Introduction

Large diameter seals are used for sealing the annulus in the rotatable plugs of PFBR, which is under commissioning in India. Figure 1a and b shows the schematic arrangement of the seals in PFBR. The seals, located in the rotating plugs mounted on the roof slab of the reactor, are used to prevent the leakage of radioactive argon cover gas in the main vessel through the wide annular gap between the Bearing Support Ring (BSR) and Top and Middle Ring (TMR) of the respective rotatable plugs. The annular gap is 5 ± 2 mm, and the nominal diameter is ~ 6400/4200 mm for large and small rotatable plugs, respectively. The level between the two seal seating surfaces is expected to vary by maximum 2 mm, as shown in Fig. 2. Seal development and qualification was carried out under a comprehensive Research & Development program, involving multiple institutions. The chronicles of seal development and other related aspects are presented in ref. [1,2,3,4,5,6,7].

Fig. 1
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(a) Sectional view of PFBR and (b) assembly details of sealing arrangement in PFBR

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Fig. 2
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Schematic diagram of cross-section of seal, seal holder and seating surfaces

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In order to qualify the seals for reactor operation, scaled down model seals of 1-m diameter are tested in a dedicated test facility, in simulated operating conditions. Being a first of its kind design, extensive testing was carried out to qualify it for reactor operation. The required performance could be achieved only after testing more than five seals. With the expertise developed and insights gained in trouble-shooting activities during testing, the design of the seals was re-visited to develop robust seals for the future.

The previous studies on the seal were focussed on the seal design aspects as well as material aspects [8]. It was found in experiments that the seal performance is interconnected with the seal holder design, and hence, the seal holder was also modeled in the present study. The liberal tolerances required on the seal were found influencing the seal performance. Hence, the current study is extended to cover the effect of seal tolerances. The study has become more relevant as the effect of the differential thermal expansion between the metal–elastomer contacts is also modeled under the present study due to elevated working temperature operation of the seal. The paper covers the brief description of the seal, testing experiences and the numerical studies done.

Seal Description

The cross-section of the seal is mainly trapezoidal with special geometric features, such as elliptical groove in the middle and lip profiles on the sealing surface, to reduce the required squeezing load & to achieve effective sealing, as shown in Fig. 2. The seal holder is a circular ring with a groove similar to dovetail groove. The groove has two retaining walls for holding the seal and a central web to position the seal in the holder. The holder is pressed against the sealing surfaces by tie rods, arranged circumferentially at regular intervals, in order to obtain uniform compression of the seal as shown in the test set-up in Fig. 3. The seal design envisages a squeeze of 5 mm for reliable operation even with a maximum level mismatch of 2 mm under a differential pressure of 25 kPa.

Fig. 3
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Photograph of test facility of large diameter seals

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The seal holder is actuated by force applied parallel to seal axis resulting in engagement/disengagement of the seal. The seal is engaged during reactor operation and disengaged before plug rotation during reactor shutdown. Design data of the seal are given in Table 1. In PFBR, the seal will be subjected to elevated temperature operation of 110 °C for 2 weeks; followed by cooling to room temperature for 1 week. Therefore, the numerical studies were carried out for both room temperature as well as elevated temperature operations.

Table 1 Design data for large diameter seal
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Testing Experiences

The seal test facility is shown in Fig. 3. During qualification testing of various such seals, improper fitting of the seal in its holder was routinely observed, which was responsible for the pre-mature failure of the seal. The outer and inner side bulging at some locations are shown in Figs. 4 and 5, respectively. At some location, outer lip got bent as shown in Fig. 6. At some location, multiple deformations are observed as shown in Fig. 7.

Fig. 4
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Photograph of large diameter seal with outer side bulging observed post-experiment

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Fig. 5
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Photograph of large diameter seal with inner side bulging observed post-experiment

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Fig. 6
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Photograph of large diameter seal with bended outer lip observed post-experiment

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Fig. 7
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Photograph of large diameter seal with multiple failures observed post-experiment

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A schematic diagram is drawn to understand such failures as shown in Fig. 8. In the figure, the base width of the seal on the left side (“a-b”) is higher than the corresponding groove size, and thus, the left ring cannot be accommodated in the groove. Hence, it rests over the central web as shown in the figure, which results in pushing the base “a-b” in upward direction. The seal base “g-h” at the right hand side sits completely inside the groove, pulling the upper lips down. These movements cause the following visible changes in seal cross-section:

  • Height difference between both the lips at the location “e” and “d” had resulted in non-uniform compression of the seal.

  • The axis had been tilted by an angle θ ~ 20°.

