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Crossflow Turbine
Abstracts
by Joe Cole
The Crossflow Turbine
Unfortunately bulletin #25 is not a "step-by-step" manual, much to the
disappointment of many. When I first saw in in 1978, I found it fragmented, elusive,
overly technical missing a few formulas. It' more like the technical ramblings of
someone explaining the concept of time and the theory of how a clock works when all
you wanted was to know the time. However with some diligent "head scratching"
over a suitable period of time you will eventually sort out the relevant pieces of
information contained in the bulletin. There are a few point to keep in mind when
reading and working on some of the calculations in the bulletin. Keep in mind that it
was originally a German document written in the early 1930s. It is very likely that
some meaning was lost in OSC translation of the original document. Also bear in
mind that some of the formulas in the document do math conventions that we use
today ie. addition, subtraction, multiplication then division. You'll have to "play
with" the brackets. However taking the bulletin as a whole it follows the same
mechanical & hydraulic principles used today in turbines & pumps. Those are a
curved blade's reaction to a jet of water (in turbines) and water's reaction to a moving
curved blade.
About half of the math in the bulletin deals with the physical relationships between
the mechanical turbine elements (blade geometry and runner inside & outside
dimensions) and the other half deals with the forces produced on the blades. The
forces are represented as "vector diagrams" Vectors diagrams help one to visualize
what is going on inside the runner. If you understand them you can analyze changes
made to the turbine and or changes made in operating parameter such as head & load.
Next to the calculus used in the bulletin, the vectors are probably the most baffling
things in the bulletin. The vectors will be explained shortly however, as for the
calculus, "I ain't goin' there."
Don't expect to "re-engineer" the crossflow runner. Banki & Mitchell "did their
homework" on it. The proportions of the blades to the runner diameters and angles
involved are fairly "fixed" and cannot be arbitrarily changes without adversely
affecting the power & speed of the runner because these changes affect the efficiency
of the turbine. As alluded to in the paragraph above, the runner diameters and blade
dimensions are a compromise of mechanical dimensions & mechanical efficiency.
Taking all the above into consideration, this article will not be a step-by-step
interpretion of bulletin #24 but will be my personal "practical inturpation &
explanation" of it. Before getting started I want to clarify something. Bulletin #25
title "The Banki Crossflow Turbine" is somewhat misleading as it only deals with the
"runner" aspect of the turbine. After discussion of the "runner" portion of this article I
will expound on the turbine design as a whole as well as some abstract theory about
the crossflow turbine.
Before calculating much of anything else we need a little understanding of vector
diagrams. It will take several stages to illustrate this
in it's entirety go get a cup of coffee and come
back. In understanding how a jet of water acts on a
surface we first use the "Flat Plate Normal to Jet"
illustration. In this a flat plate is held at a 90° angle
to the plate. In engineering terminology this is
called the flat surface held normal to the jet. Go
figure, I don't know how or why they come up with
this stuff! Anyway, the jet will be forced to make a
90°turn, thusly spreading out over the plane of the
plate. In this case the force ( F ) will have no
component in the plane of the plate. In other words
there will be no forces trying to move the plate
"sideways" to the jet. The force ( F ) is computer as
F = M * v. Again in engineering terminology it
said that "the jet's momentum in it's initial direction is wholly destroyed. This just
means as the waters energy was dissipated out radialy 90°into never-never land and
that no "work" was done. Remember in high school physics you were taught that for
"work" to be done there motion has to be imparted. In our case here we needed the
force ( F ) to cause the plate to
move for there to have been
"work" done.
On the other hand now if we
force the water through a
smooth 180°turn the force ( F ) is doubled. The force ids doubled because the
equation F =( M * v ) + ( -M * -v ). That is F = (Mass * velocity in the initial
direction + (Mass * velocity in the opposite directing. Reducing this equation gives
us simply F = 2 * M * v. One thing that might be a bit confusing in these two
illustrations is the arrows indication the direction of ( F ). It might appear that V is
moving in one direction (and it is) and that ( F ) is moving in the opposite direction
(which it is not). What the ( F ) directional arrow means is a "resistance" opposite to
the direction of ( V ). Again, it's an engineering thing.
