Pressure vessel

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A pressure vessel is a closed container designed to hold gases or liquids at a pressure different from the ambient pressure. The end caps fitted to the cylindrical body are called heads.

The legal definition of pressure vessel varies from country to country, but often involves the maximum safe pressure (may need to be above half a bar) that the vessel is designed for and the pressure-volume product, particularly of the gaseous part (in some cases an incompressible liquid portion can be excluded as it does not contribute to the potential energy stored in the vessel.) In the United States, the rules for pressure vessels are contained in the American Society of Mechanical Engineers Boiler and Pressure Vessel Code.

Contents

[edit] Uses

A pressure tank connected to a water well and domestic hot water system
A pressure tank connected to a water well and domestic hot water system

Pressure vessels are used in a variety of applications. These include the industry and the private sector. They appear in these sectors respectively as industrial compressed air receivers and domestic hot water storage tanks, other examples of pressure vessels are: diving cylinder, recompression chamber, distillation towers, autoclaves and many other vessels in mining or oil refineries and petrochemical plants, nuclear reactor vessel, habitat of a space ship, habitat of a submarine, pneumatic reservoir, hydraulic reservoir under pressure, rail vehicle airbrake reservoir, road vehicle airbrake reservoir and storage vessels for liquified gases such as ammonia, chlorine, propane, butane and LPG.

Steel Pressure Vessel
Steel Pressure Vessel

In the industrial sector, pressure vessels are designed to operate safely at a specific pressure and temperature, technically referred to as the "Design Pressure" and "Design Temperature". A vessel that is inadequately designed to handle a high pressure constitutes a very significant safety hazard. Because of that, the design and certification of pressure vessels is governed by design codes such as the ASME Boiler and Pressure Vessel Code in North America, the Pressure Equipment Directive of the EU (PED), Japanese Industrial Standard (JIS), CSA B51 in Canada, AS1210 in Australia and other international standards like Lloyd's, Germanischer Lloyd, Det Norske Veritas, Stoomwezen etc.

[edit] Shape of a pressure vessel

Pressure vessels can theoretically be almost any shape, but shapes made of sections of spheres, cylinders and cones are usually employed. More complicated shapes have historically been much harder to analyse for safe operation and are usually far harder to construct.

Theoretically a sphere would be the optimal shape of a pressure vessel. Unfortunately the sphere shape is difficult to manufacture, therefore more expensive, so most of the pressure vessels are cylindrical shape with 2:1 semi elliptical heads or end caps on each end. Smaller pressure vessels are arranged from a pipe and two covers. Disadvantage of these vessels is the fact that larger diameters make them relatively more expensive, so that for example the most economic shape of a 1,000 litres (35 cu ft), 250 bars (3,600 psi) pressure vessel might be a diameter of 914.4 millimetres (36 in) and a length of 1,701.8 millimetres (67 in) including the 2:1 semi elliptical domed end caps.

[edit] Construction materials

Generally, almost any material with good tensile properties that is chemically stable in the chosen application can be employed.

Many pressure vessels are made of steel. To manufacture a spherical pressure vessel, forged parts would have to be welded together. Some mechanical properties of steel are increased by forging, but welding can sometimes reduce these desirable properties. In case of welding, in order to make the pressure vessel meet international safety standards, carefully selected steel with a high impact resistance & corrosion resistant material should also be used.

Some pressure vessels are made of wound carbon fibre held in place with a polymer. Due to the very high tensile strength of carbon fibre these vessels can be very light, but are much trickier to manufacture.

Other very common materials include polymers such as PET in fizzy drinks containers and copper in plumbing.

[edit] Scaling

No matter what shape it takes, the minimum mass of a pressure vessel scales with the pressure and volume it contains and is proportional to the strength to weight ratio of the construction material.

[edit] Spherical vessel

For a sphere, the mass of a pressure vessel is

M = {3 \over 2} P V {\rho \over \sigma}

Where:

M is mass
P is the pressure difference from ambient, i.e. the gauge pressure
V is volume
ρ is the density of the pressure vessel material
σ is the maximum working stress that material can tolerate.

Other shapes besides a sphere have constants larger than 3/2 (infinite cylinders take 2), although some tanks, such as non-spherical wound composite tanks can approach this.

