Diesel exhaust flow calculations

[Greg Roles]

OK. I'm getting into some serious pondering about fluid dynamics and ideal exhaust pipe sizes for the TDI. I'd love some input, especially from you engineer types!

It seems there is very little info on exhaust pipe sizes outside V8 headers let alone for diesels. Before you read on, forget everything you relate to petrol exhausts, and realise that the diesel engine flows MUCH greater quantities of gas for a similar hp output to a gasser. The volumetric efficiency of a diesel is much higher than a throttled petrol engine and thus much bigger exhausts are generally recommended.

Now about all I can find anywhere diesel specific is truck information. Donaldson.com has some great info, and below are the screen captures of their CFM calculation for intake and exhaust flows. Using them with max values at 4500rpm, I get about 500CFM intake and towards 1200CFM exhaust! That seems nuts even to me! For sure it's "ideal' has no bends, muffs etc, but I'm after a figure of some sort! If indeed my TDi can flow about 1000CFM at max RPM, what sort of pipe diameter is ideal for Golf length? I'm aware there's too big, just as there is too small.

Basically I'm wondering if the stock GT TDI system at 2.5" for 170hp will be way too small at 250hp plus. Seems likely. I'm thinking 3" which has a much bigger cross section. Again, don't bother telling me what Skylines etc use, I have done a lot of reading in the turbo scene there, but it's a totally different kettle of fish.

http://www.vwwatercooled.com.au/forums/images/imported/2010/03/donaldson1-1.jpg

http://www.vwwatercooled.com.au/forums/images/imported/2010/03/donaldson2-1.jpg



Here's the full link for anyone who is interested, but it's a BIG pdf and takes time to download.
http://www.donaldson.com/en/exhaust/support/datalibrary/061237.pdf

[gldgti]

i dunno how many times i've posted this link:

www.vwdiesel.net

have a look over there cog. look in both the TDI and IDI sections, as both are home to some serious diesel tuners.

In the IDI scene, the *benchmark* performance figures are about 220hp for the 1.6l IDI engine and 300hp for the 1.9l IDI engine. I would say the most common exhaust diameter would be 2.5" (no mufflers), closely followed by 3". The big power guys running 200+hp are usually running 3" pipes.

From an engineers perspective, and being a long time hands dirty car enthusiast, I would say in your case you would be smart to just go to the largest pipe size that will happily go under the vehicle - I would guess thats 3". 90% of the time you wont be at max exhaust flow anyway - being a DD rather than a drag racer....

In my experience with modifying stock turbo-diesels, you will barely notice the difference with modifying the exhaust to overall power figures (although the DPF delete will surely help quite a lot). When you will really notice the difference is if you ever change to a larger exhaust side turbo - as you know, where a lot of the restriction is - and you just go "holy crap".

Anyway i guess thats just a long winded way of saying go 3"

[gldgti]

OK... in response to the actualy materila you posted Cog, what can we say?

if we look at your chart at the top, we see that recommended maximum exhaust "backpressure" (which is simply pressure evident immediately after the turbine, and, i suspect, in a 'static well' (i.e measure the pressure in a pocket of 'still' gas), shoudl be 3" mercury max.

lets say you want to go for half that, at 1.5"Hg.

now, we'll calculate a nominal CFM value (and so I can check how you've got yours).

we will assume the volumetric eff constant to be 2.5 (a VERY turbo'd diesel). this number actually comes from the "pressure ratio" x VE. if the actual VE is about 0.8, and pressure ratio is about 2.5 (boost about 22psi), then that ve number would be 2. But, we'll give it a bit more for when you turn up the boost. Displacement in CI is about 122. so we will say that at 5000rpm

CFM = 2.5 x 5000 x 122 / 3456 = 441CFM

to make that into exhaust flow, from the formula on the chart we have

Icfm x (1200 + 460)/540 = 1355CFM

The reason I have put 1200 in the calc instead of 1000, is because Cog has already measured his EGT's and it is fair to say that under high load this is a much more accurate value (I also see these tems in my diesel).

So there you go, we are flowing 1355CFM of exhaust gas at 1200F. What pipe size do we need for an ideal 1.5"Hg exhaust presure?
using
http://www.pressure-drop.com/Online-Calculator/index.html

and plugging in some nominal values such as a predicted gas density of 0.4kg/m3, dynamic viscosity of about 0.34kgmsx10^-6, roughness of 0.3mm (pretty dirty) ,adn length of 7m (because we assume a 90degree bend adds roughly a meter, and there are a couple of them - hey, this is fluids people!)

a 3" (76mm) pipe will give a pressure drop of 0.09bar or 2.7"Hg
a 3.5" (89mm) pipe will give a pressure drop of just 1.2"Hg.

So there ya go Cog, ideally you want a little bigger than 3", but 3" will probably do. :-D