Re: Motor Jets and thermojets.
- From: Eunometic <eunometic@xxxxxxxxxxxx>
- Date: Fri, 5 Sep 2008 06:32:01 -0700 (PDT)
On Sep 5, 6:09 am, "Keith Willshaw" <keithnos...@xxxxxxxxxxx> wrote:
"Eunometic" <eunome...@xxxxxxxxxxxx> wrote in message
news:6465e2a5-4d77-4025-b5a3-af0acee32f72@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Sep 3, 5:13 am, "Keith Willshaw" <keithnos...@xxxxxxxxxxx> wrote:
Although it initially appear we have a net output of only 220hp we do
however have about 300lbs-400lbs or jet thrust.
Well no, all you have is a lot of very hot air at 1 atm. You only get
jet thrust if you throw it away.
Indeed and that is what piston engines do: throw away exhaust energy.
Not if fitted with a turbocharger, in that case some the energy is used
to drive the supercharger.
About 15% to 20% appears to be recoverable if the R-3350 is taken as
an example.
Well, the engine at sea level running of ambient air at 37C/310K 14psi
could produce 1000hp then when running at 100,000ft if it is is supplied
supercharged air
at the same conditions it should be able to produce more power because the
back pressure on the
exhaust is so much less. Indeed it would produce around 100 horse power
even without
fuel/ignition simply
as a compressed air motor although in this case it would be transferring
heat into the engine
from the coolant. Also the Merlin produced about 300lbs jet thrust
which would only improve
due to the reduced back pressure.
Marginal at best , the formula in the simple case is jet
thrust=mass*velocity
The Merlin is dumping its exhaust into atmosphere whose pressure is at
about 0.5 atmospheres, If it is dumping the same amount of exhaust
into air at 0.01 ata it is going to come out faster and produce more
thrust.
Of course the best way to use this lowered pressure is to use a turbo-
supercharger.
A simplistic assessment, In fact for high speed flight the jet thrust
might be more useful as it will not fall off in the same way the power
delivered by the propeller does
It depends, if the power is desired for a motor jet it might be more
useful
Also note that the ambient pressure is 0.15psi so the engine will also
recover pressure since there is essentially zero back pressure on the
exhaust.
Not much - try running a diesel engine on air at 15 psi
Diesels are started on less.
Indeed , look at the power output of an alternate electric starter
In addition the output temperature of 854 kelvin (about 580C) would
cause detonation and maybe melt the final compressor stages so we
would have to cool the air. The best way to this not with an after
cooler but with several inter coolers between compressor stages since
equation 2 shows that the work required is a function of inlet
temperature. This will improve the efficiency of the compressor
significantly despite slight pressure losses in the inter coolers.
Well no, work is done by passing air through the intercoolers
due to frictional losses and much of the work done in compression
was in the form of heat. An intercooler removes that heat essentially
throwing away that work meaning you cant recuperate it. The
net result is to REDUCE efficiency.
I've already accounted for this lost energy in the 655kW/880hp needed
to drive the single stage compressor with after cooler.
The air needs to be cooled. If an aftercooler is used most of the
reject heat is wasted though at nearly 600C some of it could probably
be recovered.
The only practical way to do this would be install a steam turbine.
This is often done in land based diesel installations but has
been deemed a trifle impractical for aircraft
Several kW at 600C is a rather good heat source.
It don't take it too seriously but there are other cycles: the
stirling cycle or even the closed brayton cycle if other forms of
coolant than water are considered.
Steam turbines and boilers suitable for aircraft use are in fact very
light and compact. It is the condensers that
are the problem so one could recover a little in say the wing surfaces
or leading edges if they were not yet in use.
Extracting mechanical energy from the coolant probably reduces the
radiator area.
If an intercooler is used such that after a compression of 10:1 the
air is cooled.to say 330K and only then further compressed 10:1 then
their is a considerable reduction in work required.
