Crossflow Turbine Abstracts

Crossflow Turbine Abstracts

http://williamson.us.com/Information/Development/Hydro%20power/Crossflow/Crossflow%20Turbine%20Abstracts.html[11/11/2011 12:01:24 PM]

Crossflow Turbine Abstractsby 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 inin 1978, I found it fragmented, elusive, overly technical missing a few formulas. It' more like the technical ramblingsof someone explaining the concept of time and the theory of how a clock works when all you wanted was to know thetime. However with some diligent "head scratching" over a suitable period of time you will eventually sort out therelevant pieces of information contained in the bulletin. There are a few point to keep in mind when reading andworking on some of the calculations in the bulletin. Keep in mind that it was originally a German document written inthe early 1930s. It is very likely that some meaning was lost in OSC translation of the original document. Also bearin 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 followsthe same mechanical & hydraulic principles used today in turbines & pumps. Those are a curved blade's reaction to ajet 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 theblades. The forces are represented as "vector diagrams" Vectors diagrams help one to visualize what is going oninside the runner. If you understand them you can analyze changes made to the turbine and or changes made inoperating parameter such as head & load. Next to the calculus used in the bulletin, the vectors are probably the mostbaffling 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 proportionsof the blades to the runner diameters and angles involved are fairly "fixed" and cannot be arbitrarily changes withoutadversely affecting the power & speed of the runner because these changes affect the efficiency of the turbine. Asalluded to in the paragraph above, the runner diameters and blade dimensions are a compromise of mechanicaldimensions & mechanical efficiency. Taking all the above into consideration, this article will not be a step-by-stepinterpretion of bulletin #24 but will be my personal "practical inturpation & explanation" of it. Before getting started Iwant to clarify something. Bulletin #25 title "The Banki Crossflow Turbine" is somewhat misleading as it only dealswith 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 stagesto 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 isheld at a 90° angle to the plate. In engineering terminology this is called the flatsurface held normal to the jet. Go figure, I don't know how or why they come upwith this stuff! Anyway, the jet will be forced to make a 90°turn, thusly spreadingout over the plane of the plate. In this case the force ( F ) will have no component inthe 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 engineeringterminology it said that "the jet's momentum in it's initial direction is whollydestroyed. This just means as the waters energy was dissipated out radialy 90°intonever-never land and that no "work" was done. Remember in high school physicsyou were taught that for "work" to be done there motion has to be imparted. In ourcase 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 doubledbecause the equation F =( M * v ) + ( -M * -v ). That is F =(Mass * velocity in the initial direction + (Mass * velocity inthe opposite directing. Reducing this equation gives us simplyF = 2 * M * v. One thing that might be a bit confusing in thesetwo illustrations is the arrows indication the direction of ( F ). It might appear that V is moving in one direction (and it is) andthat ( 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 momentumtheorems or laws as they should be call to turbines is as follows. If a jet of water strikes a curved blade the water isdeflected by the angle ?.A force (F) is imparted to the blade in two directions, x & y. These forces are calculatedthusly

Fx = M * (v – v cos ° a) or Fx = M * (v – v cos ° a)

&

Fy = M*v * sin a



In this diagram the two velocities are the same but separated by angle a and the triangle is closed by closed by theline ? v as dictated by the laws of cosines

?v = the square root of v12 + v22 – 2 * v1 * v2 * cos a

?v = the square root of 2 * v2 – 2 * v2 * cos a

These two forces combined is equal to:

F=M * v * the square root 2 * (1 – cos a)

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 theabsolute path of the water jet while the right side is showing the relative path if the jet. If the wheel were "lockeddown", the water path would indeed follow the path as indicated on the left. However in a running machine the wheelis moving in the same direction as V1 . The water jet is trying to follow the inside curvature of the bucket but becausethe 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 exitfrom the bucket. The inset illustration shows what happens when the wheel (or runner) is in over speed. The pathflattens out more and you can see in the inset vector that µ 1 is approaching the same length as V1 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, isbeing spent on maintaining a high wheel speed and overcoming windage & friction. Notice that three additionalnotations are included. V2, v2 * ß. In hydraulics the following notation conventions are used.

