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# Exhaust Back Pressure Calculations

## Exhaust Back Pressure Calculations

(OP)
Hello Everyone! I've been reading these forums a lot lately and they have been extremely helpful! I can already think of a few individuals who might know this topic in depth.

I keep hearing at work that the back pressure in an aftertreatment system is not additive. In this particular example, there is a diesel oxidation catalyst, a diesel particulate filter, multiple elbows, reducers, straight runs, and a selective catalytic reduction system. One way to calculate the pressure drop for the system would be to add the pressure drop of each individual component, however I have been told (but the topic not sufficiently explained) that with a DPF, it is the "dominant portion of the system" and as such the previous method does not apply. I then hear, "in our experience, we see a" certain pressure drop in addition to the DPF, which does not correlate with the sum previously mentioned. I've been trying to wrap my head around why. I've come up with a couple of explanations, none of which seems to satisfy my curiosity. In a system without a DPF, we would simply add the pressure loss of the DOC, piping, and SCR system. Why then with a DPF would we not follow the same process?

### RE: Exhaust Back Pressure Calculations

I'm with you. The pressure drop across each component will be proportional to flow squared regardless of series pressure drops from other components. So unless the DPF is so restrictive that the flow reduces significantly, all the other pressure drops should stay the same.

je suis charlie

### RE: Exhaust Back Pressure Calculations

I have also heard assertions that the DPF pressure drop somehow doesn't add to the drop of the rest of the system, from people who were intent on selling DPF systems to our billionaire yacht owner customers, who were trying to be responsible citizens, as aftertreatment was not then required.

Some of the published documentation was just ludicrous, like showing a linear relationship between flow and pressure drop. It didn't really matter, because all of the data was extrapolated from one-ish datapoints, and because the DPF that was supposed to self- regenerate, clogged within days and had to be mechanically cleaned, then clogged within hours and had to be mechanically cleaned, then clogged within minutes and had to be mechanically cleaned.

The last step in each of our adventures with DPF systems was an emergency order for a 'test pipe' to replace the entire DPF system, each of which is now serving as an artificial reef in a faraway piece of ocean.

I suppose it is technically true that the pressure drop in t rest of the system becomes relatively insignificant when the DPF is clogged, but that's because the mass flow is way down from optimum, and is so low that the engine can barely keep itself turning. I wouldn't call that a proper design operating point.

I also would say that it's intellectually dishonest to calculate pressure drop for the remainder of the system with the DPF clogged, and then to use that pressure drop as the design pressure drop for the remainder of the system with a free flowing DPF and a much higher mass flow.
... but it does explain some of the crap I've heard about DPFs from the people who sell them, and the lack of respect I retain for the manufacturers of DPFs, and it lends extra credibility to stories about DPF misadventures with real production vehicles, and somewhat explains how engine manufacturers got bullied into using DPF systems before they were ready for prime time.

I.e., the DPF weasels will lie to anybody, including Congress and the EPA.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Exhaust Back Pressure Calculations

That's an interesting opinion Mike. That the aftertreatment companies are driving legislation. I'd always thought it was the pseudo-scientist politicians making promises the OEMs then had to implement somehow.

As an unintended (in my view) consequence of mandatory DPF use, some OEMs are discovering that because of the acoustic attentuation that comes with the high pressure drop, they are able to delete one of the exhaust mufflers. I'm guessing that the acoustic properties will vary with clogging. A bit like my old 2-stroke bike's exhaust.

DPFs really are not ready for prime time in the auto industry.

Steve

### RE: Exhaust Back Pressure Calculations

a free flowing DPF and a much higher mass flow

I suppose this means that the DPFs in question significantly reduced engine boost and/or power?

### RE: Exhaust Back Pressure Calculations

(OP)
In this application we are only dealing with 20-25"WC of back pressure for the entire system. The DPF, in a clean state, will typically consume 16"WC, and as it soot loads, increases back pressure to 22-23"WC. My concern is that if all of the other equipment's pressure losses are actually additive, we could exceed the engine's 27"WC limit.

I'm being told by my management that is not the case "in our experience". It is not a matter of mis-trust; these individuals would not say such if it weren't true. But the fact of the matter is that I don't have a good explanation as to why this is true; if I don't understand it, I can't explain it to my customers.

