Part 30 - cd3wd430.zip - Offline - Design of Small Water Turbines for Farms and Small Communities

Part 30 - cd3wd430.zip - Offline - Design of Small Water Turbines for Farms and Small Communities
MICROFICHE
REFERENCE
LIBRARY
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Desiun Of
. . Su
-4
Communitie,
by:
in Asia
Water
TUK-
for
Farms
and
Small
MohammadDt,-ali
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Program
Massachusetts Institute
of Technology
Cambridge, MA 02139 USA
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DESIGN OF SMALL WATER TURBINES FOR
FARMS AND SMALL COMMUNITIES
Mohammad Durali
Project
David
supervisor:
Gordon
Spring
Wilson
1976
TECHNOLOGY ADAPTATION PROGRAM
Massachusetts
Cambridge,
Institute
of Technology
Massachusetts
02139
L>, ;
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.
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,
,,
.
CONTENTS
CONTENTS.,
*.....................
5
LISTOFFIGURES.....................
7
PREFACE.........................
9
ACXNOWLEDGEMENT. . . . . . . . . . . . . . . . . . . . . 11
ABSTBACT........................13
CHAPTER 1
1.1
1.2
1.3
CHAPTER 2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
CHAPTER 3
3.1
3.2
3.3
3.4
3.5
CHAPTER 4
4.1
4.2
INTRODUCTION.
. . . . . . . . , . . . . . . . 15
Background,
10
Problem Statement,
10
Principles
of Our Approach,
DESIGN OF A CROSS-FLOW (BANKI)
11
TURBINE.
. . . 19
Description,
19
Advantages
of Bank Turbine,
19
Analysis
of the Machine,
21
Design of the Rotor,
24
Losses and Efficiencies,
32
Blade Design,
37
Sizing
of a Cross Flow Turbine,,
46
Mechanical
Design,
51
Evaluation
of Efficiencies,
57
Radial-Inflow
Partial-Admission
Water
Turbine,
58
DESIGN OF AXIAL-FLOW TURBINES . . . . . . . . 61
Description,
61
Advantages,
61
Analysis,
63
Design of Blades,
65
Sizing
of the Machines,
68
DISCUSSION ON ADVANTAGES OF DIFFERENT TYPES . 89
Improvements
on Reaction
Off-Design
Performance,
Machine,
92
91
APPENDIX I
TABLE OF PARTS AND WORKING DRAWINGS. . . . . 97
APPENDIX II
FRICTION LOSS IN NONCIRCULAR CONDUITS . . ..147
5
APPENDIX III
APPENDIX IV
EFFICIENCIES.
. . . . . . . . . . . . m 149
PERFORMANCE ESTIMATION OF AXIAL-h?LOW
TURBINES c . . . . . . . . . . . * .*
153
LIST OF FIGURES
PAGE
TITLE
NUMBER
(Banki)
Cross-Flow
2-2
Velocity
Diagrams of Different
Cross-Flow
Turbine
2-3
Effect
2-4
Velocity
2-5
Work Coefficient
Angle 6,
2-6
Converging
Flow Inside
2-7
Cross-Flow
Turbine-Blade
2-8
Ratio of Blade Radius of Curvature
R and
Rotor Length L over Rotor Outer Diameter
vs. Rotor Inner-to-Outer
Dia. Ratio m.
44
2-9
Ratio of Radius to Hydraulic
Diameter
R/Dh,
and Deflection
Angle of the Blade Passage
Bc vs. Rotor Inner-to-Outer
Dia. Ratio m.
44
2-10
Number of Blades
Ratio m.
Dia.
45
2-11
Radial-Inflow
Turbine
59
3-1
Inlet
and &t' -et Velocity
Flow Turbine
Stage
3-2
Blade
3-3
Impulse
3-4
B?ade Sections
Turbine
3-5
Reaction
of Blade
Water
20
2-l
Outlet
Diagram
Turbine
Angle
Locations
in
26
on Stalling
28
Terminology
Iy vsO Relative
Z vs.
Inlet
Flow
the Rotor
38
Inner-to-Outer
Water
Diagrams
of Axial-
Terminology
Velocity
31
35
Terminology
Partial-Admission
Velocity
22
62
66
Diagram
of the Axial-Flow
Diagram
7
69
Impulse
75
83
LIST OF FIGURES (Continued)
TITLE
NUMBER
Sections
PAGE
3-6
Blade
of the Axial-Flow
Reaction
Turbine
85
4-1
Characteristic
Curves
Constant
Flow Rate
of Reaction
Machine
for
93
4-2
Characteristic
Curves
Constant
Speed
of Reaction
Machine
in
94
1
Loss Factor
Nov. 65)
(ASCE, J. Hydraulic
2
Friction
Factor f vs Re. for Different
e/D.
(Rohsenow, W.M., and Choi , H.Y., Heat, Ma%,
and Momentum Transfer,
p. 58)
148
Scheme of Losses
151
APPENDIX II
for
Bends
Div.,
148
APPENDIX III
1
in Water
Turbo-Generators
APPENDIX IV
1
Turbine
Blade
and Velocity
2
Lift
3
contraction
4
Basic
5
Trailing
6
Profile
7
Secondary
Loss-Aspect
8
Secondary
Loss-Basic
Parameter,
156
156
for
Traction
Profiles
Loss
Ratio
157
157
Edge Thickness
Loss
Notation
FL
Ratio
Profile
Triangle
Losses
Against
Ratio
Loss
8
Reynolds
Factor
Factor
157
Number Effect
158
158
158
PREFACE
This report
is one of a series
of publications
which describe
various
studies
undertaken
under the sponsorship
of the Technology
Adaptation
Program at the Massachusetts
Institute
of Technology.
In 1971, the United States Department
of State,
through
the Agency for
International
Development,
awarded the Massachusetts
Institute
of
Technology
a grant.
The purpose of this grant was to provide
support
at M.I.T.
for the development,
in conjunction
with institutions
in
selected
developing
countries,
of capabilities
useful
in the adaptation
of technologies
and problem-solving
techniques
to the needs of those
countries.
the Technology
Adaptation
Program provides
the
At M.I.T.,
means by which the long-term
objective
for which the A.I.D.
grant was
made, can be achieved.
The purpose of this project
was to study alternative
water turbines
producing
5-kw electric
power from an available
hydraulic
head of 10 m
and sufficient
amount of flow, and to recommend one for manufacture.
The work consisted
of the preliminary
turbine
which could be used for this
and designed
completely.
A complete
for the selected
type.
design of different
types of water
application.
Then one was selected
set of working
drawings was produced
Four different
types of water turbine
were studies:
a cross-flow
(Banki);
two types of axial-flow
turbine;
and a radial-flow
turbine.
Each one
has some disadvantages.
One of the axial-flow
turbine
(one with rotor
blades having 50% degree of reaction)
was chosen for detailed
design as
presenting
the optimum combination
of simplicity
and efficiency.
In the process of making this T.A.P.-supported
study,
some insight
has been gained into how appropriate
technologies
can be identified
and adapted to the needs of developing
countries
per se, and it is expected that the recommendations
developed will
serve as a guide to other
developing
countries
for the solution
of similar
problems which may be
encountered
there.
Fred Moavenzadeh
Program Director
9
ACKNOWLEDGMENT
This
Program
tional
study
which
was sponsored
is
funded
Development,
and opinions
author
through
United
expressed
and do not
Technology,
necessarily
This
project
de Los Andes led
in his
report,
the Agency
for
of State.
The views
however,
reflect
those
support
of
are
the
during
by the Aria
those
Interna-
of the
sponsors.
the period
of
Mehr University
for
by the T.A.P.
discussions
by Francisco
We are grateful
from
Adaptation
the
of
Iran.
was initiated
Fred Moavenzadeh,
Technology
Department
financial
work has been provided
Tehran,
a grant
States
in this
Mohammad Durali's
research
by the M.I.T.
this
with
Rodriguez
support
program
a group
and Jorge
director,
at the Universidad
Zapp.
and help.
David Gordon Wilson,
project
supervisor
department
of mechanical
11
engineering
DESIGN OF SMALL WATER TURBINES FOR
FARMS AND SMALL COMMUNITIES
Mohammad Durali
ABSTRACT
The purpose of this project
was to study alternative
water
turbines
producing
5-kw electric
power from an available
hydraulic
head of I.0 m and sufficient
amount of flow, and to recommend one
for manufacture.
The work consisted
of the preliminary
design of different
types of water turbine
which could be used for this application.
A complete set
Then one was selected
and designed
completely.
of working
drawings
was produced
for the selected
type.
Four different
types of water turbine
were studied:
a crosstwo types of axial-flow
turbines;
and a radial-flow
flow (Banki);
Each one has some advantages
and some disadvantages.
turbine.
One of the axial-flow
turbines
(one with rotor
blades having 50%
degree of reaction)
was chosen for detailed
design as presenting
the optimum combination
of simplicity
and efficiency.
13
Chapter
1
INTRODUCTION
Not all
produced
consumers
by main power
small
isolated
costs
needed
Until
the early
electrical
customers
if
they
Sometimes
plants.
to afford
the
are to connect
1970's
an ideal
high
wind,
energy
streams,
more economical,
small
water
provided
it
is
power
not
worthwhile
transmission
way to produce
main power.
small
available
falls
a simple
for
and maintenance
amounts
or gas-engine-driven
naturally
prices,
to electrical
to the nearest
power was to use diesel-
But with
zun,
have easy access
generators.
power
and so forth
sources
can often
and cheap device
of
for
as
be
each case
can te made.
1.1
BACKGROUND
In the country
are
situated
and there
1.2
plant
and also
farmers
where
flow
is most needed.
is not very
main power
this
on streams
is sufficient
when power
power
of Colombia
to the
because
prefer
available
Although
farms
their
especially
the price
of transmission
may be extremely
the demand for
to produce
most coffee
a head of 10 m can easily
the cost
high,
in South America
electricity
be trapped
during
of mains
the
is
times
electric
of power
high.
farms
from
Because
seasonal,
own electricity.
PROBLEM STATEMENT
The effort
here
is
to design
a machine
which
can produce
the
of
many
16
5 kw electric
power
machine
be used by farmers
would
technical
structures.
should
than
by mains
the
developed
a half-kw
model
for
hight;r
total
group
regularly.
been carried
because
of their
one we have
is
plenty
solution
1.3
of water)
to energy
for
of using
of engineering
on this
using
this
the transmitted
units
They have
to modify
our work
has not
This
of sophistication.
in a period
of a cheap machine
that
to this
previously
might
For applications
needed
the design
problem.
We have reported
applications.
electricity
of the Universidad
They plan
water-turbine
degree
limited
(i.e.
very
must not need skilled
cost
cost
turbine.
levels.
of small
to a high
to avoid
power plants.
cross-flow
The design
As this
have little
is
capital
have worked
power
objects
the machine
Some members of the faculty
de Los Andes in Bogota
before.
who on average
the amortized
be less
produced
mentioned
Moreover
Finally
maintenance.
machine
the cases
one of the major
knowledge,
complicated
power
for
be
like
the
of year when there
may be a good
problems.
PRINCIPLES OF OUR APPROACH
The effort
was put
into
two different
approaches
to the
problem.
3)
Designing
any simple
workshop
cut
steel
parts.
a machine
having
which
enough
Consequently,
can easily
facilities
the machine
be manufactured
to weld,
can be built
drill
by
and
locally
in
17
each
farming
generator
tried
area.
etc.,
The parts
can be shipped
to use materials
so on which
do not
more complicated
b)
shipped
layout
processes
angle
were
a machine
to farming
is going
like
bars,
which
This
to be arranged
for
like
chain,
In this
sheet
approach
metal,
to be used.
round
we
bars
Casting
and
and other
excluded.
locations.
methods
gears,
to each area.
need much machinery
Designing
production
such as bearings,
casting
could
be manufactured
approach
a kind
manufacturing
and
of process
the machine.
and molding,
and using
The
plastic
parts
seems to be more economical.
In both
of the
next
the
rapid
the
capabilities
turbine
the
of
the design
assumptions.
desig?
