Using the convergent steam nozzle type in the entrance

Saif al-din ali Madhi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
2/7/2020 1 | P a g e
Using the convergent steam nozzle type in the entrance
region of the steam turbine
University of Baghdad
Name: - Saif Al-din Ali -B-
s.madi1603@coeng.uobaghdad.edu.iq
The fourth stage

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TABLE OF CONTENTS
1. Objective :
2. Introduction :
3. steam turbine :
4. STEAM NOZZLES:
5. Numerical analysis using simulation :
6. Discussion:

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convergent steam nozzle
abstract:
This research aims to identify a converged type of converging nozzle. The steam
turbine and nozzle types are discussed and a numerical simulation is done to
design a simple identifier of pressure and speed distribution within the nozzle
using ansys program.
1. Objective :
Using the convergent steam nozzle type in the entrance region of the steam
turbine.
2. Introduction :
Steam is a vapour. It is used as the working substance in the operation of steam
engines and steam turbines. a vapour is a partially evaporated liquid carrying in it
particles of liquid and it can be liquefied by minor changes in temperature or pressure.
Steam as a vapour would not obey the laws of perfect gases unless it is in a highly
dried condition. Steam in such a dried state is known as superheated steam and it is
assumed to behave like a perfect gas when highly superheated.
From the early days of the reciprocating steam engines, many attempts were made to
develop power from steam without the necessity of the reciprocating mechanism.
Modern steam turbine is the result of these efforts. The steam turbine differs from the
reciprocating steam engine, both in mechanical construction and in the manner in
which power is generated from the steam. In the reciprocating steam engine a to and
for motion is imparted to the engine piston by the pressure of the steam acting upon
It, and this reciprocating motion is converted into rotary motion at the crankshaft
through the medium of the crosshead, connecting rod and crank. The expansive
property of the steam is not utilized to the fullest, even in the best types of multi-
expansion steam engines.
In the impulse steam turbine, the overall transformation of heat into mechanical work
is accomplished in two distinct steps. The available energy of steam is first changed
into kinetic energy, and this kinetic energy is then transformed into mechanical work.
The first of these steps, viz., the transformation of available energy into kinetic energy
. A nozzle is a passage of varying cross-sectional area in which the potential energy
of the steam is converted into kinetic energy. The increase of velocity of the steam jet
at the exit of the nozzle is obtained due to decrease in enthalpy (total heat content) of
the steam. The nozzle is so shaped that it will perform this conversion of energy with
minimum loss.

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3. steam turbine :
In the steam turbine, rotary motion is imparted directly to the shaft by means of high
velocity steam jets striking the blades fixed on the rim of a wheel which is fastened to
the shaft. The turbine is much simpler in mechanical construction, and it utilizes the
kinetic or velocity energy of the steam instead of pressure only. The expansive
property of the steam is almost utilized in the turbine either in the admission nozzles
or in the turbine blading. Steam turbines are capable of expanding the steam to the
lowest exhaust pressure obtainable in the condenser because they are steady flow
machines and many have large exhaust outlets (with no valves) through which the
spent (used) steam must be discharged. Steam engines, however, are intermittent (non-
continuous) flow machines and must force the expanded steam out through the
relatively small exhaust valve. The lowest practical exhaust pressure for most steam
engines is therefore 15 to 20 cm of mercury absolute (i.e. 0-2 to 0-3 bar). Steam
turbines may expand steam to 2-5 cm of mercury absolute pressure or less The main
advantages of steam turbine over the reciprocating steam engine ace as follows :
(i) With the turbine much higher speeds may be developed, and a far greater speed
range is possible than in the case of the reciprocating steam engine. Because of this,
turbine units are much smaller for same power than reciprocating steam engine units
(ii) Since the turbine is a rotary machine, perfect balancing is possible. This means
foundation of the turbine is lighter and smaller.
(iii) The ability of turbine to use high pressure and superheated steam and uniflow
direction of steam flow through the turbine, combined with its greater range of
expansion and ability to utilize a high vacuum to greater advantage, make the steam
turbine much more efficient and economical than the reciprocating steam engine for
power generation
(v) As no internal lubrication is heeded, highly superheated steam can be used and
exhaust steam contains no lubricating oil.
Fig (1) steam turbine

