Help Me Win An Argument With My Boss

[russ_watters]

Yeah, that's right - I'm "That Guy". You know you love these threads...

I have an application where I need to be relatively sure of the responsiveness of an HVAC system to a control input. In a lab space that has an air change rate of 6 ACH when unoccupied and 8 ACH when occupied, the HVAC system must react quickly to an occupancy sensor noting someone entering the lab to avoid the possibility that the lab worker could walk in the door and open a container of chemicals and not have appropriate ventilation. 1 minute is a typical requirement for going from unoccupied to occupied mode. Personally, I think the whole exercise is a little silly, but that's neither here nor there...

So what is the actual responsiveness? When you walk in a door, an infrared or ultrasonic occupancy sensor will notice your presence in a fraction of a second and relay it to a computer. From there - on this system - a solenoid valve opens to send a pneumatic signal (a change from 10 to 20 psi of air) to each of 100 airflow control devices, up to 300 feet away(1). After the airflow control devices receive this signal, they change their valve position and thus their airflow in less than 1 second (by manufacturer specification). Then this new airflow travels down the duct, up to 100 feet and out a diffuser (2). The typical duct airflow velocity is about 500 fpm. The air then it enters a room at an average of 200 fpm, dropping to 50 fpm by the time it reaches a lab bencth 8' below (3).

So: how long does it take from the time the person walks into the room until the new airflow is "felt" at the lab bench? The primary point of contention is #2, but let's go over all three of the questionable ones:

1. How long does it take for a pneumatic signal to propagate 300' down a tube? Since the air is pressurized, you're basically "filling" the system with air and the change in pressure will take a little while to propagate. Maybe 10 seconds, but it is really tough to know.

2. Since air flowing through a duct at low pressure (2" water gauge here) does not change its density significantly (a tiny fraction of a percent), it can therefore be considered incompressible. As a result, conservation of mass demands that the entire mass of air in the duct change its velocity at the same time. Since this isn't quite true, what actually happens is that the velocity change propagates as a longitudinal pressure wave through the duct, just like a water hammer effect. Longitudinal pressure waves have another name: "sound waves". So the changer in airflow traverses the 100' to the diffuser at the speed of sound, taking just under a second to change the airflow in the entire duct.

3. Once it leaves the duct, the air disperses and no longer propates changes at the speed of sound. Starting at 200fpm and ending at 50fpm, the average velocity will be around 125 fpm, traversing the distance in 3.8 seconds...unless velocity drops as a square function of distance, in which case the average speed is a little higher and the time a little lower.

Thoughts?

 

[Cyrus]

Isn't 1 just the speed of sound?

 

[DaveC426913]

Isn't 1 just the speed of sound?

Well, his empirical evidence is saying somewhere on the order of 30fps, so clearly it's not the speed of sound.

 

[Cyrus]

Edit: pressure waves travel at the speed of sound in air (that reads better).

 

[russ_watters]

Well, his empirical evidence is saying somewhere on the order of 30fps, so clearly it's not the speed of sound.

That wasn't empirical evidence, it is just a guestimate.

 

[russ_watters]

Isn't 1 just the speed of sound?

It would be if the airflow capacity of the pneumatic control system is high enough to fill the system that fast. I'm not so sure it is.

But let's guestimate... 300'x100 lengths of 1/4" tubing is 10 cubic feet of system volume. A pneumatic control system with a tank can probably output a few tens of CFM of air. So you can't change the signal at the speed of sound (1/3 of a second), but you can do it in perhaps 10-20 seconds.

 

[DaveC426913]

That wasn't empirical evidence, it is just a guestimate.

Yes. Whether accurate or not, it's still a real measurement that can't be rationalized away.

And I'm pretty sure you can tell the difference between 10 seconds and 1/3 of a second.

 

[mheslep]

I don't see that the speed of sound has any bearing on what someone sitting at the lab bench would 'feel', if feel means a turnover in the localized air mass. The person might theoretically hear solenoids, etc, clicking immediately, i.e. the pressure waves can (do) travel at the speed of sound. The pressure waves have no bearing on the basic requirement, however, which is air turn over.

So this appears to be a standard fluids mass transfer problem. If the fluid is completely incompressible, then the entire mass begins to move almost instantaneously after the air handling system engages, but of course the fluid mass takes time to turn over at the rate specified.

One could go further and analyse contaminate concentrations (from something released on the bench), then it becomes a more complicated diffusion problem. But I don't think you need go that far since the specs are in terms of air turn over.

 

[Topher925]

#2 is assuming your increase in pressure is a step function, which it isn't. It will take time for the fan to spin faster or the vent to open. This time could significant depending on how the system designed.

