Blowing machine

[david_h]

Getting back to flow meters in series.
If the density of dry air at 20C and atmospheric pressure(100 kPa) is 1.19 kg/m3 then at atmospheric pressure plus 1300 mm of H2O (112.7 kPa total) it would be 1.34. So its volume would go up by about 13%. As mass is conserved with flow meters in series that is the difference in flow rate that we would expect from expansion with a clamp between the two so that the first was operating at 1300mm H2O more than the second. There would also be a difference due to the drag on the float changing.

As an aside, but on the main challenge. No need for a blowing machine, just need a supercomputer. https://phys.org/news/2015-02-supercomp ... ument.html Some interesting goings on in the windway in that first animation.

[David Cooper]

rho (Greek letter ρ) is the symbol for density, in this case the density of air. At 21 C, sea level (where Terry is), 60% humidity, the density of air is in the neighbourhood of 1.19 kg/m^3.
...
Here's an example calculation...

Thanks for the clear examples - it all makes sense to me now that I can see all the parts coming together.

Is the plan to go on from here to generate comparative lists for different types of whistle of the flow and resistance range for each note across two and a half octaves? (That's the data I'd most want to see if I made a blowing machine.)

[Tunborough]

Have we tried this arrangement, to test how the flow meters react to downstream pressure?

stop valve -> first flowmeter -> manometer takeoff -> second valve -> second flowmeter -> open air,

where the manometer is measuring relative to open air. Suppose we adjust the balance on the two valves to keep the flow on the second meter around 10 L/min and see what happens to the flow on the first meter at different pressures. (The needle valve on the second flowmeter would probably do as the second valve.)

When Terry squeezed the tubing between the flowmeters, it made a big difference to the reading on the upstream flowmeter. The only thing I can think of that would be making that difference is the downstream pressure. This would give us a chance to quantify this. Maybe density changes are enough to explain it, maybe not.

[Tunborough]

Here's my model so far ...

Let h and h1 be the height of the windway exit and entrance in mm,
w and w1 be the width of the windway exit and entrance in mm,
L be the length of the windway (the windway, not the whole whistle) in mm,
rho (ρ) be the density of air in kg/m^3,
Q be the air flow in L/min,
P be the mouth pressure in mm H2O,
v be the air speed leaving the windway.

If we know the flow rate, we can calculate the air speed in m/s as:

v = Q / (0.060 * h * w)
(The 0.060 is to convert from L/min to mL/sec.)

If we know the mouth pressure, we can calculate the air speed in m/s as:

v = sqrt(2 * 9.807 * P / (rho * K))
(The 9.807 is to convert from mm H20 to Pascals.)

Here, K is the flow loss coefficient, a dimensionless constant that is specific to a whistle. It is the sum of three parts:

K = Kb + Kdw + Ke

Kb comes from Bernoulli's principle. If the cross-sectional area of the mouth is A0 mm^2, and the area of the windway entrance is A1 = h1 * w1,

Kb = 1 - (A1/A0)^2

Kdw comes from the Darcy-Weisbach equation:

Kdw = fd * T * L/Dh

Here, fd is the Darcy friction factor, which is close enough to 0.04 for pretty much everything we're interested in.

Dh is the hydraulic diameter of the windway entrance, Dh = 2*h1*w1/(h1+w1).

T is a taper factor. Assuming most of the taper happens in the height, and the taper is more-or-less linear:

T = (1 + h/h1)/2 * (1 + h^2/h1^2)/2

Ke is an empirical adjustment. As yet, I don't have a handle on this value. For the calibrators and the Feadog it is around 0.35; for the old Gen, Killarney, and Mellow D, it is around zero. When Terry put the flowmeter after a calibrator instead of before, Ke was around zero, so Ke may be nothing more than compensation for some idiosyncrasy of the flowmeter.