"b"
a) and b),
contains
inflow
design
the
industrial
chapter
"a"
cases
design
has to be within
the country
of a cross-flow
In the end of Chapter
is
of 2 modified
of the
two latter
type
of approach.
discussed
very
axial-flow
types
of
is
turbines
the user.
turbine
2 design
briefly,
with
based on the
the
area
The
based
on
of a simple
Chapter
3 is
short
blades.
assumptions
about
The
made on
Chapter
2
DESIGN OF A CROSS-FLOW (BANKI)
2.1
DESCRIPTION
This
machine
Since
ago.
developed
then
which
was .'irst
its
is
energy
The wheel
water.
curved
horizontal
plates
to which
of the nozzle
is
the
tail
water
the
inner
2.2
energy
2-l)
is
attached.
through
the
inside
through
fixed
impulse
wheel
of an inward
between
blades
jet
of
assemblage
The jet
rotor
the
another
60 years
have been
a squirrel-cage-shaped
(Fig.
shaft
of
circular
end
of water
coming
out
inward
to
twice.
to direct
the
flow
cage and then
to drain
set
in another
of blades
it
to the
part
of
circumference.
ADVANTAGES OF BANK1 TURBINE
The cross-flow
a suitable
easy
turbine
solution
the
lubricated
The atmospheric
and well-sealed
flow,
as they
and they
has significant
to our problem.
to be manufactured.
a complicated
with
kind
from the kinetic
space
outward
of this
over
good performances.
have to be designed
open internal
Banki
radial-flow
simply
passes
by Dr.
an atmospheric
blades
Tine biades
the
models
and have given
machine
gets
designed
some low-power
in Europe
This
it
TURBINE
housing.
are out
don't
advantages
Its
simple
rotor
of the housing;
need to be sealed.
structure
avoids
The bearings
they
which
make
makes it
the need
for
have no contact
can simply
And finally,
when,
be
20
TAIL-WATER
----P-P------I_---
--
-----m--e--
---
---
-v-----
--
FIG.2-1.
-me
--
-
-
CROSS-FLOW (BANKI)
-
-
WATER TURBINE.
-
21
for
a constant
cross
section
simply
2.3
head and a given
is
obtained,
use a longer
higher
power
fixed
levels
rotor
one can
re7 tion
in design
of a turbomachine
is
the
equation,
where
U
stands
component
rotor,
rotor
velocity
respectively
fluid
peripheral
Subscripts
enthalpy.
the
for
of absolute
The rotor
of
for
a simple
ANALYSIS OF THE MACHINE
Euler
the
then
level
rotor.
The most useful
tion
power
leaving
of the
i
and
(Fig.
normally
is
o
fluid
CC
and
stand
is
h,
for
the
tangential
is
inlet
the
stagna-
and outlet
2-l).
designed
the rotor
‘e.
speed,
is
=
0
gc
A
i-o
in
so that
the absolute
the radial
direction,
velocity
so
and therefore
‘icei
and then
be
the parameter
=
"work
b
coefficient"
for
the
rotor
will
simply
of
22
FIG.2-2.
VELOCITY DIAGRAMS OF DIFFERENT LOCATIONS IN
CROSS-FLOW TURBINE.
23
From the
first
law of thermodynamics,
=
=
A
i-o
lil
but
for
water
static
are
turbines
enthaipy
to study
the rate
are very
the drop
h,
small
=
A
i-0
(h +"
of heat
and for
in height
from
+ zg)
transfer
small
inlet
units
to outlet
,
and change
like
in
the one we
is negligible,
so that,
l3
T
m
using
=
the equations
Ah, =
we had before,
uicei
=
Yu2
=
i
3 (Cf - Ci)
,
$ cc; - 2)
or finally
u: = k (CI- cf,
For an impulse
equal
AHo
to 2.0.
and
cf kinetic
written
nN
If
the
be taken
energy
machine
total
the value
hydraulic
as nozzle
through
of
head before
efficiency
the nozzle)
'Y is
then
taken
the nozzle
is
(which
covers
the
equation
(a)
can be
as follows,
u2= & (2g
AHorlN
- cz,,
i
normally
loss
24
or
C2
= f (AH, ‘I~ - $ 1
ui
From Eq.
choice
and hence
that
diagrams
rotor
for
a given
enables
hydraulic
head,
us to determine
the rotor
dimensions.
DESIGR OF THE ROTOR
The choice
important
jet
part
of water
through
of
of
the blade
the
design.
transfers
to the
circles
deviation
work
this
to the rotor
is
the
so that
in both
angles
are measured
positive
in
direction
point
the
at design
angle
geometry
is
is
we have for
true
for
one may question
to 90"
and the
choice
angles
analysis
very
small
we assume the derivation
equal
and outlet
They have to be chosen
useful
and are
we assume that
This
inlet
the
passes
the blades.
Throughout
if
we find
of the velocity
speed
2.4
(2.1)
(LJ)
inlet
is
all
all
angle
as follows.
of
so that
angle
the design
to be zero.
shaft
the
incidence
of rotation.
is
will
zero
Also
and the
not be affected
From Fig.
(2-2)
inlet
velocities.
by simple
cases
why the
(i.e.
the
from tangents
speeds
inter
outlet
and flow
stage
angle
the second
angle
of
of the first
stage).
the blades
"stage"
The reasoning
But
is
taken
or pass,
behind
this
25
in
the
Assume zero
deviation
angle
for
first
therefore,
the
flow
be equal
pass;
to the blade
the blade
at the
outlet
As you see there
This
time
will
situation
is
8, < 90"
take
shown with
the
9o".
Now assume
6
(Fig.
2-3d).
the
If
second
slightly
be near
blade
at
the
In this
outlet
the
will
angle
90'
of
(Fig.
second
2-3a).
pass.
case positive
in Fig.
(2-3~)
angle
has a value
angle
at outlet
of the
is kept
equal
as deviation
angle
"i"
(equal
the values
Therefore
between
91" to 94O.
not
so that
if
the
to 90 + 6/2)
around
first
to 90" then
i = 6 (in
the blade's
pressure
there
of a blade
the
of deviation
optimum
Obviously
cause much effect
Because
water
optimum
90'
to 8O.
not
than
angle
there
the inlet
outlet
angle
the
incidence
then
pass
of
is
will
to zero.
Normally
would
that
2-3b).
Consequently
more than
Now suppose
Now as a comparison
of incidence
pass).
velocity
is bigger
the blades
B = 90".
the blade
be an angle
relative
incidence
(Fig.
place.
leaving
pass
be negative
Therefore
will
angle.
of first
will
assume
incidence
outlet
the flow
the
is
cross-flow
and flow
Therefore
or diffuse.
passes
through
for
taking
are
the tlade
the blade
of the order
of Z"
outlet
is
angle
angle
equal
to 90
on the performance.
turbine
no static-pressure
passage.
accelerate
value
angle
the
In fact,
rotor
works
difference
flow
through
blade
the blade
totally
from
passage
inlet
a blade
passages
at atmospheric
to outlet
passage
do not
as a jet
fill
deflecting
does
with
26
\
2
0
\
\
\
(4
(b)
I
FIG-z-3,
\
EFFECT OF BLADE OUTLET ANGLE ON STALLING.
along
the pressure
,have a constant
of
friction)
area
(2-4a)
velocity
C,
Let
is at
angle
= U2
Consequently
through
will
direction
the
the passage
be determined
the
inner
diameter
are
then
as follows
(first
pass)
and the absolute
2
is in radial
rotor
(Notice
which
specifications
relative
Fig.
velocity
and the maximum flow
of the passage
outlet
of the blade.
relative
The rotor
the
side
(Fig.
2-4b)
(in
side
will
the
by the
absence
smaller
of the
(Fig.
B, = 90"
velocity
flow
rotor.
2-4):
so from
of water
leaving
01~ = 90".
us define
that
in
this
particular
case
x
is
equal
to the work
coefficient.)
and
r2
m3-
rl
r2
and
r
are
1
inner
and outer
radii
of the blading
respectively,
therefore
m=
u2
u3
'il
The above
definitions
=
will
UC
help
l
us to write
simpler
geometric
relations.
From Fig.
x
(Z-4a)
f
-51
ul
we have
=
Cl cos a1
ul
=
cos a
- cl
1
-cl cos a1 + w1 cos (3,
(2.2)
28
(4
FIG.2-4.
VELOCITY DIAGRAM TERMINOLOGY.
29
Also,
C
rl
from
(2.2)
=
Cl sin(IT
- al>
=
Wl sin(?I
- 8,)
(2,3)
and (2.3)
tan B,
x
=
B,
=
B, - tan al)
(tan
Therefore
From the
outlet
tan-'((
velocity
2
1 tan al)
triangle
(Fig.
(2.4)
2-4a)
c2=J wf+u;
If
we assume no loss
then
along
the
relative
the blade
c2
of kinetic
velocity
passage,
energy
of the water
so using
Eqs.
through
the blade
has to remain
(2.2)
and (2.3)
= ulpyi$7
.
passage,
unchanged
we have
0.5)
But
c2
Combining
(2.6)
-5z
u2
cos a
and (2.5)
=
2
m 3
cos c%
(2.6)
2
we have,
u2
=cos-lJ$$-j-
(2.7)
30
From Fig.
(2-4b)
we have;
cos(lT-f3)
but
4
as illustrated
and deviation
(2.8)
before
angles
=
u2
Therefore
"stage"
we found
geometry
second-stage
-1
(2.8)
at any condition
~1~ = a2
are assumed to be zero
then
and if
B, = B,
incidence
so from
'
(-
1
- m cos B
1
=
tan
-1
1
m cos B,
two values
(Eq.
conditions.
nondimensional
tan
1
m tan cx
3
=
we have:
tan a2
5
u3
.rn W
3
=
relation
(2.7))
(2.9)
for
c12 '
one by using
and the other
Putting
between
these
the
was found
two values
design
parameters
the
first
by using
equal
the
we get
m , x
a
and
as follows:
1
m cosB
(2.10)
l)=cos-lJg-Tp
6
FIG.2-5.
WORK COEFFICIENT$fVS.
RELATIVE 1iYLiT FLOW ANGLED,.
32
Notice
that
a1 , x
Now design
help
curves
to choose
may be,values
Solving
right
of
Figure
x
value
vs.
related
of
x
(2.10)
for
for
vs.
together
Eqs.
of the
B,
2-5 shows
Eq.
are
6,
can be drawn using
the
and values
b,)>
and
(2.4)
for
the design
the value
curves
of
X
may
curves
of nozzle
values
based
which
Two useful
values
different
(2.4).
and (2.10)
parameters.
different
%
by Eq.
angle
of m .
on Eq.
(2.4).
we get
\
x
=
1
m cosf3
-1
cos tan
For any value
of
m and
B,
vice
versa.
2.5
LOSSES AND EFFICIENCIES
In cross-flow
bent
strips
angle
could
cause high
can be listed
of flow
flow
blades
incidence
in
in
the nozzle
(2.11)
can be found,
or
made of curved
variations
in inlet
Summarily
the other
due to skin
and blade
inside
x
are normally
losses.
losses
open space
of
So small
metal.
hydraulic
as:
direction
converging
sheet
I2 -1+1
1
1
m cos B
1
the value
machines,
of thin
(
friction
passages;
the rotor;
losses
flow
losses
and change
due to
and mechanical
losses.
a>
Nozzle
losses
For nozzle
factor
a factor
can be used to define
converging
flow,
so
cv
the
which
losses
acts
as a velocity
due to skin
friction
correction
and
33
or
For the
loss
Appendix
I,
defined
due to the curved
will
be used,
the
radius
provides
for
provided
passage
the
a hydraulic
curve
diameter
given
in
is
as
Dh
If
nozzle
=
4 x flow area
wetted perimeter
of curvature
the values
different
values
is
of loss
of
(2.12)
R
then
factor
k
the curve
versus
in Appendix
deflection
I
angle
R/Dh , where
W2
1
% oss
and
is
W
1
=
5
the mean water
the mean values
of
R
velocity
and
Dh
through
should
the nozzle.
be used
Obviously
to get a better
'
result.
b)
Blade
losses
I>
for
the
diameter,
Hydraulic-friction
flow
through
and using
losses.
blade
the
passages
curve
given
The coefficient
can be found
in Appendix
of
based
I.
So
friction
on hydraulic
34
% oss
subscript
h
diameter.
"L"
relative
stands
flow
II)
is
due to flow
direction
within
in Appendix
As seen in Fig.
2-6,
flow
converges
direction
As seen in Fig.
incidence
angle
"y"
angle
It
"0".
is
the right-hand
40".