Getting a little more complicated visually but still the typevector. Here we have the Francis runner. The actual waterpath is shown in red. Again the right side of the doublevector in showing the entry of water and the exit is shownon the left. Both are shown here on orange. The Greenvector is actually the right side entry but for clarity is isduplicated somewhat larger to show the geometry of thelead edger of the blade to the outer periphery of the runner.I think before going on to the crossflow & should as Rickeywould say to Lucy, "Le me splain something to you." Inhydraulics as in any other engineering field they has it's ownset of mathematical notations and also a hierarchy ornaming conventions . Most of the confusion in vectorscomes 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 inand one out. No so with the crossflow. It's twins! It's got 2 of everything. To keep all the symbols straight I'm notgoing to "splain" it, but rather illustrate it with a chart. I think the chart and the crossflow illustration can explain thismuch 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-entersthe runner at point "C" in the "minus direction" (remember our discussion above F =( M * v ) + ( -M * -v ). Waterthen exits the runner in the minus direction at point "D"

1 st

Quad

2nd

Quad

3ed

Quad

4th

Quad

AbsoluteVelocity V1 V2

1 V11 V1

RelativeVelocity v1 v2

1 v11 v1

Blade Angle ß1 ß21 ß1

1 ß1

Attack Angle a1 a21 a1

1 a1

RunnerVelocity µ 1 µ

21 µ

11 µ 1

The problem with the crossflow is just that



“crossflow”. Only about 72 % of the watersenergy is extracted in the top of the runnerleaving only 28% to be extracted from thelower section. The exact ratio is dependanton the actual diameter of the runner, howmany blades are being, the length to diameterratio, the head, bla, bla,bla. Under "idealcircumstances, 50% of the power would beproduced in the first section and 50 % fromthe last section. This will not happenbecause of the internal crossing of the waterin the runner center section. Ideally weshould have "laminar flow" all the waythrough the runner. Laminar flow means thatthat all the water particles in a given area isflowing parallel to each other and are at thesame speed. Think of this like thetelescoping antenna on a car where theinnermost core has the fastest flow. You willnever get true laminar flow due to friction ofthe surfaces involved. Laminar flow isdestroyed by excessive restrictions andabrupt changes in flow area or directions. When it is destroyed friction is the result. When the individual jet filaments cross andinterfere with each other that too pretty much"kills ' hell" out of laminar flow. We have atremendous disruption in flow now plus ofair is now being introduced into the waterpath. By the time the water gets to point "C"

it's pretty well diffused to a wide pattern This causes the flow V11 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 ofthe bulletin. However there nothing you cab do about it.....or is there? Read on Grasshopper. We'll I think we'll all hadenough 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 reasonableexpectation of the amount of power that might be produced from a given site. For instance, don't expect to supply afull household with electricity produced from a scenic babbling brook running across your back yard. It takes a lot ofwater to produce electricity. The "head" and "Q" must first be determined. The "head" at least in the US is measuredin feet. "Q" is the quantity of water and in "micro-hydro" work it's usually given in CFM (cubic feet per minute) andin larger turbines is given in CFS (cubic feet per second). Be sure when calculation from formulas in other documentsyou 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 beusing my own site for the design & evaluation. That is the head ( H ) = 26 feet and the flow ( Q ) = 8 CFS. Theformula for determining the potential hydraulic horse power is ( H * Q * 60 ) / 660. This is the raw horse powerpotential and does not reflect any efficiency or loss's. According to the formula my potential horse power output wouldbe ( 26 * 8 * 60 )/660 or 18.9 HP. Assigning a efficiency figure is difficult. I want to be conservative in this figure solet'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 pages10 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 ?=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 formthe blades from flat stock to conform to “?”, machine the blade sections to form the 73.46° arc in item 3, & finelycut the blade to their final length (L). You then pay the man a huge sum of money & prey your calculations werecorrect. Definitely NOT the way to go. There is a much simpler & cheaper way to arrive at near the same result butfirst 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 dimensionsare fairly "fixed" and therefore cannot be arbitrary changed without some decrease in efficiency ie. power & speed

output. As a result of this there are definitedimensional relation ships between the variouscomponents of the runner. I wrote the followingformula to determine the runner diameter from theblade radius. D1=2 * ? /.326.We can use this togreat advantage because a supply of blade stock isall around us and is readily available in the form ofsteel pipe. If you've ever seen some crossflowrunners 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 theblades were fabricated from 4 inch steel pipe. You're right. But remember what your Momma told you when you were8. "Just because everybody else is doing it doesn't mean you have to." My point is al lot of these turbine werefabricated from readily available materials and hey, there's nothing wrong with that. However, waiting and searchingfor that optimal "readily available materials" will save you some money and very likely gain you some efficiency. I'llgo through what happens when you design a runner without regard to the project as a whole. Most commonlyavailable is schedule 40 pipe and below are some of it’s specs. Of course there is an almost infinite range pipe sizes inindustrial & construction grade so finding a size that will meet your needs should not be a problem. Using thismethod we supply ? and let industry supply us with tailor made materials.

