Rocket Science for Earthlings
a continuing series for the gravitationally
impaired.
Rocket Science for Earthlings 3
Chapter C, inside the engine
If your reading this, your still stuck on planet Earth, the third planet.
In the last chapter, we followed a rocket into space.
Now we will follow a molecule from the injector to the
nozzle exit of a rocket engine.
The injectors job is to rather rudely spray the fuel
and oxidizer into the combustion chamber, where they can mix
and burn to produce lots of hot high pressure gas. The
injector should produce enough pressure loss to isolate the
propellant feed system from instabilities in the combustion
chamber, and also serves as the primary metering system to
determine propellant flow rates.
The combustion process that occurs adjacent to the
injector face is really quite remarkable. With a flow rate
of nearly two pounds per second for every square inch of
injector area, the temperatures can range from -423 deg F,
to nearly 5000 deg F, within a distance of one inch.
Horsepower's can range upwards to 1000 hp per square inch of
injector area. It is still a controlled combustion, but
just barely below the rate of detonation. The velocity of
the gas leaving the injector face is limited by velocity of
combustion of the propellants.
We now pick up a molecule of carbon dioxide, a typical
combustion product, as it leaves the injector face. The
molecule is very hot, it has a lot of energy, it exhibits a
high thermal velocity. IT IS MOVING! It exists in a crowd
of other hot gas molecules and bounces against them with
tremendous energy. These energetic collisions are evident
as high pressure in the area below the injector which we
call the combustion chamber. The energy of the molecule is
so high that it is unstable and may split and recombine
several time before it reaches the nozzle exit. The gas is
so dense that our molecule will travel in the straightest
possible line to the nozzle exit, there is very little
mixing after the gas leaves the injector face.
The nozzle exit of the engine is open to the outside
environment and the hot high pressure gas at the injector
face pushes the gas in the combustion chamber towards that
lower pressure. Daniel Bernoulli and Leonhard Euler, in the
1730's discovered that the energy in a high pressure gas can
be converted to kinetic energy. Since the energy remains
the same, the formula is;
energy = pressure + 1/2*mass*(velocity squared)
The term 1/2 M(V)2, represents the kinetic energy of the
gas, and that is what we want to maximize. Note that the
velocity is much more important than the mass, therefore we
want the lightest possible gas for the combustion product.
This is the reason that hydrogen is preferred as a
propellant and gives the highest exhaust velocity. In
addition to the highest energy, we want the most force from
the mass we expend. Force = mass * acceleration, to
maximize force we want to reach a high velocity in a short
amount of time. our nozzle system must be an efficient
accelerator of gas, but also as short as possible to reduce
weight. In 1880, a steam turbine engineer named Carl Laval,
discovered the a convergent-divergent nozzle would
efficiently accelerate steam to high velocity. The gasses
in the combustion chamber accelerate to pass through the
small opening of the throat. Mach the speed of sound, is
the velocity at which it becomes difficult to compress a
gas, it begins to act like a solid. Because of
incompressibility, the gas cannot exceed mach 1 until it has
passed the smallest point of the nozzle throat. After the
gas passes that point the expansion portion of the nozzle
accelerates the gas to very high velocity, mach 4 or 5.
With the "action" of the high velocity gas out the back of
the engine, the "reaction" (any action causes an equal and
opposite reaction) causes the vehicle to be pushed forward.
The chemical energy of the propellants has been
converted to pressure energy by combustion, and the pressure
energy has been converted to kinetic energy by the nozzle.
The momentum of the gas is converted to vehicle momentum.
To demonstrate these principals I constructed a small
plastic rocket engine that runs on compressed air. With a
chamber pressure of 40 psi, the pressure at the throat is 30
psi, indicating the higher velocity. At the nozzle exit the
pressure is 5 psi below atmospheric. The exhaust velocity
is high enough that a slight vacuum exists at the nozzle
exit. The strange journey of our molecule does not end, after
leaving the nozzle it still has a considerable amount of
thermal velocity. As it collides with other gas molecules
in the exhaust stream, in the vacuum of space it may bounce
off in a forward direction, traveling with enough velocity
to overtake and pass the rocket!
The measure of the efficiency of the whole process is
called "specific impulse" or ISP and is measured in seconds.
ISP = engine thrust / propellant consumption / second. Our
nitrous oxide / propane engine has an ISP of 230 at sea
level, and 290 at high altitude where there is no
atmospheric back pressure on the engine. The F1 liquid
oxygen / kerosene engines that powered the Saturn 5,
produced an ISP of 260 at sea level and 310 at altitude.
The Space Shuttle Main Engine burning liquid oxygen and
liquid hydrogen produces 363 at sea level and 455 at
altitude. The record for specific impulse in a chemical
engine was set by an engine that burned fluorine and
lithium, with hydrogen added as a coolant and to lighten the
exhaust. The flame was intensely hot and produced an
altitude ISP of 528! However good the performance of the
engine was, the chemicals were just too difficult to handle
to be practical.
Passing Gas
The rules for gas flow. For Subsonic flow; converging sections = faster, diverging
sections = slower. For Supersonic flow; converging sections = slower, diverging
sections = faster. This has to do with the fact that at supersonic velocities, air
begins to act like a solid, it just won't compress very well.