Modelling accumulator fluid leakage 1

[Hydromechdude]

I'm trying to determine how long it would take for a hydraulic accumulator to bleed down from full working pressure to empty (no fluid remaining).

The equation that I have been using is Q = C*(deltaP)^(1/2). In order to determine the constant C, I'm using the initial conditions for Q (leakage rate through the isolation valve) at the deltaP of 3000 PSI.

In order to determine how much fluid is initially in the accumulator, I used isothermal compression/expansion P1*V1=P2*V2. I know pre-charge pressure, initial volume, and then working pressure. Solve for V2 of air. That will then mean we have Vaccumulator total - V2 for the fluid volume, Vfinitial.

Now to solve for the leakage. I did iterations of one minute in length. So, for the first minute I assumed that the leakage flow was constant at the leakage rate (say 4 cc/min). Thus, after one minute we'll have Vfinitial - 4cc of fluid and Vnewofair = V2 + 4 cc.

At this stage, I now calculate P2*V2 (working pressure start conditions) = Pnew*Vnewofair to solve for the new pressure.

Next is taking the new pressure, setting it as the deltaP in Q = C*(deltaP)^(1/2) to solve for the new leakage flow. I've iterated this for several hours to determine how long it will take to drop to initial pressure.

How does this look? I don't have a program to model this with and so I have nothing to bounce my theory off of. Testing this with a real accumulator will not be possible. I realize I'm modeling the ideal maximum as most valves will fall under the maximum 4 cc/min that I've used, however, having this time would be helpful.

Thanks.

 

[BigInch]

When the pressure is above 200 psig I think you may want to consider air's compressibility factor and when the pressure ratio is high, you should check for flow being limited by sonic velocity.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[BigInch]

Temperature considerations may also be needed at high pressure ratios.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[sailoday28]

For a slow process, isothermal is reasonable.
For the delta P, you should have choked flow.
Flow resistance should also be included in determining Q.

 

[Hydromechdude]

Thanks for the input. How do I take into account choked flow/sonic velocity?

I did some quick searching online, but didn't come up with much.

 

[BigInch]

It limits the flow across the orifice, even if pressure drop is increasing.

http://www.cheresources.com/invisio...951&pid=15681&mode=threaded&start=#entry15681

http://www.chem.mtu.edu/~crowl/cm4310/Chapter4b.pdf

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[Hydromechdude]

Thanks again for the response, BigInch.

I was reading up on the links you posted as well as some others that were linked in a thread dealing with Choked Flow and I started thinking about my calculations.

The leakage rate of the valve holding the accumulator hydraulic fluid in (i.e. closing its patch to the rest of the system) is controlled to 4 cc/minute maximum during manufacture. If the valve exceeds this value, then it either gets scrapped or reworked.

Since I want a conservative time for how long this accumulator will hold fluid/pressure, I'm using the maximum value of 4 cc/minute as the value in my calculations. Since the flow rate is set, can I ignore choked flow in this case? To me, I would only use choked flow if I had an orifice and wanted to model its leakage rate. In my case, this leakage rate has been measured. The leakage values are probably closer to 1 to 2 cc/minute maximum, but again, I'd like to go conservative.

I would also like to verify if I can 'calculate' the constant in Q = C*(deltaP)^(1/2) by plugging in the initial conditions for Q and deltaP.

Thank you, I appreciate any feedback.

 

[BigInch]

No. Just because the valves have been tested to pass or fail a certain leakage rate using certain differential pressures applied during the test conditions, does not necessarily mean that the valves have been tested to the maximum possible leakage rate, which they could experience, if higher pressure differentials are found in the field. Of course, if you know the valves will never be exposed to higher differential pressures in the field than to what they were tested to, it would be reasonable to assume the leakage rate would be limited to "X" cc/m (because you would oviously "never" have choaked flow). Then you should also set a maximum differential pressure limit. Perhaps that being the valve's maximum pressure rating also assumed as the maximum differential pressure rating too.

