Improved Knock-Down Factors for the Design of Hemispherical, Torispherical and Ellipsoidal Heads Under External Pressure

Abstract Pressure vessel heads, particularly hemispherical, torispherical, and ellipsoidal heads, are widely used in industries such as petroleum, chemical, and nuclear power. Heads with a high radius-to-thickness ratio are prone to buckle under external pressure. Due to the existence of shape imperfections, the buckling pressure of actual heads is significantly lower than that of perfect heads. The knockdown factors (KDFs) are used to correct buckling pressure. However, KDFs of these heads are still lack in investigation. In ASME BPVC VIII-2, the KDF for formed heads is set at a constant value of 0.124. NASA SP-8032 delivered KDFs by a function of geometry parameter and a KDF curve from test results. In this paper, we first established finite element models with initial shape imperfections, which were collected from in-service head using a 3D laser scanner. Next, the KDFs were determined by the radio of buckling pressure of imperfect heads to buckling pressure of perfect heads. We then analyzed the effects of starting angle of imperfection, maximum magnitude of imperfection and wall-thickness on KDFs and developed a method for calculating threshold KDFs. Finally, through a large number of simulation calculations, the new corresponding fitting formula of KDFs was obtained and compared with the current standards of ASME and NASA and the experimental data of head buckling.