Pure Substances4.1 Pure SubstancesThe pure substance is one that has a homogeneous and invariable chemical composition.

A pure substance may exist in many phases, but the chemical composition is same in all the phases.

Example: liquid water, water vapor, ice, a mixture of liquid water and water vapor are all pure substances.

In our analysis, we will deal only with simple compressible substances __ substances whose surface effects, magnetic effects, and electric effects are negligible.

Properties of a pure substance What we need to study about a pure substance __

The phases in which a pure substance may exist, The number of independent properties a pure substance may have, Methods of presenting thermodynamic properties. Understanding the properties and behavior of substances is essential for

designing and sizing various equipment. Example: We need to know properties of water to determine pipe diameter through which it has to flow. Example: We need to know properties of steam in order to design a boiler.4.2Formation of Steam at constant pressureA vapour has a partially evaporated liquid carrying particles of liquid in it . Steam is a vapour and it is used as working fluid in steam engines and steam turbines. Steam is also used for heating. Steam does not obey the law of perfect gases until it is perfectly dry or all the liquid particles have evaporated .Although steam is not considered as a perfect gas , its condition is described by properties namely pressure , temperature , volume , internal energy and enthalpy as in the case of gases . But the pressure, temperature and volume of steam are not connected by a simple relation such as the characteristic gas equation for a perfect gas.The general conservation of energy equation to steam in the same manner as it is applicable to gases.Water is an abundant substance and one of extreme importance to engineers. In thermodynamic equipments water is important both as a working fluid and as a coolant and therefore a substance whose properties must be known to the engineers.Although water is the most important vapour used as working fluid as it is readily available. There are many other substances which are also used commonly as Mercury and Freon are also used in refrigeration systems. In this chapter, the properties of water and system will be mainly dealt with. However the general principles involved in the study of water as a vapour, will apply to other vapour also. Tables of properties and chart similar to steam tables and charts are also available for these fluids. Consider one kg of water at 0 degree centigrade contained in the piston-cylinder arrangement. as the heating of water at 0 degree centigrade is continued , its temperature rises and continuous to rise until the boiling point is reached .the boiling of water at atmospheric pressure is 100 degree centigrade but it increases with increase in pressure .With the addition of heat, the temperature of water rises up to its boiling point corresponding to the pressure P exerted by the piston. Further addition of heat is used for evaporating the water and the volume increases and piston is pushed up. During the

process of evaporation the volume increases considerably. This continues until all the water gets evaporated. During the evaporation process, the temperature of steam remains constant. The temperature at which evaporation takes place is known as saturation temperature and the corresponding pressure is called saturation pressure. The heat absorbed by the water during heat from 0 degree centigrade to the boiling temperature is known as sensible heat or enthalpy of saturated water and is denoted by hf . When the steam contains some water particles, it is known as wet steam. When the steam does not contain any water particles, it is known as dry saturated steam.The heat utilized in converting water at boiling point into steam at same temperature is known as latent heat or enthalpy of evaporation and is denoted by hfg . if the steam is further heated at constant pressure , the temperature of steam starts rising in accordance to Charles’s law . Superheated steam can be treated as perfect gas as it follows the Boyle’s and Charles’s laws to some extent. The heating of dry steam above its saturation temperature is known as superheating and the steam is known as superheated steam. The temperature difference is known as degree of superheat.

Fig.4.12Formation of Steam at constant pressure

Temperature versus Total Heat (enthalpy) Graph during steam Formation

Initial Conditions:T = 0OC P = 760 mm of hg.

T increases considerably increases slightlyP remains const.

T remains const. (99.6 OC) increases very muchP remains const.

T increases increases P remains const.

The process of steam formation as discussed above can be represented on a graph taking heat (enthalpy) on X axis and temperature on Y axis . The formation of steam superheated steam from 0 degree centigrade of water at a pressure P1 kgf/cm2 . the line abcd shows the variation of temperature as the water gets convarted into superheated steam .

During the formation of superheated steam , from water at 0 degree centigrade at a given pressure P1 , heat is absorbed in m three stages .

