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.