Mechanical Engineering Systems 2008 Part 4 potx

If the steam was taken awayfrom the water from which it is produced, and more heat energy added,some of the droplets would change into pure steam, and the steam would be drier.. The stea

indicating it is what we call ‘wet steam’.

All boilers, of whatever size, are doing the same thing as the kettle,i.e boiling water For low grade applications such as heating, we mayneed only hot water For turbines we are interested in much highertemperatures and pressures to produce steam of the right quality

We have already said that the steam produced by a kettle is wet steam.This sort of steam is made up of water droplets and ‘pure steam’, i.e.steam which does not have water droplets If the steam was taken awayfrom the water from which it is produced, and more heat energy added,some of the droplets would change into pure steam, and the steam would

be drier Eventually all the water droplets would have changed state andthe steam would be dry

The steam produced from the boiling water is at the same temperature

as the water This is called the saturation temperature, ts.

The steam cannot rise above this temperature until all the waterdroplets have disappeared, because all the heat energy supplied is used

to change the state of the water droplets, i.e latent heat ofvaporization

A soon as the steam has dried, and if more heat energy is supplied, the

temperature of the steam will increase to produce superheated steam,

i.e steam above the saturation temperature of the water from which itwas produced

Using tables of steam properties – steam tables – we can find theenergy of the steam This energy is available to do work in a turbine or

to be transferred for heating purposes

The production of steam

Figure 2.6.1 shows diagrammatically the production of steam

(1) Boiling water, i.e water at saturation temperature, ts.(2) Wet saturated steam Steam composed of water droplets and ‘pure

steam’ Temperature, ts Low dryness fraction, x.

(3) Wet saturated steam More water droplets have changed into ‘pure’

steam Temperature, ts Dryness fraction, x, higher.

Key points

 Wet steam cannot be

superheated

 Steam containing water

droplets is called wet

sat-urated steam

 Steam not containing

water droplets, but which

 The degree of wetness of

saturated steam is given

by its dryness fraction, x.

This is a value between 0

and 1 The higher the

value, the drier the steam

and the more heat energy

the steam will contain

Dryness fraction is the

ratio of the mass of pure

steam to the total mass of

the steam sample, and

indicates what is called

the quality of the steam.

Key points

To fix a value in the steam

tables:

 If the steam is wet, we

need to know its pressure

and its dryness fraction

 If the steam is

super-heated, we need to know

its pressure and its

tem-perature

Figure 2.6.1 Production of

steam

(4) Dry saturated steam No water droplets Temperature, ts Dryness fraction, x = 1.

(5) Superheated steam Temperature above, ts.

The steam temperature cannot be raised above saturation temperature,

ts, until all the water droplets have gone

The temperature/enthalpy (T/h) diagram

Figure 2.6.2 shows a simplified diagram of temperature against enthalpy,

h Remember to think of enthalpy as ‘total energy’ made up of internal

energy and pressure energy Values of enthalpy are used to calculate heatenergy transfer and work transfer, as we see later in this chapter

On the diagram:

hf: enthalpy of water at saturation temperature, ts(kJ/kg)

hg: enthalpy of dry steam (kJ/kg).

hfg: hg – hf: latent heat of vaporization (kJ/kg).

All these values are found in the steam tables, which use the unitsgiven

It is worth studying this diagram carefully because it gives a clearpicture of what is happening alongside the associated steam tablevalues, and shows dryness fraction and degree of superheat

The diagram can be drawn for any pressure See Figure 2.6.3 which

is an accurate plot of temperature against specific enthalpy

Note the following:

 The liquid, wet steam and superheat regions

 The saturated liquid line

 The saturated vapour line

 The lines of constant pressure

The separating and throttling calorimeter

The quality (i.e the dryness) of wet steam can be found by using aseparating and throttling calorimeter Figure 2.6.4 shows the generalarrangement of the device

