Vapour Power Cycle

Vapour Power CycleSuresh Kumar YAssociate ProfessorMechanical EngineeringCarnot cycle

Rankine cycle

Actual Rankine cycle

Parameters affecting cycle efficiency

Rankine cycle with re-heating

Regenerative cycle

Dual cycle (binary vapour cycle).

Topics

Carnot cycle (for gases)

Carnot cycle (for steam)

Process 1-2: Reversible adiabatic compression process from P1 to P2 in the pump or a compressor.

Process 2-3: Reversible isothermal heat addition process at constant temperature TH and pressure P2 in a boiler, steam generator, nuclear reactor.

Process 3-4: Reversible adiabatic expansion process from P3 to P4 in a steam turbine or steam engine.

Process 4-1: Reversible isothermal heat rejection process at constant temperature TL and pressure P1 in a steam condenser such that the wet vapour at 4 is cooled to state-1 followed by a compression so that the wet vapour will return to its original state-2 and the cycle repeats.

TH and TL are the source and the sink temperatures.A theoretical cycle (all reversible process) is having the maximum efficiency.The practical cycle for the steam power plant is the Rankine cycle.It is difficult to device a system which can receive and reject heat at constant temperature. A wet vapour is the only working fluid which can do this conveniently.

Process 1-2: Water from the condenser at low pressure is pumped into the boiler at high pressure. This process is reversible adiabatic.

Process 2-3: Water is converted into steam at constant pressure by the addition of heat in the boiler.

Process 3-4: Reversible adiabatic expansion of steam in the steam turbine.

Process 4-1: Constant pressure heat rejection in the condenser to convert condensate into water.Cycle 1-2-3-4: Simple Rankine cycle with saturated steam expanding in the turbine.

Cycle 1-2-31-41: Simple Rankine cycle with wet steam expanding in the turbine.

Cycle 1-2-311-411: Simple Rankine cycle with super-heated steam expanding in the turbine.

Cycle 11 -21 -3-4: Carnot cycle with steam.

Modified Rankine cycle is used as the thermodynamics cycle for the vapour power cycle.

Deviations from the Carnot cycle

Mean Temperature of Heat AdditionCapacity of Steam Power PlantChange in K.E. and P.E. from one point in the cycle to another point are neglected.Analysis of the ideal cycle

Pump input(a) Effect of Superheat:Effect of Varying the Operating Conditions on the Efficiency of theSimple Rankine Cycle

Cycle 1-2-3-4-1 using dry saturated steam at the exit of the boiler Cycle 1-2-3-4-1 using superheated steam at the exit of the boiler.Area 4-3-31-41 extra work output from the cycle because of super heating.Area B-3-31-C extra heat added to the cycle.Thermal efficiency of the cycle increases.Quality of the steam leaving the turbine improves.The average temperature of heat addition increases.(b) Effect of Maximum Pressure (boiler pressure):

Here the maximum temperature of steam and the condenser pressure are held constant.Area 4-C-B-41 the net reduction in the heat rejection due to increase in the boiler pressure.The net work increases by the amount horizontal hatched area and decreases by the amount of the vertical hatched area.These two areas are approximately equal. Net work tends to remain the same. But heat rejected decreases.Cycle efficiency increases.Quality of steam leaving the turbine decreases.The average temperature at which heat is supplied increases.

(c) Effect of Condenser Pressure:

The net work is increased by the area 1-4-41-11-21-2.Heat added to the boiler is increased by the area A-21-2-B.These two areas are approximately equal.The thermal efficiency increases.Quality of steam decreases at the exit of the turbine.The temperature at which the heat is rejected decreases.The actual vapour power cycle differs from the ideal Rankine cycle because of irreversibility in various components. Fluid friction and undesired heat loss to the surroundings are the most common sources of irreversibility (piping losses frictional losses+heat transfer to the surrounding).There are pressure drops in the boiler and the condenser because of the friction. Irreversibility within the pump and the turbine also play important role in this deviation. A pump requires a greater work input and a turbine produces a smaller work output as a result of irreversibility.

Deviations of the actual cycle from the ideal cycleThe deviation of actual pumps and turbines from the isentropic ones can be accounted for by using adiabatic efficiencies as described below: Efficiency of pump:P = (h2s h1) / (h2 h1) (isentropic work input/ actual work input)Efficiency of turbine:T = (h3 h4) / (h3 h4s) (actual work output/ isentropic work output)

Condenser losses: Cooling of condensate below saturation temperature of water leaving the condenser.Efficiency of the Rankine cycle can be increased by increasing the pressure of the steam entering the turbine.This increases the moisture content of steam in the low pressure end of the turbine. In the reheat cycle the advantage of the increased efficiency with high boiler pressure is incorporated and yet avoid excessive moisture content in the low pressure stage of the turbine.Reheat cycle

