325i stage 1 turbo ?????

[jaffacake]

hi guys, came accross this website and its got loads of performance parts for the e30, wanted to turbo my 325i for a while but what do you guys think about this package---- This is a low pressure (6.5 to 7 psi) Torque increase is 40-42%. Kit includes: Cast iron exhaust manifold,TO4E turbo, Tial waste gate, 3" ceramic coated downpipe, 24 lb injectors, billet fuel pressure regulator,Bosch air bypass valve, K&N air filter, cold air intake pipe, custom computer chip, oil lines with fittings, and all necessary silicone hoses, couplers, clamps and gaskets. the site is http://www.vintagebmwsource.com/e30-engine, its 3800$ which is £2438.92, is it worth it, what do you lot think, thanks.

[eta]

That looks like Ireland enginering stroker kits and the turbo kit is from TCD. Also the TCD manifold look a lot like the car tech ones.

[eta]

Forgot to add TCD kits apparantly work well, never tried one though.

[GeoffBob]

Unless they state explicitly that it's a Turbonetics T3/T04E then I wouldn't touch it. Many swear by the Chinese Knock-off turbo's (usually those that sell them). I don't! Before I buy one I would want to know the complete spec of both the offered turbine and compressor, as well as the details of the bearing. T3 turbines, for example, come in a range A/R housings with various sized wheels. This ultimately determines at what RPM your engine will choke the turbine, and that's important to know. Find out afterwards that it's a T3 stage-1 turbine wheel in a housing with A/R=0.36 and your 325 will need a wastegate bigger than the turbine just to make it to 5500rpm.

I also suspect that the kit is for a LHD car. Unless you know for sure that the bottom-mount turbo and downpipe won't collide with your steering column (I'm assuming you have a RHD) then you could be in for some nasty mods, which on a cast-iron manifold is no fun.

I also think that US$3,800 is exorbitant for a system that doesn't include an intercooler.

Sorry to knock it, but I do believe these to be the facts.

[jaffacake]

so what should the A/R housing be with what size wheel then, and i think they make the manifolds and stuff the the specs of the car because they say to tell them the year and model. wouldnt be doing it yet any way, possible february time, and what price range should i be looking at for the whole kit including intercooler if i bought it here not abroad. thanks

[GeoffBob]

I'll work it out and get back to you.

[eta]

TCD do do RHD manifolds for $599. They also do partial RHD turbo kits. It has a T4 flange. So you could by your own T04E turbo from tubonetics and get your own intercooler. Or you could do what I am doing get an M51 manifold and get an adapter plate machined to alow it to fit to a M20 cylinder head. I plan to use a TD04HL-16T from a Volvo T5 on my 2.7i (I picked one up second hand for £120). This turbo should be even more appropriate on a 2.5, although Geoffbob I am sure will chime in on this.

Given the cost of the new exhaust system I will need, intercooler, and Emerald (+MAP sesnor) and the other bits I need, I am looking at around £2200 but for this conversion but I will getting proper engine managment system as well. Remember by the the time you have paid for a U.S import, paid VAT and duty the actual cost is more like the dollar cost in pounds.

Also a T3 super 60 similar to those found on Sierria Cossie's is a good choice too. The M51 manifold I found out after I bought the volvo turbo has a T3 exhaust flange. If your budget stretches, a GT2860R also works and again their are many different trim options and A/R choices. It depends on what your target Hp is?

http://www.squirrelpf.com/site/ is a decent place to start working out the right turbo for your car. Also try reading up on the turbo FAQ pages on turbobygarrett.

I hope the volvo T5 turbo will work or I have wasted some money.

[jaffacake]

I'll work it out and get back to you.

thanks mate

[jaffacake]

TCD do do RHD manifolds for $599. They also do partial RHD turbo kits. It has a T4 flange. So you could by your own T04E turbo from tubonetics and get your own intercooler. Or you could do what I am doing get an M51 manifold and get an adapter plate machined to alow it to fit to a M20 cylinder head. I plan to use a TD04HL-16T from a Volvo T5 on my 2.7i (I picked one up second hand for £120). This turbo should be even more appropriate on a 2.5, although Geoffbob I am sure will chime in on this.

