Abstract
The development of numerical mathematical model to calculate both the static and dynamic characteristics of a multi-shaft gas turbine consisting of a single combustion chamber, including advanced cycle components such as intercooler and regenerator is presented in this paper. The numerical mathematical model is based on the simplified assumptions that quasi-static characteristic of turbo-machine and injector is used, total pressure loss and heat transfer relation for static calculation neglecting fuel transport time delay can be employed. The supercharger power has a cubical relation to its rotating velocity. The accuracy of each calculation is confirmed by monitoring mass and energy balances with comparative calculations for different time steps of integration. The features of the studied gas turbine scheme are the starting device with compressed air volumes and injector’s supercharging the air directly ahead of the combustion chamber.
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Abbreviations
- A :
-
Heat transfer area, m2
- c :
-
Specific heat, J/(kg K)
- E :
-
Energy, J
- f :
-
Cross sections of an injector, m2
- G :
-
Moment, N-m
- H :
-
Enthalpy, J/kg
- h :
-
Heat transfer coefficient, W/(m2K)
- J :
-
Polar moment of rotor inertia, kg-m2
- k :
-
Thermal conductivity, W/(m K)
- K :
-
Feedback coefficient
- m :
-
Mass flow rate, kg/s
- m :
-
Mass of wall, kg
- n* :
-
Exponential order for heat transfer coefficients
- P :
-
Power, W
- p :
-
Pressure, Pa
- Pγ :
-
Compressor and turbine pressure ratio
- Q :
-
Heat flow rate. W
- R :
-
Specific gas constant, J/(kg K)
- S :
-
Relative stability margin coefficient
- T :
-
Total temperature, K.
- t :
-
Temperature, °C
- U s :
-
Control action signal
- U :
-
Overall heat transfer coefficient, W/(m2 K)
- u :
-
Internal energy per unit mass, J/kg
- U inj :
-
Injection coefficient
- V :
-
Volume, m3
- γ :
-
Specific heat ratio
- Δp :
-
Pressure loss, Pa
- ΔS :
-
Compressor stability margin ΔSsH=SsH-1.0
- Δτ :
-
Time step, s
- δ :
-
Channel wall thickness, m
- η :
-
Efficiency
- α :
-
Relative displacement of actuator servo
- v :
-
Kinematic viscosity, m2/s
- ξ :
-
Correlation coefficient
- ρ :
-
Density, kg/m3
- σ :
-
Coefficient for temperature distribution
- τ :
-
Time variable, s
- ω :
-
Rotor angular speed, rad/s
- a:
-
Air
- acc:
-
Accumulated
- av:
-
Average
- bra:
-
Rotor breakaway moment
- cool:
-
Cooling
- df:
-
Direct feedback coefficient
- e:
-
Exit
- f:
-
Fuel
- g:
-
Gas
- ga:
-
Gain feedback coefficient
- i:
-
Index for parameters
- in:
-
Inlet
- inj:
-
Injection coefficient
- int:
-
Intermediate
- mech:
-
Mechanical loss
- n, n+ 1:
-
Old and new time steps
- out:
-
Outlet
- p:
-
Constant pressure
- s:
-
Stability margin
- sm:
-
Servo-motor
- sur:
-
Anti surge valve
- v:
-
Constant volume
- w:
-
Wall
- wor:
-
Working
- set:
-
Pilot signal for regulator
- 0 :
-
Nominal condition
- 1 :
-
Outer surface
- 2:
-
Inner surface
- 3:
-
Injector mixing chamber
- *:
-
Injector nozzle throat area
- ^:
-
Reduced parameter
- -:
-
relative parameter
- C:
-
Compressor
- CC:
-
Combustion chamber
- DE:
-
Differential equation
- GTU:
-
Gas turbine unit
- HP:
-
High pressure
- HPC:
-
High pressure compressor
- HPT:
-
High pressure turbine
- HPTC:
-
High pressure turbo compressor
- IC:
-
Intercooler
- LHV:
-
Low heating value
- LP:
-
Low pressure
- LPC:
-
Low pressure compressor
- LPT:
-
Low pressure turbine
- LPTC:
-
Low pressure turbo-compressor
- MM:
-
Mathematical model
- PC:
-
Pipeline compressor
- PT:
-
Power turbine
- T:
-
Turbine
- TC:
-
Turbo-compressor
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Kim, S., Kovalevsky, V.P. Investigation of nonlinear numerical mathematical model of a multiple shaft gas turbine unit. KSME International Journal 17, 2087–2098 (2003). https://doi.org/10.1007/BF02982449
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DOI: https://doi.org/10.1007/BF02982449