1. The heating of water from 0 degree centigrade to its boiling temperature is shown by line ab . the temperature of water during this heating continuously increases . The heat absorbed by water during this heating is known as sensible heat or enthalpy of saturated water and is denoted as hf .

2. During the transformation of water into steam , the temperature remains constant . The heat absorbed by water during this transformation is known as latent heat of steam and denoted by hfg . This transformation is shown by line bc . The total heat of steam when steam is completely dry is the sum of sensible heat and latent heat and is denoted by hg .

hg = hf + hfg

3. The superheating of steam ( heating above its saturation temperature ) is shown by line cd . The heat absorbed by the steam during the stage of superheating is known as superheat and is given by

superheat = Cps ( Tsup - Ts )kcal/kgwhere Cps is specific heat of steam and Tsup and Ts are the superheat and saturation temperatures of steam at the given pressures .

As the pressure increases say P2(p2 >p1),the boiling temperature of the water also increases.The point 'e' represents the boiling of saturation temperature at pressure p2 and f is the point which corresponds to dry saturated steam at pressure p2 . The line fg

represents the superheating at constant pressure p2 .It is obvious from the figure that the sensible heat of water increases with increasing pressure while latent heat decreases with increase in pressure.Similarly a family of curves can be drawn for different pressures.A line joining the points a,b,e and h is known as saturated liquid line which forms the boundry between wet and superheated steam . Similarly a line joining the points c ,f ,i which represents dry saturated steam , is known as dry saturated steam line ( saturated vapour line ) which forms the boundry between wet and superheated steam . The region to the left of the saturated liquid line is known as water region and region right to the saturated steam line is known as superheated steam region .

As seen from the figure , the latent heat of steam decreases as the pressure increases and it becomes at point 'K' where liquid line and dry saturated steam line meet . This point is known as critical point . At this point liquid and vapour phase merges and

become identical in every respect . The temperature corresponding to the critical point is known as critical temperature and the pressure corresponding to the critical point is known as the critical pressure . The critical temperature and critical pressure for steam are 374 degree centigrade and 225kgf/cm2 respectively . Above the critical conditions water behave as one phase and there is no density difference between the two phases .

4.3 Condition of Steam

The steam may exist in wet , dry-saturated or superheated condition . When the steam contains water particles , the steam is known as wet steam . When the steam does not contain water particles and its temperature is equal to saturation temperature at the given pressure , the steam is known as dry steam . When the steam temperature is above the saturation temperature , the steam is known as superheated steam . The wet ,dry and superheated steam conditions are represented by by the points c , d , e .

The steam generated in any boiling vessel containing of water in contact with steam is always wet steam . It always contains water particles at boiling temperature in a finely divided state . The quality of wet steam is measured by a factor known as dryness fraction . dryness fraction of wet steam is the ratio of the mass of actual dry steam to the mass of total steam . Dryness fraction of steam is often spoken as the quality of steam and is expressed by the symbol x .

W = weight of dry steam in the steam consideredw = weight of water in suspension in the steam considered .then the dryness fraction of steam is given by

x = W/(W + w)If the quality of steam given is 80

% dry , it means that

one kg of steam contains 0.8 kg of dry steam and 0.2 kg of water particles .When the steam is completely dry then it is said that steam is 100% dry . The condition of superheated steam is measured by degree of superheat which is equal to (Tsup - Ts ) .

Advantages of Superheated Steam

In most of the power developing systems , superheated steam is generally used as it offers following advantages :

1. The heat content of superheated steam is more than saturated steam , hence its capacity to do work is increased without increasing the pressure .

2. Increase in wetness during expansion of superheated steam is less than saturated or wet steam at the same pressure and so the condensation of steam on cylinder walls of engine or in the last stage of the turbine is reduced considerably .

3. The superheating of steam is done by using the heat in the exhaust gases which would have otherwise passed through the chimney without its use .

4. The overall thermal efficiency of the plant increases by the use of superheated steam .4.4Thermodynamic Properties of Steam

In the study of various engineering processes and cycles , other thermodynamic properties of steam as enthalpy , specific volume must be known in addition to pressure and temperature of the steam .