You'll have to demonstrate those figures are accurate, I dont believe em
and you'll still need an aftercooler.
Inter coolers are a very accepted and widely used in both piston and
gas turbine engines.
Just repeat my calculations only for two 10:1 compression ratios in
series instead of one 100:1.
Assume that intake air is at 240K in both cases and assume that the
intercooler cools the exit
air of the intermediat stage.
The original for a 100:1 ratio:
Equation 1:
Power required to compress gas is
W = Cp(T2-T1)
where:
W = Power in kW
Cp = 1.005 kJ/Kg = specific heat of air at const pressure
T2 exit temperature of compressor
T1 entry temperature of compressor assume -40C or -50C at 100,000ft =
-230K
Pressure at 100,000ft = 0.15 or 0.01 ata so we need a 100:1
compression ratio to achieve ambient conditions
Equation 2 for T2
T2 = T1 x r^((L-1)/L)
r = compression ratio = 100
L = ratio of specific heats = 1.4 for air usually shown as gamma.
T2 = 230 x 100^0.285 = 230 x 3.715 = 854 kelvin
Plugging into Equation 1
1.005 x (854-230) = 655kW/880hp power to compress 1kg of air at
0.15psi to 15psi
Now for a 10:1 ratio taking intake air at 230K
Equation 1:
Power required to compress gas is
W = Cp(T2-T1)
where:
W = Power in kW
Cp = 1.005 kJ/Kg = specific heat of air at const pressure
T2 exit temperature of compressor
T1 entry temperature of compressor assume -40C or -50C at 100,000ft =
-230K
Pressure at 100,000ft = 0.15 or 0.01 ata so we need a two 10:1 x 10:1
compressors in series with an intercooler between them.
Equation 2 for T2
T2 = T1 x r^((L-1)/L)
r = compression ratio = 10
L = ratio of specific heats = 1.4 for air usually shown as gamma.
T2 = 230 x 10^0.285 = 230 x 1.92 = 442 kelvin
Plugging into Equation 1
1.005 x (442-230) = 223kW/300hp power to compress 1kg of air at
0.15psi to 15psi
Taking into account that we only need 0.85kg of air and out compressor
is only 0.85% efficient then this is the power required.
Now we cool the air to 330K (say 57C) and repeat the calculation using
T1 = 330
Now for a 10:1 ratio taking intake air at 330K
Equation 1:
Power required to compress gas is
W = Cp(T2-T1)
where:
W = Power in kW
Cp = 1.005 kJ/Kg = specific heat of air at const pressure
T2 exit temperature of compressor
T1 entry temperature of compressor assume 330K/57C taken in at 1.5psi
after intercooling.
Equation 2 for T2
T2 = T1 x r^((L-1)/L)
r = compression ratio = 10
L = ratio of specific heats = 1.4 for air usually shown as gamma.
T2 = 330 x 10^0.285 = 230 x 1.92 = 633 kelvin
Plugging into Equation 1
1.005 x (633-330) = 304kW/409hp power to compress 1kg of air at 330K
from 1.5 to 15psi.
Again assuming only 0.85kg air is required and the compressor
efficiency is 85%.
Adding the two figures 223kW/300 + 304kW/409 = 527kW/709hp
This is a lot less than the original 880hp required admittedly there
are slight pressure losses in the inter cooler and after cooler due to
friction but they are considered worthwhile. It should be possible to
circulate coolant water in the stator blades thus avoiding pressure
loss of an inter cooler entirely.
The first stage
needs about 200kW, the second stage 307kW for a total of 507kW/
671hp.
So explain why you think the first stage needs only 2/3 the power
of the second stage to compress the same mass of air by the same
pressure ratio
Because I am assuming that the inter cooler is only able to lower the
temperature from 442K to 330K instead of 230K of ambinent air at
100,000ft. I imagine somewhat better might be done.
