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Thermodynamics-Steam Turbine

Introduction..... Principles...... Impulse Turbines...... Reaction Turbines...... Rankine Cycle...... Turbine Enthalpy Cycle......



Introduction

A steam turbine is a mechanical device that converts thermal energy in pressurised steam into useful mechanical work.  The original steam engine which largely powered the industrial revolution in the UK was based on reciprocating pistons.   This has now been almost totally replaced by the steam turbine because the steam turbine has a higher thermodynamic efficiency and a lower power-to-weight ratio and the steam turbine is ideal for the very large power configurations used in power stations.   The steam turbine derives much of its better thermodynamic efficiency because of the use of multiple stages in the expansion of the steam.   This results in a closer approach to the ideal reversible process.

Steam turbines are made in a variety of sizes ranging from small 0.75 kW units used as mechanical drives for pumps, compressors and other shaft driven equipment, to 1,500,000kW turbines used to generate electricity.  Steam turbines are widely used for marine applications for vessel propulsion systems.  In recent times gas turbines , as developed for aerospace applications, are being used more and more in the field of power generation once dominated by steam turbines.




Steam Turbine Principle

The steam energy is converted mechanical work by expansion through the turbine.   Th expansion takes place through a series of fixed blades (nozzles) and moving blades each row of fixed blades and moving blades is called a stage.   The moving blades rotate on the central turbine rotor and the fixed blades are concentrically arranged within the circular turbine casing which is substantially designed to withstand the steam pressure.

On large output turbines the duty too large for one turbine and a number of turbine casing/rotor units are combined to achieve the duty.  These are generally arranged on a common centre line (tandem mounted) but parallel systems can be used called cross compound systems.


Two Turbine Cylinders Tandem Mounted

There are two principles used for design of turbine blades the impulse blading and the reaction blading.

Impulse Blading

The impulse blading principle is that the steam is directed at the blades and the impact of the steam on the blades drives them round.  The day to day example of this principle is the pelton wheel.ref    Turbines.  

In this type of turbine the whole of the stage pressure drop takes place in the fixed blade (nozzle) and the steam jet acts on the moving blade by impinging on the blades.


Blades of an impulse turbine


Velocity diagram impulse turbine stage

z represents the blade speed , V r represents the relative velocity, V wa & V wb- represents the tangential component of the absolute steam in and steam out velocities

The power developed per stage = Tangential force on blade x blade speed.

Power /stage= (V w a  +  V wb).z/1000 kW per kg/s of steam


Reaction Blading

The reaction blading principle depends on the blade diverting the steam flow and gaining kinetic energy by the reaction.   The Catherine wheel (firework) is an example of this principle.  FOr this turbine principle the steam pressure drop is divide between the fixed and moving blades.


Velocity diagram reaction turbine stage

z represents the blade speed , V r represents the relative velocity, V wa & V wb- represents the tangential component of the absolute steam in and steam out velocities

The power developed per stage = Tangential force on blade x blade speed.

Power /stage= (V w a  +  V wb).z/1000 kW per kg/s of steam



The blade speed z is limited by the mechanical design and material constraints of the blades.






Rankine Cycle

The Rankine cycle is a steam cycle for a steam plant operating under the best theoretical conditions for most efficient operation.  This is an ideal imaginary cycle against which all other real steam working cycles can be compared.

The theoretic cycle can be considered with reference to the figure below.  There will no losses of energy by radiation, leakage of steam, or frictional losses in the mechanical componets.  The condenser cooling will condense the steam to water with only sensible heat (saturated water).   The feed pump will add no energy to the water.   The chimney gases would be at the same pressure as the atmosphere.

Within the turbine the work done would be equal to the energy entering the turbine as steam (h1) minus the energy leaving the turbine as steam after perfect expansion (h2) this being isentropic (reversible adiabatic) i.e. (h1- h2).   The energy supplied by the steam by heat transfer from the combustion and flue gases in the furnace to the water and steam in the boiler will be the difference in the enthalpy of the steam leaving the boiler and the water entering the boiler = (h1 - h3).