The separator, as its name suggests, physically separates the waterdroplets from the steam sample This alone would give us a good idea

of the dryness of the steam, despite that the separation is not complete,because, as we have seen the dryness fraction is the ratio of the mass ofpure steam to the total mass of the steam

Having separated out the water droplets we can find their mass to

give us the mass of water in the sample, m1 The ‘pure steam’ is then

condensed to allow its mass to be found, m2 Then,

Dryness fraction from separator, x = m2

m1+ m2

A more accurate answer is obtained by connecting the outlet from theseparator directly to a throttle and finding the dryness fraction of thepartly dried steam

In the throttling calorimeter, the steam issuing through the orificemust be superheated, or we have two dryness fractions, neither of which

we can find Throttling improves the quality of the steam, which isalready high after passing through the separator, therefore superheatedsteam at this point is not difficult to create

To find the enthalpy of the superheated steam, we need itstemperature and its pressure

Figure 2.6.4 Separator and

throttling calorimeter

For the throttling calorimeter,

Enthalpy before = enthalpy after throttling (see page 57, ‘Applications

of the SFEE’)

hf+ x.hfg = enthalpy from superheat tables

If we call the dryness from the separator, x1, and the dryness from the

throttling calorimeter x2, the dryness fraction of the steam sample is x,

After the throttle, the pressure of the steam was 1 bar andthe temperature 150°C Find the dryness fraction of thesteam sample

Dryness from separator = m1

m1+ m2 =

10

10 + 0.55

= 0.948 = x1

For the throttle,

Enthalpy before = enthalpy after

The steam tables

Figure 2.6.5 shows a steam tables extract for a pressure of 2 bar

We are concerned at this stage only with p, ts, Vg, hf, hfg and hg Specific enthalpy, h, is the total energy of 1 kg of the steam, made up

of internal energy and pressure energy It is important because it is theenergy we want to use in the steam heater or turbine

Specific volume, v, is the volume in m3which 1 kg of the steam willoccupy It is important because the size of the boilers and piping, etc.,can be estimated using these values

Pressure is p, and saturation temperature (boiling point corresponding

to the pressure) is ts.Once again, refer to Figure 2.6.2 for an idea of these quantities

Finding values in the saturated water and steam section

 To find the enthalpy of water, look up pressure and read off hf

 To find the enthalpy of dry steam, look up pressure and read off hg.

 To find the enthalpy of wet steam, look up pressure and use

h = hf+ x.hfg

 Similarly, to find internal energy values, use uf, ug, and uf + x.ufg

 To find the specific volume of dry steam, use v = vg.

 To find the specific volume of wet steam, use v = x.vg.

Superheated steam

These tables are arranged differently from the saturated water and steam

tables Remember that dryness fraction, x, is not involved in these

values, because steam cannot be superheated unless all the waterdroplets have gone

The temperature of the superheated steam must be known Figure2.6.6 shows an extract for the details of superheated steam at 10 bar,350°C

The degree of superheat is the number of degrees above ts In thiscase, the degree of superheat is 350 – 179.9 = 170.1°C

Note that most steam tables have a table for water between 0 and100°C, with corresponding pressures in the second column This is

useful when finding the enthalpy of water, hf, between 0 and 100°C

Figure 2.6.5 Saturated water

and steam extract for a

pressure of 2 bar

Figure 2.6.6 Superheated

steam table extract for a

pressure of 10 bar, temperature

350°C

Example 2.6.2

Find the enthalpy of:

(a) Steam at 6 bar, dry From tables, hg= 2757 kJ/kg(b) Steam at 50 bar, dry From tables, hg = 2794 kJ/kg(c) Steam at 12 bar, dryness, x = 0.75

h = hf+ x.hfg= 798 + (0.75 × 1986) = 2287.5 kJ/kg(d) Steam at 70 bar, x = 0.9

h = hf+ x.hfg= 1267 + (0.9 × 1505) = 2621.5 kJ/kg(e) Steam at 10 bar 300°C From superheat tables,

Find the internal energy of:

(a) 1 kg of dry steam at 10 bar ug= 2584 kJ/kg

(b) 3 kg of water at 130°C Refer to temperature only, uf =

u = 1149 + 0.8(2597 – 1149) = 2307.4 kJ/kg

(d) 5 kg of steam at 40 bar, t = 500°C From superheat tables, u = 3099 kJ/kg For 5 kg, u = 5 × 3099 = 15 495 kJ.

