[AR] Re: Estimating Coefficient of Discharge (Cd)
- From: "Graham Sortino" <dmarc-noreply@xxxxxxxxxxxxx> (Redacted sender "gnsortino@xxxxxxxxx" for DMARC)
- To: "arocket@xxxxxxxxxxxxx" <arocket@xxxxxxxxxxxxx>
- Date: Mon, 15 Sep 2014 05:35:43 -0700
Ok thanks Bob, I can see where I’m making some obvious
mistakes now.
I’ve historically been using a very crude method to
control liquid flow, which is basically the air/nitrogen regulator on a
paintball tank. This has worked ok in the past when my orifice diameters were
very small (~0.010 in) and so when I started looking at larger engines I never
bothered to change it. However, when the orifice diameters started getting
bigger I was noticing an initial upstream pressure drop which eventually
tapered off sort of like a y=1/x curve.
As a result of this setup I was unable to measure flows with
just the pressure drop (eg. cold/hot flow @ 50 psi drop) and instead it would
be 500 down to ambient for the cold flow and 500 down to about 100 psi for the
igniter test. So I think step 1 here is for me to buy a proper regulator and
then re-do all these tests.
I had a few other questions on this subject if anyone has
the time:
1. Why should the pressure drop generally not be
greater than 20%?
2. I thought cavitation only occurred for liquids
that are choked (eg. below their vapor pressure)? I’ve historically ignored this
effect because I thought my liquid was always above it's vapor pressure. It
sounds like I’m making a mistake here.
3. For gases, I’ve experimented with choked and
non-choked flows but I believe a choked flow is easier to control since it’s
only dependent on the upstream pressure. Therefore when I test my GOX line, can
I use the same upstream pressure for both cold and hot tests? Also, does the
20% or so drop apply to the gas flow as well?
4. Bob, if you don’t mind me asking how did you
integrate flow meters into your test-stand. I made a decision a while back to
use
just pressure transducers but I’m starting to regret that and I’d like to look
at buying a few flow meters. I haven’t done much research on these yet but I’d
like to ideally get something that has an analog output that I can feed into a
micro-controller or data logger rather than using something with a thermometer
style gauge that I have to visually inspect.
On Sunday, September 14, 2014 10:28 AM, Robert Watzlavick
<rocket@xxxxxxxxxxxxxx> wrote:
The large jump in Cd (0.65 to 0.47) between 0.023 to .035 doesn't seem right.
How are you measuring the flow rate? If you're squirting it into a bucket,
there may be some evaporation or splashing going on. Check the L/d - if it is
in the range of 4-6, it might be flipping back and forth between fully
developed and separated flow (see the hydraulic flip notes in SP-8089).
Your upstream pressures seem really high - typically you want the
injector orifice pressure drop to be around 20% of the chamber
pressure. Since your "chamber" is the atmosphere for a cold test,
you should test at the same dP values you will see in the hot
run. So say your chamber pressure is 200 psi, you would be
shooting for an injector dP of 40 psi. I would run a set of cold
tests at 5 or 10 psi increments from 10 to 60 psi and plot them to
see any trends. If you run a cold test above 100 psi, you are
probably getting cavitation that won't be happening in the real
test. Then in the real test, you would set your regulators to run
at 200 + 40 = 240 psi.
I've had mixed success trying to measure discharge coefficients on
my injectors. As folks have pointed out, one of the big
uncertainties is the hole diameter for non-precision holes.
However, when using water tests to predict the performance for a
hot fire, the two unknowns (Cd and A) can be grouped together. So
you don't really know the hole area but if you use the same Cd and
A values, it should get you close for the hot fire. I added flow
meters to my test stand to try and address this exact problem and
I found that the Cd increases slightly between the cold and hot
tests. In one case, the fuel Cd was 0.35 using water and 0.40
during the hot fire. Note: the fuel Cd is really low because
it's the effective value for the cooling jacket + injector holes
since I can't easily separate them. In that same test, the LOX Cd
was 0.63-65 with water and 0.72-0.77 during the hot fire. This is
after taking into account any density and viscosity differences.
Other variables to consider are:
1. Static pressure vs. tank pressure - If the passages leading up
to the injector holes are small, the static pressure may be quite
a bit lower than the measured tank pressures due to the high
velocity of the fluid.
2. Back pressure effects - Someday I want to set up a rig where I
run the water tests into a big pressurized reservoir and try to
quantify this.
3. Pressure vs. Cd effects - In theory Cd should be constant vs.
pressure but I don't see that. In a cold water test of my LOX
orifices, the Cd was 0.66 at 20 psi and 0.62 at 100 psi.
4. Cross flow due to the combustion effects
5. Hydraulic flip - avoid L/d between 4 and 6
Eventually I stopped worrying about trying to exactly match the Cd
between the cold and hot test. I use it as a starting point, then
just adjust the tank pressures over a series of runs until the
flowmeters indicate the desired mixture ratio. Of course, there's
always the chance I calibrated the flowmeters incorrectly,
especially for the LOX line since it will shrink and read high.
One thing I haven't done is run the cold tests with kerosene,
mainly because it makes such a mess. If you're using ethanol, it
might not be so bad.
-Bob
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