[edit] Cylindrical vessel with hemispherical ends

For a cylinder with hemispherical ends:

M = 2 \pi R^2 (R + L) P {\rho \over \sigma}

where:

  • R is the radius
  • L is the middle cylinder length only, and the overall length is L + 2R

[edit] 2:1 Cylindrical vessel with hemispherical ends

In a vessel with a 2:1 aspect ratio:

M = 6 \pi R^3 P {\rho \over \sigma}

[edit] Gas storage

In looking at the first equation, the factor PV, in SI units, is in units of (pressurization) energy. For a stored gas, PV is proportional to the mass of gas at a given temperature, thus:

M = {3 \over 2} nRT {\rho \over \sigma} (see gas law)

The other factors are constant for a given vessel shape and material. So we can see that there is no theoretical "efficiency of scale", in terms of the ratio of pressure vessel mass to pressurization energy, or of pressure vessel mass to stored gas mass. For storing gases, "tankage efficiency" is independent of pressure, at least for the same temperature.

So, for example, a typical design for a minimum mass tank to hold helium (as a pressurant gas) on a rocket would use a spherical chamber for a minimum shape constant, carbon fiber for best possible ρ / σ, and very cold helium for best possible M / pV.

[edit] Stress in thin-walled pressure vessels

The stress in a thin-walled pressure vessel in the shape of a sphere is:
\sigma_\theta = \frac{pr}{2t}
Where σθ is the hoop stress, or stress in the circumferential direction, p is the internal gage pressure, r is the radius of the sphere, and t is the thickness. A vessel can be considered "thin-walled" if the radius is at least 20 times larger than the wall thickness.[1]

The stress in a thin-walled pressure vessel in the shape of a cylinder is:
\sigma_\theta = \frac{pr}{t}
\sigma_{\rm long} = \frac{pr}{2t}
Where σθ is the hoop stress, or stress in the circumferential direction, σlong is the stress in the longitudinal direction, p is the internal gage pressure, r is the radius of the cylinder, and t is the wall thickness.

[edit] Winding angle of carbon fibre vessels

Wound infinite cylindrical shapes optimally take a winding angle of 54.7 degrees, as this gives the necessary twice the strength in the circumferential direction to the longitudinal.[2]

[edit] Design Standards

  • BS 4994
  • ASME Code Section VIII Division 1
  • ASME Code Section VIII Division 2 Alternative Rule
  • ASME Code Section VIII Division 3 Alternative Rule for Construction of High Pressure Vessel
  • ASME PVHO (Safety Standard for Pressure Vessels for Human Occupancy)
  • BS 5500
  • Stoomwezen
  • AD Merkblätterasa
  • CODAP
  • AS 1210
  • ISO 11439 [3]

[edit] Alternatives to pressure vessels

Depending on the application and local circumstances, alternatives have come about which can replace pressure tanks. An example to this is in the private sector (for use in domestic water collection systems). Non-pressure vessel systems are increasingly seen with:

  • no storage tank or pump at all (gravity controlled systems) [4] Gravity-controlled systems are usually created by placing the water harvester on an elevation (e.g. rooftops). This will produce about 0.5 PSI per foot of water head (height difference). However, municipal water or pumped water is typically around 90 PSI.
  • or with either inline pump controllers or pressure-sensitive pumps [5]:

[edit] History of pressure vessels

Large pressure vessels were invented during the industrial revolution, particularly in England, for making steam engines.

Design and testing standards came about after some large explosions lead to loss off life and a system of certification and testing mutations.

[edit] See also

[edit] External links

Wikimedia Commons has media related to:

[edit] Further reading

  • Megyesy, Eugene F. (2004, 13th ed.) Pressure Vessel Handbook. Pressure Vessel Publishing, Inc.: Tulsa, Oklahoma, USA. Design handbook for pressure vessels based on the ASME code.

[edit] References

  • A.C. Ugural, S.K. Fenster, Advanced Strength and Applied Elasticity, 4th ed.
  • E.P. Popov, Engineering Mechanics of Solids, 1st ed.

Pressure Vessel Handbook, 14th Edition Eugene F. Megyesy PV Publishing, Inc. Oklahoma City, OK

[edit] Notes

  1. ^ Richard Budynas, J. Nisbett, Shigley's Mechanical Engineering Design, 8th ed., New York:McGraw-Hill, ISBN 978-0-07-312193-2, pg 108
  2. ^ MIT pressure vessel lecture
  3. ^ Gas cylinders -- High pressure cylinders for the on-board storage of natural gas as a fuel for automotive vehicles
  4. ^ Domestic water collection systems also sometimes able to function on gravity
  5. ^ Alternatives to pressure vessels in domestic water systems