Do FSAE engines actually reach choked flow?

[RacesWithWolves]

I have come across several references from different FSAE teams claiming that the velocity of the air flowing through the infamous 20mm restrictor will reach the speed of sound at some RPM in their operable range. From my research, 15,000 RPM seems to be the absolute maximum RPM for any FSAE engine (please correct me if I am wrong).

My goal was to find out, at what RPM will our 600cc engine reach choked flow. To my surprise, I found that flow will not be choked even at 15,000 RPM.

I am hoping someone can either confirm my calculations or explain what I did wrong here. I am attempting to calculate the average velocity of the air flowing through the 20mm intake air restrictor when a 600cc engine (4 stroke) is operating at 15,000 RPM.


Engine Displacement = 600 cm3

Volumetric Flow Rate @ 15,000 RPM = (600 cm3)*(15,000/2) = 4.5e6 cm3/min

Cross-sectional Area of Restrictor = 3.14159*12 = 3.14159 cm2

Velocity of Air Through Restrictor = (4.5e6 cm3/min)/(3.14159 cm2) = 1.432395e6 cm/min

Velocity converted to m/sec = (1.432395e6 cm/min)*(1/100)*(1/60) = 238.7 m/sec


The calculated average velocity of 238.7 m/sec is much less than the average speed of sound (roughly 343 m/sec). Assuming the engine will never operate above 15,000 RPM, it can be concluded that: a naturally aspirated, 600cc, 4-stroke engine with a 20mm intake air restrictor will never reach choked flow.


Are there any variables I did not account for? I know that the pressure drop through the restrictor can be ignored for this calculation due to the relationship between the bulk modulus of elasticity of the air, density and the speed of sound. In simpler terms, the pressure drop will not decrease the relative speed of sound at the restrictor; which would make it easier to achieve choked flow.

[RacesWithWolves]

I should also add that the volumetric flow rate of 4.5e6 cm3/min is assuming a V.E. of 100%. In reality, as the mach index through the restrictor increases past .6 (which will happen around 11-12000 RPM), the V.E. of the engine will begin to drop off significantly; decreasing the volumetric flow rate.

I guess this is common sense to most of you but, essentially the restrictor makes the engine operate as if it were a smaller displacement. This will happen no matter what your engines displacement is. However, the larger your displacement, the larger % drop in V.E. So a 450cc engine may operate as if it were 400cc while a 600cc engine with the same restriction would operate as if it were 500cc. I did not do the math on those numbers, they are just an example, so don't reference them.

This begs the question, how do forced induction teams match their turbos to their engines? I'd be willing to bet that most are using a turbo that is too large. But that is a different issue that doesn't apply to my original question. /end tangent

[Jan_Dressler]

Engine Displacement = 600 cm3

Volumetric Flow Rate @ 15,000 RPM = (600 cm3)*(15,000/2) = 4.5e6 cm3/min

Cross-sectional Area of Restrictor = 3.14159*12 = 3.14159 cm2

Velocity of Air Through Restrictor = (4.5e6 cm3/min)/(3.14159 cm2) = 1.432395e6 cm/min

Velocity converted to m/sec = (1.432395e6 cm/min)*(1/100)*(1/60) = 238.7 m/sec


Are there any variables I did not account for?
http://en.wikipedia.org/wiki/Choked_flow


I guess this is common sense to most of you but, essentially the restrictor makes the engine operate as if it were a smaller displacement. This will happen no matter what your engines displacement is. However, the larger your displacement, the larger % drop in V.E. So a 450cc engine may operate as if it were 400cc while a 600cc engine with the same restriction would operate as if it were 500cc.
Hm. At all engine speeds?

[RacesWithWolves]

http://en.wikipedia.org/wiki/Choked_flow

What section of this page are you referring me to? The minimum pressure ratio section? If I understand it correctly, choked flow should occur IF the pressure through the restrictor reaches about 50 kPa.



Hm. At all engine speeds?

Yes and no. The restrictor is more limiting at high RPM than low RPM but, it still has an effect at all engine speeds.