Now that we are up to speed on velocity, mass & force, lest look at some vector
diagrams along with the blade shapes that produced them. In this diagram the jet is
being deflected by 70°or so. In applying these momentum theorems or laws as they
should be call to turbines is as follows. If a jet of water strikes a curved blade the
water is deflected by the angle ?.A force (F) is imparted to the blade in two
directions, x & y. These forces are calculated thusly
Fx = M * (v – v cos ° α) or Fx = M * (v – v cos ° α)
&
Fy = M*v * sin α
In this diagram the two velocities are the same but separated by angle α and the
triangle is closed by closed by the line ∆ v as dictated by the laws of cosines
∆v = the square root of v12 + v22 – 2 * v1 * v2 * cos α
∆v = the square root of 2 * v2 – 2 * v2 * cos α
These two forces combined is equal to:
F=M * v * the square root 2 * (1 – cos α)
Here is the general text book vector of a Pelton wheel in motion.
This is the path & vector diagram of a Pelton wheel. It is showing 2 buckets. The
bucket on the left is showing the absolute path of the water jet while the right side is
showing the relative path if the jet. If the wheel were "locked down", the water path
would indeed follow the path as indicated on the left. However in a running machine
1
the wheel is moving in the same direction as V . The water jet is trying to follow the
inside curvature of the bucket but because the bucket is trying to move away from the
jet the path is straighter as indicated in blue then had it mage the near U-turn of the
absolute path. The vector is compound, in other words its is showing more then just
one part of the blade. The left triangle is the vector for the entry of the jet to the
bucket & the right side is of course showing the water exit from the bucket. The inset
illustration shows what happens when the wheel (or runner) is in over speed. The
1
path flattens out more and you can see in the inset vector that μ is approaching the
1
same length as V Very little power is now being produced and aa a matter of fact the
power that is being produces is rather in driving the intended load, is being spent on
maintaining a high wheel speed and overcoming windage & friction. Notice that
2, 2
three additional notations are included. V v * β. In hydraulics the following
notation conventions are used.
Getting a little more
complicated visually but
still the type vector. Here
we have the Francis
runner. The actual water
path is shown in red.
Again the right side of the
double vector in showing
the entry of water and the
exit is shown on the left.
Both are shown here on
orange. The Green vector
is actually the right side
entry but for clarity is is
duplicated somewhat larger to show the geometry of the lead edger of the blade to the
outer periphery of the runner. I think before going on to the crossflow & should as
Rickey would say to Lucy, "Le me splain something to you." In hydraulics as in any
other engineering field they has it's own set of mathematical notations and also a
hierarchy or naming conventions . Most of the confusion in vectors comes from
water velocities. If the notation is a big V, then that velocity is an absolute one. If it's
a little v, then its a relative velocities. Most turbo machinery only has one in and one
out. No so with the crossflow. It's twins! It's got 2 of everything. To keep all the
symbols straight I'm not going to "splain" it, but rather illustrate it with a chart. I
think the chart and the crossflow illustration can explain this much better then I can.
Just so we are clear, the term "quadrants" is mine. The 1st in the entry of water to the
at point "A". The 2nd is the exit of water from point "B". The water then crosses the
interior of the runner and then re-enters the runner at point "C" in the "minus
direction" (remember our discussion above F =( M * v ) + ( -M * -v ). Water then
exits the runner in the minus direction at point "D"
1 st 2nd 3ed 4th
Quad Quad Quad Quad
Absolute
Velocity
V1 V21 V11 V1
Relative
Velocity
v1 v21 v11 v1
Blade
Angle
β1 β21 β11 β1
Attack
Angle
α1 α21 α11 α1
Runner
Velocity
μ1 μ 21 μ 11 μ1
The
problem
with the
crossflow
is just that
“crossflow”
. Only
about 72 %
of the
waters
energy is
extracted in
the top of
the runner
leaving
only 28%
to be
extracted
from the
lower
section.
The exact
ratio is
dependant
on the
actual
diameter of
the runner,
how many
blades are
being, the
length to diameter ratio, the head, bla, bla,bla. Under "ideal circumstances, 50% of
the power would be produced in the first section and 50 % from the last section. This
will not happen because of the internal crossing of the water in the runner center
section. Ideally we should have "laminar flow" all the way through the runner.
