Flange for pressure vessel with undercut fillet

A flange for a pressure vessel comprising:

• a rim with an annular surface for abutting an annular end of a cylindrical wall of the pressure vessel;
• a sealing seat with a cylindrical surface for abutting an inner surface of the cylindrical wall of the pressure vessel nearby the annular end;
• an undercut fillet between the rim and the sealing seat, wherein a concave surface of the undercut fillet extends the annular surface of the rim radially inward and then curves back outward to intersect the cylindrical surface of the sealing seat
• wherein the concave contour includes a sequence of arc segments, with each of the arc segments having a respective radius selected to distribute a stress in a distribution along the concave contour and to limit a maximum concentration of the stress in the distribution, the stress produced when an external pressure outside the pressure vessel is higher than an internal pressure inside the pressure vessel;
• and
• wherein the sequence of arc segments includes a first, second, third, and fourth arc segment,
• the first arc segment adjoining an inner edge of the annular surface of the rim at an offset X radially outward from the cylindrical surface of the sealing seat and at a first continuous slope perpendicular to the symmetry axis in the cross-sectional plane, the first arc segment having the offset X≈0.130×L and a radius R1≈0.446×L, where L≈0.040×R is an axial length of the concave contour of the undercut fillet and R is an outer radius from the symmetry axis of the cylindrical surface of the sealing seat,
• the second arc segment adjoining the first arc segment at a second continuous slope having a length Y≈0.054×L and an angle of 42° from the symmetry axis in the cross-sectional plane, the second arc segment having a radius R2≈0.876×L,
• the third arc segment adjoining the second arc segment at a third continuous slope substantially parallel to the symmetry axis in the cross-sectional plane, the third arc segment having a radius R3≈0.200×L, and
• the fourth arc segment adjoining the third arc segment at a fourth continuous slope and a linear extension adjoining the fourth arc segment at a fifth continuous slope perpendicular to the symmetry axis in the cross-sectional plane, the fourth arc segment having a radius R4≈0.260×L, the linear extension perpendicularly intersecting the cylindrical surface of the sealing seat and having a length Z=0.244×L.

A flange for a pressure vessel comprising:

• a rim with an annular surface for abutting an annular end of a cylindrical wall of the pressure vessel;
• a sealing seat with a cylindrical surface for abutting an inner surface of the cylindrical wall of the pressure vessel nearby the annular end;
• an undercut fillet between the rim and the sealing seat, wherein a concave surface of the undercut fillet extends the annular surface of the rim radially inward and then curves back outward to intersect the cylindrical surface of the sealing seat;
• and
• wherein the sealing seat includes one or more grooves in the cylindrical surface of the sealing seat, each of the grooves for receiving an O-ring for forming a seal between the cylindrical surface of the sealing seat and the inner surface of the cylindrical wall of the pressure vessel.