## Simulation CFD

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# compressable flow from pressurized bottle to atmosphere...

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I am trying to model the flow from an air bottle (8000 psi at 1500C) through a 0.25" orifice to the atmosphere. (14.7 psi, 72F)

An incompressible model yields a maximum flow of mach 2.479 -- so I tried a compressible flow.

8000 psi, 1500C, and mach 2.479 implies a total temperature of 6109..86 rankine and a total pressure of 132,286.98 psi. (right ?)

with boundary conditions of "unknown: and 0 psi ... using a transient analysis with a microsecond step

by 1 millisecond -- I find a pressure in the vessel of -2400 psi (negative ?) and a temperature of 5650 F

Suggestions ...

/Steven

# Re: compressable flow from pressurized bottle to atmosphere...

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Hi Steven,

Are you setting these as initial conditions?

Do you have air set to variable or is it still incompressible?

I would not advise both unknown AND p=0, just use unknown for now perhaps. Otherwise you are leaving it free and constraining it at the same time.

Kind regards,

Jon

**Jon Wilde**

# Re: compressable flow from pressurized bottle to atmosphere...

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# Re: compressable flow from pressurized bottle to atmosphere...

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Hi Paul,

Please do and let us know. It may well be that you need a pressure, just not both conditions at once.

Typically we use unknown for compressible models but usually when we have a prescribed mass flow rate at the inlet, here this is unknown so it might be more suitable to assign a known pressure. So long as it really is the true pressure on the plane you are assigning it.

Would you be able to share the support file (CFZ) with us at all?

Best regards,

Jon

**Jon Wilde**

# Re: compressable flow from pressurized bottle to atmosphere...

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The instant the bullet clears the barrel, the propellent (45% nitroglycerine and 55% nicrocellulose) has completed combustion; leaving the barrel full of gas (0.672 g CO2, 0.282 g N2, 0.0277 g O2, 0.360 g H2O, 0.0408 g CO) with the properties: 8000 psi, 2822 F, and a velocity of 2800 ft/s. Over the next few milliseconds the pressure, temperature, and velocity of the exiting gases, essentially drop to ambient.

For the time being, I am using "air" (gamma=1.4) as the fluid -- it's close to the weighted mean average of the actual gas composition: [CO2=1.3, N2=1.4, O2=1.4, H20=1.3, CO=1.4]. Also the speed of sound in air (343 m/s) is close to the weighted mean average of the speeds of sound in the actual gas composition: (CO2=267, N2=349, O2=326, H20(vapor)=405, CO=336)

In the barrel the speed of sound is 2808 ft/s ... so the bullet and gas are at mach 0.997. But once the gas hits the divergent cone, at 72F, it becomes supersonic (mach 2.48); therefore it should (initially) accelerate in the divergent cone.

But no settings I have found get remotely close to the actual behavior for the pressure or temperature or velocity of the exiting gases.

I have tried dozens of permutations and possible values for initial and boundary conditions -- I don't recall which were used for this run.

The conditions which make sense (I think) are these :

speed of sound in air at 72F is 1129.5 ft/s

so mach number is 2800/1129.5 = 2.478973 -- so we should use compressible flow

gamma for air is 1.4 at 72F

total temperature would be:

T0*(1 + 0.5*(gamma-1)*mach*mach)

= (2822+459)*(1 + 0.2 * 2.478973 * 2.478973)

= 7313.550 Rankine

total pressure would be:

P0*(1 + 0.5*(gamma-1)*m*m) ^ (gamma/(gamma-1))

= 8000*(1 + 0.2 * 2.478973 * 2.478973) ^ 3.5

= 132,286.984 psi

initial conditions in the diverging cone are: velocity=0; total_temp=72F; total_pressure=0

I was using transient solution; step=1e-6 seconds; stop=.003 seconds; flow and heat transfer -- but no radiation.

Also, because of the (anticipated) existence of shock waves and shock fans I would use a small mesh.

/S