There is a little computation that I can't quite wrap my head around with respect to the design of exhaust headers. So, allow me a little background to set up the question I have.
Headers attempt to align two different gas phenomonoms inorder to augment engine performance. One is is the pressure wave that runs down the primary header pipe at the local speed of sound and reflects off of changes in the primary pipe diameter. The other is the momentum of a gas moving at a significant speed (wanting to keep moving at the same speed).
The momentum part is goverened by the piston speed and the area ratio between the bore and the primary header pipe. At the tuned RPM, one want the gas flow speed to be in the neighborhood of 240-260 fps. As the piston decelerates nearing TDC, the momentum of the moving gas continues to pull residual gas from the cyclinder.
The pressure wave part is where I can't quite get figured out.
Just before the exhaust valve opens, the cyclinder contains about 70 PSI of pressure, and the primary pipe contains a gas around 500dF that is not moving. As the exhaust valve opens, this pressure pushes a pressure wave into the primary pipe which travels down the primary at the local speed of sound (about 1500 fps at 500dF). When the pressure pusle reaches the (first) merge-collector it sees a larger area (and volume). This creates a negative pulse that travels back up the primary pipe (and also creates a positive pulse that travels back up the other primary pipes.) This negative pressure wave will extract residual gas from the cylinder and if the intake valve is open will start drawing in fresh mixture before the piston starts downward.
As the pressure wave traveled down the primary the previously exhausted gas is not moving and close to 500dF. As the reflection travels back up the primary it passes through a gas flowing outward at
250 fps and at 900dF. So the local speed of sound while passing back up should be 1800 - 250 = 1550 fps.The exhaust headers (factory) on my car are of 4-2-1 (tri-Y) with
1.55" * 19" primaries and 1.88" * 6" secondaries, and a 2.2" * 15" expansion chamber (followed by cats and the rest of the exhaust.)When I run the pressure wave equations for this primary pipe, it should take 1.28 milliseconds for the pressure wave to run down the primary pipe (and the 3" inside the head to the back side of the vavles). It should take another 1.16ms for the pressure wave to run back up the primary pipe; for a total time of 2.44 ms.
{Using the expansion chamber (after the second collector) as the point of reflection only ups this to 3.22 ms.}
At the peak TQ RPM of this engine (6,000) it takes 10 ms for a 360 degree revolution and 6.56 ms from exhaust valve open (56 dBBDC) to TDC. At peak HP of this engine (8250 RPM) it takes 7.27 ms for a rev, and 4.77ms from EVO to TDC.
So both pressure waves needs to be traveling about 2.4X slower than the SoS at peak TQ in order to arrive back at the exhaust valve when the piston is near TDC, and about 1.9X slower at peak HP.
So, where have I screwed up the SoS and pressure wave computations?
Thanks in advance,
Mitch