Hillside and tangential nozzles: what WRC 537 covers

Cut a round tube through a flat surface at an angle θ from the normal and the hole is an ellipse. Its short axis is the tube diameter d whatever the angle; its long axis is d/cos θ. The usual conservative practice for a non-radial nozzle is to take the short axis, the shortest chord, as the size of an equivalent round attachment. That is the same size as the radial nozzle, so the calculator uses the same r₀ and the same β, and the curve coefficients do not change.

This rests on the flat-tangent-plane picture that the bulletin's shallow-shell theory uses throughout. It holds well for a small offset and grows less reliable as the angle grows. No safe tilt limit has been sourced, so the calculator states the assumption in the report and does not invent one.

Where a hillside nozzle differs is the pressure stress at its edge. The opening cut in the shell is longer round the circumference than the nozzle is wide, so pressure acts on a larger area. The calculator works the pressure stress intensity factor I of ASME Section VIII Division 2 with that longer cut.

• On a cylinder, the nozzle is entered with its offset from the shell axis. The radius used in the pressure force is half the arc length of the opening in the circumferential plane, never less than the nozzle radius (4.5.6).
• On a formed head, the nozzle is entered as hillside (axis parallel to the vessel axis, away from the pole) or perpendicular (axis square to the vessel axis). The radius used is Rₙ/cos θ or Rₙ/sin θ (4.5.11).
• A head nozzle marked tilted without saying which gets the radial factor, with a note: a non-radial head nozzle can have a factor up to about a third higher.

Three cases are refused with a message that names the shell model. A nozzle inclined at a free angle in a shell or head. An offset or tilted nozzle on a cone, where only a radial nozzle or one along the cone's own axis is taken. And a tangential nozzle, whose axis runs along the shell's surface rather than into it.

The tangential case shows plainly why. As the angle from the normal approaches 90°, the long axis d/cos θ grows without limit. The model's own geometry has stopped describing the junction: the nozzle no longer pierces a nearly flat patch of shell, it runs along a curved one. That is a sign the shallow-shell assumption has failed, not a real result.

The shell model builds the nozzle along its real axis and meshes the real intersection curve with the shell. The orientations it takes are radial, offset (hillside), tangential, angled, tilted in any direction, and on heads parallel or perpendicular to the vessel axis.

A tangential nozzle is placed so its outside wall lines up with the shell's inside surface, on either side. It must be round, and its outside radius must be smaller than the shell's inside radius. The optional solid detail at the junction does not take tangential nozzles or tilts over 50°.