1. Pressure and Saturation Temperature . The boiling temperature or the

temperature at which steam is formed is fixed for each given pressure . Steam has one and only one saturation temperature at a given pressure . The saturation temperature increases with increase in pressure as mentioned earlier .

2. Enthalpy or Total Heat . The energy content of steam above water at 0 degree centigrade is known as enthalpy or total heat .

Dry Saturated Steam . the heat content of dry saturated steam per kg at the given pressure is equal to sensible heat and latent heat .

Therefore , hg = hf + hfg

Wet Steam . The heat content of the wet steam per kg at a given pressure is equal to the sum of the sensible heat and latent heat of the wet steam . If the dryness fraction of the steam is x , then the total heat or enthalpy of steam is given by

h = hf + xhfg

Superheated Steam . The heat content of superheated steam per kg at a given pressure is equal to the total heat of dry steam and the superheat . If the temperature of the steam at pressure P is Tsup , then the total heat of the superheated steam is given byThe 'de' repesents isentropic expansion which is commonly assumed in steam turbines. The work done per kg of steam passin throgh turbine is given by the difference of enthalphy at points 'd' and 'e'/The 'fg' represents throttling ( throttlin is a constant enthalphy process ) so the final condition of the steam can be directly read from the chart at point 'g' . The principle is used for finding they dryness fraction of steam and governing the steam engines. The ananlysis of steam process and cycles require a ready knowledge of enthalpies in most cases and these can be found readily from h-s diagram therefore is widely used in all practical applications.3. Specific Volume and Density: The specific volume of steam is the volume occupied by one kg of steam at the given pressure and temperature.

The density of the steam is the mass of steam per unit volume of steam at the given pressure and temperature. The density is always the reciprocal of specific volume.

The specific volume of dry saturated steam is represented by a notation vg and specific volume of saturated liquid is represented by a notation vf .

Dry Saturated Steam: The specific volume of dry steam is the volume occupied by 1 kg of steam and is denoted by vg . It decreases with increasing pressure.

The density of dry steam is given by:

ρ = .

Wet Steam: If the dryness fraction of steam is x then one kg of steam contains x kg of dry steam and ( 1 – x ) kg of saturated liquid . The volume of one kg of wet steam is equal to the volume of x kg dry steam and volume of ( 1 – x ) kg of saturated liquid .

Therefore the specific volume of wet steam is given by : v = x vg + ( 1 - x ) vf

where vg and vf are the specific volumes of dry steam and saturated liquid at given pressure.

Under normal working pressures, vf vg .

v = x vg The density of wet steam is given by:

ρws =

Superheated Steam: It is always assumed that the steam is generated at constant pressure. The dry and superheated steam obeys the gas laws as mentioned earlier. Therefore , the specific volume of superheated steam is given by :

vsup = vg

Where Tsup and Ts are the temperatures of superheated steam and saturated steam at given pressure in absolute units. vg is the specific volume of dry steam. The density of superheated steam is given by:

ρsup =

4. Internal Energy of Steam : Consider the formation of dry steam at

pressure p from water at .

Saturated Liquid Saturated Steam

The heat given for the formation of one kg of steam is equal to h = hg + hfg. During the evaporation, the work is done by the steam in lifting the weight through a vertical height. The amount of work done is given by:

W= = = kcal/kg.

Therefore the amount of energy present in the steam in the form of stored energy out of hg is known as internal energy. Out of hg heat given to the water for the formation

of steam, is used for doing external work. The energy available in steam is

known as internal energy and it is denoted by u and is given by: u = hg – p (vg-vf)/ J

as vf vg

u = hg – p.vg/JThe internal energy of wet steam is given by:

u = ( hf + xhfg ) – p( xvg)/JThe internal energy of superheated steam is given by :

u = hg + Cps( Tsup + Ts ) – pvsup/J

where, vsup = vs

Entropy of Steam: As heat is added to water at 0 , in the process of

formation of steam, the entropy of water increases. The entropy increases during the various stages can be calculated as follows: (i) Heating upto saturation condition :

sf = Cpw . ln

where Tg is the saturation temperature.(ii) Evaporation:

sfg =

(iii) Dry saturated condition: sg = sf + sfg

= Cpw × ln +

(iv) Superheated condition;

s= sg + Cps. ln

Where, Tsup is the temperature of superheated steam. (v) Wet steam; s= sf + x.sfg

4.5 Steam Tables

The properties of dry saturated steam like saturation temperature, sensible heat, latent heat, total heat and specific volume vary with pressure. The values of these properties are obtained by experiments. These properties obtained by experiments are made available in tabular form as Steam Tables.