Process 1-2, isentropic compression of water from condenser pressure to boiler pressure.Process 2-3, constant pressure heat addition in the boiler.Process 3-4, first stage expansion in high pressure turbine.Process 4-5, constant pressure heat addition in the reheater.Process 5-6, second stage expansion in low pressure turbine.Process 6-1, constant pressure condensation of steam in the condenser.The unique feature of this cycle is that steam is expanded to some intermediate pressure Pi in the high pressure turbine and is then reheated in the boiler after which it expands in the low pressure turbine to the condenser pressure.Total work done by both stages wT = (h3-h4)+(h5-h6)

Work done by the pumpwP = h2-h1

Heat added in the boiler, qH= h3 h2

Heat added in the reheater = h5 h4

Heat rejected in the condenser = h6 h1

Rankine efficiency =(wT wP)/(h3 h2)+(h5 h4)

Because of that the Rankine cycle efficiency is less than that of the corresponding Carnot cycle.In the regenerative cycle, the working fluid enters the boiler at some state between 2 and 21 and consequently the average temperature at which heat supplied is increased. Hence improving the cycle efficiency.Regenerative cycleIn the Rankine cycle without superheating, the average temperature of working fluid is much lower during 2-21 than during the evaporation process 21-3.

Idealised regenerative cycle

Feed water temperature is raised to the saturation temperature corresponding to boiler pressure before it enters the boiler.

Here the condensate circulates round the turbine casing, counter-flow to the direction of the steam flow in the turbine, resulting in the heat transfer from the vapour to the liquid flowing round the turbine casing.

The curve 3-4-5 represents the state of vapours flowing through the turbine and is parallel to the curve 1-2-21 which represents the pumping process 1-2 and 2-21, the state of the liquid flowing round the turbine casing.

The area a-2-21-b representing the heat transfer to the liquid and area c-4-3-d representing the heat transfer from the vapour and are equal to each other.

Thus area 21-3-d-b represents the heat transfer to the working fluid during the constant temperature process 21-3.

Area 1-5-c-a represents the heat transfer from the working fluid during the process 1-5 which is exactly equal to the area 11-41-d-b, that is the heat rejected in the related Carnot cycle.

Thus the efficiency of the idealised regenerative cycle is exactly equal to the efficiency of the Carnot cycle with the same heat supply and heat rejection temperature.

This cycle is not practical because It would not be possible to effect the necessary heat transfer from the vapour flowing inside the turbine to the feed water circulating round the turbine casing.The moisture content of the vapour leaving the turbine is considerably increased as a result of heat transfer.

The practical regenerative cycle involves the extraction of some of the vapour after it has partially expanded in the turbine and the use of the feed water heater.

Open Feed water Heaters

Regeneration increases efficiency of vapour power plant.

It involves raising the temperature of the liquid leaving the pump (called the feed water) before it enters the boiler.

This is achieved by extracting steam from turbine. This steam (which could have produced more work by expanding further in the turbine) is used to heat the feed water.The device where this takes place is called a regenerator or a feed water heater.

A feed water heater is basically a heat exchanger where heat is transferred from the steam to the feed water either by:Mixing the two fluid streams (Open feed water heaters), orWithout mixing them (Closed feed water heaters).

In the cycle:Steam enters the turbine at the boiler pressure (state 5) and expands isentropically to state 6. Here some steam is extracted to the feed water heater, while rest expands isentropically to the condenser pressure (state 7).

Steam leaves the condenser as a saturated liquid at state 1. The condensed water (also called feed water) enters a pump where it is isentropically compressed to the feed water heater pressure (state 2), and is routed to the feed water heater, where it mixes with the steam extracted from the turbine.The fraction of the steam extracted is such that the mixture leaves the heater as a saturated liquid at the heater pressure (state 3).

A second pump raises the pressure of the water to the boiler pressure (state 4).

Water in the boiler is now heated to the turbine inlet state (state 5).

In this case the mass flow rates are different through different components of the cycle.For example, if 1 kg of steam leaves the boiler and expands partially in the turbine to state 6,here m kg of steam is extracted to the feed water heater and the remaining (1-m) kg expands to the condenser pressure state 7.qh = h5-h4qL = (1-m) (h7-h1)wT = (h5-h6) + (1-m) (h6-h7)wP = (1-m) wP1 + wP2Energy balance for the feed water heater m*h6 + (1-m) (h2) = 1*h3Efficiency = (wT - wP )/ qhAnalysis of the cycle

Closed regenerative cycle

Binary vapour cycleHigh critical temperature at relatively low pressure.Low triple point temperature.Condenser pressure should be slightly above atmosphere.High enthalpy of vaporisation.Saturation dome that resembles an inverted U.Easy availability at low costs.

For best performance the working fluid for vapour power cycle should have the following characteristics:

Mercury-water binary vapour cycle

Combined gas vapour power cycle

Super saturated flow