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Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)

Copyright by Brij Bhooshan @ 2013

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In This Chapter We Cover the Following Topics

Art. Content Page

13.1 Steam Turbine 3

13.2 Impulse Turbines

The Single-Stage Impulse Turbine

Velocity Diagram and Calculations for Impulse Turbine

Optimization of Turbine Stage

6

6

7

10

13.3 Methods of Reducing Wheel or Rotar Speed

Compounding in Impulse Turbine

The Velocity - Compounding of the Impulse Turbine

Pressure Compounding or Rateau Staging

Pressure- Velocity Compounding

11

11

12

13

14

13.4 Reaction Turbine 14

13.5 Stage Efficiency and Reheat Factor 16

References:

1. M. J. Moran and H. N. Shapiro, Fundamentals of Engineering Thermodynamics, 6e,

John Wiley & Sons, Inc., New York, 2008.

2. G. J. Van Wylen, R. E. Sonntag, C. Borgnakke, Fundamentals of Thermodynamics,

John Wiley & Sons, Inc., New York, 1994.

3. J. P. Holman, Thermodynamics, 4e, McGraw-Hill, New York, 1988.

4. F. W. Sears, G. L. Salinger, Thermodynamics, Kinetic theory, and Statistical

Thermodynamics, 3e, Narosa Publishing House, New Delhi, 1998.

5. Y. A. Cengel and M. A. Boles, Thermodynamics: An Engineering Approach, 2e,

McGraw-Hill, New York, 1994.

6. E. Rathakrishnan, Fundamentals of Engineering Thermodynamics, 2e, PHI Learning

Private Limited, New Delhi, 2008.

7. P. K. Nag, Basic and Applied Thermodynamics, 1e, McGraw-Hill, New Delhi, 2010.




2 Chapter 13: Steam Turbines

8. V Ganesan, Gas Turbine, 2e, Tata McGraw-Hill, New Delhi, 2003.

9. Y. V. C. Rao, An Introduction to Thermodynamics, 1e, New Age International (P)

Limited, Publishers, New Delhi, 1998.

10. Onkar Singh, Applied Thermodynamics, 2e, New Age International (P) Limited,

Publishers, New Delhi, 2006.

Please welcome for any correction or misprint in the entire manuscript and your

valuable suggestions kindly mail us [email protected].




3 Basic and Applied Thermodynamics By Brij Bhooshan

13.1 STEAM TURBINE

A steam turbine converts the energy of high-pressure, high temperature steam produced

by a steam generator into shaft work. The energy conversion is brought about in the

following ways:

1. The high-pressure, high-temperature steam first expands in the nozzles emanates

as a high velocity fluid stream.

2. The high velocity steam coming out of the nozzles impinges on the blades mounted

on a wheel. The fluid stream suffers a loss of momentum while flowing past the

blades that is absorbed by the rotating wheel entailing production of torque.

3. The moving blades move as a result of the impulse of steam (caused by the change

of momentum) and also as a result of expansion and acceleration of the steam

relative to them. In other words they also act as the nozzles.

A steam turbine is basically an assembly of nozzles fixed to a stationary casing and

rotating blades mounted on the wheels attached on a shaft in a row-wise manner. In

1878, a Swedish engineer, Carl G. P. de Laval developed a simple impulse turbine, using

a convergent-divergent (supersonic) nozzle which ran the turbine to a maximum speed

of 100,000 rpm. In 1897 he constructed a velocity-compounded impulse turbine (a two-

row axial turbine with a row of guide vane stators between them.

Auguste Rateau in France started experiments with a de Laval turbine in 1894, and

developed the pressure compounded impulse turbine in the year 1900.

In the USA , Charles G. Curtis patented the velocity compounded de Lavel turbine in

1896 and transferred his rights to General Electric in 1901.

In England , Charles A. Parsons developed a multi-stage axial flow reaction turbine in

1884.

Steam turbines are employed as the prime movers together with the electric generators

in thermal and nuclear power plants to produce electricity. They are also used to propel

large ships, ocean liners, submarines and to drive power absorbing machines like large

compressors, blowers, fans and pumps.

Turbines can be condensing or non-condensing types depending on whether the back

pressure is below or equal to the atmosphere pressure.

