PROCESS EQUIPMENT DESIGN - ICL 206

Course Instructor : Dr. Tapas K Mandal

Design Of Vessel’s Head And Closures (Flat And Conical)

By: Ajay Tyouharia - 10010704 Abhishek Gupta - 10010703 Abhishek Anand - 10010702 Aakanksha - 10010701

Contents :

• Introduction

• Pressure Vessel Components

• Heads And Closures

• Stress Analysis And design Of Heads ( Flat

and Conical Heads only)

Introduction

Pressure vessels are used in many industries (e.g., hydrocarbon

processing, chemical, power, pharmaceutical, food and beverage). The

mechanical design of most pressure vessels is done in accordance with

the requirements contained in the ASME(founded as the American

Society For Mechanical Engineers) Boiler and Pressure Vessel Code,

Section VIII.

Main Pressure Vessel Components

• Pressure vessels are containers for fluids that are under pressure. They are

used in a wide variety of industries (e.g., petroleum refining, chemical,

power, pulp and paper, food, etc.) . The main components of pressure vessel

are:

1. Shell :

The shell is the primary component that contains the pressure.

Pressure vessel shells are welded together to form a structure that has a common

rotational axis. Most pressure vessel shells are either cylindrical, spherical, or

conical in shape.

2. Head :

All pressure vessel shells must be closed at the ends by heads (or another shell section). Heads are typically curved rather than flat.

Curved configurations are stronger and allow the heads to be thinner, lighter, and less expensive than flat heads. Heads can also be used inside a vessel. These “intermediate heads” separate sections of the pressure vessel to permit different design conditions in each section.

3. Nozzle :

A nozzle is a cylindrical component that penetrates the shell or heads of a pressure vessel. The nozzle ends are usually flanged to allow for the necessary connections and to permit easy disassembly for maintenance or access. Nozzles are used for the following applications:

· Attach piping for flow into or out of the vessel.

· Attach instrument connections, (e.g., level gauges, thermowells,

or pressure gauges).

· Provide access to the vessel interior at man ways.

· Provide for direct attachment of other equipment items, (e.g., a heat

exchanger or mixer).

4. Support :

The type of support that is used, depends primarily on the size and

orientation of the pressure vessel. In all cases, the pressure vessel support must be adequate for the applied weight, wind, and earthquake loads. The design pressure of the vessel is not a consideration in the design of the support since the support is not pressurized. Temperature may be a consideration in support design from the standpoint of material selection and provision for differential thermal expansion.

Vertical Drum

Design Of Heads And Closures

The ends of cylindrical vessel are to be closed before putting into operation. This is done by means of heads and closures, which are of different shapes.

The vessels are usually provided with the following types of heads:

(a) Flat Head :

For larger vessels or at higher pressure, the flat head cover will be too bulky, otherwise, it will tend to collapse. From fabrication point of view this is the simplest type head to construct just cutting a circular piece from a flat plate. As a result, for a particular diameter and operating conditions, materials cost for flat head is maximum, though fabrication cost is very low.

Flanged only/ Flat Head Design

FLAT HEAD PRESSURE VESSEL

(b) Flanged Shallow Dished and Flanged Standard Dished (Tori

spherical) Heads :

While pressing into dished shape, such heads consist of two radii, namely ‘crown’ radius and ‘knuckle’ radius.

• Flanged shallow dished: Crown radius > Shell outer diameter

• Flanged Standard dished: Crown radius ≤ Shell outer diameter

• Due to small Knuckle(small inside-corner) radius localised stresses are very high and do not serve the code requirement.

Flanged Shallow Dished Head

Flanged Standard Dished Head

Making Of Torispherical Head

(c) Elliptical dished Heads :

Elliptical Dished Heads are formed on dies in

which the diametrical cross-section is an ellipse. Most of the

standard elliptical dished heads are manufactured on 2:1 ratio of

major to minor axis.

• These type of heads are generally recommended in the pressure

range of 0.7 MN/m2 and preferably for the vessels designed to

operate above 1.5 MN/m2.

• The strength of such heads is approximately equal to strength of

seamless cylindrical shell having corresponding inside and outside

diameters.

Elliptical Dished Head

Elliptical Dished Head

(d) Hemispherical Heads :

A hemisphere is the ideal shape for a head, because the

pressure in the vessel is divided equally across the surface of the

head.

• Small hemispherical heads are made by spinning, but large heads

are fabricated by welding pressed plate sections in the shape of a

crown and petals, or by forging.

• These heads can be used to resist approximately twice the pressure

rating of an elliptical head or cylindrical shell of same thickness and

diameter.

Hemispherical Head

Making Of A Large Hemispherical Head

(e) Conical Heads and Reducers :

Conical heads are used as bottom for a

variety of process equipment like evaporators, spray driers,

crystallizers, settling tanks, silos etc.

