Staged Turbo Sizing Math

santaclaus

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pd130
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 :D , 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
 

dvst8r

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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. :eek: 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.
 

nicklockard

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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.
 

vwmikel

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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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dvst8r

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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.
 

dvst8r

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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.
 

johnnloki

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http://www.youtube.com/watch?v=t7maXP3ShXs

Jeremy Clarkson in the above episode of Top Gear at 2:20 or so said:
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.
 

TDIMeister

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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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santaclaus

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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 ? :confused:


Anyways cheers for the help guys :D ,
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 :confused:
 

TDIMeister

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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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Rub87

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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?
 

TDIMeister

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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.
 

Rub87

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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..
 

santaclaus

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it seems every time i try and calculate this i get in a muddle some where , just dont know where ?

take example - target 400whp , purely hypothetical , i know the engine cant take it but its a nice round figure worthy of twins to work with,

-- first off figured that a capacity of 116ci with a VE of 85% say at 4000rpm , ambient temp 85f , AFR 17 , BSFC 0.365 say - Requires 41 lb min at a PR of 5 ( 71 psi absolute )

-- Next sized the secondary - not much effort, say - vnt20 at 4000rpm makes 22lb min ( half total flow ) @ 2.7 P.R ( almost half total pressure ) at 65% compressor efficiency

--- Now as i have the vnt20's P.R of 2.7 , i thought i should be looking to size a primary to include a P.R of 2.3 and 40 lbs min - 2.7 + 2.3 * 14.7 = 73.5 absolute ( required for 400whp )
but im not sure thats relevant as its not figured for density .

-- So with intercooling between stages ( WI would be better i know )
unknown primary as yet but - inlet temp 85f - inlet psi 14.7 - output pressure 2.3 P.R 34psi absolute - targeted compressor efficiency say 70%
= an output temp of 399f - P.R 3.31 - density ratio 2.1

-- when put through first stage of intercooling which is 80% efficient - 1 psi loss - 80f outside temp
= Outlet temp 144f - P.R 3.24 - density 2.93

-- Now with 144f output temp + 34psia plugged through density calculations once again but for the VNT20 but with 144f as inlet temp - inlet psi 47.6 absolute 3.24 P.R - 65% compressor efficiency - output pressure 73.5 psi absolute P.R 5
= Outlet temp 425f - P.R 2.54 - density ratio 1.74

-- After 2nd stage of intercooling ( same efficiencies as the 1st )
= Overall Outlet temp 149f - Overall P.R 2.52 - Overall density ratio 2.51

-- With the engine being in normally aspirated form the calculations with capacity , VE , and rpm being unchanged at - 116ci , 85% , 4000rpm , show the engine to consume 12.82lbs min before boost

-- so when applied with the overall density ratio from above which equates with the overall required P.R from both stages 73.5 psi absolute
12.82 * 2.51 = 32lbs min - suggesting that, that is the primary flow to be sized ?
which seems to have lost me completely 32lbs min ? , if any one can put me back in line , i'd be hugely grateful , pull apart at will ! :( ( ive been on a wing an a prayer from the very start to be honest )
cheers especially tdimeister :cool: - though despite your best efforts + valued Patience my meatloaf still appears to be letting me down :rolleyes:
 

Rub87

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Why do you use 22lbs for the first vnt20? if the engine needs 41lbs, 41lbs shall need to go trough both stages..

I also think the compressor effeciciency of the second stage vnt20 will be slightly higher due the more compact volume..
 

vindaloo

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NB: In no way a practical expert.

If you look at Des's teasing in his thread, regarding turbo sizing, his primary (LP) was a (relatively) BFO Holset and secondary (HP), a VNT15 or similar.

My guess is... Just size the LP turbo for your power goals. Keep it real and give great thought to the packaging and mapping/controls. Maybe use a chargecooler or two to avoid excessive inlet tract lengths.

J.
 

Rub87

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So there's no way to find out what compressors you want by using just maps? Is it a fact that more dense charge air slows the comp down more? the secondary turbo (VNT15) has to flow 25lbs/min + at PR of 2, this will be very close to the choking line..
 

