[AR] Re: Estimating Coefficient of Discharge (Cd)
- From: "Monroe L. King Jr." <monroe@xxxxxxxxxxxxxxxxxx>
- To: arocket@xxxxxxxxxxxxx
- Date: Sun, 14 Sep 2014 16:42:15 -0700
I've seen this same thing happen with NO2 injection systems for
automotive applications on a plate type injector with a dual orifice at
even higher pressure. (we purge the lines on the line to ensure liquid
at the injector) It's an interesting phenomenon. A 2500 HP engine would
go lean toward the end of a run and grenade due to the same effect. We
solved it by pressurizing the NO2 with nitrogen. Plenty of guy's still
think it's due to the pressure drop but it was injector lock. (in part
due to a pressure drop but not enough to lean the mixture enough to
grenade the engine)
Which is a big reason I don't much care for the way self pressurized
hybrids fly. I know they can't possibly be efficient. (Unless fuel flow
is controlled by oxidizer flow) I've not seen any that function that way
however.
A simple name for this phenomenon is "injector lock"
Monroe
Here's a good way to prove it to yourself. Any fuel injector shop has a
injector test chamber, plug the other injector stands and run your
injector in one. Run some test check out what you see. ;)
> -------- Original Message --------
> Subject: [AR] Re: Estimating Coefficient of Discharge (Cd)
> From: Robert Watzlavick <rocket@xxxxxxxxxxxxxx>
> Date: Sun, September 14, 2014 7:27 am
> To: arocket@xxxxxxxxxxxxx
>
>
> 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
>
>
>
>
> On 09/13/2014 03:03 PM, (Redacted sender gnsortino@xxxxxxxxx for DMARC)
> wrote:
> > I was just performing some flow tests of my injector with water and I
> > noticed that the Coefficient of Discharge (Cd) surprisingly changed
> > from 0.65 to 0.47 when the orifice diameter was also changed from 0.23
> > in to 0.035 in. In both of these cases the downstream pressure was
> > ambient, however, for the first test the upstream pressure was about
> > 412psi although for the second it was closer to 380 psi. Presumably
> > the pressure difference is due to my regulator unable to keep up with
> > higher flow-rates.
> >
> > I have 3 theories about what could possibly cause this difference:
> >
> > (1) Cd is sensitive to the orifice diameter (eg. The larger the
> > diameter the lower the Cd)
> >
> > (2) Cd is sensitive to the upstream pressure or pressure drop
> >
> > (3) A combination of 1 and 2
> >
> > My suspicion is that most of the difference is due to higher pressure
> > drop. Unfortunately, I don’t have an easy way of proving this without
> > buying a new regulator.
> >
> > Does this this theory somewhat make sense? I also found 2 links to
> > formulas online (both formulas are fairly similar) that estimate Cd.
> > Is this a viable approach to do at least a first approximation of
> > correct Cd values?
> >
> > _http://www.valvias.com/flow-equations-discharge-coefficient-c.php_
> >
> > _http://en.wikipedia.org/wiki/Discharge_coefficient_
> >
> >
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