# Computational Simulation of PT6A Gas Turbine Engine Operating with Different Blends of Biodiesel—A Transient-Response Analysis

^{*}

## Abstract

**:**

^{®}using a block-oriented approach. Transient simulations of the PT6A engine start-up have been carried out by changing the original Jet-A1 fuel with biodiesel blends. Time plots of the main thermodynamic variables are shown, especially those regarding the structural integrity of the burner. Numerical results have been validated against reported experimental measurements and GasTurb

^{®}simulations. The computer model has been capable to predict acceptable fuel blends, such that the real PT6A engine can be substituted to avoid the risk of damaging it.

## 1. Introduction

^{®}[23], among others. Academic research has exploited the architectures given by Matlab-Simulink

^{®}[22] and Modelica

^{®}[24], where different engine types can be created in a visual interface approach. However, most of these works simulate the steady-state thermodynamic cycle of the engine without describing the dynamic behavior of the air that crosses the stages of the engine and nearly all are linearized versions that do not work far from the linearization point —like when the engine operates with blends of biodiesel fuel. Instead, the coupled non-linear version of the equations are solved with the Newton-Raphson method but it requires the computation of the Jacobian and may not converge to the actual numerical solution at all operating regimes. The particular methods that we are interested in, are the ones that do not require an extensive iterative process to obtain the numerical solution of the set of algebraic and differential equations. Those arrange the equations in such a way that the output values can be obtained from the input variables. This is consistent with the flow of air through the engine components: the input variables are referred to the entering flow conditions, while the output solved variables are the exiting flow.

^{®}offers the capability of coding those blocks and connecting them to configure any gas turbine engine. It also gives the possibility of using a graphical interface which is more user-friendly, but the relevant feature of this software is that it makes possible to generate source code in C language to generate a much faster executable program. Block diagrams make also possible to link the engine software to control devices, with the capability of driving input/output signals for data acquisition and control. All these features being relevant in the on-live prediction of the gas turbine engine.

## 2. The PT6A Engine Model

^{®}software [28], which possess a graphical user interface for building algebraic block diagrams that give solution to the governing differential equations. Hence, we present the global block diagram of the governing equations in Figure 2, where the engine model is represented at a component level. An extended explanation of each engine’s component and how we represent it, will be developed through the following paragraphs. Moreover, each component’s block diagram will be presented through the detailed explanation of each sub-system. We list inputs, parameters, variables and outputs for every block diagram.

#### 2.1. Air Inlet

#### 2.2. Compression Section

#### 2.3. Burner

#### 2.4. Turbine Section

#### 2.5. Rotating Shafts

#### 2.6. Compatibility Conditions

## 3. Numerical Results

^{®}. A fourth-order Runge-Kutta numerical scheme for the temporal integration is used for solving the differential equations. A maximum integration step of 1ms is used to guarantee the stability of the temporal solution. The first scenario is the steady response of the engine which is intended to validate the computational model. Two models are set up, one with the present approach and the other one using GasTurb

^{®}[23]. We test both models to ensure the accuracy of the developed model at steady-state operation conditions, and to validate our results with the engine test data and the commercial software simulation. Then, we solve the steady-state operation by using the blends with biodiesel and compare our numerical results with the ones obtained with GasTurb. Finally, we address the transient operation of the engine using the fuel blends, specifically at the start-up of the engine when the maximum temperature can be reached. We suppose in all scenarios an on-ground operation so that the inlet velocity is zero.

#### 3.1. Validation of the Computational Model

#### 3.2. Stationary Operation of the PT6A-65 Using Fuel Blends

#### 3.3. Transient Operation of the PT6A-65 Motor Using Fuel Blends

## 4. Conclusions

^{®}software and different simulation scenarios have granted the predictive capacity of our computational model concerning the systemic and transient response of the engine. Thus, protecting the actual PT6A-65 plant and incurring in considerable computational advantages like accuracy, economy, expedition and applicability.

