STEAM TURBINES INTRODUCTION A steam turbine is a prime mover in which the potential energy of the steam is transformed into kinetic energy and latter in its turn is transformed into the mechanical energy of rotation of the turbine shaft. A steam turbine may be utilized in most diverse fields of industry, for power generation and for transport. The transformation of potential energy into mechanical energy of rotating shaft can be brought in different ways. CLASSIFICATION OF STEAM TURBINES The steam turbines can be broadly classified as follows: (1) According to action of steam: (a) Impulse turbine: In impulse turbine, steam coming out through a fixed nozzle at a very high velocity strikes the blades fixed on the periphery of a rotor. The blades change the direction of steam flow without changing its pressure. The force due to change of momentum causes the rotation of the turbine shaft. Examples: De-Laval, Curties and Rateau (b) Reaction turbine: In reaction turbine, steam expands both in fixed and moving blades continuously as the steam passes over them. The pressure drop occurs continuously over both moving and fixed blades. (c) Combination of impulse and reaction turbine (2) According to the number of pressure stages: (a) Single stage turbines with one or more velocity stages usually of small power capacities: These turbines are mostly used for driving centrifugal compressors, blowers and other similar machinery. (b) Multistage impulse and reaction turbines: They are made in a wide range of power capacities varying from small to large. (3) According to the direction of steam flow: (a) Axial turbines: In these turbines, steam flows in a direction parallel to the axis of the turbine rotor. (b) Radial turbines: In these turbines, steam flows in a in a direction perpendicular to the axis of the turbine; one or more low pressure stages are made axial. (4) According to the number of shafts: (a) Single shaft turbines: In these turbines, the rotors of the multi-cylinder turbines are mounted on the same shaft and coupled to a single generator. (b) Multi shaft turbines: In these turbines, separate rotor shafts are provided for each cylinder placed parallel to each other. (5) According to the method of governing: (a) Turbines with throttle governing: In these turbines, fresh steam enter through one or more (depending on the power developed) simultaneously operated throttle valves. (b) Turbines with nozzle governing: In these turbines, fresh steam enters through one or more consecutively opening regulators. (c) Turbines with by-pass governing: In these turbines, the steam besides being fed to the first stage is also directly fed to one, two or even three intermediate stages of the turbine. (6) According to the heat drop process: (a) Condensing turbines with generators: In these turbines, steam at a pressure less than the atmospheric is directed to the condenser. The steam is also extracted from intermediate stages for feed water heating (min. 2 – 3 to max. 8 – 9). The latent heat of exhaust steam during the process of condensation is completely lost in these turbines. (b) Condensing turbines with one or more intermediate stage extractions: In these turbines, the steam is extracted from intermediate stages for industrial and heating purposes. (c) Back pressure turbines: In these turbines, the exhaust steam is utilized for industrial or heating purposes. Turbines with deteriorated vacuum can also be used in which exhaust steam may be used for heating and process purposes. (d) Topping turbines: In these turbines, the exhaust steam is utilized in medium and low pressure condensing turbines. These turbines operate at high initial conditions of steam pressure and temperature, and are mostly used during extension of power station capacities, with a view to obtain better efficiencies. (e) Back pressure turbines with steam extraction from intermediate stages at specific pressure: These turbines are meant for supplying the consumer with steam of various pressures and temperature conditions. (f) Low pressure turbines: In these turbines, the exhaust steam from reciprocating steam engines, power hammers, presses, etc., is utilized for power generation purposes. (g) Mixed pressure turbines: In these turbines, the exhaust steam after passing through two or three pressure stages can be supplied to its intermediate stages. (7) According to the steam conditions at inlet to turbine (a) Low pressure turbines: These turbines use steam at a pressure of 1.2 ata to 2 ata. (b) Medium pressure turbines: These turbines use steam up to a pressure of 40 ata. (c) High pressure turbines: These turbines use steam at a pressure above 40 