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4. STEAM NOZZLES:
Nozzle is a duct by flowing through which the velocity of a fluid increases at the
expense of pressure drop. if the fluid is steam, then the nozzle is called as Steam
nozzle. the flow of steam through nozzles may be taken as adiabatic expansion. The
steam possesses a very high velocity at the end of the expansion, and the enthalpy
decreases as expansion occurs. Friction exists between the steam and the sides of the
nozzle; heat is produced as the result of the resistance to the flow. The phenomenon
of super saturation occurs in the steam flow through nozzles. This is because of the
time lag in the condensation of the steam during the expansion. The area of such
duct having minimum cross-section is known as throat. A fluid is called
compressible if its density changes with the change in pressure brought about by the
flow. If the density changes very little or does not change, the fluid is said to be
incompressible. Generally the gases and vapors are compressible, whereas liquids
are incompressible.
• Simple Area Change
- Continuity equation in partial form
𝜌𝑉𝐴 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
ln𝜌 + ln 𝐴 + ln𝑉 = ln𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
- For frictionless and absence of change of height , momentum equation
becomes Euler equation :
𝑉𝑑𝑉 =
- Velocity of sound
𝑑𝜌
+
𝑑𝑉
+
𝑑𝐴
= 0
𝜌 𝑉 𝐴
𝑉𝑑𝑉 = − 𝑑𝑃
𝜌
( Multiple and divide by 𝑑𝜌 )
𝑑𝜌
𝑑𝑃 + 𝑉𝑑𝑉 = 0
𝜌
(1)
(2)

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(4)
d= Change = Final value - Initial value
𝑑𝑉 = 𝑉2 − 𝑉1
𝑑𝐴 = 𝐴2 − 𝐴1
Fig (2) Effect of area change on Mach number and velocity
(3)

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• Types of Nozzles:
There are three types of nozzles
1. Convergent nozzle
2. Divergent nozzle
3. Convergent-divergent nozzle.
A nozzle is an element whose primary function is to convert enthalpy (total
heat) energy into kinetic energy. When the steam flows through a suitably
shaped nozzle from zone of high pressure to one at low pressure, its velocity
and specific volume both will increase.
The equation of the continuity of mass may be written thus :
In order to allow the expansion to take place properly, the area at any
section of the nozzle must be such that it will accommodate the steam
whatever volume and velocity may prevail at that point
As the mass flow (m) is same at all sections of the nozzle, area of cross-section
(A) varies as V/v` The manner in which both V and v vary depends upon the properties
of the substance flowing. Hence, the contour of the passage of nozzle depends upon
the nature of the substance flowing
For example, consider a liquid- a substance whose specific volume v remains almost
constant with change of pressure. The value of V/v` will go on increasing with
change of pressure. Thus, from eqn. 5 . the area of cross-section should decrease
with the decrease of pressure. Fig. 3 (a) illustrates the proper contour of longitudinal
section of a nozzle suitable for liquid. This also can represent convergent nozzle for a fluid
whose peculiarity is that while both velocity and specific volume increase, the rate of
specific volume increase is less than that of the velocity, thus resulting in increasing value
of
(5)

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Fig. 3. General forms of Nozzles.
Fig. 3 (b) represents the correct contour for some hypothetical substance for which
both velocity and specific volume increase at the same rate, so that their ratio V/v` is
a constant at all points. The area of cross-section should therefore, be constant at all
points, • and the nozzle becomes a plain tube.
Fig. 3 (c) represents a divergent nozzle for a fluid whose peculiarity is that V/v`
decreases with the drop of pressure, i.e., specific volume increases at a faster rate than
velocity with the drop of pressure. The area of cross-section should increase as the
pressure decreases.
Fig. 8-1 (d) shows the general shape of convergent-divergent nozzle suitable for gases
and vapors. It can be shown that in practice, while velocity and specific volume both
increase from the start, velocity first increases faster than the specific volume, but after
Fig. 3 (d) shows the general shape of convergent-divergent nozzle suitable for gases
and vapors. It can be shown that in practice, while velocity and specific volume both
increase from the start, velocity first increases faster than the specific volume, but after
a certain critical point, specific volume increases more rapidly than velocity. Hence
the value of V/v` first increases to maximum and then decreases, necessitating a
nozzle of convergent-divergent form. The above statement may be verified by
referring to table 1 , which shows the properties of steam at various pressures when
expanding dry saturated steam from 14 bar to 0-15 bar through a nozzle, assuming
frictionless adiabatic flow.