[Racer-X]

We reach chocked flow at around 10k I believe. There are a few variables to look at and I would say the easiest way to do this is use an online calculator to find the max flow rate thought the 20mm restrictor. Then do your rpm/2 * discplacement * VE calc.

Look at the dyno results, most 4 cylinder teams peak somewhere around 80-85 crank horsepower and hold that for a few thousand RPM. That's chocked flow.

[tromoly]

The thing to remember is that your total displacement is 600cc, but that doesn't mean there is constant draw on the intake. As I'm guessing you're running an inline-4 engine, the intake pulses are 180-degrees apart, with the actual intake pulses varying through the piston stroke. So while at a constant intake draw the velocity is low enough to never be choked, it's the impulses that cause the air velocity to spike and cause the airflow to choke.

I don't have any actual data, this is all from observing last year's team and drawing a conclusion, if anything is wrong please point it out and it'll be noted.

[RacesWithWolves]

We reach chocked flow at around 10k I believe. There are a few variables to look at and I would say the easiest way to do this is use an online calculator to find the max flow rate thought the 20mm restrictor. Then do your rpm/2 * discplacement * VE calc.

I'm getting .0075 kg/s or 9.92 lb/min for the max mass flow. And that won't occur until >15,000 RPM.

[RacesWithWolves]

The thing to remember is that your total displacement is 600cc, but that doesn't mean there is constant draw on the intake. As I'm guessing you're running an inline-4 engine, the intake pulses are 180-degrees apart, with the actual intake pulses varying through the piston stroke. So while at a constant intake draw the velocity is low enough to never be choked, it's the impulses that cause the air velocity to spike and cause the airflow to choke.

I don't have any actual data, this is all from observing last year's team and drawing a conclusion, if anything is wrong please point it out and it'll be noted.

That might be true if the intake pulses were actually 180 degrees apart. But most stock cam profiles have overlap between cylinders. Also, a well designed manifold should greatly smooth out the pulses on a 4 cylinder engine.

[RacesWithWolves]

Hm. At all engine speeds?


I did some quick calculations for a 600cc engine. The "Effective Displacement" represents the displacement that the engine performs as due to the mass flow limiting of the restrictor. I was surprised to see that the results are very linear.

RPM Effective Displacement (cc)
2000..........592
4000..........556
6000..........521
8000..........486
10000..........450
12000..........415
14000..........380

Again these numbers are calculated for an extremely ideal situation where V.E. is 100% (if unrestricted).

[RenM]

Your calculation is wrong. What you didnt consider is, that the density of the air decreases as the flow is accelerated through the nozzle (see Bernoulli). This increases the volume flow and flow speed at a given mass flow.
You need to calculate the choked mass flow with a formula describing the flow through a nozzle.

If you do that, you will see that a 600cc engine with a VE of 1 will choke at around 10.500 and this can also be seen in reality.

You mentioned the influence of the restrictor on your VE:
The VE is hardly influenced by the restrictor before you reach choked mass flow. Your gas exchange is much more important and a VE greater then 1 can be achieved.

[RacesWithWolves]

Your calculation is wrong. What you didnt consider is, that the density of the air decreases as the flow is accelerated through the nozzle (see Bernoulli). This increases the volume flow and flow speed at a given mass flow.
You need to calculate the choked mass flow with a formula describing the flow through a nozzle.

If you do that, you will see that a 600cc engine with a VE of 1 will choke at around 10.500 and this can also be seen in reality.

You mentioned the influence of the restrictor on your VE:
The VE is hardly influenced by the restrictor before you reach choked mass flow. Your gas exchange is much more important and a VE greater then 1 can be achieved.

I am aware of the decrease in density through the restrictor, but I am confused as to how that increases the volume flow rate when it is defined by fixed geometry. Could you please provide an example calculation to show choked flow at 10500 RPM?

And a decrease in density definitely decreases V.E. the same way that an increase in density (forced induction) increases V.E.

[RenM]

A decrease in density INcreases your volume flow for a given mass flow.
With increased volume flow and fixed flow area the flow speed is increased.

Increased flow speed means that choked flow is reached at a lower mass flow.