Given the cost of the new exhaust system I will need, intercooler, and Emerald (+MAP sesnor) and the other bits I need, I am looking at around £2200 but for this conversion but I will getting proper engine managment system as well. Remember by the the time you have paid for a U.S import, paid VAT and duty the actual cost is more like the dollar cost in pounds.

Also a T3 super 60 similar to those found on Sierria Cossie's is a good choice too. The M51 manifold I found out after I bought the volvo turbo has a T3 exhaust flange. If your budget stretches, a GT2860R also works and again their are many different trim options and A/R choices. It depends on what your target Hp is?

http://www.squirrelpf.com/site/ is a decent place to start working out the right turbo for your car. Also try reading up on the turbo FAQ pages on turbobygarrett.

I hope the volvo T5 turbo will work or I have wasted some money.

thanks for the info. so how much would an adapter plate cost and around how much would the m51 manifold cost. i think target bhp is around the 350 mark, no less than 280bhp at least and possibly +400bhp by the end of 2011, but will be doing thinks such as shrick cam, biger throttle body, and all the other bits. and yeah that price wasnt VAT included but it was shipping included.

[jaffacake]

and the price you said of £2200 is pretty much the same as their selling the kit for and i suppose i will kind of know that i am getting good quality parts other than buying off them and getting crap parts that wont last.

[GeoffBob]

[GeoffBob]

Right Jaffa, I pulled the calculator out the drawer and worked out the following for you based on a max power figure of 350bhp at 6600rpm:

First off, as a rule of thumb you’ll need to flow 34lbs/min of air into your engine (regardless of engine speed) to put out 350bhp. In metric units that equates to roughly 0.26 kg/second of air. Since your M20B25 can’t induct that amount of air by itself a pump is required, in your case a turbocharger.

Following all the usual equations (that I have posted up on the zone before) and assuming a volumetric efficiency of 85% at 6600rpm for the 2-valve per cylinder M20B25 engine, you will need to pump your intake manifold to 690 Pascals of pressure per degree Kelvin temperature of the air inducted into the engine.

Please note that this is ABSOLUTE pressure, not BOOST pressure! Air pressure at sea-level is typically around 1bar or 100,000 Pascals or 14.7psi ABSOLUTE pressure. This is the figure you would read of a barometer on the wall. Also, temperature here is in KELVIN (not Celsius or Fahrenheit). To get from Celsius to Kelvin simply add 273 to the temperature in Celsius. In other words, 20’C = 293K.

The reason I present the above figure as so many Pascals pressure per degree Kelvin temperature is to help you understand that the hotter the air inducted into your engine the more pressure you will require to get your specified 350bhp. This is important to understand because the unfortunate truth is that the air coming out of your turbocharger can get extremely hot. One of your best mechanisms, therefore, to achieve your target bhp, is to cool the air coming out of the turbocharger using an intercooler, rather than continually aiming for higher and higher boost figures. I can categorically state that you will not achieve 350bhp on an M20B25 engine without fitting an intercooler.

Right then, at an ambient temperature of 293K (20’C) we shall assume an air temperature in the plenum of 308K (35’C). This means your plenum must be pressurised to 690 x 308 = 213 kPa (1000Pa =1kPa). Assuming an ambient air pressure of 100kPa then your required boost pressure is effectively 113kPa (1.13bar or 16.3psi). This equates to a pressure ratio (across the compressor) of 213kPa/100kPa = 2.13.

Now, assuming a compressor efficiency of around 70% (unless you are prepared to fork out for a Garrett GTR turbo), and taking adiabatic heating into account, the air coming out of your compressor will be 394K or 121’C And that’s for real, it really does get that hot at those kind of pressure ratios. Thank goodness for intercoolers!

Assuming your intercooler is at least 85% efficient, then the air coming out of your intercooler will be at exactly 308K (35’C), as assumed above. Any greater efficiency than that and you’ll gain power, any less and you’ll lose power.

Now, all that remains is to find the right turbocharger for the job. Basically, you require a compressor that can flow 34lbs/minute of air at 1.1bar of boost at no less than 70% compressor efficiency, and a turbine that can drive the compressor to flow this much air without choking the exhaust gas. Simple really. Get this right, along with the right intercooler and right plumbing, and you’ll have your 350bhp.

I’ll recommend a turbocharger for the job once I finish scanning my catalogues.

[Gunni]

All the TCD turbos are turbonetics and work great. They come in a number of sizes of compressors

T4oE - 50trim , 60trim and GT35R wheel.

[GeoffBob]

But is that turbo kit from TCD? I don't see that stated explicitly on the Vintage BMW website, other than for what looks like "TCD" stamped on the exhaust manifold. Could easily be a TCD manifold with goodness knows what turbo underneath, or a case of "picture is for purposes of illustration only". Worth checking. The source of that picture is Ireland Engineering BTW, not VintageBMW. So are VintageBMW selling on an outside product (with markup) or are they selling something similar and using Ireland Engineerings picture for illustration purposes? Probably the former, but still worth knowing for sure (In which case you might as well buy it cheaper from Ireland Engineering).

Still not worth looking at if you are chasing 350hp Jaffa.

[GeoffBob]

Interesting. The VintageBMW sales catalogue is a direct duplication of the Ireland Engineering catalogue. How odd.

That turbo-kit is on the Ireland Engineering website at he same price.

[GeoffBob]

All the TCD turbos are turbonetics and work great.

Gunni, see the TCD turbo kit here

That does not look like a genuine Turbonetics turbocharger to me. Turbonetics compressor housings do not look like that.

That kit is good for 240hp according TCD.

And I REALLY don't like that log manifold.

[Gunni]

That log works nicely though, It´s not good, but at low backpressure it still works.

that "kit" is only setup for 240rwhp , the turbo itself is capable of much more as that kit is
without a intercooler.

I don´t know what to tell you about the turbonetics part but they use a on center housing for their
manifolds , so a off-center turbo isn´t going to fit very nice, and most china stuff is copies of off-center stuff .

[GeoffBob]

[GeoffBob]

Jaffa, following on from where I left off on choosing a turbo...

Follow Eta's suggestion and buy yourself a RHD M20 log manifold for $599 from TCD (see here). So far as I can tell this is just their LHD manifold turned upside down, but if it floats their boat to sell it as a separate item then so be it

You will now need to find yourself a suitable T4 turbine. I would recommend a T4 turbine housing, A/R=0.5 (part# 30252-2), with trim-O (that's letter O not number 0) turbine wheel (part# 20460) from Turbonetics. This will choke at approaching 20lbs/min air flow, from which point you will need to flow the remainder of your 35lbs/min exhaust flow through your wastegate. The TCD manifold includes a 38mm wastegate port which is sufficient for this purpose. The T4 turbine will bolt straight onto the manifold which includes a T4 flange. Depending upon your space constraints you can request the turbine housing with either a tangential or on-centre mounting.

Next you will need a compressor, and the 62-1 compressor wheel (62mm inducer, 76.2mm exducer, part# 20255T) in a 60-series housing (part# 20249) clearly sticks out as the ideal candidate for your 2500cc engine. Shown below is the flow map for this compressor.



Please note that I have specified the ”abig-shaft”a turbine and compressor wheels as these are more durable than the ”asmall-shaft”a variants.

I would recommend that you contact Turbonetics here for a quote on the above items. Ask them to fill in the details in terms of the CHRA, bearing type, back-plate etc so that they can quote you for an assembled and balanced turbocharger ready to ship. This turbocharger will likely cost you around the $1000 mark (excluding shipping) and will look similar to this one here If you have the extra cash available you can have it with the optional ceramic ball-bearing for reduced turbo-lag.

You’ll pardon me not specifying the remainder of the required parts as if you are not serious about the above then it just isn’t worth my effort. If, however, you are interested in the above then we can talk more later about the required wastegate, intercooler, plumbing etc. to make all the above work. Unless you are yourself proficient with a TIG welder you will, ultimately, need someone like Gunni or Ant to plumb in the exhaust and wastegate for you. You are also going to need an aftermarket engine management unit such as VEMS (from Gunni) or Emerald, Megasquirt, Omex etc. I would not venture to run a 350hp M20B25 engine off the stock Motronic ECU.