ata. (d) Very high pressure turbines: These turbines use steam at a pressure of 170 ata and higher and temperatures of 550C and higher. (e) Supercritical pressure turbines: These turbines use steam at a pressure of 225 ata and higher. (8) According to their usage in industry: (a) Stationary turbines with constant speed of rotation: These turbines are primarily used for driving alternators. (b) Stationary turbines with variable speed of rotation: These turbines are meant for driving turbo- blowers, air circulators, pumps, etc. (c) Non-stationary turbines with variable speed: These turbines are usually employed in steamers, ships and railway locomotives. ADVANTAGES OF STEAM TURBINES OVER STEAM ENGINES The following are the principal advantages of steam turbines over reciprocating steam engines: (1) The thermal efficiency of steam turbines is much higher than that of steam engines. (2) As there is no reciprocating part in steam turbines, perfect balancing is possible and therefore heavy foundation is not required. (3) Higher and greater range of speed is possible in case of steam turbines. (4) The lubrication is very simple in steam turbines as there are no rubbing parts. (5) The power generation in steam turbines is at uniform rate and hence no flywheel is required. (6) The steam consumption rate is lesser in steam turbines than in reciprocating steam engines. (7) Steam turbines are more compact and require less attention during operation. (8) Steam turbines are more suitable for large power plants. (9) The machine is highly simplified in construction and operation, as parts like piston, piston rod, cross head, connecting rod are not required. Hence maintenance cost is reduced. (10) Considerable overloads can be carried at the expense of slight reduction in overall efficiency. DIFFERENCES BETWEEN IMPULSE AND REACTION TURBINES Impulse turbine Reaction turbine (1) The steam completely expands in the (1) The steam expands partially in the nozzle nozzle and its pressure remains constant and further expansion takes place in the during its flow through the blade passages rotor blades (2) The relative velocity of steam passing (2) The relative velocity of steam passing over over the blade remains constant in the the blade increases as the steam expands absence of friction while passing over the blade (3) Blades are symmetrical (3) Blades are asymmetrical (4) The pressure on both ends of the moving (4) The pressure on both ends of the moving blade is same blade is different (5) For the same power developed, as (5) For the same power developed, as pressure pressure drop is more, the number of drop is small, the number of stages stages required are less required are more (6) The blade efficiency curve is less flat (6) The blade efficiency curve is more flat (7) The steam velocity is very high and (7) The steam velocity is not very high and therefore the speed of turbine is high. therefore the speed of turbine is low. IMPULSE TURBINES In impulse turbine, steam coming out through a fixed nozzle at a very high velocity strikes the blades fixed on the periphery of a rotor. The blades change the direction of steam flow without changing its pressure. The force due to change of momentum causes the rotation of the turbine shaft. Examples: De-Laval, Curties and Rateau turbines. Impulse Principle: The impulse turbine consists basically of a rotor mounted on a shaft that is free to rotate in a set of bearings. The outer rim of the rotor carries a set of curved blades, and the whole assembly is enclosed in an airtight case. Nozzles direct steam against the blades and turn the rotor. The energy to rotate an impulse turbine is derived from the kinetic energy of the steam flowing through the nozzles. The term impulse means that the force that turns the turbine comes from the impact of the steam on the blades. The toy pinwheel can be used to study some of the basic principles of turbines. When you blow on the rim of the wheel, it spins rapidly. The harder you blow, the faster it turns. The steam turbine operates on the same principle, except it uses the kinetic energy from the steam as it leaves a steam nozzle rather than air. Steam nozzles (hereafter referred to as nozzles or stationary blades) are located at the turbine inlet. As the steam passes through a nozzle, potential energy is converted to kinetic energy. This steam is directed toward the turbine blades and turns the rotor. The velocity of the steam is reduced in passing over the blades. Some of its kinetic energy has been transferred to the blades to turn the rotor. Impulse turbines may be used to drive forced draft blowers, pumps, and main propulsion