There seems to be a lot of 4 inch steel pipe around. Let's seeif we can design a runner around that size. We start by findingthe jet thickness which started at item 4 on page 17 of thebulletin. Area of Jet = Q/V = 8 / 40= .2 ft. (28.8 in^2). Thevalue of So according to the bulletin is So = Jet Area /Length. According to the formula at reference 34 in thebulletin:

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 withthe initial blade length calculated as 25.5 inches, divide the "Jetarea" 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 goodhydraulic principle and design a good gate/nozzle you should be able to achieve an nozzle coefficient of .98.That’sonly a 2% off peak which would be 1.356 which translate to a .223 increase in runner width to compensate. Thiswould 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 grinsand 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 widesmall diameter turbine is going to be a machining & welding nightmare. Building the runner itself it not too bad but Iwould add in 2 extra center support disk for rigidity. Of course you’ll want to extend the runner length again tocompensate 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 dohave 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 bladesections from. We might select it because it look good & stout and because it is relatively easy to come by. That willmake us a runner 12.27 inches in diameter. At this point my horse is telling me “there aint no way”, you’re getting 8cubic feet of water a second through a 12 inch runner without major difficulty. It’s not impossible just not practicaland 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 thesystem 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 havein the neighborhood of 11,550 pounds of force acting just on the top panel of the gate. Even if your welds held, thethings 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 preverbalmonkey wrench into the mix, lets fix this problem first. To get anarrower runner we need to make it'd diameter larger. This is donemake it larger by choosing a blade with a larger radius. This timewe'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. Themechanical stresses by water pressure would be reduced almost 70%. The machine will cost more to build mainly due to the heaverdrive components required because of the slower speed & greatertorque when compared to the smaller machines of equalhorsepower. But here you’re getting into a serous machine of muchhigher durability and a much greater potential for increasing theefficiency beyond the apparent fixed limit or 87%.I’ll comment onthis a little later. The runner built from 8 inch pipe is even betterwith some qualifications. Again, the cost will be higher because ofeven larger bearings and shafting required. However building anozzle, gate & transition 13 inches would really be a piece of cake.The biggest concern with a runner this large in diameter is the theloss in head due to the higher inlet. It's only a couple of feet in thisexample but may be a consideration.

Alright, as promised, I'm throwing a monkey wrench into theworks. The problem comes when calculating how long the runnerneeds to be. Notice in the calculations & illustrations in thebulletin all the math used an infinitely thin blade. If this is notrealized it will cause you to calculate the runner too short. Youmight 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 thespacing used. Using our 12.27 turbine as an example, if we multiply it’s diameter by pi we have a circumference of38.52 inches. This gives a blade spacing( t )in the outer periphery of the runner of 2.14 inches. The illustration to theright shows the problem very well using a exaggerated blade thickness in blue. The original S1 value "A" that shouldbe is 1.25 inches had been reduces to "B" 1.04 inches. Ourjet thickness So "C" has dropped from .85 inched to "D".64 inches. That's a 21% decrease in jet area from theoriginal calculated value. This means to keep the efficiencyas high as possible the runner length will have to beincreased 21%. You don't need any fancy math or trig. tofigure out just subtract the blade thickness from thecalculated value of So. Calculate the percent difference &multiply you original blade length by that percentage aswe've done above.



Specific SpeedSpecific speeds is a dimensionless number. In broadcast engineering they call this term "normalizing", if any of youare familiar with Smith Charts. The term is used to “level the playing field” if you will, so that all types of runners canbe evaluated under the same conditions .As a result the term via it’s number define the shape of the runner. Iremember from a long time ago one hydraulic document described it this way. If a model of any given turbine werebuild with a 1 foot diameter and operated with a 1 foot head, then the specific speed is the speed that the runner wouldturn 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 thenone with a low specific speed. An extreme example are the Pelton wheel which has a very low specific speed. It isusually thought of as a high-head machine. However it can be very efficient a low heads. It’s just that it turns so slowat low heads that the cost the equipment needed to increase the shaft to something usable by a alternator may cause thewhole project scrapped or re-dome with a turbine of a higher specific speed. Also a low specific speed is also thoughtof as a low volume unit. This really makes it an ideal selection for mountainous terrains where large quantities maynot be available.

