I take the easy way out of detailed injector delta-P analysis and use
cavitation venturis. Then the respective pressure drops are whatever they
become
with O/F predetermined by the precalibrated venturis. I do
measure injection and chamber pressures and learn how close I nailed Cd and
the aforementioned Bernoulli's equation which I committed to memory as a
young teen reading RPE by Sutton.
As far as Tube&sleeve injectors, I haven't built one but if I did it
would treat it no different than any other injector, use venturis to
hydraulically characterize the injector.
K
On Thu, Jan 28, 2021 at 2:42 PM Norman Yarvin <yarvin@xxxxxxxxxxxx> wrote:
On Thu, Jan 28, 2021 at 12:31:15PM +0000, Peter Fairbrother wrote:
Anybody got any knowledge or refs on the effect of the venturi effect on
coax injectors?
Presumably the moving outer stream exerts an effect on the inner stream
- and possibly vice-versa? - and lowers the injector pressure drop on
the inner fluid. But is this significant?
The venturi effect (or to be precise the Bernoulli equation) is a good
candidate for the most widely overused concept in fluid dynamics.
People tend to forget all the conditions and limitations that apply to
that equation. For starters, it applies only along the length of a
streamline; different streamlines may start out with different
energies from each other. The equation is a form of the conservation
of energy, saying that any potential energy lost from pressure goes
into velocity. As such there also has to be no energy loss, though as
usual the equation can be used in an approximate sense when there is a
bit of energy loss. Another limitation is that the flow has to be
steady; without that there are no well-defined streamlines in the
first place. A lot of what people ascribe to Bernoulli is due to
entrainment: faster-moving fluid collides and mixes with a
slower-moving fluid and drags it away from some place, lowering the
pressure in that place.
So, for instance, in a carburetor, where people say "the flow speeds
up in the venturi and that lowers the pressure and draws the fuel in",
a more thorough characterization starts by saying that the engine is
sucking in both fuel and air (both starting at atmospheric pressure),
using the suction from its pistons. The constriction of the venturi
does indeed serve to locally lower the pressure, but merely sucking in
fuel not the reason for having the venturi: the engine would suck fuel
into the intake manifold even if there were just a fuel tube leading
into it. The problem with that would be that the fuel would be
dribbling in rather than getting shot out in a jet into the middle of
a fast-moving stream of air. That's what the venturi really is there
for: effective mixing of fuel and air.
To finally get to fuel injectors: in subsonic conditions, when fluid
emerges from an opening it does so at the same pressure as the
surroundings (or at higher pressure; but if it's a liquid the higher
pressure just means it expands a tiny bit after emerging). So in that
situation thoughts should not be of Bernoulli but purely of what
entrainment will do.
In the case of a coaxial injector, it will instantly suck away all the
air in the gap between the two fluids, after which they'll come into
contact with each other while exiting and be at the same pressure. So
in terms of 'do I have to adjust mixture ratio to compensate for this
effect' -- no, not if they're coming out at the same velocity. On the
other hand, if you did have a central injector which you'd designed to
flow slower than the outer injector, the outer flow will entrain the
inner and drag it along, lowering the pressure and increasing the
pressure drop across the inner injector, making it flow faster.
In practice I suspect that even this is to be ignored: there are
enough hard-to-analyze things in injector flow that one tunes the area
ratio by cut-and-try rather than thinking theoretical analysis will
nail it on the first shot. Or, instead of static tuning, one provides
for independent control of fuel and oxidizer pressures, done by
measuring flows in real time, again making it so one doesn't have to
think about subtle influences on flow.