Lesson 15

Pressures in time

Design and Audit answer what the pressure is once everything has settled. The Dynamic mode shows how it gets there: a consumer opens, the line sags, the compressor catches up. This lesson runs the network of lesson 14 through one second of work, millisecond by millisecond, and then gives it a compressor that cannot keep up with the peak.

What the dynamic run is

The network is cut into volumes — the halves of every pipe, the tee, a tank — joined by resistances and valves. The run starts from rest and steps through time, every 0.02 ms by default: air flows from volume to volume, pressures rise and fall, the consumers open and close at the moments of their cyclogram. Each volume has one pressure, so waves along a long pipe are not reproduced; what you see is how the volumes fill and empty.

1. Give the cycle a millisecond scale

   Open lesson14.gf9 and save it as lesson15.gf9. A one-minute round at a step of 0.02 ms would be three million steps; the default dynamic run lasts the round plus 50 ms, but not more than 2 s. A pneumatic network settles in fractions of a second, so make the round one second long and put the same story into it.

   Open the cyclogram, choose Actions → Clear and clear all rows. Then Actions → Time interval: Sec 1, the other fields 0, Set. Give the two pipes their rounds as text (lesson 14, step 4) — B1:

   EasyCAS cyclogram 1
   cycle_ms=1000
   initial=off
   100	on
   800	off

   and B2:

   EasyCAS cyclogram 1
   cycle_ms=1000
   initial=off
   300	on
   600	off

   B1 opens at 100 ms, B2 joins it at 300 ms and stops at 600, B1 stops at 800. Mind what the run starts from: the design state, in which both pipes blow and the ends of P2 and P3 are at 6 bar. The cyclogram starts with both closed, so in the first 100 ms nothing leaves the network and it fills up to the pressure of the source. You will see this filling on the curves, and COMP will warn about it (step 6).

   Close the cyclogram and press Calculate. The design pressures are the starting point of the run; if you forget, the program calculates the design itself before the first run.

2. Switch to Dynamic

   Click Dynamic on the Design | Audit | Dynamic switch, or tick View → Dynamic mode. Like the audit, the mode is marked in several places, here in purple:

   • a purple frame round the sheet with the banner DYNAMIC MODE;
   • the window title starts with [Dynamic];
   • the Calculate button reads Dynamics.

   Click COMP: below its rows there are now three optional inputs of the mode, Dyn Pset, Dyn Qmax and Dyn droop. Like every row, they are shown in the units of the Units tab — Dyn Qmax in NL/min with the units of these lessons. Leave them empty for now: the compressor is then an ideal source that holds the design pressure whatever is taken from it. The mode is saved in the file with the other two.

3. Look at the settings

   Choose Scenario → Dynamic settings.... The window Dynamic calculation opens. The defaults suit this network; check that Duration covers the switching you want to see:

   Field	Value
   Step (ms)	0.02	must divide 1 ms; the program takes a smaller one by itself if a small volume needs it
   Duration (ms)	1050	the round plus 50 ms
   Sampling (ms)	0.1	how often the curves are stored
   Polytropic n	empty	adiabatic; 1 would be isothermal
   Calculation mode	Exact	Fast and Very fast enlarge the smallest volumes

   Next to each calculation mode the dialog shows the step it would take and an estimate of the run time; both follow Step and Duration as you type. On this small network all three take 0.02 ms and less than a second. Press Run — or Cancel and press Dynamics. A progress window shows the run; Esc stops it, and then nothing is shown.

   Open the dialog again after the run: the top now tells what the run found — step used 0.02 ms (set 0.02 ms). 1 s of process time takes about 0.94 s of calculation. The model stays stable up to a step of 0.0697 ms — a larger Step speeds the run up. On a big scheme that line tells you whether a larger Step, a Fast mode or a shorter Duration is the way to a quicker run.

4. Read the pressures

   The Dynamic results window opens. On the left is the list of signals, three kinds of them:

   Signal	What it is	Here (IDs as in lesson 14)
   p …	the pressure of a volume, named after the items that share it; the end of a pipe is ID in or ID out	p ID9 out / ID4 in — the end of P1 and the inlet of T1; p ID6 in / ID4 / ID7 in — the outlets of T1 with the starts of P2 and P3; p ID6 out — the end of P2, where B1 sits; p ID7 out — the end of P3, where B2 sits
   G …	the flow through a link, NL/min	G ID9, G ID6, G ID7 — the pipes; G ID4 — the tee; G ID12, G ID14 — what B1 and B2 blow
   ups …	the opening of a valve or a switched consumer, from 0 to 1	ups ID12, ups ID14 — the cyclograms of B1 and B2

   An open pipe is not a volume: it is the hole the air leaves through, a link of the model. So there is no pressure signal with ID12 or ID14 in its name — the pressure in front of B1 is the end of P2, p ID6 out, and in front of B2 the end of P3, p ID7 out. There is no signal at the compressor either: an ideal source holds its pressure, so there is nothing to draw. Type ID12 in Find element on the toolbar and the window selects the row of B1's first ticked signal.

