UNIT 4 PRINCIPLES OF WORKING OF STEAM TURBINES
Structure
4.1 Introduction
Objectives
4.2 Principle of Action of Turbine
4.2.1 Impulse Principle 4.2.2 Reaction Principle
4.2.3 Principle of Action of Steam Turbine
4.3 Elements of Steam Turbine
4.3.1 Steam Nozzles 4.3.2 Steam Turbine Blades
4.4 Steady Flow Energy Balance Equations for Turbine, Nozzle and Blade
4.4.1 Energy Balance Equation for Turbine 4.4.2 Energy Balance Equation for Nozzle 4.4.3 Energy Equation for Steam Blade
4.5 Impulse Steam Turbine
4.5.1 Velocity Diagram for Impulse Turbine 4.5.2 De Laval Turbine
4.6 Reaction Steam Turbine
4.6.1 Axial Flow Reaction Turbine
4.6.2 The Radial Flow, Double-motion Reaction Turbine
4.7 Velocity and Pressure Compounding
4.7.1 Velocity Compounding Principle 4.7.2 Pressure Compounding Principle
4.8 Velocity Compounded Impulse Turbine 4.9 Pressure Compounded Impulse Turbine
4.10 Velocity-Pressure Compounded Impulse Turbine 4.11 Summary
4.12 Key Words 4.13 Answers to SAQs
4.1 INTRODUCTION
The steam turbine, in a crude form, is said to have been used many centuries ago and today it stands as the most important prime mover in existence. It has several advantages over other prime movers.
From a thermodynamic point of view, the steam turbine occupies a
favourable position, as it can translate into mechanical work a relatively large fraction of the heat energy rendered available by the expansion of the steam in the turbine. Its thermal economy is also fairly good, especially in turbines of large output and operating at fairly high pressure.
From the mechanical point of view, the turbine is ideal, because the
propelling force is applied directly to the rotating element of the machine and has not, as in the reciprocating engine, to be transmitted through a system of connecting links which are necessary to transform efficiently a reciprocating motion into rotary motion. Hence, since the steam turbine possesses for its moving parts rotating element only, if the workmanship is good and the machine is correctly designed, it ought to be free from out-of balance forces.
When one considers that is practically impossible to balance any
reciprocating engine, the superior merits of the steam turbine in this respect are immediately apparent.
The impulse applied by the steam to the blades of a turbine comes with such regularity and .constancy that if the load applied to the machine is maintained constant, and the steam flow through the turbine is maintained at a steady value, the torque applied at the turbine coupling due to such impulse will be quite uniform. Therefore, if turbine is employed to drive a machine which offers over a given period of time a sensibly constant resisting torque, the speed of the turbine and the driven machine will be uniform.
Certain driven machines such as electric generators, centrifugal pumps, centrifugal gas compressors, etc., when operating under steady conditions as regards to output, offers a fairly constant resistance. Such machines are also essentially high speed machines.
Consequently the steam turbine is, from every point of view, eminently suitable as a prime mover for driving such machines.
Objectives
After studying this unit, you should be able to
understand the fundamentals of the two basic principles on which turbines work,
explain the roles of the steam turbine elements,
analyse the steady flow energy equations for turbine, nozzle and blades,
appreciate the working principle, construction, operation and performance of the various types of steam turbines,
describe the principles of velocity and pressure compounding, and
define the characteristics and performances of the turbines based on these principles.
4.2 PRINCIPLE OF ACTION OF TURBINE
There are two basic principles on which various categories of turbines, like steam turbine, water turbine or gas turbine work. These are:
(i) Impulse principle, and (ii) Reaction principle.
4.2.1 Impulse Principle
If a jet of fluid (water, gas or steam) from a nozzle at high speed strikes a stationary plate, it exerts a pressure on the plate due to the destruction of momentum, the force exerted being equal to the momentum destroyed per second. If the plate is moving away from nozzle the force exerted is less but work is done since the plate is moving. It a series of such plates are mounted on the rim of a wheel we have a simple form of impulse turbine. The
efficiency of such a turbine defined as the fraction of the energy supplied which converted to work, would be low.
Following are the different types of turbines which work on the Impulse principle.
(i) Impulse steam turbine (a) De Laval (b) Ratean
(ii) Impulse water turbine
(a) Peton (iii) Impulse gas turbine 4.2.2 Reaction Principle
When the fluid issues from a nozzle there is a backward reactive force on the nozzle equal to the amount of momentum generated per second in the nozzle.
If a series of nozzles mounted on the rim of a wheel and it is possible to arrange for fluid to enter the nozzles at a low velocity and leave it at a high velocity, the nozzle will move backward and the wheel will do work. In this case, we have a simple form of reaction turbine.
Following are the different types of reaction turbines which work on reaction principle.
(i) Reaction steam turbine (a) Parson turbine (ii) Reaction water turbine
(a) Francis turbine (b) Kalpan turbine (iii) Reaction gas turbine.
4.2.3 Principle of Action of Steam Turbine
The steam turbine depends wholly upon the dynamic action of steam. The steam is caused to fall in pressure in a passage or nozzle; due to fall in
pressure, a certain amount of heat energy is converted into mechanical kinetic energy, and the steam is set moving with a greater velocity. The rapidly moving particles of steam enter the moving part of the turbine and here suffer a change in the direction of motion which gives rise to a change of
momentum and therefore a force. This constitutes the driving force of the machine. The processes of expansion and direction changing of steam may occur once, or a number of times in succession.
The passage of steam through the moving part of the turbine, commonly called the blade, may takes place in such a manner that the pressure at the outlet side of the blade is equal to that at the inlet side. Such a turbine is broadly termed as impulse turbine. On the other hand, the pressure of the steam at the outlet from the moving blades of the turbine may be less than that at the inlet sides of the blades; the drop in pressure suffered by the steam during its flow through the moving blades causes a further generation of kinetic energy within the blade and adds to the propelling force which is applied to the turbine rotor. Such a turbine is broadly termed as reaction turbine.