HTH
Geoff

[jaffacake]

thanks everyone for your views and info, geoff, i sent them an email just now asking for a quote, and yeah fair enough, thanks for all the help anyway

[eta]

Jaffa, I have been quoted £270 for the manifild adapter for the M51 manifold, but that just one quote I have yet to get others which will hopefully be a bit cheaper. As I intend to run low boost pressure on my engine with the volvo T5 turbo (Geoffbob your right it's a mitsubishi turbo) and should get around 220 hp. Not alot but its all I want (for now). The flow from the TDO4HL-16T turbo at a pressure ratio of 1.5-1.6 should deliver this ammount of air without choking. I should only need around 0.164 kg/s of air or 21.6 lbs/min. I have worked out it can deliver enough air for 250 hp with a higher pressure ratio but can then can the clutch take the torque that will result hense my lower target.

It's Geoff bobs posts that have allowed me tp work all of this out and find a turbo thats work. My turbo suggestion where based on a much lower target horsepower figure which I assumed. Given you want 350hp Geoff bob is of course right with his suggestions.

"I would recommend a T4 turbine housing, A/R=0.5 (part# 30252-2), with trim-O (that's letter O not number 0) turbine wheel (part# 20460) from Turbonetics. This will choke at approaching 20lbs/min air flow, from which point you will need to flow the remainder of your 35lbs/min exhaust flow through your wastegate"

I presume the when you say flow the remainder of your 35 lbs/min thorough your waste gate you mean 20lbs/min drives the turbine and the other 15 lbs/min is just watsed and flows straight out down the exhaust.

Geoff how do you determine the choke flow of the of the turbine housing? Incidently I was at a workshop today and the owner had exactly the turbo you described above in a box of turbo parts. The M51 manifold has a T3 flange and I think the TD04HL-16T turbines (given BMW use the TD04-11G on the 525TDS) use a T3 turbine housing. How will I work out the choke flow of my turbine housing, I need to make sure I have the right wastegate. I am only guessing the Volvo T5 one will be sufficent.

[GeoffBob]

[eta]

I have just measured the waste diameter, it ~30mm. I think its that circular disc in this photo.
This is the first turbo I have ever seen up close so I really am guessing at what everything does. These are the photos;

What are those two "modules" with the singular hose coming out of them. I think one is the boost pressure sensor, the diaphram connected to that rod which opperates what I presume to be the wastegate.
I hope the other is the recirculation valve or something similar that these turbo's are equipeed with.



Your assumptions Goeff are similar to those I made but I get peak power at 5000 rpm and peak torque around 4000 rpm.

I want to check my method;
I started with a desired inlet manifold pressure of 151500 pa (0.5 bar of boost)
I assume a intercooler pressure loss of 10340 pa.
I therefore "know" the compressor exit pressure.
I have calculated compressor exit air temperature (I also assume a presure drop across the air filter of 1720 Pa) to be 82 Celcius assuming a compressor efficency of 0.7 (thats an underestimate).
Assuming an intercooler efficency of 0.7 the inlet manifold temperature should be 40 Celcius.
Using the ideal gas law I therefore determine the air flow through the engine from 3000 rpm (I assume I will have 0.5 bar of boost by then) as I know the Ve of the engine from the last dyno curves. I assume the turbo will not change the Ve much as I will have a more free flowing exhaust to go with it. A poor assumption but...
From air flow I determine power and torque.

So at least my predictions are roughly in line with what you worked out.

[GeoffBob]

What are those two "modules" with the singular hose coming out of them. I think one is the boost pressure sensor, the diaphram connected to that rod which opperates what I presume to be the wastegate.
I hope the other is the recirculation valve or something similar that these turbo's are equipeed with.

Yip. One is your wastegate actuator, the other is your recirculation valve. Nice that it's all built into the turbo for you.

[GeoffBob]

[Mikey_Boy]

A freely breathing exhaust is as important to a turbo engine as it is to a normally aspirated engine, if not more so. You should, ideally, enlarge the exhaust system in order to both cope with the additional mass-air-flow, and prevent even higher turbine pressure. The higher exhaust back-pressure, the higher the pressure in the turbine in order to maintain a constant pressure ratio across the turbine.

+1

Geoff is (as always) bang on with what he states above - but especially the quote above - it is absolutely vital that the exhaust on a turbo'd engine is well sorted, the immediate downpipe being the most critical area after exhaust manifolding. Outside of absolute flow and matching your turbo well, getting transient response right is key to a great conversion. Turbos spool up best with pulses and not linear flow as most folks expect, hence getting manfolding right - on a 6, you are normally well sorted with pretty much any manifolding configuration and turbos, but good gains to be had with a well thought out exhaust manifold - it's much trickier with a 4 cylinder to get it right.

Your (as low as possible, large diameter) back pressure exhaust downpipe will help enormously with tip in (squeeze throttle) response as well a quick push to wide open throttle.

Don't worry too much on the intake side within reason - long pipe runs to intercoolers and intakes are Ok so long as the pressure drop for each of the components isn't high (compressor out to intercooler) across intercooler, intercooler to throttle) - nice smooth transitions and no nasty bends or section changes. Have a look at Geoff's race car thread for an example of an excellent intake and intercooler installation! I remember an exercise on a Bentley engine where the car made 45hp more for 0.25 bar LESS boost after the downpipes were better optimised and a few intake mods - better driveability too!

One final thought - having the recirculation valve integrated into the compressor housing can be a mixed blessing - it takes a bit of the hassle away, but they tend to have a harder life as they are running hotter which means their life can be shorter. Positioning of the recirculation valve on the cool side of the intercooler can help and there is always a lot of debate about the best position which is driven by the application. You also need to choose the spring for that as carefully as the one in the wastegate!

More for you to mull over...!
Cheers,
Mike

[eta]

Well I have had a price for a 3" system with straight through mufflers. The guy who will build it does this sort of thing regularly for turbo cars M5's e.t.c soI am confident the exhaust will up to to the standard required.

[eta]

As for calculating the how the boost builds with rpm; would it be fair to assume that a turbine and compressor that have the same diameter have similar maps? As you have previously stated (and my searches have turned up nowt) the turbine maps are unobtainable unless you happen to work for manufacturer.

Geoffbob, What books go into real detail regarding modeling of engine, exhaust temperature and just more of physics and thermodynamaics of engine/turbo's. I have read through maximium boost and performance engine tuning (I think that was the title) and while they where good and illuminating they have left many questions unanswered.

I feel a good read coming on as I instintively like you, want to have an understanding of this from first principals. It's a bit of an eye opener really.

[Mikey_Boy]

This was always a bit of a starting point bible when I was developing engines:



And this is a good read for practical applications for turbos:

http://www.bevenyoung.com.au/turbo.pdf

I am sure Geoff has some other great suggestions!



Cheers,
Mike

[GeoffBob]

As for calculating how the boost builds with rpm; would it be fair to assume that a turbine and compressor that have the same diameter have similar maps? As you have previously stated (and my searches have turned up nowt) the turbine maps are unobtainable unless you happen to work for manufacturer.

Sadly, no. Turbines have very different maps to compressors since they flow in different directions to each other, both in terms of actual direction through the housing (turbine inducer is compressor exducer and vice versa) and the fact that the compressor flows air against the pressure gradient (from Lo-P to Hi-P, while the turbine flows air with it (from Hi-P to Lo-P). It is for this reason, for example, that the airflow through a turbine will never surge. A turbine map is a very different beast to a compressor map, and generally says more about the flow restriction posed by the housing that it does about the aerodynamics of the blades. Here’s one from Garrett for the GT3071R I have ordered, clearly showing the effect of the A/R value of the housing upon flow through the housing.



Even with a turbine map, however, you still don’t know the actual air flow through the turbine unless you know the temperature of the exhaust gas.

Geoffbob, What books go into real detail regarding modeling of engine, exhaust temperature and just more of physics and thermodynamaics of engine/turbo's. I have read through maximium boost and performance engine tuning (I think that was the title) and while they where good and illuminating they have left many questions unanswered.

Was going to suggest Internal Combustion Engine Fundamentals by John Heywood, but Mike beat me to it . I didn’t know that one was still in print TBH, so well worth getting one new if you can. Turbochargers and superchargers are discussed from page 248 onwards as part of gas exchange processes in chapter 6. The equations that deal with turbochargers are fairly explicit, but the values to put into the equations are generally unknown.

Another good book is "Internal Combustion Engines: Applied Thermosciences" by Feguson and Kirkpatrick (see here)

Be warned, the popular books (A. Graham Bell, Corky Bell etc.) are all great books, but are intended for enthusiasts rather than academics. Mathematics ruins the experience for many and can, in most cases, be avoided while retaining the focus on the fun bits. There is also no reason why you can't build a very effective turbocharged engine while knowing little or nothing about thermodynamics and fluidmechanics. You don't need to know how a thermostat works on an oven to bake great bread. However, if it is knowledge of the nitty-gritty that you desire then those two books listed above will keep you busy for the next few years. Get Heywood's book first if you can.

[eta]

Thanks for those links, they are expnsive though, argh cristmas is coming up. I dug up a paper today "Cylinder Pressure in a Spark-Ignition Engine: A
Computational Model"
(I saved it a while back and forgot about it) dealing with the thermodynamics of combsution in spark engine and it provided a handy way to determine the temperature at the end of combustion.

mass of fuel = mf
mass of air = ma
FAR = Fuel to air ratio = 1/12
Total mass of gases in cylinder = mt
Tf = temperature when combustion is finished
Ts = temperature just before spark = 293*9.34^0.4 = 716 K Compression ratio = 9.34
C= coeeficent of combsution ~0.95 as not all fuel is burnt.
Cv = specific heat of the gas at constant volume
QHV = heating value of fuel in J/kg. This could be the inverse of BSFC and therefore should have a value of 12E6 J/kg is BSFC is 8.333E-8 kg/J. The paper gives a value of 44E6 J/kg.

mf = ma*FAR
mt = ma + mf = ma*(1+FAR)
Assumption all the energy released in combustion is used to heat gasses in the cylinder

mt*Cv*(Tf-Ts) = C*mf*QHV

So ma*(1+FAR)*Cv*(Tf-Ts) = C*ma*FAR*QHV

(1+FAR)*Cv*(Tf-Ts) = C*FAR*QHV
Cv = 20.8 J/mol/K = 716 J/kg/J
Temperature after combustion = 716 +(0.95*0.8333*12E6)/(1.08333*716) = 1940K!!!!!!! thats hot, too hot???

As the value of QHV is probably not the inverse of BSFC as the BSFC value must take into account the efficiency of the internal combustion engine then using the figure of 44E6 J/kg then the temperature at the end of combsution will be nearly 4 times hotter. That must be too much heat.

I feel the need for one of those books right know.

It also provides a complete thermodynamic model of an engine. Handy. When combustion ends the piston is not in the "power stroke" but has begun its decent. So I now need to figure out the expansion ratio of the engine which will be lower the compression ratio as the temperature in the cylinder will drop as the piston moves to bottom dead centre. If I know the expansion ratio which I don't the temperature when the piston reaches bottom dead centre will be easy. I hope I can then take the temperature in the cylinder at bottom dead centre as the exhaust temperature. If I can I then have an approximation of exhaust temperature.

[GeoffBob]

Assumption all the energy released in combustion is used to heat gasses in the cylinder

Ooooooh, that's a crude model! Surely that’s not a journal publication you have to hand Malcolm?

From the first law of thermodynamics (essentially a statement of conservation of energy) the change in internal energy (U) of a working fluid (in our case a mixture of air and fuel) must be balanced by the heat (Q) added to (or taken from) and the mechanical work (W) performed upon (or done by) said working fluid.

To assume that all the energy (U) released during combustion contributes to heat (W) only is just plain bonkers If this were the case the engine would be standing still (W=0) and its only useful function would be as a heater!