The gas equations dont change just because you do
the compression in two stages
The work done is purely a ratio of the inlet temperature, therefore if
you can lower inlet temperature you reduce work.
If the work is divided up between 12 stages of 1.46 compression with
an inter cooler between each stage to keep temperature below 330K the
power required is even lower. I get 34kW per stage and only 408kW/
550hp.
There are some pressure losses but they are not so
significant. This gives us a net power of 1000-671 = 330hp.
Intercooling is worthwhile and even gas turbines can benefit from it.
Inter cooling is worthwhile because it reduces the outlet gas
temperature which is essential for a piston engine and it reduces
the physical size of the compressor as the density in secondary
stages and burners is higher. This can increase power output but unless
you can recuperate that heat the energy is lost reducing thermal
efficiency
We've already given it away so no need to recuperate, the limitation
in petrol engines is octane rating and the limitation in gas turbines
is inlet temperature. Diesels are more tolerant of high inlet
temperatures.
In an ideal world the gas turbine doesn't need inter cooling but Gas-
turbines with high pressure ratios can use an intercooler to cool the
air between stages of compression, allowing you to burn more fuel and
generate more power. Remember, the limiting factor on fuel input is
the temperature of the hot gas created, because of the metallurgy of
the first stage nozzle and turbine blades. One turbine using this
cycle is the General Electric LM1600 / Marine version
As for their usefulness for gas turbines while they are widely
used in land and marine based applications their weight rules
them out of aviation usage
I bet its more a maintenance issue than a weight issue. Imagine a RB.
211 or Trent. If the IP compressor stator
blades are hollow and water cooled then the pressurized water can be
flashed into steam in the hollow cowling to take advantage of all of
that bypass air, alternatively sodium-Potassium cooling or heat pipes
might be used to 'wick' the heat to the inner cowling.
The engine will require a fairly large and efficient supercharger with
a lot of intercoolers and radiators.
Indeed so we now have used beteeen 90 and 95% of the
power of the engine just to produce air for combustion
in that engine.
No where near 90%.
Easily 90%
Ok, I did make an minor error in the scenario of a purely after cooled
engine, the compressor power is 880hp leaving only 120hp.
However in the case of effective inter cooling between 10:1 and 10:1
stages only between 700hp is required if perfect inter cooling is used
the power requirement is only around 550hp
Perfect inter cooling is the situation where the gas is never allowed
to rise in temperature in subsequent stages.
It can be accomplished by integral inter cooling of an axial
compressor. Cooling a water jacket is normal on an
axial compressor, in this case cooling of the stator blades would be
required as well. This can be accomplished with no
pressure loss at all.
We've used between 67% and 78% of a 1000hp engines gross output to
power a supercharger to provide 0.86kg/sec of air at slightly above
sea level pressure (15psi) that was produced from air at 0.01
atmosphere.(0.15psi) so that we have somewhere between 220 to 330hp
net output and probably 100hp more when reduced back pressure is
considered.
100hp is insanely optimistic and you have fudged the figures to
even get to 78%
Without inter cooling power required is 880hp which gives a net of
120hp.
With inter cooling down to 330K it is 709hp which gives a net of
291hp.
With very good inter cooling its down to 550hp.
Lets get back to reality. The single stage supercharger on the Merlin 20
required almost 150hp to drive it at full power and even then the power
output fell off rapidly at altitude.
Actually it gained power before falling off with the fall off not
becoming rapid until after full pressure altitude which in itself
varied as to supercharger gearing and settings.
The two stage supercharger at full output in high altitude flight absorbed
around 400 hp and its power output at 35,000 ft was still much lower
than at sea level
The Merlin 61 supercharger required 800hp to deliver air with
24" boost. You are specifying close to 29" boost
Of course an engine running at 24 inches boost is delivering more than
1 atmosphere boost and the Merlin is more than a 1000hp engine. In
English units: 1 inHg = .491098 psi, or 2.036254 inHg = 1 psi so this
is 12 inches boost on top of 14 ie 1.88 ata.
The Merlin engine is not that optimized for high altitude as it is set
up for power from a small block, it has a relatively low compression
ratio of 6.3:1 which limits its expansion ratio and on top of that
while the two stage supercharger was supposedly efficient for its day
it is unlikely to have exceeded 70% by much. You also haven't
specified the operating altitude, Even the Merlin supercharger wasn't
that powerful. When the Germans finally introduced two stage
superchargers DB605L and Jumo 213E1 they had critical altitudes of
around 9600m (nearly 32,000ft)
Once you figure in all the losses the power required to deliver sea
level pressure air at 100,000 ft going to require more power
than the engine can produce.
With inter cooling we have around 291hp net available, assume some
additional parasitic losses in pumping coolant water and some pressure
losses and we are down to say 200hp.
We still have 300lbs jet thrust or 200hp that can easily be recovered
by an exhaust gas turbine.
> I don't think their is going to be a problem achieving
85% efficiency in the supercharger and even if that efficiency isn't
quite achieved the use of inter-cooling will substantially cut the
work required down
The work done compress n kg of gas from Pressure 1 to Pressure
2 doesnt change just because you use an intercooler.
It does for the subsequent stage because the work of compression is
always dependent on the absolute inlet temperature.
What it does do is help the efficiency of your compressor
by increasing density.
Yes it reduces the size of the turbo machinery and allows it to run
slower but it also reduces the work required of any down stream stage
in achieving a certain compression ratio.
If you need to produce compressed air at a certain temperature it is
better to intercool than aftercool.
On top of that we have hundreds of hp available in the exhaust for use
in either a turbine for either turbo compounding or turbo-
supercharging that would boost our power from 220-330 by about 20% of
1000hp ie 200hp to 440hp-530hp as exhaust gas turbines in turbo
compounded engines recover about 20% of exhaust gas energy which is
almost the same as shaft hp. In our case I think this would be much
more due to the very low backpresssue,
Nonsense, you have already accounted for that energy by giving yourself
the extra 100hp in the engine and you have already boosted the inlet
pressure with your supercharger. The very act of fitting a turbocharger
RAISES the backpressure. This negates your hoped for 100hp
and also loses you the jet thrust
Let me repeat:
worst case scenario with an 85% efficient compressor and aftercooler
is
880hp required power which leaves 120hp net power.
medium case scenario with 85% efficient compressor and inter cooling
with aftercooling is
709hp required power which leaves 291hp net power output.
best case scenario with near perfect inter cooling using an integrally
inter cooled axial compressor is
550hp (or less) which leaves 450hp net output. (this has no pressure
drop)
http://www.wipo.int/pctdb/images1/PCT-PAGES/1997/371997/97031192/97031192.pdf
We still have at least 200hp in the exhaust or 300lbs jet thrust at
the very minimum.
So at 100,000ft it is possible to produce usefull levels of power
albeit with superchargers and radiators and even more with a turbo.
The supercharger isn't going to be to big and heavy as the IC engine
doesn't need to much air and the lightly loaded first stages aren't at
too much pressure.
More wishful thinking.
I've done the maths, without inter cooling there is just enough power
to produce a tiny net output of 12% which would reduce a little when
after cooler pump losses are considered. With inter cooling there is
a significant net output of around 29% of sea level output with 45%
being the theoretical limit.
parasitic pressure losses in the inter cooler are not that significant
while the water pump power required is no more than the coolant
required in normal engine cooling as it is in the same order of
magnitude.
I not the that you have ignored the drag caused by forcing air through
the intercoolers.
The losses are less than what is gained. If we assume a 20% pressure
loss after the first stage which then requires a 12:1 ratio then the
power required is only increased by about 5% in the power required for
the LP compressor.
While we are talking about intercoolers bear in mind
that the intercooler on the Merlin XX required around 30 gallons of
water per minute to reduce the charge temperature to a reasonable
level.