Laminar flow means that that all the water particles in a given area is flowing parallel
to each other and are at the same speed. Think of this like the telescoping antenna on
a car where the innermost core has the fastest flow. You will never get true laminar
flow due to friction of the surfaces involved. Laminar flow is destroyed by excessive
restrictions and abrupt changes in flow area or directions. When it is destroyed
friction is the result. When the individual jet filaments cross and interfere with each
other that too pretty much "kills ' hell" out of laminar flow. We have a tremendous
disruption in flow now plus of air is now being introduced into the water path. By the
time the water gets to point "C" it's pretty well diffused to a wide pattern This causes
1
the flow V1 to enter the blade at an attack angle varying widely from the the 16° it
should be. That why the 28% of the available power is extracted there. This is
illustrated in fig 3 of the bulletin. However there nothing you cab do about it.....or is
there? Read on Grasshopper. We'll I think we'll all had enough turbine dynamics for
this week so lets move on not to some actual calculations.
Before any "design work" is to be done their are a few things that must be known.
First you must have a reasonable expectation of the amount of power that might be
produced from a given site. For instance, don't expect to supply a full household with
electricity produced from a scenic babbling brook running across your back yard. It
takes a lot of water to produce electricity. The "head" and "Q" must first be
determined. The "head" at least in the US is measured in feet. "Q" is the quantity of
water and in "micro-hydro" work it's usually given in CFM (cubic feet per minute)
and in larger turbines is given in CFS (cubic feet per second). Be sure when
calculation from formulas in other documents you pay attention to & convert units as
necessary. In this article I use CFS.
To begin we first determine the power potential of our site. For convenience, (mine)
throughout this article I'll be using my own site for the design & evaluation. That is
the head ( H ) = 26 feet and the flow ( Q ) = 8 CFS. The formula for determining the
potential hydraulic horse power is ( H * Q * 60 ) / 660. This is the raw horse power
potential and does not reflect any efficiency or loss's. According to the formula my
potential horse power output would be ( 26 * 8 * 60 )/660 or 18.9 HP. Assigning a
efficiency figure is difficult. I want to be conservative in this figure so let's use an
overall plant efficiency of 75%. Therefore 18.9 * .75 = 14.18 HP. One HP is
equivalent to 745.7 watts so 14.18 * 745.7 = 10574 watts or 10.57kW of electrical
power. This is enough to "do a house."
Now having that out of the way we can start to design a runner that will
accommodate the site. In the bulletin pages 10 through 15 deal with the construction
proportions of the runner. The information we need from these pages are: Formula
#35 Q=volume of water, Formula #36 L= blade length, Formula #37 ρ=blade
radius & Item (E) Central angle on page 15. Once these values ate known you take
these figures to a machine shop and have them form the blades from flat stock to
conform to “ρ”, machine the blade sections to form the 73.46° arc in item 3, & finely
cut the blade to their final length (L). You then pay the man a huge sum of money &
prey your calculations were correct. Definitely NOT the way to go. There is a much
simpler & cheaper way to arrive at near the same result but first a quick discussion on
one aspect of Banki's design. The dimensions and angles in the bulletin represent the
"near" optimum dimensions & angles to satisfy mechanical advantage & un-restricted
passage of the
water. These
dimensions are
fairly "fixed" and
therefore cannot
be arbitrary
changed without
some decrease in
efficiency ie.
power & speed
output. As a result of this there are definite dimensional relation ships between the
various components of the runner. I wrote the following formula to determine the
runner diameter from the blade radius. D1=2 * ρ /.326.We can use this to great
advantage because a supply of blade stock is all around us and is readily available in
the form of steel pipe. If you've ever seen some crossflow runners up close before,
they mostly look the same, say 12-16 inched in diameter and have an aspect ratio of
1:2, that is 23 -32 inches in length. They also look like the blades were fabricated
from 4 inch steel pipe. You're right. But remember what your Momma told you when
you were 8. "Just because everybody else is doing it doesn't mean you have to." My
point is al lot of these turbine were fabricated from readily available materials and
hey, there's nothing wrong with that. However, waiting and searching for that
optimal "readily available materials" will save you some money and very likely gain
you some efficiency. I'll go through what happens when you design a runner without
regard to the project as a whole. Most commonly available is schedule 40 pipe and
below are some of it’s specs. Of course there is an almost infinite range pipe sizes in
industrial & construction grade so finding a size that will meet your needs should not
be a problem. Using this method we supply ρ and let industry supply us with tailor
made materials.
There seems to be a lot of 4
inch steel pipe around. Let's
see if we can design a runner
around that size. We start by
finding the jet thickness
which started at item 4 on
page 17 of the bulletin. Area
of Jet = Q/V = 8 / 40= .2 ft.