turbines. Construction & Principle of operation: It primarily consists of a nozzle or a set of nozzles, a rotor mounted on a shaft, one set of moving blades attached to the rotor and a casing. A simple impulse turbine, also called De-Laval turbine, after the name of its inventor, can be diagrammatically represented below. This turbine is called simple impulse turbine since the expansion of the steam takes place in one set of nozzles. The uppermost portion of the diagram shows a longitudinal section through the upper half of the turbine, the middle portion shows the actual shape of the nozzle and blading, and the bottom portion shows the variation of absolute velocity and absolute pressure during the flow of steam through passage of nozzles and blades. The expansion of steam from its initial pressure (steam chest pressure) to final pressure (condenser pressure) takes place in one set of nozzles. Due to high drop in pressure in the nozzles, the velocity of steam in the nozzles increases. The steam leaves the nozzle with a very high velocity and strikes the blades of the turbine mounted on a wheel with this high velocity. The loss of energy due to this higher exit velocity is commonly known as carry over loss (or) leaving loss. The pressure of the steam when it moves over the blades remains constant but the velocity decreases. The exit / leaving / lost velocity may amount to 3.3 percent of the nozzle outlet velocity. Also since all the KE is to be absorbed by one ring of the moving blades only, the velocity of wheel is too high (varying from 25000 to 30000 RPM). However, this wheel or rotor speed can be reduced by different methods. DISADVANTAGES OF IMPULSE TURBINE (1) Since all the KE of the high velocity steam has to be absorbed in only one ring of moving blades, the velocity of the turbine is too high i.e. up to 30000 RPM for practical purposes. (2) The velocity of the steam at exit is sufficiently high which means that there is a considerable loss of KE. VELOCITY DIAGRAMS / VELOCITY TRIANGLES OF SIMPLE IMPULSE TURBINE: The following figure shows the velocity triangles / velocity diagrams for the single stage impulse turbine. The notations used are: V1 Absolute velocity of steam at inlet in m/s 1 Nozzle inlet angle u Blade velocity in m/s Vr1 Relative velocity of steam at inlet in m/s Vw1 Tangential velocity of steam at inlet in m/s Va1 Axial velocity of steam at inlet in m/s 1 Blade inlet angle 2 Blade outlet angle Vr 2 Relative velocity of steam at outlet in m/s Vw 2 Tangential velocity of steam at outlet in m/s Va 2 Axial velocity of steam at outlet in m/s K Vr 2 Blade velocity coefficient Vr 1 V2 Absolute velocity of steam at outlet in m/s 2 Angle made by absolute velocity V 2 with the tangent of the wheel at outlet The procedure for drawing the combined velocity triangle is given below: (1) Draw a horizontal line AB equal to blade velocity u to some suitable scale (2) Draw a line AC at an angle 1 with AB. Cut AC V1 (3) Join B and C. the line BC represents the relative velocity at inlet Vr1 . The blade inlet angle 1 is measured and the value is noted down. (4) From point C, draw a perpendicular CE on AB produced. CE represents axial velocity at inlet Va1 and AE represents tangential velocity at inlet Vw1 (5) From point B, draw a line BD at an angle 2 (blade outlet angle). Cut BD Vr 2 KVr1 . Join A and D. AD represents the absolute velocity at outlet V 2 . The angle 2 is measured and noted down. (6) From point D, draw a perpendicular DF on BA produced. Then AF represents tangential velocity at outlet Vw 2 and DF represents the axial velocity at outlet Va 2 . This completes the velocity triangle. WORK OUTPUT, POWER, BLADE EFFICIENCY AND STAGE EFFICIENCY Forcein the tangential direction Rate of change of momentumin the tangential direction. Mass per second changein velocity Newtons (1) mVw1 Vw2 Newtons Force in the axial direction Rate of change of momentum in the axial direction. mVa1 Va 2 Newtons (2) (axial thrust) Work done by steam on blades mVw1 Vw 2 u N - m/s (3) mVw1 Vw2 u Power developed by the turbine kW (4) 1000 Work done on the blade(s) mVw1 Vw2 u 2uVw1 Vw2 u Blade efficiency 2 (5) Energy supplied to the blade(s) 1 2 V1 mV1 2 1 Energy lost due to blade friction m Vr1 Vr2 2 2 2 N - m/s (6) Work done on the blade(s) mVw1 Vw 2 u Vw1 Vw 2 u Stage efficiency Total energy supplied per stage mH 1 H 2 (7) Hd Where H d H 1 H 2 Heat drop in the nozzle ring MAXIMUM WORK AND MAXIMUM DIAGRAM EFFICIENCY From the combined velocity triangle (diagram), we have Vw1 V1 cos1 Vr1 cos 1 u , and Vw2 V2 cos 2 Vr 2 cos 2 u V cos 2 Vw1 Vw2 Vr1 cos 1 Vr 2 cos 2 Vr1 cos 1 1 r 2 Vr1 cos 1 1 KC Vr1 cos 1 V cos 2 Where K