Normally a turbine stages is classified as

1- Impulse stage;

2- Reaction stage

An impulse stage is characterized by the expansion of the gas which occurs only in the

stator nozzles. The rotor blades act as directional vans to deflect the direction of flow.

Further they convert the kinetic energy of the gas in to work by changing the

momentum of the gas more or less at constant pressure.

A reaction stage is one in which expansion of the gas takes place both in the stator and

in the rotor. The function of the stator is the same as that in the impulse stage but the

function in the rotor is two fold

1. A rotor converts the kinetic energy of the gas in to work,

2. Contributes a reaction on the rotor blades.

The reaction force is due to the increase in the velocity of gas relative to the blades. This

results from the expansion of the gas during its passes through the rotor.





Classification

Based on the blade flow passage

In steam turbine thermal energy available with steam is converted in to kinetic energy

which in turned produces driving thrust on the shaft. Base upon the rotor blades the

flow passage may be of

1- Constant cross-section area type from blade inlet to exit;

2- Varying cross-section area type from blade inlet to exit.

Turbine having former type blading are termed as impulse turbine while later type are

in reaction type.

The mechanism of impulse and reaction forces getting by Newton’s Second law

F = m.a = m.(dV/dt)

F = mass flow rate × change in velocity

Tangential Force (Ft) = mass flow rate × change in tangential component of the velocity

The impulse force can be defined as the force because of change in tangential component

of velocity of fluid which may be due to change in direction or magnitude. Diagram 13.1

shows the impulse force generating because the use of the change in velocity of fluid.

Diagram 13.1

Diagram 13.1(a) the impulse force is available due to change in magnitude of velocity

and shall be given by the product of mass flow rate and change in velocity. In case B the

impulse force is generated due to change in direction of velocity and if the blade is

stationary and frictionless then there shall be no decrease in magnitude of velocity.

Reaction force is available when the tangential velocity of fluid is increased and is

opposite in reference to the direction of velocity.

In case Diagram 13.1(b), the total force exerted on the blade is actually a combination of

impulse and reaction. Impulse force is available in the entrance half of the blade where

jet impinges causing a force to right. While in the exit half the leaving jet exerts a

reactive force on the blade which also acts to right. Combined effect of the two forces on

the impulse force.

Reaction force available due to increase in tangential velocity of fluid can be seen in case

of nozzle due to acceleration of fluid.

Diagram 13.2

Based on cylinder flow arrangement:

a) Single flow single casing turbine;

Fr = m (0 V1) = m V1

V1 > 0

Fv

Fr

V0 = 0

Impulsive force due to change in direction of

velocity.

(b)

Impulse force due to change in

magnitude of velocity

(a)





b) Double flow single casing turbine;

c) Tipple cross flow compound turbine with double row;

d) Cross flow compound turbine with single row;

e) Cross flow compound turbine with double row

Based on the direction of flow:

a) Radial flow turbine;

b) Axial flow turbine;

c) Tangential flow turbine

In Radial flow turbines the steam is inject in middle near shaft and steam flow radially

outwords through the successive moving blades placed concentrically. In radial flow

turbines there are no stationary blades so pressure drop occurs in moving blade passage

concentric moving blades rings are designed to move in opposite directions.

In tangential flow turbines the nozzle directs steam tangentially into bucket at the

periphery of single wheel and steam reverses back and re-enters other bucket at its

periphery. This is repeated several times as steam follows the helical path. Tangential

flow turbines are very robust but less efficient.

In axial flow turbines steam flows along the axis of turbine over blades. These axial flow

turbines are well suited for large turbogenrators and very commonly used presently.

Based on the No. of stages:

a) Single stage turbine;

b) Multi stage turbine

Single stage turbines have the expansion occurring in single stage while in multi stage

turbines the expansion occurs in more than one stage of turbine.

Based on speed of turbine

a) Low speed steam turbine < 3000;

b) Normal speed steam turbine = 3000;

c) High speed steam turbine > 3000

Based on pressure in steam turbine

a) Low pressure steam turbine < 20 kg/cm2.

b) Medium pressure steam turbine < 20 kg/cm2.

c) High pressure steam turbine < 20 kg/cm2.

d) Super pressure steam turbine < 20 kg/cm2.