In fact, none of these are purely impulse or purely reaction types. In each case, steam is expanded from a given pressure to a lower pressure in nozzles or their equivalent, thus converting heat into kinetic energy. This kinetic energy (or velocity energy) is then converted into work in the moving blades.
SAQ 1
(a) What is the difference between impulse and reaction principles?
(b) Explain the action of steam in each of the impulse and reaction turbines. 4.3 ELEMENTS OF STEAM TURBINE
4.3 ELEMENTS OF STEAM TURBINE
The majority of steam turbines have two important elements, or sets of such elements.
These are:
(i) The nozzle, in which the steam expands from a high pressure and a state of comparative rest to a lower pressure and a state of
comparatively rapid motion.
(ii) The blade or deflector, in which the stream of steam particles has its direction and hence its momentum changed. The blades are attached to the rotating element of the machine, or rotor, whereas, in general, the nozzles are attached to the stationary part of the turbine, which is usually termed as the stator, casing or cylinder.
4.3.1 Steam Nozzles
The nozzle is one of the most important element in a steam turbine, for in it takes place the conversion of pressure energy into kinetic energy. The shape and finish of the nozzle should be such that this conversion takes place with the highest possible efficiency. The basic requirements may be enumerated as follows:
(i) Sudden changes in direction of the flowing steam, especially at high velocities should be avoided.
(ii) The inlet of the nozzle should be designed to utilize the carrying over energy from the previous stage to the greatest possible extent.
(iii) The wall surface should be as smooth as possible in order to reduce friction, especially when the steam velocity is high.
(iv) The design should be such as to permit of ease of manufacture and finishing, and also to obtain accurate channel sections, especially at high pressure end of the turbine.
In steam turbine, steam at a high pressure expanding through the nozzles secured to the turbine casing expands and gains in velocity. The high velocity jet leaving the nozzle is made to impinge on the blades mounted on a wheel attached to turbine shaft. The kinetic energy of steam thus drives the turbine wheels, producing useful work.
Nozzles are classified into three categories as follows (Figure 4.1).
(i) Convergent Nozzle
It produces subsonic fluid velocity and exit pressure equal to or more than critical pressure,
(ii) Divergent Nozzle
It produces supersonic fluid velocity.
(iii) Convergent-Divergent Nozzle
It produces subsonic flow in the converging section and
supersonic flow in the diverging section. The velocity at the throat
is sonic. A convergent-divergent nozzle produces exit pressure lesser than critical pressure.
Suppose for example, a convergent-divergent nozzle is designed to operate with a steam with certain initial pressure p1 and outlet pressure P2. If the actual pressure in the space into which the nozzle discharges is higher than p2, then as the steam in the nozzle will expand down nearly to p2 the steam is said to be over expanded.
If on the other hand, the pressure on the discharge side is lower than P2, since the nozzle is restricted in its capacity for expanding the steam, the steam in the nozzle is said to be under expanded. In both cases, there are fairly serious losses involved. Consequently even convergent-divergent nozzle requires to be carefully designed for conditions under which it has to operate.
The convergent nozzle is not subjected to the same restrictions. Provided the pressure on the outlet side does not fall below the critical pressure, the nozzle will function in a satisfactory manner in spite of variations in outlet pressure.
This statement refers to efficient operation and not to mass flow.
Figure 4.1: Type of Nozzles(a)Convergent,(b)Divergent, (c)Convergent-divergent
The great variety of turbine nozzles are of convergent type: the convergent- divergent nozzle is hardly ever used except in small turbine and in
conjunction with velocity compounded wheels.
General Relationship between Area, Velocity and Pressure in Nozzle Flow
Let us consider the steady flow through a nozzle under adiabatic and frictionless conditions as shown in Figure 4.2. In this figure we have two transverse plane sections separated by𝛿x. We make two assumptions:
(i) the nozzle runs full, and t
(ii) the velocity is uniform across any section.
Then by the equation of continuity,
W = =( )( )…(4.1) where, W = Mass flow rate of steam, A = Cross-sectional area of the nozzle, V = Velocity of the steam, and where,
v = Specific volume of the steam.
From Eq. (4.1) we have in the limit (as the differences 𝛿v, 𝛿A, etc.
approach to zero).
+ − = 0…(4.2)
Figure 4.2: Flow Through Steam Nozzle
Since the flow is adiabatic and frictionless, P vn = constant …(4.3)
Taking log and differentiating, we get
log P + n log v = log (constant) …(4.4) + 𝑛 = 0…(4.5)
from which = − …(4.6 )
Also, since the flow is frictionless, the momentum equation gives the following equations:
. = - v dP…(4.7)
= − . . …(4.8)
Using Eqs. (4.2), (4.6) and (4.8), we have the following equation:
𝑑𝐴
𝐴 =1
𝑛 .𝑑𝑃 𝑃
𝑔. 𝑛. 𝑃. 𝑣
𝑉 − 1 … (4.9) Writing S for the sonic velocity in steam at pressure P and specific volume v, we have,
𝑑𝐴 𝐴 =1
𝑛 .𝑑𝑃 𝑃
𝑆
𝑉 − 1 … (4.10) The ratio of velocity V to the local acoustic velocity 'S’ is known as the Mach Number, denoted by 'M’
𝑖. 𝑒., 𝑀 =𝑉
𝑆 (4.11)
𝐻𝑒𝑛𝑐𝑒, 𝑑𝐴
𝐴 =1
𝑛 .𝑑𝑃 𝑃
1 − 𝑀
𝑀 (4.12) Eqs. (4.10) and (4.11) give a useful insight into the change of nozzle area under certain interesting conditions. Some of them are briefly discussed below:
Case I
𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑒𝑑 𝑓𝑙𝑜𝑤,𝑑𝑃
𝑃 , 𝑖𝑠 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒
(a) Vis less than S, M<1. Then must be negative. This corresponds to the convergent part of the nozzle. As soon as V reaches the value S (i.e., M = 1). Then = 0 and the throat of the nozzle is reached.