r 2 and C Vr1 cos 1 (or) Vw1 Vw 2 V1 cos 1 u 1 KC Rate of doing work per kg of steam per second = V1 cos 1 u 1 KC u Diagram efficiency, b 1 V cos 1 u 1 KC 2 V1 u Let, Blade speed ratio V1 Then, Diagram efficiency, b 2 cos 1 2 1 KC From the above equation, it is evident that diagram efficiency depends on the following factors: (1) Nozzle angle, 1 (3) Blade angles, 1 and 2 (2) Blade speed ratio, (4) Blade velocity coefficient, K If the values of 1 , K and C are assumed to be constant, then diagram efficiency depends only on the value of blade speed ratio, d b In order to determine the optimum value of for maximum diagram efficiency, 0 d cos1 Then becomes equal to 2 cos1 cos2 1 cos2 1 Maximum Diagram efficiency, b max 21 KC . cos1 1 KC 2 4 2 Assuming that the blades are symmetrical and friction is absent, then 1 = 2 . Therefore, C=1 and K=1. Maximum Diagram efficiency, b m ax cos 2 1 Rate of doing work per kg of steam per second = V1 cos 1 u 1 KC u Then maximum rate of doing work per kg of steam per second 2u 2 METHODS OF REDUCING ROTOR SPEED (COMPOUNDING OF IMPULSE TURBINES) If high velocity of steam is allowed to flow through one row of moving blades, it produces a rotor speed of about 30000 rpm which is too high for practical use. It is therefore essential to incorporate some improvements for practical use and also to achieve high performance. This is possible by making use of more than one set of nozzles, and rotors, in a series, keyed to the shaft so that either the steam pressure or the jet velocity is absorbed by the turbine in stages. This is called compounding. Two types of compounding can be accomplished namely (1) Velocity compounding, and (2) Pressure compounding. Either of the above methods or both in combination are used to reduce the high rotational speed of the single stage turbine. Velocity compounding: It consists of a set of nozzles and a few rows of moving blades which are fixed to the shaft and rows of fixed blades which are attached to the casing. As shown in figure, the two rows of moving blades are separated by a row of fixed blades. The steam is expanded from the boiler pressure to the condenser pressure in the nozzle only. Due to the decrease in the pressure, the steam acquires a very high velocity. This high velocity steam first enters the first row of moving blades, where some portion of the velocity is absorbed. Then it enters the ring of fixed blades where the direction of steam is changed to suit the second ring of moving blades. There is no change in the velocity as the steam passes over the fixed blades. The steam then passes on to the second row of moving blades where the velocity is further reduced. Thus a fall in velocity occurs every time when the steam passes over the row of moving blades. Steam thus leaves the turbine with a low velocity. The variation of pressure and velocity of steam as it passes over the moving and fixed blades is shown in the figure. It is clear from the figure that the pressure drop takes place only in the nozzle and there is no further drop of pressure as it passes over the moving blades. This method of velocity compounding is used in Curtis turbine after it was first proposed by C.G. Curtis to solve the problems of a single-stage impulse turbine for use with high pressure and temperature steam. Advantages 1) The arrangement has less number of stages and hence less initial cost 2) The arrangement requires less space 3) The system is reliable and easy to operate 4) The fall of pressure in the nozzle is considerable, so the turbine itself need not work in high pressure surroundings and the turbine housing need not be very strong Disadvantages 1) More friction losses due to very high velocity in the nozzles 2) Less efficiency because ratio of blade velocity to steam velocity is not optimum 3) Power developed in the later rows is only fraction of first row. Still all the stages require same space, material and cost. Pressure compounding: It consists of a number of fixed nozzles which are incorporated between the rings of moving blades. The moving blades are keyed to the shaft. Here the pressure drop is done in a number of stages. Each stage consists of a set of nozzles and a ring of moving blades. Steam from the boiler passes through the first set of nozzles where it expands partially. Nearly all its velocity is absorbed when it passes over the first set of moving blades. It further passes to the second set of fixed nozzles and is partially expanded again. It is further passed through the second set of moving blades where the velocity of steam is almost absorbed. This process is repeated till steam leaves at condenser pressure. By reducing