^{®}. Since the present results and the ones obtained with such software have been compared, we have granted that steady descriptions of the PT6 engine given by our model are at least as accurate and reliable than those by GasTurb

^{®}; The relative error between the present results and those reported in the manual is below $10\%$ for most of the stages. But also, that the transient analysis gives a clear advantage to our computational approach.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Nomenclature | Greek letters | |||

c | Speed of sound | $\alpha $ | Air angle | |

${C}_{b}$ | Pressure loss coefficient | $\beta $ | Blade angle | |

${c}_{p}$ | Specific heat capacity at constant pressure | $\gamma $ | Quotient between specific heats of the air | |

${I}_{r}$ | Mass moment of inertia | $\eta $ | Isentropic efficiency | |

$i,j$ | Axial stages counters | ${\eta}_{b}$ | Brayton’s cycle efficiency | |

$LHV$ | Low Heating Value | ${\eta}_{r}$ | Brake efficiency | |

$\mathit{M}$ | Torque | $\mathsf{\Pi}$ | Pressure ratio | |

m, $\dot{m}$ | Mass, mass flow | $\rho $ | Density | |

Ma | Mach’s number | $\omega $ | Angular velocity | |

n | Polytropic index | Subscript | ||

N | Number of revolutions per minute | a | Air | |

p | Pressure | atm | Atmosphere | |

R | Constant of gases | b | Burner | |

r | Radius | c | Compressor | |

T | Temperarture | f | Fuel | |

t | Time | g | Gas | |

V | Volume | l | Leading edge | |

$\mathit{v}$ | Velocity | p | Propeller | |

t | Trailing edge |

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**Figure 11.**Pressure distribution along the engine stages. Results for the stationary engine operation with the 60% (

**left**) and 100% (

**right**) throttles.

**Figure 12.**Temperature distribution along the engine stages. Results for the stationary engine operation with the 60% (

**left**) and 100% (

**right**) throttles.

**Figure 13.**GasTurb results. Temperature (

**left**) and pressure (

**right**) results for the stationary engine operation with the 100% throttle.

**Figure 14.**Transient pressure at the compressor’s discharge. Results for the start-up operation with the 60% (

**left**) and 100% (

**right**) throttles.

**Figure 15.**Transient temperature at the burner. Results for the start-up operation with the 60% (

**left**) and 100% (

**right**) throttles.

Blade | Symbol | 1st-Stage Rotor | 2nd-Stage Rotor | 3th-Stage Rotor |
---|---|---|---|---|

Inlet air angle, deg. | ${\alpha}_{l}$ | 61.5 | 59.8 | 58.0 |

Exit air angle, deg. | ${\alpha}_{t}$ | 54.4 | 48.9 | 42.0 |

Inlet metal angle, deg | ${\beta}_{l}$ | 56.8 | 57.85 | 57.1 |

Exit metal angle, deg. | ${\beta}_{t}$ | 50.5 | 43.5 | 36.2 |

Inner radius, mm. | ${r}_{0}$ | 72 | 76 | 80 |

Outter radius, mm. | r | 100 | 96 | 92 |

**Table 2.**On-ground steady operation conditions using Jet-A1 fuel. Extracted from Ref. [29].

Standard Conditions | Value |
---|---|

Atmospheric temperature | 288 K |

Atmospheric pressure | $101,352.9$ Pa |

LHV of Jet-A1 fuel | $42.8$ MJ/kg |

Jet-A1 fuel mass flow | $0.062$ kg/s |

Propeller’s load (at propeller’s shaft) | $2684.51$ N.m |

**Table 3.**Temperatures and pressures for PT6A-65 engine at 850 shp and ISA standard conditions. Extracted from Ref. [29].