 

[russ_watters]

#2 is assuming your increase in pressure is a step function, which it isn't. It will take time for the fan to spin faster or the vent to open. This time could significant depending on how the system designed.

As I said, the airflow control device (a special venturi valve) actuates to produce a new airflow in less than one second. That's surprisingly fast, but true. Here's the product: http://www.phoenixcontrols.com/why-phoenix-advantages.htm

Check out the video at the bottom right. It's pretty impressive how fast these things adjust.

Also, since the percentage change in airflow isn't too large, I'm presuming that the when the valve opens and the system pressure drops, it won't drop enough for the airflow to miss its new target even though it may take a full minute for the fan to speed up. The static pressure setpoint is high enough to absorb changes in system flow rate.

 

[R Power]

Yeah, if airflow is at a lower pressure in the duct then a pressure wave should be setup and then it would take under a second only for new airflow to be set up in the system but only when your air control device works the way you think them to.
If you are able to find a device that fills air within a second then you could save time further in one by similar pressure waves. Ha Ha :)
BTW what did your boss argue with you on your analysis? Would be interesting to know!

 

[russ_watters]

It wasn't exactly an argument, but he didn't think that the airflow in the duct would change so rapidly.

 

[Q_Goest]

Hi Russ,
For #1, you mentioned a solenoid valve opens to change the pressure from 10 to 20 psi, and this volume is dead headed. I was going to suggest simply making a spreadsheet and given some flow in (calculated from the dP across the solenoid valve and valve Cv) you could perform a transient analysis. If it were me, I’d set up an Excel spreadsheet and each row would constitute a small time step (say 0.01 seconds) and the flow into the tube would be calculated for each time step along with the pressure in the tube. The curve created should rise quickly and taper off as pressure rises. One simplifying assumption would be the volume is all at the same pressure, so there’s no pressure drop in the tube that would increase pressure downstream of your solenoid. That’s probably a reasonable assumption but you’d need to make that determination and possibly put a ‘fudge factor’ in such as assuming there’s a 10% pressure drop in the tube so that pressure downstream of the valve is actually 10% higher than the gross volume of the tube. Maybe you could do that by determining pressure drop using the Darcy Weisbach equation and putting something in for the flow rate over some distance. The only problem I have with all this is I don’t know what’s upstream of the solenoid valve. Is it a constant pressure fed by a regulator? Can you assume that pressure is constant? Or can this upstream pressure fluctuate after the solenoid valve opens? If it’s a regulator, it would tend to have some droop that would make the assumption of a constant pressure upstream of the solenoid valve much less conservative. Regardless, you might consider doing a transient analysis like this if you can quantify how the pressure upstream of the solenoid valve behaves when the valve opens and any other minor non-conservative assumptions that you put into it.

For #2, I’d agree with your description of what happens in the duct, but don’t know how to rigorously quantify the time it takes for velocity to reach steady state. The pressure wave propagates along the duct at the speed of sound as you say, but I would imagine there being a series of waves set up. The transient wouldn’t necessarily be over as soon as the first wave reaches the end of the duct, though I suspect that’s a pretty decent estimation. Could you instead say that the air in the duct has a given mass, and it’s this mass that has to be accelerated to the steady state velocity in order for all the air in the duct to come to steady state? For that matter, there’s air upstream of the valve that’s opening that may also have to accelerate to come to steady state. So at some point upstream of the valve, all the air has to be accelerated from some initial velocity to a final velocity. To do this, a force has to be applied to the mass which is the pressure times the area of whatever is accelerating the air (fan or higher pressure reservoir?). This is just a quick and dirty F=ma (or dP A=ma) analysis to show how quickly a mass of air can be accelerated given an upstream pressure. I’ve done something similar before for liquids and haven’t had anyone argue it is too far away from reality to give a rough number. It might not be as accurate as some fancy CFD analysis, but it should put you in the ballpark. With an analysis like this to back up the analysis you’re doing assuming speed of sound pressure wave propagation, if the numbers come out close to each other, there’s simply that much more analysis to show how fast the transient occurs.

I don’t know why you’re concerned with #3. Once you have the air coming out of the duct and going into the room at steady state, isn’t that the definition of the transient being over?

One last thought, would it be possible or even reasonable to do some testing on this? It shouldn't be hard for example, to get 300 feet of tube, put the soleniod valve on it with whatever is upsteam and operate it just like it would be in the actual system. Or perhaps measure an existing system you have access to that has a similar arrangement. If you did a transient analysis and modified it to estimate these other similar systems, your transient analysis would then have solid experimental data to back it up.