Restrictor Choke RPM

[Kemper]

Hello everyone, I'm from KAIST's FSAE team. We are having a lot of technical problems, most of them related to "lack of technical knowledge". Yes, it's kinda hard for a rookie team to start up.
Anyway, we need help concerning "Choke RPM". We decided to run an Aprilia SXV 550 engine on our first car. We have the engine but haven't test yet, and to design the exhaust pipes would be good to know our running RPM. We heard that the more RPM the better (generally), until our air restrictor chokes. Does anyone knows how to calculate the air restrictor choking RPM? Or, is there any team running Aprilia engines that knows what would this magical RPM be?

Thank you all guys, in advance

Paulo Kemper

Dynamics & Electronics Team Captain
KAIST FSAE Team 2008-9

[Grant Mahler]

It sounds like time to go talk to your Fluids professors, and ask them about dynamic compressible flow, choked flow, coefficients of discharge, conical diffusers/inlets and a host of other subjects.

Or, if you cannot get ahold of those professors, and noone on the team has fluids experience, start with Munsen Young and Okiishi's Introduction to Fluid Dynamics.

Or search these forums.

[mjdavidson]

That's good advice from Grant. The approach you take will probably depend on what you have to work with. If you have an engine dyno (or access to one) you might want to build the best restrictor you can come up with and build an intake and exhaust to test with. You'll see when it chokes on the dyno.

That would seem to be the most direct way to find out because even if you know exactly how much air comes through the restrictor you still need to know some things about the engine that are more difficult to measure/calculate.

Good luck with your Aprilia.

[Professor Gas Can]

Kemper,
I've got a couple suggestions to help you guys out as you've asked a mouthful of engine development. We were (still are) in a similar situation not too long ago so I feel ya.

First we can start by determining what the restrictor chokes at. You will find, from this site and from your simulations (whether they be 1D, 3D CFD, or even physical testing on a flowbench), that a restrictor chokes at about 72-74 g/s. Volumetric flow rate for our particular restrictor was 136 cfm at the inlet and 208 cfm at the restricted portion but yours will probably differ. Easiest way to get that information is to model up your design in a 1D simulation program such as GT-Power/Ricardo and impose a pressure difference across it until it chokes. It's like your own little flowbench. Take your bore/stroke/rpm and figure out what volumetric flow rate your engine is flowing assuming 100% volumetric efficiency. Compare the volumetric flow rate you get from your engine to that of what your restrictor is choking at and you will see what affect the restrictor has on your engine. Unfortunately, there are a few assumptions to go along with this baseline calculation. This is steady state remember, unlike how real engines are...where there are pulsations in the intake manifold. This will give you an upper range at least.

For further development, you will need to make an engine model if you haven't already got one. I am partial to GT-Power because I used it at work, that and it couples nicely with Fluent for coupled 3D analysis. This will give you a glimpse of what is happening with the pulses.

Determining your redline is a trickier business than you might think. One of the easiest is to put the engine on the dyno and see where the horsepower starts to fall off, assuming that is, you don't plan to do any work with your camshafts, or reciprocating mass. Determine that your valves will not float as well as that could be a determining factor of your redline. This could be tied all the way back to your transmission as well, as how will you be shifting, where will the car spend most of it's time in the RPM range, as this could be changed with the camshafts. Basically there are a lot of reasons to choose a particular redline so go with what you guys like.

Take this for what it's worth, just throwing ideas out there for you.
Best of luck with your Aprilia.

SUNY-Buffalo

[Kemper]

Everybody, thank you! It is really nice to see that people do help each other here at the forums. I hope soon I have more to add than to take from you =)

Grant, please don't think I'm lazy, but as we are on summer vacations now (meaning no teachers around), we are a first year team and I am more concerned reading about chassis and suspension, reading about fluid dynamics now is kinda impossible. But thanks for the book suggestion, I'll tell the engine guys to buy that and try to study.

Mjdavidson, dynos are kinda hard to find around here in Korea (specially in the city we are) but as soon as we find one we will go there. Did you run Aprilia engine too? I would like to know at least someone's calculated RPM to have as parameter in order to check if we are doing the right math or not...