(28.8 in^2). The value of So
according to the bulletin is So
= Jet Area / Length.
According to the formula at
reference 34 in the bulletin:
L = 210.6 * Q / D1 * H^.5
L = 210.6 * 8 / 12.27 * 5.099 = 25.5 inches.
Oh by the way, H^.5 is the same thing as "the square root of "H". It took me a while
to figure out that one. Anyway with the initial blade length calculated as 25.5 inches,
divide the "Jet area" of 28.8 square inches by 25.5 to get the So which in this case =
1.13 inches.
The only thing we need to factor in now is the nozzle efficiency and adjust the length
accordingly. If you follow good hydraulic principle and design a good gate/nozzle
you should be able to achieve an nozzle coefficient of .98.That’s only a 2% off peak
which would be 1.356 which translate to a .223 increase in runner width to
compensate. This would bring the runner length to 25.72 inches. If it were me I’d
bring the runner on out to 26 to28 inches just for grins and a little more error margin.
Now we’re looking at a D:L ratio of 1:2.08 Not terribly bad but! A 28 inch wide
small diameter turbine is going to be a machining & welding nightmare. Building the
runner itself it not too bad but I would add in 2 extra center support disk for rigidity.
Of course you’ll want to extend the runner length again to compensate for the width
of the extra center supports. We’ll we’re now out to 28.5 inches. Do I here 30?
My Daddy used to tell me, “You’ve got to use some horse sense”. Although I was
never very good with math, I do have to ability to “visualize” how things function &
anticipate problem areas. Having some “horse since” also helps. Here comes the first
major problem in designing a turbine. Let’s tentatively select 4-inch pipe to make out
blade sections from. We might select it because it look good & stout and because it is
relatively easy to come by. That will make us a runner 12.27 inches in diameter. At
this point my horse is telling me “there aint no way”, you’re getting 8 cubic feet of
water a second through a 12 inch runner without major difficulty. It’s not impossible
just not practical and here’s why. Anyway fabricating all the flat stock for the gate &
nozzle assembly will really be the difficult part. That’s an awfully wide gate
assembly. At a 26 foot head you only have a shade over 11 PSI at the lower end of the
system but think about it. You have a 28.5 inch wide gate perhaps transitioning back
several feet to a round penstock. That might present top panel behind the gate valve
of 28.5 x 36 inches. Multiple that times 11.25 PSI and you’ll have in the
neighborhood of 11,550 pounds of force acting just on the top panel of the gate. Even
if your welds held, the things going to bulge out & distort like a balloon. Personally
I’d give it around a 100% failure rate within 10 minutes.
What's a fellow do do? We'll
before I through the preverbal
monkey wrench into the mix, lets
fix this problem first. To get a
narrower runner we need to make
it'd diameter larger. This is done
make it larger by choosing a blade
with a larger radius. This time
we'll step up to blades made from
6 inch pipe. Building a 18 gate &
nozzle would be child’s play
compared to a 28 or 30 inch gate.
The mechanical stresses by water
pressure would be reduced almost
70 %. The machine will cost
more to build mainly due to the
heaver drive components required
because of the slower speed &
greater torque when compared to
the smaller machines of equal
horsepower. But here you’re
getting into a serous machine of
much higher durability and a
much greater potential for
increasing the efficiency beyond
the apparent fixed limit or
87%.I’ll comment on this a little later. The runner built from 8 inch pipe is even better
with some qualifications. Again, the cost will be higher because of even larger
bearings and shafting required. However building a nozzle, gate & transition 13
inches would really be a piece of cake. The biggest concern with a runner this large in
diameter is the the loss in head due to the higher inlet. It's only a couple of feet in this
example but may be a consideration.
Alright, as promised, I'm throwing a monkey wrench into the works. The problem
comes when calculating how long the runner needs to be. Notice in the calculations
& illustrations in the bulletin all the math used an infinitely thin blade. If this is not
realized it will cause you to calculate the runner too short. You might not notice this
until you go to full load and “it just aint makin’ it”. Refer to page 9 of the bulletin to
figure 5 for the spacing used. Using our 12.27 turbine as an example, if we multiply
it’s diameter by pi we have a circumference of 38.52 inches. This gives a blade
spacing( t )in the outer periphery of the runner of 2.14 inches. The illustration to the
right shows the problem
very well using a
exaggerated blade
thickness in blue. The
original S1 value "A" that
should be is 1.25 inches
had been reduces to "B"
1.04 inches. Our jet
thickness So "C" has
dropped from .85 inched
to "D" .64 inches. That's
a 21% decrease in jet area from the original calculated value. This means to keep the
efficiency as high as possible the runner length will have to be increased 21%. You
don't need any fancy math or trig. to figure out just subtract the blade thickness from
the calculated value of So. Calculate the percent difference & multiply you original
blade length by that percentage as we've done above.