GoFaster

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Trouble is that compressor maps are all based on standard temp/pressure conditions. There are a set of equations called the "fan laws" that I recall from fluid dynamics in university ... unfortunately that was 18 years ago, but most of them were common sense. The compressibility complicates things a bit but still you can get the general idea. If you double the inlet air density and you hold turbine RPM constant, it will proportionally increase everything related to mass flow rate by double. The pressure ratio will be the same. The mass flow rate will be double what it says on the chart. The shaft power of the compressor will be double. Thus, for the "outer" turbocharger, it's appropriate to use the mass flow rate that it indicates on the compressor map. But for the "inner" turbo, you have to proportion everything according to the density ratio.

Complicating matters is that the inner and outer turbochargers, if they are different sizes (which they SHOULD be), will not spin up at the same rate. If your boost control system is calling for a pressure ratio of 3, and the "design condition" is that it's 1.5 from the outer turbo and 2 from the inner one, but the outer one is slower to spin up because of its larger size, the operating conditions on the inner turbo are going to be interesting for that moment until the outer one catches up.

If I were designing this at an OEM level, I'd be putting pressure sensors for barometric and for after the first stage and for after the second stage, and independently control pressure ratio across each stage, to minimize the risk of something going boom.
 

Rub87

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I see, thats why a little vnt15 will sustain..

But as the shaft power needed will be double it's maybe better to use slightly bigger turbine in the inner turbo? keeping PR's reasonable should keep the rpm down and could let you use a bit bigger turbine wheel to supplie the needed power at reasonable PR across the turbine..
 
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TDIMeister

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OK, first of all, what I am posting here will likely ruffle some feathers and I’m sure there will be debates about my results. The people who don’t want to share information and “trade secrets” for matching staged turbochargers either don’t actually know of a systematic way of doing this; or stand to lose something, like having a whole bunch of new people thinking they now have the know-how to match- and build turbo systems and jump into the market… I’m presenting one way of doing this; others will undoubtedly have their own ways. Take this for what it is: information given out on the Internet. :rolleyes:

Second of all, we need to get to defining and settling on some ground rules. You want to build a hypothetical 1.9L TDI making 400 BHP – fair enough, this is a discussion about matching staged-turbochargers, so I won’t get any further into debating the feasibility or hardware/software of how you’re going to realize this. But, a few points beg at least some scrutiny before we move on, because it defines some global parameters that we need in order to make a reasonably accurate match.

Making 400 BHP at 4000 RPM means that your 1.9 TDI will be producing 400*5252/4000 = 525.2 lb.·ft. (i.e. 712 Nm) of torque at that RPM, which equates to a BMEP of 47.2 bars. NOT GOING TO HAPPEN.

I would say that peak power will have to occur at a minimum of 4750 RPM (don’t ask how THAT’S going to happen, that’s the topic of a whole other thread), which will result in 400*5252/4750 = 442.3 lb.·ft. (i.e. 600 Nm) of torque and a BMEP of 39.8 bars. Still awfully high numbers, but not out of the realm of possibility… high-output truck, industrial and marine engines are producing over 30 bar.

Third of all, running an AFR of 17:1 (lambda ~1.17, if the stoichiometric AFR is assumed to be 14.6:1) while still achieving a BSFC of 0.365 g/HP·hr (~222 g/kWh if a fuel LHV of 41.85 MJ/kg is assumed per VW Motorsport’s R-TDI paper) is also not going to happen. Running such a low lambda will be very smoky in the best of circumstances; I would say lambda 1.2 is the absolute minimum, but 1.25 (AFR = 18.25:1) is best to use, especially if you’re going to use another fuel like propane or methanol somewhere in the mix later on, and assume a BSFC of 235 g/kWh (0.386 lb/HP·hr) at maximum power. This BSFC figure would correspond to a brake thermal efficiency of 36.6% {was 41.8%} -- pretty darn good!

Fourth of all, a volumetric efficiency of 85% at 4000 RPM is a bit of stretch, but I used roughly that figure in the analysis of the R-TDI engine. However, at 4750 RPM, I would bring that value down to 80%.