Basic Rankine Cycle

The ratio output work / Input by heat transfer is the thermal efficiency of the Rankine cycle and is expressed as

Although the theoretical best efficiency for any cycle is the Carnot Cycle the Rankine cycle provides a more practical ideal cycle for the comparision of steam power cycles ( and similar cycles ).   The efficiencies of working steam plant are determined by use of the Rankine cycle by use of the relative efficiency or efficiency ratio as below:



The various energy streams flowing in a simple steam turbine system as indicated in the diagram below.   It is clear that the working fluid is in a closed circuit apart from the free surface of the hot well.  Every time the working fluid flows at a uniform rate around the circuit it experiences a series of processes making up a thermodynamic cycle.

The complete plant is enclosed in an outer boundary and the working fluid crosses inner boundaries (control surfaces).. The inner boundaries defines a flow process.

The various identifiers represent the various energy flows per unit mass flowing along the steady-flow streams and crossing the boundaries.  This allows energy equations to be developed for the individual units and the whole plant...

When the turbine system is operating under steady state conditions the law of conservation of energy dictates that the energy per unit mass of working agent ** entering any system boundary must be equal to the rate of energy leaving the system boundary.

**It is acceptable to consider rates per unit mass or unit time whichever is most convenient

Steady Flow Energy Equations

Boiler

The energy streams entering and leaving the boiler unit are as follows:

F + A + h d = h 1 + G + hl b   hence    F + A = G + h 1 - h d + hl b


Turbine

The energy streams entering and leaving the boiler unit are as follows:

h 1 = T + h 2 + hl t    hence   0 = T - h 1 + h 2 + hl t


Condenser Unit

The energy streams entering and leaving the boiler unit are as follows:

W i + h 2 = W o + h w + hl c   hence     W i = W o + h w - h 2 + hl c


Feed Water System

The energy streams entering and leaving the Feed Water System are as follows:

h w + d e + d f= h d + hl f   hence  d e + d f = - h w + h d + hl


The four equations on the right can be arranged to give the energy equation for the whole turbine system enclosed by the outer boundary

That is ..per unit mass the of working agent (water) the energy of the fuel (F) is equal to the sum of

-  the mechanical energy available from the turbine less that used to drive the pumps (T - (d e+ d f)

-   the energy leaving the exhaust [G - A] using the air temperature as the datum.

-  the energy gained by the water circulating through the condenser [W o - W i]

-   the energy gained by the atmosphere surrounding the plant Σ hl

The overall thermal efficiency of a steam turbine plant can be represented by the ratio of the net mechanical energy available to the energy within the fuel supplied.   as indicated in the expressions below...








Turbine Vapour Cycle on T-h Diagram


Steam cycle on Temp - Enthalpy Diagram

This cycle shows the stages of operation in a turbine plant.   The enthalpy reduction in the turbine is represented by A -> B . The reversible process for an ideal isentropic (reversible adiabetic) is represented by A->B'. This enthalpy loss would be (h g1 - h 2 ) in the reversible case this would be (h g1 - h 2s ).

The heat loss by heat transfer in the condenser is shown as B->C and results in a loss of enthalpy of (h 2- h f2) or in the idealised reversible process it is shown by B'-> C with a loss of enthalpy of (h 2s- h f2).

The work done on the water in extracting it from the condenser and feeding it to the boiler during adiabetic compression C-> D is (h d - h f2 ) = length M

The energy added to the working agent by heat transfer across the heat transfer surfaces in the boiler is (h g1 - h d ) which is approx.( h g1 - h f2 )

The Rankine efficiency of the Rankine Cycle AB'CDEA is

The efficiency of the Real Cycle is

For notes on the Rankine Cycle modified for superheat Rankine superheat

....More notes to follow....


Steam Turbine Links
  1. Wikipedia- Steam Turbines..A series of very informative notes and diagrams
  2. Steam Turbines..A one page article with very good graphics
  3. Technology Characterization Steam Turbine ..A downloadable paper including lots of useful relevant information
  4. Tpub-Steam Turbines ..Lots of useful Information and very nice sketches

This page is being developed


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Last Updated 27/01/2013