For the discharge coefficient, Cd = 1/sqrt(K)

For the "resistance", resistance = sqrt(P)/Q = 0.2657 * h * w / sqrt(rho * K) = 0.2657 * h * w * Cd / sqrt(rho)

[david_h]

[ Crossing - I was typing this as you posted ! - it refers to the previous draft ]

As you are around Tunborough and the equations have come up, please can you confirm I have this right.

If p1 and v1 are the pressure and velocity on the inlet side
and p2 and v2 the same on the outlet side then the case of Bernoulli's equation in use is:

p1 + rho/2*v1*v1= p2 + rho/2*v2*v2

and we are treating v1 as negligible and p2 as the same as the low pressure end of the manometer

so we would have p1= rho/2*v2*v2 for a zero length tube (i.e. K=1 so not used)

[Tunborough]

If p1 and v1 are the pressure and velocity on the inlet side
and p2 and v2 the same on the outlet side then the case of Bernoulli's equation in use is:

p1 + rho/2*v1*v1= p2 + rho/2*v2*v2

and we are treating v1 as negligible and p2 as the same as the low pressure end of the manometer

so we would have p1= rho/2*v2*v2 for a zero length tube (i.e. K=1 so not used)

Yes, that's the form of Bernoulli's equation we're working with.

If we call the "mouth" of the blowing machine the inlet and the whistle window (or open air) the outlet, then we're assuming p2 is zero, relative to atmospheric pressure. The earlier draft assumed v1 was negligible. The more recent draft doesn't; the term -(A1/A0)^2 in Kb adjusts for a non-zero v1 = Q/A0. For a zero-length tube with no obstructions, and assuming A0 >> A1, we would have K = 1 and p1= rho/2*v2*v2.

However, it would seem that any obstruction, particularly the abrupt narrowing of the airflow between the mouth and the windway, would add an additional loss coefficient to K. Reading this, https://neutrium.net/fluid-flow/pressur ... and-exits/, I'm surprised that we don't see a significant additional loss (which would show up in Ke) for whistles like the old Gen.

[Terry McGee]

So, since the shut-off valve has been shown to be a non-issue, how about another case as follows:

1. new improved super-duper-tape.
2. use 1 meter from 0-20lpm
3. use 2 meters in parallel for 14-28, intentionally including the overlap, just to see.

OK:

Code: Select all

12 March 2023: Old Gen head after Flow Meters singly and in parallel, taped better.				
LH	RH	L+R	Press.	Res.
2		2	4	1.000
4		4	6	0.612
6		6	9	0.500
8		8	17	0.515
10		10	29	0.539
12		12	40	0.527
14		14	55	0.530
16		16	71	0.527
18		18	90	0.527
20		20	119.5	0.547
7	6.8	13.8	44	0.481
8	8	16	63	0.496
9	9.3	18.3	84	0.501
10	10	20	103	0.507
11	11.2	22.2	123	0.500
12	12.1	24.1	145	0.500
13	13	26	169.5	0.501
14	14	28	202	0.508
				
Average Resistance		0.55
Average Resistance above 4L/Min 0.51

So, yes we are seeing differences between single meter and paralleled meter readings. Can we identify why?

And note I've slipped a date into the data label. I'll try to do that to help us keep track of changes to rig or thinking.

[Terry McGee]

Have we tried this arrangement, to test how the flow meters react to downstream pressure?

stop valve -> first flowmeter -> manometer takeoff -> second valve -> second flowmeter -> open air,

where the manometer is measuring relative to open air. Suppose we adjust the balance on the two valves to keep the flow on the second meter around 10 L/min and see what happens to the flow on the first meter at different pressures. (The needle valve on the second flowmeter would probably do as the second valve.)

When Terry squeezed the tubing between the flowmeters, it made a big difference to the reading on the upstream flowmeter. The only thing I can think of that would be making that difference is the downstream pressure. This would give us a chance to quantify this. Maybe density changes are enough to explain it, maybe not.

I set that up and had both meters reading 10. Pressure across lower meter already 614mm.
Increased flow to both reading 12. Pressure now 833mm
Started to close RH Needle Valve to pull it back to reading 10, but quickly exceeded the Manometer's max, 1400!