According to Method of governing

Turbine with throttle governing: in which fresh steam enters through one or more

simultaneously operated throttle valves.

Turbine with nozzle governing: in which fresh steam enters through two or more

consecutively opening regulators.

Turbine with by-pass governing: in which steam turbines besides being fed to the 1st

stage as also directly fed to one, two or even three intermediate stages of the turbine.





According to heat drop pressure:

a) Condensing turbine with generators;

b) Condensing turbine with one or two intermediate stage extractions.;

c) Back pressure turbine;

d) Non-condensing turbine;

e) Pass-out turbine;

f) Topping turbine;

g) Back pressure turbine with steam extraction from intermediate stages at specific

pressure;

h) Low pressure turbine;

i) Mixed pressure turbine.

According to usage in industry:

a) Stationary turbine with constant speed of rotation - primarily used for driving

alternators.

b) Stationary steam turbine- with variable speed meant for driving turbo-blowers,

air circulators, pump, etc.

c) Non-stationary turbines with variable speed turbine of this type are usually

employed in steamers, ships and railway locomotive.

13.2 IMPULSE TURBINES

Impulse turbines (single-rotor or multi-rotor) are simple stages of the turbines. Here the

impulse blades are attached to the shaft. Impulse blades can be recognized by their

shape. They are usually symmetrical and have entrance and exit angles respectively,

around 20°. Because they are usually used in the entrance high-pressure stages of a

steam turbine, when the specific volume of steam is low and requires much smaller flow

than at lower pressures, the impulse blades are short and have constant cross sections.

The Single-Stage Impulse Turbine

The single-stage impulse turbine is also called the de Laval turbine after its inventor.

Diagram 13.3 Schematic diagram of an Impulse Turbine

The turbine consists of a single rotor to which impulse blades are attached. The steam is

fed through one or several convergent-divergent nozzles which do not extend completely





around the circumference of the rotor, so that only part of the blades is impinged upon

by the steam at any one time. The nozzles also allow governing of the turbine by

shutting off one or more them.

The velocity diagram for a single-stage impulse has been shown in Diagram 13.3.

Diagram 13.4 shows the velocity diagram indicating the flow through the turbine

blades.

Diagram 13.4 Velocity diagram

Velocity Diagram and Calculations for Impulse Turbine

Let us consider

V1 = absolute velocity of steam at inlet to moving blade or velocity of steam leaving

nozzle.

V2 = absolute velocity of steam at exit of moving blade

V1w = Whirl velocity at inlet to moving blade or tangential component of absolute

velocity at inlet to moving blade.

V2w = Whirl velocity at exit of moving blade or tangential component of absolute velocity

at exit of moving blade.

V1a = Flow velocity at inlet to moving blade or axial component of absolute velocity at

inlet to moving blade.

V2a = Flow velocity at exit of moving blade or axial component of absolute velocity at exit

of moving blade.

Vr1 and Vr2 = Inlet and outlet relative velocity (Velocity relative to the rotor blades.)

U = mean blade speed / linear velocity of blade ( dN/60)

d = mean diameter of wheel

N = speed in rpm

m = mass of steam flowing over blade

ρ = Ratio of linear velocity of blade and absolute velocity of steam at inlet to moving

blade = U/V1

K = Co-efficient of blade velocity

= Angle of absolute velocity w.r.t. the direction of blade motion

1 = Angle of absolute velocity at inlet to moving blade or nozzle angle.

2 = Angle of absolute velocity at outlet to moving blade or inlet angle of fixed blade in

next stage.

β = Angle of relative velocity w.r.t. the direction of blade motion

β1 = Angle of relative velocity at inlet or inlet angle of moving blade

V2a

U

Vr2

V2

U V2w

U V1w

V1 V1a Vr1

V2a

Vr2

V2

V2w

U V1w

V1

V1a Vr1





β2 = Angle of relative velocity at exit or exit angle of moving blade

Let the mass flow rate be m, kg/sec

Tangential Force

FT = m × change of tangential component of velocity or whirl velocity.

