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As one of the antisurge techniques, the adjusting scheme of VSV under off-design conditions has a significant impact on the performance of gas turbines. In this paper, the one-dimensional characteristic of the compressor calculation program is embedded into the zero-dimensional overall gas turbine model, which replaces the original compressor characteristic module. Based on the assembling relationship of the actual components of the marine gas turbine, the architecture of the modular model library is designed, and an integrated simulation platform of marine gas turbine is developed by using MATLAB/GUI software. The influence of the first 3 rows of variable stator vanes of the 9-stage axial compressor working alone on the performance of the compressor at different speeds and different angles was analyzed by the HARIKA compressor characteristic calculation program. Taking the economics and stability of the gas turbine as the optimization objective, the optimization of the first three-stage stator vanes regulation schemes under different working conditions was carried out. The steady-state performance parameters under each working condition of gas turbine of power generation with or without variable stator vane mode were calculated. The study results can provide references for the adjusting scheme of VSV under gas turbine off-design conditions operating process.

As an important part of the gas turbine, the compressor should have high performance and enough margin and have higher efficiency [

Today, gas turbines are developing in the direction of complexity, scale, and diversification. The simulation process of a gas turbine becomes more complex [

Simulation flow chart of high precision component modeling based on the NPSS framework [

The Russian Central Aero-Engine Research Institute (CIAM) developed the Computer Gas Turbine Engine Simulator (CGTES) to support the CT3 (Turbine Engine Test Technology) program [

The off-design performance of marine gas turbines has great significance for the economy and stability of ships. As one of the surge-preventing measures of the compressor, variable stator vane (VSV) can be used to change the installation angle of the cascade with the working conditions changing to improve the compressor performance in the off-design conditions [

VSV technology has a long history and has been used in various applications of gas turbines. In the early 1940s, Germany’s first turbojet engine Jumo004 applied the technology of VSV [

Stage numbers of VSV in the compressor [

In the field of ground power generation and marine gas turbines, VSV technology is also widely used [

Through the review of the research status, we can know that the current research on VSV mainly focuses on the effect of VSV on compressor performance. The research on the influence of VSV on the performance of the whole gas turbine is relatively scarce. The research on the adjustment regulation of VSV mainly focuses on the performance of the compressor, and the research on the performance of the whole gas turbine is relatively less. Under the background of gas turbine integrated simulation, the method of simulating research on a certain part of the gas turbine from different perspectives is gradually mature by using the integrated modeling resources. Aiming at the problem mentioned above, this paper takes one three-shaft marine gas turbine for generation as the research object, adopts the modular modeling idea, establishes the general simulation model of (0-1D) variable dimension gas turbine considering a variable-geometry compressor, and optimizes the adjustment scheme of the top three stages of the variable stator vanes of the low-pressure compressor, and the influence of the variable stator vanes on the steady-state performance of the gas turbine was studied emphatically. The main contents of this paper are as follows.

Design an integrated simulation platform for marine gas turbines and build a simulation model library including a compressor, combustion chamber, turbine, rotor, and volume. According to the characteristics of the variable-geometry compressor, build the new compressor characteristics modules and interface modules.

A variable dimension turbine simulation model considering the variable-geometry compressor is established.

From the angle of the performance of the whole gas turbine, taking the top three grades of the variable stator vanes of the low-pressure compressor as the optimization variable, the economic efficiency and stability of the gas turbine under various working conditions are optimized. The results show that the optimized variable stator vane adjustment scheme can improve the performance of the gas turbine.

As the core part of the variable-geometry compressor model, the compressor interface module is the key to ensure the data transfer between the zero-dimensional models and one-dimensional characteristic calculation program. The whole interface module was built by S-function/MATLAB. The function of the compressor interface module mainly contains two parts: (

The process of collaborative running is shown in Figure

The process of collaborative running.

When Simulink is working, it first enters the simulation initialization phase. In this phase, the solver determines all the parameters of the module through the callback function and passes the signal width, data type, and state number. Meanwhile, the execution order, initial value, and the sampling time of each module are also determined.

Finally, other tasks in the initialization phase are performed before the simulation cycle phase. After entering the simulation cycle, the Simulink solver calculates the output of each module according to the predetermined order and uses the callback function to calculate the module status in the current sampling time, update the discrete state value, and calculate the differential value and the output value of the corresponding module.