So backed off back to 10 each with needle valve open, started closing it, while increasing flow and monitoring pressure to keep it below 1400.
Didn't get very far: LH 9.7, RH 10, Pressure 1354.

So we're reminded:
- these meters have a lot of resistance (back pressure)
- you don't have to close the needle valve far to get a lot more!
- the first meter in the chain reads lower when the pressure is on
- the good news (I guess) is that we only saw a 3% droop in the LH meter at the enormous pressure of 1354mm. On our whistles we rarely get much above 300mm.

You'll notice I didn't use your first stop valve to control the flow. I did plumb it in and tried it. Being a ball valve, it's very quick acting, and so unsuited to incremental control. I used the Pressure Regulator in conjunction with my recently added Resistor to control flow into the LH flow meter, etc. Hope that's OK for your experiment. Clarify if I've misunderstood the instructions.

Any further instructions on this question?

[Tunborough]

Thanks, Terry. That answers my question, but I'm still in the dark about what's going on.

When the RH meter was discharging to atmospheric pressure, and the LH meter was discharging into 13% higher pressure, the LH meter was reading only 3% lower. I would have expected the LH air density to be 13% higher, and that leads to only a 3% change in the reading? When you squeezed the tubing between the flowmeters, you got the upstream flowmeter to drop by 36%. Do you think that squeeze was enough to raise the pressure by an atmosphere or two?

When you put the two flowmeters in parallel in the experiment above, for say 100 mm pressure at the beak of the whistle, the pair of meters gave a flow reading about 7% higher than one meter on its own would have. Earlier, when you moved the flowmeter after the 30 x 4 calibrator instead of before, at 100 mm H20 across the calibrator, it was reading about 18% higher.

Anyone else have any ideas?

[Terry McGee]

I'll have a think about those questions, Tunborough.

But I've just been having a play on a bit of a whim. Remember earlier, I'd said:

"I'm imagining that we need to connect the end of the food chain to a servo-controlled vacuum source, connected to sense the pressure at the junction between whistle and flow meters, and strive to keep that at zero by cranking up the vacuum. That way both whistle and flowmeters will be functioning at atmospheric. This is the kind of stuff I used to have to design and build back in the Research School of Physical Sciences and the Research School of Earth Sciences at ANU. But fortunately fate intervened, and I became a fat-cat flute maker instead. Ahem...."

The notion of trying to balance out the pressure across the device-under-test by applying a vacuum where normally it vents to air has stayed with me. And I racked my brains, (both cells at once!) to remember what if any sources of vacuum I could pull into play. And then remembered a ghastly little airbed pump/sucker I had somewhere. I turned all the somewheres upside down and found the sucker. Mine is red, but it looks suspiciously like this one:



Connecting its Deflate port to the output side of a 20L/Min flow gauge revealed it was capable of sucking about 8 L/Min. I'd have liked more, and some way of controlling its suction, but beggars and choosers applies. Aha, "some way of controlling its suction"? You've got a variac, haven't you? (Younger readers might need to look that word up. Essentially its an autotransformer - a crude electromagnetic way of controlling mains voltage via a big knob.) And sure enough, I can now control my vacuum flow from 0 to 8L/Min, and the vacuum pressure from 0 to -360mm.

So I set up the Pressure Regulator feeding the LH Flow Meter, feeding the 30 x 4mm calibrator, now feeding the suction pump, with a pressure takeoff between flow meter and calibrator. And wound up the Pressure Regulator for 20LMin flow with the sucker off. I could hear the flow coming out of the sucker blow hole and vents. The pressure meter showed 110mm - that's the backpressure from the Calibrator and the so-far inactive suction pump. Now turn the pump on and start advancing the voltage from the variac, and the pressure meter drops down to zero. And if I keep going, starts indicating negative. The flow meter might have dropped a smidgeon - perhaps to 19.7 - rather hard to be sure of. But we are now operating with both the Calibrator and the Flow Meter at atmospheric pressure. A bit harder to do with a whistle but if we can run any calibrating tests with a Calibrator we would appear to be ahead.