The properties of steam are tabulated either on pressure basis or temperature basis as shown below in table 3.1 and table 3.2.

Pressure kgf/cm2

Saturation Temp.

Specific

volume m3/kg

Enthalpy kcal/kg

Entropy kcal/kgK

Ts vf vg hf hfg hg sf sfg sg

1 99.6 0.00144 1.725 99.2 539.9 638.8 0.310 1.449 1.759

10 179 0.00112 0.198 181.3 482 663.3 0.509 1.056 1.575

Table 3.1 Properties of Steam on Pressure Basis Table 3.2 Properties of Steam on Temperature Basis Temp.

Saturati

on pressure kgf/cm2

Specific volume m3/kg

Enthalpy kcal/kg

Entropy kcal/kgK

Ts P vf vg hf hfg hg sf sfg sg

50 0.126 0.00101 12.04 50.0 569.0 619 0.168 1.761 1.929

80 0.483 0.00103 3.41 80.0 551.3 631.3 0.257 1.561 1.818

4.6 Temperature-Entropy and Enthalpy-Entropy Charts for Steam.The p-v diagram has very limited utility in dealing with vapours. Therefore T-s

and h-s diagrams are universally used for vapours. Temperature-Entropy Chart: From the steam tables, the liquid entropy,

saturated steam entropy and boiling or saturation temp are known. Therefore, the points a, a1 and a2 and b, b1 and b2 can be marked on the T-s diagram as shown in Fig.3.5 . The line joining the points a, a1 and a2 is known as saturated liquid line and the line joining the points b, b1 and b2 is known as saturated vapour line. The two lines join at the point X known as critical point and the corres. pressure and temperature at that point are known as critical pressure and temperature. On the left of the saturated liquid line is the region of pure liquid and on the right of saturated vapour line is the region of pure gas. The region enclosed by these two lines is known as region of wet vapour.

If the heat is added after point b, the temperature of the steam increases at constant pressure and it can be represented by point c and line bc represents superheated

line at constant pressure. The constant saturation temperature lines ab, a1b1 ……. also represent constant pressure lines.

Other important lines are the constant volume and constant dryness fraction lines. If the lines ab, a1b1 and a2b2 are equally divided into ten equal parts and if the 9th part of each line ( points d, d1, d2….. ) is joined by a line then it represent the 0.9 dryness fraction line. Similarly if all the 5th part of each line then 0.5 dryness fraction line .

The constant volume lines are also similarly plotted. The specific volume of saturated steam at Ta is vb which can be obtained from steam tables. Similarly vb1 will represent the specific volume of saturated steam at Ta1. However there will be a state of steam at Ta1 in the wet region, where it will have a dryness fraction x1 such that:

vb = x1vb2 Let f1 be this state on T-s diagram. Similarly there will be a state of steam at Ta2 at

dryness fraction x2 such that: vb = x2vb1

If f2 represent this then, b, f1, f2 will represent equal specific volumes, all numerically equal to vb and can be joined to form the specific volume line . vb, x1, x2 can be found from above equations as vb1 and vb2 are known from steam tables.

The constant temperature heating is shown by line ab, and constant pressure heating is shown by abc. Isentropic expansion is shown by de. The constant volume heating is shown by fg as shown in Fig.3.6.

Fig.3.6

h-s (Mollier) Diagram

Enthalpy-Entropy Chart: Diagram involving enthalpy and entropy was first introduced by Richard Mollier in 1904 and it is popularly known as Mollier chart. It is more convenient than temperature-entropy diagrams for the solution of certain problems. It is a chart on which enthalpy is taken as ordinate and entropy as abscissa.