Merlin XX is a single stage Merlin?
How much did the coolant pump for the remainder of the engine require?
Of course at Mach 0.66 or 200ms or 440mph the 300lbs of jet thrust is
worth 240kW and some of that would be surrendered in the gas turbines.
Now you are triple accounting, The Merlin had useful jet thrust because
it had no turbocharger. You are not only trying to have your cake and
eat it , you are trying to sell it afterward
Not triple counting, I'm just pointing out the range of possibilities.
You can
1) Boost the output of the piston engine by having zero back pressure
2) Drive a turbosupercharger
3) Use the energetic exhasut for jet propulsion
What you cant simply add the totals for each option as you have done
Well both 1) and 3) should naturally increase together even if we do
nothing as when exhaust backpressure is reduced not only does piston
power increase but so does exchaust velocity and therefore thrust.
As for 2) it is true that we have removed 20% of the exhaust energy
which adds about 20% in power yet there is still a little power for
jet thrust, more importantly the 20% increase in power seen on the CW
R-3350 turbo compound could be more at 100,000ft than 30,000ft because
of reduced back pressure.
Feel free to list the engines with mechanical superchargers and
exhaust turbines that produced significant jet thrust
CW R-4360 VDT (Variable Discharge Turbine) several hundred pounds jet
thrust
http://www.time.com/time/magazine/article/0,9171,887932,00.html
Napier Nomad 2 (without reheat) about 318lbs
It seems that all that is required is a variable area nozzle.
Now take a look at the combined weight of your dieselSure, the gas turbine might be better but there is not indication that
engine, intercoolers and compressor and compare that
with a gas turbine of the same power
for subsonic aircraft that piston engined aircraft can't fly as high
as jets though they do seem to use turbochargers. Technically the
heat exchangers/radiators are probably the most challenging task.
There is one indication - NONE OF THEM DO
66000ft for the boeing condor and 80000ft for the Grob Strato 2C
The max altitude at which a turbo/supercharger system can deliver
sea level pressure air is called the critical altitude. Typically for
late piston engines this was around 25,000 ft and they required several
hundred hp to do this. You seem to think that you can do better and
take it up to 100,000 ft
It can be done. Key is
1 Highly efficient compressor
2 Effective Intercooling.
I suggest a compressor with a stage compression ratio of 1.414:1 can
achieve 100:1 in 13 stages will do this.
The compressor will need an intake area of about 0.66sqm inorder to
gulp air at 100m/s at 100,000ft less if the a/c moves faster.
Intercooling will be by compressor water jacket and hollow stator
blades. Integral gearing will be used to optimize efficiency.
Plugging into equation 2 for intake temperature of 230K we have a
temperature rise of
230 x 1.414^0.285 = 230 x 1.10 = 253.
Plugging into equation 2 we get 253-230 x 1.05 = 24kW
It can be seen that with a 10% increase in temperature per stage that
if we aim to keep temperature below 330K that the first four stages
won't even need intercooling.
Subsequent stages will have an inlet temperature of 330 and an outlet
of 330 x 1.1 = 363 which leads to 33kW work per stage.
Assume the first stage needs 24kW and the next 12 need 33kW then we
have a total of 420kW or 556hp. Stages 2, 3 and 4 actually require
less than 33kW.
That leads to a net power of 450hp being available. This scenario is
harder to achieve as the radiators must dispose of 42kW with only a
360K temperature into a 230K environment. 60 gallons a minute should
do it.
A 1000hp engine block on its own will probably weigh 800lbs, assume
the supercharger compressor will weigh half as much again as much
again its going to be pretty light due to the low pressure (no more
than 1 ata) and we end up with a 1200lb engine producing 450hp and
300lbs jet thrust as the best case.
Sheesh
An engine can be made to run at that altitude. It's as simple as
that.
Keith
.
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