  • The left wall “b-c-d” had distorted into convex shape, and the right wall “e-f-g” had distorted into concave shape, thus bulging of the left outer wall. (Bulging of the inner wall can be understood similarly if width of seal-base at “g-h” is higher than the corresponding groove width)

Fig. 8
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Schematic diagram to represent improper sitting of the seal into its holder

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The cross-sectional view of uncompressed seal assembled in its holder is shown in Fig. 9a. Figure 9b shows that the edge of the horizontal elliptical cavity bites into the seal with increasing compression of the seal thereby acting as a source of crack initiation. This is significant as the seal is subjected to fatigue loading.

Fig. 9
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(a) Seal without compression and (b) seal with compression of 5 mm showing biting impression

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The fitment problems, as described above, were observed for each and every seal. Thus, the chipping off the seal width by using emery paper was done routinely prior to seal testing. The finished dimensions of all five seals were different even though the seals were supplied by the same manufacturer.

Proposed Numerical Studies

The reliability of the seal can be improved, and its life can be enhanced by modifying the seal configuration so as to achieve a favorable stress distribution. Hence, numerical study is carried out with four different geometric configurations of the seal.

It is understood that variation in the friction coefficient between seal & its holder and the clearances between the seal and the holder are important factors that affect seal performance. A friction coefficient of 0.5 is suggested for rubber–metal contact, and the same may vary from 0.3 to 0.7 due to ageing and prolonged working condition [7].

The maximum radial gap between the central web and the seal is taken as 1 mm. The various tolerances on the seal dimensions influence the clearances between the seal inner/outer surfaces and the central web of the seal holder. These clearances may alter the stress distribution within the seal. Accordingly, sensitivity studies with varied clearances at these regions were carried out. Based on engineering judgment, clearances values of 0.5 and 1 mm were considered. Studies were carried out to analyze the effect of these parameters on seal performance. The outline of numerical studies carried out is given in the flowchart.

Numerical Modeling

Commercially available FEM package was used to model the geometry of seal, seal holder & seatings of the seal [9]. The FEA study involves nonlinearity with respect to geometry, material and contact, along with large deformations of the seal due to 5-mm squeeze. The seal and seal holder were modeled using deformable axisymmetric element, while seating surfaces were modeled using axisymmetric analytical rigid. The material property of silicone rubber was assigned to the seal [10], while seal holder was assigned with the property of carbon steel having modulus of elasticity of 200 GPa and Poisson’s ratio of 0.3. Both the materials were assumed to be isotropic, incompressible and homogeneous throughout the study. Marlow material model was used based on stability study. The assembly involves four parts, in which the mesh size for seal and its holder was taken as 1 and 2 mm, respectively, while remaining two parts (seatings) were considered rigid. Surface-to-surface contact logic was employed to establish the interaction between the parts. Surfaces associated with the seatings of seal & seal holder were assumed as master surface, & the surface of seal was taken as slave surface. In interaction properties, tangential behavior was defined using penalty-based technique with 0.5 value of the friction coefficient between master and slave surfaces. The friction coefficient for self-contact of the seal was taken as 1.0.

Displacement boundary condition of 5 mm was given to the seal holder, while seatings of the seal were provided with fixed boundary condition by arresting all the degree of freedom. Space between the two lips in the bottom region of seal was provided with pressure of 25 kPa to simulate the pressure of the sealed argon cover gas. To examine the seal performance at elevated temperature, room temperature of 25 °C was taken in the initial step, which had been propagated in the next step for simulation at 110 °C. Validation of the numerical model was performed with the benchmark data obtained from the literature [11, 12]. The seal squeezing force, distribution of contact pressure between the seal and mating surfaces, the von Mises stress distribution and maximum principal stress distribution were obtained from each numerical simulation. With four different geometries, with new & old seal holder, at room temperature and at elevated temperature, and with different friction coefficients; the total number of simulations added to sixty numbers.

The design parameters should conform to the specified limits, viz, (a) peak von Mises stress and peak maximum principal stress should be lower than the tensile strength (5 MPa) of the seal material (silicone rubber), and (b) contact pressure should be higher than the design differential pressure (25 kPa) for effective sealing.

