Exhaust headers

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

Reply to
MitchAlsup
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also the density of the gas and to some extent, its viscosity.

what about the momentum of the inlet gas? you have overlapping valve timing don't you?

what equations are you using????????????????????????????

Reply to
jim beam

SoSm = 331.3*SQRT( 1+( t /273.13)) // from Wikipedia "speed of sound" SoSf = SoSm *39.36/12 // convert metre/s to feet/s at 59dF SoSf = 1116 f/s

time = length / speed

Temperatures/pressures from "NASCAR restrictor plate exhaust manifold design strategies"; Dollhoph

Lengths and ODs from actual header measurements.

Mitch

Reply to
MitchAlsup

does that explain your objective? the first post didn't seem to state one either.

as for calculations, rather than reinvent the wheel, and i'm presuming your objective is to build some headers, why don't you just use a source like this?

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if you want to derive from first principles, you're going to need to look at and include a lot more than simple speed of sound values. and if you want to go second order, pressures, flow velocities, densities, momentum, are all dynamic quantities, not static like the first order math presumes.

bottom line, there's still some empirical factoring in the header game. if someone else has done this empirical stuff for you, you'd have to have a damned good reason not to use it.

Reply to
jim beam

The objective is to understand the physics of the problem space.

I have been to that site and various others (hundreds actually). But none of them explain how the pressure pulse takes so much time to reflect off the points of expansion and return at the proper moment in time. Everyone indicates that the sonic wave runs up and down the pipe at the SoS, but nobody expalins how this process takes longer than the simple SoS calculation (by significantly more than a factor of 2).

Is the SoS slower in a pipe like the SoL is slower in a transmission line?

And yes, I know everythinig is in dynamic convulsion while all this is going on.

Mitch

Reply to
MitchAlsup

in order to understand a problem, you have to first grasp what you don't understand. doesn't seem like you're even at that stage yet.

maybe they're presuming the reader understands the obvious - this is not a static system, nor simple.

because it's neither static nor simple. as said before, velocity changes, density changes, temperature changes, momentum changes...

not when it's static, but when it's dynamic, yes. the reason you're not finding this stuff stated in terms of simple formulae is because the real stuff in not simple. if you're trying to be real world, you have two choices - the empirical route, with a bit of simple math to guide you along the way, or the "Hard Math" route, and you'd need to be pretty danged good as gas flow dynamics and computer modeling for that.

then you shouldn't be surprised that a simple one-dimensional static is not giving you the answers.

seriously, your best bets are either mapping out some variables empirically like the ancients did, and trying to add a bit of simple math, or getting a phd constructing your computer models. mit is where this stuff originated - go there.

Reply to
jim beam

Found the answer on page 5 of:

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Mitch

Reply to
MitchAlsup

You are only thinking about the next wave. Think of two or three waves later.

Reply to
Steve Austin

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