# Modeling and Simulation of a Gas-turbine System

Description
MODELING AND SIMULATION OF A GAS-TURBINE SYSTEM
Categories
Published

View again

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
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

Jul 23, 2017

#### The Oxus and the Indus (1874) by Major Evans Bells

Jul 23, 2017
Search
Similar documents

View more...
Tags

## Gases

Related Search
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks
SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...

Sign Now!

We are very appreciated for your Prompt Action!

x