FT = m(V2 cos 2 V1 cos 1) = m(V2 cos 2 + V1 cos 1)

FT = m Vw [13.1]

Driving Thrust

FD = FT = m(V2 cos 2 + V1 cos 1)

FD = m Vw [13.2]

From Velocity triangles

V2 cos 2 + V1 cos 1 = Vr2 cos 2 + Vr1 cos 1

Vw = Vr

FD = m Vw = m Vr

FD = m(Vr2 cos 2 + Vr1 cos 1) [13.3]

Rate of work done or the rotor

W = FD U = m Vw U [13.4a]

Work done per unit of steam mass flow

W = FD U = Vw U [13.4b]

Rate of work done will be the power produced by the turbine stage

W = mU (V1 cos 1 U) (1 + KZ) [13.6

where K = Vr2/Vr1, Ratio of cosines of blade angles (Z) = cos β2/cos β1.

For perfectly smooth and symmetrical blade both K and Z shall have unity value i.e. K =

1, Z = 1.

Therefore for simple impulse turbine stage having perfectly smooth and symmetrical

blade, rate of work done,

W = mU (V1 cos 1 U)

From Diagram U = AB, ΔCw = EF

W = m × AB × EF

Second Approach: The work is available at rotor can also be obtained using steady

flow energy equation b/w section 1 and 2. Assuming no change in P.E. from inlet to exit

across the moving blade and no heat interaction across the stage, the SFEE can be given

be





In case of impulse stage of change in enthalpy from section 1 and 2 can be given by the

change in K.E. associated with relative velocity from 1 to 2.

Rate of work done

For perfectly smooth moving blade Vr1 = Vr2, h1 – h2 = 0.

Hence for stage with smooth blade

From velocity triangle at inlet

From velocity triangle at outlet

Combining above two we get,

We know that

The rate of work done

Axial thrust

Axial component of velocity or flow velocity change causes creation of axial thrust. Axial

thrust due to change in momentum because of change in flow velocity

Blading/ Diagram Efficiency

Stage/ Gross Efficiency

Stage efficiency refers to the ratio of work done and energy supplied to the stage. Energy

supplied to the stage can be accounted by the change in enthalpy between section 0 and

1 i.e. inlet of nozzle to exit of nozzle.

Stage efficiency is thus the output of stage divided by the available energy for the stage.

Energy supplied to stage = m(h0 –h1)





Nozzle Efficiency

It is the ratio of K.E. available and enthalpy change occurring across the nozzle i.e.

between inlet and outlet (Sec. 0 to 1)

Overall Efficiency

The overall efficiency of stage can be given by the ratio of work delivered at turbine

shaft to the energy supplied to the stage.

where ηm = mechanical efficiency.

Optimization of Turbine Stage

Turbine being work producing machine is designed with the aim of providing maximum

work output. The ηD of the turbine should be maximized as it indicates the rate of work

done per unit of energy supplied to the rotor.

Work output per unit time in a simple impulse turbine stage is

m, V1, U, , K, Z = Dependable quantity

Thus the work cannot be maximized by only selecting the minimum value of angle 1

and so requires optimization of turbine stage performance with respect to some other

parameter.

The ηD should be maximized with respect to suitable parameter.

Let ρ = U/V1, then

K = 1, Z = 1, for perfectly smooth and symmetrical blade.

Second order differential of ηD with respect to ρ indicates that the diagram efficiency is

maximum corresponding to the blade speed-steam velocity ratio given as





Hence, maximum diagram efficiency,

For perfectly smooth and symmetrical blade maximum diagram efficiency,

Max. Rate of Work done

Wmax = mU2 (1 + KZ)

For perfectly smooth and symmetrical blade K = 1, Z = 1.

Wmax = 2mU2

The variation of diagram efficiency can be plotted with varying blade, steam velocity

ratio as shown in Diagram 13.5.

Diagram 13.5

13.3 METHODS OF REDUCING WHEEL OR ROTAR SPEED

Under the handling simple impulse turbine that if the steam is expanded from the boiler

pressure to condenser pressure in one stage the speed of the rotor becomes tremendously

high which crops up practical complicacies. There are several methods of reducing this

speed to lower value, all these methods utilize a multiple system of rotor in series, keyed

on a common shaft and the steam pressure or jet velocity is absorbed in stages as the

steam flows over the blades. This is termed as compounding. Compounding is a

thermodynamic means for reducing the speed of turbine where speed reduction is

realized without employing a gear box.