For these
is very
d)
cause
range
2-6
jets
I,
the
by this
that
will
negative
W is
the
of magnitude
In this
the
case we
the nozzle.
of actual
This
second
velocity
effect
set
will
leaving
cause
the maximum
is half
of the admission
central
stream
line
remains
the
admission
angle
is,
the closer
get
to the
work
for
inner
surface
on the second
as small
pass.
of the
angle
angle
the loss
A
is between
20* to
due to this
small.
Efficiencies
Normally
defined
as;
the
overall
efficiency
for
a water
rotor
Therefore
as possible.
admission
of admission
a
of blades.
geometry,
effect
has to be kept
values
as for
from simple
the bigger
of admission
reasonable
and
change,
the direction
entering
assumed
side
will
the angle
of hydraulic
passage
to one point.
caused
Also
undeflected.
and that
on basis
of the blade
rotor
in
evaluated
length
given
blades
change
values
the
different
w2
velocity.
Losses
Losses
for
the
can use the curve
4
L
fhTxz'
=
turbine
is
effect
35
F&2-6.
CONVERGING FLOW INSIDE THE ROTOR.
36
where
all
is
nh
the hydraulic
the hydraulic
losses
efficiency
across
of the
turbine,
and covers
{See also
the blading.
Appendix
11).
'h
where
AH
turbine
-
stands
inlet
T
between
or mechanical
rim
friction
and bearings
hydraulic
head of the
T-I
Q
and the
flow
efficiency
covers
and so on and is
all
the
defined
losses
as;
T - Tloss
T
=
represents
Finally
leakages
difference
and outlet.
rl,
where
AH
for
The term
due to disk
AH
- Hloss
the
is
shaft
torque.
the volumetric
which
passes
efficiency
the
turbine
which
without
covers
the
giving
any
power
where
Q
is
the volume
The important
a turbine
is
to find
part
flow
rate.
of the
the hydraulic
evaluation
efficiency.
of the
This
efficiency
term
of
is very
37
sensitive
to the blade
In order
to get
Eq.
last
section
2.6
BLADE DESIGN
(2.15),
in terms
to the output
the bending
only
a relatively
long
plates
two end plates
power
rotor
can be reinforced
level
smaller
rotor
speed.
The cost
higher
complexity.
with
will
be cut out
the whole
diameter
for
rotors
i.e.
with
longer
stiffer
having
is
all
transexperience
the blades
one would
radial
between
Therefore
volume
flow
like
chord.
the blades
for
rate,
if
a
the
one r-an go for
and hence
advantages
we have chosen,
no stiffer
any
torque
small
rotors.
rotors
of a circle.
tubes,
the
as at each moment
plates
apparent
joined.
Therefore
a specified
of design
in
con-
the blades
stress,
flow.
and longer
these
turbine
turbine
transmission,
and blades
with
III).
mentioned
the
may be used to support
be segments
of thin-wall
are
so that
periodic
and hence
For the type
concerned
the blades
and so allow
given
the losses
by the blades,
blades
crossflow
in a crossflow
shaft,
higb
carry
rotor
Stiffer
profiles
to which
shaft
(see Appendix
head.
moment due to torque
a few blades
to avoid
all
the rotor
do not have a through
come under
the
before
angles
&ency of the
of hydraulic
of two end plates
mitted
all
effic'
one has to write
As mentioned
designs
and flow
the hydraulic
using
sists
profile
is
that
we will
plates.
Therefore
or made of strips
higher
Also
shaft
of the
only
be
the blade
the blades
of
thin
sheet
can
38
Zr number of blades
di:
inner
dia.
doz outer
dia.
L =, length
of
FIG.&7.
rotor
CROSS-FLOW TURBINE-BLADE TERMINOLOGY.
39
metal
rolled
around
specified
is
"ml' which
affects
length,
a pipe.
the ratio
The most
of inner
most
design
parameters
which
relate
to outer
of the other
number of blades,
etc.,
parameters.
m
Eqs.
(See Fig.,
of
such as
on other
blade
(2.13a)
to
2-7
blade
for
to be
the rotor
parameters,
of
using
parameter
diameter
rotor
effect
can be found
these
important
(2.13f)
notation.)
0
5
y-
=
2y - 4 = B -
dO
c sin
y = 2
R =
0
(2.13a)
s
(2J3b)
sin
QI
(2.13~)
(2.13d)
2 sinTBc/2)
do - di
c
y + dO sin
cos
Q/2
=
2
(2.13e)
C
CT
=
dl
The solidity
to the
Eqs.
sin
of
It
be easier
(2.13a)
to
(2.13f)
'
(5 is defined
spacing
will
n/Z
the blades
(2.13f).
as the ratio
on the
inner-diameter
to work with
Let's
define
of
the blade
side
the nondimensional
chord
of the
forms
rotor.
of
40
and
then,
=
Y
EIc/2
27-e=
(2.14a)
2A sin
y
=
2 sin
m sin
As discussed
passage
curvature
of the blade
values
that
values
is
shorter
of m.
3 (l-m)
(2.14e)
(2.14f)
'
a function
section
camberline
and the
ratios
inner-to-outer
and more curved
the hydraulic
of the ratio
the variation
curvature
of rctor
=
the last
passage
2-8 shows
the blade
($/2
n/Z
in
the blade
Figure
(2.14d)
x
=
of the
(2.14~)
4
y
X cosy 4- sin
diameter
sin
x
5 =
0
(2.14b)
B-s
(centerline)
deflection
of
over
of
rotor
diameter
blades
result
the
angle
of
outer
ratio,
from
through
radius
over
the ratio
the
loss
of
the hydraulic
of the blade.
the
rotor
length
diameter
versus
These curves
using
bigger
and
show
41
As mentioned
passage
in
Section
is a function
the passage
hydraulic
angle.
Bigger
values
us less
loss.
Both
geometrical
2.5
the
loss
of the ratio
R/Dh
diameter
8
of
R/Dh
these
parameters
and
through
and
is
C
introduced
ec , where
the blade
and smaller
parameters
values
Dh
is
deflection
8c
of
can be found
in Eqs.
the blade
in
give
terms
of
(2.13)
and (2.14),
the blade
passage
as
follows:
but
=
-
Dh
as defined
as pointed
out before,
deflection
of a jet
so the jet
thickness
is
of the blade
diameter
side
of
Dh
that
the flow
pressure
side
relative
velocity
admission
angle
fairly
rotor.
=
for
side
constant.
aid
=
and
the hydraulic
by the inner-
of Fig0
fill
walls
the wetted
2-7 we then
perimeter
the passage
have
guide
through
the
the passage
at the inner-diameter
WIA
=
'lL
If
flow.
side
a.
--d
360
i
as (L +2s)
Only
fully.
have:
Q
the
of the blade
Consequently
can be determined
By the
defining
of water
then
pressure
is
4 x (LXS)
L + 2s
does not
and side
through
along
passage
the
The reason
flow
of water
diameter
is
4 x flow
-.
wetted perimeter
Wl
and
the blade's
is
a
is
the
the
of the rotor
rotor
we
42
but
as
m -5 di/do
L
Defining
, then
Q
ci IT .Wl m d
0
360
=
CI E c/s
S
C
CT
=
h = c/d o
and
dO
=
these
=
into
the
relation
a
-7TmW
360
both
7rmW
the denominator
Q
E
a
IT d2 W
360
01
then
we have
c’
4--XDh
=
m
we have:
x
ad
2>A
1 do
and naming
c’
Dh
1 do
+
3%
for
x- do x
0
Q
Dividing
therefore,
=
44
Dh
(2.14)
0
k
Substituting
(Eq.
0
and the numerator
by
do
43
Also
from
Eqs.
(2.14)
5
we have the
+-
definition
of
,
0
or
R=tdo
,
Therefore
or
R
iq
<(C'cl + 2Xm)
4C' x
=
The parameter
units
of this
velocity
Ill
c'
kind
Figure
and the variation
at values
With
reference
factor
for
58")
the
does not
a function
from
of
From Fig.
happens
of
be a constant
(t ur b ines
diagrams).
solidity.
will
of
to Fig.
range
change
having
2-9 we find
closer
I-l
the maximum value
5),
much with
R/Dh
m
that
in
I)
geometry
of
lower
values
a chosen
seems to lead
Bc
values
of
of
R/Dh
the loss
(between
41"
to
but
is
of
R/Dh (values
value
to the
versus
increases.
that
we have
and
ec
different
we find
variations
for
of
as solidity
angle
for
for
homologous
the maximum value
to unity
of deflection
Consequently
of
versus
(Appendix
R/Dh , especially
1 to about
similarity
for
2-9 shows the variation
R/Dh
m
value
strongly
of solidity
efficient
CT,
passage.
44
FIG.2-8.
RATIO OF BLADE RADIUS OF%R"ATURERAND
ROTOR LENGTH fa
OVER ROTOR OUTER DIAMETER VS. ROTOR INNER-TO-OUTER DIA.
RATIO m
.
8
80
6
60
2
0
0
0
”
‘5
,6
.7
.0
.9
II
FltG.2- -9. RATIO OF RADIUS TO HYORAULTC DIAMETER R/Dh g AND DEFLECT ION
ANGLE OF THE BLADE PASSAGE& VS. ROTOR INNER-TO-OUTER DIA. RATIO ml.
I
I
ROTOR ANGLE OF
I
.5
FIG.2-10.
I
.6
NUMBER OF BLADES
-1
I
-7
m
I
.8
VS. INNER-TO-OUTER DIA.
I
.‘9
RATIO m.
46
The design
of the
rotors
mechanical
design
of
mum loss.
Using
2-10
with
no stiffer
plates
than
by optimization
the blades
Eqs.(2.14a)
to
(2-14f),
is more dominated
to get
the curves
by
the mini-
shown in Fig.
can be drawn.
These curves
solidity
show the number
and rotor
of blades
width
is
is
reduced
lessened
increases
to outer
the rotor
(Fig.
assuming
2mm steel
plate
for
because
the throat
the blade
the blades
of stress
chord
become
and stiffness
properties
the blades),
of
As the number
ratio.
decreases
material
each choice
although
On the basis
typical
for
longer
Therefore
of blades
in bending.
conclusion,
diameter
becomes
2-8).
as the number
more flexible
(e.g.
inner
of blades
and thickness
we have let
18 as the
minimum number of blades.
When the number
but
shorter,
the manufacturing
become progressively
in Fig.
stiffness
2.7
number
2-10,
give
increased,
difficulties
for
Points
designs
rotor
small
We have chosen
of blades.
better
the
workshops
60 as the
inside
as far
can be
the closed
as losses
curve
and structural
are concerned.
SIZING OF A CROSS FLOW TURBINE
For a machlne
velocity
Therefore
affects
is
more severe-
maximum desirable
drawn
of blades
of jet
of water
the choice
the size
of this
of
leaving
of inlet
the
type
rotor,
working
under
the nozzle
absolute
a small
flow
nozzle
is
constant
fixed
angle
angle
head,
(Section
the
2.4).
from the nozzle
being
desirable.
47
As discussed
be kept
in Section
small
losses
in order
due to flow
angle
of admission
absolute
flow
that
design
line
(i.e.
2.5,
to reduce
the
the blades
is
equal
angle
taken
crosses
the water
within
designed
also
rotor
The
The inlet
incorporating
In
was 16O.
on an approximately
points
and
pass.
by Banki
and draining
casing
the
in the second
the rotor
entrance
should
to 30 in our machine.
in a prototype
the flow
of admission
losses
entering
He used a cast
line).
the angle
are
horizontal
on a horizontal
the nozzle
for
his
turbine.
As we have tried
our design
processes,
design
had.
metal
covers;
confines
Rather
we used a steel
there
the water
will
giving
in
least
complexity
2.4
the
drawing
absolute
be vertically
be a main
spray,
frame
combination
complex
avoid
structures
does not have a cast
to the
the
to
cover
around
will
angle
30'.
inlet
Section
of
flow
2.8.)
angle
like
framework
of the structural
in
casing
angle
The nozzle
a nozzle
and manufacturing
Banki's
with
the
rotor
be a separate
That
value
"~11" will
which
part
reference
be 150".
fixed
resulted
(See nozzle
design.
So with
sheet
rotor
to Section
Draining
will
downward.
