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Old January 21st, 2008, 09:21   #16
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 - though despite your best efforts + valued Patience my meatloaf still appears to be letting me down
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Old January 21st, 2008, 10:07   #17
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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..
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Dyno'd area, Old VNT20 setup dyno'd 192whp
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Old January 21st, 2008, 10:30   #18
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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.

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Old January 21st, 2008, 13:29   #19
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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..
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Dyno'd area, Old VNT20 setup dyno'd 192whp
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Old January 21st, 2008, 14:54   #20
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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.
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Old January 21st, 2008, 15:02   #21
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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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Dyno'd area, Old VNT20 setup dyno'd 192whp

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Old January 21st, 2008, 17:12   #22
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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.

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/HPhr (~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/HPhr) 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.

Let’s now set some general parameters:
Ambient temperature will be 25C (77F, 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 25C (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 25C 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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Last edited by TDIMeister; January 22nd, 2008 at 00:12.
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Old January 21st, 2008, 19:09   #23
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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.
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Old January 21st, 2008, 20:43   #24
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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.
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Old January 21st, 2008, 21:35   #25
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Wow you guys are so far over my head. The difference between OEM designing and backyard.

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.
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Old January 21st, 2008, 22:55   #26
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Quote:
Originally Posted by vwmikel
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.
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Old January 21st, 2008, 23:38   #27
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Quote:
Originally Posted by TDIMeister
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
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Old January 22nd, 2008, 09:00   #28
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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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Old January 22nd, 2008, 13:10   #29
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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 !

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Old January 23rd, 2008, 04:15   #30
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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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