Professor Gas Can, thanks for the guidelines! I know it may sound weird, but our team is composed basically of freshmen and this kind of information helps us to guide our efforts instead of "wasting time" (please, dont get me wrong) reading all fluid dynamics stuff. I know, one day or another knowing fluid dynamics will be one of the keys to have a top level engine, but for the first year, a "let's do it and check" approach sounds better. I will try to get the programs (any idea where?) and give to the engine team.

Once again, thank you all guys, any other hints, just post =)

Paulo Kemper

Dynamics & Electronics Team Captain
KAIST FSAE Team 2008-9

[Grant Mahler]

Making basic assumptions and understanding a few things can get you a long ways.

What is the volume of your engine? Is it a two or four stroke engine (i.e. is it filling every cycle, or every other)? What is the maximum speed at which air can travel (generally accepted to be significantly less than Mach 1)? From these you can get a volumetric flow rate through a known area...

This makes a HUGE number of assumptions, but it gives you a starting point.

Also, it doesn't deal at all with the shape of the restrictor, the size or shape of the plenum, the intake and exhaust (tuned) lengths, or a host of other things which are important. But it is a starting point.

[Professor Gas Can]

As with any professional software for FSAE use, you can simply ask the company for it. You'll find that most of them can give it to you free/close to free. Don't forget to be nice to them and include them as your sponsor.

Not sure what a "do it and check it" method would entail, but don't be caught doing something just because you heard it was the way to go. As you can imagine, "Because that's what the forums said to do" is not a valid design defense. Ultimately, you'd want to tie all your design decisions back to how many more points it would get you in the competition. For example, we put a turbo on our car because it would increase HP over this RPM range, and this would allow us to extract this much more power for this much more lap time for this much more places in the competition for this much more points. You probably already know all of this but it never hurts to hear it twice.

[Wesley]

Aprilias redline at 12,000, I would not recommend exceeding that. Ever.

As for choked flow... the theoretical approach is one thing, but no matter what, you're not going to reach the theoretical "choked flow" point. Those calculations depend on steady state flow, which you will never see in an engine.

Expansion rate of the restrictor, smoothness of the transition from the restrictor to the plenum (standing waves etcetera) will greatly affect where you find your flow is choked. The smoother you can make the flow through the restrictor (larger plenum) the better for overall flow rate, but you trade throttle response.

[Scrappy]

Originally posted by Professor Gas Can:
Volumetric flow rate for our particular restrictor was 136 cfm at the inlet and 208 cfm at the restricted portion but yours will probably differ.
SUNY-Buffalo

Professor Gas Can, how would you flow 136 cfm at the inlet of your diffuser, and flow 208 cfm at the restricted portion at the same time? It is impossible to flow more than the other numbers you quoted, so how did you come up with that number? CFM @ inlet = CFM @ restrictor = CFM @ outlet if you are steady state on the bench.

[Drew Price]

I guessed those were velocity, or possibly pressure values. Of course the flow must be the same. Unless you guys know something I don't. I'd love a 50% increase in airmass once it has passsed through the restricting orifice!

Best,
Drew

[Barnaby]

The volumetric flowrate doesn't have to be constant if you have a change in density as long as the mass flowrate stays the same, so at atmospheric conditions at the entrance to the restrictor it has one density and as it passes through the pressure is reduced (by the restrictor)and the air expands to a greater volume, with a lower density but the same mass

[Chris Boyden]

Professor Gas Can, how would you flow 136 cfm at the inlet of your diffuser, and flow 208 cfm at the restricted portion at the same time? It is impossible to flow more than the other numbers you quoted, so how did you come up with that number? CFM @ inlet = CFM @ restrictor = CFM @ outlet if you are steady state on the bench.

I'm not a fluids guy, (I'm just an EE but physics is physics), but don't you need to take the pressure loss at the restricted portion into account? i.e. lower pressure due to higher velocity coupled with higher flow rate = lower flow rate at higher pressure.