The one thought I had the other night was that the work done by the engine on the exhaust gas changes as the gas moves through the system. When you consider the total work done to move the exhaust gas through the system, the DPF is an enormous portion of the work, especially when it is loaded with soot. Could this perspective provide a plausible explanation?

BTW, thank you to everyone for chiming in so quickly! I had expected this thread to go nowhere for several days, if at all.

### RE: Exhaust Back Pressure Calculations

I was rereading your original post and thinking to myself "why the heck wouldn't that apply" ... when it occurred to me that perhaps you're talking about manual calculations based on some book figures for each of the components in the system, whereas the DPF is a manufacturer-specified value? If that's the case, then perhaps the calculated values for all the other components are traditionally conservative (and it doesn't matter much) whereas when the DPF is considered and those components become important to achieving a suddenly-difficult goal, the conservative estimates aren't accurate enough to yield success?

### RE: Exhaust Back Pressure Calculations

I'm used to doing manual calculations for marine Diesel exhaust gas systems, elbow by elbow, spool by spool, etc., using ASHRAE factors for each, and using turbo exit gas temperature and flow for the entire system, whether wet or dry. I've tried modeling with something closer to the actual gas temperature and density for each section, and found it usually wasn't worth the trouble.

The ASHRAE based calcs for backpressure are not strongly conservative; they come out pretty close to what is subsequently measured.
... and must be measured for each boat in order to secure a warranty from the engine manufacturer. All of them take backpressure very seriously.

My limited experience with DPF manufacturers, several years ago, suggested that they didn't have much flow/pressure data and didn't know how to measure it, but were perfectly willing to fabricate it. If a request for a flow resistance curve results in a graph with straight lines on linear paper, you can't be looking at real data, except for maybe one point.

If you are able to insert some science under your management's assertion that DPF backpressure does not add arithmetically to backpressure in the remainder of the system, I _really_ want to hear about it.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Exhaust Back Pressure Calculations

(OP)
I should have prefaced all of this with the fact that we are in the business of designing and selling after-treatment systems. We have done exhaustive testing on the DPF system by itself and we often generate non-linear curves of back-pressure vs. engine load to ensure that the DPF will not exceed the engine manufacturer's limits. I am confident that our calculations for the pressure drop across each component of the system are accurate. From what I'm hearing, no-one else who has responded has the "experience" my management has suggested.

I think it would simplify the conceptualization a lot if we were to consider the DOC, DPF, and SCR as orifice restrictions of different sizes. In this example, the DOC would be the least restrictive (largest bore diameter) while the DPF would be the most restrictive (smallest bore diameter).

The mass transfer across an orifice restriction is directly related to the bore diameter and the sonic velocity of the gas at that temperature. I'm not entirely sure that the exhaust gas is able to reach a sonic velocity within the DPF since the mass transport mechanism is entirely different, but for the sake of example I'm going to continue this line of thought.

In a system with only DOC and SCR, the mass transport across the DOC is not terribly different from the mass flow rate exiting the turbine, while the mass transport of exhaust gas across the SCR is less. These restrictions in mass transport are what are creating the pressure drops. When you evaluate a system with a the DPF, the mass transport across the DPF is much less than in the previous example. Because there is a reduced mass transfer rate approaching the SCR, the reduction in mass transport across the SCR is less severe, meaning less restriction is present.

### RE: Exhaust Back Pressure Calculations

Mike Halloran
Pembroke Pines, FL, USA

### RE: Exhaust Back Pressure Calculations

(OP)
DOC: Diesel Oxidation Catalyst - non-selective catalytic reduction of CO, HC, and other minor emissions species
DPF: Diesel Particulate Filter - traps and oxidizes soot and other particulate matter
SCR: Selective Catalyst Reduction - targeted catalytic reduction of NOx

In a typical exhaust system you might have a DOC and SCR solution; in this case the pressure drop across each component is additive because the mass transport across both are similar. The SCR system is more restrictive (less mass transport), however the magnitude of the difference between the pressure drop of the DOC vs the SCR is typically less than 2X. When the same solution includes a DPF, the DPF is placed between the DOC and the SCR. The magnitude of the difference between the pressure drop of the DOC+SCR system vs the DOC+DPF+SCR is typically more than 3X.