Specific Speed
Specific speeds is a dimensionless number. In broadcast engineering they call this
term "normalizing", if any of you are familiar with Smith Charts. The term is used to
“level the playing field” if you will, so that all types of runners can be evaluated under
the same conditions .As a result the term via it’s number define the shape of the
runner. I remember from a long time ago one hydraulic document described it this
way. If a model of any given turbine were build with a 1 foot diameter and operated
with a 1 foot head, then the specific speed is the speed that the runner would turn to
produce 1 horsepower. I guess that about sums it up for a level playing field.
What it all means is that a turbine with a high specific speed will while running a
full load, be turning faster then one with a low specific speed. An extreme example
are the Pelton wheel which has a very low specific speed. It is usually thought of as a
high-head machine. However it can be very efficient a low heads. It’s just that it
turns so slow at low heads that the cost the equipment needed to increase the shaft to
something usable by a alternator may cause the whole project scrapped or re-dome
with a turbine of a higher specific speed. Also a low specific speed is also thought of
as a low volume unit. This really makes it an ideal selection for mountainous terrains
where large quantities may not be available.
On the
other hand
you have the
Kaplan
Turbine
which is an
axial flow
(propeller)
turbine. It has
a large
specific speed
and is used
mainly on
large dammed hydro sites where then the is somewhat low but the quantities of water
available are staggering. These turn relatively fast rate when compared to the
crossflow, Francis & Pelton. They would not be suitable for medium to hi-head as
they would turn much to fast to be practical. When every thing above is considered
the crossflow would be an excellent choose for low to medium head operations.
However it’s not a weekend project and must be engineered properly if it’s going to
be efficient and last. If I were King of the world I’d make all crossflow builder
applicants take the following test. Can you draft? Can you weld? Can you run a
milling machine and a lath? What is the square root of 2? Convert 1 PSIG to Head.
If you’re carrying all the feathers you can carry, can you carry one more? You had
better be able to rattle off without blinking, “yes, yes, yes, 1.414, 2.31 and no. ”The
point is this is a real engineering project and is not for the typical do-it-yourselfers.
Nozzles
I believe that bigger is better up to a point. In the case of selecting a runner
diameter, using a larger & therefore narrower runner not only saves money and add
durability but does offer up a few extra chances at increasing the efficiency of the
crossflow. Take a second look at the Horse power formulas #2 & #6 on page 7 of the
1
bulletin. Remember the lows of cosines? The 16 ° α is usually chosen as a
compromise between hydraulic efficiency and mechanical clearances in adjusting So.
Therefore if a1 is reduced the efficiency & power output will increase. With a large
diameter runner this is much easier then in a small turbine. You could lay that angle
down to maybe as low as 8 °.Of course you would want to lengthen the runner to
compensate for the smaller So.
General Layout of Flow In Nozzle
The nozzle diagram above is meant to show some general proportions. For
maximum efficiency the runner should be designed for single blade operation.
However in the interest of construction difficulties in building a wider runner, a
double nozzle - blade arrangement may be used at some loss in efficiency. The
proportions are general. For instance I chose the radius of the nozzle curvature
arbitrarily at 2 times the runner diameter. The exact radius in not important so long at
it gives a nice long gentle sweep into the blades. The arc of the nozzle is also an
arbitrary figure. I placed this one at 73 degrees “just because”. That long sweep &
mechanical clearance is all that matters. You could go “straight in” as the folks a OSC
did when they built their turbine using the freshly translated document from Banki’s
original papers. By the way, does anyone know how to get or has a copy of the
“original Banki papers? However they had some pretty horrible efficiency numbers
with their turbine. They may have been “Jim Dandy” mathematicians but would have
made a few changes on their nozzle design & transition assembly. Probably the thing
that hurt them the most was the nozzle. It was a sliding gate that opens & closed
“laterally”, that is across the runner face. What happened when you pot your thumb
over the end of a garden hose? Using their arrangement that’s exactly what happened
in their turbine. My guess is that at small gate openings the water might have been
disbursed by 10-20 degrees. Another thing that hurt a little was not having a smooth
transition between their supply pipe and the nozzle. It was a blunt sharp edge
transition. That hurt them more at full power then anything else. I’m not trying to
belittle any of the people involved I’m just trying to make you aware of “design flaws
in engineering.” Left click on the illustration above to save it to your computer. It's
actual size is about twice what you are seeing here.