The *mass* flow rate at all points must be equal however.

Gas can is talking in volumetric flowrate not mass.

[Scrappy]

Barnaby, are you talking about the change in density due to higher subsonic mach numbers? I forgot about compressibility effects on flows above Mach .3 or so. my fluids class in school always assumed incompressible, isentropic flows, and after a while that seemed to dictate how I think.

Although the fluid density change that comes from higher subsonic Mach number flow isnt negligible from a text book standpoint, I would still like to hear how the 208 cfm number came up. Every choked flow calculation Ive ever done gives you the mass flow rate, and you can derive the volumetric flow rate from that if you assume an air density at a given temperature. If the temperature and density change at the throat of a diffuser so much that you get a number like 208 cfm at the throat, thats pretty wild.

[Professor Gas Can]

Damn, why the hate?
m=pVA
Q=AV

As stated before I got a mass flow rate of 72.6 g/s, and yes, for both portions of the restrictor.

Inlet:
m = (1140 g/m3)(0.00095 m2)(67.2 m/s)
m ~ 73 g/s

Q = AV = (0.00095 m2)(67.2 m/s) = 0.06384 m3/s = 135 cfm

Throat:
m = (740.7 g/m3)(0.000308 m2)(319 m/s)
m ~ 73 g/s

Q = AV = (0.000308 m2)(319 m/s) = 0.0982 m3/s = 208 cfm

These are numbers straight from GT-Power (1D). What are you 3D guys getting? I don't think it's wrong (and are at least in the ball park), as I cross checked it with the choked flow equation. And yes, volumetric flow rate is not mass flow rate....

[Brian Schien]

This is off base from you question but one thing you need to mind on the Aprilia is that it is very loud it has a very low frequency @ 8500 rpm where they due the sound test so you need to pay attention to this and make sure you can get it quiet enough to pass sound at around 11:30 on Friday in Detroit there were three cars with the mythical Aprilia lined up at sound trying to pass you should have seen the stupid looking mufflers these car had on them with pipes welded on at goofy angels trying to send it away from the db meter.

[Drew Price]

..... And yes, volumetric flow rate is not mass flow rate....

You are exactly right, no hate, just a little behind on the fluids too! I would never have guessed that the pressure drop across the orifice would be enough to effect a 50% change in the volumetric flow rate. That's rad.

Back to suspension stuff.

Best,
Drew

[Kemper]

hehehe, seems that fluid dynamics goes a little bit deeper than what I learnt in Physics 1 course... lol

Guys, thanks for all the replies, it gave a good help. Now, sorry being a little bit too stupid, but to find the RPM I want would be something like this:

RPM = Volumetric flow (in cc/min) / ( volume of engine * 2 ) ?

The "origin" of this formula is the straight-forward thinking: if is a 4-stroke engine, every 2 cycles it "sucks" 1 engine volume, if we find how much volume of air comes in one minute, we got how many cycles! =D

It might be too simple, and I know I'm not dealing with densities because I didn't figure it out yet what would be the density of the air on the engine. Remember, I'm EE freshman and did only Physics 1...

aah, by the way, with that formula and 550cc for the aprilia I got a value of 5350RPM. Is this a realistic value? Seems reasonable for an automobile engine, but not for a motorcycle engine that used to go 10k+...

[screwdriver]

You've got 2 cylinders. So you've got to account for that. Replace engine volume by volume/cylinder and you're there (Double your calculated RPM).

You're also forgetting one major ingredient. Fuel.
The amount of fuel injected also reduces the amount of air that fits into the cylinder without compression.

[Wesley]

Eh, it's easier to assume 100% VE.

Remember, for each rotation of the crankshaft, only one cylinder fires. (it takes two rotations to complete a cycle)

[Kemper]

Screwdriver and Wesley
Maybe I didn't express myself too clear or I did forget something, so I will insist on the same question:

Assuming that the engine has 550cc and the cylinders are symmetric, each of them has half of the total volume (225cc), right (Screwdriver's info)? And every cycle just one of them fire, meaning that every two cycles one full engine volume is consumed, right(Wesley's info)?
So:
2 RPMs = 1 volume of engine per minute = 550cc/min

Leading to if we find the maximum volume of air that flows through the restrictor in one minute and divide it by two times the volume of the engine we get the total of RPMs of the choked flow. Am I right?