(b) V is greater than S, M> 1. Then must be positive. This corresponds to the divergent part of steam nozzle.
Case II
Retarded flow, , is positive. This applies to diffusers in which the kinetic energy of flow is converted into pressure energy and has little application in steam turbines.
(a) Vis less than S, M<L. Then must be positive, i.e., the diffuser must be of divergent type.
(b) V is greater than S, M>1. Here must be negative and the diffuser must be of convergent type.
These four cases are summarized in Figure 4.3.
Type of Flow Accelerated Flow Falling Pressure
Retrated Flow Rising Pressure Subsonic
Convergent nozzle Divergent nozzle Supersonic
Divergent nozzle
Convergent nozzle Figure 4.3: Four Cases of Nozzles
Determination of Dimensions of the Nozzle
Let us consider a typical nozzle devised by de Laval as shown in Figure 4.4.
Figure 4.4: De – Laval Nozzle
The minimum cross-section of the nozzle can be represented as:
𝑆 .= …(4.13)
The cross-section at the outlet can be expressed as:
𝑆 = …(4.14)
The angle of divergence is taken to be not above 10 . From Figure 4.4, we can write:
𝑡𝑎𝑛 𝛼
2 = 𝑑
2𝑙 or, 𝑙 = …(4.15)
and, tan = ×
or, l1 + l2 = …(4.16)
Using Eq. (4.15) for l1, l2 may be expressed as l2 = …(4.17)
4.3.2 Steam Turbine Blades
Blade is one of the essential part of the turbine. The function or purpose of the blades is to change the direction, and hence the momentum of the jet or jets of fluid (water, gas or steam) and so they produce a force which propels the blades.
The turbine blades can be classified mainly into two categories. These are Impulse blade and Reaction blade. These are described in the following sections.
Impulse Blade
These are used for Impulse turbines and may be classified broadly into two types:
(i) The plate blade, and (ii) The profile blade.
Various forms of plate blades are shown in Figure 4.5. Figure 4.5(a) shows an early form of Rateau turbine blade constructed
from sheet metal. In order to reduce impact losses at inlet, the inlet edge is chamfered, leaving an edge thickness of 0.025 cm.
Figure 4.4(b) shows a symmetrical plate blade. The inlet and outlet angles are equal. The concave side of the blade is usually an arc of a circle, the blade is of constant thickness, and both inlet and outlet edges are chamfered. Figure 4.5(c) shows a further modification. The blade section shown in Figure 4.5(d) is provided with a straight outlet edge of uniform thickness. The objective of this is to give better control of the jet of out flowing steam. The plate type blade in simple to manufacture, and because of the comparatively light section the centrifugal force on the blade and hence the stresses imposed on the rotor due to edge loading are relatively light.
Figure 4.5: Plate Blades Profile Blade
In this type of blade the section of the blade is extended so as to occupy its eddy space as shown in Figure 4.6. A symmetrical
equiangular blade is shown in Figure 4.6(a). By making the centres of curvature of the convex and concave sides of adjacent blades
coincide, the channel width is kept constant. Figure 4.6(b) shows an equiangular blade with a straight outlet edge to give a controlled jet, It is necessary to give the blade a certain thickness at the inlet and outlet edges so that it will have the necessary strength and rigidity to
withstand the strains incidental to matching.
Figure 4.6: Profile Blades Forces on the Impulse Blade
In accordance with Newton's third law, the force exerted by the steam on the blades is equal and opposite to that exerted by the blades on the steam.
This is shown in Figure 4.7. The resultant force may be resolved into two components, viz:
(i) A useful thrust or tangential force parallel to the wheel plane.
(ii) An ideal thrust, perpendicular to wheel plane, i.e., parallel to the turbine axis.
Figure 4.7: Forces on the Impulse Blade Power Developed and Blade Efficiency
Let us assume,
W = Steam flow through nozzle,
u = Mean velocity of the movement of the blade, Vw = Tangential component of the changed velocity or velocity of whirl, and
V1 = Steam velocity at outlet of the nozzle.
Then, work done per sec.
E1 = . . …(4.18) Horse power developed = . . …(4.19)
The energy of the steam entering the blade,
E2 = …(4.20) The efficiency of the blade is
nb =
=
. .
= . . Reaction Blades
These are used for reaction turbine, where a pair of blades comprising one fixed row and one moving row of blades as shown in Figure 4.8 are used.
In the well known Parsons turbine the section of the blades is the same in both fixed and moving rows of blades. The reason for this is that the blades are often made from long section bars which are extended through standard dies. The longer blades are sometimes machined from forging and demand special consideration.
If, as is frequently the case, the blades of a turbine are divided into group or expansions containing several rows of blades having the same mean diameter and the same radial height, then, since specific volume of the steam is increasing as the pressure falls, the velocity of steam also increases, and in addition to the variation in the blade speed ratio from row to row, the heat drop in each row of blades is somewhat greater than that in the row preceding it, and thus the degree of reaction is rather more than one-half.
Figure 4.8: Reaction Blades
However, we generally assume that the mean diameter of the blade is kept constant, and the height of the blades is so increased that the
steam velocity at exit from each row of blades is uniform throughout the group.
Forces on the Reaction Blade
The forces on the reaction blades are shown in Figure 4.9. The resultant force can be resolved into two
components. viz :
(i) Impulse force, and (ii) Reaction force.
