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Modeling and Simulation of a Gas-turbine System

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MODELING AND SIMULATION OF A GAS-TURBINE SYSTEM
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    MODELING AND SIMULATION OF A GAS-TURBINE SYSTEM  Assumptions: i.   The mass added in the form of fuel in the combustor is negligible ii.   Pressure drop in the combustor is negligible so that  p 2 =p 3  iii.   Heat transfer to the environment is insignificant iv.   Assume perfect gas properties throughout the cycle with a constant C   P   of 1.015kJ/(kg.K) Unknowns:  P  C    :   Power required by compressor in kW  P  S   : Output power of the turbine in kW  P  T   : Power delivered by the turbine in kW  p 2   :   Compressor pressure in kPa  p 3   : Combustor pressure in kPa  p 2 =p 3 =p  (according to the assumption-ii) T  2  : Combustor inlet temperature in o C T  3   : Combustor outlet temperature in o C m  : Mass flow rate in kg/s Knowns: The rate of energy added to the fluid at the combustor by burning fuel, q =5500kW Compressor inlet air temperature, T  1 =29 o C Compressor inlet air pressure,  p 1 =101kPa Turbine exhaust gas pressure,  p 4 =101kPa  (a) Developing a mathematical model for the system Performance characteristics of compressor: Variation of p with m Assumption: performance of the compressor is represented by a second order algebraic equation with one independent variable. Then a polynomial of degree n = 2 can be employed to exactly fit 2 + 1 = 3 data points of figure 2  –   graph 1. Then the general form of the polynomial is taken as p = f(m) = a 0 + a 1 m + a 2 m 2   ………………..1*    by figure 2  –  graph 1 at m=3kg/s, p=310kPa.  by 1*; 310 = a 0 + 3a 1  + 9a 2 ………………… ....1 at m=5kg/s, p=240kPa  by 1*; 240 = a 0  + 5a 1 + 25a 2 …………………2  at m=7kg/s, p=110kPa  by 1*; 110 = a 0  + 7a 1  + 49a 2 …………………3   by solving simultaneous equations 1, 2 and 3; a 0 = 302.5 a 1 = 25 a 2  = -7.5 According to 1* p = 302.5 + 25m  –   7.5m 2 ……………1*   Variation of P c  with p Assume above variation is represented by a second order algebraic equation with one independent variable. Then a polynomial of degree n = 2 can be employed to exactly fit 2 + 1 = 3 data points of figure2  –   graph2. The general form of the polynomial is then taken as P c  = f(p) = a 0  + a 1 p +a 2 p 2 ……………2*    by figure 2  –   graph 2 at p = 100kPa, p c  = 40kW  by 2*; 40 = a 0  + 100a 1  + 100 2 a 2   ……………1 ’    at p = 210kPa, p c  = 160kW  by 2*; 160 = a 0  + 210a 1  + 210 2 a 2 ……………2 ’   at p = 315kPa, p c  = 360kW  by 2*; 360 = a 0  + 315a 1  + 315 2 a 2   …………… 3 ’    by solving simultaneous equations 1 ’ , 2 ’ and 3 ’;  a 0 = 10.4017 a 1 = -0.0826 a 2  = 0.0038 According to 2* P c  = 10.4017  –   0.0826p + 0.0038p 2 ……………2*  Performance characteristics of gas turbine: Variation of m with p and T 3  Assume above variation is represented by a second order algebraic equation with two independent variables. Then following polynomial can be employed to exactly fit 9 data points of figure3  –   graph1. Then the general form of the polynomial is m = (a 0  + a 1 p + a 2 p 2 ) + (b 0  + b 1 p + b 2 p 2 )T 3 + (c 0  + c 1 p + c 2 p 2 )T 32 ………….3*   by figure3  –   graph1; at T 3 = 500 0 C;  by 3*; m = (a 0  + a 1  p + a 2  p 2 ) + (b 0  + b 1  p + b 2  p 2 )x500 + (c 0  + c 1  p + c 2  p 2 )x500 2  = (a 0  + 500b 0  + 500 2 c 0 )+ (a 1  + 500b 1  + 500 2 c 1 ) p + (a 2  + 500b 2  + 500 2 c 2 )p 2  at p = 100kpa , m =3.5kg / s  by 3*; 3.5 = a 0  + 500b 0  + 500 2 c 0  + 100a 1  +500x100b 1 + 500 2 x100c 1  + 100 2 a 2  + 500x100 2  b 2  + 100 2 x100 2 c 2 …………………1  at p = 200kPa, m = 5.2 kg/s  by 3*; 5.2 = a 0  + 500b 0  + 500 2 c 0  + 200a 1  + 500x200b 1  + 500 2 x200c 1 + 200 2 a 2  + 500x200 2  b 2  + 500 2 x200 2 c 2 …………………2  at p = 300kPa, m = 6.4kg/s  by 3*; 6.4 = a 0  + 500b 0  + 500 2 c 0  + 300a 1  + 500x300b 1  + 500 2 x300c 1  + 300 2 a 2  + 500x300 2  b 2  + 500 2 x300 2 c 2 …………………3  
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