What is Pressure vessel?
A pressure vessel is a container designed to hold gases or liquids at a pressure substantially different from the ambient pressure.
The pressure differential is dangerous, and fatal accidents have occurred in the history of pressure vessel development and operation. Consequently, pressure vessel design, manufacture, and operation are regulated by engineering authorities backed by legislation. For these reasons, the definition of a pressure vessel varies from country to country.
Design involves parameters such as maximum safe operating pressure and temperature, safety factor, corrosion allowance and minimum design temperature (for brittle fracture). Construction is tested using nondestructive testing, such as ultrasonic testing, radiography, and pressure tests. Hydrostatic tests use water, but pneumatic tests use air or another gas. Hydrostatic testing is preferred, because it is a safer method, as much less energy is released if a fracture occurs during the test (water does not rapidly increase its volume when rapid depressurization occurs, unlike gases like air, which fail explosively).
In most countries, vessels over a certain size and pressure (15 PSI) must be built to a formal code. In the United States that code is the ASME Boiler and Pressure Vessel Code (BPVC). These vessels also require an authorized inspector to sign off on every new vessel constructed and each vessel has a nameplate with pertinent information about the vessel, such as maximum allowable working pressure, maximum temperature, minimum design metal temperature, what company manufactured it, the date, its registration number (through the National Board), and ASME’s official stamp for pressure vessels (U-stamp). The nameplate makes the vessel traceable and officially an ASME Code vessel.
Pressure vessel features
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. A common design is a cylinder with end caps called heads. Head shapes are frequently either hemispherical or dished (torispherical). More complicated shapes have historically been much harder to analyze for safe operation and are usually far more difficult to construct.
Theoretically, a spherical pressure vessel has approximately twice the strength of a cylindrical pressure vessel with the same wall thickness, and is the ideal shape to hold internal pressure. However, a spherical shape is difficult to manufacture, and therefore more expensive, so most pressure vessels are cylindrical with 2:1 semi-elliptical heads or end caps on each end. Smaller pressure vessels are assembled from a pipe and two covers. For cylindrical vessels with a diameter up to 600 mm (NPS of 24 in), it is possible to use seamless pipe for the shell, thus avoiding many inspection and testing issues, mainly the nondestructive examination of radiography for the long seam if required.
A disadvantage of these vessels is that greater diameters are 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 91.44 centimeters (36 in) and a length of 1.7018 meters (67 in) including the 2:1 semi-elliptical domed end caps.
Many pressure vessels are made of steel. To manufacture a cylindrical or spherical pressure vessel, rolled and possibly forged parts would have to be welded together. Some mechanical properties of steel, achieved by rolling or forging, could be adversely affected by welding, unless special precautions are taken. In addition to adequate mechanical strength, current standards dictate the use of steel with a high impact resistance, especially for vessels used in low temperatures. In applications where carbon steel would suffer corrosion, special corrosion resistant material should also be used.
Some pressure vessels are made of composite materials, such as filament wound composite using carbon fiber held in place with a polymer. Due to the very high tensile strength of carbon fiber these vessels can be very light, but are much more difficult to manufacture. The composite material may be wound around a metal liner, forming a composite over-wrapped pressure vessel.
Other very common materials include polymers such as PET in carbonated beverage containers and copper in plumbing.
Pressure vessels may be lined with various metals, ceramics, or polymers to prevent leaking and protect the structure of the vessel from the contained medium. This liner may also carry a significant portion of the pressure load.
Pressure Vessels may also be constructed from concrete (PCV) or other materials which are weak in tension. Cabling, wrapped around the vessel or within the wall or the vessel itself, provides the necessary tension to resist the internal pressure. A “leak-proof steel thin membrane” lines the internal wall of the vessel. Such vessels can be assembled from modular pieces and so have “no inherent size limitations”. There is also a high order of redundancy thanks to the large number of individual cables resisting the internal pressure.
Leak before burst
Leak before burst describes a pressure vessel designed such that a crack in the vessel will grow through the wall, allowing the contained fluid to escape and reducing the pressure, prior to growing so large as to cause fracture at the operating pressure.
Many pressure vessel standards, including the ASME Boiler and Pressure Vessel Code and the AIAA metallic pressure vessel standard, either require pressure vessel designs to be leak before burst, or require pressure vessels to meet more stringent requirements for fatigue and fracture if they are not shown to be leak before burst.