   Tick p ID6 out, p ID7 out, G ID12 and G ID14. Each ticked signal gets a band of its own on a common time axis. Click a band to move the visor; the line under the plot gives every ticked value at that moment.

   Time	What happens	p ID6 out (at B1), bar	p ID7 out (at B2), bar
   0 – 100 ms	both closed: the network fills from the design state up to the source pressure	6.00 → 6.17	6.00 → 6.17
   100 – 300 ms	B1 opens; its line sags and settles	≈ 6.07	≈ 6.11
   300 – 600 ms	both blow: the pressures fall towards the design state	6.0117 at 406 ms, ≈ 6.005 at 600	6.0421 at 406 ms, ≈ 6.03 at 600
   600 – 800 ms	B2 closes	≈ 6.07	≈ 6.11
   800 – 1050 ms	B1 closes; the network fills back	→ 6.17	→ 6.17

   The flows tell the same story — an open pipe blows in proportion to the pressure in front of it, Qn = design Qn × (p + 1) / (6 + 1). At 406 ms G ID12 reads 1049.82 NL/min against the 1048.25 of the design, so the end of P2 is at 1049.82 / 1048.25 × 7 − 1 = 6.01 bar; G ID14, 592.79 against 589.64, gives 6.04 bar — the same as p ID6 out = 6.0117 and p ID7 out = 6.0421 under the plot. With both open the pressures go towards the design ones — 6 bar at the pipes — because the ideal source holds exactly the Pout the design found for that case. With one pipe open the line loses less and the pipe gets more than 6 bar, and blows a little more.

   The interesting part is between the levels. Hold Ctrl and turn the wheel over 100 ms to zoom in: the pressure at B1 does not jump to its new level, it slides down, and each slide is still going on when the next switching comes: by 600 ms the ends of P2 and P3 are 0.005 and 0.03 bar above the design state, 300 ms after B2 opened. It is the air stored in P1 and P2 running out through B1: the step in G ID12 is sharp, and its slow drift after it is the pressure going down. That store is the reason a short peak does not reach the compressor at once. Double-click the plot to see the whole run again; drag with the wheel button or the right button to pan.

5. Put two curves on one band

   Drag the band of p ID7 out by its scale (left or right of the plot) and drop it with its middle on the band of p ID6 out: the two curves now share one band and one scale. A click on the band picks the curve nearest to the pointer, and the rows of that element are drawn bold in the list. Right-click a band for Merge with the graph above / below, Separate the merged graphs and Hide graph.

   Merge the two flows the same way. Bands of different units can share a band too — each unit then gets a scale of its own, in the colour of its curve. The ticks, the order and the merged bands are kept for the next run of the same file.

   Export CSV... writes the ticked signals to a text file: separator ;, time in milliseconds, a decimal point — ready for a spreadsheet.

6. Read the rows of the run

   Close the results window and click the items. The run has written Dyn ... rows below the ordinary results — on COMP under CO2, starting with the orange Dyn initial imbalance. The list is now longer than the panel: scroll it down, or drag the divider under it.

   Item	Row	Expected
   COMP	Dyn source pressure	6.1656 bar	no Dyn Pset: the design Pout
   COMP	Dyn air delivered	936.704 NL/min	normal flow averaged over the run: 16.4 NL in 1.05 s
   COMP	Dyn air per run	19.4836 g	the same air as a mass: 16.4 NL × 1.19 g/L
   COMP	Dyn mass balance error	0	delivered against stored and blown; large — take a smaller step
   COMP	Dyn initial imbalance (orange)	28 %	the design state is all consumers on, the round starts with them off — see step 1
   COMP	Dyn mode, Dyn step used	Exact, 0.02 ms
   P2	Dyn p min ID6 out, Dyn p max ID6 out	≈ 6.00 / ≈ 6.17 bar	of the volume at its outlet, in front of B1; P2 also has the pair of ID6 in
   B1	Dyn flow max	1065.55 NL/min	at the first moment of opening: 1048.25 × (p + 1) / 7 with about 6.12 bar in front of B1. A normal flow, like Qn (builds up to 5.30 labelled it L/min)
   P1	Dyn velocity max	≈ 8 m/s	at its lower-pressure end

   No Dyn rows under CO2? Then an ordinary calculation has run since the run. With Preferences → Autocalc ticked, typing into any row is one: the design is recalculated and the Dyn rows are gone. Press Dynamics again — if nothing has changed since the run, the rows and the window come back at once, without a new run. (Builds up to 5.30 did not redraw the table of the item that was selected during the run: click another item and then COMP again.)

