Ellipsoidal heads pressure

Cone-bottom vertical vessels are sometimes used where solids are anticipated to be a problem. Most cones have either a 90 apex (a = 45 ) or a 60 apex ia = 30 ). These are referred to respectively as a 45 or 60 cone because of the angle each makes with the horizontal. Equation 12-4 is for the thickness of a conical head that contains pressure. Some operators use internal cones within vertical vessels with standard ellipsoidal heads as shown in Figure 12-2. The ellipsoidal heads contain the pressure, and thus the internal cone can be made of very thin steel. 

Standard torispherical heads (dished ends) are the most commonly used end closure for vessels up to operating pressures of 15 bar. They can be used for higher pressures, but above 10 bar their cost should be compared with that of an equivalent ellipsoidal head. Above 15 bar an ellipsoidal head will usually prove to be the most economical closure to use. 

All test accumulators (pressure vessels) were mounted direcdy below the test table. These vessels were mounted vertically with 2 1 ellipsoidal heads on top and bottom. The top head has a well-rounded outlet nozzle sized equal to the SRV inlet to be tested. To test smaller-orifice SRVs, ring-shaped adapter plates having an opening equal to the SRV inlet are used. This arrangement reduces the possibility of starving the flow to the valve. 

Select a vessel head. If the internal pressure is 150 psig (10.3 barg) or less, select a torispherical head. If the internal pressure is above 150 psig (10.3 barg), select a 2 1 ellipsoidal head. 

The ASME design formula from UG-32 for ellipsoidal heads having a major-to-minor axis ratio of 2 1 and being subjected to pressure on the concave side is t = PD/ 2SE — 0.2P), where t is the minimum thickness of the head (in.), P is the MAWP (psi), D is the internal diameter of the major diameter of the ellipsoid (in.) (and equal to the inside diameter of the vessel), S is the allowable stress of the material, as listed in ASME Section II, and E is the weld joint efficiency. ... 

Figure 3.16 is a cutaway view of this reactor. The reactor vessel is a cylinder 13 ft in diameter with an ellipsoidal bottom. The top of the vessel is closed with a flanged and bolted ellipsoidal head, which is removed for refueling. When in operation the reactor is filled with water at a pressure of 155 bar (15.5 MPa). The water enters the inlet nozzle at the left at a temperature of 282 C and leaves the outlet nozzle at the right at 317 C. The effective average temperature of the water is 301.6 C, which will be taken as the temperature of the Maxwell-Boltzmann component of the neutron flux. 

The ellipsoidal dished head with a major to minor axis ratio of 2 1 is popular for economic reasons, even though the theory for thin-walled vessels predicts that the head of this shape should have twice the thickness of a hemispherical head where the major and minor axes are equal. Such an ellipsoidal head used for vessels under internal pressure has the same thickness as the cylindrical shell if the same allowable stresses and joint efficiencies are applied to both parts. The 1962 ASME Code Section VIII, Division 1 gives the following equation for the thin-walled ellipsoidal dished heads with a 2 1 major to minor axis ratio ... 

This is why most high pressure vessels do not use typical pressure vessel heads such as hemispherical or semi ellipsoidal. These heads are impractical in high pressure applications. So the economics and mechanical limits of the materials will determine the ultimate shape of the vessel. 

Cover gas in the SG expansion cap mitigates the pressure transients during large sodium-water-reaction (SWR) events. The SWRPRS is connected to the exit nozzle at the center of the lower ellipsoidal head. 

Eor an internal pressure P, the thickness t of the ellipsoidal head is given by... 

A 12-in.-insidfs-diameter pressure vessel is fabricated of an iiiiu r. shell of copp r 1 in. thick and an outer shell of steel in. thick in such a manmir that the inUd fact f res.sure is /xtro and the two shells are in contact with each other. The reactor is 4 ft long from tangent litu to tangent line with ellipsoidal heads (also of double layer). 

Example 8.2. A seamless cylindrical shell with an outside diameter of 30.0 in. is butt-welded to seamless ellipsoidal heads. The circumferential seams are not x-rayed. Find the required shell thickness if the allowable stress is 15,(XM) psi and the internal design pressure is 250 psi. Use Section Xni, Division 1 rules. 

Example 11.6. Determine the reinforcement requirements of an 8 in. ID nozzle that is centrally located in a 2 1 ellipsoidal head. The inside diameter of the head skirt is 41.75 in. The allowable stress of both the head and nozzle material is 17.5 ksi. The design pressure is 700 psi and the design temperature is 500 F. There is no corrosion and the weld joint efficiency is = 1.0. See Fig. 11.13.1 for details of a nozzle. 

As the size or the pressure goes up, curvature on all surfaces becomes necessary. Tariks in this category, up to and including a pressure of 103.4 kPa (15 Ibf/in"), can be built according to API Standard 620. Shapes used are spheres, ellipsoids, toroidal structures, and circular cylinders with torispherical, elhpsoidal, or hemispherical heads. The ASME Pressure Vessel Code (Sec. TII of the ASME Boiler and Pressure Vessel Code), although not required below 103.4 kPa (15 Ibf/in"), is also useful for designing such tanks. 

Internal-pressure design rules and formulas are given for cylindrical and spherical shells and for ellipsoidal, torispherical (often called ASME heads), hemispherical, and conical heads. The formulas given assume membrane-stress failure, although the rules for heads include consideration for buckling failure in the transition area from cylinder to head (knuckle area). 

External-pressure failure of shells can result from overstress at one extreme or n om elastic instability at the other or at some intermediate loading. The code provides the solution for most shells by using a number of charts. One chart is used for cylinders where the shell diameter-to-thickness ratio and the length-to-diameter ratio are the variables. The rest of the charts depic t curves relating the geometry of cyhnders and spheres to allowable stress by cui ves which are determined from the modulus of elasticity, tangent modulus, and yield strength at temperatures for various materials or classes of materials. The text of this subsection explains how the allowable stress is determined from the charts for cylinders, spheres, and hemispherical, ellipsoidal, torispherical, and conical heads. 

Although spherical vessels have a limited process application, the majority of pressure vessels are made with cylindrical shells. The heads may be flat if they are suitably buttressed, but preferably they are some curved shape. The more common types of heads are illustrated on Figure 18.16. Formulas for wall thicknesses are in Table 18.3. Other data relating to heads and shells are collected in Table 18.5. Included are the full volume V0 and surface S as well as the volume fraction V/V0 corresponding to a fractional depth H/D in a horizontal vessel. Figure 18.17 graphs this last relationship. For ellipsoidal and dished heads the formulas for V/V0 are not exact but are within 2% over the whole range. 

Figure 18.17. Types of heads for cylindrical pressure vessels, (a) Flat flanged KR = knuckle radius, SF= straight flange, (b) Torispherical (dished), (c) Ellipsoidal, (d) Spherical, (c) Conical, without knuckle, (f) Conical, with knuckle, (g) Nonstandard, one of many possible types in use.

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