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Old January 18th, 2008, 13:45   #1
santaclaus
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Default Compound Turbo Sizing Math

hi there being a newbie this might be a little too much to ask , but does any one know how you would go about the math for plotting and over laying compressor maps for sizing series turbos aka compounds , please dont shoot me down , its not for any fixed application and i dont have any targets or data to expolate from , im purely after formulae and technical insight to help broaden my horizons , im just a fellow tdi'er who loves theory and all things a little unique in turbo tech , i must say ive been a observer of the forum for many years and imo have yet to find more educated and rational members of any forum or indeed any corner of the net , period , so if you guys cant throw me a few calc's etc to digest i doubt i'd be lucky enough to find a knowledge base the equal of tdi folk , ( and down to earth with it ) cheers
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Old January 18th, 2008, 17:27   #2
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Turbo sizing is a bit of a black art, to begin with, there are very few people out there that can size a set of sequential's properly, without the trial and error method that most rely on and those people aren't talking.

There are one maybe two people on this site that I know of that would have a decent grasp on the math, and background that would have a decent shot at it.

I am not one of these people. I have been fortunate to have been around sequential diesel's since I was born, and have a decent idea of the sizes that work well together, but I am by no means an expert, and I am not really willing to share publicly what I do know. Sorry.
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- Where a tdi turbo upgrade isn't big unless that "56" referrers to the inducer size.

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again, not a topic for this forum...take it to "people who give a ****" forum.....the only numbers hear we care about are hp/ftlbs...
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Old January 18th, 2008, 18:43   #3
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Search for any and all posts by TdiMeister and GoFaster on this topic. Read those threads start to finish. Then, read them backwards. Then, go to the Honeywell websites listed and do the same.

Then, start sketching out your air mass needs (you can find this by logging your Tdi with a vag com's MAF readings.) You need to know how much mass of air to move.

Next, realize that the only thing that matters is mass balance.

Mass of air in + mass of fuel in

MUST

equal mass of exhaust gas out.

Then begin your sizing quest. You will learn enough from those guys and threads to tell what the tradeoffs are. All of them require sacrificing something. None of the real-world, available solutions are ideal. They all involve big compromises.

So then determine where you can let go of power, and what kind of powerband you can live with.

You'll have a good start. Control mechanisms will be your bugaboo. You'll pretty much have to engineer some flaps and valving and actuators from the ground up..and find a way to integrate them all under some robust control mechanism, be it vacuum (duty cycle proportional control,) servo, solenoid (mechanical or vacuum....) and etcetera.
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Old January 18th, 2008, 19:13   #4
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I started running calculations like this a few years ago and actually made an excel document so that you could vary the numbers without having to run through a whole page of stuff again. The thing you need to look at is that the first turbo in your series is breathing air at 14.7 psi absolute at sea level, and then the second turbo in the series sees whatever the first one put out in absolute pressure. So, if you're running a pressure ratio of 2 you should be getting 14.7 PSI of boost from the first turbo and then your second turbo will push that up to almost 60 PSI absolute since it sees about 29.4 PSI absolute coming out of the first turbo. Your first turbo in the series is larger because it has to flow a high volume but at a relatively low pressure ratio. There is actually a book which is outdated but covers this. It is called "Turbochargers" by Hugh MacInnes.

I've given twins a lot of thought but I think this might be a little beyond anything streetable. It works well for truck guys because they only rev to 3000 RPM, but with TDI's we're trying to make good boost from 2-5000 RPM and any turbine that makes a lot of boost at 2000 RPM will be restrictive by 5000 RPM. Adding 2 turbos in sequence isn't going to solve the problem and actually will make backpressure worse. So, if it's torque you're after then twins are the way to go but if you want horsepower you ought to be looking at the single turbo route.
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Old January 18th, 2008, 19:50   #5
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Actually the truck guys that would do twins are going to run 4k+
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Old January 18th, 2008, 20:08   #6
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Twins, like a single are still a trade off, twins that work well in trucks at 4000+ are not the same ones that work well for towing, and have great spool up.

Take a look at some common twin setups for the 5.9L cummins.

Towing twins used a stock turbo, with a bigger primary.
Street / Strip used a common upgrade turbo, with the similar bigger primary
Race twins used a huge upgrade turbo, and a MONSTER primary.

To put this into VW TDI terms:

Towing twins would use a VNT15 with a bigger primary (yes I have a very good idea what this is, but no I will not share)
Street / Strip twins would use a VNT17 with a similar primary as the first but a bit different config.
Race twins would use a VNT25 or bigger, and a Monster priamary.