Fig. 3.7 shows a commonly used h-s chart. The thick curve line represents the saturation line which is the same as the saturated vapour line of the T-s diagram. Other lines below and roughly parallel to it are constant dryness fraction lines.

In the wet region, the constant pressure lines are straight lines. This is because, the relation between the total heat and entropy for wet steam at constant pressure is linear one. In wet steam region, constant pressure is associated with constant temperature. Points in the superheated region for constant pressure lines are plotted from the total heat and entropy tables for superheated steam. The constant pressure lines curve a little after the saturation line. Above the saturation line, the roughly horizontal curves represent constant temperature lines. Constant specific volume lines are also represented on the same diagram using the procedure described for drawing T-s diagram. The state of steam can be readily represented on this diagram if atleast two parameters among pressure, temperature, enthalpy, entropy, dryness fraction, and specific volume are known.

Different processes can be easily represented on h-s diagram and enthalpy difference for each process can be easily read on diagram directly.The abc represents the superheating of steam passing through superheater at constant pressure as shown in Fig. 3.8. The heat added per kg of steam in superheater is given by the heat at point ‘c’ and heat at point ‘a’ which can be directly read from the chart.

Thermodynamic processesThe general energy equation applicable to perfect gases is also applicable to vapours and the procedure adopted for finding the changes of internal enrgy is also same. The different processes of expansion and compression used for gases are also adopted for vapours but the results may be different. The equation developed for work sone by gases are also applicable for vapours since the equation for the work done are based on mathematical laws.The different thermodynamic processes for vapours are discusse dhere.

1. Constant Volume ProcessConsider m kg of wet steam (dryness factor x1) at pressure p1 is heated at constant volume till its pressure becomes p2 . Assume the dryness factor after heating is x2.The mass of steam before and after heatin is same. The constant volume is v m(mass) = volume * density =vp1=vp2p1=p2 x1*vs1=x2*s2 x2= x1 * vs1/vs2vs1 and vs2 are the specific volumes of dry saturated steam at pressures p1 and p2 respectively which can be obtained from steam tables. If x2>1, it indiacates that steam is superheated . x1*vs1=vsup2and vsup2=vs2 *Tsup2/Ts2From the above equation ; Tsup2 can be calculated and the degree of superheated steam is given by (Tsup2 - Ts2 )The change of internal energy per kg of steam is given by

/\u=u2-u1 = [h2 - p2(x2vs2)/J] - [h1 - p1(x1vs1)/J] = [(hf2 +x2*hfg2) - (p2(x2*vs2)/J] - [(hf1 + x1*hfg1) - p1(x1*vs1)/JThe work done (W) =0 as change in volume is zero.Applyin the first law energy equation

q=/\u +W =/\u as W=0Note : If the steam becomes superheated then the necessary changes in the equations should be made.The same procedure is adopted for cooling also. The example of constant volume heating and cooling is the process occuring in a pressure cooker.

2. Constant Pressure Process. If the staem is heated at constant pressure and its dryness fraction changes from x1 to x2, the work done per gof steam is given byW=p(x2*vs2)/J - p(x1*vs1)/J =pvs1/j - (x2-x1) kcal/kgvs1=vs2 as pressure remains constant The heat transfer is given by Q=W+/\u=W+(u2-u1) =W + [(h2-p(x2*vs1)/J)-(h1-p(x1*vs1)/J)] as vs1=vs2 =pvs1/J(x2-x1) + (h2-h1) - pvs1/J(x2-x1) = h2-h1 = (hf2+x2*hfg2)-(hf1+x1*hfg1) = hfg1(x2-x1) Kcal/kg as hf1=hf2 and hfg1=hfg2This states that the heat added to the steam at constant pressure is equal to the change in enthalphy.If the steam becomes superheated after heating, the changes in the above expressions will be W=p*vsup2/J - p(x1vs1)/J =p(vs2 * Tsup2/Ts2)/J - p(x1vs1)/J =pvs1/J[Tsup2/Ts1 - x1] as vs1= vs2 and Ts1=Ts2 The heat transfer Q when steam is superheated is given by Q=h2-h1 =[hf2+hfg2+cps(Tsup2 - Ts2) - [hf1 +x1hfg1] =[hfg1(1-x1)+cps(Tsup2 - Ts2]as hf1=hf2 and hfg1=hfg2During the process of constant pressure heating, the temperature of the steam remains constant till it becomes dry saturated. Once the steam becomes saturated, the further heating will not be isothermal.An example of constant pressure heating is the generation of steam in boilers under steady state condition.