From the fact
that
the work
coefficient
is
equal
to 2.0 we
have
%1
=
Assuming
(nozzle
2Ul ,
a total-to-total
and rotor),
from
Eq.
efficiency
(2.1)
we get,
of 75% for
the turbine
48
0 (UC*) =
69,20
m2/s2
then
u1
cl
-wl
The choice
outer
diameter
:.ztween
gear
m/s
=
13088
m/s
=
9.00
m/s
speed
can be and what
shaft
300 rpm.
5.88
of shaft
As we were
bearings.
=
This
speed
up ratio
is
are
bore
lower
is needed
than
to reach
speed).
In future
to specify
bearings
to run at high
specifying
dO
We would
(see
general
drawing
like
possible
number of blades
riveting
the bent
Fig.
2-10
in the
the
=
for
the
velocity
sliding
us to a shaft
speed
studies
the
speed of
because
shaft
a high
to 1800 rpm
it
would
be justifiable
speeds.
we get
0.3743m.
the blades
to the
side
and nozzle-rotor
Therefore
in order
section
the rotor
limitations
desirable,
we would
to get
ends of the blades
last
speed
bearings
design
drawing
2.81,
on how large
N = 300 rpm
to join
arrangement
in Section
the
limited
(generator
Therefore
depends
to use wooden
and bearing
.
we get
sufficient
m = 0.6
by rivets
combiExtj.on
like
to the side
plates
to have the
space
plates.
for
Using
and 24 blades.
least
49
Now using
results
(zero
Eqs.
and blade
incidence)
(2-13a)
to
parameters.
(2-13f)
First
we get
from
the
following
the velocity
diagram
we get
B
=
130"
53'
=
52" 58'
Y
=
26" 29'
R
=
0.0956
m
s
=
0.0293
m
and then
8
C
C = 0.0843
we have previously
chosen,
Z
The inner
diameter
=
24
m =
0.6
of the
losses
20% extra
and the
power
losses
power has to be 6 Kw.
Q =
The length
in
then will
0.2246
is
the generator
= 0.0857
then
will
be
m .
specified
The volume
W
A(U Ce)
of the rotor
rotor
=
di
If
m
flow
m3/s
be
to cover
the mechanical
then
the output
rate
required
shaft
will
be
50
I-&-L-=
~adiW
L=
a
being
O.l64 m
1
the admission
angle,
Once more recalling
we can write
the
the velocity
folPowing
WJ C(j)
triangles
shown in Fig.
relation
=
A(u Ce)
+ A&J ce)
1st
total
2nd pass
pass
or
=
A@ Ce)
- u2ce
(UICe
1
but
>
+
(U3Ce
- u4y3
1
4
3
2
as we specified,
u
2
$3,
=
u3
,
u1
=
,
u4
CO2 = c03 = u2
= 2u
1
'
s4
=
0
and
AN
= 2Uf
ce>
total
Therefore
=
AW Ce)
1st
2$
- Ui =
2Ui
pass
2
2u$
- 5
>
and
= u;
A@ Cal
2nd pass
= m2U2
.1
- m21J: =
2-4,
51
The above
relations
transferred
to the
and only
This
entrance
in
total
very
the
energy
a value
of
pass
82% of
is
is
received
m = 0.6
within
the
pass
do not
affect
, the
the
by the
losses
second
total
energy
second
rotor
energy
pass.
and the
the
performance
of
much.
MECHANICAL DESIGN
The manufacturing
processes
made have been the most
design.
The general
rotor
in
for
in first
as hydraulic
losses
turbine
2.8
rotor
18% of the
means that
the
show that
combination
the
following
described
dominant
arrangement
under
parameters
drawing,
and an isometric
view
Different
parts
pages.
which
the
in
turbine
is
to be
the mechanical
scheme of
the nozzle
of the machine
are submitted
of the machine
are briefly
as follows:
Rotor
The turbine
has a squirrel-cage-shaped
and 165 mm long.
is
The optimum
rotor,
380 mm 0-D.
speed
under
the design
each blade
being
simply
head of 10 m
300 rev/min.
It
has 24 blades,
Blades
can be rolled
on the
general
side
plates
of 2 mm galvanized
arrangement
with
The rotor
the bearing
out
rivets
goes through
(Part
14).
(Part
has no drive
housing
which
drawing).
which
the
steel
sheet
They are joined
segment.
(see Part
to the rotor
12).
Power is
shaft.
rotates
rotor
a circular
with
bearing
transmitted
the rotor,
supports
only
through
and the shaft
the
rotor
11
52
t-1
_----I
-+
F
I
11
I! IiY
E-R0 TOR COMBINA TION OF
CROSS- FL0
R/RBINE
54
ISOMETRIC VIEW OF CROSS-FLOW
MACHINE
55
Bearings
The bearfng
steel
pipe,
rotor
side
is weided
plates
Bearings
there
this
It
works
wear
Chain
with
which
of circular
is
fixed
oil-impregnated
wood.
the maximum permissible
and simplicity
Furthermore
as in dry
to the
13).
low cost
applications.
'j
piece
it
speed
makes it
does not
conditions.
It
Although
for
suitable
need lubrication.
requires
no seal
15).
In our design the bearing
rotates
.a
on the wooden bearing
and increasing
with
the
rotor,
the bearing
so equalizing
life.
transmission
chain
which
and gear
transmitted
i s welded
derailleur
to tihe bearing
gear
housing
is
generator
fixed
(Part
by means
to the
s speed
gives
circular
21).
speed of 1800 rev/min.
is used which
hub and set
is
used for
The unnecessary
an 18-tooth
and a circular
gears,
A 52-tooth
to the
ratio
A chain
of about
six
to generator.
gear
and only
the rotor
has a constant
combination
turbine
from
and gears.
A complete
the
plate
(Part
for
its
The generator
rotor)
rivets
in wet as well
of bicycle
from
a short
are made of a special
Power is
plate
is
to a circular
of bearing,
low-speed
(Part
which
are some limitations
kind
for
housing,
is
fixed
the
gears
gear
plate
of five
in
(being
with
to the gear
chain
second
the
speed
gear
driven
set
step
are
for
bore,
The latter
a bicycle
up (Part
replaced
by a 52-tooth
a central
set,
cogs
gear
22).
by spacers
on the
the same as one of
circular
plate
is
56
be fixed
with
step
(Part
the
generator
a 36-tooth
The last
23).
an oil
Chapter
machine
In order
that
not
bath
would
do further
to increase
two chains
be installed
around
the
life
speed-up
chain
this
the
chain.
makes it
as the
difficult
see in
final
choice,
transmission
system.
and sprockets,
Therefore
to
machine
As you will
on its
be used.
by side
turbine
be selected
of the
in
for
chain.
improvements
in parallel
side
this
the
not
we have
be provided
in
second
and must be fixed
level
should
transmission
to incorporate
the
gear has 17-teeth
condition
The two-step
4 this
used for
For the power
shaft.
a good lubrication
so we did
gear being
we recommend
two sprockets
should
on each shaft,
Housing
The housing
It
has a fixed
door
servicing.
It
with
completely
section
a removable
section
is
which
(Part
32),
covers
placed
has a lifting
two simple
made of thin
handle
latches
galvanized
most of the
in
the back
and is
(Parts
rotor
of
sheet
(Part
the
fastened
steel.
31),
turbine,
to the
and
for
fixed
34 and 35).
Frame
The frame
generator
size
is
mounting
may vary
totally
is
made of angles,
a steel
when using
plate
different
welded
welded
together.
to short
legs
(Part
38).
generators
The
and its
Nozzle
The nozzle
(Part
different
41).
is
The flow
output
completely
made of steel
can be changed
powers.
This
is
and set
possible
plates,
on different
by chaning
welded
together
valves
the angle
for
of
57
flap
(Part
to the
42).
flap
The semi-circular
has holes
for
never
Warning:
channel
different
(Part
43) which
is welded
settings.
change ---the
flow
while
the
turbine
&
-in operation
As the system
of flow
while
the piping
before
which
can result
this
changing
the
and the
2.9
a change
"water-hammer"
in
valve
before
to the shut-off
After
setting,
the nozzle.
position
the valve
must
gently.
of installing
has not been studied,
cost
of the
a surge-tank
because
it
would
as a shock
increase
the size
turbine,
EVALUATION OF EFFICIENCIES
Knowing
hydraulic
method
the size
efficiency
given
in the
of different
of the
last
efficiency
is
the
parts
turbine
=
the
Following
the
76%
total-to-total
efficiency
prediction,
so the design
is
of the
energy
by drain
into
rl t-s
turbine
we get:
to our
loss
of the
can be found.
sections
'h
This
almost
position,,
head,
damage.
has. to be a gate
reduced
flap
high
can cause
in serious
there
The possibility
absorber
a relatively
is working
must be slowly
be opened
under
the turbine
To avoid
The flow
works
flow
=
60%
acceptable,
account
and is very
Taking
we get,
close
the effect
58
If
efficiency
a mechanical
of 90% is
of 94% and a generator
efficiency
assumed then
rl t-sm
=
56.5%
rl t-su
=
51%
and
(See Appendix
2010
II.)
RADIAL-INFLOW
PARTIAL-ADMISSION
WATER TURBINE
Description
This
flow
type
and axial
of
is a potential
simply
rectangular
cross
section
portions
of 80".
The rotor
fastened
at one end only,around
in
its
inward
radial
distributes
cross-
are rolled
out
the
passes
and subsequently
of sheet
the rotor
through
is
flow
in
each one being
metal
circumference
enters
distributor
the
circumference,
The flow
motion,
plane,
the axial
to the
of a spiral-shaped
which
inner
blades
as cantilevers.
radially
the
of
consists
opposite
disk
alternative
types.
The turbine
with
turbine
of
with
the blades
deflected
two
an arc
and are
the turbine
a swirling
while
to leave
still
the
in
rotor
direction.
Flow Control
This
type
the volsume flow
velocity
consequently
through
as described
to the
diagrams
would
the
turbine
the whole
range
rotor
gives
under
keep their
would
work
of power.
the possibility
constant
head.
design-point
at its
of controlling
Therefore
geometry
design-point
the
and
efficiency
ROTATABLE SLEEVE
BLADES
SPIRAL
NOZZLE BLADES
FIG.&-11.
RADIAL-INFLOW PARTIAL-ADMISSION
WATER TURBINE.
60
The control
the angle
sleeve
of
the
flow
This
of admission.
between
rotor
could
be easily
could
could
be brought
fixed
sleeve
to vary
more or less
the
admission
by reducing
be done by installing
and distributor.
which
achieved
a rotatable
The sleeve
would
alignment
with
into
have ports
ports
on a
area.
Dimensions
For specified
of this
type
450 rpm.
ing
head
would
have a diameter
with
However,
problems
on the
2).
problem
To solve
340 mm would
speed
this
inner
side
which
the
the spiral
the draining
problem
reduce
the
axial
(5.5
there
would
at
be drain-
rotor.
rotor
diameter
geometry
of
brings
and size
by increasing
width
kw) a turbine
220 mm when turning
of the rotor
of the
is
output
of about
size
increasing
Unfortunately,
another
(10 m) and power
the
the rotor
out
(see Fig.
diameter
to
to 55 mm and the
to 300 rev/min.
This
would
require
(55 mm).
To keep the
dimension
of the spiral
a spiral
fluid
distributor
velocity
would
in
of
the spiral
the
same width
small,
the radial
have to be increased.
Conclusions
A rectangular
result
(in
entry
we are working,
turbine
cross
For the
port).
dimensions
unattractive.
section
of the order
range
as large
We have not
of specific
as this
taken
of 60 x 200 mm would
speed
make the
the design
in which
radial
further.
inflow
Chapter
3
DESIGN OF AXIAL-FLOW TURBINES
3.1
DESCRIPTION
In this
flow
chapter
turbines
design
machines
with
rotor
all
then
blades,
to the
reaction
for
water
flows
some simple
We have
ratio
axial-
chosen
which
to
enables
the blading.
through
a set
the circumference
passes
the rotor
The turbine
tailwater.
to design
hub-to-tip-diameter
blades
around
is
to the problem.
high
Principally,
(installed
the task
as a solution
us to use untwisted
3.2
*
of nozzle
blades
of the hub disk),
blades
and through
can be designed
into
the
the diffuser
as an impulse
or a
machine.