What is important is the angle the water hits the blade at. This is generally taken at
16 deg. However, that is "relative: to the blade angle B, which itself is relative to the
periphery of the runner. Through out the bulletin you see constant reference to a1.
This is an extremely important angle, for it more then any other factor, determines the
power output of the runner. However I’d have to say that 16 degrees is the maximum
angle that one should use. Us it as a design figure then see if you can go smaller.
Getting small requires “laying the nozzle down” closes to the runner. If you use a
large enough radius and a long enough arc for the nozzle, you could get a1 on down to
the 8 to 12 degree range. Any smaller though, and you’ll have to start thing about
lengthen the runner. Going to excess on this could get you a nozzle with a low
coefficient because of excess friction because of excess length.
There are several
nozzle arrangements that may be used. Most of the
commercial crossflow turbines built in Europe use mutable
blade inlets. In all of these the nozzle in intrigal with the
turbine housing. If you are making commercial turbines
that's a very good idea because it saves manufacturing cost and makes an extremely
ridged turbine assembly. This method is a little impractical for us little guys because
not too many of us have casting facilities in our back yards or want to shell out major
bucks for some "real machine shop work" Besides if the nozzle is cast in with the
housing we can't adjusts the attack angle now can we? I took my design from one of
the old Ossburger design. In stead of the water following the runner housing after it
leaves the gate it follows a curved guide which is the top of the nozzle assembly. In
mine I'll use a nylon or duron spring loaded back seal on the gate shaft. The side seals
and shaft bearing are not show in my illustration but they are mounted externally on
the nozzle housing. The sealing method on edges of the gate plate are not shown but
they are also nylon A
deviation of the
"sharp-edge orifice" is
used to help eliminate
the spreading of the jet
as it leaves the nozzle
The actual length of
the nozzle is a bit
longer then shown and
the nozzle will have an
adjustable pivot mount
at the end of the
assembly where it
meets the runner
housing. The other
end its attached to the
transition/diffuser assembly witch is mounted at the other end of the turbine sub frame
assembly. There are two critical considerations when mounting a nozzle like this.
Because the runner, nozzle and transition/diffuser are mounted together on the same
frame, the alignment to the penstock is critical to that undue stress is not imposed and
ether assembly. Ideally a flexible coupling would be the ticket but a commercial
coupling would be rather expensive for a 12 inch penstock. Later I'll be adding to this
section about flexible coupling and alternatives. A flexible coupling does three
things. It does allow for some mis-alignment, It isolated the penstock from the
turbine from mechanical vibration, it allows for expansion & contraction of the
penstock due to temperature and it will allow for some movement should the penstock
try to settle of shift due to waterhammer.
Something Radical
A large
diameter
narrow
turbines
lends itself
well to a
radical
departure
from
standard
design.
Since all the
blades are
fixed and
have a fixed
relationships
no part of
any blade
can be
moved by
itself. In
other words
1 2
likeβ & β
1
and β 1 &
β21.
However it
2 2
is possible to in effect change β 1. While β 1 itself does not actually change, you can
2
change the angle at which the water enters quadrant 3 an angle β 1 by using an inside
guide within the runner. This would necessitate having an “open faced” on one side.
I can already here some folks now in that condescending nasally voices. "Well if you
do that then all the water will run out! Then what are you going to do?" Not really.
Anyway what do I care what they think . Besides, these are the people who failed my
test miserably!
Using just one blade set water leaves the blade between A & B. It re-enters the
runner for it's 3ed quadrant of operation at D through E. At full gate operation using 2
blade sets, water leaves quadrant 3 from A to C & then re-inters at D through F. In
the illustration shown here the water path for single blade operation is the blue lines.