One other thing: From here on I will only use metric units (kg, m, °C, kW, Nm, bar, J, etc.) and only mention Imperial if it’s convenient for my calculations or explanation. I really hate dealing in Imperial units, and it’s not an anti-British or -American thing. :p

Let’s now set some general parameters:
Ambient temperature will be 25°C (77°F, 298 K) and atmospheric pressure will be 1 bar (14.5 PSI, 100 kPa). For the first iteration, I will use compressor efficiency at each stage of 75%; a single intercooler after the second stage with an efficiency of 85% and pressure loss of 1.5 PSI (0.1 bar).

Therefore, to achieve 400 BHP, you will require a mass air flow of about 47.31 lb/min (0.3577 kg/s) at a PR of 5.86 {Link}. Anyone who tells you that you can get 400 BHP in a Diesel engine with much less mass air flow doesn’t know what he’s talking about (and we’re talking no cheaters like propane, nitrous, methanol and water injection), although the PR is subject to change depending on RPM and VE at maximum power. The mass airflow to achieve a certain power output is only a function of the AFR and BSFC – nothing else – and the numbers I gave for them above are realistic if already optimistic values for a TDI Diesel engine. I will arbitrarily assume for the first iteration that the PR will be achieved by splitting the job between the two stages at 2.8 and 2.1 bar respectively (2.8*2.1 = 5.88), and there are negligible pressure losses between stages. Boost control and layout suggestions will be addressed in later posts.

The matching of the first turbocharger stage is pretty simple, since you already have most of the information required to make a match. You need to find a turbocharger that will deliver a mass flow of 47.3 lb/min at a PR of 2.8 with the best possible efficiency (I said 75%). Better efficiency will result in lower charge temperatures after the first stage; this will reduce the compressor work in the second stage, and although it doesn’t change the required mass air flow, you can achieve the same mass flow (for the same BHP) using a lower overall PR. Minimizing compressor work in any stage also minimizes turbine work by definition, which in turn minimizes EMPs and makes for a better responding system.

For the first turbocharger stage, a good match for this application might be the one below:

Note that the necessary mass flow of about 47 lb/min at a PR of 2.8 achieves an efficiency of 76% with still some margin for flow and PR, plus to the left there is a beneficial leftward bulge in the surge line.

Now, the dealing with the second stage is a little harder, but GoFaster gave the correct hint: all compressor maps are related back to the inlet at reference test conditions (for most newer Garrett turbos after 2002, this is 1 bar inlet pressure and 25°C (298 Kelvins) ambient temperature – how convenient!). The keyword in the maps is “corrected”. Corrected means the mass flows are corrected to the reference conditions. Well, at the inlet of the second stage, the conditions are anything but 1 bar pressure and 25°C temperature. Not to worry, the equation for correcting the mass flow for any pressure and temperature is:
mcorr = m*sqrt(T1/298)/(P1/1)

Here, T1 is the compressor inlet temperature in Kelvins and P1 is the compressor inlet pressure in bar divided ambient (1 bar).

Using my handy worksheet, the corrected mass flow at the inlet of the second stage compressor is 47.31*0.4137 = 19.57 lb/min or 0.148 kg/s {was 20.2 lb/min}. Now I just have to look for a compressor that will give me good efficiency at that mass flow and PR of 2.1.


This turbo is operating right at its sweetspot at the calculated mass flow and PR, achieving an efficiency of 79%, and again with plenty of flow- and PR margin (the latter is important in both stages if operating at high altitude). {In light of the corrected calculation above (thank doing math at 2 a.m. for that), it appears that the second stage turbocharger should be rematched, and it could stand a smaller compressor to give better surge margin.}

However, it is vitally important to plot points at several operating conditions and RPMs. At the very least, you should calculate points at maximum power and maximum torque, plus full-load points every 1000 RPM including redline. At every sampled operating point, make sure that you clear the surge line in both stages with some margin of safety, and also leave a good amount of margin for shaft RPM, maximum PR and choking flow. It is also important to note that, as GoFaster alluded to, turbo bench tests are performed at standard reference inlet conditions. At conditions that deviate from this, even after correction factors, the maps are no longer completely applicable. You don’t need to completely throw out and discount the maps, but they are subject to other factors and error that is best dealt with through a combination of testing, experience and engineering judgment.

This first iteration is by no means optimal, and I’m not suggesting that you run out and buy these two suggested turbochargers and start building your own system. For one, I used compressor maps that I could find from publicly available sources, and there may be even better ones out there. Generally, you want to operate both turbochargers at their highest total efficiencies at the operating points of interest, and apportion most of the compressor work to the stage operating at the highest total efficiency. This may mean adjusting the PR that each stage contributes to the total.

