﻿ 微型燃气轮机动态特性仿真
 舰船科学技术  2020, Vol. 42 Issue (11): 91-95    DOI: 10.3404/j.issn.1672-7649.2020.11.018 PDF

Numerical study on dynamic characteristics of micro gas turbine
LI Hao-dong, LIU Yong-bao, HE Xing
College of Power Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: Aiming at the dynamic simulation of micro gas turbines, a component-level thermodynamic model is established by using Simulink. Compressor and turbine characteristics are fitted by experimental data. The method of variable specific heat capacity is used to calculate the thermophysical properties of gas turbine working fluids. The calculation results are compared with the experimental data. The results show that the error between the simulation results and the experimental data is small, and the error is analyzed. Part of the acceleration process is simulated, and the trend is consistent with the experimental data. The accuracy of the model is verified by comparing simulation with experimental data, which lays a foundation for further research on control strategy.
Key words: micro gas turbine     dynamic simulation     variable specific heat capacity
0 引　言

1 部件特性线

 图 1 压气机流量特性 Fig. 1 Flow characteristics of compressor

 图 2 压气机效率特性 Fig. 2 Compressor efficiency characteristics

 图 3 涡轮流量特性 Fig. 3 Turbine flow characteristics

 图 4 涡轮效率特性 Fig. 4 Turbine efficiency characteristics
2 微型燃气轮机的数学模型

2.1 燃气热力性质计算

 $\frac{{\lg (e)}}{{{R_g}}}\int_{{T_0}}^T {\frac{{{C_p}{\rm d}T}}{T}} = \lg {{\text{π}} ^0}\text{。}$ (1)

 $\lg \frac{{{P_2}}}{{{P_1}}} = \lg {\text{π}} _2^0 - \lg {\text{π}} _1^0\text{。}$

 $h = \int_{{T_0}}^T {\frac{{{C_p}{\rm d}T}}{T}} \text{，}$ (2)

 ${C_p} = {a_4}{T^3} + {a_3}{T^2} + {a_2}{T^1} + {a_1}\text{。}$ (3)

 ${f_h}\left( T \right) = \frac{1}{4}{a_4}{T^4} + \frac{1}{3}{a_3}{T^3} + \frac{1}{2}{a_2}{T^2} + {a_1}T + e\text{，}$ (4)
 ${f_{\text{π}} }\left( T \right) = \frac{{\lg \left( e \right)}}{{{R_g}}}\left( {\frac{1}{3}{a_4}{T^3} + \frac{1}{2}{a_3}{T^2} + {a_2}T + {a_1}\ln T + e} \right)\text{。}$ (5)

 $T = f_h^{ - 1}\left( h \right)\text{，}$ (6)
 $T = f_{\text{π}} ^{ - 1}\left( {\lg {{\text{π}} ^0}} \right)\text{。}$ (7)

 ${h_b} = {h_{b = 0}} + {B_m}\left( {{h_{b = 1}} - {h_{b = 0}}} \right)$ (8)
 $\lg {{\text{π}}_b} = \lg {{\text{π}} _{b = 0}} + {B_m}\left( {\lg {{\text{π}} _{b = 1}} - \lg {{\text{π}} _{b = 0}}} \right)$ (9)

2.2 压气机模块

 ${G_{cnp}} = {f_1}\left[ {{n_{cnp}},{{\text{π}} _c}} \right]\text{，}$
 ${\eta _c} = {f_2}\left[ {{n_{cnp}},{G_{cnp}}} \right]\text{。}$

 ${n_{cnp}} = \frac{{{n_c}}}{{{n_d}}}\sqrt {\frac{{{T_1}}}{{{T_{cin}}}}}\text{，}$
 ${G_{cnp}} = {G_c}\frac{{{P_1}}}{{{P_{cin}}}}\sqrt {\frac{{{T_{cin}}}}{{{T_1}}}} \text{，}$
 ${{\text{π}} _c} = \frac{{{P_{cout}}}}{{{P_{cin}}}}\text{。}$

 ${h_{cin}} = {f_h}\left( {{T_{cin}}} \right)\text{，}$
 $\lg {\text{π}} _{cin}^0 = {f_\pi }\left( {{T_{cin}}} \right)\text{，}$

 ${\text{π}} _{cout}^0 = {\text{π}} _{cin}^0 \cdot {{\text{π}} _c}\text{，}$

 ${T_{csout}} = f_{\text{π}} ^{ - 1}\left( {{\text{π}} _{cout}^0} \right)\text{，}$

 ${h_{csout}} = {f_h}\left( {{T_{csout}}} \right)\text{。}$

 ${h_{cout}} = {h_{cin}} + \left( {{h_{csout}} - {h_{cin}}} \right)/{\eta _c}\text{，}$

 ${T_{cout}} = f_h^{ - 1}\left( {{h_{cout}}} \right)\text{，}$
 $N{e_c} = {h_{cout}} - {h_{cin}}\text{。}$
2.3 涡轮模块