ADVANTAGES
These designs
The design
type.
processes
plastic
if
of these
they
are
will
give
and off-design
machines
simpler
machines
besides
have
comparable
machines
advantages
provides
to be mass produced
with
the
Banki
easy manufacturing
(i.e.
sand casting
and
molding).
The blades
which
should
are made of molded,
accurate
profiles
performance.
is higher
than
of the
transmission
and a lower
can also
be used as a drive
the
generator.
or cast
and consequently
Moreover
that
extruded
the shaft
Banki
gear-up
motor
type
ratio
plastic
a better
speed
design
in these
and therefore
will
to drive
a
be needed.
other
These
machines
FIG.S-1.
INLET AND OUTLET VELOCITY DIAGRAMS 0FAX.IAL-FLOW TURBINE STAGE.
63
3.3
ANALYSIS
Similar
can write
to the analysis
Euler's
specifications
together
h01
But if
rotor
equation
is
AH
0
-
=
the
different
cross-flow
turbine,
we
velocity-triangle
3-l).
ulcel
total
- u2ce2
hydraulic
(3.1)
l
head difference
ac'ross
the
then
h01 - h02
where
Appendix
n
is
tt
the
=
total-'
AHog
%t
(3.2)
co-total
efficiency
of the
turbine
(see
II).
The three
and reaction
blading
to relate
(Fig.
h02
the
shown for
parameters:
which
flow
specify
are defined
the
respectively
coefficient,
type
of the velocity
coefficient
diagram
and
as follows:
cX
@
work
(3.3a)
-T-
- u2ce2
UICel
qJ z
(3.3b)
u2
m
R
E
%l
l--=r--
+ 532
(3*3c)
64
The analysis
case where
outlet
C
X
is
done for
remains
constant
Now for
of the rotor.
be chosen,
hence values
A good approach
type
with
different
angle
to the rotor
(i.e.
R and 9).
of
from
"ol"
I/J,
$
and
constant
a velocity
and to vary
can
can be specified.
of different
is
triangle
to
machines
to keep
the
the
inlet
two rtfher
of this
flow
parameters
we have
g AHo
u = %t YJ
of shaft
the usual
to the nozzles
R
of reaction
and (3.3b)
Now, choice
inlet
each design
to the design
degrees
From (3.2)
the mean diameter,for
.
(3.4)
speed gives
us the mean diameter
60 U
IT @J-)
(3.5a)
=
dt+dh
2
(3.5b)
rate
will
be
&
=
dm
=
and
d
and mass flow
where
W is
m
the output
W
A(U Ce)
power
(3.6)
of the
turbine.
65
The annulus
area
then will
be
.
Aa
where
p
diameters
is
=
(3.7)
the density.
the annulus
Aa
area
before
high
to be able
value
for
this
we try
ratio
and hence
ce)
are
found.
(3.5ai
gives
u9L9a
Zq.
(3,5bj
and (3.8)
If
the
3.4
be
- d;
Then the
ratio
of hub to tip
blades.
triangle
(3.4),
shaft
diameter
A reasonable
gives
(3.6)
speed
dh
and
is not
the
.
can be determined
we can find
dh/d,
us the value
and (3.7)
of mean diameter.
to optimize
of hub and tip
(3.8)
us the value
Of
terms
0.8.
of velocity
Eq.
in
j
to keep the
around
from
ratio
has to be chosen
will
to use untwisted
is
Now, a choice
AU
we know that
= $ (d:
As mentioned
enough,
Also
d,
values
of
and using
Then using
Eqs.
.
acceptable
the dh/dt
of
a new shaft
speed
ratio.
DESIGN OF BLADES
Figure
3-2 shows
procedure.
To find
information
I
and curves
relations
approximate
the
blade
angles
given
the
terminology
from
used in this
flow
in Reference
curves
given
angles
(2).
in Ref.
design
we may use the
The following
(2) with
a good
two
66
b-
BLADE WIDTH
r
0
LEADING EDGE /'
\
FLOW INLET
\
\
\\\
\
\
t
FLOW OUTLET
ANGLE /3r
MADE OUTLET
AXLE &
STAGGER A!JGLE
DEVIAT ION ANGLE6
'NG EDGE
FiG.3-2.
RLADE TER!lIrJOLOGY.
L
1
67
for
accuracy,
incidence
and deviation
angles.
(3.9)
60-X
2
0.08
+
(
300.1
6
8_
=
c/s
c
Please
see Fig.
formulae.
In Eq.
for
3-2
information
These two formulae
eC
so the blade
=
6, + Mind
angles
B2
Suggested
or blade
ec
(3.101,
=
values
re
It
will
are
on parameters
useful
turning
+
6,
(3.10)
angle
+
used in above
in preliminary
is
equal
design.
to
6
be
B,i-6
for
leading
and trailing
=
(0.03
to o.os>c
=
(0.02
to O.Ol)C
edge radii
are
68
The design
angle
"A"
solidity
and an optimum
can be estmated
width-to-chord
=
from Fig.
t
C
from Eqs.
for
value
the blades
for
is
solidity
by the Zweiffel
to choose
o .
a stagger
The optimum
criterion
for
the value
of
ratio;
b
s
also
procedure
cos2c12(tgal
2.5
+ tgcx2)
(3.11)
3-2,
=
(3.12)
cos
(3.12)
x
and (3.11)
we find
o ,
cl=;.
In steam and gas turbines
the number
of the blades
reasonable
value
In our
concerned.
number
of
for
are normally
chord
case,
the blades
the dimensions
as far
as blades
which
gives
of
determined
short,
and
by choosing
as vibration
are
the blades
a
and stresses
are
a good choice
for
us a reasonable
blade
passage
the
seems
to be a good approach.
Then finding
blade
3.5
shapes
by trying
the
dimensions
different
of the blades
curves
for
we can find
the blade
the
profile.
SIZING OF THE MACHINES
Single-stage
axial-flow
turbines
are normally
named on the
69
basis
of
their
velocity
types
of velocity
triangle
The design
total-to-total
designed
method
procedure
with
given
the
turbine
specifications
hydraulic
a)
turbine
are
will
efficiency.
Finally
be calculated
using
can then
power
for
of
the
generator
power.
5,5 Kw. output
the
be optimized.
from
10% extra
for
power
So the
and 10 m.
head,
Design
of an impulse
Assumptions
velocity-diagram
(implicit
gives
The design
be designed
a value
Then the machine
will
5Kw. electrical
will
of the
III.
to guess
turbine.
the efficiency
to get
itself
the
and most common
and 50%-reaction.
to the estimated
in Appendix
In order
impulse
in each case is
for
respect
machine
Two possible
are:
efficiency
be designed
the
triangles.
are a total-to-total
specifications
in an impulse
an acceptable
absolute
direction,
velocity
from Fig.
leaving
=
efficiency
of:
machine),
nozzle
to minimize
AH0
machine
work
Also
the rotor
leaving
Ho1 - Ho2
losses
=
coefficient
and flow
angle).
is
of 0.80
of 20
coefficient
we will
to be in
therefore
and
of 0.8
specify
that
(which
the
the axial
we have,
10 - $
3-3 we have,
Fig.
3.3.
IMI'CLSE VELOCITY DIAGRAM
Substituting
for
the last
two relations
into
Eqr.
(3.4)
U we have:
u
rl g Hcl
=
++$
applying
numerical
values
u
=
n
we have
5.90
(at
mean diameter);
m/S
so
A(UCe)
Then from Eq.
= $U2 = 69.75
(3.6)
the volume-flow
Q
lpnn
A Ibaa from
=
a2
=
68.2O
=
O"
=
51.34O
=
51.34O
and
I
B,
\ B2
rate
0.0791. m3/s
the velocity
OL1
i
m2/s2
diagram
is
.
and rearranging
71
and
c1
w1
c2
The choice
=
3.54
=
7.38 m/s
m/s
speed has to be done with
a) the value
0.8;
which
The minimum number
at 1800 rev/min
by almost
all
With
is 24 teeth.
regard
for
sprocket
This
80 teeth
then wili
be
d
=
m
for
the big
0.2087
m
value
the value
diameter
ratio
ratio
available
on the generator
sprocket
is
recommended
of shaft
should
speed
lead
to
teeth.
to the above discussion
gives
diameter
a l/2"-pitch
Therefore
the hub-to-tip
number
for
to the
,of two standard
us 1800 rev/min
of teeth
manufacturers.
by specifying
an available
gives
regard
of hub-to-tip
and b) a combination
can be found
spinning
rotor
w2
be around
shaft.
rev/min
=
m/s
considerations:
sprockets
gotten
13.26
of the shaft
following
should
=
sprocket,
a shaft
speed of 540
The dimensions
of the
72
and
dt
dh
=
0.2347
m
=
0.1827
m
blade
The ratio
separately
diameter
Nozzle
design.
for
ratio
is
then
0.78
which
is
in
an
this
machine
and rotor
as they
blades
should
have different
be designed
flow
inlet
and
angles.
First
for
information
given
having
solidity
tried
0,026O m
range.
Blade
cases
=
of hub-to-tip
acceptable
outlet
height
nozzle
blades:
in Ref.
(2)
best-looking
profiles
with
blade
and inlet
angle,
angle
other
(3.9)
A9
ind
6
angles
are
i
I
and (3.10)
=
19.25"
=
5*09O
19.25O
=
72.29O
B2
curves
staggers
we have:
.
but
this
and
profiles,
for
an optimum
of 45" are suggested.
then
B1 =
through
different
profile,)
From Eqs.
The blade
for
the same deflection
of 1,5 and a stagger
several
by looking
value
(We
gave the
73
To choose
the number of the blades
From the
spacing.
-b
=
cos 45
=
1.5
C
-C
S
(See Fig.
above specifications
=
to specify
the
we have
0,71
3-21,)
In this
case a different
number
15 blades
seemed to be a good number
sectional
area
prefer
we have
for
the blades
to have blades
with
cross-sectional
area).
With
the above
of blades
as it
(as we want
bigger
specification
gives
were
tried,
a reasonable
to use plastic
chordal
length
nozzle
blade
Finally
cross-
blades,
we
and hence more
sizes
are as
follows:
=
0.0434
m
C
=
0.0651
m
b
=
0.0462
m
=
0.0025
m
=
0.0005
m
S
m
rt
9
In the same way calculations
done.
for
The results
blade
sections.
are
tabulated
for
in Table
the rotor
3-1,
blades
Also
were
see Fig.
3-4
B;
NOZZLE
BLADES
ROTOR
BLADES
o oo
51.3
6;
Z
68.2
15
51.3
16
TABLE 3-l:
CT
AC
AOind
8O
1.5
45
19.25
5.09
19.25
1.5
30
5.13
6.27
56.34
IMPULSE TURBINE BRING
B;
S
C
b
73.29
43.4
65.1
57.57
40.7
61.6
B;
0
rR
rt
46.2
2.5
0.5
12.4
53.35
2.5
0.5
21.8
2
DIMENSIONS (DIMENSIONS IN mi)
75
NOZZLE BLADES
ROTOR BLADES
-
FIG.304.
. ----
_
BLADE SECTIONS OF THE AXIAL-FLOW IMPULSE TURBINE.
76
Evaluation
in Appendix
each loss
of efficiencies,
III
and information
parameter
Nozzles
blades
the blades
N
Pt
X
Pt
X
ar
X
2.48
0.97
1.13
0.10
4.2
7.20
9.04
0080
1.12
0.10
1.2
20.20
rl
given
the value
N
pr
Substituting
for
about
to the method
of
can be found.
TABLE 3-2:
equation
we got
respect
Pb
X
Rotor
With
BLADES LOSS FACTORS
the numerical
and assuming
values
for
1 mm. radial
the parameters
clearance
for
in
the
the rotor
we have,
=
r) t-t
The assumed value
to the optimum
for
80.6%
rltt
of the
that
flow
mechanical
90% then
II
diffuser
blades
down to
.75 of its
n t-s
if
was 80%; therefore,
we are
close
enough
design.
Then from Appendix
specify
.
efficiency
the machine
=
we can find
after
the
value
other
rotor
when it
efficiencies.
will
leaves
reduce
We
the velocity
the rotor
so,
75%
is 95% and generator
and the unit
efficiencies
efficiency
will
be;
equal
to
77
Mechanical
of
design.
the mechanical
description
the
about
11
t-sm
=
71.0%
rl t-su
=
64.1%
It
is not
design
in
different
general-arrangement
The machine
seen.
chain
and sprocket
is
combination.
--
bush
gives
a feature
Also
(even
all
ins ,c+Lled
a smooth
center
blades
the
inner
will
In the next
drawing
pages
can be
by means of
descriptions
are
for
the
bush allows
the center-section
blades
section.
has high-accuracy
transmit
(see
blades
(Part
(Part
drawing
1, Part
12) with
13) are molded
flow
hubs
of the
to the nozzles.
bush
to the duct
(Part
15).
surrounding
This
the
rotor,
efficiency.
us to use low-c<.st
housing
tribe
the rotor-thrust-bearing
materials
(Part
li)
15 blades,
into
The nose up-stream
in a plastic
surface
increase
plastic
The diffuser
to the
for
nozzle
14) euides
rustable)
details
a short
1800 RPM generator
The rotor
(Part
this
the
only
section
combination
rotor,
which
be given.
Further
the
These are
Therefore
and turbine
This
diffuser
as bearings
blades
all
as follows:
The up-stream
and the downstream
nozzle
will
to he made of plastic.
has 16 blades.
act
parts
transmission.
Rotor-nozzle
which
report.
to run a 5Kw.,
given
to describe
this
drawing
individualiy
components
necessary
22).
force
73
L
79
80
The bushing
molded
is
fixed
to the upstream
between
fixed
the flanges
end (i.e.
of Parts
to the bushing
are
front
the
is
similarly
flanges
*'
through
bearing.
small
holes
Housing
adaptor.
water
pipe
turbine
the
rotor
blading
is
in
the bushing.
blading
with
the
end
After
resin
-Is also
adhesive.
fastened
to
The diffuser
adhesive.
to a flanged
front
enables
of
bushing,
clamped
between
Water
flows
the nose and lubricates
to the back bearing
has three
the
The center
downstream
individual
section,
us to connect
and the
water.
the
through
hub.
The upstream
and flange.
with
flows
The housing
together.
itself
in
to the bushing
Then some water
It
clamped
projections
are lubricated
in
and frame.--
are bolted
is
The nozzle
slots
by structural
bearings
in the
which
22 and 23.
the hole
front
fastened
fastened
of Parts
The rotor
in
21 and 22.
of the nozzle
the hub of the nozzles
blading
size),
by square-cross-section
the blades
The nose in
be means of a flange
nozzle
These match up with
of each blade.
assembly
to the housing
Part
turbine
section
section
sections
21,
is actually
to a standard
(Part
(Part
which
10"
22) encloses
23) is
an
the
the outlet
collector.
sheets
Different
parts
welded
to steel
facilities
from
cast
for
iron.
of the housing
flanges.
sand casting,
can be made of rolled
However,
Parts
if
there
21 and 22 would
are
steel
local
be better
made
81
The frame
The turbine
through
of
(Part
is bolted
to the
the housing
the
25) is made of steel
frame
back
frame
plate
(Part
supports
the
Transmission
system.
Power is
output
by the meansof
shaft
has four
in
slots
the bore
on its
the
of
As the disk
transmit
output
only
transmitted
stub
which
plate
the
(Part
match
bolts
(Part
26)
shown in Figure
from
disk
together.
flange
The upper
These are
a coupling
loosely
tovque,
rotor
2,
to the
31).
This
up with
small
disk
teeth
shaft.
in
contact
and no bending
with
the
rotor
it
moment or thrust
can
force,
to the
shaft.
(Part
33) which
flange
bearing
leaking
tapered
shaft
i- b fixed
into
32) is
supported
to the housing
seal
in
by a flange
back plate
the
drain
bearing
by bolts.
side,
which
The
prevents
the bearing.
bearing
bush and a nut
the right
(Part
has a rubber
The ball
in
the
with
flange
locking
bearing,
washer,
together
keeps
the
with
a
shaft
in
position.
In order
combination
(Parts
rotor
welded
some of the
24).
generator.
circumference
is
The output
water
using
angles
to raise
the rotor
of two sprockets
34 and 35).
chain
(bicycle
chain).
rotor
and generator
The chain
is
speed
used with
used in
The sprockets
shafts,
to the generator
respectzvely.
this
a tooth
system
ratio
is
speed
a
of four
standard
have 80 and 24 teeth
l/2"
on the
52
We do not
in
this
case.
loading
recommend
the use of standard
To transmit
five
them up to their
bicycle
sprockets
kw at a speed of 1800
kPM would
maximum strength
and would
leave
be
no safety
margin.
To fix
the
larger
(Part
36)
is
bushing
hammering
Using
to the
installed
the
turbine
will
This
lower
turbine
is
rotor
shaft
done to avoid
than
five
at a power
a split
taper
any need for
a meter
work
before
at its
less
than
five
kw,
the
by the means of a value
the
best
kw
level
has to be reduced
at least
turbine
to the
on the shaft.
in powers
To run the
flow
used.
or pressing
the unit
sprocket
turbine
efficiency
inlet.
Obviously
when it
is
run fully
the
output
loaded.
Different
by installing
result
some kind
for
users
would
Design
turbine.
as for
increase
not
find
of a reaction
This
section
is
impulse
results
will
turbines
are also
the
of this
machine
in
were
studied,
size
and complexity.
possibilities
but
all
power
cases
I feel
attractive.
machine
concerned
with
design
of the calculations
machine.
tabulated
drawing
these
The principles
the
controlling
of mechanism
in a significant
that
b)
possibilities
Therefore
be presented.
In fact
same, so to avoid
it
is not
only
of a 50% reaction
are exactly
the assumptions
the
repeating
submitted
as it
structure
axial
the same
and
of both
the mechanical
is
quite
similar
83
to impulse
given
in
machine.
But a short
the following
and nozzle
specify
rotor
a work
of the
blades
will
coefficient
and reaction
The absolute
will
axial
direction.
guess
for
velocity
machine
is
have
the
same cross
absolute
is
that
section.
flow
angle
its
We
to the
both
leaving
then be in
the
the
The first
the total-to-total
diagram
efficiency
calculation
B2
%
U
A(UC6)
Q
=
68.2“
=
O*O"
=
8.84
=
78 . 08 m2/s2
=
0.0704
m3/s
=
9,52
=
Wl
=
C2
A suitable
dh/dt
Cx
shaft
is
is
85%.
The result
of the
is:
m/s
3 =w2
1
accpetable
differences
turbines.
flow
rotor
50% reaction
of one,and
to be the same for
impulse
of the
paragraphs.
The significance
rotor
description
speed for
or
J/Kg
m/s
=
3.54
above
720 RPM,. Therefore;
m/s
results
which
can give
an
84
d
m
dt
dh
blade
height
=
0.2345
=
0.2615
=
0.2075
=
0.027
5-lfdt =
Blade
be used for
between
of bladings
a stagger
From the
0.79
nozzle
number of
m
For simplicity
design.
both
m
and rotor
the blades
for
of 45",
I.5 blades
for
criterion
(Eq.
=
O.&l,
=
cosx=
S
blading.
nozzle
section
But because
and the
For preliminary
be different.
-b
rotor-blade
the nozzle
will
Zweiffel
the
of differences
rotor,
design
and 16 blades
(3.11))
for
rotor
will
the solidity
let's
select
for
the rotor.
blades
we have
also
-b
c
Then blade
Z
S
0.71
dimensions
b
will
.
be as follows
(Table
3-3):
C
AR0
in
6
0
C
B1
B2
re
rt
NOZZLE
BLADES
15
48.76
39.3
55,3
20.0
6.4
94.6
20
74.6
2.5
0.5
ROTOR
BLADES
16
45.76
39.3
55.3
20.0
604
94.6
20
74.6
2.5
0.5
TABLE 3-3:
REACTION-TURBINE BLADE DIMEKSIONS.
85
NOZZLE BLADES
ROTOR BLADES
-
FIG.3-6.
-.
-.
BLADE SECTIONS OF THE AXIAL-FLOW REACTION TURBINE.
86
The blade
cross-sections
Evaluation
Appendix
given
of different
sb
Npr
Npt
NOZZLES
4.15
1.0
1.12
ROTOK
4048
1.03
0012
be found,
tip
which
then
design
that
is
design
absolute
to-static
the value
that
are as
'ar
'
0.1
4.0
8.75
0.1
4.0
9.27
clearance
for
the
rotor
efficiency
can
85.6%
is close
diffuser
velocity
will
enough
to the
first
guess,
so
95% mechanical
as before
blades
when leaving
will
diffuse
the flow
to
the rotor,
then
the
total-
be,
rl t-s
are assumed
Upt
of total-to-total
=
this
efficiency
If
coefficients
in
acceptable.
we specify
of its
given
is,
For preliminary
if
loss
1. to 1,5 mm radial
r7t-t
the
the method
LOSS FACTORS OF REACTION-MACHINE BLADING
Specifying
on the
3-5.
3-4:
TABLE 3-4:
half
'Using
of efficiencies.
the values
III,
in Table
blade
are shown in Fig.
=
efficiency
then
83.6%
and 90% generator
the machine
and the unit
efficiency
efficiencies
are,
87
=
rl t-sm
Mechanical
design.
impulse
and reaction
details
about
mentlon
the differences
of this
machine
turbine
itself
this
reaction
generator,
altogether).
the
and give
that
sizes
blades
better
T-$ su
=
71.5%
mechanical
the
same.
will
design
be given,
of the
in
of the units
and axial
diffusion,
but
which
other
than
turbine,
there
(turbine,
diffuser
no further
The output
impulse
size,
on both
Therefore
and performance.
bigger
total
The diffuser
increase
in size
slightly
in
are
machine
is more than
is
,
The general
machines
difference
longer
79.4%.
in
results
speed
and the
is not much
frame
this
to
and
machine
are
in a few points
in efficiency.
The transmission
is used with
and rotor
ratio
two sprockets
shafts,
respectively.
is
having
2.5
and the same size
24 and 60 teeth
chain
on the
(l/2")
generator
Ghapter
4
DISCUSSION ON ADVANTAGES OF DIFFERENT TYPES
As seen in
had individually
from
parameters
in
machines
are
All
Therefore
cost
The crossflow
locally
areas
turbine
which
the
processes
molding,
Technology
molders
cross-flow
which
could
which
Program
provide
In that
turbine
it
is
of being
improvements
are
turbines
should
the
under
intermediate
axial-flow
processes
the
be preferred
industries
be
of processes
but
in industry
manufactured
in industrial
To satisfy
might
needed
to be discussed.
be made are mostly
case encouraging
may be of great
have
The type
etc.),
is
maintenance.
manufactured
fabrications,
of
machine.
need more sophisticated
goals
(i.e.
of the
to choose
in
the developing
such as plastic
importance.
The amount of labor
cross-flow
being
to farms.
and casting,
Adaptation
and service
to need skilled
But axial-flow
turbine
the turbine
possibilities
and/or
and shipped
have parts
plastic
countries.
both
to farms.
which
of the best
not
Looking
the price
requirements
such as sheet-metals
turbines
processes
designed
gives
prototypes
country,
under
of maintenance
the choice
areas
and shipped
made centrally
processes
type
studied
and some disadvantages.
and manufacturing
in farming
each of the
the vieC: of a developing
to be made and the
important
chapters,
the manufacturing
turbine,
going
last
some advantages
at the problem
the
the
which
much higher
has to be put
than
into
making
each
what has to be done for
the
90
axial-flow
type.
because
The axial-flow
of automation
machines
and their
smaller
would
size
probably
be cheaper
when produced
in
large
numbers.
Comparison
high
of
speed of the
and cross
flow
reaction
generator,
in chain
and sprockets
bath
even for
the
low speed of cross-flow
becoms
necessary.
A big
cost.
be similar
for
scale
production
axial
types.
machines
the
impulse
to the
and lower
forces
for
cross
but
initial
otherwise
two-step
construction
will
scale
transmission
cost
is
investments
for
the
seems likely
production.
cost
will
transmission
to
For large
be much more costly
the material
it
Therefore
machine.
more expensive
small
flow
reaction
the chain
of each of the units
of the
is because
is small
the
the
up ratio
transmission
and its
a far
of the price
units
This
gear
lubricated,
flow
turbine
The rest
all
a lower
over
speed we have chosen
the axial
because
portion
generator
an advantage
a simple.-
and be well
last
unattractive,
shows that,
are entailed.
not
mkes it
is
provides
of generator
in an oil
long
as it
so that
For the kind
of the turbines
machine
machines,
electrical
must work
the structures
for
than
the axial
molds
the
flow
and dyes are
required.