On the other hand you have the KaplanTurbine which is an axial flow (propeller)turbine. It has a large specific speed and isused mainly on large dammed hydro siteswhere then the is somewhat low but thequantities of water available are staggering. These turn relatively fast rate when comparedto the crossflow, Francis & Pelton. They wouldnot be suitable for medium to hi-head as theywould turn much to fast to be practical. Whenevery thing above is considered the crossflowwould be an excellent choose for low tomedium head operations. However it’s not aweekend project and must be engineeredproperly if it’s going to be efficient and last. If I were King of the world I’d make all crossflow builder applicants takethe following test. Can you draft? Can you weld? Can you run a milling machine and a lath? What is the square rootof 2? Convert 1 PSIG to Head. If you’re carrying all the feathers you can carry, can you carry one more? You hadbetter be able to rattle off without blinking, “yes, yes, yes, 1.414, 2.31 and no. ”The point is this is a real engineeringproject 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 & thereforenarrower runner not only saves money and add durability but does offer up a few extra chances at increasing theefficiency of the crossflow. Take a second look at the Horse power formulas #2 & #6 on page 7 of the bulletin. Remember the lows of cosines? The 16 ° a1 is usually chosen as a compromise between hydraulic efficiency andmechanical clearances in adjusting So. Therefore if a1 is reduced the efficiency & power output will increase. With alarge 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 bedesigned for single blade operation. However in the interest of construction difficulties in building a wider runner, adouble nozzle - blade arrangement may be used at some loss in efficiency. The proportions are general. For instance Ichose the radius of the nozzle curvature arbitrarily at 2 times the runner diameter. The exact radius in not important solong at it gives a nice long gentle sweep into the blades. The arc of the nozzle is also an arbitrary figure. I placed thisone at 73 degrees “just because”. That long sweep & mechanical clearance is all that matters. You could go “straightin” as the folks a OSC did when they built their turbine using the freshly translated document from Banki’s originalpapers. By the way, does anyone know how to get or has a copy of the “original Banki papers? However they hadsome pretty horrible efficiency numbers with their turbine. They may have been “Jim Dandy” mathematicians butwould have made a few changes on their nozzle design & transition assembly. Probably the thing that hurt them themost was the nozzle. It was a sliding gate that opens & closed “laterally”, that is across the runner face. Whathappened when you pot your thumb over the end of a garden hose? Using their arrangement that’s exactly whathappened 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 belittleany of the people involved I’m just trying to make you aware of “design flaws in engineering.” Left click on theillustration 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 seeconstant reference to a1. This is an extremely important angle, for it more then any other factor, determines the poweroutput of the runner. However I’d have to say that 16 degrees is the maximum angle that one should use. Us it as adesign figure then see if you can go smaller. Getting small requires “laying the nozzle down” closes to the runner. Ifyou use a large enough radius and a long enough arc for the nozzle, you could get a1 on down to the 8 to 12 degreerange. Any smaller though, and you’ll have to start thing about lengthen the runner. Going to excess on this could getyou a nozzle with a low coefficient because of excess friction because of excess length.

There are several nozzle arrangements that may beused. Most of the commercial crossflow turbines built inEurope use mutable blade inlets. In all of these the nozzlein intrigal with the turbine housing. If you are makingcommercial turbines that's avery good idea because it savesmanufacturing cost and makesan extremely ridged turbine

assembly. This method is a little impractical for us little guys because not too many of ushave casting facilities in our back yards or want to shell out major bucks for some "realmachine shop work" Besides if the nozzle is cast in with the housing we can't adjusts theattack angle now can we? I took my design from one of the old Ossburger design. In steadof the water following the runner housing after it leaves the gate it follows a curved guidewhich is the top of the nozzle assembly. In mine I'll use a nylon or duron spring loaded backseal on the gate shaft. The side seals and shaft bearing are not show in my illustration but they are mounted externallyon 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 helpeliminate the spreading of the jet as it leaves the nozzle The actual length of the nozzle is a bit longer thenshown and the nozzle will have an adjustable pivotmount at the end of the assembly where it meets therunner housing. The other end its attached to thetransition/diffuser assembly witch is mounted at theother end of the turbine sub frame assembly. There aretwo critical considerations when mounting a nozzle likethis. Because the runner, nozzle and transition/diffuserare mounted together on the same frame, the alignmentto the penstock is critical to that undue stress is notimposed and ether assembly. Ideally a flexible couplingwould be the ticket but a commercial coupling would berather expensive for a 12 inch penstock. Later I'll beadding 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 fromthe turbine from mechanical vibration, it allows for expansion & contraction of the penstock due to temperature and itwill allow for some movement should the penstock try to settle of shift due to waterhammer.



