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PROCESS EQUIPMENT DESIGN - I CL 206 Course Instructor : Dr. Tapas K MandalDesign 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)
IntroductionPressure vessels are used in many industries (e.g., hydrocarbonprocessing, chemical, power, pharmaceutical, food and beverage). Themechanical design of most pressure vessels is done in accordance withthe requirements contained in the ASME(founded as the AmericanSociety 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 acommon rotational axis. Most pressure vessel shells are eithercylindrical, 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 bethinner, lighter, and less expensive than flat heads. Heads can also beused inside a vessel. These “intermediate heads” separate sections ofthe pressure vessel to permit different design conditions in each section.3. Nozzle : A nozzle is a cylindrical component that penetrates the shell orheads of a pressure vessel. The nozzle ends are usually flanged to allowfor the necessary connections and to permit easy disassembly formaintenance 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 andorientation of the pressure vessel. In all cases, the pressure vessel supportmust be adequate for the applied weight, wind, and earthquake loads. Thedesign pressure of the vessel is not a consideration in the design of thesupport since the support is not pressurized. Temperature may be aconsideration in support design from the standpoint of material selectionand provision for differential thermal expansion.
Design Of Heads And ClosuresThe ends of cylindrical vessel are to be closed before putting intooperation. This is done by means of heads and closures, which are ofdifferent 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 coverwill be too bulky, otherwise, it will tend to collapse. From fabricationpoint of view this is the simplest type head to construct just cutting acircular piece from a flat plate. As a result, for a particular diameter andoperating conditions, materials cost for flat head is maximum, thoughfabrication cost is very low.
(b) Flanged Shallow Dished and Flanged Standard Dished (Tori spherical) Heads : While pressing into dished shape, such headsconsist 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 arevery high and do not serve the code requirement.
(c) Elliptical dished Heads : Elliptical Dished Heads are formed on dies inwhich the diametrical cross-section is an ellipse. Most of the standardelliptical dished heads are manufactured on 2:1 ratio of major tominor axis.• These type of heads are generally recommended in the pressurerange of 0.7 MN/m2 and preferably for the vessels designed tooperate above 1.5 MN/m2.• The strength of such heads is approximately equal to strength ofseamless cylindrical shell having corresponding inside and outsidediameters.
(d) Hemispherical Heads : A hemisphere is the ideal shape for a head, because thepressure in the vessel is divided equally across the surface of thehead.• Small hemispherical heads are made by spinning, but large headsare fabricated by welding pressed plate sections in the shape of acrown and petals, or by forging.• These heads can be used to resist approximately twice the pressurerating of an elliptical head or cylindrical shell of same thickness anddiameter.
(e) Conical Heads and Reducers : Conical heads are used as bottom for avariety of process equipment like evaporators, spray driers,crystallizers, settling tanks, silos etc.• The particular advantage lies in the accumulation and removal ofsolids from such equipment.• Another common application of conical head is a reducer,providing a smooth transition between two parts of different diameterin cylindrical process vessel.
Stress Analysis And Design Of heads1) Flat Cover Head : The stress analysis flat cover head is made on thebasis of bending of uniformly loaded circular plates of constantthickness.CASE- I : when edges of plates are assumed to be clamped preventingit from rotating only and not otherwise restrained, i.e. there is no strainin 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, thuseliminating the edge bending moment.
General Deflection EquationFor Uniformly loaded circular plate, general deflection equation isgiven 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 platet = thickness of the plate,µ = Poisson‟s ratio,C1,C2,C3 = Constants of integration,Constants of integration are determined in each particular case ofloading by the edge conditions of the plate.
For Case-I: When edges of circular plates are clamped, the equationof 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 bypressure and Mr acts along cylindrical sections and Mθ alongdiametrical 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 thecentre are obtained as follows: (8)eq. 6,7,&8 shows that expression for maximum moment is given byeq. 6. This indicates that the maximum stress is at the edge of theplate and equals to: (9)
For Case- II : When the edges of a uniformly loaded cylinder plateis 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 ̔σmax‟ is substituted by allowable stress „f‟ of thematerial and „R‟ is replaced by D0/2, where D0 is the effectivediameter of the flat head, a general expression for calculating thethickness 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 headthickness.• 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 onthe inside. D0 = Di ; C = 0.55.
5. Covers riveted or bolted to the end of shell with an additional filletweld on the inside. D0 = Bolt-circle diameter; C = 0.42.6. Covers with narrow face bolted flange joint, i.e., gasket is placedwithin bolt holds. D0 = mean diameter of gasket ;Where, FB is the bolt loadand hG = ½(bolt circle diameter - D0)
2) Conical Head : Geometry of cone may be compared with that of acylinder 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 samereference point R = r / cosα Thickness of the cone is: (16)Where : Dk is inside diameter of cone at the position under consideration.
• From the consideration of stress analysis, a cone is divided into tworegions:(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 isgiven 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 aconical head to eliminate moment and shear at the junction. A factorZ is taking into account the influence of this discontinuity stresses istherefore introduced into the basic thin-shell equation to determinethe thickness of the cone at the junction or knuckle, For a cone, Z depends upon apex angle and knuckle radius, Z valuesfor a sharp cone (without knuckle radius) are given below: α = 20̊ 30̊ 45̊ 60̊ Z= 1.00 1.35 2.05 3.2
• Equations for surface area and volumetric capacity of a conicalhead are given by: