CAESAR II provides a tool which simplifies this analysis, a flange analysis module — accessible from the WRC 297, SIFS, FLANGES submenu — which allows the user to evaluate leakage of flanges under load — a more realistic analysis process than performing an equivalent pressure analysis. The flange analysis module also automates the ASME B&PVC Section VIII, Division I flange stress calculations.
The CAESAR II flange leakage model assumes that the user has already selected the gasket, has a flange design, and has analyzed the piping flexibility to compute the forces and moments exerted by the piping on the flange (possibly including the effects due to fit-up tolerance, which can be done using restraints with CNODES and imposed forces or displacements).
The ASME codes eliminate some of the decisions involving leakage by the publication of the gasket "m" factor. The "m" factor is the leak pressure ratio — the ratio of the pressure on the gasket required to prevent leakage, to the line pressure, times a factor of safety. These values are currently the subject of close scrutiny by many organizations, but the existing values have been use with a reasonably successful design history. It is with the "m" factor that the CAESAR II flange leakage calculation starts and upon which it depends. It is recommended that the user aim for an "m" factor greater than 1.0. This should provide a safety factor greater than 2.0, and is consistent with other safety factors used in pipe stress analysis. If the flange analysis module predicts an "m" factor less than 1.0, then the loads on the flange should probably be reduced.
The flange modeler determines the initial pressure on the gasket due to the tightening of the bolts, and the loss of pressure on the gasket due to the line pressure and the forces and moments acting on the flange. If the resulting pressure on the gasket (i.e., the initial minus all losses) exceeds the gasket factor "m" times the line pressure, then the flange is considered to be "safe".
There are a great many different types of flanges, facings, an gaskets. For the purpose of the flange modeler, all of these were generalized into a single model for leakage. Once this was done, the critical variables affecting leakage were retained in the analytical model, and the unnecessary variables were eliminated. It was determined that the deformation of the annular plate forming the flange, in conjunction with the deformation of the bolts and gasket, when subjected to bending, pressure, and axial forces were the critical variables to be evaluated.
Various simplified elastic models were tested and a final model agreed upon that most closely correlated the results from finite element analyses of several typical flange configurations subject to bending and axial loads. Loads on the gasket were predicted within 15% for standardly dimensioned flanges, and other calculated values were within similar tolerances. The modeler also confirmed leakage of numerous flanges in actual plant applications as well.
The basic flange deformation modes assumed to contribute most significantly to the unloading of the gasket are shown in Figure 3-122.
The limitations of the model are that:
The gasket reaction and stiffness are concentrated at a point load at the center of the gasket loading area.
The bolt reaction and stiffness are concentrated at a single point and is assumed to be uniformly distributed around the annular plate which models the flange.
The pipe/hub interface is assumed to be flexible enough to allow rotation at the flange inner diameter at the point around the circumference where the bending moments produce a maximum stress in the pipe, so that the absolute rotation at the flange inner diameter is zero.
The gasket is assumed to be fairly stiff, so that the flange rotational stiffness is of the same order of magnitude as the gasket stiffness.
These analytical limitations imply other more practical "usage" limits:
Full face gaskets cannot be modeled.
Leakage at self-energizing gaskets cannot be predicted.
Leakage for flanges with ring-type joints cannot be predicted.
Shear load effects on leakage are ignored.
The effect of the hub and pipe wall are not variable, and so are considered only approximately.
Leakage analysis for joints made up of flexible gaskets should not be attempted, since the effect of very flexible gaskets on leakage tends to be a function of factors other than the flexibility of the annular flange plate and bolts.
Complete instructions for the operation of the flange leakage analysis module are provided in the CAESAR II User's Manual. A brief description if given here. The data screen for the module is broken into two sections. The first section contains the input required for the leakage calculations, while the second section contains the additional input required for making the ASME Section VIII, Division 1 stress calculations. The flange leakage module permits (much of the data is optional) entry of the following information:
Flange dimensions:
FLANGE INSIDE DIAMETER FLANGE THICKNESS
Dimensional data for standard flanges (along with their bolts and gaskets) can be accessed from a built in database in the program.
Bolt data:
BOLT CIRCLE DIAMETER NUMBER OF BOLTS BOLT DIAMETER BOLT INITIAL TIGHTENING STRESS
The bolt initial tightening stress can be estimated as:
S = 12 x T / (K d)
Where:
S = preload stress, psi T = bolt torque, ft-lb K = nut factor (as per the Standard Handbook of Machine Design, Figure 3-123) d = nominal diameter of bolt, in
If not entered, the program defaults to a bolt prestress of 45000/d^1/2 psi, a typical rule of thumb applied when field tightening bolts.
Gasket data:
EFFECTIVE GASKET DIAMETER UNCOMPRESSED GASKET DIAMETER UNCOMPRESSED GASKET THICKNESS EFFECTIVE GASKET WIDTH EFFECTIVE GASKET MODULUS LEAK PRESSURE RATIO
Typical values for the effective gasket modulus are between 300,000 and 400,000 psi for spiral wound gaskets. The greater the modulus, the greater the tendency for the flange to leak. Therefore errors on the high side will tend to be more conservative.
The leak pressure ratio is the "m" factor discussed above; the required value for each type of gasket is given in Table 2-5.1 of the ASME Section VIII, Division 1 code. It is also accessible with the program HELP facility.
Load data:
EXTERNALLY APPLIED MOMENT EXTERNALLY APPLIED FORCE PRESSURE
For the optional ASME Section VTII, Division 1 stress calculations, the following additional data is requested:
Flange dimensions:
FLANGE TYPE FLANGE OUTSIDE DIAMETER SMALL END HUB THICKNESS LARGE END HUB THICKNESS HUB LENGTH
As above, dimensional data for standard flanges can be accessed from a built in database in the program. Any of eight standard flange types recognized by Section VIII can be selected from a graphic representation.
Operating and loading data:
DESIGN TEMPERATURE GASKET SEATING STRESS
Permissible gasket seating stresses are provided in the program HELP facility.
Material allowables:
FLANGE STRESS ALLOWABLES BOLT STRESS ALLOWABLES STRESS ALLOWABLE MULTIPLIERS
Allowable stresses for both flanges and bolts may be accessed from the program material database. Certain codes permit increases in the stress allowables in certain circumstances. The program HELP facility identifies those codes and the corresponding multipliers which may be used. The program provides output in terms of Safety Factors — values of less than one usually indicate trouble. Sample input and output screens are shown in Figures 3-124 and 3-125 respectively.
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