Exponential Bell Curves & Runner Efficiency

[TravisR]

I have really tried to pin down runner inlets for combustion engines in order to reduce the coefficient of discharge. I can't quite put my thumb on optimal though and would like any help or expertise you can offer.

Here is what I've found...(I think)

Round bell mouths exponentially reduce runner area, meaning velocity must exponentially increase as it moves into the runner. This causes air to accelerate toward the center of the runner where the air gains too great of a velocity to remain any amount of Newtonian. Having insufficient viscosity to then resist this movement of high velocity air to the middle it compresses the air in the middle of the runner and disassociates it from the edges of the runner. This causes the eddy's on the side of the runner which impede flow.

Exponential bell mouths (hyperbolic or elliptical) allow you to precisely control the velocity in each axis. The real question is, how much velocity in each axis can the runner accept before disassociation from the wall occurs.

Lastly what does runner entry geometry have to do with specifically efficiency of flow? On most 4 valve heads the head at least starts as an oval. So I was contemplating making the runner and the throttle body oval as well. From a CFD perspective it seems to not make that much difference, but real world maybe quite different. Is there a standard number of inches in which the efficiency of the transfer from round to oval is worth the friction of using a runner the same shape as the head?

If it is more efficient to run an oval shape over my distance (about 5 inches) then....

Realistically having the bell mouth a shape that gives a larger perimeter to area ratio would have what effect? Differentially thinking this means for every piece of air that flows over the perimeter it should move slower with a larger perimeter and then it is accelerated into the air stream by the shear forces from the middle. Too much area and the flow is mixed into eddy's at the edges and alot of energy is wasted...

I have a lot of half truths and thinking here and I'm striving for the full truths, anyone want to set me straight?

 

[PedroCG]

hi there, if you are trying to design a bellmouth the optimal shape is elliptical and round, length should be same as small diameter, big diameter should be 2.13 times the small one and the radius at entry 0,08 times big diameter. all i know about bellmouths is what i've read in an article that you can find here:

http://www.profblairandassociates.com/RET_Articles.html

tird one from the top

hope this helps

 

[rmw]

Exponential bell curves---I thought this was going to be a thread about some Six Sigma initiative.

rmw

 

[TravisR]

haha, I appologize for the misleading title, I didn't even think of the ambiguity.

I really appreciate the link, its very interesting. Its the same cfd I was doing, but at a more methodical approach, and time intensive approach. Although it does leave out some amount of specifics. So now that he and I came to the same conclusion that exponential bell mouths are idea, what dx/dy generates the best discharge coefficient?

Also, does anyone have a rule of thumb from tansition to round from oval? His testing suggests I certainly want a round bellmouth. I always get turbulence on the conversion though, I've never tried anything besides a basic loft between the two shapes (which would be a linear interpolation between nearest points.)

 

[TravisR]

I found your reference in the article pedro, I was a bit confused by what you had said until i read it in the article and its clear now...

Just to resolve the transition from oval to round...

I wish Larry Meaux was around to explain how he exactly calculated plenum entry area in his pipemax software. He sent it to me years ago, and I'm unsure if he still visits the forum. Runner taper has always been a mystery, and performance trends is nearly a useless motor tuning tool when it comes to correctly analyzing its effects. Right now my runners are set to .5 deg of taper from centerline by area of a circle (regaurdless of geometry).

 

[PedroCG]

bout the transition, from my knoledge about fluid dynamics (little) you should avoid angles bigger then 12º on expansions, so theres no separation. if you dont want the loft to be a linear interpolation from 2 shapes you can use more shapes between the 2, you can use solid works to check if you dont get bigger angles then 12º.
i dont know what's your purpose but from the article the diference from perfect shape to nearly perfect is less than one percent, so the gain in Hp would be nearly unmeasurable.

 

[TravisR]

Well my problem is that the area changes between the interpolations. I need to build guide lines which maintain the correct area throughout the transition, otherwise you get the speed up and slow down that causes the turbulence. Its very complicated math it seems. You would have to fit the output of the area integral to a constant value, and then control the parameters so that it meets other boundary conditions (less then 12 degrees for instance). The shape also has not even close to the same mathematical form, as the shape at the head is a flat oval (2 flat sides with radius's on the end) and the entry way is a circle.

I was contemplating injecting from the plenum so I'm concerned with spit back if I use an oval shape. He seemed to indicate there was atleast some danger of this.