Compounding in Impulse Turbine

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

For stage with losses

For K=1, Z=1





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:

(a) velocity compounding;

(b) pressure compounding; and

(c) velocity- pressure compounding.

(Either of the above methods or both in combination are used to reduce the high

rotational speed of the single stage turbine).

The Velocity - Compounding of the Impulse Turbine

The velocity-compounded impulse turbine 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. The Curtis stage turbine, as it came to be called, is composed of one stage of

nozzles as the single-stage turbine, followed by two rows of moving blades instead of

one.

Diagram 13.6 Velocity Compounding arrangement

Steam is expanded through a stationary nozzle from the boiler or inlet pressure to

condenser pressure. So the pressure in the nozzle drops, the kinetic energy of the steam

increased due to increase in velocity. A portion of this available energy is absorbed by a

row of moving blades. The steam (whose velocity has decreased while moving blades)

then flows through the second row of blades which are fixed. The function of these fixed

blades is to re-direct the steam flow without altering its velocity to the flowing next row

moving blades where again work is done on them and steam leaves the cut away section

of such a stage and changes in pressure and velocity as the steam passes through the

nozzle, fixed blades and moving blades. In the Curtis stage, the total enthalpy drop and

hence pressure drop occur in the nozzles so that the pressure remains constant in all three

rows of blades.

Velocity is absorbed in two stages. In fixed (static) blade passage both pressure and

velocity remain constant. Fixed blades are also called guide vanes. Velocity compounded

stage is also called Curtis stage. The velocity diagram of the velocity-compound Impulse

turbine is shown in Diagram 13.6.

The fixed blades are used to guide the outlet steam/gas from the previous stage in such a

manner so as to smooth entry at the next stage is ensured.

M = Moving Blade,

F = Fixed Blade,

N = Nozzle

N M F M

Leaving velocity Ve

Back pressure pe

Boiler

pressure pi

Entering

velocity Vi

Steam out

Steam in





Diagram 13.7 Velocity diagrams for the Velocity-Compounded Impulse turbine

The blade velocity coefficient may be different in each row of blades

Work done (W) = mU (∆Vw1 ∆Vw2) [13.8a]

End Thrust = mU (∆Vf1 ∆Vf2) [13.8b]

The optimum velocity ratio will depend on number of stages and is given by

Work is not uniformly distributed (1st >2nd )

The first stage in a large (power plant) turbine is velocity or pressure

compounded impulse stage.

Diagram 13.8 Pressure-Compounded Impulse Turbine

Pressure Compounding or Rateau Staging

To alleviate the problem of high blade velocity in the single-stage impulse turbine, the

total enthalpy drop through the nozzles of that turbine are simply divided up,

essentially in an equal manner, among many single-stage impulse turbines in series

Stages

1 2 3

N M N M N M

Initial Steam Velocity

Boil

er

Pre

ssu

re

Exhaust Pressure

Lost

Velocity

First Stage

Vf1

U

21 21 11

11

Vr11

V11

Vr21

V21

Vw1

Second Stage

Vf2

U

22 22 21

12

Vr12

V12

Vr22

V22

Vw2





(Diagram 13.8). Such a turbine is called a Rateau turbine, after its inventor. Thus the

inlet steam velocities to each stage are essentially equal and due to a reduced Δh.

Diagram shows rings of fixed nozzle in corporate between the rings of moving blades.

The steam at boiler pressure enters the first set of nozzles and expands partially. The

kinetic energy of the steam thus obtained is absorbed by the moving blades (stage 1).

The steam is expands partially in the second set of nozzles where its pressure again falls

and the velocity increases, the kinetic energy so obtained is absorbed by the second ring

of moving blades (stage 2). This is repeated in stage 3 and steam is finally leaves the

turbine at low velocity and pressure. The number of stages (or pressure reduction)

depends upon the number of rows of nozzles through which the steam must pass.

This is most efficient turbine since the speed ratio remains constant built it is expensive

owning to a large number of stages.