So, of course, my mind races ahead. How far can we push this thing? I plumb in the 2nd flow meter, and crank up the flow. I can't get all the way to 40Lpm and balance out the back pressure of the Calibrator and suction pump, but I can get to around 34.4. Pressure is now 306mm until balanced out by the added suction.

And so then comes the big question. The system is sitting there pushing 34 odd L/Min through the flow meters and calibrator, but we have the pressure at that junction balanced out by the suction. So I should be able to disconnect the lower end of the Calibrator from the sucker pump and it shouldn't make any difference. We're replacing "0mm pressure relative to atmospheric" with atmospheric itself. Sure enough, maybe a little flicker but not measurable.

So this suggests to me that we don't have a significant problem with the simple setup of Pressure Regulator > Resistor > Flow meters including the valve> Manometer takeoff > Device-under-test > atmosphere. Sure there will be back pressure applied to the flow meters, but it doesn't seem to affect them dramatically.

Have I convinced anyone? Does this new facility offer any new ways to further investigate your various concerns?

[trill]

. . . And then remembered a ghastly little airbed pump/sucker I had somewhere . . . I turned all the somewheres upside down and found the sucker . . . You've got a variac, haven't you? . . . And sure enough . . .

McGee, I swear, every day you make me laugh out loud !

Anyone who's got a variac lying around is my kind of guy !

[trill]

. . . And note I've slipped a date into the data label. I'll try to do that to help us keep track of changes to rig or thinking.

Nice touch ! I'll do the same !

[trill]

. . .
OK:

Code: Select all

12 March 2023: Old Gen head after Flow Meters singly and in parallel, taped better.				
LH	RH	L+R	Press.	Res.
2		2	4	1.000

Once again, Terry, thank you for running the cases. Here's the plot:



Some comments:

1. At 5lpm, the two single-meter readings agree. Very glad to see that. The *huge* disparity with 2 meters went away.

2. The blue + black cases track very closely. Actually, a 5% change in density puts blue right on top of black.
(So, what could cause a 5% change in density ? From one day to the next ? One test-session to the next ?)

3. There's a down-bump at 10lpm (single meter) and 20lpm (2 meters), which is 10 on each. Honestly, that makes me wonder if there might be an error in the meters. Honestly, that's my guess at this point.

4. As to the difference between using 1 meter or 2 on the same day, I really am at a loss. There is a difference. It looks systematic, not random. I'll think on it, but right now, I'm out of ideas.

At the risk of sounding foolish . . . wouldn't it be nice to have a single flowmeter we could trust ?

Also, I confess, I haven't had a chance to process all the traffic above. It's just a lot all at once for me. It may take me a while.

[trill]

<rant>
Also, one little bit more.

Here are the screen-scaled increments Terry listed out a few days ago:



Never have I seen a sensor designed for lab use with a scale like that.
</rant>

[Terry McGee]

. . . And then remembered a ghastly little airbed pump/sucker I had somewhere . . . I turned all the somewheres upside down and found the sucker . . . You've got a variac, haven't you? . . . And sure enough . . .

McGee, I swear, every day you make me laugh out loud !

Well, you've got to admit I've picked an easy audience. The kind of people who will read 500 plus responses on a topic as dry as machine-blown flageolets are clearly desperate for entertainment!

Anyone who's got a variac lying around is my kind of guy !

Heh heh, it is over 55 years since I put it in a custom metal box I folded up myself. I made it to control a Scope soldering iron's temperature in the days before we had temperature-controlled soldering. But perhaps surprisingly, I still use it all the time. It controls the speed of the hand-held Dremel tool I use for undercutting. And it controls the hot-wire polystyrene cutters I use to excavate the curved slots for flutes in my cases. And now it's found a new job!