How WRC 537 handles a nozzle on a cone

The cone can be entered as it appears on a drawing: the inside diameters at the large and small ends, the axial length between them, and the axial distance from the large end to the point where the nozzle centreline meets the inside surface. From those the calculator finds the half-apex angle and the local inside diameter. The inside diameter changes linearly along the axis.

From there the work is the cylinder check: the mean radius Rm from the local inside radius and the corroded thickness, γ and β from Rm, the curve coefficients, the stresses at the eight points, and the limits 1.5S and 3S. Nothing in the load stresses knows the shell is a cone.

The pressure stress at the opening is not taken from the cylinder. The Division 2 pressure check at the opening has a conical-shell form, and the calculator uses it with the half-apex angle and the direction of the nozzle axis. Three directions are accepted: normal to the cone surface, perpendicular to the vessel axis, or parallel to it. The axis changes the size of the opening in the cone and so the pressure stress; it does not change the load stresses.

Anything else is refused with a reason. An offset or freely tilted nozzle on a cone is outside WRC 537, and so is a clip on a cone; the calculator says to use the shell model for them.

The cylinder curves were drawn for a shell whose radius does not change. On a cone it changes across the nozzle's own footprint: in the illustration above by about 6 % either side of the value used. The larger the nozzle against the local radius, and the steeper the cone, the larger that spread, and the less one radius stands for the shell round the nozzle.

The meridian of a cone is also inclined to the vessel axis, so the membrane forces under pressure differ from those in a cylinder of the same local radius. The calculator does not try to correct for this. It states the approximation on every cone result instead of hiding it.

A cone meets a cylinder or a head at a junction where the shell changes direction. That junction carries bending of its own under pressure, and the bending dies out over a few decay lengths √(Rm·T). A nozzle inside that zone is not alone: the junction stiffens one side of it and adds its own stresses. WRC 537 assumes neither.

The note printed with every cone result says not to use it near a cone-to-cylinder or cone-to-head junction. The calculator does not measure that distance from the cone geometry. If the distance to the nearer end is typed in, it is checked against the same 0.5·Rm limit as on a cylinder, which is a much shorter distance than the junction's bending zone. In the illustration 2.5·√(Rm·T) is about 235 mm from the edge of the nozzle or its pad.

The shell model meshes the cone itself, so the changing radius and the inclined meridian are in the geometry, not approximated. The cone is given by its two end diameters, axial length and thickness. A half-apex angle above 75° is refused as too flat for a cone, and a cone that closes to an apex is not supported.

• Nozzles on the cone body: radial, offset, tilted and tangential, and up to four attachments together, refused when too close.
• A nozzle on the small end, coaxial with the cone, meshed into the cone's end row.
• Clips and other structural attachments on the cone.
• The large end is the support: held along the meridian and round the circumference, its rotation left free, because a cone's meridian rotates under pressure. The small end is free and closed, and carries the closing thrust.

The model is the cone alone. The cylinder or head beyond each end is not meshed; its place is taken by the end condition. For a nozzle near a junction that matters, and the result should be read with it in mind.