Just to ask: the density of air after the restrictor and the density of air that goes inside of the cylinder are different? If yes, is there a way to calculate that?

I like this concept of the "consider the fuel too". Does anyone know how much fuel is injected in one cylinder (no need for extremely precise values, just to have an idea)?

Once again, thank you very much guys!

[screwdriver]

The amount of fuel injected is pretty arbitrary and depends mostly on how much you tell your Engine-ECU to inject under the given circumstances. So Wesley is right that it's too complicated.

Your calculation is off again, I think. Shouldn't it be something like <max possible rpm> = <max restrictor throughput> / 225[cc/rpm].

Since that value assumes a continuous flow, it is a very rough estimate. Taking valve timing into the equation the, result will be different.

[Wesley]

So, using the oft-quoted 72.6g/s flow rate and assuming air density to be at atmospheric (1.2kg/m^3) within the engine at 100%VE,

1.2 kg/m^2 = .0012 g/cm^3

[total mass flow] = [cylinder fills per second][displacement per rev][density of air]

72.6 g/s = (RPM/60 s*m^-1) * (225cm^3 * .0012 g/cm^3)

RPM = 16,133 @ theoretical choked flow.

Now, clearly that is a very high estimate. But there are a number of factors that were mentioned previously that make it impossible for the engine to create that kind of flow through the restrictor.

It is on this fact that I disagree with almost every design judge, in that flowbench data is just about useless when it comes to restrictors. An engine is a transient environment. While you can do studies with flowbenches to minimize flow loss through the restrictor, you are never going to see 72 g/s unless you have an infinitely large plenum to create a constant pressure differential. The calculations tell us our F4i should choke at about 14.5k, but in reality it's at about 12k. I'd imagine, similarly, that the Aprilia chokes at somewhere around 13, which, while it is outside the operating range, as you approach mach, your flow losses skyrocket. So you lose power not just at choked flow, but up to it.

[murpia]

If you have access to an accurate, calibrated AFR meter, then one way of measuring air mass flow directly during steady state dyno running is to measure fuel mass flow accurately and multiply by AFR.

I've seen this done by OEMs to measure VE.

Regards, Ian

[BeaverGuy]

Wesley,

Using the equation you have there an F4i would choke at 12,100 RPM which seems to agree with your observation. http://fsae.com/groupee_common/emoticons/icon_wink.gif
I agree that you can't actually reach fully choked flow over a complete engine cylcle. But you will choke your restrictor and see 72g/s over portions of the cycle and as a result VE will drop because MAP will have to decrease. This will occur before you reach the theoretical choke RPM but is a function of many variables and can be mittigated somewhat. I would have to look up the data but I seem to recall reaching 68~70g/s.

[Wesley]

Right, as the pressure waves peak, you'll probably see choked flow, but it will be oscillating madly, and you'll average less than that.

And I guess my math is broken... I blame MS Calc.

[Krautsalat]

Right, as the pressure waves peak, you'll probably see choked flow, but it will be oscillating madly, and you'll average less than that.

The higher the rpm the more even the massflow through the restrictor gets, but you are right it will never reach choked conditions for a complete cycle.

http://img390.imageshack.us/img390/2291/massenstromdrehzahlld6.png

Krautsalat

[Pete M]

Assuming 100% VE is a rather broken assumption, even if you have a 4 cyl. And the less cylinders you have, the worse an assumption it'll be. The VE you end up with will depend heavily on your intake volume, which will tend to smooth out the pulses in engine air demand.

Still it's not a half bad thing to calculate. You can mostly neglect fuel. Your AFR is massive, 13:1 or so and fuel is more dense so it takes up even less as a volume ratio. Your other inaccuracies (pulses, etc) will swamp any effect fuel will have.