Example 2.6.5

A boiler produces steam at 50 bar, 350°C What is the degree

of superheat of the steam?

The degree of superheat is the number of degrees abovesaturation temperature,

i.e degree of superheat = t – ts.

In this case, degree of superheat = 350 – 263.9 = 86.1°C

Example 2.6.6

A vessel of volume 0.2816 m3contains dry steam at 14 bar.What mass of steam does the vessel contain?

Specific volume of dry steam at 14 bar = vg= 0.1408 m3/kg

We have 0.2816 m3, which is twice this volume, therefore thevessel contains 2 kg

Example 2.6.7

A steam space in a boiler drum has a volume of 0.5 m3 If itcontains steam at 10 bar, dryness = 0.75, what is the mass

of steam in the drum?

Specific volume of the steam, v = x.vg = 0.75 × 0.1944

(e) Steam at 20 bar, 250°C

(f) Dry saturated steam at 8 bar

(2) If steam at a pressure of 40 bar has a temperature of 450°C,what is the degree of superheat?

(3) Find the volume of 6 kg of steam at 5 bar, x = 0.8.

Key points

 The steam tables values

are specific, i.e for 1 kg

 Values of enthalpy and

internal energy are kJ/kg

 For enthalpy of water

between 0 and 100°C,

use the page of the steam

tables where temperature

is in the first column

When finding the enthalpy

of water, refer to the

tem-perature only,

disregard-ing the pressure which

makes little difference

 In the superheat tables,

for convenience the

sat-uration temperature is in

brackets beneath the

pressure

 It is necessary to

inter-polate between values if

a value is in between the

values given See page

86, ‘Maths in action’

(4) The steam drum in a boiler contains steam at 30 bar, 350°C.

If the volume of the drum is 0.4525 m3, what mass of steamdoes it contain?

(5) Find the internal energy of 6 kg of steam at 5 bar, dryness0.9

(6) Steam at 6.5 bar passes from a steam main through aseparating and throttling calorimeter The condition of thesteam after throttling is 1 bar, 125°C The mass of steamcondensed after throttling is 25 kg and 1.31 kg of water iscollected in the separator Calculate the dryness of thesteam

It is important to have a good working knowledge of the steamtables, and be able to use them routinely for finding the valuesrequired

Steam flow processes

We have already seen the application of the steady flow energy equation

in gas processes

In applying the same equation to steam, instead of using theexpression

h = m.cp.T

which applies only to a perfect gas, we refer to steam tables and read off

values of h for wet, dry or saturated steam, as required.

Figure 2.6.8 shows the heater.

From the SFEE,

(2) In a steam turbine plant, the steam supply to the turbine is 44bar dry saturated and the exhaust steam is 0.04 bar with adryness of 0.69 Determine the power output from the turbinefor a steam mass flow rate of 3 kg/s

(3) A turbo-generator is supplied with superheated steam at apressure of 30 bar and temperature 350°C The exhauststeam has a pressure of 0.06 bar, dryness 0.88 Find:(a) The enthalpy drop per kg of steam;

(b) The power developed if the steam flow rate is 0.25 kg/s.(4) Steam enters the heating coils of an evaporator at 3 bar,300°C and leaves as water at 25°C How much heat energyhas been given up per kg of steam to the water in theevaporator? If there are 75 kg of water at 25°C in theevaporator, to what temperature will it rise after 6 kg of steamhave passed through the heating coil? Specific heat ofwater = 4.2 kJ/kgK