At the moment I am at work, so i dont have the time to write down the calculation, but if you search for "choked flow" in Wikipedia you will find the formula you need to calculate the mass flow for a nozzle flow.

[RacesWithWolves]

A decrease in density INcreases your volume flow for a given mass flow.
With increased volume flow and fixed flow area the flow speed is increased.

Increased flow speed means that choked flow is reached at a lower mass flow.

At the moment I am at work, so i dont have the time to write down the calculation, but if you search for "choked flow" in Wikipedia you will find the formula you need to calculate the mass flow for a nozzle flow.

Sorry that was a mistake I meant to say increase.

But the thing I still don't understand is how a naturally aspirated engine can flow a greater volume than it's (displacement * RPM / 2). The volume of the system is defined by the physical geometry of the plenum, restrictor nozzle, runners, port size, engine, etc. I don't understand how volume flow rate is the dependent variable at a given RPM.

As RPM and volume flow increase, mass flow approaches a constant rate. So the reason it reaches that constant rate is because, at some point, any further increase in volume flow (increased RPM) will cause a proportional decrease in density. The density drop is the result of the air flowing through the nozzle. If it were the other way around, a venturi nozzle would be able to flow air by itself. Volume flow is an independent variable, and density is a dependent variable.

Please forgive me if there is something I am still not understanding.

[Mbirt]

I guess this is common sense to most of you but, essentially the restrictor makes the engine operate as if it were a smaller displacement. This will happen no matter what your engines displacement is. However, the larger your displacement, the larger % drop in V.E. So a 450cc engine may operate as if it were 400cc while a 600cc engine with the same restriction would operate as if it were 500cc. I did not do the math on those numbers, they are just an example, so don't reference them.

This begs the question, how do forced induction teams match their turbos to their engines? I'd be willing to bet that most are using a turbo that is too large. But that is a different issue that doesn't apply to my original question. /end tangentYou should drop the effective displacement terminology and explain the situation with VE instead to prevent confusion. The restrictor goes into choke, VE begins to decrease, torque decreases proportional to VE, and power remains constant with constant airflow if not slightly decreasing due to frictional losses with increasing speed.

Speaking from experience, engines of less displacement can behave as unrestricted and make greater than stock power naturally aspirated with proper intake design and an FSAE-spec restrictor. It is not unreasonable to expect 60 hp/35 ft*lb from a 450 cc single and 80 hp from a Genesis 80fi 500cc inline twin.

The two compressors offered for sponsorship by Honeywell (MGT1238Z and GT15V) are quite efficient in the 60-90 hp range and the turbines are small enough that boost creep can be an issue on single and twin-cylinder engines in our displacement range.

[RacesWithWolves]

You should drop the effective displacement terminology and explain the situation with VE instead to prevent confusion. The restrictor goes into choke, VE begins to decrease, torque decreases proportional to VE, and power remains constant with constant airflow if not slightly decreasing due to frictional losses with increasing speed.

I thought it made it easier to explain why a turbo matched to an unrestricted 600cc engine is too big for a restricted 600cc engine. Sorry if I confused anyone.

The restrictor causes VE to decrease sharply before it reaches choked flow. Once the mach index reaches .6, that is where VE begins to sharply decrease. According to my calculations, that will happen on a NA 600cc engine right around 10500 RPM. Which explains why so many teams think they reach choked flow at that RPM. The sharp drop in VE will cause power to level off and begin decreasing slightly; just as you described above. So, while it is true that the restrictor begins to decrease power output at that RPM, truly choked flow is never reached.

[RacesWithWolves]

Also, wouldn't RPM be limited by choked flow? After all, that's exactly why your engine won't rev up when idling. The almost closed throttle (a variable restrictor) limits mass flow, in turn limiting RPM.

[BeaverGuy]

I am aware of the decrease in density through the restrictor, but I am confused as to how that increases the volume flow rate when it is defined by fixed geometry. Could you please provide an example calculation to show choked flow at 10500 RPM?

And a decrease in density definitely decreases V.E. the same way that an increase in density (forced induction) increases V.E.