• The particular advantage lies in the accumulation and removal of

solids from such equipment.

• Another common application of conical head is a reducer,

providing a smooth transition between two parts of different diameter

in cylindrical process vessel.

Conical Head

Making Of A Conical Head

Stress Analysis And Design Of heads

1) Flat Cover Head :

The stress analysis flat cover head is made on the basis of bending of uniformly loaded circular plates of constant thickness.

CASE- I : when edges of plates are assumed to be clamped preventing it from rotating only and not otherwise restrained, i.e. there is no strain in the neutral plane of the plate.

• In this case there are negative end bending moments.

CASE-II : When edges are consider to be freely supported, thus eliminating the edge bending moment.

General Deflection Equation For Uniformly loaded circular plate, general deflection equation is given by:

(1)

In the above equation:

p = load intensity (say pressure)

x = Distance of any part of plate under consideration from centre,

D = flexural rigidity of plate

t = thickness of the plate,

µ = Poisson’s ratio,

C1,C2,C3 = Constants of integration,

Constants of integration are determined in each particular case of loading by the edge conditions of the plate.

For Case-I: When edges of circular plates are clamped, the equation of deflection is:

( 2)

Where : R= radius of the plate at the point of support.

• Maximum deflection is at the centre of plate (x = 0) equal to

(3)

• If Mr and Mθ are bending moment per unit length caused by pressure and Mr acts along cylindrical sections and Mθ along diametrical sections of plate, then,

(4)

(5)

Moments at the edge of the plate is obtained by substituting x = R,

(6)

(7)

Similarly, by substituting x = 0 in eq. 4 & 5 , the moments at the centre are obtained as follows:

(8)

eq. 6,7,&8 shows that expression for maximum moment is given by eq. 6. This indicates that the maximum stress is at the edge of the plate and equals to:

(9)

For Case- II : When the edges of a uniformly loaded cylinder plate is simple supported the deflection equation becomes:

(10)

At x = 0, maximum deflection at the centre becomes,

(11)

Bending moment equations are:

(12)

(13)

The maximum bending occurs at the centre where,

(14)

And corresponding maximum stress is:

(15)

In Eqs. 9 & 15, if Iσmax’ is substituted by allowable stress ‘f’ of the material and ‘R’ is replaced by D0/2, where D0 is the effective diameter of the flat head, a general expression for calculating the thickness of flat heads and covers obtained:

(16)

Where, C: factor depending upon the method of attachment to shell.

Eq. 16 is given in IS : 2825-1969 for calculating the flat head thickness.

• Following are the few case where C values are indicated (IS: 2825-1969).

1. Flanged flat heads butt welded to shell. D0 = Di ; C = 0.45.

2. Plates welded to inside of the shell , D0 = Di ; C ≥ .55

3. Plates welded to the end of the shell (no inside welding).

D0 = Di ; C = 0.7.

4. Plates welded to the end of the shell with and additional fillet on the inside. D0 = Di ; C = 0.55.

5. Covers riveted or bolted to the end of shell with an additional fillet weld on the inside. D0 = Bolt-circle diameter; C = 0.42.

6. Covers with narrow face bolted flange joint, i.e., gasket is placed within bolt holds. D0 = mean diameter of gasket ;

Where, FB is the bolt load

and hG = ½(bolt circle diameter - D0)

2) Conical Head : Geometry of cone may be compared with that of a cylinder in which diameter is continuously changing.

R: radius of curvature of the element

in the hoop direction ( i. e.

perpendicular to meridian)

r: radius of cone at the same reference point

R = r / cosα

Thickness of the cone is:

(16)

Where : Dk is inside diameter of cone at the position under

consideration.

Stresses in a Conical Head

• From the consideration of stress analysis, a cone is divided into two regions:

(a) Region around knuckle or junction not exceeding a distance,

(De t/cosα)1/2 , from the junction or knuckle, where De is the

outer diameter of conical section or end.

(b) Region away from knuckle or junction.

• The inward compressive force produced by the conical head is given by,

Where: P is axial tension in the shell per unit shell circumference.

• If T is axial tension in the cone due to internal pressure, at

equilibrium,

P = T cos α, and C = T sin α = P tan α = (pD/4) tan α.

As a result of this compressive force, it is impossible to design a conical head to eliminate moment and shear at the junction. A factor Z is taking into account the influence of this discontinuity stresses is therefore introduced into the basic thin-shell equation to determine the thickness of the cone at the junction or knuckle,

For a cone, Z depends upon apex angle and knuckle radius, Z values for a sharp cone (without knuckle radius) are given below:

α = 20> 30> 45> 60>

Z= 1.00 1.35 2.05 3.2

• Equations for surface area and volumetric capacity of a conical head are given by:

AJay