As the pressure vessel is designed to a pressure, there is typically a safety valve or relief valve to ensure that this pressure is not exceeded in operation.
Pressure vessel closures
Pressure vessel closures are pressure retaining structures designed to provide quick access to pipelines, pressure vessels, pig traps, filters and filtration systems. Typically pressure vessel closures allow maintenance personnel.
No matter what shape it takes, the minimum mass of a pressure vessel scales with the pressure and volume it contains and is inversely proportional to the strength to weight ratio of the construction material (minimum mass decreases as strength increases).
Scaling of stress in walls of vessel
Pressure vessels are held together against the gas pressure due to tensile forces within the walls of the container. The normal (tensile) stress in the walls of the container is proportional to the pressure and radius of the vessel and inversely proportional to the thickness of the walls. Therefore, pressure vessels are designed to have a thickness proportional to the radius of tank and the pressure of the tank and inversely proportional to the maximum allowed normal stress of the particular material used in the walls of the container.
Because (for a given pressure) the thickness of the walls scales with the radius of the tank, the mass of a tank (which scales as the length times radius times thickness of the wall for a cylindrical tank) scales with the volume of the gas held (which scales as length times radius squared). The exact formula varies with the tank shape but depends on the density, ρ, and maximum allowable stress σ of the material in addition to the pressure P and volume V of the vessel. (See below for the exact equations for the stress in the walls.)
For a sphere, the minimum mass of a pressure vessel is
M is mass, (kg)
P is the pressure difference from ambient (the gauge pressure), (Pa)
V is volume,
ρ is the density of the pressure vessel material, (kg/m^3)
σ is the maximum working stress that material can tolerate. (Pa)
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.
Cylindrical vessel with hemispherical ends
This is sometimes called a “bullet” for its shape, although in geometric terms it is a capsule.
For a cylinder with hemispherical ends,
R is the radius (m)
W is the middle cylinder width only, and the overall width is W + 2R (m)
Cylindrical vessel with semi-elliptical ends
In a vessel with an aspect ratio of middle cylinder width to radius of 2:1,
In looking at the first equation, the factor PV, in SI units, is in units of pressure energy. For a stored gas, PV is proportional to the mass of gas at a given temperature, thus
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 pressure 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.
Stress in thin-walled pressure vessels
Stress in a shallow-walled pressure vessel in the shape of a sphere is
where σΘ is hoop stress, or stress in the circumferential direction, σlong is stress in the longitudinal direction, p is internal gauge pressure, r is the inner radius of the sphere, and t is thickness of the sphere wall. A vessel can be considered “shallow-walled” if the diameter is at least 10 times (sometimes cited as 20 times) greater than the wall depth.
Stress in a shallow-walled pressure vessel in the shape of a cylinder is
- σΘ is hoop stress, or stress in the circumferential direction
- σlong is stress in the longitudinal direction
- p is internal gauge pressure
- r is the inner radius of the cylinder
- t is thickness of the cylinder wall.
Almost all pressure vessel design standards contain variations of these two formulas with additional empirical terms to account for wall thickness tolerances, quality control of welds and in-service corrosion allowances.
For example, the ASME Boiler and Pressure Vessel Code (BPVC) (UG-27) formulas are:
where E is the joint efficient, and all others variables as stated above.
The factor of safety is often included in these formulas as well, in the case of the ASME BPVC this term is included in the material stress value when solving for pressure or thickness.
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.
Pressure vessels are used in a variety of applications in both industry and the private sector. They appear in these sectors as industrial compressed air receivers and domestic hot water storage tanks.
Other examples of pressure vessels are diving cylinders, recompression chambers, distillation towers, pressure reactors, autoclaves, and many other vessels in mining operations, oil refineries and petrochemical plants, nuclear reactor vessels, submarine and space ship habitats, pneumatic reservoirs, hydraulic reservoirs under pressure, rail vehicle airbrake reservoirs, road vehicle airbrake reservoirs, and storage vessels for liquified gases such as ammonia, chlorine, and LPG (propane, butane).
A unique application of a pressure vessel is the passenger cabin of an airliner; The outer skin carries both the aircraft maneuvering loads and the cabin pressurization loads.
- A.C. Ugural, S.K. Fenster, Advanced Strength and Applied Elasticity, 4th ed.
- E.P. Popov, Engineering Mechanics of Solids, 1st ed.
- Megyesy, Eugene F. “Pressure Vessel Handbook, 14th Edition.” PV Publishing, Inc. Oklahoma City, OK