During the expansion through the blade the velocity increases and it gives rise to the reaction force.
Figure 4.9: Forces on the Reaction Blade SAQ 2
(a) What are the basic requirements of steam nozzle?
(b) State the working principles of the various types of nozzles.
(c) What is the difference between impulse and reaction turbine blades?
(d) With the help of diagram compare the different types of forces acting on the impulse and reaction steam turbine blades.
4.4
STEADY FLOW ENERGY BALANCE EQUATIONS FOR TURBINE, NOZZLE AND BLADE
Let us consider a general steady flow energy system as shown in Figure 4.10.
The conditions at inlet and outlet are represented with suffix 1 and 2 respectively.
From 1st law of thermodynamics, we can write
Q – Wx = ΔE
…(4.22)
where Q = Heat supplied or removed, J/s Wx = External work done, J/s
Δ E = Change is internal energy of the system.
Figure 4.10: A General Steady Flow Energy System
Again, Δ E = m [(u2 – u1) + (p2 v2 – p1 v1) + − + g (Z2 – Z1)] ...(4.23)
Δ E = m [(h2 – h1) + − + g (Z2 – Z1)]…(4.24)
= m [Δ h + + g Δ Z]
where, m = Mass flow rate of steam, kg/s h = Enthalpy, kJ/kg
= u + pv
Δh = h2 – h1 = (u2 + p2 v2) – (u1 + p1v1) = Change in enthalpy u = Specific internal energy, kJ/kg p = Pressure, kg/m2 v = Volume, m3
C = Velocity, m/s Z = Level or Height, m
4.4.1 Energy Balance Equation for Turbine
Let us consider a steam turbine system as shown in Figure 4.11.
Figure 4.11: Steam Turbine
The general steady flow energy balance Eq. (4.24) already obtained can be applied to this system.
(i) In case of turbine, g (Z2 –Z1) ≈ 0. So, Eq. (4.24) can be modified as
Q – Wx = m [Δ h + Δ C2] …(4.25)
(ii) For proper design of turbine, it can be made
− = 0
Hence, Q – Wx = m Δ h …(4.26)
(iii) If heat loss is negligible i.e., Q ≈ 0, then – Wx = m Δh Or, Wx = m (h1 – h2)
Example 4.1
In a steady flow steam turbine system following data is given:
h1 = 3200 kJ/kg, C1 = 10 m/s, m = 2 kg/s h2 = 2800 kJ/kg, C2 = 50 m/s, Δz = 3 m
(i) Find the work done by the turbine if heat loss is negligible.
(ii) Find the heat loss if Wx = 780 kJ/s.
Solution
Using Eq. (4.24), we obtain
Q – Wx = m [(h2 – h1) + − + g (Z2 – Z1)]
(i) Case I: Q ≈ 0
Hence, - Wx = 2 (2800 − 3200) + + . × . or, - Wx = 2 [-400 + 1.2 + 0.03]
→ Wx = 797.5 kJ / s (ii) Case II :Wx = 780 kJ /s
Hence, Q – Wx = -797.5 Q – 780 = -797.5
or, Q = - 17.5 kJ / s
4.4.2 Energy Balance Equation for Nozzle
Let us consider a nozzle carrying steam as shown in Figure 4.12
Figure 4.12: Steam Nozzle
(i) Using continuity equation the mass flow rate, m, of steam through nozzle can be written as
m = 𝜌 A1 C1 = 𝜌 A2 C2…(4.28) where, 𝜌 = Density of the steam, kg/m3 C1 = Inlet velocity, m/s
C2 = Outlet velocity, m/s
A1 = Cross-section area at the inlet, m2 A2 = Cross-section area at the outlet, m2
(ii) Since, the nozzle is a small device, (a) The heat loss, Q ≈ 0 (b) No shaft work, Wx = 0
(c) Difference in the levels, Δ Z = 0
So, the general steady state energy balance, Eq. (4.24), can be expressed as Δh +
or, Δh = -
or, h1 – h2 = - (𝐶 − 𝐶 )…(4.29) i.e., Kinetic energy generated = Enthalpy drop.
Example 4.2
For a steam nozzle system, following data is given:
h1 = 9400 J/kg, A1= 1 m2 h2 = 1000 J/kg, C1 = 200 m/s
Find the outlet cross-section area of the nozzle and the steam velocity for incompressible flow.
Solution
Using energy balance Eq. (4.29) for the nozzle, we can write, (𝐶 − 200 ) = - (9400 – 1000)
𝐶 = 40000 – 16800
C2 = 152.3 m /sec.
Since , the flow is incompressible, 𝜌 = constant and using continuity equation
Eq. (4.28), we get, A1 C1 = A2 C2
or, A2 = = 1 X
= 1.313 m. 2
4.4.3 Energy Equation for Steam Blade In case of steam blade,
(i) Q ≈ 0 (ii) ΔZ = 0 (iii) Δh = 0
Hence, from Eq. (4.24) we get, - Wx = Δ C2
or, Wx = (𝐶 − 𝐶 )…(4.30)
SAQ 3
(a) Write down the expression for steady state energy balance equation for turbine, nozzle and blades considering the heat loss or heat transfer as negligible for the system in each case.
(b) Steam issues from the nozzles of a de Laval turbine with a velocity 200 m/s. The mass flow through nozzle and blading is 1 kg of steam per sec. If the change in enthalpy of the outlet and inlet of the nozzle is 5000 J/kg, find the velocity of the outlet of nozzle and hence the work done by the blade.
4.5 THE IMPULSE STEAM TURBINE
The class of turbine in which steam is allowed to expand before entering the moving blades but not in them is called an impulse steam turbine. In the impulse type turbine, there is a drop of pressure in the nozzle, but no drop of pressure through the moving blade.
