Accumulator Sizing

[AeroNucDef]

Hi all,

Could someone help me out with this. I'm trying to do a rough calculation of sizing a accumulator (whats the required volume), but I've not done this before and I'm completely stuck. I asked a work mate but he just stared blankly at me. I think I've got to apply boyles law, but I'm just going around in circles.

The things that I know;

Max system pressure 200bar
Min system working pressure 150bar
Accumulator precharge pressure: 100bar
Pump flow rate : 0.8 litres per second

What other things do I need to do this calc?

Regards

aero.

 

[SceneryDriver]

Have a look at this:

http://hydraulicspneumatics.com/200/TechZone/Accumulators/Article/False/43954/TechZone-Accumulators

-SceneryDriver

 

[hydromech]

The basic concept of a hydraulic accumulator does rely on Boyle's law, but that does not cover everything.

There are aspects of the application that will dictate whether you use a bladder acc, or a piston acc...or a diaphragm acc.

There is also the discharge rate to consider. Isothermal compression adiabatic discharge..? On rapid discharge, the gas will cool and contract and you may run out of the useful energy before the job/cycle is complete.

What are you trying to do?

How much oil do you need and at what pressure?

 

[AeroNucDef]

Thanks SceneryDriver,

Thats quite useful. The website is OK as well.

Hydromech,

I'll be using a gas bladder accumulator. I've just got 4 actuator to move, 3 linear (piston) and 1 rotary. I think the required oil is about 48L. The only pressures that I know are the ones I listed. I know the flow requirements of each actuator and the time the actuator will take to do a stroke. For instance the piston actuator will need about 6L (3L/s for 2 sec's) for the piston's stroke to be at maximum.

I've been able to find a similar calc in a book, so I'm going have another go at sorting out this problem.
Thanks for your help.

Regards

aero.

 

[PNachtwey]

I wrote that article in H&P. You need to know how long a machine cycle is and how much oil is used during each machine cycle.
See this:

http://deltamotion.com/peter/Mathcad/Mathcad - Accumulator-NG.pdf

This is simple because there is only one cylinder. When there are three cylinders and one motor you must add up all the flows as a function of time within each machine cycle to find the worst case time within a cycle.

During a machine cycle I assume that no heat is lost or gained. I have been to many installations and put my hand on the accumulators. I have never felt the temperature change over short periods of time but I do believe the temperature can change when pre charging the accumulators because there is a longer period of time between when the accumulators are pre-charged to when they are put into operation.





Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

 

[Oldhydroman]

You need to be clear in your mind about what you want the accumulator to be doing for you. For example, if you have a particular machine cycle that you wish to complete and there are significant variations in flow demand during that defined and repetive cycle, then a properly sized accumulator will mean that your pump needs only supply the average flow demand - the accumulator will soak up the flow surpluses (when they exist) and use this to make up the flow shortages at other times in the cycle. Another use for the accumulator is to enable the machine to complete its cycle or return to a "home" position should there be a mains power outage (or engine stall/breakdown/run-out-of-fuel). Other applications are when the flow requirement is very intermittent: you can charge up the accumulator and then turn off the pumps completely. You start the pumps again when the stored volume reaches a minimum pressure - in this sense the pump works like the compressor in a domestic refrigerator.

You should do all of the calculations on the gas volume and then reflect this back to the oil volume. If the gas volume in the accumulator shrinks by 10 Litres then the oil volume stored in the accumulator will have grown by 10 litres. Assume the gas pressure and the oil pressure are the same (except when the gas volume has expanded so much that there is no oil at all in the accumulator).

The specific heat capacity of the gas is so much less than the steel body of the accumulator that you will be unlikeley to feel any temperature changes in the gas - but the temperature changes are there and the effects these changes have on the volume and pressure is significant.

Be aware of the extremes of temperature in which your accumulator system has to work. You might set the pre-charge pressure at 20°C but when you start the machine up at an ambient temperature of -10°C you will find that you have lost 10% of this initial pressure. Similarly if you run the machine with oil at 60°C you will find your precharge pressure will have gone up by about 13%. A lower than expected precharge pressure will make the accumulator softer: it will swallow more oil before it reaches the upper pressure limit but the pressure will drop faster as you draw on this oil store. The converse happens when the precharge pressure is higher than you expect.

Don't worry about supreme accuracy in your calculations. Bladder accumulators are only generally available in a discrete range of sizes and the steps between the sizes are quite large. You could, for example work out that your accumulator volume needed to be 14.445 Litres - then you look in the catalogue and say to yourself "Twenty litres it is then!".

If you are contemplating a rapid flow rate into or out of the accumulator then you will need to apply an adiabatic calculation, as others have noted, but the exponent value of 1.4 only really applies at ambient pressure. It is particularly irritating that the exponent value varies with both temperature and pressure. Google "variation of adiabatic index with temperature and pressure" and some suitable graphs should be delivered.

DOL

 

[kcj]

Expanding on Don's post:
There are two different temperature change causes and effects:
-One is the steady state temperature of the ambient and of the gas. If the shell and gas are at nominally -10C or +60C the precharge and performance changes as he explained. This would be the temperature measured on the outer stell shell when the system is steady state.

-The other significant change is determined by how long the discharge or charge cycles are.
If it is slow, (minutes) it can be considered isothermal, constant temperature gas. The expansion or compression is slow enough such that the energy converted to or from heat dissipates out to the rubber or oil or steel. The gas law exponent is picked for isothermal. Typical isothermal conditions would be holding clamping pressure or brake pressure or brake release pressures over longer periods of time.

If the change is fast (seconds), it is adiabatic compression or expansion (constant thermal energy, no heat in or out of the gas during the time of compression/expansion). The expanding or compressing gas heats or cools faster than the heat energy can equalize, and the temperature rise/fall affects the pressures in the gas. Adiabatic compression does not store as much fluid as isothermal, and does not give up as much on discharge. The gas exponent would be chosen as adiabatic.
An adiabatic change would of course slowly dissipate heat in or out and become isothermal over a longer time. As Don noted, the amount of heat stored and the amount of temperature change of the gas vs. oil and steel is such that the steel shell will not measurably change temperature, but the gas temperature can be changing a lot.
Adiabatic would be most accumulators used for assisting pump flow through a valve work cycle, or actuating a large valve to close it during an emergency shutdown, or for starting a large engine through a hydraulic starting motor.

You definitely want to use the proper condition, and most spread sheets have input to pick one or the other. It is not black/white, no clear cutoff. Run the calculations both ways and see the effects. Then, as noted, because accumulators (bladder ones at least) come in standard increments of sizes, you will end up jumping up consdierably anyway. More is better if you have the space and weight to spare.