3. Isothermal or constant Temperature Process The constant pressure process is also a constant temperature process as mentioned earlier till the steam becomes dry saturated. As soon as the steam becomes superheated, it behaves like a perfect gas and will follow hyperbolic law at constant temperature(pv=constant)Therefore the isothermal process is constant pressure process for wet stam and hyperbolic process for superheated steam.

4.Hyperbolic Process.The hyperbolic process pv=constant is not an isothermal process as in the case of perfect gases. The hyperbolic process may be regarded as isothermal for superheated steam as superheated steam behaves like a gas. Consider 1 kg of steam at pressure p1 and dryness fraction x1 expanded in a cylinder according to the law pv=constant until the pressure becomes p2Applying the given law to the expansion processp1v1=p2v2

p1(x1vs1)=p2(x2vs2)x2=x1p1/p1*vs1/vs2If x2 is found to be greater than unity , it indicates that the steam is superheated.The above equation can written asp1(x1*vs1)=p2(vsup2)=p2(vs2*Tsup2/Ts2)From the above equation. the value of Tsup2 can be calculated as all other variables as known.Work sone is given byW=p1v1/J *log(V2/V1) =p1(x1vs1)/J *log(x2vs2/x1vs1) kcal/kg =p1(x1vs1)/J* log(p1/p2) as V2/V1=p1/p2Applying the first law energy equationQ=W+/\u =W+(u2-u1)where u2-u1=[h2 - p2(x2vs2)/J] -[h1 - p1(x1vs1)/J] =h2-h1 as p1(x1*vs1)=p2(x2*vs2)This indiactes that the change in internal energy durin hyperbolic expansion is equal to change in enthalphy Q=W+(h2-h1)

5 Isentropic ProcessDuring isentropic proces, the heat transfer is zero and change in entropy is also zero.If one g of steam at pressure p1 and dryness fraction x1 expands isentropically until the pressure falls to p2 then the entropy of steam before expansion is equal to the entropy of steam after expansion.sf1+x1*sfg1=sf2+x2*sfg2x2=[(sf1-sf2)+x1*sfg1]/sfg2If the steam initially is superheated, then sg1+Cps log(Tsup1/Ts1)=sf2+x2*sfg2x2=[sfg+Cps log(Tsup2/Tf1)-sf2]/sfg2The change in internal energy is given by( when steam is wet before expansion)/\u=u2-u1 =[h2-p2(x2vs2)/J] -[h1-p1(x1*vs1)/J]Applying the first law energy quation to the expansion process Q=W+/\uW=-/\u=-(u2-u1)=(u1-u2) as Q=0This states that the external work done during an isentropic process is equal to change in internal energy.If the steam flowing through the steam turbine follows isentropic law, the energy equation for this process can be written as h1-W+Q=h2 assuming PE=0 and /\KE=0W=h1-h2 as Q=0 for isentropic process.This indicates that the work done during isentropic flow process is equal to change in enthalphy. The isentropic process can be represented aspV1.13=constant( for wet steam)pV1.3=constant (for superheated steam)

6.Throttling Process The steam is said to be throttled when steam is forced through a small orifice under pressure or when steam passes through a partially open valve.As there is no change in potential energy and assuming /\KE=0, we can write energy equation for the above process ash1+W+Q=h2As W=0 and Q=0 h1=h2 Thsi indicates that the total enthalphy of steam remaining constant dusring throttling.The above equation can be written ashf1+x1*hfg1=hf2+x2*hfg2 x2=(hf1+hfg1-hf2)/hfg2If x2 is greater than unity, the steam is superheated after throttling. The above equation can be rewritten ashf1+x1hfg1=hg2+Cps(Tsup2-Ts2)/\T=(Tsup2-Ts2)=[hf1 + xhfg1-hg2]/Cps This can be regarded as adiabatic process with internal friction which converts all kinetic enrgy into heat.