 

[PedroCG]

well i've done the math for a pure ellipse (image), the angle teta would be 6 and not 12 in this case in your case (flat oval) first you would need to define a way (function) of how this form would meet the circle (or ellipse) that would be the hard part.

http://img185.imageshack.us/my.php?image=transitionex9.jpg

 

[TravisR]

Hrrrm, given what you've written, I think the first dz would create a full oval from the the flat oval, because for every dx/dz and dy/dz of the circle the corresponding dx/dz and dy/dz for the flat ellipse is different. Maybe I could make the first step(.001 in), do a curve interface capture of this fit an oval, then I already know the parameters of the circle.

So doing this you would just constitute solving the general form of an ellipse for the area, then picking maybe 2 points to define the parameters of the general form of the ellipse? This would only amount to really modifying h and k until they goto zero.

http://teachers.henrico.k12.va.us/math/ito/06Conics/6LES3/ellipse_n.pdf

(second page)

I suppose you could hold one angle constant, and define the other angle as a function to meet the area requirement... I think the more proper way would be to minimize dx/dz and dy/dz (maybe minimal of sqrt((dx/dz^2+dy/dz^2)) and make both angles a function instead of an angle? I'm going to play with this a bit on paper, thank you again for taking time to help.

 

[PedroCG]

holding one angle constant is what i've done, tg(teta) in this case is dx/dz, then i defined B as a function of lenght (i called x but its actually z sorry) in order to mantain the area constant (A x B = R^2). dy/dz is dB/dz in this case: (-tg(teta)R^2)/(xtg(teta) + R^2)^2
the result are two simple functions because you only need two things to define the ellipse (A and B). in the flat ellipse A and B is not enough to define the figure, i'll try to find a solution but this realy seems complicated

 

[TravisR]

Thats what i was saying in not so clear langauge. The flat ellipse doesn't stay a flat ellipse any length of time whenever you step toward the circle. The first movement of dz out from the flat ellipse changes it into a full ellipse. So from that perspective you just start from some defined ellipse, and work from there.

 

[TravisR]

I just checked it, and its not a flat ellipse and it its not a full ellipse, its some kind of high order polynomial...

 

[PedroCG]

well in that case its better to do as you say, change the port into an ellipse (with same area) with a simple loft avoiding sharp angles. i also sugest you filled the edges otherwise they're going to cause separation.

 

[PowerTripp]

This is a good discussion, however, there are times when all the best design elements, CFD analysis, and theory just do not work in the real world.

I have seen straight wall/limited radius (1/3 turn) bellmouth stacks outperform ones that perfectly matched Blair's work. And round stacks placed on oval throttles make noticeable improvements on the dyno and the track.

I have seen this happen on 6000rpm V8s, and 16,000 rpm I4s when everything else was correctly optimized. Sometimes there is just no escaping actual testing.

 

[TravisR]

Certainly, but for a good first approach, I always try to use the very best scientific methods and research for a starting point.

By the way pedro, I've got it worked out!

Does anyone have any definite research articles on relating CFM @ pressure differential to an effect on horsepower? Or perhaps another parameter CFM @ pressure differential against runner cross section produces a parameter which would indicate excellent performance, or poor performance? I'm making the first runners from stereo lithography and flow testing them on a head at various lifts. I want to know what would be considered reasonable, and using this information how changes in geometry could be beneficial. I haven't seen much on the relationship. Doing a full scale version for every change and then dynamometer testing is unacceptable from a cost perspective and a little foolish really.

I don't play the lottery much if you couldn't tell!

Thanks!

 

[PedroCG]

hi Travis, an engine will pull the same cfm whatever the restrictions you put on it (not quite because the scavenging will not be so good, but for the pumpimg phase...) i think mdot relates more directly to hp. in the article they mention the work of some student, dont know how easy one could acess that... you also have to take in account that PR is not the same during all the cycle (if it wore hp would relate directly to mdot), and that will vary from engine to engine a lot (camshaft, piston speed...).
i guess if you test an engine with a tipe of runner, than you test the flow performance of this runner and another one, the mean relative increse in mdot over the range of PR of the engine, will relate more or less to the increase in hp, but PR will decrease for the better runner... this is to complicated XD

 

[PowerTripp]

Travis,
For head flow data, on normal output engines under 2hp/cubic inch, multiply max camshaft lift CFM@28inches times .257 to give approximate hp per cylinder.

As specific output increases above 2.2hp/ci. the multiplier can change as ports become more efficient, but the above is good for many performance engines.

The issue also comes down to the minimum cross section area (MCSA) of the port in relation to the valve diameter. With the correct mcsa and port taper, many engines do not like to see flow velocities at 28 inches of depression above 350fps (measured at the mcsa), but as specific output increases beyond 2.2hp/ci. in steeply downdraft ports, higher velocities can be used more effectively - especially in well designed 4-valve ports.

I hope this helps.