the pressure in stages, the velocity of steam entering the moving blades is considerably reduced. Hence the speed of the rotor is reduced. This method of compounding is used in Rateau and Zoelly turbines. Pressure-Velocity compounding: In this method of compounding, both pressure and velocity compounding methods are utilized. The total drop in steam pressure is carried out in two stages and the velocity obtained in each stage is also compounded. The rings of nozzles are fixed at the beginning of each stage and pressure remains constant during each stage. This method of compounding is used in Curtis and More turbines. REACTION TURBINES A turbine in which steam pressure decreases gradually while expanding through the moving blades as well as the fixed blades is known as reaction turbine. It consists of a large number of stages, each stage consisting of set of fixed and moving blades. The heat drop takes place throughout in both fixed and moving blades. No nozzles are provided in a reaction turbine. The fixed blades act both as nozzles in which velocity of steam increased and direct the steam to enter the ring of moving blades. As pressure drop takes place both in the fixed and moving blades, all the blades are nozzle shaped. The steam expands while flowing over the moving blades and thus gives reaction to the moving blades. Hence the turbine is called reaction turbine. The fixed blades are attached to the casing whereas moving blades are fixed with the rotor. It is also called Pearson’s reaction turbine. WORK OUTPUT AND POWER The work done per kg of steam in the stage (per pair) = u Vw1 Vw 2 N m The work done per kg of steam per second in the stage (per pair) = mu Vw1 Vw 2 N m / s where, m = mass of steam flowing over blades in kg/s muVw1 Vw2 Power developed (per pair) = kW 1000 work done per kg of steam in the stage per pair u Vw1 Vw 2 Efficiency, Enthalpy drop in the stage per pair 1000 H where, H = Enthalpy drop in the stage per pair in kJ/kg DEGREE OF REACTION The degree of reaction is defined as the ratio of isentropic heat drop in the moving blades to the isentropic heat drop in the entire stage of reaction turbine. It is denoted by R. Enthalpy drop in the moving blade dH 2 R Enthalpy drop in the stage dH1 dH 2 V1 V2 2 2 Where, dH1 Enthalpy drop in the fixed blade per kg of steam = kJ / kg H 1 H 2 2 Vr 2 Vr1 2 2 dH 2 Enthalpy drop in the moving blade per kg of steam = kJ / kg H 2 H 3 2 Also, dH1 dH 2 = Enthalpy drop in the stage per kg of steam = H1 H 3 = Work done by the steam in the stage = u Vw1 Vw 2 Vr 2 Vr1 2 2 Degree of Reaction,R 2u Vw1 Vw2 Note-1: In Pearson’s turbine, the degree of reaction, R=0.5, then, 1 2 and 2 1 . This means that moving blade and fixed blade have the same shape. Note-2: If degree of reaction, R=0, then the turbine is a simple impulse turbine. Note-3: If degree of reaction, R=1, then the turbine is a pure reaction turbine. BLADE EFFICIENCY AND STAGE EFFICIENCY The condition for maximum efficiency is calculated considering the following assumptions: The degree of reaction, R = 0.5, i.e. 1 2 and 2 1 The fixed and moving blades are symmetrical, i.e. V1 Vr 2 & V2 Vr1 2 V The kinetic energy supplied to the fixed blade per kg of steam = 1 2 Vr 2 V r 1 2 2 The kinetic energy supplied to the moving blade per kg of steam = 2 V Vr 1 2 2 2 V Total energy supplied in the stage per kg of steam = 1 r 2 2 2 Since blades are symmetrical, V1 Vr 2 & V2 Vr1 & from velocity triangles, Vr1 V1 u 2 2 V1 u cos 1 2 2 V u 2 2 V1 u cos 1 2 Therefore, total energy supplied in the stage per kg of steam = V1 1 2 2 Work done per kg of steam is given by, Work Done = u Vw1 Vw 2 = u V1 cos1 Vr 2 cos 2 u = u 2V1 cos 1 u ( 1 2 and V1 Vr 2 ) Diagram efficiency is given by, Work done per kg of steam Diagram efficiency, = d Total energy supplied per kg of steam u 2V1 cos1 u = V u 2 2 V1 u cos1 2 V1 1 2 2 2u 2V1 cos 1 u = V1 u 2 2 V1 u cos 1 2 u 2uV1 2 cos1 V1 = 2 2 u u V1 1 2 2 cos1 V 1 V1 u u 2 2 cos1 V1 V1 = u2 u 1 2 2 cos1 V V1 1 2 2 cos 1 u d where 1 2 2 cos 1 V1 =Blade speed ratio d d The efficiency is maximum when the term 1 2 2 cos 1 is minimum or when 0 d d d 1 2 2 cos1 0 (or) 2 2 cos 1 0 (or) cos 1 Therefore efficiency is maximum when cos 1 2 cos1 2 cos1 cos1 2 cos2 1 Then, d max 1 cos2 1 2 cos1 cos1 1 cos2 1 2 cos 1 2 d max 1 cos2 1 GOVERNING OF TURBINES Governing is the method of maintaining the speed of the turbine constant irrespective of variation of the load on the turbine. A governor is used for achieving this purpose which regulates the supply of steam to the turbine in such a way that the speed of the turbine is maintained as far as possible a constant under varying load conditions. The