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Hello,

I normally get these things working but I am a bit stuck as i don't feel I am getting sensible answers...

The problem is simple (!):

I am doing this in excel so formula are what I've copied out of that. I have:

For reference, I've worked this out by:

As an example:

Putting a practical head on, i can picture that sort of flow rate for that pressure and nozzle etc.

Going for a pressure closer to the critical point, just as we fall out of sonic flow, i get we should be looking at not too much over

3.16458E-06 kG/sec 5319.65L/min - however any way i try to implement the sonic calculations, i get wildly different answers!

What I've tried(!):

This is a bit of a cheat as i would really like to get my sonic flow calculation correct and working.

One other odd effect i had not expected...

Using the sub-sonic flow method as described, it doesn't matter what input pressure P0 i have, whether its 10bar or 300bar, i always get the same volumetric flow rate, but a different mass flow rate, for example:

I think the effect of the decreasing pressure P0 reducing the density is cancelling out the conversion from gravimetric to volumetric, although i would have thought less pressure = less density (OK) = less mass (OK) = less flow (not OK)... So that's probably an issue!

Anyway, I've attached the spreadsheet I am working on, sorry its a bit of a work in progress!

Sorry for the long question, i am hoping there's just a few simple mistakes in there... :)

Any help would be appreciated - its consumed an evening with much head scratching, i even asked my 5 year old Daughter and told me "stop being silly" and walked away...

Thanks,

Stuart G

I normally get these things working but I am a bit stuck as i don't feel I am getting sensible answers...

The problem is simple (!):

Q: Model the flow through an orifice with an upstream/supply pressure of 301BarA where the downstream pressure is in the range 1BarA to 301BarA. The orifice is 0.5mm in diameter and gas is Helium at 0C

I am doing this in excel so formula are what I've copied out of that. I have:

P0 as 301BarA

P1 as 1 to 301BarA

T1 as 0C

>> Determined density as p0 =((4*P0)/(0.0821*(T1+273)))/1000/1000 to get kG/cu.m so i get 5.35396E-05 which i believe to be correct.

(checked at 1BarA aligns with textbook values)

cp as 5.193

cv as 3.116

>> Determined specific heat ratio as y = 1.6667 which aligns with textbook values

>> Determined p* as =(2/(y+1))^(y/(y-1)) which for helium is 0.487 which i think is OK too

Critical pressure CP* = P1 / p*

>> For example, with a P1 of 100BarA i get the critical pressure as CP* = 205.28BarA

Determining sonic flow by p1/p2 and where p1 is greater than the critical pressure (else subsonic)

>> eg 200BarA into 96BarA is supersonic flow as 200Bar is greater than (P2/p*) 96/0.487 = 197BarA

but 200BarA into 104BarA is subsonic flow as 200Bar is less than 213.49BarA

From this, i have a column which is intended for a sonic mass flow calculation and another for subsonic, and just an IF statement to use the appropriate calculation for the final result.

Finally, the orifice is defined as

Cd = 0.6 (arbitrary typical number)

SupplyDia = 5mm (upstream pipe diameter)

OrificeDia = 0.5mm >> calculated as 1.9635E-07 sq.m

So, i think I've been successful in doing the subsonic flow, engineering toolbox has a calculator for this and my numbers align.For reference, I've worked this out by:

mass flow kG/S mdot = Cd*(PI()/4)*((OrificeDia/1000)^2)*p0*(2*(((P0-P1)*100000))/(p0*(1-(OrificeDia/SupplyDia)^4)))^0.5

As an example:

P0 = 200BarA, P1 = 160BarA

>> mass flow mdot = 1.99086E-06 kG/s which i convert to volumetric by =(mdot/p0)*1000*60 or 3346.6 L/min

Putting a practical head on, i can picture that sort of flow rate for that pressure and nozzle etc.

Going for a pressure closer to the critical point, just as we fall out of sonic flow, i get we should be looking at not too much over

3.16458E-06 kG/sec 5319.65L/min - however any way i try to implement the sonic calculations, i get wildly different answers!

What I've tried(!):

From engineering tool box (no calc for this, just eqn)

mdot = (Cd*OrificeArea)*(SQRT(y*p0*P0*((2/y+1)^((y+1)/(y-1)))))

>> Given the same just at the critical point entering into sonic flow, this gives mdot = 6.21982E-08 kG/se or 104.55L/min which i feel too low

from chemeurope, a version which didnt need the density

mdot = =(Cd*OrificeArea*P0*100000)*SQRT(((y*4.003)/((1+0.0045*0.1*P0)*8314.5*(T0+273)))*(2/(y+1))^((y+1)/(y-1)))

>> this gives a result of 0.00218 kG/s or 3,658,503.09 L/min which is certainly too high!