Design Solutions and Numerical Studies

The design solutions considered with respect to the geometry of the seal are shown in Fig. 10. Geometry-I is the solid trapezoidal design which is taken as a reference design for comparison purpose. Geometry-II is the existing design of the seal wherein the cavity is oriented horizontally. Geometry-III is similar to II, but the cavity is oriented vertically. With this geometry, it is expected that the seal cross-section dimensions change more uniformly during compression loading with respect to geometry-II, resulting in low stress concentration. The cavity more or less retains its shape upon loading; the abrupt changes in geometry are not as great as for the horizontal cavity, upon loading. Hence, the vulnerability of the geometry for the fatigue failure is less. Initially, the aspect ratio (i.e., ratio of the major axis to the minor axis) of the ellipse was kept the same as that of the present geometry. Later, parametric study with the aspect ratio was also carried out. Geometry-IV consists of a circular cavity, which has the advantage of lesser volume of the material and therefore lower seal compression force when compared to the other three configurations.

Fig. 10
figure 10

Cross-section of large diameter seal having (I) solid trapezoidal shape, (II) elliptical cavity with horizontal major axis, (III) elliptical cavity with vertical major axis and (IV) circular cavity, and seal holder having retaining walls

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The proposed seal holder design is shown in Fig. 11. The retaining walls are replaced by locking strips. The seal is guided by central web, and the locking strips are fixed to the holder at regular intervals along the circumference. There is a radial gap of 2.8 mm and axial gap of 2 mm, between the seal and locking strips. Hence, the locking strips contact the seal only during its handling, and there will not be any contact during normal operation. With this seal holder, the seal is unrestrained, and hence, the effect of dimensional tolerances would be negligible.

Fig. 11
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Schematic diagram of proposed seal holder

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Results and Discussion

Seal Geometry

Distribution of von Mises stress and maximum principal stress for various seal geometries are shown in Fig. 12. These results correspond to room temperature and without level mismatch between the two seating surfaces. The deformed shape of the geometry-II (refer Fig. 10) clearly shows the increased sharpness at the edge of the ellipse upon loading. The stress varies uniformly within the solid trapezoidal, whereas slight stress gradients are observed in other geometries. Peak von Mises stress occurs on the inner surface of the ellipse in the geometry-II, III & IV whereas it occurs in the bulk material in geometry-I. The peak maximum principal stress (tensile) for both geometry-II & III occurs at the bottom end of the ellipse; however, their magnitudes are very much different.

Fig. 12
figure 12

Distribution of von Mises stress (top row) & maximum principal stress (bottom row) for geometry-I, II, III and IV, at room temperature and without level mismatch

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Figure 13 shows the von Mises stress and maximum principal stress distribution with a level difference of 2 mm between the two seating surfaces for all the geometries. It can be seen that the deformed shape of the seal is not symmetrical (about the center line of the seal in its 2-D view) due to differential compression. The magnitudes of various stresses vary slightly with respect to the case without level mismatch. As expected, the peak values of stress metrics occur in the highly compressed side of the seal. From Fig. 13 and Table 2, one can infer that the level difference does not enhance the peak values of various stresses, but alters the stress distributions within the seal.

Fig. 13
figure 13

Distribution of von Mises stress & maximum principal stress for geometry-I, II, III and IV, at room temperature and 2-mm level mismatch

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Table 2 Magnitudes of stresses and compression force for geometry-I, II, III and IV in different conditions
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The magnitudes of performance indices for geometry-I, II, III and IV in different conditions are tabulated in Table 2. The variation of these indices is shown graphically in Fig. 14 for the case of room temperature and without level mismatch. With increased temperature, the stress distribution remained the same where as the magnitude of various stress indices increase due to higher coefficient of thermal expansion of elastomer than the steel. Peak von Mises stress in all geometries is of the same order, but the peak maximum principal stress (tensile) is minimum for geometry-I & III. When compared to geometry-I, the seal compressive force for geometry-III is low. Hence, geometry-III is the optimum among the studied geometries and is recommended for future seals.

Fig. 14
figure 14

Graphical representation of performance indices for geometry-I, II, III & IV, at room temperature & without level mismatch

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The parametric study on the seal aspect ratio involved keeping the major axis of the elliptical cavity the same and varying the minor axis as 40, 50, 60 and 75% of the major axis. As the length of minor axis increases, seal compression force decreases and maximum principal stress increases. The value of von Mises stress at the extremes of the minor axis of vertical elliptical cavity increases with increasing the length of minor axis. The “depth of tensile zone” and “the peak value of the maximum principal stress at the bottom surface of the cavity” increase with increase in the size of minor axis. Based on these findings, elliptical cavity having major axis of 20 mm and minor axis of 10 mm is selected.

Seal Holder Design

Before taking up the analysis of the seal with new seal holder, the effect of retaining walls on the stress distribution in the seal was studied. Figure 15 shows the von Mises stress distribution with and without retaining walls for geometry-III. Other results are tabulated in Table 3. Table 3 shows that there is only minor variation in the absolute values of the peak von Mises stress, peak maximum principal stress and peak contact pressure, while almost 10% reduction in the seal compression force for seal holder without sidewalls. Hence, it can be inferred that the removal of side walls does not alter the seal performance.