7. MixingWhen the quantity of stean generated by one boiler is not sufficient then two or more boilers can supply steam to a steam engine or turbine. The boilers B1 and B2 are supplying steam to a common main. The mass of steam supplied by boiler B1 is m1 and by boiler B2 is m2. The pressure of steam of both boilers is same and so there is no pressure loss during the mixing of the steam.If the quantity of the steam supplied by each boiler is different then the quality of steam in the main will have to be calculated using enthalphy balance.If the quality of steam supplied by the boiler B1 has dryness fraction x1 and the steam supplied by the boiler B2 is superheated. If it is assumed that the steam in the main is wet, then we can write downm1[hf1+x1*hfg1]+m2[hf1+hfg1+Cps(Tsup2-Ts1)]=(m1+m2)[hf1+x2*hfg1]If we get x2>1 after solving the above equation it indicates that the steam is superheated and the maximum possible value of x2 is 1. h=hf + hf g + Cps ( Tsup – Ts )where, Ts is the saturation temperature of steam at the given pressure and Cps is the specific heat of superheated steam.

Where Tsut3 is the temperate of the steam passing through the steam main.

8. Superheating. The steam coming out of boiler is always wet as it remains in contact with water. Therefore it is to be superheated by passing through a superheated where the heat of hot gas is used for superheating the steam. The superheating arrangement used in locomotive boiler is shown in fig. 3.12

The steam from the bolder is passed through superheated tuber through receiving box. The steam becomes superheated passing fuel gas tubes. The heat of flue gases passing through the flue gas tubes is given to the steam passing through the superheated tubes and steam is superheated.

Assuming there is no pressure loss passing through the superheated, the heat given to the steam passing through the superheated is given by

where x is the dryness fraction of steam at the time of entering into the super heater and Tsup is the superheated temperature of steam coming out of superheated hf, hfg and Ts are the properties of steam at pressure p.

9. Desuperheating of Steam. The temperature of steam coming out of the superheated is to be controlled for the safe operation of the engine or the steam turbine and if the temperature of steam leaving the superheated is above the predetermined temperature then the temperature of steam entering the turbine is controlled by injecting the water into the steam in the form of spray.

The arrangement of a desuperheater is shown in fig. 3.13 Water is injected into the steam of steam as shown in the figure. The excess superheat is reduced by giving this heat to the water injected.

The temperatures of steam entering and leaving the desuperheater are Tsup1 and Tsup2 . The mass of steam flowing and mass of water injected per unit time are m s and mw

kg respectively.

Assuming that there is no pressure and heat loss, and applying the law of conservation of energy.

where hj1, hfgq and Ts are the properties of steam at pressure p1 and h f is the enthalpy of water inject into the desuperheater and t is given by h f-1xTw where Tw is the temperature of water injected.4.11 Measurements of dryness fraction

Measurement of Dryness Fraction of Steam

In various applications of steam it, is necessary to find the quality of steam. The steam used may be wet, dry or superheated, consider the flow of steam passing through k a pipe. its pressure and temperature may be direly measure. I with the help or pressure gauge and thermometer. if the observed temperature is above the saturation temperature of steam at the observed pressure which is known form steam tables. the steam is superheated and its degree of superheat is (Trup-Ts) on the other hand if the observed temperature corresponds to the saturated temperature of steam at observed pressure, then the steam may be dry or wet. Under this condition it is necessary to find the quality of steam in order to calculate other properties of the steam.

The dryness fraction of steam is measured with the help of steam calorimeter. Different types of calorimeters used in practice are discoursed here.

1.Separating Calorimeter. This calorimeter is used to measure probable value of dryness fraction of steam when the steam is very wet. The components of this calorimeter are shown in fig. 3.14 the steam whose dryness fractions is to be determined is passed through a sampling tube. The moisture is separated mechanically form steam passing through the separator. The water particles are separated due to inertia of the water droplets as the steam is passed through perforated trays. The outgoing steam is then condensed in a bucket kilometer.