Ive done a bit of a cheat in excel which is to determine the highest mass flow rate (using the sub-sonic calculation) before we enter sonic flow, on the basis just before sonic flow and just after sonic flow are not going to be a million miles different.This is a bit of a cheat as i would really like to get my sonic flow calculation correct and working.

One other odd effect i had not expected...

Using the sub-sonic flow method as described, it doesn't matter what input pressure P0 i have, whether its 10bar or 300bar, i always get the same volumetric flow rate, but a different mass flow rate, for example:

P0 | P1 | m (total) | volumetric | P0 | P1 | m (total) | volumetric | P0 | P1 | m (total) | volumetric | P0 | P1 | m (total) | volumetric | |||

BarA | BarA | kg/sec | L/min | BarA | BarA | kg/sec | L/min | BarA | BarA | kg/sec | L/min | BarA | BarA | kg/sec | L/min | |||

300 | 126 | 4.7469E-06 | 5319.650936 | 200 | 84 | 3.16E-06 | 5319.651 | 100 | 42 | 1.58E-06 | 5319.651 | 50 | 21 | 7.91E-07 | 5319.651 | |||

300 | 132 | 4.7469E-06 | 5319.650936 | 200 | 88 | 3.16E-06 | 5319.651 | 100 | 44 | 1.58E-06 | 5319.651 | 50 | 22 | 7.91E-07 | 5319.651 | |||

300 | 138 | 4.7469E-06 | 5319.650936 | 200 | 92 | 3.16E-06 | 5319.651 | 100 | 46 | 1.58E-06 | 5319.651 | 50 | 23 | 7.91E-07 | 5319.651 | |||

300 | 144 | 4.7469E-06 | 5319.650936 | 200 | 96 | 3.16E-06 | 5319.651 | 100 | 48 | 1.58E-06 | 5319.651 | 50 | 24 | 7.91E-07 | 5319.651 | |||

300 | 150 | 4.7217E-06 | 5291.478222 | 200 | 100 | 3.15E-06 | 5291.478 | 100 | 50 | 1.57E-06 | 5291.478 | 50 | 25 | 7.87E-07 | 5291.478 | |||

300 | 156 | 4.6263E-06 | 5184.568651 | 200 | 104 | 3.08E-06 | 5184.569 | 100 | 52 | 1.54E-06 | 5184.569 | 50 | 26 | 7.71E-07 | 5184.569 | |||

300 | 162 | 4.5289E-06 | 5075.407612 | 200 | 108 | 3.02E-06 | 5075.408 | 100 | 54 | 1.51E-06 | 5075.408 | 50 | 27 | 7.55E-07 | 5075.408 | |||

300 | 168 | 4.4294E-06 | 4963.846569 | 200 | 112 | 2.95E-06 | 4963.847 | 100 | 56 | 1.48E-06 | 4963.847 | 50 | 28 | 7.38E-07 | 4963.847 | |||

300 | 174 | 4.3275E-06 | 4849.719898 | 200 | 116 | 2.89E-06 | 4849.72 | 100 | 58 | 1.44E-06 | 4849.72 | 50 | 29 | 7.21E-07 | 4849.72 | |||

300 | 180 | 4.2232E-06 | 4732.842002 | 200 | 120 | 2.82E-06 | 4732.842 | 100 | 60 | 1.41E-06 | 4732.842 | 50 | 30 | 7.04E-07 | 4732.842 | |||

300 | 186 | 4.1163E-06 | 4613.003766 | 200 | 124 | 2.74E-06 | 4613.004 | 100 | 62 | 1.37E-06 | 4613.004 | 50 | 31 | 6.86E-07 | 4613.004 | |||

300 | 192 | 4.0065E-06 | 4489.96816 | 200 | 128 | 2.67E-06 | 4489.968 | 100 | 64 | 1.34E-06 | 4489.968 | 50 | 32 | 6.68E-07 | 4489.968 |

I think the effect of the decreasing pressure P0 reducing the density is cancelling out the conversion from gravimetric to volumetric, although i would have thought less pressure = less density (OK) = less mass (OK) = less flow (not OK)... So that's probably an issue!

Anyway, I've attached the spreadsheet I am working on, sorry its a bit of a work in progress!

Sorry for the long question, i am hoping there's just a few simple mistakes in there... :)

Any help would be appreciated - its consumed an evening with much head scratching, i even asked my 5 year old Daughter and told me "stop being silly" and walked away...

Thanks,

Stuart G