Filament Wound Pressure Vessel Design

Pressure vessels constructed by using filament winding methods are a perfect example of the advantages that fiber-reinforced composite materials offer. Typical pressure vessels are usually designed with a center cylindrical section and two spherical-type end caps with optional polar openings (see examples below). The relative dimensions of the different sections of the vessel are designed according to the space and weight requirements along with the expected pressure levels that the vessel is expected to withstand. Along with these thickness and length dimensions, the shape of the end caps also plays a vital role in the design. This is due to the fact that the dome regions undergo the highest stress levels and are the most critical locations with regard to failure of the structure.

Traditionally, pressure vessels constructed from isotropic materials, such as steel or aluminum, utilized an elliptical shape for the end caps to reduce the critical stresses within the structure. With the advent of orthotropic fiber reinforced materials with preferred stiffness and strength directions parallel to the fibers, it was discovered that the ideal shape profile for the dome was an isotensoid. Isotensoid implies that all locations within a pressurized dome undergo the same level of tensile stress, and the design is formulated so that the major stresses are carried solely by the fibers of the composite. Thus there is a direct correlation between the dome shape, shell stiffness parameters, and the winding pattern that is used within the manufacturing process. Netting analysis is used to formulate and solve the nonlinear equations that result from this interaction between the dome shape and fiber orientation angles. The resulting minimum weight design solution can take into account many particular features of a filament wound pressure vessel, such as the size and type of the polar opening, the method of filament winding (such as geodesic or planar winding), and the effect of multiple zones that each possess different polar openings and winding angles.

One aspect of filament wound pressure vessels that is somewhat unique is the fact that increasing the amount of material incorrectly can actually decrease the load-carrying capability of the structure. This is due to the fact that extra layers of filament wound plies alter the stiffness distribution of the shell and thus necessitate a corresponding change in the shape of the isotensoid dome profile. Since the end cap geometry is usually dictated by the mandrel on which it is formed and thus cannot be changed without re-tooling, the incorrect addition of filament wound plies leads to a design that fails below the desired load levels.

To illustrate this idea further, some results from a consulting project conducted by ADOPTECH are shown here. A filament wound pressure vessel was analyzed that was incorrectly designed by ignoring the effect of multiple filament wound zones on the shape of the dome profile. The figure below indicates the existing dome shape and an ideal solution that is based on the correct variation of the dome profile for the given polar openings and geometry of the structure.

To analyze this structure, a finite element model of the dome region was constructed using composite shell elements. Each element was defined from the stacking sequence at the particular point along the dome profile according to the fiber angle produced by the filament winding process. Stresses within each ply were calculated to determine the highest stress levels and amount of bending for each design. The results for the outermost filament wound ply are shown below. Obviously, the profile of the dome significantly affects the stress levels within the ply.

These results highlight the importance of being able to tailor the filament winding techniques with the desired size and load requirements of a filament wound pressure vessel. Correct design techniques lead to highly weight efficient and reliable pressure vessels that can significantly outperform their metallic counterparts for a variety of applications. ADOPTECH is able to offer their clients both the analysis and re-design of existing pressure vessel structures, as well as original minimum weight designs for a given set of dimensional and loading parameters.
http://www.adoptech.com/pressure-vessels/main.htm

PRESSURE VESSEL DESIGN

Pressure Equipment Engineering Services, Inc. has extensive experience in design, analysis and re-rating of Pressure vessels used in refineries, chemical plants, power plants, nuclear plants and other processing facilities. Some of the capabilities of PEESI in the area of pressure vessels are listed as follows:

• · Design and analysis of Pressure Vessels (Tall Columns, Vertical Pressure Vessels, Horizontal Pressure Vessels, Spherical Vessels, Reactors etc.) based on ASME Boiler & Pressure Vessel Code, Section VIII, Div. - 1, Div. - 2 and Div. - 3.

• · Analysis of Power Boilers per ASME Boiler & Pressure Vessel Code, Section-1

• · Calculations for repair and alteration of existing Pressure Vessels per API-510 and National Board Inspection Code.

• · Calculation of minimum retirement thickness values for existing pressure vessels / pressure vessel components to maximize the remaining safe and useful life.

• · Re-rating of pressure vessels for a new set of design parameters.

• · Calculations to check the suitability of vessels for in-situ PWHT.

• · Fitness-for-service evaluations for pressure vessels to assure the structural integrity of equipment for the intended design parameters and to offer life extension considerations.

• · Fatigue analysis to calculate the fatigue life of pressure vessels subjected to pressure cycles, temperature cycles and startup / shutdown cycles.

• · Failure Analysis to identify the root cause of failure for the failed pressure vessels or pressure vessel components.

• · Finite Element Analysis for pressure vessels and pressure vessel components.

• · Pressure vessel certification, calculations and rating / re-rating for pressure vessels that do not contain sufficient design information in their files.

• · Design of Structural systems and supports for continued operation of leaked vessels or vessels that violate the minimum required thicknesses based on structural considerations.

• · Evaluation of cracks and Flaws in pressure vessels by applying Fracture Mechanics techniques.

• · Evaluation of Minimum Safe Operating Temperature (MSOT) for existing vessels which do not meet the current MDMT requirement of the ASME Code.

• · Evaluation of Pressure Vessels after accidental over-pressurization.

• · Discontinuity Analysis for Pressure Vessels involving special situations of Structural and Material discontinuity.

• · Analysis to assure Mechanical Integrity of Pressure Vessels for following type of flaws: Generalized corrosion, Localized corrosion / Thinning, Blisters, Laminations, Bulges, Gouges, Dents, Cracks etc.