A simple schematic diagram of a impulse steam turbine is shown in Figure 4.13.
Figure 4.13: A Schematic Diagrammatic Arrangement of Simple Impulse Turbine
The top portion shows a longitudinal section through the upper half of the turbine, while the lower portion shows a development of the nozzles and blading. This type of turbine is termed as 'simple' impulse turbine because the expansion of steam takes place in one set of nozzles only. Generally, the nozzle has a form similar to that shown in Figure 4.13 i.e., having a rounded entrance leading into a constriction, termed as the ‘throat’ and a diverging outlet or mouth. The pressure of the steam falls from that in the steam chest to that existing in the condenser (or atmosphere, if the turbine is non-
condensing), while steam flows through the nozzle. Hence, the pressure in the wheel chamber is practically equal to condenser pressure.
There is thus a relatively great ratio of expansion of the steam in the nozzles with the result that the steam issues from the nozzle outlet with a very high velocity e.g., about 1070 m/sec. But for good economy the velocity of the blades should be about one-half of the steam velocity, i.e., about 530 m/sec.
In practice the maximum blade velocity reaches in this type of turbine is about 400 m/sec, or about 950 miles/hour.
For economic reasons - since this type of turbine is only employed for relatively small powers - the rotor diameter is kept fairly small and in
consequence the rotational speed is high, reaching 30,000 rpm in some of the smaller machines.
The characteristics of the simple impulse turbine are, therefore, a single expanding nozzle, or set of such nozzles, with the high pressure steam confined to the steam chest and a casing subjected internally to the lower pressure only; high steam and blade velocities, with consequent high speeds of rotation; and lastly, a high carry over loss. The principle example of the type is the well-known De Laval turbine.
4.5.1 Velocity Diagram for Impulse Turbine
It is a matter of prime importance that we should be able to estimate the propelling force that would be applied to turbine rotor under any given set of conditions, We can also calculate the work done and hence the power . Since, the force is due to the change of momentum caused mainly by a change in the direction of flow, it becomes essential to draw diagrams showing how the velocity of the steam varies during the passage through the blade.
Figure 4.14, shows the nozzles and blades either of a single-stage impulse turbine or one stage of a multistage turbine. To draw velocity diagram, let us consider the following notations:
V1 = Steam velocity at outlet from nozzles, U1 = Steam velocity relative to the blades at inlet, U2 = Steam velocity relative to the blades at outlet, V2= Absolute velocity of steam at outlet from blades,
u = Peripherial velocity of blades (unless otherwise stated, this is the mean velocity),
α = Jet angle,
β1 = Inlet angle of blades, β2 = Outlet angle of blades, and
γ = Absolute direction of steam leaving blades.
Figure 4.14: Arrangement of Nozzles and Blade in Impulse Turbine
Since V1 is the initial absolute velocity and V2 is the final absolute velocity of the steam, the change of velocity which the steam undergoes in passing through the blades is represented by the vector BD, as shown in Figure 4.15.
Let, W = steam flow through the blades, kg/sec.
Then the resultant force necessary to produce the change of velocity BD is Fr = X BD kg . wt. …(4.31)
This is inclined at the angle ψ to the plane in which the wheel rotates.
Figure 4.15: Velocity Diagram for the Impulse Steam Turbine The resultant force has two components as shown in Figure 4.15.
(a) A tangential force parallel to wheel plane and is equal to Ft = BG = Vw…(4.32)
Where Vw is the tangential component of the change of velocity and is usually termed as velocity of whirl.
(b) An ideal thrust, perpendicular to the wheel plane, i.e., parallel to the turbine (4) axis. This equals to
Fp = DG…(4.33)
Using the velocity diagram shown in Figure 4.15, the work done by the blade, the power developed and the blade efficiency can be obtained by using Eq.
(4.18), (4.19) and (4.21) respectively, 4.5.2 De Laval Turbine
The De Laval turbine is a simple impulse turbine, in which the steam expands from boiler pressure to condenser pressure before entering the wheel
containing the blades. The velocity thus attained by the steam is very high, being about 2.0 m/sec. where the absolute pressure is 11.5 kgf/cm2 on
entering and the condenser pressure is 0.07 kgf/cm2. A general view of the De Laval wheel with four nozzles is shown in Figure 4.16 in which a section of one of the expanding nozzles is also shown. The wheel is made solid and the shaft is bolted to the wheel.
Figure 4.16: De Laval Wheel Example 4.3
Steam issues from the nozzles of a De Laval turbine with a velocity of 1000 m/s. The nozzle angle is 20°, the diameter of the blade is 25 cm and the speed of the rotation is 20,000 r. p. m. The mass flow rate of steam through the turbine nozzle and the blading is I kg/sec. If the friction loss in the blade channels is 33% of the kinetic energy corresponding to the relative velocity at inlet to the blades, draw the velocity diagram and calculate the following:
(i) Velocity of whirl,
(ii) Tangential force on the blades, (iii) Axial force on the blade, (iv) Work done on the blades,
(v) Horse power of the wheel, (vi) Efficiency of blading, and
(vii) Inlet angle of the blade for shockless inflow of steam.
Solution
Blade speed = 𝜋 × 0.25 × = 262 m/sec.
The velocity diagram ABC, (Figure 4.17) may now be constructed and the following results obtained either graphically or by
calculations.
Figure 4.17: Velocity Diagram
V1 = 670 m/sec, Axial velocity at inlet, 𝑉 = 312 m/sec.
CE = V1 cos β1 = 593 and β1 = 27° 48’
Since, the fraction loss in the blade channel is 0.33 X 𝑉 = 0.67 𝑉
= 0.8185 U1
∴V2 = 548 m /sec
The velocity diagram may now be completed, bearing in mind that β1
= β2. The additional result obtained are:
𝑉 = 0.8185 𝑉 = 256, CF = V2 cos β2 = 485 V2 = 337m/sec
(i) Then, Vw= 593 + 485 = 1078 m/sec.
