DETERMINATION OF LEAKAGE GAP AND LEAKAGE MASS FLOW OF FLANGE JOINTS SUBJECTED TO EXTERNAL BENDING MOMENTS Robert Kauer Klaus Strohmeier1 Institute for Apparatus Engineering and Plant Design Technical University of Munich Germany
Leakage analyses have to be done for safety relevant parts of a plant and its components, like flange joints, which are, in a great number, part of every piping system.
Within the authorisation procedure, the operator of a plant is obligated to execute safety analyses. For this purpose, conceivable accidents and resulting damage scenarios have to be discussed. The intention of this regulation is to prevent danger from man and environment, on the one hand by excluding possible errors during design, on the other hand by minimizing the consequences of malfunctions after putting the plant into operation. For this, it is necessary in view of all possible sources of danger, those conditions are defined which might lead to a damage. This includes the existence of physical founded relations for estimating the hazardousness of plants and their components. The results related to the expected releases are used for the evaluation of safety precautions, which should be available in case of emergency.
A non-linear, 3-D, 1800 Finite Element Model, including elastic-plastic material behaviour and contact condition between gasket and flange, is developed to describe the gap caused by external moments. Based on this gap the mass flow through this leakage sectional area can be calculated. Results are compared with experimental data, to verify the Finite Element Model. This is done by measurement of gasket stress, flange deformation and bolt loads. The calculated release rates are checked with those one, measured on a real flange under various loadings .
NOMENCLATURE FB FP FV M MBY MB P u v V
total bolt forces axial force due to internal pressure referred prestress referred bending moment yield moment bending moment internal pressure gap witdh referred volume flow release rate
[N] [N] [-] [-] [Nm] [Nm] [MPa] [µm] [cm3/s/mm] [cm3/s]
Prof. Dr.-Ing. K. Strohmeier, Dipl.-Ing. R. Kauer, Lehrstuhl für Apparate- und Anlagenbau, Techn. Universität München
It is obvious how important the knowledge of leakage sectional areas and release rates is. But until now it is common in chemical engineering to assume fictitious, overly conservative leakages. Safety precautions determined by such assumptions are neither economic nor technically reasonable, because the magnitude of the sectional area not only has influence on the mass flow but also on the state of the releasing medium and therefore on the kind precaution systems which should be installed and on the safety measures which should taken. So it is decisive to know leakage sectional areas of various plant components under different loadings (Strohmeier, 1993). As a soluble junction, flange joints are, in a great number, parts of each plant. Therefore the static free behaviour of these standard elements is of central importance for the functioning of complete branches. Along with the stress analysis, a chief task of flange design is to assure durable tightness under different loading conditions. In spite of various efforts, the design of flange joints is full of
Finite Element investigations, for the most part, concentrate on the stresses of the flange and bolts (Ghonheim and Haverty, 1990) or they are axisymmetric or reduced to minimum of symmetry (Zahavi, 1993) and therefore no moment caused pressure distribution can be calculated.
THE FINITE ELEMENT MODEL Figure 1: Parameters for tightness of flange joints
uncertainty as can be seen by numerous damages. Cases of loss very seldom lead to a mechanical breakdown of the flange, but rather to leakages which cause further defects.
The Finite Element Modelling of real influence of external loads, like bending moments, requires a minimum symmetry of 180 degree, if a full pressure distribution on the gasket shall be calculated. Nevertheless many influence parameters on the quality of the Finite Element Model can also be tested on an axisymmetric model.
A great number of accidents with often disastrous results can be traced back to the leakage of a flange. In Plötner (1978) 20% of every malfunction in chemical plants is caused by these leaks. Numerous problems have been reported in Bockholts and Plötner (1992) and Payne (1985) for DIN as well as for ANSI flanges. Decisive for the tightness of the junction is the pressure distribution on the sealing under each possible loading condition. This is only possible, if the interaction between every component of the flange joint is taken into account. Figure 1 shows these main influence parameters.
Figure 2: Compression Curve for a PTFE Gasket
For the appearance of leakages non-rotationalsymmetric loadings are significant. They can be caused by external forces and moments or failure of bolts. So, the consequence is a sickle-shaped loss of gasket pressure which allows the medium to escape through this gap. Except for the ASME Code, Section III, NB, NC and ND other pressure vessel and piping codes do not contain design rules for flange joints under bending moments. In this subsections only an empirical formula is given, which converts the longitudinal bending moment in an equivalent internal pressure to be added to the design pressure of the flange. Due to the difficult correlations between the flange components and the different kind of loadings, experimental and numerical work gained increasing influence for getting new knowledge. Through tests, made in connection with the determination of suitable gasket testing procedures, it is known that bending moments show considerable influence on the measured leak rate (Schwind and Micheely, 1980). However, used test rigs only allow the measurement of leak rates caused by porosity of gasket material. In Kämpkes and Schwind (1985) the influence of non rotational symmetric gasket pressure due to failure of singular bolts is examined. A increasing leak rate was also measured.