Le: Wv = weight of water separated.

Ws = weight of steam condensed in the bucket calorimeter.

Ws = W2-W1

where W1 = weight at bucket with water before mixing.

W2 = weight of bucket with water after mixing the steam.

The dryness fraction of steam is given by

It is not possible in practice to remove all the suspended water particles and therefore the dryness fraction obtained by this calorimeter will not be very accurate. The only advantage of this calorimeter is a quick determination of the probable dryness fraction of very wet steam sample.

2. Throttling Calorimeter. This type of calorimeter is used to measure the dryness fraction of steam when the drones fraction is considerably high (0.95). The arrangement of calorimeter is shown in. The sample of the steam is passed through a throwing valve and is allowed to throttle down to a lower pressure until it comes out is superheated state. The pressure and temperature of superheated steam coming out of throttle valve are measured with the help of a water manometer and mercury thermometer as shown in.

1. Let p1 = Gauge pressure of steam before throttling (kg/cm2)

x1 = Unknown dryness fraction

Hg= barometer reading in cm of mercury

pa = Atmospheric pressure (Hgx1.033/76) kg/cm2

Ts1 =Saturation temperate of steam at (p1+pa)

hf1 = Sensible heat of steam at (p1+pa)

hfg1 = Lenten heat of steam at (p1+pa)

hw = Manometer reading in cm of water shooing the pressure of steam above atmosphere

p2 = Absolutes pressure of steam after throttling

all temperatures are in 0C.

Science the enthalpy of steam remains constant during throttling

The condition for the successful operation of this calorimeter its that the steam smuts be superheated after throttling. The limiting case is, the steams be at least completely dry. In this case, the above equation is reduced to

However it is practically not possible to measure this limit value of dryness fraction as at least few digress of superheat (1 to 20C) is necessary.

The dryness fraction of the steam cannot be determined by this calorimeter if the dryness fraction of the steam too low (<0.9). The minimum dryness fraction that can be measured depends upon the initial pressure of the steam as the pressure of deepens upon the initial pressure of the steam as the pressure of the steam after throttling virtually

remains near atmospheric, the extreme case being the exit pressure being equal to atmospheric pressure.

3. Separating and Throttling Calorimeter. It is already stated that the dryness fraction of the steam can be found by using throttling calorimeter only if the dryness fraction so greater than 0.95 when the dryness fraction is less than 0.9, then part of the water is removed first passing the steam through separating calorimeter and then it is passed through a throttling calorimeter. With a combined arrangement of separating and throttling calorimeter as shown in even low values of dryness fraction steam can be easily determined.

In a separating and throttling calorimeter, the steam from sampling tube is first passed through the separating calorimeter where it is partly dried up and then it is further rapeseed on to the throttling calorimeter from where it comes out as superheated steam. The steam coming out from throttling calorimeter is contused in a condenser and the weight of the condensate coming to of the condenser is recorded. The weight of water separated in separating calorimeter and the pressure and temperature of steam coming out of throttling valve are also recorded.

Let W = weight of steam condensed and collected from condenser.

w = weeding of water collected from separating calorimeter.

x = actual dryness fraction of steam in the main pipe.

x1 = Apparent dryness fraction of steam assuming the steam coming out of separating calorimeter is complete dry.

X2 Actual dryness fraction of steam entering into the throttling calorimeter which can be calculate as discussed earlier by equalizing enthalpy of steam before and after throttling.

Amount of water initially in the steam

= (1-x) (W+w)

Amount of water separated by separating calorimeter

= (1-x1) (W+w)

The amount of water carried by the steam entering into the throttling calorimeter

= (1-x2) W

The quantity of water in the steam given by equation 3.20 must be equal to the quantities of water given by equation 3.21 and 3.22

Substituting the value of W/(W+w) from equation 3.19 in the above equation

Solved problems

The following formulae are used for solving the problem

The density is the reciprocal of specific volume

Take Cps=0.55 kcal/kg K for steam if its value is not given in the problem.