More specifically:

DOC = ~2-3"WC BP (fresh)
SCR = ~3-5"WC BP (fresh)
DPF = ~15-20"WC BP (fresh)

DOC+SCR = ~5-8"WC BP (fresh)
DOC+DPF+SCR = ~16-23"WC BP (fresh)

Does that help?

### RE: Exhaust Back Pressure Calculations

Quote:
The mass transfer across an orifice restriction is directly related to the bore diameter and the sonic velocity of the gas at that temperature. I'm not entirely sure that the exhaust gas is able to reach a sonic velocity within the DPF since the mass transport mechanism is entirely different, but for the sake of example I'm going to continue this line of thought.

I'm quite certain that with less than 1 psi total pressure drop within the complete exhaust system there is never anything remotely approaching sonic velocity. You can treat this as incompressible flow for calculation purposes.

----------------------------------------

The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

### RE: Exhaust Back Pressure Calculations

In a typical exhaust system you might have a DOC and SCR solution; in this case the pressure drop across each component is additive because the mass transport across both are similar.
...but not identical because you add a urea solution between them?

The SCR system is more restrictive (less mass transport)
shouldn't there be more mass going through the SCR system than through the DOC, since you've added urea and lost nothing? Or is there exhaust gas getting lost somewhere?

however the magnitude of the difference between the pressure drop of the DOC vs the SCR is typically less than 2X.
I believe that

When the same solution includes a DPF, the DPF is placed between the DOC and the SCR. The magnitude of the difference between the pressure drop of the DOC+SCR system vs the DOC+DPF+SCR is typically more than 3X.

Because the DOC and SCR are both channel-flow, whereas the DPF is wall-flow and much more restrictive, right? (in other words, the exh gas passes through the walls of the DPF material to get from inlet to outlet, whereas with the SCR and DOC it simply flows through some open-but-restrictive channels to get from one end to the other)

...so where is the mass going that passes through one of these devices and not the next? An EGR circuit?

### RE: Exhaust Back Pressure Calculations

That was the point I was trying to bring up:
Three pipe-like devices connected in series must all have the same mass flow.

Volume flow may be different because of heat added or lost.

The DEF mass flow must be small enough to ignore, else you couldn't carry enough on a moving vehicle.

As Ivymike pointed out, the mass flow calcs get more interesting if there is recirculation in the system, with which we are unfamiliar, lacking a more complete description, schematic, or web link.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Exhaust Back Pressure Calculations

(OP)
There's no EGR loop to consider. Mass transport must be constant due to conservation of mass, so the mass exiting the engine must be the mass exiting the tail pipe, although they exact conditions at any point between them may be different.

The point I'm not clear on: is the mass flow rate of the system equal to the mass flow rate at the most restrictive condition, or is the mass flow rate of the system the same as what is exiting the engine?

The point about sonic flow not occurring due to limited pressure differential is a good one.

### RE: Exhaust Back Pressure Calculations

There are a few operating points of consequence.

For propulsion engines on a boat, you have to run the boat at nominal max rated RPM, at which the rated mass flow and temperature will be assumed present.

You also run the boat at WOT, at which time the mass flow will usually be proportionately greater. The WOT rpm can be a bit higher than the rated RPM, and is subject to an absolute maximum limit, so prop selection may need adjustment after the first sea trial.

At both conditions, the measured back pressure at the turbo flange must be within the engine manufacturer's limit.

( Last time I checked, Volvo also specified a minimum backpressure, a requirement that I think comes from a misunderstanding of the turbo map, but the edict came out of the mother ship in Sweden, so the dealers didn't question it.)

At that point, the dealer will certify the engine for warranty coverage.

If your system clogs soon after, the backpressure will go up. The mass flow will go down, eventually enough that the boat will not be able to reach max RPM. On a few boats, the high bp will set an alarm before the engine is damaged. On many boats, the exhaust valves and/or pistons will burn, or the cap'n will slow down, or stop to unclog your stuff and repair collaterial damage, and be late arriving at the next port of call to meet the owner's plane.

Similarly for generators, except the tests are conducted dockside with a load bank set to absorb the max rated output.

In any case, if there's no 'cushion' for a little clogging, you will be getting irate phone calls from an angry owner.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Exhaust Back Pressure Calculations

You should make your DPF easy to remove/replace/delete for the consumer

"Formal education is a weapon, whose effect depends on who holds it in his hands and at whom it is aimed." ~ Joseph Stalin

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