(ii) Tangential force on blades
= . ×
. = 44 kg (iii) Axial force on the blades
= .
. (312 – 256) (iv) Work done on the blade = 44 X 262
= 11528 kg-m
(v) Horse Power developed = = 153.7 h. p.
(vi) Kinetic energy supplied by steam jets per sec. = . ×
× .
= 20408.16 kg-m
∴ Efficiency of the blading =
. = 0.5648
= 56.48 %
(vii) Inlet angle of blades for shockless inflow of steam = β1 = 27°
48’
SAQ 4
(a) Explain the working principle of De Laval turbine.
(b) What is the importance of velocity diagram of the impulse steam turbine.
4.6 REACTION STEAM TURBINE
Turbines, such as Parson turbines, in which the steam expands in moving as well as stationary blades (equivalents of nozzles) are known as reaction turbines. Actually there is a combination of impulse and reaction in this type.
A pure reaction turbine is illustrated diagrammatically in Figure 4.18. It comprises two or more radial tubes rotating on and communicating with another pipe through which steam is supplied to nozzles which are screwed into the ends of the radial pipes, and arranged with their axis in the tangential direction.
Figure 4.18: Pure Reaction Turbine with Velocity Diagram
Steam expands in the nozzles and issues with a certain velocity which is represented by the vector AB. If CD represents the peripherial velocity of the nozzle, then ED will represent the velocity of the steam relative to a fixed point at a given instant. Due to the change of velocity which occurs, there is a thrust or reaction on the rotating tube and tangential to it. This reaction constitutes the driving force, hence, the name.
The pure reaction turbine is not a practical type, although efforts to develop it were made by the Late Sir A. Parsons.
On the basis of the types of flow of steam, the reaction turbines can be classified into two groups:
(i) Axial flow reaction turbine, and
(ii) Radial flow double motion reaction turbine.
4.6.1 Axial Flow Reaction Turbine
In this type of turbine, we have a joint application of the impulse and reaction principles of operation. There are a number of rows of moving blades
attached to the rotor and an equal number of rows of fixed blades attached to the casing. The fixed blades correspond to the nozzles mentioned in
connection with the impulse turbines. Steam is admitted for the whole circumference, and thus there is what is termed "all round or complete admission". In passing through the first row of fixed blades, the steam undergoes a small drop in pressure and its velocity is somewhat increased. It then enters the first row of moving blades and, just as in the impulse turbine, it suffers a change in direction and, therefore, of momentum. This gives rise to an impulse on the blades. During its passage through the" moving blades, however, the steam undergoes a further small drop in pressure and, in consequence, there is a certain increase in steam velocity produced in the moving blade which gives rise to a reaction in the direction opposite to that of the added velocity. Thus the gross propelling force is the vector sum of the impulse and the reaction. This type of turbine is commonly termed as a reaction turbine, although the term is not exact.
The steam velocities in this type of turbine are comparatively moderate, the maximum being, about equal to the blade velocity. In practice, the steam velocity is commonly arranged to be greater than the blade velocity in order
to reduce somewhat the total number of blade rows. The leaving loss for this type of turbine is normally about the same as for the multi-stage impulse turbine having single-row wheels. This type of turbine has been and
continues to be very successful in practice. Its practical development was due to the genius and engineering skill of late Sir Charles A. Parsons. The turbine bears the name of its illustrious inventor.
4.6.2 Radial Flow, Double-motion Reaction Turbine
The turbine described hitherto, with the exception of the pure reaction turbine, have been of the axial flow type i.e., the general direction of steam flow has been roughly parallel to the turbine. It is, however, possible to arrange the groups of blades in concentric rings and attached to the sides of separate discs. If one set of blade is stationary, then we have a single-motion radial-flow turbine. The steam may be arranged to flow from the centre outward or from outside towards the centre. Assuming that such a turbine operates as a reaction turbine, then the most economical steam velocity from the blades in any stage is approximately equal to the peripherial velocity of the blades in that stage, and usually a fairly large number of stages are required.
Suppose now that the disc to which the fixed rings of blades are attached is arranged to rotate in the opposite direction to the moving blades, then the action will be generally the same as before except that the effective blade speed is doubled. Hence, the steam velocity may be doubled and the turbine may, for a given size, be made more efficient.
The practical representative of this type is the Ljungstrom turbine.
SAQ 5
(a) State the working principle of a reaction turbine.
(b) What is the difference between axial flow and radial flow double- motion reaction turbines?
4.7 VELOCITY AND PRESSURE COMPOUNDING
There are some special types of steam turbines which work on velocity compounding, pressure compounding, and velocity-pressure compounding principles. For example, the turbine developed by Professor A. Rateau of Paris, and Dr. Zolley of Zurich, is based on pressure compounding principle whereas the turbine developed by American Engineer Mr. C. G. Curtis, is based on velocity compounding principle.
4.7.1 Velocity Compounding Principle
Instead of using single stage as in the case of simple turbine, if many stages with rotating blades and guide blades are used and the steam is allowed to move from one stage to another, there will be a velocity drop gradually due to friction and thus the steam gives up a part of its kinetic energy. Finally the steam leaves the wheel of the last row in a more or less axial direction with a certain residual velocity. This is equivalent to the splitting up of velocity drop of steam. This is the principle of velocity compounding.
The velocity compounding principle leads to relatively large head drop per stage and therefore, to a comparatively small number of stages.
4.7.2 Pressure Compounding Principle
By arranging the expansion of the steam in a number of steps, it is possible to arrange a number of simple impulse or reaction machines, in series on the same shaft, allowing the exhaust steam from one turbine to enter the nozzles of the succeeding turbine. Each of the simple impulse or reaction machines would then be termed a 'stage of the turbine', each stage comprising its set of nozzles and blades. This arrangement can be used for splitting up the whole pressure drop into a series of smaller pressure drops; hence the term "pressure compounded".