Figure 3: Comparison of measurement and axisymmetric FE-Model
Figure 4: DIN 2634 DN80 flange and gasket deformation due to combined loading
The Axisymmetric Finite-ElementModel A main question which can be discussed within the axisymmetric Finite Element Model is the material and contact behaviour of the gasket. Figure 2 shows the very nonlinear stress strain relation of a typical sealing material under compression. To realize such behaviour inside the numerical model, many calculations were necessary to get the best fit with regard to the present case combined with a tolerable use of CPU time. Also the simulation of the prestress condition can be varified. Figure 3 demonstrates the satisfactory coincidence between the Finite Element calculation and the measurement on a real flange after bolt make up.
The three dimensional 180 degree Model With those basic experiences the three dimensional 180 degree section can be designed. For this purpose a Fortran program allows the user to create various flange and gasket geometries within reasonable time.
-1.1% -1.2% -1.2% -1.1% -1.2%
Pi and MB +14.6% +7.5% -4.2% -8.0% -9.0% Table 1: Change of bolt force relative to prestress
8 noded solid elements were used for gasket, flange and bolts. This requires a total number of about 40000 degrees of freedom.
Figure 5: Gasket stress distribution due to combined loading
Contact condition between gasket and flange enables the sealing surfaces to form a real gap. The nonlinear gasket behaviour shown in Fig. 2 just as the hardening material of flange and bolts determined by tensile tests is integrated. The loading includes bolt make up, internal pressure, external forces and moments and each combination. Figure 4 shows a DIN2634 DN80 flange subjected to prestress, pressure and longitudinal bending moment. Table 1 clarifies the nonlinear stress distribution by means of change of boltforce. The deformation of the flange reveals the gap on the tension side of the moment. It can also be seen that the radial deformation on this side is nearly twize than on the pressure side. This can be explained with the loss of friction force due to the loss of axial pressure on the gasket. In Fig. 5, the distribution of the normal displacement of the sealing is depicted as well as the deformed shape on the tension side and on the compression side of the gasket. This plot also illustrates the sickle shaped area where the axial pressure decreases to zero.
THE TESTING INSTALLATION Volume Flow Determination For getting relations between mass flow and a given leakage gap, a testing procedure was found which simulates the conditions on a real flange, like geometric properties. The pressure is applied by a hydropuls system, which is able to hold constant pressure up to 10 MPa. The releasible volume amounts to 20 dm3. The gap width is measured with displacement pickups. The roughness of the sealing surfaces can be varified between technical smooth and flange specific grooved. Therefore it is possible to get typical release rates for different gaskets and sealing surfaces. Figure shows the measured data for the sealing conditions on a DIN 2634 DN80 flange depending on various internal pressures.
Release Rates The results from these tests can be transferred to real flanges, if the release area is known. To confirmate the results from
The results show suitable agreement with the Finite Element Model. Figure 7 depicts the calculated and measured release rates for a DIN 2634 DN80 flange with a 3 mm PTFE gasket under different bolt make ups and bending moments. These expressions are made dimensionless by using the following relations:
FB FV =
FP Figure 6: Release rates for a grooved DIN 2634 DN80 sealing surface
the Finite Element Analyses and from the mass flow determination a real flange is subjected to an external moment. The obtained experimental data can be used to verify the three dimensional Finite Element Model as well as the calculated release rates. For this purpose, the following quantities were obtained by measurement: • • • • • • •
gasket pressure distribution release rate bolt load flange strain flange deformation internal pressure bending moment
where FP corresponds to the axial force due to internal pressure and MBY is the moment where yield stress occurs in an undisturbed pipe.
CONCLUSION On a DIN 2634 DN80 flange with a 3 mm PTFE gasket, release rates through gaps caused by external loadings are calculated using the Finite Element Method. For this purpose, relations between mass flow and leakage gap are determined for flange specific conditions. Measured data produced on a real flange shows satisfactory agreement between experimental and calculated values.
Figure 7: Release rates for a DIN 2634 DN80 flange under bending moment
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