 ${G_{tnp}} = {f_1}\left[ {{n_{tnp}},{{\text{π}} _t}} \right]\text{，}$
 ${\eta _t} = {f_2}\left[ {{n_{tnp}},{G_{tnp}}} \right]\text{，}$

 ${T_{tout}} = f_h^{ - 1}\left( {{h_{tout}}} \right)\text{，}$
 $N{e_t} = {h_{tin}} - {h_{tout}}\text{。}$
2.4 燃烧室模块

1）流动方向上无传热量；

2）燃烧室容积大小不变；

3）燃烧室内气体混合充分且温度均匀分布；

4）燃烧室效率不变。

 $d\left( {\rho V} \right) = {G_{bin}} + {G_f} - {G_{bout}}\text{，}$
 $d\left( {\rho Vu} \right) = {G_{bin}}{h_{bin}} + {G_f}{h_f} - {G_{bout}}{h_{bout}} + Q\text{。}$

 $P = {R_g}\rho T\text{。}$

 $\frac{{{\rm d}{P_{bout}}}}{{{\rm d}t}} \!=\! \frac{{{R_g}{T_{bout}}}}{V}\left( {{G_f} \!+\! {G_{bin}} \!-\! {G_{bout}}} \right) \!+\! \frac{{{P_{bout}}}}{{{T_{bout}}}}\frac{{{\rm d}{T_{bout}}}}{{{\rm d}t}}\text{，}$
 $\frac{{{\rm d}{T_{bout}}}}{{{\rm d}t}} \!=\! a\left[ {k\left( {{G_{bin}}{h_{bin}} \!+\! Q \!-\! {G_{bout}}{h_{gout}}} \right) \!-\! {h_{gout}}\left( {\frac{{{\rm d}m}}{{{\rm d}t}}} \right)} \right]\text{。}$

 $a = \frac{{{R_g}{T_{bout}}}}{{{P_{bout}}V{C_{pg}}}}\text{，}$
 $\frac{{{\rm d}m}}{{{\rm d}t}} = {G_f} + {G_{bin}} - {G_{bout}}\text{。}$

 $Q = {G_f}{H_u}{\eta _b} - {G_{{\rm{C}}{{\rm{O}}_2}}} \cdot \Delta {h_{{\rm{C}}{{\rm{O}}_2}}} - {G_{{{\rm{H}}_2}{\rm{O}}}} \cdot \Delta {h_{{{\rm{H}}_2}{\rm{O}}}}\text{。}$

 ${G_{{\rm{C}}{{\rm{O}}_2}}} = {G_f}\frac{{{\mu _{{\rm{C}}{{\rm{O}}_2}}}}}{{{\mu _{{{\rm{C}}_8}{{\rm{H}}_{16}}}}}}\;\;\;{G_{{{\rm{H}}_2}{\rm{O}}}} = {G_f}\frac{{{\mu _{{{\rm{H}}_2}{\rm{O}}}}}}{{{\mu _{{{\rm{C}}_8}{{\rm{H}}_{16}}}}}}\text{，}$
 $\Delta {h_{{{\rm{CO_2}}}}} = {h_{{{\rm{CO_2}}}{T_{bout}}}} - {h_{{{\rm{CO_2}}}25{\text{℃}}}}\;\;\Delta {h_{{\rm{H}}_2}{\rm{O}}} = {h_{{{\rm{H}}_2}{\rm{O}}{T_{bout}}}} - {h_{{{\rm{H}}_2}{\rm{O}}25{\text{℃}}}}\text{。}$

 ${P_{bout}} = {P_{bin}}\sigma{\text{，}}$

 $b = \frac{{{G_f}}}{{{G_{bin}}}}\frac{{{\mu _{air}}}}{{{\mu _{{C_8}{H_{16}}}}}} \times 57.17{\text{。}}$

2.5 转子模块

 $\frac{{{\rm d}n}}{{{\rm d}t}} = \frac{1}{J}\frac{{900}}{{{{\text{π}} ^2}}}\frac{1}{n}\left( {N{e_t} - N{e_c} - load} \right)\text{。}$

 图 5 微型燃气轮机动态仿真模型 Fig. 5 Dynamic simulation model of micro gas turbine
3 仿真结果分析

3.1 稳态点对比

 图 6 排气流量仿真数据与试验数据 Fig. 6 Exhaust flow simulation and test data

 图 7 燃油流量仿真数据与试验数据 Fig. 7 Fuel flow simulation and test data

 图 8 涡轮出口温度仿真数据与试验数据 Fig. 8 Simulation and test data of turbine outlet temperature

 图 10 压气机出口压力仿真数据与试验数据 Fig. 10 Simulation and experimental data of compressor outlet pressure

 图 9 涡轮进口压力仿真数据与试验数据 Fig. 9 Simulation and test data of turbine inlet pressure
3.2 加速仿真

 图 11 启动加速喷油规律 Fig. 11 Start-up accelerated fuel injection law

 图 12 转速仿真数据与试验数据 Fig. 12 Speed simulation and test data

4 结　语