Yes, of course Cv can be calculated using any conditions. The question is if C holds constant as it should over all flowrates within the valve's range such that it meets the conventional definition of a Cv constant, or if for some reason it varies, such as to dP^n, some other power of dP. You can determine that by assuming the first value of Cv you calculate from measured conditions is constant and then calculate the value of n at various differential pressures and measured flows to give the same Cv. If n appears to be a constant 1/2, then you can do it according to the conventional Cv definition, which assumes n is = 1/2. If not, you will have to modify the standard formula for a power other than 1/2. From here, I don't see a reason now why it would not be 1/2, but I've been wrong before once or twice. For example, I might expect some variation at extremely small flow rates and dPs, but normally those would be in flow ranges where the pressure drop isn't very important either, probably being very close to zero psi. If you have some real data, just check that aspect of it and you'll know for sure.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[Hydromechdude]

Thanks again, BigInch.

Yes, 3000 PSI will be the highest differential pressure that this valve will see. The system operating point is 3000 PSI and it is tightly controlled.

Regarding calculating Cv, I appreciate the feedback. I unfortunately will not be able to check the n number against real data, so I'm going to assume n = 1/2. We buy the system from a supplier who purchases all of the sub components.

 

[BigInch]

Works for me.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[sailoday28]

Hydromechdude (Aerospace) You have stated "In order to determine how much fluid is initially in the accumulator, I used isothermal compression/expansion P1*V1=P2*V2. I know pre-charge pressure, initial volume, and then working pressure. Solve for V2 of air. That will then mean we have Vaccumulator total - V2 for the fluid volume, Vfinitial.
For an isothermal process of a perfect gas
P(V/M)=constant. I don't see how you are accounting for all three variables.

 

[BigInch]

Opps. Telephone ringing.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/

 

[Hydromechdude]

sailoday, I'm assuming you're saying that (P*V)/M = constant for ideal gases, where the M is mass of the gas?

I'm looking at a piston type accumulator that has a set mass of nitrogen pumped into it, to reach the 'pre-charge' value. I'm negating any nitrogen leakage as the accumulator is being compressed, due to it probably being a very small amount. The nitrogen and hydraulic fluid are separated by the piston and are not allowed to mix. The nitrogen end is capped to atmosphere and the fluid end is open to the hydraulic system.

My assumption is that the mass of nitrogen will remain constant (aside from small nitrogen leaks) over a typical day/night of using the accumulator in the system.

Do you disagree?

 

[sailoday28]

Hydromechdude (Aerospace) P1*V1=P2*V2. Does 1 and 2 refer to air which is separate from the nitrogen in the accumulator? ---With one of the subscripts for the initial condition?

 

[Hydromechdude]

I'm using P1 and V1 as the initial pressure and volume of the air/nitrogen. Sorry, I haven't been consistent with identifying the actual gas in the accumulator as nitrogen, instead of regular air.

The initial nitrogen pressure is the pre-charge pressure and the volume is the entire volume of the accumulator. For simplicity's sake, I'm using the initial volume as that of the accumulator specification, say 25 cubic inches.

P2 and V2 would then be the working pressure and volume of the nitrogen. I know the working pressure, but am trying to compute the volume.

 

[sailoday28]

What fluid is moving out of the accumulator? What subscript are you giving it?

 

[Hydromechdude]

I used Vfinitial to denote fluid volume. For the gas (nitrogen) I used Vnewofair and V2. I tried to distinguish whether I was talking about hydraulic fluid or nitrogen except for the cases of isothermal compression/expansion.

The hydraulic fluid is a synthetic phosphate ester.

 

[sailoday28]

Sorry, but I can't picture how your accumulator is constructed.

 

[Hydromechdude]

Is it okay to hot link to outside images? I did a quick search under 'Site Policies', but didn't find anything.

 

[sailoday28]

Can I assume the fluid side is loosing mass?