Something RadicalA large diameter narrow turbines lends itselfwell to a radical departure from standarddesign. Since all the blades are fixed and havea fixed relationships no part of any blade canbe moved by itself. In other words likeß1 &ß2 and ß 11 & ß2

1. However it is possible

to in effect change ß21. While ß2

1 itselfdoes not actually change, you can change theangle at which the water enters quadrant 3 anangle ß2

1 by using an inside guide within therunner. This would necessitate having an“open faced” on one side. I can already heresome folks now in that condescending nasallyvoices. "Well if you do that then all the waterwill run out! Then what are you going to do?" Not really. Anyway what do I care whatthey think . Besides, these are the people whofailed my test miserably!

Using just one blade set water leaves theblade between A & B. It re-enters the runnerfor it's 3ed quadrant of operation at D throughE. 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 quadrantof operation. I plotted the water path graphically and came up with the curve necessary for an internal guide shown inred. The pink area shows the water path for single blade operation. The light blue shows the path should 2 blades beused. In single blade operation point E is about as far back to your right as the jet will reach at normal speeds.. WhatI've attempted to do here is re-direct the water back open more blade set and inter at 16 degrees at that point. Asimilar situation occurs when the 2nd blade section is added. The water in confined to a course that does not vary withspeed and it is always forces to enter quadrant 3 at 16 deg.

The bottom surface of the guide would be either the center redportion above or the left red portion depending on weather youwere using one or two blades in operation. The right red outlineshows the top edge of the side walls of the guide. Theillustration here is the concept of what the guide might looklike. It's only a Photoshop assisted freehand drawing but I think



you can see what I'm getting at here. A guide like this presentsme with some interesting possibilities. However it is mounted,the mounting mechanism should be extremely ridged. Therewould of course be a standard fixed mount that would duringinstallation but what about an "on the fly adjustment?" One wayof doing this would have the lower edge be the pivot point so thequadrant 3 entry angle could be varied to suit flow & loadconditions. 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" typesuitable for such as wet environment. The guide would have alever attached between it and the activation mechanism

As mentioned above in order to use this type of guidethe runner would have to be open faced. This doespresent a small engineering problem. With this runner itis not necessary that the shaft extend thru the runner. Itonly need to can if the guide were under hung from itusing pillow block bearings. However a more likelymounting configuration is what's called " an overhungload. An overhung load is defined as the radial load onthe output shaft extension produced by a pulley, chainsprocket, gear, crank arm, cam or other similar device. Itnecessitates using a larger diameter shaft & beadings. Inaddition it requires a larger mounting boss to the runnerend 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 tomy lack of understanding or motion mechanics I’m forced to take Banki’s word on this one. However I can tell youwhat is going on in the formula. In the formula “C” is the nozzle coefficient. He’s accounting for that in the first part

of the formula in dealing with ? 1 & V1.In the middle of the formula the term y is the factor describing the loss ofenergy caused by the separate jets crossing each other between the 3ed & 4th quadrants. I believe that the loss ofpower is also represented in ? due to “shock” loss. Shock loss is when the relative velocities v2

1 & v11are not

parallel (in the vector diagram). This can be seen on page 11 of the bulletin on the left side of fig 7.The relativevelocity of v2

1 suggest that the inside diameter of the runner at point “B” in the drawing above is turning at adifferent 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 is the velocity difference between V1 & ? 1to extractpower.

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-Basicprograms that calculate this I found a discrepancy withW.As stated earlier W the weight of water per cubic foot of atsea 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. InQ-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 tothat power is produced.

(1+y) * (cos b1 / cos b2) the lump sum factor or runner coefficients taking into account the cosine bladeangles of the 1st quadrant and the 4th quadrant. Their ratio would always be 1:1 because they are physically thesame 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 coverevery aspect of building a crossflow turbine. I welcome comments on this page. Please let me know of any mistakesyou find or clarifications that nee to be made. I will also entertain contributions to this page. Just email me and lettalk about it.



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