4.8 VELOCITY COMPOUNDING IMPPULSE TURBINE
This type of turbine is shown diagrammatically in Figure 4.19. It comprises a nozzle or set of nozzles and a wheel fitted with two or more rows of moving blades. The example shown in Figure 4.19 has three rings of moving blades on the rotor and such a wheel is referred to as "three-row wheel". There are also a number of guide blades, suitably arranged between the first and second and second and third rows of moving blades, respectively. These fixed guide blades need not necessarily extend around the full circumference of the casing. It is only necessary to arrange them roughly infront of the nozzle or nozzles but covering a somewhat larger area of circumference than the nozzles themselves.
Figure 4.19: Velocity Compounded Impulse Turbine
Steam entering the nozzle expands from the initial pressure down the exhaust pressure. Thus, in general, the steam velocity is very high, as in the simple impulse turbine. The provision of two or more rows of moving blades, however, enables the blade velocity to be made appreciably less than would be necessary for turbine having a single row of blades, it being assumed that the efficiency is the maximum in both cases. On passing through the first row of moving blades, the steam gives up only a part of its kinetic energy and issues from this row of blades with a fairly high velocity. It then enters the first of the two rows of guide blades and is redirected by them into the second row of moving blades. There is a slight drop in velocity in the fixed guide blades due to friction. In passing through the second row of moving blades the steam suffers a change of momentum and gives up another portion of its kinetic energy to the rotor. It is re-directed in the second row of guide blades,
does work on the third row of moving blades, and finally leaves the wheel in a more or less axial direction with a certain residual velocity. This velocity is comparatively small and hence the leaving loss is small, being 2 per cent of the initial available energy of the steam. Generally speaking, owing to its low efficiency, this type of turbine having three rows of moving blades is used largely for small turbines driving auxillary machinery. The two-row wheel is appreciably more efficient than the three-row wheel and, is often incorporated in turbines of other types with advantage.
The velocity compounding principle leads to relatively large heat drop per stage and therefore, to a comparatively small number of stages. Thus the initial cost of a velocity compounded turbine is likely to be low, but the disadvantage is of low efficiency ratio and therefore a high steam consumption.
4.9 PRESSURE-COMPOUNDED IMPULSE TURBINE
This type of turbine is shown diagrammatically in Figure 4.20. It is a
combination of many simple impulse turbines connected in series on the same shaft. It allows the exhaust steam from one turbine to enter the nozzles of succeeding turbine.
The nozzles are usually fitted into partitions, termed diaphragms, which separate one wheel chamber from the next. The wheel is mounted
individually on the shaft or spindle, and carry the blade on their periphery.
Expansion of steam takes place wholly in the nozzles, the space between any two diaphragms being filled with steam at constant pressure. The pressure on either side of any diaphragm are therefore different, the greatest difference of pressure occurring in the first few stages. Hence, steam will tend to leak through the space between the bore of the diaphragm and the surface of the shaft or wheel hubs. Special devices are fitted to minimize these leakages.
Figure 4.20: Pressure-compounded Impulse Turbine
The pressure compounding causes a smaller transformation of heat energy into kinetic energy to take place in each stage than in simple reaction turbine.
Hence steam velocities are much lower, with the result that the blade
velocities and the rotational speed may be lowered. It is fairly clear that a given constant quantity of available energy per kilogram of steam, the speed may be reduced at will simply by increasing the number of stages, but for low speeds the number of stages may become excessive.
Although the leaving velocity may bear the same ratio to the steam velocity at the nozzle outlet as it does in the simple impulse turbine, yet the kinetic energy per stage is now only a fraction of the total available energy.
Consequently, the leaving loss in the pressure compounded turbine is also only a fraction of that associated with the simple turbine and is usually only about or 2 per cent of the total available energy.
4.10 PRESSURE-VELOCITY COMPOUNDED IMPULSE TURBINE
This type of turbine is based on both velocity and pressure compounding principle.
As has already been mentioned, the two-row wheel is more efficient than the three-row wheel. But for the best economy it may be shown that the blade speed would have to be about 0.23 of the steam speed or about 280.4 m/sec.
The construction of the wheel required to carry two rows of blades at this velocity would present some difficulty but is more or less possible depending on the length of the blades. But an obvious way to reduce the blade velocity would be to split up the available energy by having two or more simple velocity compounded turbines in series on the same shaft. The total pressure drop is then effected in as many steps as there are wheels on the shaft, and hence, the turbine is pressure compounded as well as velocity compounded. As in other type of impulse turbine, the steam is expanded wholly in the nozzle, and the wheel rotate in steam at constant pressure. Thus ample clearances are permissible in the radial direction, while the clearances in an axial direction should, from the point of view of efficiency, be kept a small as possible.
The pressure and velocity compounded impulse turbine is shown
diagrammatically in Figure 4.21. The bottom portion of this figure is intended to show roughly how this and other type of impulse turbine may be controlled so as to give the best efficiency under varying loads. It is well known that for high efficiency the difference between the initial pressure after the governor valve and the condenser pressure should be as great as possible. If the governing is affected by throttling the steam, then at high load, the efficiency will be considerably reduced. In Figure 4.21, two sets of nozzles are shown, one set having 2 nozzles and the other 4 nozzles. Thus, there are 6 nozzles in all, and for the sake of illustrations, we shall assume that the steam delivered by each nozzle under the full pressure drop is sufficient to develop 10 H. P.