With a good design the decrease in density is only at the throat of the restrictor, meaning you are still intaking air at Atmospheric pressure into the cylinders. You calculated ~75g/s as the choked mass flow, what RPM will this occur at in a 600cc engine with intake conditions at atmospheric pressure and 20oC?

[RacesWithWolves]

With a good design the decrease in density is only at the throat of the restrictor, meaning you are still intaking air at Atmospheric pressure into the cylinders. You calculated ~75g/s as the choked mass flow, what RPM will this occur at in a 600cc engine with intake conditions at atmospheric pressure and 20oC?

Nowhere in the operable RPM range.

[billywight]

Nowhere in the operable RPM range.

Try again...

[RenM]

You seem to confuse quite a bit and i was not specific enough.

The decrease in density at the restrictor throat increases the volume flow rate at the restrictor throat. Thus the decrease in density leads to a chocking at lower mass flows compared to a calculation with atmospheric pressure like you did.

How do you come up with this 0.6 mach? The restrictor chokes at mach 1 and a good designed restrictor difusor can regain most of the pressure loss that occurs before the restrictor actually chokes the mass flow. -> A good restrictor only affects your engine performance when your mass flow reaches the choke massflow of the restrictor.
And this does happen at 10.500 to 11.000 with a VE of 1 for a 600cc engine. Recheck your calculations! At this point the flow reaches a velocity of mach 1 at the restrictor throat and you reached the critical pressure difference. A further increase in overall volume flow is not possible! Please (re)read some literature about nozzle flow and if its just the Wikipedia article on "choked flow" which includes the correct formula to calculate the mass flow through a nozzle.

As to the VE of the engine. The VE is always based on atmospheric pressure. So of course the VE is a variable dependent on the charge density, which is dependent on the gas exchange of the engine. Pressure losses decrease your VE and charge effects from your intake runners or a compressor increase your VE.

[RacesWithWolves]

You seem to confuse quite a bit and i was not specific enough.

The decrease in density at the restrictor throat increases the volume flow rate at the restrictor throat. Thus the decrease in density leads to a chocking at lower mass flows compared to a calculation with atmospheric pressure like you did.

How do you come up with this 0.6 mach? The restrictor chokes at mach 1 and a good designed restrictor difusor can regain most of the pressure loss that occurs before the restrictor actually chokes the mass flow. -> A good restrictor only affects your engine performance when your mass flow reaches the choke massflow of the restrictor.
And this does happen at 10.500 to 11.000 with a VE of 1 for a 600cc engine. Recheck your calculations! At this point the flow reaches a velocity of mach 1 at the restrictor throat and you reached the critical pressure difference. A further increase in overall volume flow is not possible! Please (re)read some literature about nozzle flow and if its just the Wikipedia article on "choked flow" which includes the correct formula to calculate the mass flow through a nozzle.

As to the VE of the engine. The VE is always based on atmospheric pressure. So of course the VE is a variable dependent on the charge density, which is dependent on the gas exchange of the engine. Pressure losses decrease your VE and charge effects from your intake runners or a compressor increase your VE.

Thanks for the clarification, I am starting to understand now. I will do some more reading and then redo my calculations.

[Jan_Dressler]

What section of this page are you referring me to? The minimum pressure ratio section? If I understand it correctly, choked flow should occur IF the pressure through the restrictor reaches about 50 kPa.
Sorry that my first answer was a bit short, but it seems you are on the right track now :)

By the way, if you are interested, there are some actual dyno measurements of different cars on the same dyno available here: http://www.formulastudent.de/fileadmin/user_upload/all/2008/Results/FSG08_Dyno_Results.xls

Jan

[mech5496]

Slightly offtopic, but I have a (possibly stupid) question. Please forgive my ignorance as I am by no means an engine guy, I just like to learn stuff.


Assuming a turbocharged engine while its' restrictor is chocked. The fact that is chocked, should mean (according to Wiki) a pressure ratio of 0.528 across the restrictor, thus meaning that the turbocharger inlet pressure is only 7.76psi. Now, assuming a (relatively high for a GT12) turbo pressure ratio of 2.5, you end up with 19.4psi on your intake (or 4.7psi of boost...