various methods of governing of steam turbines are: (1) Throttle governing (2) Nozzle governing (3) By-pass governing (4) Combination of (1) & (2) or (2) & (3) Throttle governing: The throttle governing of a steam turbine is a method of controlling its speed by varying the quantity of steam entering the turbine. The centrifugal governor is driven from the main shaft of the turbine. The control valve controls the direction of flow of oil either in the pipe AA or BB. The relay cylinder has a piston whose motion is connected to a spear which moves inside the nozzle. Let us consider an instant when the load on the turbine increases. As a result the speed of the turbine decreases. The fly balls of the governor will come down. The fly balls bring down the sleeve. The downward movement of the sleeve will raise the control valve rod. The mouth of the pipe AA will open. Now the oil under pressure will rush from the control valve to the right side of the piston in the relay cylinder through the pipe AA. This will move the piston and the spear towards the left which will open more area of the nozzle. As a result the steam flow rate into the turbine increases, which in turn brings the speed of the turbine to the normal range. Nozzle governing: In this method of governing, nozzles are grouped together in 3 or 5 or more groups and each group of nozzle is supplied steam controlled by valves. The arc of admission is limited to 180 or less. The nozzle control governing is restricted to the first stage of the turbine the nozzle area in other stages of the turbine remains constant. It is suitable for the simple impulse turbine and for larger units which have an impulse stage followed by an impulse reaction turbine. By-pass governing: The steam turbines which are designed to work at economic load, it is desirable to have full admission of steam in the high pressure stages. At the maximum load, which is greater than the economic load, the additional steam required could not pass through the first stage since additional nozzles are not available. By-pass regulation allows for this in a turbine which is throttle governed, by means of a second by-pass valve in the first stage nozzle as shown in figure. This valve opens when throttle valve has opened a definite amount. Steam is by-passed through the second valve to a lower stage in the turbine. When by-pass valve operates, it is under the control of the turbine governor. The secondary and tertiary supplies of steam in the lower stages increase the work output in these stages, but there is a loss of efficiency and curving of the Willian’s line. LOSSES IN STEAM TURBINES Residual velocity loss: The steam leaves the turbine with a certain velocity which results in loss of some kinetic energy. This loss is about 10 to 12% in a single stage turbine. This loss can be reduced by using multistage. Losses in regulating valves: The produced in the boiler has to flow through the stop and regulating valves before entering into the steam turbine. At these valves, the steam gets throttled and as a result the pressure of steam at entry to the turbine is less than the boiler pressure. Loss due to steam friction in nozzle: Friction occurs both in nozzles and turbine blades. In nozzles, the effect of friction is considered by introducing the factor of nozzle efficiency which is the ratio of actual enthalpy drop to the isentropic enthalpy drop. In turbine blades the effect of friction is considered by taking the factor called blade velocity coefficient (or) blade friction factor. This loss is about 10%. Loss due to leakage: The leakage occurs between the shaft, bearings, and stationary diaphragms carrying the nozzles in the case of impulse turbines. In reaction turbines, the leakage may occur at the blade tips. The total leakage loss is about 1 to 2%. Loss due to mechanical friction: This loss occurs in the bearings and may be reduced by proper lubrication. Loss due to wetness of steam: In multistage turbine, condensation of steam occurs in the last stages, because water and steam have different velocities and will not form a homogeneous mixture. The water particles have to be dragged along with the steam and so a part of the kinetic energy of the steam is lost. Radiation loss: As the turbines are heavily insulated to reduce the heat loss to surroundings by radiation and so these losses are negligible. OVERALL EFFICIENCY AND REHEAT FACTOR: The effect of friction on the flow of steam when passing over the blades is to decrease the relative velocity of steam, the energy thus lost is converted into heat which in turn causes an increase in entropy and consequently a slight decrease in