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Table 1Properties of steam at various pressures when expanding dry saturated steam
from 14 bar to 0.15 bar through a nozzle, assuming frictionless adiabatic flow.
• Converging nozzle
consider a converging nozzle as shown in figure (4-a) below,
Fig.4 Converging nozzle
Figure (4-b) shows the pressure ratio p/po along the length of the nozzle. Where p is
the static pressure. The inlet conditions of the gas are at the stagnation state ( Po, To)
which are constants. The pressure at the exit plane of the nozzle is denoted by Pe
and the back pressure is Pb which can be varied by the adjustment of the valve.
Case (i): As shown in fig (b), case (i); the pressure Po is throughout, i.e. Po=Pe=Pb
There will be no flow through the nozzle.
Case (ii): As we decrease Pb gradually ,the flow rate will increase. The pressure will
decrease in the direction of the flow as shown in fig (b), case (ii). The pressure Pe at
the exit plane of the nozzle shall remain equal to Pb as long as the maximum discharge

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condition is not reached. The flow rate is directly proportional to mass flow rate,
so as the flow rate increases mass flow rate will also increase.
Case (iii): Fig (b), case (iii); illustrates the pressure distribution in the maximum
discharge situation. The flow rate/mass flow rate has attained its maximum valve,
i.e. when Mach, Ma = 1 is achieved and the nozzle is said to be choked. Pe is equal
to p∗ (pressure for M=1). Since the nozzle does not have a diverging section, further
reduction in Pb will not accelerate the flow to supersonic condition. As a result, Pe
will continue to remain at p∗ even though Pb is lowered further.
Case (iv): Since Pb is less than p∗ , the flow leaving the nozzle has to expand to match
the lower back pressure as shown in fig (b), case (iv); This expansion is three-
dimensional and the pressure distribution can’t be predicted by one dimensional
theory.
Fig.5 Isentropic flow through converging nozzle
Figure(6):The effect of back pressure Pb on the mass flow rate and the exit pressure Pe.
- From the above figure,

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- For all back pressures lower that the critical pressure, exit pressure = critical
pressure, Mach number is unity and the mass flow rate is maximum (choked
flow).
- A back pressure lower than the critical pressure cannot be sensed in the
nozzle upstream flow and does not affect the flow rate.
- If a convergent nozzle is operating under choked condition, the exit Mach
number is unity.
- The exit flow parameters are then defined by the critical parameters.
- To determine whether a nozzle is choked or not, we calculate the actual
pressure ratio and then compare this with the critical pressure ratio.
- If the actual pressure ratio > critical pressure ratio, the nozzle is said to be
choked
5. Numerical analysis using simulation:
(Discovery Live 2020 R1) was used for simulation and drawing
Water vapor was used at a speed of 330 m / s and a temperature
of 200 degrees
Figure(7): Convergent-divergent nozzle
Figure(8): Extrusion tube

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Figure(8): velocity simulation
Figure(9): Pressure simulation

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Figure(10): Convergent nozzle
Figure(11): velocity simulation

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Figure(12): Pressure simulation
6. Discussion
Increasing the speed of fluids and decreasing pressure by shifting
energy forms is the most important reason for using this type in the
steam turbine to exploit the largest amount of energy for the steam
and convert it into work that can be used in generating electric energy
through the movement of the main axis of tubing.
A design was made on a simulation program to know the fluid state
and the amount of change in its energy. It is a simple laboratory design

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References :
1. A TEXTBOOK OF FLUID MECHANICS AND HYDRAULIC MACHINES
in SI UNITS Er. R.K. RAJPUT M.E. (Hons.), Gold Medallist; Grad.
(Mech.Engg. & Elect. Engg.); M.I.E. (India); M.S.E.S.I.; M.I.S.T.E.; C.E.
(India)
2. Introduction to Compressible Fluid Flow S E C O N D E D I T I O N
HEAT TRANSFER A Series of Reference Books and Textbooks SerieS
editor Afshin J. Ghajar Regents Professor School of Mechanical and
Aerospace Engineering Oklahoma State University
3. ELEMENTS OF HEAT ENGINES VOLUME II (IN SI UNITS)
B y Late Prof. R. C. Patel B.E.TMech.) Hons., B E. (Elect.) Hons..
A.R.C.S.T. (Mech.) Hon., (Glasgow). M Sc. (Birmingham), F.I.E.
(India), F.I.A.E. (India), M.I.S.T.E., M.I.F.M.. M.I.I.M. Former Vice
Chancellor M.S. University of Baroda, BARODA. AND Late C. J.
Karamchandani D.M.E.E. (Karachi), Senior Lecturer (Retd.).
Mechanical Engineering Department. Polytechnic. M.S. University
of Baroda, BARODA.
4. Dr. Sajida Lafta Gas dynamics “CHAPTER THREE
ISENTROPIC FLOW”

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