Now this would be a vague gideline, but fairly proven. Now if infact you are really a keener, you could look up and see what the primary turbo's used are in each one of those apps, find a map for each one, and then use the maps from each to make a starting point of the ratio's of secondary to primary for what a good twin setup would consist of.

I can draw a sketchy map, but i can't tell you how to get there.
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- Where a tdi turbo upgrade isn't big unless that "56" referrers to the inducer size.

Quote:
Originally Posted by qmark
again, not a topic for this forum...take it to "people who give a ****" forum.....the only numbers hear we care about are hp/ftlbs...
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Old January 18th, 2008, 20:13   #7
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Oh and I am sure that there are many, many people on here that are smart enough to do the math, but there are very few that have the access to ALL of the information.
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- Where a tdi turbo upgrade isn't big unless that "56" referrers to the inducer size.

Quote:
Originally Posted by qmark
again, not a topic for this forum...take it to "people who give a ****" forum.....the only numbers hear we care about are hp/ftlbs...
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Old January 18th, 2008, 22:49   #8
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http://www.youtube.com/watch?v=t7maXP3ShXs

Quote:
Originally Posted by Jeremy Clarkson in the above episode of Top Gear at 2:20 or so
Anyone can make a big 3 liter diesel engine make a lot of power you just give it a big turbo, but if you do that, you have a lot of turbo lag... ... ... So what BMW have done, is given it a small turbo- no lag- and then as the revs build, a BIG turbo kicks in. So it's got like, two turbo chargers: little one, big one.
As if that's not technical or scientific enough for you (snicker), then they compare the 540 V8 with the 535d on the track with the stig (their super secret professional race driver always hidden behind his helmet, for those who don't watch the show) driving the V8 and Clarkson, who is at best a very aggressive enthusiast but no pro, at the wheel of the D. The 540 won by about 3 seconds (really about the difference you'd expect between a great driver and a pro on a single lap).

But anyway, when I see this, I start thinking that it's a shame that there's not more of a tuning market for bimmer diesels- either this side of the pond or the other- unfortunately anyone buying a new 535D is buying it because it's peppy from the factory, and not because they imagine or want to spend money and time modifying it. But if there were more of a demand for tuners to play around with these compounded turbo cars which seem to behave very much like a bigger brother to the 1.9s we all have, than I'd be willing to bet that the knowledge base would transition over to our models rather nicely. Again, though, I've a pretty tough time imagining that many people who buy a new 535d do it with any intention of modifying it beyond rims/tires/suspension/intake. Too bad.
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Old January 19th, 2008, 01:57   #9
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When I have the time, I will write a little applet to calculate air flows over each stage of different turbocharger/supercharger layouts; single, parallel-twins and staged-duals. Unfortunately, this is not that time.

In the meantime, some years ago I created a little Excel worksheet that calculates the density ratio of boosted air, given input parameters like pressure ratio, turbocharger efficiency and intercooler efficiency.

Basically the performance boost in an engine, regardless whether Diesel or gasoline, is closely related to the charge density ratio, NOT pressure ratio. Which means, doubling the boost pressure will NOT double the engine power, but doubling engine power will require a doubling of the density ratio, if fuelling is increased proportionately. Since the density is influenced by charge heating due to non-ideal compression in the turbo-/supercharger and non-ideal cooling in the intercooler, the density ratio will always be less than the pressure ratio to some degree.

In its current state, the worksheet is pretty limited. Basically it predicts how much boost pressure you need given a desired power level and efficiencies. Unfortunately, the prediction currently assumes a baseline engine that is naturally aspirated. However, people who know what they are doing can easily use the result to apply it for boosted engines as well. The worksheet doesn't do all the work for you; it's more of just a look-up table, and the results that it gives will be heavily influenced by the input data (garbage in = garbage out). For example, doubling the horsepower of a given engine with 75% turbocharger efficiency and 75% intercooler efficiency will require a pressure ratio of 2.3. It doesn't really matter if you have a staged setup -- this is the additional pressure ratio you need for any additional stage to go reach the target horsepower from the baseline level.

However, one resource that is already in the Internet does 95% of what is needed to do very complete turbocharger calculations. Granted, it assumes a single turbocharger stage, but again, someone who knows what he's doing can extend that to apply in a multiple-turbo setup. With the right input information, it can calculate to a good accuracy the mass airflow in lb/min and well as volume airflow in CFM. From there you can go ahead to dimension your staged setup. To get you started on using the right input data, I've filled some of it in already. The turbo calculator can be found here.

