[AR] Re: Estimating Coefficient of Discharge (Cd)
- From: Robert Watzlavick <rocket@xxxxxxxxxxxxxx>
- To: "arocket@xxxxxxxxxxxxx" <arocket@xxxxxxxxxxxxx>
- Date: Mon, 15 Sep 2014 09:31:16 -0500
The 20% pressure drop is the minimum recommended value to improve combustion
stability by isolating feed pressure and chamber pressure. It certainly can be
larger but then you're carrying around extra pressuring gas and probably a
heavier structure for the gas tank. I'm not sure about the rule of thumb for
gaseous propellants. For my igniter, I had a much higher gas pressure drop than
the main engine because the igniter pressure was lower than the main chamber
but they both have the same feed supply.
I use Cox AN and FTI series turbine flowmeters for the test stand. Pretty much
all of them have a magnetic pickup and put out pulses proportional to the
volumetric flow rate. You can use a frequency to voltage converter to get an
analog signal out of it. There is a schematic on my test stand page for an
LM2917 based circuit. With low tempco resistors and caps, the output is very
repeatable and linear. Or you can just measure the frequency directly with a
counter, microcontroller input, etc. The main thing to remember is liquid
flowmeters don't like gas blowing through them so you have to shut off the flow
before you run out of propellant. With the tank pressures on a typical
pressure fed rocket engine, just gas blowing through can destroy the bearings.
Both Cox and FTI have good application notes full of useful info.
-Bob
> On Sep 15, 2014, at 7:35, "Graham Sortino" <dmarc-noreply@xxxxxxxxxxxxx>
> (Redacted sender "gnsortino@xxxxxxxxx" for DMARC) wrote:
>
> 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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