Here are some examples of Pressure Vessel Design / Analysis performed by Pressure Equipment Engineering Services, Inc.

Here are some more examples:

• · Fitness for service evaluations were performed for hundreds of vessels and heat exchangers experiencing generalized corrosion. Based on the half life criteria of the inspection codes, more frequent inspections must be performed for these vessels and heat exchangers to avoid violating the code or jeopardizing the safety of the equipment. In some cases, these vessels and exchangers start approaching scenarios indicating life depletion because of the loss of intended corrosion allowance. The code calculations are performed (using Pressure Vessel & Heat exchanger COMPRESS) for each component of the vessel / exchanger to calculate the minimum retirement thickness for that component for the intended design parameters. The combined set of minimum thickness for all components acts as a guide for future inspection interval for the vessel / exchanger. The calculated minimum thickness values are compared to the actual field measured values to make sure that there is sufficient future safe and useful life available for all the components of the vessel / exchanger. If enough life is not available for several components, then de-rating of vessel / exchanger may be necessary. In case one or two components are limiting the MAWP, local repairs may be specified to maintain the original MAWP of the vessel / exchanger.

• · Fitness for service evaluation was performed for several pressure vessels experiencing temperature lower than the MDMT. The fitness for service criteria was used to evaluate the MSOT (Minimum Safe Operating Temperature) for the vessel. Based on the evaluation, it was concluded for some cases that the MSOT for the vessel was below the intended temperature of operation and thus the vessel was re-rated to the lower requested temperature. However, when the MSOT for the vessel is above the intended temperature of operation, the vessel can not be re-rated to the lower requested temperature.

• · Fitness for service evaluation for several tall vessels was performed before being subjected to in-situ PWHT at temperature of 1150 °F. Sometimes the vessel is heat treated for the circumferential zone containing the repair areas and at other times, the vessel is heat treated using gas firing such that the entire vessel is subjected to PWHT temperature. The actual vessel stresses due to dead weight and wind loading are calculated at the location of the circumferential PWHT zone and compared to the allowable stress values. For cases where the actual stresses are within the allowable stresses, the vessels can be post weld heat treated without any external support. For the other cases, it is found that the vessel stresses exceed the allowable stress values. In these cases, it is recommended that the vessels must be supported with the help of a crane before PWHT is performed for the circumferential vessel zone.

• · Fitness for service evaluation was performed for the top bed of a stainless steel reactor with the intent to calculate the maximum permissible pressure differential allowed by the structural capacity of the bed. The packed bed had 3 distinct stainless steel fabricated beams. The bed was getting plugged during operation. This was causing significantly higher pressure drop on the bed leading to very high stresses in the beams. The intent was to shut down the reactor before the pressure drop reaches a scenario causing the structural failure of the bed. The structural calculations (per AISC code) were performed to check the stresses in the beams, welds and the beam support grating. These structural calculations were automated using MathCAD to calculate the maximum allowable pressure drop through the bed for design case, upset case and failure case. For each of these cases, the limiting pressure drop for the three distinct structural beams and the associated grating support was calculated. The design pressure drop through the reactor bed was 100 psig. The maximum allowable pressure drop for the upset case was specified to be 138 psig. At this pressure drop, all the design criteria were satisfied and this pressure drop was safely permissible. The maximum allowable pressure drop for the failure case was specified to be 158 psig. At this pressure drop, the code allowable stress criteria were not satisfied and the structural components start to yield. Using the pressure drop guidelines specified by these set of calculations, the plant increased the safe operating time before the next shut down.

• · Fitness for service evaluation for a large spheroid vessel experiencing general corrosion. FEA using ANSYS was performed to complete the evaluation. The life of the vessel got extended by a few years.

• · Fitness for service evaluation for a horizontal reactor vessel for higher design loading. FEA using ANSYS was performed to complete the evaluation. The results of the analysis indicated that we did not need additional stiffener rings as was being pointed out by conventional stress analysis.

• · Fitness for service evaluation for the bottom head of a reactor experiencing pitting corrosion. FEA using ANSYS was performed to complete the evaluation. The life of the vessel got extended by a few years.

Pressure Equipment Engineering Services, Inc.
402 Wild Peach Place
Missouri City, Texas 77459
Phone: (281) 261-4628
Fax: (281) 261-4629
Email: info@peesi.com

PRESSURE VESSEL

A pressure vessel is a closed, rigid 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.

In addition to 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.

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.

Shape of a pressure vessel

Theoretically a sphere would be the optimal shape of a pressure vessel. Most 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 should be used. Most 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 1000 litres, 250 bar (25,000 kPa) pressure vessel might be a diameter of 450 mm and a length of 6500 mm.

Scaling

No matter what shape it takes, the minimum mass of a pressure vessel scales with the pressure and volume it contains.

For a sphere, the mass of a pressure vessel is

Where:

M is mass

p is the pressure difference from ambient- 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.

As can be seen from the equation, there is no theoretical efficiency of scale to be had in a pressure vessel; and further, for storing gases at high pressure relative to ambient, tankage efficiency can be shown to be independent of pressure.

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

The stress in a thin-walled pressure vessel in the shape of a sphere is:

Where σ_θ 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:


Where σ_θ is the hoop stress, or stress in the circumferential direction, σ_long 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.

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]

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
• BS 5500
• Stoomwezen
• AD Merkblätter
• CODAP
• AS 1210

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.

References

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

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