Possibility is that you regain some of the pressure before the turbocharger inlet (like you would in an NA engine plenum) but is this the case?

[Jay Lawrence]

mech5496, not sure if that pressure ratio is correct, especially for the entire choked RPM range. Our results showed a maximum manifold pressure of about 220kPa abs. (about 17psi boost pressure) at something like 7000RPM using a GT15. The compressor inducer is exposed to ~atmospheric pressure a little bit prior to choking (assuming a decent intake path and restrictor), and as you choke and as engine speed increases you reduce that pressure thus reducing your pressure ratio but maintaining ~0.07kg/s mass flow. Thus the turbo helps you to choke for the largest RPM range possible (greatest torque magnitudes and spread). Towards the end of our RPM range, we were seeing ~atmospheric pressure in the plenum, indicating that by that point the choked restrictor is having the effect you describe.

[mech5496]

Jay, thanks for your clarification. I understand that mass flow rate in chocked flow remains constant at about 71gr/sec, but I would like to see what happens and if teams get past the surge line in their turbochargers. The original thought-question in my head was how I could use an electric motor coupled to a compressor side of a FSAE sized turbocharger and how the massflow/boost map would be with respect to motor RPM.

[Jay Lawrence]

If you are getting into the surge area of the compressor then you are not at choked flow (or you have chosen the wrong compressor). If you were to drive the compressor with an electric motor you would have to heavily gear the motor or you wouldn't reach sufficient speed. The best bet for that application would probably be to make it a fixed speed compressor (rather than using some kind of VFD on the electric motor) attached to a fixed speed engine driving a CVT. If you were to use it as a generator you would probably just create too much "backpressure" for it to be useful.

[Dan Radulescu]

Hi

I did my calculations on the choke flow.
I did it by 2 methods, from different sources.

I the theoretical engine airflow demand using the equation
ThFlow= Displacement x RPM x VE( assumed =1 ) / Engine Stroke ( 2 ) and converting it to m^3/sec


Method 1
by Fundamentals of Fluid Mechanics 5th - Bruce R. Munson, Donald F. Young, Theodore H. Okiishi

Initial conditions ISA
p0=101325 Pa
t0=15 deg Celsius
rho0= 1.1839 kg/m^3

I ended up with a Mass Flow Rate of 0.075 Kg/s in the following critical conditions
cP= 53528.152 Pa
cT=240.125 deg Kelvin
cRho= 0.777 Kg/m^3

If I calculate Volume flow rate as VFL=MFL/density
using ambiental air density I get 0.062 m^3/s
using critical air density I get 0.098 m^3/s


Method 2
using an 2 euqations found in an article entitled
Improvement of Intake Restrictor Performance for a Formula SAE Race Car through 1D & Coupled 1D/3D Analysis Methods
by Mark Claywell and Donald Horkheimer from Univeristy of Minnesota

Using an equation for volume flowrate at choking point I get 0.063 m^3/s


In the case I get 0.063 m^3/sec I will reach choked flow at around 12600 RPM
In the case I get 0.099 m^3/sec I get it nowhere near the operable RPM

Where am I doing wrong in here? Should I take the ambiental air density when calculating the Volume flow rate ? If that's so I will reach choke flow at around 12600 RPM not 10500.

I attached a download link with my calculus ( Excel & Mathcad ) for both ways, available for 7 days starting 11 December 2013.
http://we.tl/R405Tf0r5i

Thank you in advance!

[Simon Dingle]

Hi Dan,

Try converting your "theoretical engine airflow demand" into mass flow rate and comparing that to Method 1. I'm afraid I'm not familiar with Method 2, but I've used Method 1 and got an almost identical answer to you.

A couple of things to be aware of when doing this sort of analysis:
1. The volumetric efficiency of an engine can exceed 1 if the intake manifold is designed correctly. (I'm assuming that you're using an R6/CBR600 or similar)
2. The calculation you describe in Method 1 is for finding the isentropic mass flow rate. In reality any restrictor that you make will not actually achieve this flow rate. One of our team members measured the isentropic efficiency of two throttle/restrictor/diffuser assemblies and found them both to be between 80 and 90%.

I hope that helps