blog about Comparing Hemispherical Ellipsoidal Torispherical and Flat Pressure Vessel Heads

Pressure vessels serve essential functions across chemical, petroleum, and pharmaceutical industries. As the component sealing container ends, heads must withstand internal pressure while integrating with cylindrical shells to form complete pressure boundaries. Head selection profoundly influences vessel safety, manufacturing complexity, and operational economics.

Our analysis focuses on a cylindrical vessel constructed from 0.5-inch thick SA-516 Grade 70 steel, featuring 48-inch outer diameter and 47-inch inner diameter. With material rated for 20,000 psi at 100°F, fully radiographed welds, and no corrosion allowance, ASME VIII-1 calculations establish a 420 psi design pressure. We evaluate four head alternatives:

* Includes 1.5-inch straight flange

The hemispherical design's simple radial geometry achieves optimal stress distribution, requiring only 0.2474-inch thickness—half the cylinder's wall thickness. While material-efficient for high-pressure applications, these heads typically require multi-piece welded construction, increasing manufacturing complexity.

• Advantages: Superior material utilization (45% lighter than cylinder); uniform stress distribution; ideal for spherical storage tanks.
• Limitations: Significant manufacturing costs; substantial height requirements.
• Applications: High-pressure systems; large-diameter vessels; material-sensitive projects.

The common 2:1 semi-elliptical design (depth = 1/4 diameter) offers practical compromise between performance and manufacturability. Requiring 0.4947-inch thickness in our case study, these heads can be formed from single plates, making them economically favorable for low-pressure applications.

• Advantages: Simplified fabrication; moderate height profile; cost-effective for standard pressures.
• Limitations: Higher stress concentrations than hemispheres; thickness approaches cylindrical requirements.
• Applications: Medium/low-pressure vessels; height-constrained installations; budget-sensitive projects.

Featuring a 48-inch crown radius and 2.973-inch knuckle radius, torispherical heads achieve minimal height (10.29 inches) but require 0.8901-inch thickness—78% thicker than the cylinder. Stress concentrations often necessitate post-forming heat treatment.

• Advantages: Minimal height profile; suitable for moderate pressures.
• Limitations: Severe stress concentrations; complex fabrication; nozzle placement restrictions.
• Applications: Space-constrained installations; moderate-pressure systems.

Relying entirely on bending resistance, flat heads demand extreme thickness (3.912 inches) while providing planar internal surfaces. Engineers often employ alternative solutions like reinforced thin plates or concrete linings to reduce weight.

• Advantages: Simple construction; flat interior surfaces.
• Limitations: Excessive weight (3.8× cylinder mass); high stress concentrations.
• Applications: Special processes requiring flat surfaces; low-pressure systems.

ASME VIII-1 formulas for cylindrical and hemispherical components produce Tresca stresses near the 20,000 psi design limit. Transition zones show elevated stresses (23,060 psi) that remain within VIII-2 allowances. Notably, von Mises calculations yield 12% lower stresses in cylinders but equivalent values in hemispheres.

Both semi-elliptical and torispherical designs demonstrate higher transition stresses, with torispherical heads frequently exceeding VIII-2 limits near nozzles. Flat head analyses reveal center stresses at half the allowable 30,000 psi bending limit, indicating conservative design rules.

Optimal head selection balances pressure requirements, spatial constraints, manufacturing capabilities, and economic factors. Hemispherical heads excel in high-pressure scenarios despite fabrication challenges, while semi-elliptical designs offer practical solutions for routine applications. Torispherical heads serve height-sensitive installations, and flat heads remain specialized solutions. As finite element analysis advances, designers gain opportunities to optimize thickness profiles while maintaining safety margins.