Figure 4.21: Pressure-velocity Compounded Turbine
Then at full load, all 6 nozzles will be delivering steam at full pressure and the turbine will operate at maximum efficiency. Similarly, at 20 H. P., only two nozzles will be open, and at 40 H. P. only set of 4 nozzles will be delivering steam, in both cases at full pressure.
The pressure-velocity compounded turbine is comparatively simple in construction and is much more compact than the multistage pressure
compounded impulse turbine. Unfortunately, its efficiency is not so high. At one time, it was widely used in power station, but is now obsolete type.
SAQ 6
(a) What is the difference between velocity compounding and pressure compounding principles?
(b) What are the advantages and disadvantages of the following turbines?
(i) Velocity compounded impulse turbine (ii) Pressure compounded impulse turbine
(iii) Velocity-pressure compounded impulse turbine.
4.11 SUMMARY
The function of the steam turbine is to convert heat energy of steam into mechanical energy.
Two basic principles on which the steam turbines are used to work are Impulse and Reaction principles.
The majority of steam turbines have two important elements or sets of such elements. These are nozzles and blades (or deflectors).
There are two types of nozzles: Simple Convergent type and Convergent- divergent type.
There are mainly two types of steam turbine blades, namely, Impulse blades which are classified into plate blade and profile blade, and Reaction blades.
De Laval turbine is an example of simple impulse steam turbine.
Parson turbine is an example of a reaction steam turbine.
On the basis of velocity and pressure compounding principles, the steam turbines can be classified into velocity compounded turbine, pressure compounded turbine and velocity-pressure compounded turbine.
4.12 KEY WORDS
Impulse Steam Turbine: Device that converts heat energy of steam into mechanical energy using impulse principle.
Reaction Steam Turbine: Device that transforms heat energy of steam into mechanical energy using reaction principle.
Steam Nozzle: It converts heat energy of steam into kinetic energy.
Turbine Blade: It converts kinetic energy into useful work.
Velocity Diagram: It shows how velocity of steam varies during the passage through the blade.
Pressure Compounded Turbine: It works on pressure compounded principle.
Velocity Compounded Turbine: It works on velocity compounded principle.
Pressure-velocity Compounded Turbine: It works on both velocity and pressure compounded principle.
4.13 ANSWERS TO SAQs
SAQ 1
(a) In case of impulse, the stationary plates move away from the nozzle due to the force when the jet of fluid issues from the nozzle at high speed and strikes it. In case of reaction, there is a backward reactive force on the nozzle when the fluid issues from a nozzle and this force equal to the amount of momentum generated per second in it.
(b) The passage of steam through the moving part of the turbine,
commonly (q) called blade, may take place in such a manner that the pressure at the outlet side of the blade is equal to that an inlet side.
Such an action is observed in the case of impulse turbine. On the other hand, the pressure of the steam at the outlet from the moving blade of the turbine may be less than that at inlet sides of the blades; the drop in pressure suffered by the steam during its flow through the moving
blades causes a further generation of kinetic energy within the blade and adds to the propelling force which is applied to the turbine rotor.
Such an action is the characteristics of the reaction turbine.
SAQ 2
(a) The basic requirement of the steam nozzles are as follows:
(i) Capacity to utilize the carrying over energy from the previous stage to the greatest possible extent.
(ii) In case of high velocity, its wall surfaces should be as smooth as possible to reduce friction.
(iii) Channel sections should be accurate.
(b) Convergent nozzle: It works on the principle of expanding steam from any given pressure to any pressure higher than the corresponding critical pressure.
Convergent-divergent nozzle: It works on the principle of expanding steam from any given pressure to any pressure lower than the
corresponding critical pressure.
(c) Impulse blade converts kinetic energy of steam into mechanical energy using impulse principle. On the other hand reaction blade converts that of the same using reaction principle.
(d)
SAQ 3 (a) Q ≈ 0
(i) Turbine: Wx = m (h2 – h1) (ii) Nozzle: Δ h = ΔC2 (iii) Blade: Wx = m . ΔC2
(b) Wx = (𝐶 − 𝐶 ) C1 = 200 m/s m = 1 kg/sec.
Again, Δ h = (𝐶 − 𝐶 )
5000 = (200 − 𝐶 ) => C2 = √40000 − 10000 = 173.2 m/sec.
Wx = X 5000 = 2500 Joules.
SAQ 4
(a) De Laval turbine is a simple impulse turbine in which steam expands from boiler pressure to condenser pressure before entering the wheel containing the blades.
(b) It shows how velocity of steam varies during the passage through the blade. Hence, knowing velocities at different stages, the work done by the turbine, etc. can be calculated.
SAQ 5
(a) A reaction turbine works on the principle that the steam expands in moving blades as well as stationary blades and kinetic energy of steam is transformed into mechanical energy by reaction principle.
(b) In case of axial-flow reaction turbine, there are a number of rows of moving blades attached to the rotor and equal number of rows of fixed blades attached to the casing, On the other hand, groups of blades are arranged in concentric rings and attached to the sides of separate discs, with one set of stationary blades in radial flow, double motion reaction turbine.
SAQ 6
(a) In velocity compounding principle, the steam is allowed to move from one stage to another stage having moving blades and guide blades respectively to cause velocity drop gradually due to friction and to give up a part of kinetic energy of steam. On the other hand, expansion of steam is made in number of steps, by arranging a number of simple impulse machines in series on the same shaft and thus splitting up of the whole pressure drop into a series of smaller pressure drops are caused in pressure compounded principle.
(b) (i) Advantages
(a) Low cost (b) Large heat drop per stage.
Disadvantages
(a) Low efficiency ratio (b) High steam consumption.
(ii) Advantage
(a) Leaving loss is low.
Disadvantages
(a) Leakage of steam (b) Low blade speed.
(iii) Advantages
(a) Compact (b) Simple in construction.
Disadvantages
(a) Obsolete type now (b) Efficiency not so high.
