Mathematical modelling of steam turbine

Mathematical modelling of steam turbine

1. Mathematical Modelling Of Steam Turbine BY, TUSHAR VILAS GHAG M.E MACHINE DESIGN

2. Contents Introduction Mathematical modelling of steam turbine unit Block diagram of steam turbine configuration 2

3. Introduction The steam turbine converts stored energy of high pressure and high temperature steam into rotary energy, which in turn is converted into electrical energy by the generator. Each turbine section consists of a set of a moving blades attached to rotor and a set of stationary vanes in which steam is accelerated to high velocity. The kinetic energy of the high velocity steam is converted into shaft torque. A large variety of steam turbines have been built, with respect to the capacity, application and desired performance. To increase the thermal efficiency in applications, steam turbines consist of multistage steam expansion. 3

4. Types Of Steam Turbine 4

5. Rankine Cycle 5

6. Rankine Cycle With Reheat 6

7. Mathematical Modelling Of Steam Turbine Unit In many cases, the steam turbine models are simplified, many intermediate variables are omitted. The transfer function of a steam turbine and the expression for mechanical power developed by a turbine are based on the continuity equation. Where, W = weight of steam in the turbine (kg)   7

8. Mathematical Modelling Of Steam Turbine Unit V = volume of turbine ( = density of steam (kg/ ) F = steam mass flow rate (kg/s) t = time (sec) Assuming the flow out of the turbine proportional to pressure in the turbine. = P …………………………… (2) Where, P = Pressure of steam in the turbine ( kPa ) = Rated pressure = Rated flow out of the turbine   8

9. Mathematical Modelling Of Steam Turbine Unit With constant temperature in the turbine: From equations (1), (2) & (3), result the mathematical model: …………………… (4) …………………………………. (5)   9

10. Mathematical Modelling Of Steam Turbine Unit After Laplace transform, the transfer function is: ………………………… (6) Where, = V is the time constant ( sec )   10

11. Mathematical Modelling Of Steam Turbine Unit The turbine torque is proportional to the steam flow rate: = k . F(t) Where, k = constant of proportionality.   11

12. Mathematical Modelling Of Steam Turbine Unit …………………………… (7) …………………………….... (8) ……………………………. (9)   12

13. Block Diagram Of Steam Turbine Configuration Fig. Steam turbine configuration 13

14. Block Diagram Of Steam Turbine Configuration 14 Fig. Block diagram of steam turbine configuration

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