(5) Steam enters the superheaters of a boiler at a pressure of 20bar, dryness 0.8, and leaves at the same pressure at atemperature of 300°C Calculate the heat energy suppliedper kg of steam in the superheaters and the increase involume of the steam through the superheaters

Figure 2.6.8 Example 2.6.9

Steam plant

If we consider all the items in a simple steam plant, we have boiler,turbine and condenser For calculation purposes it is usual to neglect thefeed pump which supplies water to the boiler Figure 2.6.9 shows thebasic steam plant Each of these items involves a steady flow process,and as we saw in Section 2.5, and in the foregoing examples, the SFEEcan be reduced to a very simple form

For each item then, it is a simple matter to find the work or heatenergy transfers if we know the condition of the steam or thetemperature of the water as the case may be We can then find turbinepower, heat energy lost to condenser cooling, heat energy supplied tothe boiler and plant efficiency

If we made the plant more sophisticated by adding feed heaters(steam heaters which pre-heat the boiler feedwater), multi-stageexpansion in the turbines, de-aerators (to remove oxygen from the feed

to reduce corrosion), and other refinements, we could use the simplifiedSFEE for these too, since they are all steady flow

It is convenient to show steam processes on axes of properties, and acomplete steam plant cycle can then be seen

In the introduction to steam, we looked at a simplified temperature/enthalpy curve as an aid to understanding the production of steam and thevalues shown in the steam tables To show steam processes in steam plant,pressure/volume, temperature/entropy, enthalpy/entropy and pressure/

enthalpy diagrams can be used, but usually the T/s diagram is sufficient The h/s diagram is available as a chart from which values can be read

instead of using the steam tables

The p/h diagram is usually used for refrigerant plant.

Figures 2.6.10, 11, 12 and 13 show the form of these plots for anyvapour They can be produced for water by taking values from the steamtables

For each plot note:

 The saturated liquid and saturated vapour lines

 The liquid, vapour and superheat regions

 The critical point is at the turning point of the saturated liquid andthe saturated vapour lines, where there is a zero value of latent heat

of vaporization, and therefore boiling to produce the vapour doesnot occur

Figure 2.6.9 Basic steam plant

Figure 2.6.10 p/V diagram for

vapour

Figure 2.6.11 T/s diagram for

Figure 2.6.14 shows the basic steam plant and the thermodynamic cycle

on T/s axes, with superheated steam entering the turbine at 1, wet steam

leaving the turbine, 2, and condensation to saturation temperature (i.e.only enough heat energy removed to produce condensation into water –further cooling, called sub-cooling, would take the process to the left ofthe saturated liquid line), 3 The feed pump raises the pressure of thefeedwater to boiler pressure, and the feed enters the boiler at 4 Heating

of the feed begins at this point, in a preheater or in the boiler itself ifthere is no economizer Note that the boiler is a constant pressure

process and follows the constant pressure line in the T/s diagram.

Carnot and Rankine cycles

We have looked at the Carnot cycle, consisting of two isothermals andtwo isentropics, as a reference cycle, which could, if it were possible toproduce it, give the greatest efficiency for the available maximum andminimum temperatures occurring in the cycle

Figure 2.6.15 shows the Carnot cycle for a vapour on the T/s

diagram

It would be very difficult to stop the condensation at point 3, and thencompression of a wet vapour follows, which is also not realistic TheCarnot cycle, therefore, is not suitable in this case as a referencecycle

Instead, the modified Carnot cycle, called the Rankine cycle is used

Figure 2.6.16 shows this cycle on the T/s diagram There is isentropic

compression in the feedpump from 3 to 4 and isentropic expansion from

1 to 2, but condensation is extended to the saturated liquid line From 4

to 1 the feed is at first heated to saturation temperature and then changesinto steam at constant temperature, because of latent heat of vapor-ization Note that the constant pressure heating follows the constantpressure line on the diagram

If the enthalpies are known, it is an easy matter to calculate Rankineeficiency

R = turbine workheat supplied at boiler =

Figure 2.6.17 shows the plant and the process on T/s