I don't think it's such a black art, but certainly the math is not easy for the uninitiated. That's why applets like that above do them all in the background and only needs the user to plug-in numbers. Whether the numbers make any sense at all is a whole other matter, but that's maybe where the knowledge and black art lies.

The very basics of turbo matching can be found at the Garrett website and in this thread.
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Old January 19th, 2008, 13:01   #10
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Yes ''LA'' ive been just an observer for some time , cant say that im much of a talker , just a reader , so without wishing to sound like im trying to push arse kissing levels into choke . iI can honestly say that im content to just follow people like TDImeister / dvstsr / diesel des and a few other selected members posts avidly , purely for insight , So ive had no real inclination to join till now , is that so hard to belive ?


Anyways cheers for the help guys ,
So if i have a 116 ci engine and the single thats on it is running at a max P.R of say 2 , i would have on paper a virtual engine capacity of say 232 ci and size the primary accordingly as an estimate , then when i find turbo frame in range , i select a map that will spool well enough as a starting point - and i take the P.R and efficiency from the plot of my chosen rpm etc, and apply that to the map of the secondary taking into account the adiabatic compression and there fore the density ratio by possibly recalibrating the secondaries maps temp + pressure correction ( no idea how to do ? ) - Then by a process of trial + error plug the numbers back and forth till i find a pair of turbos that give me a final P.R and density ratio for a given target .
- Or am i so wide of the mark that all ive done is to compound my own drivel from start to finish , please correct me
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Old January 19th, 2008, 13:51   #11
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My approach (due to ease and availability of publicly accessible tools online) would be to define the desired horsepower level. This will automatically define the amount of fuelling required, and by extension the amount of airflow. Once you've determined the CFM or lb/min (which up to this point is completely independent of the turbocharger and to a large extent engine design), now you need some engine details like displacement, RPM and volumetric efficiency, which will help you determine the required boost pressure ratio. In some specific cases, you can use the density ratio method (which is valid when displacement, RPM, volumetric efficiency and thermodynamic characteristics remain basically constant).

Now, you have the air flow and PR information, with which you can plot points on a turbo map.

Dealing with staged (serial) turbocharging is not that much more complicated than dealing with a single setup if you remember some rules. As nicklockard said, mass must be conserved across the compressor and turbine sides, and this applies across all stages as well. Pressure ratios, in the absence of plumbing losses, get multiplied across each stage. Therefore, for example, if each stage puts out a PR of 2, the overall PR is 2*2=4 (remember, these are in absolute pressure). Calculation of charge heating is a little bit more complicated, but once you've cleared earlier hurdles, that is not a big challenge.

After all is said and done, I must say that the decision to go with a staged setup is largely academic. In a majority of cases, a single stage will do the job just fine, and properly matched, modern turbochargers can operate at PRs of 3.5 or more (36+ PSI boost pressure), and I've seen PRs of almost 5! (58 PSI!); in other words, more than enough boost to blow a TDI engine to kingdom come.

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Old January 19th, 2008, 14:37   #12
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A thing I always had troubles to understand is:

Mass flow is the same in every comp and turbine (when you add fuel mass)..

Mass flow is the same.. the volume will be bigger in first stage due lower density, but on every comp map you see mass flow..?

How could you determe size of the first stage charger as you only know the needed mass flow and PR.. you could calculate the volume flow but this is not visible on the map..

Only factors that is responsible for difference in first and second stage compressor size is density, and density depends on absolute pressure and temp..

Or are there also comp maps that reads in cfm?
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Old January 19th, 2008, 14:46   #13
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You can translate CFM to mass flow and vice-versa for the first-stage very easily because CFM is referred to inlet (i.e. ambient) conditions. But because mass flow is always constant and doesn't change across stages in relation to temperature and pressure like CFM, it's much more convenient work with mass flow. What density should you use in the calculation for the second stage? You would need to know the charge temperature and pressure at the inlet of the second stage, and both are variable. Too complicated, even for me.
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Old January 19th, 2008, 14:52   #14
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Yes I know but when only looking at mas flow and desired PR there would be no need for bigger primary compressor..

Yhen you would just search 2 identical compressors that just have their sweet spot at the flow/pr you want.. but n reality everyone uses bigger primary because it needs to flow same mass with bigger volume..

Now my question was how to determe by maps what would be good for first/second stage..? the only difference between is the density they work on.. if PR's are the same..
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Old January 19th, 2008, 20:10   #15
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I think that a good place to start is the SAE web page for info.
www.sae.org

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