Finally
there
is
often
the
efficiencies
surplus
requiring
a lower
channels,
values
water
water
flow
and so forth.
of the machines
While
differ.
flow
available
a high
will
therefore
require
efficiency
less
costly
machine
pipes,
91
The following
table
shows the
efficiencies
of the different
machines.
Cross-Flow
Turbine
Axial-Flow
Impulse Turbine
Axial-Flow
Reaction
Turbine
85%
t-t
76%
80%
t-s
60%
75%
83.5%
71%
79.5%
64%
71.5%
t-sm
56.5%
t-su
51%
Key :
t-t
E
total-to-total
t-s
2
total-to-static
efficiency
of turbine
blading
t-sm
Z
total-to-static
efficiency
of machine
(shaft
t-su
E
total-to-static
efficiency
of unit
efficiency
Based on all
the best
4,l
solution
of turbine
considerations
we chose
blading
power)
(electrical
the
power)
reaction
machine
as
chapter
has some
to the problem.
IMPROVEMENTS ON REACTION MACHINE
The preliminary
questionable
design
features.
much as possible.
shown in
Here we try
Following
are
the last
tc improve
some items
on that
which
it
design
as
seems necessary
to cover.
By looking
this
nozzle
chapter
at the general-arrangement
(DRN, No, AF301),
combinaticns
in
the
two schemes
drawing
difference
can be seen.
between
submitted
the rotor-
in
92
This
improved
design
rotor.
The atvlospheric
central
hole
pressure
to the other
side
covered
friction
and give
on sliding
with
melt.)
in the rotor
water
supplied
adaptor
new adapter
enables
The smaller
tube
The oil
lubricating
bath
in
settling
angle
size
for
performance.
4.2
Off-Design
the
profiles
are also
reduce
pressure
is possible
turbine
the
and velocity
can not
last
by the
and
aid
The lubricant
in the
machine
force
and diffuser
which
the holo-s
reduces
the chain
of 38" and their
best
through
system's
rotor
on the plates.
the back of the
the transmission
The blade
surfaces
the
the axial
of plastic
in the improved
and valve
the
the high
kinds
us to connect
conditions
increases
upstream
equalizing
sheets
hub and grooves
from
hence
between
on the
the rotor
and reducing
(For
of these
force
through
rotor,
stainless-steel
life,
Lubrication
The front
of the
even the best
of holes
is
thin
hydrostatic
is bypassed
surfaces
a long
surfaces
less
of the rotor
The sliding
rotor.
hubs are
they
pressure
on the two sides
on the
provides
is
stator
changed.
hub.
The
to 8" diameter
piping.
the cost.
turbine
provides
and sprockets,
good
and hence
life.
changed.
shapes
The new blades
are also
optimized
have a
for
the
Performance
The type
of
use a gate
valve
assumption
is
that
flow
installed
the
control
we recommend for
the machine
one m. ahead of the machine.
turbine
is
going
to be run
under
is
to
The basic
fairly
steady
180
I60
i20
loo
80
60
40
20
0
zoo
0
400
600
SHAFT SPEE’
FIG.401.
800
1000
1200
1400
R.
CHARACTERISTIC CURVES OF REACTION MACHINE FOR CONSTANT FLOW RATE.
r6
02
J
00 a
0 v 40
45
50
FLOW RATE
FIG.4-2.
0
55
60
65
70
m3,lrn
CE.ARACTERISTIC CURVES OF REACTION MACHINE IN CONSTANT SPEED.
75
95
loads.
slight
Therefore
changes
the
in
required
frequency
More sophisticated
big
increases
machine
in size
unattractive
Based on this
systems
and price
assumption
curves
and based on predictions.
the method
to have a high
degree
on the machine
and
be acceptable.
to control
the
of the machine,
turbine
which
will
cause
makes the
co customers.
are shown in Figures
using
can be set
up to 5% would
turbine
cated
power
given
the
4-1
characteristic
and 4-2.
These
The off-design
in Reference
of accuracy.
curves
(3),
curves
of the
are theoretical
performance
which
is
predi-
has been found
APPENDIX I
TABLE OF PARTS AND WORKING DRAWINGS
Following
reaction
machine.
numbers
all
provided.
process
given
information
under
under
the
complete
Each drawing
Special
which
about
each part
information
the
part
on material,
should
"Remarks."
For the case of
complicated
or sr;bparts
"B, (1 I, C,"
for
etc.,
after
'axial-flow
are
submitted
the master
reaction
working
drawings
has a reference
the heading
sections
stands
are
of the modified
number.
can be found
type
Using
from the
parts,
drawings
which
are marked
turbine.")
reference
table
of manufacturing
be made, or sub-drawings,
part's
these
for
are
additional
by letters
number.
"A,"
(AF300
98
TABLE OF PARTS AND
LIST OF DRAWINGS OF REACTION TURBINE COMPONENTS
PART-
KUM~ER ,I
I
NAME OF PART
NUMBER
REQ'D
MATERIAL
REMARKS
AF311
I,
FRONT ADAPTOR
1
CAST IRON
AF312
(
MIDDLE SECTION
1
CAST IRON
HOLES OF FLANGES SHOULD
BE ALIGNED
DRAIN CHUTE
1
STEEL
SEE SUBDRAWINGS
BACK PLATE
1
1 OMM PLATE
FRONT FLANGE
1
1 5MM PLATE
CURVED PLATE
1
8MM PLATE
SIDE PLATE
2
5MM PLATE
FRONT PLATE
1
5MM PLATE
AF313
'AF313A
AF313B
AF313C
AF313D
AF313E
I
/
. . . contl'nued
TABLE OF PARTS AND
LIST OF DRAWINGS OF REACTION TURBINE COMPONENTS(Continued)
NUMBER !
REQ'D 1
NAME OF PART
NOSE
AF314(1
AF314(2
1 ;;;if
1
AF316A
AF316B
AF316C
I
STATOR BLADING
I AF317
3
11
NOZZLE AND ROTOR
BLADE SECTION
:
AF3l8A
AF318B
DIFFUSER BLADING
AF319
DIFFUSER-BLADE
SECTION
AF320
BUSH
SEE AF317 FOR BLADES
PROFILE.
1
ROTOR BLADING
REMARKS
SEE ADJACENT TABLE FOR
PROFILE COORDINATES
1
I
1
MATERIAL
GLASS-FIBER-REINFORCED
POLYESTER THERMOSET
POLYESTER RESINS
30% GLASS BY WT.
THE 1.5MH STAINLESS-STEEL
SHEET SHOULD BE JOiNED TO
SLIDING SURFACE BY METALBONDING. EPOXY.
SEE ADJACENT TABLE FOR
BLADE PROFILZ.
1
GLASS-FIBER REINFORCED
POLYESTER THERMOSET
POLYESTER RESINS
30% GLASS BY WT.
THE 1.5MM STAINLESS STEEL
SHEET SHOULD BE JOINED TO
SLIDING SURFACE BY METALBONDING EPOXY.
SEE ADJACENT TABLE FOR
BLADE PROFILE.
1
GLASS-FIBER REINFORCED
POLYESTER THERMOSET.
POLYESTER RESINS
30% GLASS BY WT.
. ..continued
TABLE OF PARTS AND
I
LIST OF DRAWINGS OF REACTION TURBINE COMPONENTS
(Continued)
NUMBER
PART j
NAME OF PART
NU%EER i
IREQ'D
MATERIAL
AF321A
1 SLOTTED DISK
1
ALUM1NW
AF321B
'
2
HARD STEEL
1
STAINLESS STEEL
-AF322
KEY
1 SHAFT
,1
1 HUB ASSEMBLY
AF323A
HUB HOUSING
1
CAST STEEL
AF323B
FRONT CAP
1
1.5MM STEEL SHEET
AF323C
BALL BEARING
1
M.R.C. BEARING 206-SX
ADAPTER AND NUT G-Y
AF323D
SEAL
1
GARLOCK 78, 0542
REMARKS
EQUIVALENT STANDARD
PARTS WITH THE SAME SIZE
CAN ALSO BE USED.
COMP NO. 26448-35
DES. GRP. D.
AF323E*
i
(3/16"~32)~5/16"
BOLT
ROUND HEAD
3
I
I
. ..continued
*no drawing;
standard
component
TABLE OF PARTS kND
LIST CT DRAWINGS OF REACTION TURBINE COMPONENTS(Continued)
PART
NUMBER
NAME OF PART
NUMBER
REQ'D
MATERIAL
REMARKS
AF324
BIG SPROCKET
1
BROWNING 4OP60
TYPE 4
BUSHING Pl
NO. OF TEETH 60
PITCH l/2"
PITCH CIRCLE DIA. 9.554”
FOR TYPE 40 CHAIN
AF325
SMALL SPROCKET
1
BROWNING 4024
NO. OF TEETH 24
PITCH l/2”
PITCH DIA. CIRCLE 3.831”
FOR TYPE 40 CHAIN
AF326*
CHAIN
1
BROWNING NO. 40
l/2"
PITCH
NO. 40 A.S.R.C.
-I--
. ..continued
*no drawing;
standard
component
-
TABLE OF PARTS AND
LIST OF DRAWINGS OF REACTION TURBINE COMPONENTS(Continued)
!
PART
1
NAXE OF PART
-
-_-I
f1
II NUKBER
REQ'D
I
FRAME
1
SIDE ANGLES
TOP ANGLE
1 AF327C
#
TOP PLATE
1 AF327D
j AF327D
1
1, BAR
j
1I AF327E
]1 ri,“,DATION
FOUNDATION PLATE
j AF328
I
/
I
OIL BATH
j AF329
'
OIL-BATH
STEEL
2+2
II
i
!
I
1
80X80X8
L
2
80X80X8 L
1
80MM PLATE
2
40x8 FLATBAR
;4
1OMM PLATE
2 OFF AS DRAWN
OPPOSITE HAND
I
COVER
REMARK!!
MATERIAL
I
2 AND 3MF1STEEL
SHEETS
I
SEAMWELDED
2MM STEEL SHEET
I
. ..continued
TABLE OF PARTS AND
LIST OF DRAWINGS OF REACTION TURBINE COMPONENTS(Continued)
NUMBER
REQ'D
,_--
NAIVE OF PART
8
; AF330*
I
I
I
f
i1
AF331A*i
j
1
GENERATOR
I
j
1
i
(5/8"~12)~2
AF331B *[
5/8"x12
/ AF331Cj
5/8"
1 AF332A"I
(l/2%12)
j AF332B*/
1/2"x12
1 AF332C*[
I
I
I
l/2"
l/2"
l-1/2"
NUT
LOCK WASHER
HEXAGON HEADED
4
AF333C *j
9/16"
PLAIN WASHER
4
9/16"
LOCK WASHER
BOLT
4
_
--
4
ALIGNMENT-PIN
4
AF335A"I
(3/8%16)
1
AF335B*/
3/8"
AF335C*!
(3/8'k16)
2" BOLT
PLAIN WASHER
I
HEXAGON HEADED
1
WING NUT
compcnent
HARD STEEL
2
-standard
I
4
4
I
I*no drawing;
HEXAGON HEADED
4
BOLT
(9/16"xl2)xNUT
*I
VOLTS
20
LOCK WASHER
AF333B*
AF334
4 POLE, 5KW, 115/230
21.7 AMP.
60 CYCLE
1800 R.P.M.
1 PH.
20
NUT
(9/16"xl2)x2"
,
WiNCO INC.
