Rolf, Mark and All,
I have to correct my previous post. Mark was right. The total
pressure
in the turbine is the sum of the static and dynamic pressure.
This is exactly what Bernoulli's Equation tells us:
Along a streamline: static pressure + dynamic pressure = total
pressure
Expressed mathematically:
static pressure + (density * Velocity^2 / 2) = total pressure
In reference to that turbine chart, the pressure obviously shows
the sum
of hte static and dynamic pressure.
The reason the flow does not back up is still explained by
inertia, but
it is true that the total pressure equals the dyanmic and static
pressure, as Bernoulli tells us. No doubt about it.
Regards,
Gordon.
Gordon,
(I cut the bottom of message off as we all know it.)
Good that we have it correct now. At least I agree with it.
One point, would the 'dynamic' pressure not be the same as is
described
by 'inertia" of the gas.
I think that is one and the same thing. How do you see it?
However, if so, the dynamic pressure would have a direction, it
would be
a vector quantity.
The direction, of course, is toward the exhaust nozzle.
Any comments on that?
Regards
Rolf
The Rotary Engine NewsLetter. Powered by Linux.
ACRE NL web site. http://www.rotaryeng.net
Copyright 1998-2006 All world wide rights reserved.
Rolf,
I'm glad this thread has come up -- it gives us a chance to brush up
on some basic physics that are fundamental to both aerodynamics and
propulsion. I realized just how rusty I was on these basics when I
started thinking about Doug's question about turbine size.
You are right, of course, that dynamic pressure, which describes
air or another fluid that is flowing, is a vector quantity -- it has
both magnitude and direction.
The tricky part is that static pressure is a scalar quantity. If a
gas is static and not flowing, the measured pressure is the same in
all directions. But if the gas is moving, then the measured pressure
depends on the direction of motion.
Now about the inertia part. I believe it is correct to say that the
moving gas inside that turbine engine does not reverse direction and
flow back to an area of lower pressure due to its inertia. However,
this is not a full explanation of what is going on. Remember that
inertia also applies to objects at rest, which resist being
disturbed by an outside force. Newton gave us this idea of inertia
in his First Law of Motion.
So yes, this tells us that the moving gas in the turbine will resist
changing direction because of its inertia.
But I believe Newton's Second Law gives us better insight into the
question of fluid flow because it deals with the question of
"force." Specifically, it tells us that force is a change in
momentum over time, or mass times acceleration. With this insight
we can now go further and figure out just how much force the moving
air is exerting.
To understand dynamic pressure, we turn to the conservation of
momentum, a fundamental concept of physics.
Remember the analogy of sticking your hand out the window of your
moving car? The faster you go, the greater the force on your hand.
This is how the pitot tube works to move the needle on our airspeed
indicator. The greater the dynamic pressure, the more the needle is
deflected.
As noted earlier, dynamic pressure is simply half the product of
density and velocity squared:
Q = rho * V^2 / 2 = 0.5 * rho * V^2
If we add to this the coefficient of lift and wing area, we have the
lift equation:
L = 0.5 *rho * V^2 *Cl *Sref
And if we add dynamic pressure to the thrust equation, we can
analyze propeller thrust. So right off the bat we have lift and
thrust, which is pretty much everything there is to flight. Yes,
understanding dynamic pressure is a good thing to understand if we
aspire to fly...
There is a good page on the NASA educational website that gives a
more detailed explanation of dynamic pressure:
http://www.grc.nasa.gov/WWW/K-12/airplane/dynpress.html
Btw, I think we should be able to make some progress on Doug's
question about turbine size. We should be able to work out the
thermodynamics of the rotary engine using standard equations that we
use in gas turbines. After all both are internal combustion engines.
From there, we use the same tools to figure out the right size
recovery turbine.
I'm going to keep plugging on this one. I think we should have a
spreadshet for the exhaust side like the one I put together for
compressor selection.
Regards,
Gordon.
Thanks Gordon,
I appreciate your comments and the link. Good stuff.
Although I did not follow Doug's question, but the above are all good
tools.
PS: As a side note, I trust the pitot tube works by narrowing the air
passage through it, thereby increasing the air velocity which equals a
reduction in air pressure, and this reduced pressure is read by the
needle. It is not a positive dynamic (impact) pressure that is being
read. Is this right?
Regards
Rolf
I think you are speaking of a venturi Rolf.
A pito tube measures impact pressure.
For a simple minded example:
If one holds a one square flat plate out the window of one's
car at 100 MPH at sea level one will measure a force of
26 pounds or 26/144 = .18 psi. Pito tubes work on this simple
principle. There is no airflow into the pito tube.
One could stick the pressure sensor out the window and get
the same result.
The simple equation I use is force (drag) = .0026 times MPH squared
times the area of the flat plate.
The .0026 constant is related to the air density. It is
not the air density per se.
The same equation is used when calculating drag on a streamlined
object where C sub d is the drag coeff. of that object. In that
case the formula is Drag = C sub d X Frontal Area X .0026 X
MPH squared.
The term C sub d X Frontal Area is frequently called the flat
plate equivalent drag number.
The terms impact pressure and dynamic pressure are interchangeable.
Paul Lamar ...No rotor no motor.
Gordon, Paul et all
Every six months I check back in to see what Catapillar Inc. is doing with
their mechanical as well as electric turbo compounding schemes. If you do a
Google search for "Caterpillar turbo compound turbine" you will find
several interesting PDF files there.
The first one you can skim through it. It is titled
"Diesel Engine Waste Heat Recovery Utilizing Electric Turbocompound" ...
This report has some clear pictures and gives an understanding of what it
takes to perform this task. As much as we may love the concept this PDF
will give a clear indication of the sizes and technology involved to pull it
off or for us not:) To heavy for flight, even if it is scaled down to our
rotary. Switched reluctance generators are also very challenging to develop.
The second PDF I recommend looking at is called "Engine System Approach to
Exhaust Energy Recovery". There are some little tibits of information that
are real jewels, hints perhaps for our use. I'll let you read it first and
then we can discuss it.
In another PDF report I found the statement that Garrett was the only
company that had successfully manufactured a turbo compound system.
Hmmmm???? I don't think so.
Best Regards
Doug Fir
"Engine System Approach to Exhaust Energy Recovery"
Hard to fathom this stuff as it is power point presentations
with little or no text explanation. Probably puts everybody
to sleep that watches it :)
What is the base line engine power and BSFC?
IMHO the TC stuff is marginally cost effective
as they are starting with a cool exhaust diesel.
I wonder if it will actually go into production.
Paul Lamar ...No rotor no motor.
Paul
The point is the amount of effort they are expending to raise the efficiency
of the system 10%. One interesting quote and graph at the end of the
article was about how mechanical turbocompounding systems can go south real
fast with increased backpressure. Can we interpret that to mean they are
talking about the inline power turbine?
Regards
Doug
You got me Doug. Without seeing the dialog that goes with
all those power point presentations I am not exactly sure
what they are talking about. Very little of that is applicable
to aircraft rotaries anyway as those engines weigh 1500 to 2000
pounds.
Frankly I doubt they will put them into production anyway
unless diesel fuel goes to $10 a gallon. As far as I can tell Scania
discontinued the TC diesel in Europe and diesel fuel over there
is $5 to $8 dollars a gallon. If Scania can't make it pay off at
$8 a gallon it is not going to happen any time soon.
Do you recall what you paid for gasoline in Germany?
Paul Lamar ...No rotor no motor.
The Rotary Engine NewsLetter. Powered by Linux.
ACRE NL web site.
http://www.rotaryeng.net
Copyright 1998-2006 All world wide rights reserved.