heat drop. The effect of friction on adiabatic flow of steam can be demonstrated on Mollier diagram as shown in figure. Let A1 represents the initial condition of steam. In the first stage, the steam expands adiabatically from pressure P1 to P2. This is represented by the vertical line A1B1. Due to blade friction, the heat generated is represented by the line B1C1. If a horizontal line is drawn from C1 up to back pressure P2 to meet at A2 which represents the final condition of steam at exit from the first stage. The same process can be repeated during the second stage. The final condition of steam at exit from the second stage is represented by the point A3 and so on for the remaining stages. If the friction is neglected, the adiabatic expansion of steam through all the stages is represented by the line A1D. Reheat factor: It is defined as the ratio of cumulative heat drop to the adiabatic heat drop in all the stages of the turbine. The value of reheat factor depends on the type and efficiency of the turbine, the average value being 1.05. Cumulative heat drop A1B1 A 2 B2 A 3 B3 Reheat factor Adiabatic heat drop A1D Stage efficiency: It is defined as the ratio of useful heat drop in the stage to the adiabatic heat drop in the same stage. Useful heat drop in the stage AC A C AC Stage efficiency 1 1 2 2 3 3 Adiabatic heat drop in the stage A1B1 A 2 B 2 A 3 B3 Internal efficiency (or) Adiabatic efficiency (or) Turbine efficiency: It is defined as the ratio of total work done on the rotor (or total useful heat drop) to the total adiabatic heat drop. Total work done on the rotor A1C1 A 2 C 2 A 3C3 Internal / Adiabatic / Turbine efficiency Total adiabatic heat drop A1 D Overall efficiency: It is defined as the ratio of total useful heat drop to the total heat supplied. Total useful heat drop A1C1 A 2 C 2 A 3C3 Overall efficiency Total heat supplied H A1 - h D PROBLEMS ON STEAM TURBINES Classroom problems (1) Steam with an absolute velocity of 360 m/s enters a stage of an impulse turbine provided with a single row wheel. The nozzles are inclined at 20 to the plane of the wheel. The blade rotor with 95.5 cm diameter rotates at 3000 RPM. Find (i) suitable inlet and outlet angle for the moving blade so that there is no axial thrust on the blade. It may be assumed that friction in blade passages is 19% of the kinetic energy corresponding to the relative velocity of the steam at inlet to the blades (ii) power developed in blading for a steam flow rate of 1 kg/s, and (iii) kinetic energy of steam finally leaving the stage. (2) The blade speed of a single ring of an impulse turbine is 300 m/s and the nozzle angle is 20. The isentropic heat drop is 473 kJ/kg and the nozzle efficiency is 0.85. Given that the blade velocity coefficient is 0.7 and the blades are symmetrical, draw the combined velocity triangle and calculate for a mass flow rate of 1 kg/s: (i) axial thrust on the bearing (ii) steam consumption per brake power per hour if the mechanical efficiency is 0.9 (iii) blade efficiency, stage efficiency and maximum blade efficiency, and (iv) heat equivalent of the friction of blading. Home Assignment problems: (3) In a certain stage of an impulse turbine, the nozzle angle is 20 with the plane of the wheel. Four nozzles each of 1 cm diameter expand steam isentropically from 15.2 bar, 250C to 0.5 bar. The mean diameter of the blade ring is 2.8 metres. It develops 55.2 kW at 2400 RPM. The axial thrust is 3.45 N. Calculate (i) blade angles at inlet and outlet, and (ii) power lost in blade friction. (4) A single stage steam turbine is supplied with steam at 5 bar, 200C at the rate of 50 kg/min. It expands into a condenser pressure of 0.2 bar. The blade speed is 400 m/s. The nozzles are inclined at an angle of 20 to the plane of the wheel and the outlet blade angle is 30. Neglecting friction losses, determine the power developed, blade efficiency and stage efficiency. (5) A simple impulse turbine has a mean blade speed of 200 m/s. The nozzles are inclined at 20 to the plane of rotation of the blades. The steam velocity from the nozzles is 600 m/s. The turbine uses 3500 kg/hr of steam. The absolute velocity at exit is along the axis of the turbine. Determine (i) the inlet and outlet blade angles (ii) power output of the turbine (iii) diagram efficiency, and (iv) the axial thrust per kg of steam per second. (6) The following data refers to a single stage impulse turbine: Steam velocity = 600 m/s Blade speed = 250 m/s Nozzle angle = 20 Blade outlet angle = 25 Neglecting the effect of friction, calculate the work developed by the turbine for a steam flow rate of 20 kg/s. Also calculate the axial thrust on bearings.