SERIES 5KS4G-3
20
BOLT
AF333A*;
A:Z33D*/
REMARKS
MATERIAL
. ..End
105
I
106
f
co
107
WI
108
109
=:
0
CURVED PLATE
111
112
s
1 113
7
-
114
0.0
2.5
5.0
7.5
10.0
15.0
20.0
25.0
30.0
35.0
40.0
50.0
60.0
70.0
80.0
90.0
ZE
120:o
130.0
140.0
150.0
160.0
2xax
25:5
31.5
36.0
45.0
51.0
56.5
62.0
66.0
70.0
77.0
82,O
87.0
91.5
95.0
98.0
100.0
101.5
102.5
103.0
103.5
104.0
115
I
-
116
117
II
118
I
OS
119
m
7 I
ROTOR BLADING_
A
121
Yc mm
0.0
1.0
2.5
3.75
5.0
6.25
10.0
12.5
15.0
17.5
20.0
22.5
25.0
30.0
32.5
35.0
37.5
38.75
40.0
41.25
42.5
43.5
44.5
45.5
46.5
47.5
48.75
50.0
Xt mm I t mm
0.0
E5
2:o
3.0
6.0
E5
4:75
129::
15.0
18.0
21.0
24.0
27.0
30.0
31.5
33.0
36.0
37.5
39.0
42,O
45.0
S5
10.0
11.5
12.5
13.25
13.85
14.0
13.85
13.25
12.6
12.0
11.25
10.5
9.12
8.62
7.75
6.75
x5
210
0.0
E
51:o
54.0
57.0
60.0
-!l
0.0
0.76
0.86
i-y8
1:43
1.76
2.02
2.52
3.28
3.78
4.13
4.34
4.34
4.43
4.59
4.54
4.28
4.13
4.03
3.53
2.83
2.17
0.0
123
cu
Lc
0
-
124
125
t
/’
I
r,
\
‘t
X
R/=1.0
mm
Rf=0.2
mm
mm
t
mm
0.0
0.0
0.69
K5
0:75
1.5
0.84
1 , Of,
1.52
1.96
2.38
2.74
3.30
3.73
4.05
4.28
4.43
4.50
4.47
4.33
4.08
3.37
3.31
2.84
2.33
1.79
1.25
0.73
0.28
0.0
i-i
6:0
1E
15:o
18.0
21.0
24.0
27.0
30.0
33.0
36.0
39.0
42.0
45.0
48.0
51.0
54.0
57.0
60.0
126
--
127
128
129
i
SHAFT
220
I II I
HUB HOUSING (1 of 2
132
133
134
“I
135
a
136
137
- -I
138
?
Tr
------m--A------
e--m---
‘,
-.
t
I
--v-----------i
--
FRAME (plan
view)
2 of 2
-a------.
----
140
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
402
-i
I
Q
00
TOP ANGLE
I
142
I
I
I
I
I
I
a
I8
144
\
Y
8G9
‘1
\
\
\
\
\
145
35
I
I
0I
ALIGNMENT-PIN
--
APPENDIX II
FRICTION LOSS IN NONCIRCULAR CONDUITS
Pressure
section
due to flow
bend can be found
where
is
drop
K
is
the loss
cross-section
angle
K
and the
of the bend
The hydraulic
radius
pressure
in
of D
h'
terms
where
factor
E/D
L is
then
fh
cross-
flow
of hydraulic
as well
velocity
and
diameter
of the
as the deflection
I-l),
is defined
as;
'
due to friction
loss
can also
be expressed
as:
the length
of
the conduit
of hydraulic
be defined
Re
average
4 x flow area
wetted perimeter
drop
on the basis
should
the
of the bend,
diameter
ADh 5
and then
v
is a factor
(Fig,
a non-circular
from;
factor,
the mass density.
through
diameter.
is
fh
and
using
Fig.
E/D
I-2.
147
the
Obviously
as,
v Dh
E 7
can be found
and
F $-
friction
Re
and
p
148
0.20
i
0.15
1 VALUES OF R/a
0
FIG.
20
I
7.
DEFLECTION ANGLE
LOSS FACTOR FOR BENDS.(ASCE,J.HYDRAULIC
DIV.,NOV.
65)
e.
0.004
CI
*
0.003
--- -IO3
IO4
IO5
Re = VII/v
FIG, 2. FRECTlON FACTOR f VS. Re. FOR DIFFERENT e/D.
H.Y.Choi,
Heat,Mass and Momentum Transfer
P 58 1
IO7
(W.M.Rohsenew
and
149
APPENDIX III
EFFICIENCIES
The total-to-total
?J
This
efficiency
is
defined
turbine
output
power
enthalpy
drop from inlet
total
and temperature
to outlet
total
E
tt
of a turbine
definition
of efficiency
is
concerned
as
pressure
pressure
with
the blading
hydraulic
losses.
The total-to-static
defined
pressure
Turbine
output
enthalpy
drop
and temperature
concerns
the amount
=
-
t-s
efficiency
turbine
by drain
flow
For a turbine
efficiency
disk
as,
plus
friction
and other
TJ
m
is
losses.
total
static
going
losses
an overall
can be defined
mechanical
power
from inlet
to outlet
of energy
the internal
as a machine
of the machine
rl t-sm
where
of a turbine
is
as,
n
This
efficiency
of
out
pressure
of the
the blading.
total-to-static
which
should
That
include
the
is
-rltsxrlm
the mechanical
efficiency
of the machine
and defined
150
T -T
loss
T
'i,'
where
T
stands
for
shaft
For a turbo-generator
should
also
be taken
%
=
-
Then the overall
II-1
unit
the efficiency
account
which
output
electrical
input mechanical
efficiency
rl t-su
See Fig.
into
torque.
E
of
is
energy
work
the
unit
l
nt,sXrlmxll
g
.
of the generatar
will
be defined
as;
151
HYDRAULIC LOSSES
ENERGY LEP,VI%
TtfE TURBIiIE TO
TAIL-MTER
FIECHANICAL LOSSES
GENERATOR LOSSES
OUTPUT ELECTRICAL
PONER
(GENERATOR)
FIG. 1 --
SCHEME OF LOSSFS Ii! GlATER TIJRRO-GENERATORS.
APPENDIX IV
PERFORMANCEESTIMATION OF AXIAL-FLOW TURBINES
There
axial-flow
are several
ways to evaluate
The method
turbine.
straightforward
is based
by H.R.M.
and H.J.A.
Craig
of Mechanical
given
here which
on the method
Enginetring,
the efficiency
given
of an
seems very
in
the paper
Cox and published
in
the
Volume
1970-71.
185 32/71,
written
Institution
THE METHOD
For an axial-flow
Group
two groups..
of the nozzle
friction,
1 losses
and rotor
leakages,
1 losses.
turbine
factors
is convenient
based on relative
X
n
secondary
and
losses
X
r
etc.
are
for
blade
=
the group
velocities.
153
losses
are due to disk
only
with
group
as
1 losses
1 losses
as loss
Therefore,
w2
+ Xr $
the sum of loss
the nozzle
and secondary
can be defined
outlet
c2
Xn $
into
be concerned
efficiency
to evaluate
can be divided
2 losses
work done in blading
done in blading
+ group
Group 1 losses
where
and group
Here we will
blading
losses
due to profile
blading,
l-lt-tb 2 work
It
are
etc.
Therefore
stage,
factors
and rotor,
due to profile
respectively.
and
-.
154
Then to take
account
the
losses
we have to multiply
the area
ratio
Ar
Evaluation
defined
.
due to tip
the value
of loss
leakage
and etc.
of blading
into
efficiency
by
as follows;
Rotor blade swept
annulus
area
E
The blade
‘.
area
factors
loss
factor
X
and secondary
P
defined
as
loss
xP = x pb 'pi
is
the sum of profile
loss
Xs , where
former
factor
Npr Npt + mp,
Each one of these
are
+ (Axp)s,e
defined
the
factor
one is
+ (ax 1
Pm
as:
X
Pb
5 basic
profile
loss
N
Pi
5 loss
correction
factor
due to incidence
N
Pr
= loss
-
correction
factor
due to high
N
Pt
5 loss
correction
factor
due to trailing
Reynolds
Number
edge
Wp) t
z profile
loss
factor
increment
due to trailing
iAx >
p s/e
- profile
radius
loss
factor
increment
dtle to back surface
E profile
loss
factor
increment
due to high
(oxp lrn
edge
Mach number
155
This
method
can acceptably
turbines
of the kind
case for
design-point
N
Pi
would
Each of
these
Figs.
III-2
blade
opening
=
P
x
pb Npr Npt
design
form
+
axial-flow
concerned
(mpjrn
for
water
In this
with.
, (fip)s,e
will
X
P
and
be
(axpIt
can be found
using
curves
Number is
given
defined
in
on the
as;
*2O2
E 7
for
the
or
terminology
The secondary-loss
where
xS
is
The Reynolds
to 111-B.
III-1
and III-8,
report
and the simple
parameters
Re
See Fig.
this
preliminary
be zero
X
that
be used for
5
factor
the secondary-loss
(Ns+qb
I
x
clol
V
of the blades,
can be found
factor
using
XS
(Xsjb
where
('s)b
E
basic
secondary-loss
z
(Ns$i/b-
secondary-loss
ratio.
factor
is
Figures
defined
III-7
as
156
Fig. 1. Turbine
blade
and velocity
triangle
16
I
__
10
20
:i
Fluid Inlet
at mln.rdcl
,cont,!!on
40
F:il:O
!Iw
50
60
CiJ: - ET :N;LE -B
speed ccnc bon)
Fig.2 . Lift parameter,
70
FL
notation
I
orgee
loss
cn
90
157
I
I
I
-G-l
0
01
I
I
0.2
I
c3
I
I
I
I
'24
05
06
07
0.8
RATIO-I-~
.
Fig.3.
.- .
.,
s%33
for average
profiles
,
/
J
05
5s
I
/
/
I
I
I
I
I
I
I
I
I
I
I
MODIFIED
Fig.4.
LIFT
1
I
/
!
I
5 20
I
2
C0c:~crt.o~
rc:,o
m
ratio
!!
i
p: 25
Y
5
Contraction
ri
I
CGEFc.Z EYT -
Basic profile
;x:s,%:
loss
r
VI
TRAMr;
E3;E
Tr!'CKSESS
Fig. 5 .Traiiing
TC PITPI
R;T.G -tc/s
edge thickness
losses
158
REYNOLDS li.NE_~
Fig.6,
Profile
Rz,, -based
against
loss ratio
on biade o~enq
Reynolds
number
effect
--.._
L
7
/ /’
---I
25
33 -,b/h
4or------
-35
/F
c:
I//
t
45 bit,
--
/
,
50
- sj
/
I
!5
NVLQSE ASPECT RATIO -b/h
Fig.
7. Secondary
loss-aspec:
ratio
factor
(
55
98
10
SQUARE OF 1-F. FF:A-iJE YECN VE:SC:TY
RATIO ACROSS 3LA: ‘.; -et tie x~ry~ou!~e? bcc:o;i:#
Fig.
8. Secondary
loss-bask
loss factor
159
LIST OF SYMBOLS
area
blade
angle
width
of
flow
the blades
velocity,
chord
of
absolute
the blade
diameter
friction
factor
g
acceleration
due to gravity
H
hydraulic
h
blade
h
enthalpy
i
incidence
angle
K
head-loss
factor
L
length
lil
mass flow
N
rotational
0
opening
head
height
rate
speed
of
the blades
pressure
volume
flow
rate
radius
S
spacing
T
torque
of the blades
. ..continued
'LIST OF SYMBOLS(continued)
U
blade tangential
velocity
W
relative
Z
number of blades
ci
angle of absolute
velocity
B
angle of relative
velocity
A
deop or rise
6
deviation
velocity,
flow
of a vaiable
angle
efficiency
turning
angle
stagger
or setting
angle
mass density
CT
solidity
flow coefficient
work coefficient
w
speed of revolution
(angular
*
*
velocity)
*
161
SUBSCRIPTS
annulus
hub
inlet
leading
edge
m
mean value
n
nozzle
0
outlet
P
profile
r
rotor
t
tip
X
axial
0
and radial
direction
stagnation
inlet
direction
property
to the blade
out of blade
tangential
direction
*
*
*
163
REFERENCES
(1)
Horlock, J.H. Axial Flow Turbines. Robert E. Kreiger
Publishing
Co., Huntington,
New York, 1973.
(2)
Dunavent, J. C.,and Erwin, J. R. Investigation
of Related
Series of Turbine Blade Profiles
in Cascade. National
Advisory Committee for Aeronautics,
Washington, NACA. TN3802.
i3)
Craig, H. R. M., and Cox, H. J. A. Performance Estimation
of -Axial Flow Taurbines. The Institution
of Mechanical
Engineers (Thermodynamics and Fluid Mechanics Group),
Volume 185 32/71, 1970-71.
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