Total efficiency implies considering also the turbine, something we have totally ignored up to this point in this analysis. However, as a ground rule, as GoFaster again stated, the compressor work in the second stage will effectively be multiplied by the density ratio (the mass flow correction is a similar analog to this). Here, a hybrid turbo with a small turbine would make a lot of sense. To be able to spool either compressor, you will need a fairly low A/R turbine housing (or if using a VNT for any stage, it will have to be in a fairly closed position). Matching operating points in the turbine side are pretty much exactly the same as on the compressor side already explained, but the maps look completely different and mass flow corrections use different reference temperature and pressure.

Please note that as I’m finishing this post, it is past 2 a.m. local time so I’m fried. There may be some errors, edits and additional posts in the next days before I’m satisfied that everything is correct as best I know it.

Peer review is welcome (GoFaster, nicklockard, uponblocks, others), but please keep posts constructive and on-topic.

Edits where noted
 
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GoFaster

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2006 Jetta TDI
Dave, that's a great post. I further the "not going to happen" regarding that total intake manifold pressure ... Peak cylinder pressure will be off the scale and a certain con-rod bender. But nevertheless ... I've got only two comments.

Dave's calculation basically picks the best efficiency point based on the maximum RPM of the engine. As Dave suggested, unless you are building a "dyno queen" (As revs build, you get nothing nothing nothing nothing then KABOOM one massive spike of torque just before redline and then nothing as the engine hits the rev limiter) you will want to repeat the calculation for lower RPM points, with a view towards making the turbochargers *smaller*. It's instructive to repeat this exercise with the RPM halved - i.e. let's see what happens if we cut the mass flows in half to see what happens at the bottom of the powerband (2350 rpm or thereabouts). Actually you'll get a little better than half mass flow at half rated RPM due to better volumetric efficiency in the engine itself, but for simplicity of calculation let's use half.

The inner turbo at 10.1 lb.min and 2.1 pressure ratio is still right of its surge line, but it's uncomfortably close. The outer turbo at 23.5 lb.min and 2.8 pressure ratio is on the wrong side of the surge line.

Welcome to the engineering process ... you take an initial guess and see what happens. In this case, even though those two turbochargers look okay at rated RPM and max load, the application is trouble at half rated RPM and max load. I would suggest that the next iteration would involve one size smaller on the inner turbo (VNT17?) and one or maybe two sizes smaller on the outer one. Yes, it will probably mean that the operating points at max rated RPM and load would be to the right of the peak efficiency island, but when considering the WHOLE operating range, they'll be in better shape, and will spin up quicker (less lag).

And ... I stress once again that this analysis considers only steady-state operating conditions. You really have to consider transient conditions, too. For example, let's suppose in the above example, that the engine is sitting at 2350 rpm (half rated speed) and no load, and the driver mashes the accelerator to the floor instantly. The boost control system requests 5.8 pressure ratio right away. Certainly the smaller inner turbo will spin up quicker than the outer one. Worst case is that the inner turbo is responsible for generating the whole pressure ratio - you effectively have a single-stage turbo for a moment. If we make that assumption, the inner turbo's operating point will be 5.88 pressure ratio - and we don't need to even concern ourselves with the corrected mass flow rate, because that pressure ratio is off the scale. If the exhaust side is capable of delivering it - Ka-Boom! In reality one would have to select the exhaust side so that the VNT mechanism (if equipped) is incapable of closing up far enough to cause that ka-boom, no matter what the control system told it to do.
 

vwmikel

Vendor , w/Business number
Joined
May 5, 2005
Location
Las Vegas, NV
TDI
'94 Golf Sport TDI
Just to throw something else in there....not every turbo will surge right at the surge line. I've been able to push turbos well to the left of the surge line before problems occur. Some are just more prone to causing problems than others.
 

dvst8r

Veteran Member
Joined
Dec 6, 2004
Location
Airdrie, AB
TDI
'03 Wagon
Wow you guys are so far over my head. The difference between OEM designing and backyard. :p

I figure out the approx total flow needed (I take avg flow needed for gasser hp stuff add about 30%), and the approx PR, and then sift through thousands of maps I have saved over the years, and stuff online, start with something close and see how it works, go test it and go from there. After building a few dozen sets, I have a decent idea of what works, maybe not why, but seems to work out ok.