Adding a 2nd blade is shown by the green lines. This illustrated the spread of the
water upon entering the 3ed quadrant of operation. I plotted the water path graphically
and came up with the curve necessary for an internal guide shown in red. The pink
area shows the water path for single blade operation. The light blue shows the path
should 2 blades be used. In single blade operation point E is about as far back to your
right as the jet will reach at normal speeds.. What I've attempted to do here is re-
direct the water back open more blade set and inter at 16 degrees at that point. A
similar situation occurs when the 2nd blade section is added. The water in confined to
a course that does not vary with speed and it is always forces to enter quadrant 3 at 16
deg.
The bottom surface of the
guide would be either the
center red portion above or the
left red portion depending on
weather you were using one or
two blades in operation. The
right red outline shows the top
edge of the side walls of the
guide. The illustration here is
the concept of what the guide
might look like. It's only a
Photoshop assisted freehand
drawing but I think you can see
what I'm getting at here. A
guide like this presents me with
some interesting possibilities.
However it is mounted, the
mounting mechanism should be extremely ridged. There would of course be a
standard fixed mount that would during installation but what about an "on the fly
adjustment?" One way of doing this would have the lower edge be the pivot point so
the quadrant 3 entry angle could be varied to suit flow & load conditions. Another
possible mount scenario would be to "hang" the guide from the runner shaft using
pillow block bearings. These bearing would of course be of the "double sealed" type
suitable for such as wet environment. The guide would have a lever attached between
it and the activation mechanism
As mentioned above
in order to use this type
of guide the runner
would have to be open
faced. This does
present a small
engineering problem.
With this runner it is
not necessary that the
shaft extend thru the
runner. It only need to
can if the guide were
under hung from it
using pillow block
bearings. However a
more likely mounting configuration is what's called " an overhung load. An overhung
load is defined as the radial load on the output shaft extension produced by a pulley,
chain sprocket, gear, crank arm, cam or other similar device. It necessitates using a
larger diameter shaft & beadings. In addition it requires a larger mounting boss to the
runner end plate. More to come as this page expands.
APPENDIX I
Notes on the "Efficiency Formula" in Bulletin #25
The efficient formula is every bit a complicated as it looks. I really have very little
though on how it works. Due to my lack of understanding or motion mechanics I’m
forced to take Banki’s word on this one. However I can tell you what is going on in
the formula. In the formula “C” is the nozzle coefficient. He’s accounting for that in
1 1
the first part of the formula in dealing with ? & V .In the middle of the formula the
term y is the factor describing the loss of energy caused by the separate jets crossing
each other between the 3ed & 4th quadrants. I believe that the loss of power is also
2
represented in ? due to “shock” loss. Shock loss is when the relative velocities v 1 &
v11are not parallel (in the vector diagram). This can be seen on page 11 of the
2
bulletin on the left side of fig 7.The relative velocity of v 1 suggest that the inside
diameter of the runner at point “B” in the drawing above is turning at a different
speed to the corresponding point “C”These actually turning at different speeds id
clearly impossible since they the same physical surface. The last part of the formula
1 1
is the velocity difference between V & ? to extract power.
APPENDIX II
Notes on the "Horse Power Formula" in Bulletin #25
The Horse power formula is not as complicated as it might seem. The formula can be
divided into parts.
(W * Q * ? 1 / g)the momentum part.g=gravity constant at 32.3 In checking
my Excel and Q-Basic programs that calculate this I found a discrepancy withW.As
stated earlier W the weight of water per cubic foot of at sea level is 62.2 ft. However
to make the formula produce the correct answer in Excel a value of .13 has to be
used. At the moment I don’t have time to fix it so I use the correction multiplier of
.00291 in the horse power equations. In Q-Basic the value of 62.6 works just fine. I
think they mean "mass" rather then weight.
((V1 * cos(a1) – u1) takes account of the laws of cosines & subtracts the
wheel peripheral speed from V1 to that power is produced.
(1+y) * (cos b1 / cos b2) the lump sum factor or runner coefficients taking
into account the cosine blade angles of the 1st quadrant and the 4th
quadrant. Their ratio would always be 1:1 because they are physically the
same piece of steel.
This page will be an ongoing document. It will be up-dates and expanded as I have
time. Eventually I hope to cover every aspect of building a crossflow turbine. I
welcome comments on this page. Please let me know of any mistakes you find or
clarifications that nee to be made. I will also entertain contributions to this page. Just
email me and let talk about it.
Email
More to come........This upload March 9, 2004 1:45 PM
