Help design a conical compressor

[HirenBanker]

Hi,

Request you all to help me on this.

I have an idea of making a compressor wherein the container would be conical in shape (instead of the usual cylindrical). I think I have got a solution as to how to make a piston to move inside this conical container.

My belief is that the conical shape would be far better than the cylindrical shape because as I push the piston from the bottom dead center to the top dead center, the cross-sectional area decreases and hence the pressure that can be achieved would be far greater compared to what can be achieved in the conventional cylindrical one.

My issue is - can someone tell me how to show this mathematically if what I believe is correct or not ?

Thanks a lot for reading this, and would be great if you can guide me to the correct direction.

Thanks
Hiren

[JAlberts]

I am not sure what the final goal of your new design is but its basic premise is interesting. Although the initial reaction would be that it would give a higher compression, I am not sure of the answer either because if you use the same piston stroke for both cylinders (which you should initially do in the following calculations) then when you replace the cylindrical cylinder with your conical one then the bottom of stroke volume and therefore the initial gas fill volume of your design will be less than that of the standard cylindrical one.

The way to determine if there is an advantage to your design is to first calculate the volume of a standard cylindrical form container at both the bottom of the stroke and the top of the stroke (I realize that the distance between the piston top and the container top will be very small at the top but it will not be zero. Next divide the top of stroke volume by the bottom of stroke volume for each container configuration. The result of this calculation is known as the compression ratio. Next repeat this same calculation for your conical design. If the compression ratio for your design is greater than the one for the cylindrical one then your assumption is correct.

Just as a note, one issue you will run into the application of your concept is that, even if the discharge pressure is greater, the actual volume of gas discharged with each stroke will be reduced on your unit and it will have to be run at a higher rpm or for a longer period to deliver the same gas volume as a current conventional unit.

The equation for the volume of your conical shape is: V=.2618h(D^2 + Dd + d^2) where, h = the height, D = the diameter of the larger end, and d = the diameter of the smaller end
Note: D^2 = D squared, etc

[RWOLFEJR]

I'm not seeing any advantage to cone shaped over round? Displacement is displacement?

[jboggs]

I'm not seeing how it is even possible. A cone-shaped piston inside a cone-shaped cylinder? Are you thinking of some kind of multi-body shape-shifting piston? A diagram would help.

[Cake of Doom]

I'm not seeing how it is even possible. A cone-shaped piston inside a cone-shaped cylinder? Are you thinking of some kind of multi-body shape-shifting piston? A diagram would help.

I had a similar thought except I pictured being more of a flexible diaphragm rather than a piston head as such. Still though; this would have to be some super material because, depending on the amount of use the wear and tear on it would be huge!

[HirenBanker]

Hi everybody,

Thanks for the replies.

I am attaching a basic calculation of what I think will this design give.

I think I did not say in my earlier post that my assumption was to keep the volume of both - the conical and cylindrical compressor same and then see whats the difference in power requirement. The attachment might help a lot to see what I am trying to look for. Please see if this thing helps.

I have kept the comparable items in green whereas the difference that I am looking for are in pink/amber.

Thanks a lot again.

Hiren

(I am so happy that this can help attach a file or I was going to copy/paste the whole thing).

[jboggs]

Numbers have no value without a picture to explain the geometry of the concept.

[RWOLFEJR]

I had a similar thought except I pictured being more of a flexible diaphragm rather than a piston head as such. Still though; this would have to be some super material because, depending on the amount of use the wear and tear on it would be huge!

Pictured that too. Like a washerless faucet seal.
Other issue that comes to mind is now you need to guide this cone from somewhere further back or out ahead of it somehow?

You said... "My belief is that the conical shape would be far better than the cylindrical shape because as I push the piston from the bottom dead center to the top dead center, the cross-sectional area decreases and hence the pressure that can be achieved would be far greater compared to what can be achieved in the conventional cylindrical one."

I don't see this. Displacement is where you get your pressure. 10 lbs. in a 5 lb. bag either way. The pressure of "x" volume squished into "y" volume will be the same regardless of shape. The thing I'm trying to get my head wrapped around without doing the math is whether or not the curve will be straight line like a round cylinder or not. Will you compress more or less at either end of the stroke because of the different shape? (which is what I think you are thinking...?)
I really don't think so...

I'll grab another cup of coffee and think about it more.

[JAlberts]

Hiren, I opened your spreadsheet, did a bit of manipulating and found that by increasing your top of stroke height to 18mm your unit would deliver a 94% increase in discharge pressure and 23% increase in cfm delivery of the standard cylinder arrangement with at essentially the same SEC, which appears to confirm your basic concept.

As to how you intend to achieve the design of the piston etc., that is entirely a independent issue from the concept confirmation.

[HirenBanker]

Hi,


Thanks again for the response.


RWOLFEJR:
I think that P/V curve could be very different for the conical compressor because after a point, the incremental decrease in volume is far greater than the cylindrical compressor. I'll try to put this in a graph and see how it comes up.


JAlberts:
Thank you for looking into the calculation, I am encouraged by your support.


Can you all please check if the formulae that I am applying to find the power required and the application of them is correct or not. I think I might be wrong somewhere as industry does not seem to agree to my calculations - they say that the figures for SEC which I am showing in my spreadsheet are very high. Attached is a link to a pdf file I found online which shows that the SEC for a single acting air compressor should be between 0.22 to 0.24 Kw/cfm.

compressed_air_sourcebook.pdf

[JAlberts]

Hiren
I did not find the specific formula for the KW calculation in your above reference link but the standard basis in this type of calculation is generally scfm at standard conditions not acfm (actual cfm). The equation for the formal reverse calculation can be found at: www.pdblowers.com/t6-scfm-standard-cfm-vs-acfm-actual-cfm.php. Using their quick calculator and entering trial scfm values to achieve to your acfm, I found this will reduce your SEC's to values more in line with the above order of magnitude lower expected values.
PS In my trial, I ignored the increase in temperature at the discharge pressure which is not actually realistic due to the heat of compression temperature rise that is experienced in actual applications.

[JAlberts]

Hiren
I looked at the the above pdf reference but could not find the specific equation you used for an SEC calculation but I suspect that the problem you are having is that the majority of equations of this type are all based on standardized flow in SCFM rather than CFM @ discharge pressure, so you should check your reference equation to see if this is true for it. If so, you need to convert your calculated flow at the discharge pressure to the standardized SCFM flow at 14.7 psig. (ie. SCFM = CFM * Pdischarge / 14.7) and use that value in your SEC calculation. I did a trial on one of the values on your spreadsheet and found that this will reduce your SEC by an order of maginitude to a level more in line with the generally accepted values you state above.

For a more sophicated calculation of the CFM to SCFM conversion take a look at:

Flow-Calculations-Gases.pdf


Just as a note I was looking at your volume equations =PI()*(B4/1000)^2*(B3/1000)/12 in cell B5 and =(F10*(D10/1000))/3 in cells G5-G10 and I this appears to me to be an error in your calculations and you should be using the conical volume equation I show in my above first post to determine the initial B5 conical volume of your cylinder and the volumes at each successive lower piston height; or am I overlooking something here.

Hirem
Please check your private mail for some additonal input from me.