I'm very interested in this despite the fact that it is way past me. Keep it going. :cool:
 

TDIMeister

Phd of TDIClub Enthusiast, Moderator at Large
Joined
May 1, 1999
Location
Canada
TDI
TDI
vwmikel said:
Just to throw something else in there....not every turbo will surge right at the surge line. I've been able to push turbos well to the left of the surge line before problems occur. Some are just more prone to causing problems than others.
In like manner, not every turbo will begin to surge exactly at the plotted line; certain conditions may cause it to surge at mass flows further to the right of surge line, and you have to consider altitude and transients as well. That's why you have a surge margin. Besides, operating near at at the onset of surge is terrible for efficiency, and nobody wants to be blowing hot air.
 

vwmikel

Vendor , w/Business number
Joined
May 5, 2005
Location
Las Vegas, NV
TDI
'94 Golf Sport TDI
TDIMeister said:
In like manner, not every turbo will begin to surge exactly at the plotted line; certain conditions may cause it to surge at mass flows further to the right of surge line, and you have to consider altitude and transients as well. That's why you have a surge margin. Besides, operating near at at the onset of surge is terrible for efficiency, and nobody wants to be blowing hot air.
Efficient or not it is good to have the boost at low RPM just for driveability sake. It is just another compromise we make for the larger turbo ;)
 

nicklockard

Torque Dorque
Joined
Aug 15, 2004
Location
Arizona
TDI
SOLD 2010 Touareg Tdi w/factory Tow PCKG
The only thing I would add is that I think possibly a water/methanol injection device should be mandatory for home-made compound turbos, as it may buy you a slight margin of safety by keeping EGT's lower and peak cylinder pressures under control--you're not going to get the ECU mapping/fueling/boosting profiles right during the first ten iterations, so that insurance might buy you safety.

And dangit, if I could just find the Hyland and Wexler tables I'm looking for (what's the compressibility of air versus Rh% versus P-T...) Compressibility factor Z of humid air should go up with increasing pressures--
 
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santaclaus

New member
Joined
Jan 17, 2008
Location
dover
TDI
pd130
I have to say ,as some sort of little disclaimer that when i started this thread i hastened to expect some sort of backlash , (been lucky it seems ) but as tdi says if this constructive analysis ruffles feathers then may be those inherent parties have more to lose in face value than most likely trade value , This thread only involves like minded theorist , and to my end no ill gotten intent , to either (A) profit from, or ( B ) attempt to expose anyones hardly defined setup , ( other wise the hypotheticals in any of the preceeding posts would not have been the focus of unrealistic targets or parameters )

Im a firm believer that nothing in engineering should be regarded with any kind of mythical construct or even undaring complexity , and to this degree most subjects should at least be open to a domain of freethinking and enthusiastic reason especially when addressing systematics established more than half a century before even the age of tdi membership . -- anything in this light should open to interpretation to anyone willing to give it a go, without fear of reprisal by people who feel threaten by it content

so without wishing to sound like im trying to dictate a vendors prerogative here, in my pretty narrow opinion a commercial vendor in this sector would probably levy more potential success to irrefutable product quality and the informed nature of its clientele than any form of principle disclosure or unreasoned outcry . after all im sure no logical person could correlate a dramatic decline in aftermarket installation sales purely in part to amateur sizing of single turbos
Hell even a company as competitive as garrett warrant free licence to size any compressor on their site ive noticed , they even supply a 101 guide, lol

but i do sincerely apologise if the instigation of this thread treads on any ones toes

P.S Your guys rock ! ;)

tdimeister your definition of afr and bsfc workings, opened my eyes alone , the rest will be food for thought for a long time to come . cheers You Da Man ! :cool:
 
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hatemi

Veteran Member
Joined
Aug 25, 2005
Location
Finland
TDI
Audi A6 4F 3.0TDI
Heres a comparison between GT1548(blue), GT3267(green), HX35(red) and the S200 that I will be using. Seems like its pretty good match for my goal ;)
 
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