Station | Location | Temperature (K) | Pressure (Pa) |
---|---|---|---|

0 | Ambient | 288 | 101,352.9 |

1 | Compressor Inlet | 288.2 | 102,042.4 |

1.5 | Compressor Interstage | 415.4 | 307,506.2 |

2 | Compressor Discharge | 610.4 | 787,381.28 |

3 | Turbine Inlet | 1212.1 | 770,144.39 |

3.5 | Interturbine | 967.1 | 246,142.8 |

4 | Turbine Exit | 811.5 | 113,074 |

5 | Exhaust | 811.5 | 106,179.3 |

**Table 4.**Polytropic index and efficiency gathered values for the compression and expansion sections of the PT6A-65 engine.

Description | Stages | Polytropic Index n | Irreversible Efficiency $\mathit{\eta}$ |
---|---|---|---|

Axial Compressor | 1–1.5 | 1.496 | 0.862 |

Centrifugal compressor | 2.5–3 | 1.693 | 0.698 |

Hot turbine expansion | 3–3.5 | 1.247 | 1.442 |

Cold turbine expansion | 3.5–4 | 1.291 | 1.267 |

Blade | 1st-Stage Rotor | 2nd-Stage Rotor | 3th-Stage Rotor |
---|---|---|---|

Inlet metal angle, deg | 0 | 0 | 0 |

Exit metal angle, deg. | 80 | 43 | 43 |

Inner radius, mm. | 92 | 90 | 88 |

Outter radius, mm. | 117 | 125 | 142 |

**Table 6.**Present and GasTurb simulation results. Stationary temperatures and pressures at different stations of the PT6A-65 engine. The relative error is calculated against the reported results in Table 3.

Station | Present Simulation | GasTurb Simulation | ||||||
---|---|---|---|---|---|---|---|---|

T (K) | Error (%) | p (pa) | Error (%) | T (K) | Error (%) | p (pa) | Error (%) | |

1.5 | 433.63 | 4.39 | 423,635.89 | 37.76 | 420.11 | 1.12 | 318,248 | 3.37 |

2 | 510.44 | 16.38 | 749,710.57 | 4.78 | 611.03 | 0.10 | 814,715 | 3.35 |

3 | 1289.15 | 6.35 | 727,219.25 | 5.57 | 1212.1 | 0 | 773,979 | 0.48 |

3.5 | 925.3 | 4.11 | 240,006.35 | 2.49 | 863.07 | 12.05 | 137,405 | 44.17 |

4 | 759.69 | 6.38 | 111,067.77 | 1.77 | 829.8 | 2.20 | 122,816 | 7.93 |

Blend | $\mathit{LHV}$ (MJ/kg) | Notation in Plots |
---|---|---|

KB0 | 42.8 | ◯ |

KB10 | 42.14 | ⋆ |

KB20 | 41.49 | Δ |

KB30 | 40.84 | ∗ |

KB100 | 36.29 | □ |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bayona-Roa, C.; Solís-Chaves, J.S.; Bonilla, J.; Rodriguez-Melendez, A.G.; Castellanos, D.
Computational Simulation of PT6A Gas Turbine Engine Operating with Different Blends of Biodiesel—A Transient-Response Analysis. *Energies* **2019**, *12*, 4258.
https://doi.org/10.3390/en12224258

**AMA Style**

Bayona-Roa C, Solís-Chaves JS, Bonilla J, Rodriguez-Melendez AG, Castellanos D.
Computational Simulation of PT6A Gas Turbine Engine Operating with Different Blends of Biodiesel—A Transient-Response Analysis. *Energies*. 2019; 12(22):4258.
https://doi.org/10.3390/en12224258

**Chicago/Turabian Style**

Bayona-Roa, Camilo, J.S. Solís-Chaves, Javier Bonilla, A.G. Rodriguez-Melendez, and Diego Castellanos.
2019. "Computational Simulation of PT6A Gas Turbine Engine Operating with Different Blends of Biodiesel—A Transient-Response Analysis" *Energies* 12, no. 22: 4258.
https://doi.org/10.3390/en12224258