After the simulation cycle phase, the Simulink solver calls the callback function to release the system storage space and performs other tasks that need to be done after the simulation step is completed.

The input files of HARIKA include the following: import conditions of variable-geometry compressors (i.e., import total pressure, import total temperature, and import airflow angle), relative speed, the main geometric size at all levels, and parameters such as the opening of variable static blade.

The output file mainly involves the compressor characteristic parameters including pressure ratio, flow rate, speed, and efficiency, which are calculated by the calculation program of compressor characteristics.

When multiple variable stator vane angles change, the characteristics of the compressor will be changed in different angles. So, using only the zero-dimensional simulation cannot meet the need of modeling. One-dimensional simulation is mainly related to the component loss model, backward angle model of rotating parts, and some empirical coefficients. Therefore, the one-dimensional compressor performance calculation program can accurately reflect the variable-geometry compressor characteristics.

In this paper, HARIKA algorithm was used to calculate the one-dimensional compressor characteristic. Based on a large number of test data, HARIKA algorithm uses the statistical relationship of the stage synthesis characteristics to determine the stage parameters under off-design condition. The algorithm has been empirically modified along the vane height, and it has been empirically modified for various characteristic parameters of vane type as well. After obtaining the total pressure ratio and efficiency of one stage of the compressor, the velocity triangle at the outlet of this stage is further obtained. Using the velocity triangle as the inlet parameter of the next stage of the compressor, the parameters at the outlet of the next stage are obtained by the same method. The characteristics of the whole compressor can be obtained by repeating the process. The algorithm is more suitable as the calculation program of the characteristics of variable-geometry compressor components.

Figure

The compressor characteristics of experiment and calculation.

According to the compressor inlet temperature and compressor pressure ratio, we can determine the logarithmic ratio of the compressor outlet. Then, we determine the compressor exit enthalpy, and we can calculate the outlet temperature and compressor power.

The specific calculation process is as follows:

During the process of establishing the model of combustion, we always consider the combustion chamber as a uniform field.

The turbine module is similar to the compressor module, and the mathematical model is as follows:

where

From the moment of momentum theorem, the product of the angular velocity of the rotor and the moment of inertia is equal to all the external torque on the rotor.

where

With the connection of the main components of the gas turbine, the flow space of the volume module can be regarded as global. In the volume, the flow rate of the working fluid is fast and the retention time is short, so we assume that the medium of heat transfer and import and export pressure is zero and assume central pressure instead of the average pressure of the working fluid inside the volume. According to the principle of conservation of mass, there is the following relationship:

This paper takes the triaxial gas turbine of a certain type as the physical model (as it is shown in Figure

Performance specifications of the gas turbine at standard sea level static ISA condition.

Air mass flow rate (kg/s) | 82 |

Fuel flow rate (kg/s) | 1.62 |

Turbine entry temperature (K) | 1542 |

Thermal efficiency (%) | 34.94 |

Ambient pressure (kPa) | 101.325 |

Ambient temperature (K) | 288 |

Physical model of the triaxial gas turbine.

In the environment of MATLAB/SIMULINK, a simulation model of variable specific heat capacity of three shaft gas turbine was built, which includes compressor, combustion chamber, turbine, volume, rotor and engine controller, which is shown in Figure

The simulation model of the gas turbine.

Based on the gas turbine’s overall performance, this part of the paper has considered variable-geometry compressor’s (0-1) variable dimensions of the gas turbine overall simulation model, aiming at optimizing the gas turbine’s economics by taking angles of variable stator vane as the optimized variables. In the process of selecting optimized variables, the adjustable angles of the variable stator vane have been taken as optimized variables to improve the design of stator vane adjustment scheme. The optimization target is the economy of the gas turbine, whose specific measurement index is the fuel consumption rate and efficiency during the operation of the gas turbine. The gas turbine efficiency is defined as the formula below:

At the same time, the surge margin should be considered in the optimization target of the optimization scheme as well, and the surge margin is defined as follows:

There are 3 stages of variable stator vanes in this paper. Considering the combination number of three optimization variables and the selection rules of optimization variables, this paper adopts the optimization scheme of traverse tree algorithm (Figure

The schematic diagram of traverse tree algorithm.