The temperature (T) of a gas is an indicator (gauge if you like) of the internal energy (U) stored in a gas. I say this because, from your above post, you seem to equate heat with temperature. The two are actually mutually exclusive. A high temperature does not necessarily indicate a high heat content, and vice versa. Heat is a measure of the energy that flows between two objects of differing temperature in an effort to bring about thermal equilibrium. A change in temperature is simply a measure of what happens to the internal energy of an object when energy is transferred to or from it. If we could measure the internal energy (U) of our working fluid directly, temperature would be a redundant property. Keep this in mind Malcolm ”“ you need to be think in terms of U, not T, if you ultimately want to calculate W. T is just something we use to gauge U because we can conveniently measure T.

Now, to determine the temperature of a fixed mass of gas after it has undergone a process you need (following the 1st law) to account for all energy put in (or taken out) in the form of heat and mechanical work.

In the case of an engine we need to account (essentially) for four things.

• 1) The work done upon said gas during the compression stroke.
  2) The heat transferred to said gas when the chemical energy of the fuel is released.
  3) The work done by said gas during the power stroke.
  4) Heat lost from the system (since this is a non-adiabatic process).

Only when all of the above are taken into account will you arrive at a reasonable estimation of exhaust gas temperature.

At first glance, what you have posted above appears to be in error because the work performed by the gas during the power stroke is not taken into account. Also, the energy content of the fuel has been grossly underestimated (only ~25% of what it should be) in order (I would say) to discount that portion of the fuel energy that is transferred to mechanical energy.

Remember Malcolm, the whole point to combusting the fuel at the height of compression is to raise the internal energy (U) of the working fluid. We then desire to extract as much of that energy as mechanical work (W) as possible, and the minimum as heat (Q). This is the whole process that defines, ultimately, the thermal efficiency of the engine.

If, however, we can calculate that fraction of the internal energy produced during combustion that contributes to the rise in heat content of the gas, then we can calculate the temperature of the exhaust gas, keeping in mind that any additional process whereby heat is transferred (further heat loss to the head and manifold say) and work is done upon or done by the gas (such as driving a turbine) will (following the first law) contribute to a further change in temperature of the gas.

[GeoffBob]

Eta, I googled that paper and found it, and it's quite legitimate.

That assumption you quoted above only applies to the instant at which combustion occurs, and not across the four strokes

So I now need to figure out the expansion ratio of the engine which will be lower the compression ratio as the temperature in the cylinder will drop as the piston moves to bottom dead centre. If I know the expansion ratio which I don't the temperature when the piston reaches bottom dead centre will be easy. I hope I can then take the temperature in the cylinder at bottom dead centre as the exhaust temperature. If I can I then have an approximation of exhaust temperature.

Exactly as you say.

[GeoffBob]

If I know the expansion ratio which I don't the temperature when the piston reaches bottom dead centre will be easy. I hope I can then take the temperature in the cylinder at bottom dead centre as the exhaust temperature. If I can I then have an approximation of exhaust temperature.

Why don't you know the expansion ratio? Your engine is driving a turbine that is operating at a fixed pressure as a function of the mass-flow-rate of air inducted through the engine. So, you know your pressure and volume at the begining of the power stroke and at the end of the exhaust stroke. Now, calculate the total change in internal energy of your working fluid (from the 1st law) during the power and exhaust stokes, and you'll have your temperature. Just don't forget to assume some heat loss since the whole process is hardly adiabatic. If it were we wouldn't need radiators and water pumps on our cars

[GeoffBob]

QHV = heating value of fuel in J/kg. This could be the inverse of BSFC and therefore should have a value of 12E6 J/kg is BSFC is 8.333E-8 kg/J. The paper gives a value of 44E6 J/kg.

No, 44E6 J/kg is correct.

BSFC is concerned only with that fraction of the fuel energy which contributes to the mechnical work output (W). While the "QHV" you quote above is the TOTAL energy content of the fuel. The author assumes the total energy is transferred to the working fluid during combustion and then calculates what percentage goes each way into either heat or mechanical work.

In a very basic calculation you might simply assume an average thermal effciency (across the range of rpm) of 27% (for a petrol engine), and hence, 12E6 J/kg is transferred to the mechancial output.

This is a VERY bad assumption to make though as this figure varies from engine to engine as well as across the range of RPM and timing angle! It's identical to saying that 10lbs/min or air gets me 100hp of mechancial power. It points you in the right direction, but it's hardly thermophysics. I do it all the time