stackrel{.}{\text{Q}}$ | heat transfer rate; [kW] |

r | reheat degree; [kJ/kg] |

R | ideal gas constant; [kJ/kg K] |

s | specific entropy; [kJ/kg K] |

T | temperature; [°C o K] |

AFT | adiabatic flame temperature; [°C o K] |

w | specific work output; [kJ/kg] |

$\stackrel{.}{\text{W}}$ | power; [W] |

x | ratio of ideal gas constant to specific heat at constant pressure; [-] |

y | ratio of temperature inlet high pressure turbine to temperature inlet compressor; [-] |

## Greek letters

Δ | drop, increase or difference |

$\gamma $ | c _{P}/c_{v}, isentropic index; [= 1.4 air] |

$\epsilon $ | specific exergy; [kJ/kg] |

η | efficiency; [-] |

φ | exergetic efficiency; [-] |

π | pressure ratio; [-] |

τ | exergetic temperature factor; [-] |

## Subscripts

0 | dead state |

a | air |

C | compression |

cc | combustion chamber |

f | fuel |

g | exhaust |

in | added |

m | mechanical |

max | maximum |

p | product |

avg | average |

r | reactive |

SUM | supplied |

HPT | high pressure turbine; [-] |

LPT | low pressure turbine; [-] |

GT | gas turbine |

tp | output |

TH | thermal |

## Superscripts

Q_{f} | heat transfer |

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**MDPI and ACS Style**

Lugo-Leyte, R.; Salazar-Pereyra, M.; Méndez, H.D.L.; Aguilar-Adaya, I.; Ambriz-García, J.J.; Vargas, J.G.V.
Parametric Analysis of a Two-Shaft Aeroderivate Gas Turbine of 11.86 MW. *Entropy* **2015**, *17*, 5829-5847.
https://doi.org/10.3390/e17085829

**AMA Style**

Lugo-Leyte R, Salazar-Pereyra M, Méndez HDL, Aguilar-Adaya I, Ambriz-García JJ, Vargas JGV.
Parametric Analysis of a Two-Shaft Aeroderivate Gas Turbine of 11.86 MW. *Entropy*. 2015; 17(8):5829-5847.
https://doi.org/10.3390/e17085829

**Chicago/Turabian Style**

Lugo-Leyte, R., M. Salazar-Pereyra, H. D. Lugo Méndez, I. Aguilar-Adaya, J. J. Ambriz-García, and J. G. Vázquez Vargas.
2015. "Parametric Analysis of a Two-Shaft Aeroderivate Gas Turbine of 11.86 MW" *Entropy* 17, no. 8: 5829-5847.
https://doi.org/10.3390/e17085829