Pressure- Velocity Compounding

This method of compounding is the combination of velocity and pressure compounding.

The total drop in steam pressure is divided into stages and velocity obtained in each

stage is also constant during each stages. The rings of nozzles are fixed at the begning of

each stage and pressure remains constant during each stages. The change in pressure

and velocity are as shown in Diagram 13.9.

Thus hear one or more ‘curtis stage’ velocity compound followed by ‘Rateau stage’ reduce

pressure to a moderate level with high proportion to work per stage and then the highly

efficient ‘Rateau stage’ absorb the remaining energy available.

Diagram 13.9 Pressure- Velocity Compounding Impulse Turbine

13.4 REACTION TURBINE

A reaction turbine, therefore, is one that is constructed of rows of fixed and rows of

moving blades. The fixed blades act as nozzles. The moving blades move as a result of

the impulse of steam received (caused by change in momentum) and also as a result of

expansion and acceleration of the steam relative to them. In other words, they also act

as nozzles. The enthalpy drop per stage of one row fixed and one row moving blades is

divided among them, often equally. Thus a blade with a 50 percent degree of reaction, or

a 50 percent reaction stage, is one in which half the enthalpy drop of the stage occurs in

the fixed blades and half in the moving blades. The pressure drops will not be equal,

N M F M N M F N


Boil

er

Pre

ssu

re

Exhaust Pressure

Lost Velocity





however. They are greater for the fixed blades and greater for the high-pressure than

the low-pressure stages.

The moving blades of a reaction turbine are easily distinguishable from those of an

impulse turbine in that they are not symmetrical and, because they act partly as

nozzles, have a shape similar to that of the fixed blades, although curved in the opposite

direction. The schematic pressure line (Diagram 13.10) shows that pressure

continuously drops through all rows of blades, fixed and moving. The absolute steam

velocity changes within each stage as shown and repeats from stage to stage. Diagram

13.11 shows a typical velocity diagram for the reaction stage.

Diagram 13.10 Three stages of reaction turbine indicating pressure and velocity distribution

Pressure and enthalpy drop both in the fixed blade or stator and in the moving blade or

Rotor

A very widely used design has half degree of reaction or 50% reaction and this is known

as Parson's Turbine. This consists of symmetrical stator and rotor blades.

Diagram 13.11 The velocity diagram of reaction blading

The velocity triangles are symmetrical and we have

Energy input per stage (unit mass flow per second)

Fixed Blade

U

F M F M F M


Boil

er

Pre

ssu

re

Exhaust Pressure

Lost Velocity





From the inlet velocity triangle we have,

Work done (for unit mass flow per second) = W = UΔVw

Therefore, the Blade efficiency

Put ρ = U/V1, then

For the maximum efficiency dηB/dρ = 0, and we get

from which finally it yields

Diagram 13.12 Velocity diagram for maximum efficiency

Absolute velocity of the outlet at this stage is axial (see Diagram 13.12). In this case, the

energy transfer

(ηB)max can be found out by putting the value of ρ = Cosα1 in the expression for blade

efficiency

η is greater in reaction turbine. Energy input per stage is less, so there are more number

of stages.

13.5 STAGE EFFICIENCY AND REHEAT FACTOR

The Thermodynamic effect on the turbine efficiency can be best understood by

considering a number of stages between two stages 1 and 2 as shown in Diagram 13.13.

The total expansion is divided into four stages of the same efficiency ηs and pressure

ratio.

U





Diagram 13.13 Different stage of a steam turbine

The overall efficiency of expansion is η0. The actual work during the expansion from 1 to

2 is

R.F is 1.03 to 1.04

If ηS remains same for all the stages or ηS is the mean stage efficiency.

We can see:

This makes the overall efficiency of the turbine greater than the individual stage

efficiency.

The effect depicted by Eqn (13.b) is due to the thermodynamic effect called "reheat". This

does not imply any heat transfer to the stages from outside. It is merely the

reappearance of stage losses an increased enthalpy during the constant pressure

heating (or reheating) processes AX, BY, CZ and D2.

Entropy

Enthalpy

W

px

Wa py

A pz

p2

p1 1

Z

Y

X

2

2 D

C B

A

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