Restrictors And Plenums And Sometimes Turbos
1. Start from first principles with the restrictor.
The more air inside a cylinder, the more fuel can be efficiently combusted inside the cylinder.
Therefore, the more air inside a cylinder, the more potential torque per combustion pulse.
The more rpm, the more combustion pulses, the more power.
This is why flow benches, physical and virtual, are so important for IC engines.
Warning: Some cylinder head changes that increase flow might ruin in-cylinder mixing.
2. The maximum mass air flow through a restrictor is related to:
cross sectional area
air density
pressure differential
coefficient of discharge.
The air will not go through the smallest area faster than the speed of sound.
(A little less actually, because of slower speed near the surface of the restrictor vs. sonic in the middle.)
The Wikipedia article on critical flow is shockingly good and detailed.
3. Engine power is limited by the flow through the restrictor at the speed of sound.
You can look up different coefficients of discharge, combine with the stoichiometric (air::fuel) ratio, and get a good start at this point with theoretical maximum engine power.
If your team currently has a low quality design, like a flat plate, you can make a big improvement in available airflow very easily.
Try to figure out how much space to leave behind a wide-open throttle for the airflow to be as steady as possible.
Do your own math and analysis like this team to determine optimal converging and diverging restrictor angles:
http://www.iaeng.org/publication/WCE2013/WCE2013_pp1847-1851.pdf
Take a look at their references too.
If you are keeping the same engine, and go from a low coefficient of discharge to a higher one, you should be able to easily show that on a dyno or from in-gear acceleration times.
And it should be easy to compare to theoretical power improvements.
4. Everything has been steady-state before this.
With wide open throttle, ambient pressure (or maybe some ram-air effect) is on the inlet side of the restrictor.
When the intake valve opens, the intake stroke reduces the pressure in the intake plenum, on the outlet side of the restrictor.
Consider piston speed: airflow into the cylinder starts slow, then goes faster.
Consider momentum: airflow into the cylinder gets fast, and stays pretty fast until the intake valve closes.
Integrating, the pressure behind the restrictor drops slowly, then quickly, then hits a minimum.
When the pressure differential is large enough, airflow through the restrictor cannot flow any faster.
Choked flow could start off as part of an intake stroke, then grow to the length of the entire intake stroke.
Above that rpm, the restrictor flow rate stays the same, but the intake stroke takes less time, so less air goes into the cylinder, for less torque.
But, based on flow rate * stoichiometric ratio, peak power can theoretically be maintained as rpm continues to increase.
5. the purpose of the intake plenum is to smooth out the pressure differential.
5a. And make it possible for other engines to compete with 4-cylinders.
Ideally, the intake plenum damps the low pressure pulses into a more continuous standing wave.
In addition to the effects of mass flow, the closing intake valve bounces the fast-moving intake air backwards.
With no plenum or too small a plenum, the high pressure could reduce or make airflow backwards through the restrictor.
With no plenum or too small a plenum, engines with fewer than 4 cylinders could only reach choked flow during the intake stroke.
3 cylinder: only 75% of 4+cylinder airflow and power. 2 cylinder: 50%. Single cylinder 25%.
Plenum volume causes restrictor flow to continue even when the intake valve is closed, because pressure is still below ambient.
My knowledge is running out, so it is conceivable to me that the pressure in even a single cylinder plenum could stay low enough for the entire 720 degrees that the restrictor stays sonic.
And maximum mass air flow reaches the plenum, and therefore the cylinder.
^^That may be far from what is possible.
6. Plenum volume affects restrictor flow and throttle response.
In general, larger plenum volumes have more damping, therefore more steadier flow and more power.
But larger plenums require more air volume for a given pressure change, resulting in slower throttle response.
I don’t know if a response time spreadsheet comparing throttle position flowrates vs. plenum volumes is useful.
Because I haven’t done it myself, nor have I seen a team present this in design.
To potentially include the cylinder(s), the necessary systems math about about a bucket flowing into a bucket flowing into one or more buckets is usually taught in third year engineering.
This topic is a rare time when it is appropriate to move quickly from hand calculations to powerful computer software.
7. There is lots of good information out there.
Look at all of the event handbooks, listing displacement, engine, and power.
Scour the library and the internet.
My interpretation is:
Their plenum sizing and plenum response analysis is solid.
The variable aspect makes a nearly unnoticeable difference and is much more trouble than it was worth.
RPM and throttle change too fast for most systems to keep up or for any meaningful difference to be detected.
Source: My team looked into this ages ago.
8. Arguments for forced induction:
Steadier low pressure behind restrictor due to compressor intake (especially for single cylinders).
Potential for the same peak power for a smaller displacement and lighter engine.
Potentially earlier critical flow, maintaining critical flow over a larger rpm range (approximating constant power).
Much quieter exhaust with a turbo.
9. Arguments against forced induction:
System mass
System complexity
Strength needed to keep pressurized plenum from cracking
Pressure vessels should not have flat sides or sharp corners
Availability of appropriately sized components
Complexity of drivability tuning
Very high power consumption of positive displacement superchargers
Lots of heat overwhelming cooling system and exhaust components to cause engine failure
OEM components not designed for higher loads
Feedback properties of turbocharging make it very easy to for extra heat or forces to blow up an engine.
10. Myths about Forced Induction:
10a. FALSE: Plenum volume and runner length do not matter for turbocharged or supercharged engines.
If you have no budget or knowledge, more boost does equal more power. Stop turning the knob before parts fail.
Turbocharged engines are very responsive to Helmholtz intake and exhaust length, just like non-turbocharged engines.
There are some pressure & temperature effects on the intake, but not enough to really change our test runner length range.
The compressor should have a damping effect on intake pressure waves, potentially reducing the influence of plenum volume.
The plenum response math should be similar to the proposed calculation at the end of part 6.
10b. Pedantic No: Turbocharging increases efficiency.
There is no automatic increase in Brake Specific Fuel Consumption (BSFC).
Turbochargers use exhaust pressure and kinetic energy to force more air into cylinders during intake.
There can be savings by reducing intake pumping losses.
But, the point of more air in a cylinder is burning more fuel for more power.
And the air is usually hotter, which doesn’t help, and may take even more fuel to cool and prevent detonation.
There are potential losses due to increased exhaust backpressure.
The gains of an Atkinson/Miller cycle are generally larger.
Simulates having a larger expansion ratio than compression ratio.
Super high pumping losses, pulling air in, then forcing it back out before closing the intake valve late.
Less air, less fuel, less peak power, more expansion, higher efficiency.
The main efficiency gains from turbocharging are from allowing a smaller displacement engine to make higher power for brief periods.
Smaller displacement should lead to mass and frictional savings.
Efficiency at full power may or may not be better than a larger displacement engine.
There is an argument for turbo-compounding: exhaust turbine mechanically connected to drive the crankshaft.
And an argument for an exhaust turbine driving an electric generator rather than using a wastegate.
10c. Qualified Yes: Exhaust turbines use energy from the exhaust.
A precise way of expressing this is: energy from the pressure and volume inside the cylinder.
Exhaust turbines do not convert heat.
Even if it says MGU-Heat on the side, it’s a pressure device. Think momentum and expansion.
The exhaust from inlet to outlet of the turbine is not substantially cooler, it is substantially lower pressure.
I doubt there is a useful pressure increase due to remaining gas in the runners heating up in front of the exhaust pulse.
Combustion continuing in the exhaust pulse is incredibly inefficient.
