Pressure tank model
Pressure Tank:
The pressure generation system consists of a tank, a regulator, and a line that connects to the pressure manifold. The tank will hold whatever substance we decide to use to pressurize the system, many amateur hybrid designs use liquid CO2 or nitrous oxide to charge the system. Since these substances would require heavy thick walled tanks, we decided to try dry ice, solid CO2. Dry ice is cheaply available at your local grocery store and should be able to generate and maintain the system pressure required during operation. Using dry ice will also allow us to use a lighter low pressure tank instead of the heavy 3000 psi tanks. The main drawback to using dry ice is the amount of time required to build up pressure in the tank. The tank chosen for our reservoir is an old aluminum fire extinguisher rated at 720 psi. The tank was tested, see the data section, to make sure the tank could hold the pressure that it was rated to, the test was successful. The top of the fire extinguisher was then modified to allow us to attach a lightweight regulator, as seen in the photos. With the modified top and new regulator attached, a second test was conducted to see if the tank could be pressurized to the critical point of CO2, about 1073 psi, the results are also in the data section.
The complete fire extinguisher. |
The pressure reservoir. |
The modified top. |
Tank considerations:
Most tanks are marked with a working pressure rating, this rating is typically the failure pressure divided by a factor of safety. When choosing a tank using the rating, it is best to multiply the design pressure by a factor of safety and choose a tank with a rating in that range. If a tank must be designed or is not rated there are two parameters that should be considered before using the tank, the longitudinal and hoop stresses.
These stresses are planer stresses in the walls of the tank resulting from the pressure in the tank. There are no shear stresses in the tank walls, so the principle stresses are the longitudinal and hoop stresses. Assuming the tank is under static equilibrium, we can make a virtual cut across the tank to look at the longitudinal forces in the tank walls. The longitudinal stress can then be calculated using Newton's first law of motion because the pressure forces and stresses will be equal.
Longitudinal stress |
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Similarly, if we virtually cut the tank in a longitudinal direction, we can analyze the forces to calculate the hoop stress of the tank. Again the pressure forces will be related to the wall stresses using Newton's first law of motion.
Hoop stress |
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Failure of the tank will occur when the principle stresses in the tank walls exceed the yield stress of the tank material. So, using these equations we can narrow down possible tank materials and calculate the parameters of the tank. A factor of safety should always be considered in the design and when possible, the tank's working pressure should be verified before it is integrated into the design.
Regulator:
The regulator chosen was an AIM-68 adjustable regulator with a gauge. This regulator was chosen because of its lightweight aluminum construction and its two outlets. If needed we can replace the gauge with a relief valve to make sure the system pressure doesn't exceed its rating. Further testing with the regulator attached to the tank will tell us if the relief valve is required, if not then we have a gauge to read the reservoir pressure during engine tests. This was also chosen because the range of this regulator is advertised to be from 0 psi to 600 psi.
Regulator front view |
Regulator side view |
Properties of CO2:
| CAS Number |
124-38-9 |
| Gas |
UN1013 |
| Liquid refrigerated |
UN2187 |
| Solid (Carbonic anhydride; Dry ice) |
UN1845 |
| Molecular weight : |
44.01 g/mol |
| Latent heat of fusion (1,013 bar, at triple point) : |
196.104 kJ/kg |
| Solid density : |
1562 kg/m3 |
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Liquid phaseLiquid density (at -20 °C (or -4 °F) and 19.7 bar) : |
1032 kg/m3 |
| Liquid/gas equivalent (1.013 bar and 15 °C (per kg of solid)) : |
845 vol/vol |
| Boiling point (Sublimation) : |
-78.5 °C |
| Latent heat of vaporization (1.013 bar at boiling point) : |
571.08 kJ/kg |
| Vapor pressure (at 20 °C or 68 °F) : |
58.5 bar |
| Critical temperature : |
31 °C |
| Critical pressure : |
73.825 bar |
| Critical density : |
464 kg/m3 |
| Triple point temperature : |
-56.6 °C |
| Triple point pressure : |
5.185 bar |
| Gas density (1.013 bar at sublimation point) : |
2.814 kg/m3 |
| Gas density (1.013 bar and 15 °C (59 °F)) : |
1.87 kg/m3 |
| Compressibility Factor (Z) (1.013 bar and 15 °C (59 °F)) : |
0.9942 |
| Specific gravity (air = 1) (1.013 bar and 21 °C (70 °F)) : |
1.521 |
| Specific volume (1.013 bar and 21 °C (70 °F)) : |
0.547 m3/kg |
| Heat capacity at constant pressure (Cp) (1.013 bar and 25 °C (77 °F)) : |
0.037 kJ/(mol.K) |
| Heat capacity at constant volume (Cv) (1.013 bar and 25 °C (77 °F)) : |
0.028 kJ/(mol.K) |
| Ratio of specific heats (Gamma:Cp/Cv) (1.013 bar and 25 °C (77 °F)) : |
1.293759 |
| Viscosity (1.013 bar and 0 °C (32 °F)) : |
0.0001372 |
| Poise Thermal conductivity (1.013 bar and 0 °C (32 °F)) : |
14.65 mW/(m.K) |
| Solubility in water (1.013 bar and 0 °C (32 °F)) : |
1.7163 vol/vol |
| Concentration in air : |
0.03 vol % |
Vapor pressure graph for CO2
Phase diagram for CO2
Final Configuration:
From extensive testing, we found that CO2 by itself in the tank took well over an hour and a half to build up a pressure to around 600 psi. So, discussed in the data section, we added 2 teaspoons of tap water to the dry ice in the pressure tank to increase the rate of sublimation. By doing this we reduced the charging time to around 40 minutes, since the tank pressure needed to be around 500 psi to maintain the desired system pressure during the burn. For the test stand we added a pressure gauge to monitor the system pressure during the test to allow us to calculate the mass flow rate of the gas and oxidizer during the tests as well as monitor the system pressure for anomalies during operation. The gauge on the pressure tank was removed during the test because we found in the third round of pressure test that the tank charging times were extremely reliable and it took about an hour to load the propellants. Below are some images of the pressure tank and regulator.
Pressure tank and regulator assembly.
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System pressure gauge and regulator assembly. |