In the optimization scheme shown in Figure

Due to the scope of the optimization variables and the limit of selection rules, the total number of all opening degree combinations is still at an acceptable level. At the same time, considering the complexity of the relationship between the optimization variable and the optimization target, it can be found that the optimization problem has obvious unimodality in the optimization process. In each variable stator vane stage, there is always an optimization target corresponding to the opening degree in the range of its opening degree, which is the optimal value, showing a unimodal phenomenon. According to the law, we can greatly reduce the number of variable stator vane opening degree combinations and simplify the optimization process.

The low-pressure compressor variable stator blade adjustable regulation law has been optimized at different off-design points of the gas turbine. Table

Optimization results of variable stator blade at each condition.

Operating conditions (%) | Speed of compressor (r/min) | Outlet pressure of compressor (Pa) | Adjustment value of the zero stage (°) | Adjustment value of the first stage (°) | Adjustment value of the second stage (°) |
---|---|---|---|---|---|

100 | 7395 | 448850 | −8 | −12 | 0 |

90 | 7227 | 431587 | −10 | −12 | −2 |

80 | 7087 | 414645 | −14 | −12 | −4 |

70 | 6950 | 395360 | −18 | −14 | −4 |

60 | 6712 | 375084 | −18 | −14 | −10 |

50 | 6468 | 353210 | −18 | −16 | −12 |

The system simulation results of two kinds of schemes at high work conditions.

Parameter | 100% conditions | 70% conditions | ||
---|---|---|---|---|

Original | Optimized | Original | Optimized | |

Air mass flow (kg/s) | 85.2 | 85.54 | 72.86 | 73.83 |

Fuel flow (kg/s) | 1.6921 | 1.6866 | 1.2582 | 1.2432 |

Efficiency | 33.58% | 33.69% | 31.61% | 32.00% |

LC surge margin | 38.33% | 34.03% | 37.3% | 36.54% |

HC surge margin | 38.02% | 38.23% | 41.19% | 41.76% |

It can be calculated in the low-pressure compressor characteristic curves of each condition by inputting optimized adjustment schemes of variable stator vane into the model, as shown in Figures

Mass flow and pressure ratio.

Mass flow and efficiency.

The changing curves of gas turbine efficiency and fuel quantity in various conditions by applying the optimized variable stator blade adjustment scheme to the simulation model are shown in Figures

The efficiency of the gas turbine.

The fuel flow of the gas turbine.

The speed of the low-pressure rotor.

The speed of the high-pressure rotor.

The fuel flow of the gas turbine.

The surge margin of the low-pressure compressor.

The steady-state calculation of a three-shaft gas turbine for a certain type of ship’s power generation is carried out, which is under the original adjustable stator blade adjustment scheme, the optimal regulation scheme, and the no adjustment scheme. The comparison results of the various parameters of the gas turbine engine used in the marine power generation are shown in Figures

Specific analysis of simulation results is as follows.

From Figures

The efficiency of the gas turbine.

In consideration of the characteristics of the variable-geometry compressor, a characteristic calculation program of a one-dimensional compressor was used in the 0D simulation model of the gas turbine through scaling simulation. In the end, the simulation model of the gas turbine with variable dimension was built. The three-stage VSV of the low-pressure compressor is used as the optimization variable, the economy of the gas turbine under different conditions is used as the optimization goal, and the best adjustment angles of the three-stage VSV were got under different working conditions. From the optimization results, we can find that the optimized control scheme can improve the efficiency of the gas turbine and reduce fuel consumption. Although the surge margin is less than the original program’s surge margin under high working conditions, in the low and medium conditions, the optimization scheme has more advantages. Through the reasonable adjustable stationary blades adjustment scheme, we can improve the gas turbine compressor surge margin under the working condition of low and medium. Meanwhile, we can expand the operating range of the compressor, and the gas turbine can get a better operation state. The operating performance of the gas turbine under different operating conditions is improved. It is believed that the reasonable adjustment scheme of the stator has a positive effect on the overall performance of the gas turbine.

Variable stator vane

Low-pressure compressor

High-pressure compressor.

Enthalpy

Temperature

Power

Mass flow

Pressure

Specific heat at constant pressure

Gas constant

Low calorific value of fuel

Volume

Rotor inertia

Torque

Power.

Pressure ratio

Efficiency

Index adiabatic of combustion chamber

Angular speed.

Inlet of compressor

Outlet of compressor

Compressor

Isentropy

Combustion

Inlet

Outlet

Turbine

Fuel

Load.

The authors declare that they have no conflicts of interest.

The present work is supported by the Fundamental Research Funds for the Central Universities of China (no. HEUCFM170301).