   The Dyn rows live only in this mode: the next ordinary calculation removes them, and the report of Design or Audit does not show them. Items that share a volume show the same Dyn p min and Dyn p max.

7. Give the compressor a limit

   A real compressor does not deliver any flow at a fixed pressure. Click COMP and type:

   Row, COMP	Value
   Dyn Qmax	70 Nm³/h	= 1167 NL/min: enough for B1 alone, not for both. Type the number for the unit the row shows
   Dyn droop	empty	0.1 bar: the whole Dyn Qmax comes when the outlet is 0.1 bar below Dyn Pset

   With the units of these lessons the row shows NL/min: type 1167. Or click its unit cell, pick Nm³/h and type 70. A row with a unit of its own gets an orange frame round the unit cell — Dyn Qmax has one on the screenshots of this lesson. The choice is saved with the file and holds for the Dyn Qmax row of every source; As on the Units tab in the same menu takes it back.

   The compressor now works like a regulator: it holds Dyn Pset — empty here, so the design Pout, 6.1656 bar — and gives the more air the lower its outlet pressure falls, all of Dyn Qmax at 0.1 bar below, at 6.07 bar.

   With Autocalc on, the Dyn rows of the first run disappear as you type — expected. Press Dynamics. Two signals are new at the bottom of the list: p ID9 in — the node of the source with the start of P1, which is no longer held fixed — and G ID1, what the compressor delivers. Tick them with p ID6 out and p ID7 out and put the visor at 600 ms. Nothing else has changed, so you can compare the two runs directly:

   • 0–100 ms, nothing blows: the network still fills from the design state (the 28 % imbalance) — G ID1 rises to about 480 NL/min and falls back to about 230;
   • 100–300 ms, B1 alone: the compressor follows the demand through the droop — about 940 NL/min at 300 ms with p ID9 in at 6.09 bar, still under its limit; the pressure in front of B1 (p ID6 out) eases from 6.14 to 6.00 bar;
   • 300–600 ms, both pipes: they ask for about 1600 NL/min. G ID1 reaches its limit, 1167 NL/min, at about 390 ms and stays there; the rest comes out of the volume of the pipes, and every pressure falls steadily. At 600 ms the visor reads p ID6 out 5.8516, p ID7 out 5.8945 and p ID9 in 5.9876 bar — below the 6 the pipes need, and about 0.15 bar under the first run;
   • 600–800 ms, B1 alone again: the pressures stop falling and climb slowly, the compressor still at its limit;
   • after 800 ms nothing blows: G ID1 leaves the limit at about 885 ms and is down to about 190 NL/min at the end; the pressures come back to 6.14 bar — the pipes are still filling when the round ends.

   This is what the ordinary calculation cannot show: the design Pout was enough, but only if the compressor can deliver the peak. The cures are the ones of lesson 9 — a bigger machine, a receiver near the consumers — or the shift of B2 from Try this next of lesson 14, which takes the peak away.

   Mind the unit when you type Dyn Qmax. The screenshot below is the same run with 70 typed into a row that showed NL/min — a compressor of 4.2 Nm³/h, about a twentieth of the peak. The two pressures (merged on one band, as in step 5) fall from the first opening and hardly come back after 800 ms; p ID9 in, the source, gives way from 6.1656 at 0 ms down to about 5.4 bar.

8. Save it

   Save lesson15.gf9. The dynamic settings, the Dyn inputs and the mode are kept in the file; the curves of the run are not — they live until the program is closed. After opening the file, press Dynamics and the run is made again. Within a session, if nothing has changed since the last finished run, the button does not run again: it puts the Dyn rows back and shows the results window as it was.

When it does not work

Try this next

• Set Dyn droop of COMP to 0.3 bar and run again: the source gives way earlier, and the pressure starts lower before B2 opens.
• Shift B2 to 700 – 1000 ms (lesson 14, Shift-drag): it now blows together with B1 for 100 ms instead of 300. Run with the same Dyn Qmax and compare how deep the pressure falls and how long G ID1 stays at its limit.
• Put an air tank between T1 and P3 — a card of type AIRTANK; type tank in the catalog filter — with its row Volume (l) at 50 and run with Dyn Qmax 70 Nm³/h: the tank pays out the peak, and the sag at B2 is much smaller.
• Change Polytropic n to 1 (isothermal) and compare the speed of the sag.

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