Fig. 15
figure 15

Distribution of von Mises stress for geometry-III with and without retaining walls of seal holder

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Table 3 Magnitudes of stresses and compression force for geometry-III, with and without retaining walls
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Figure 16 shows the von Mises stress, maximum principal stress and contact pressure distribution for the seal geometry-III along with new seal holder. The seal geometry is modified by providing steps of 2.7 mm (at 10 mm from the top of the seal surface on both sides) which is provided for holding the seal into the locking strips during the disengagement of the seal. Magnitudes of various stresses and compressive force are almost similar to that in the case of without retaining walls (i.e., Table 3). These findings validate the new holder design.

Fig. 16
figure 16

Distribution of von Mises stress, maximum principal stress and contact pressure for seal geometry-III, with proposed seal holder

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Friction Coefficient & Tolerances

As indicated earlier, the value of friction coefficient between the seal and its contacting surfaces varies from 0.3 to 0.7. Hence, the sensitivity of seal performance was investigated with three different values of friction coefficient (0.3, 0.5 and 0.7).

The obtained results reveal that the magnitudes of performance indices are not varied much with variation in friction coefficient (0.3–0.7). Thus, we can infer that the performance of seal is in-sensitive to variation in friction coefficient.

Study on the various tolerances reveals the minor change in the magnitudes of different parameters when the clearance is increased to 0.5 mm from zero, for both the inner and outer surfaces. But, the values are essentially the same for clearances of 0.5 and 1 mm. The lateral expansion of seal walls, upon compression, is less than 0.5 mm, and hence, the seal walls do not interact with the central web when the clearance is more than 0.5 mm. Thus, the magnitudes of various stresses and the compression force remain the same for all clearances beyond 0.5 mm. The schematic diagram of optimized assembly (seal geometry-III & proposed seal holder) is shown in Fig. 17.

Fig. 17
figure 17

Schematic diagram of optimized assembly (seal geometry-III & proposed seal holder)

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Important Inferences

The above studies demonstrate the robustness of the selected design of the seal and the holder. The following inferences can be drawn from all the studies carried out:

  • Backup seal of solid trapezoidal shape is not preferred due to its higher seal compression force requirement, and the performance of seal geometry having vertical elliptical cavity is superior to the geometry having horizontal elliptical cavity.

  • Due to deformation, the curvature at the edges of the major axis of elliptical cavity in geometry-II is reducing, which is acting as stress raiser. Size of tensile zone in geometry-III is less as compared to geometry-II & IV. The absolute values of the stresses are more if level mismatches.

  • Value of maximum principal stress is less in case of geometry having vertical elliptical cavity as compared to geometry having horizontal elliptical cavity, less value of maximum principal stress is desirable to avoid stretching of the bottom side of the cavity or to avoid the formation as well as propagation of the crack in the bottom side of the cavity, (since argon cover gas pressure is supporting the stretching caused by maximum principal stress).

  • Value of maximum contact pressure is more in case of geometry having vertical elliptical cavity as compared to geometry having horizontal elliptical cavity. More value of maximum contact pressure will enhance the leak tightness property of the seal.

  • The performance of geometry having vertical elliptical cavity is superior to the geometry having horizontal elliptical cavity for both seal holders. Requirement of total seal compression force is 10% less if there are no side walls on seal holder & the same trend was observed in case of improved design of seal holder.

  • The improved design of seal holder is superior in such a way that the side walls are not touching the seal, and hence, the tolerances on the seal geometry can be relaxed.

  • No much variation is observed in the performance indices as well as stress distribution of the seal with different values of friction coefficient (0.3, 0.5 and 0.7) between the silicone rubber and the carbon steel.

  • No significant changes are observed in the performance of the seal due to tolerance of 0.5 and 1.0 mm at the inner as well as outer vertical region of the central ring of the seal holder; however, sitting of seal in its holder will improve.

  • New seal holder design can accommodate the manufacturing tolerances in the seal geometry, without altering the seal performance.

Conclusion

The present work highlights the analytical and experimental work done to enhance robustness and to reduce the seal failure incidents of large diameter seals used in the Prototype Fast Breeder Reactor. The finite element-based stress analysis of the seal has provided insights into the stress distribution within the seal. Various parameters such as von Mises stress, maximum principal stress, contact pressure and the seal compression force were analyzed. The study enabled us to arrive at more robust seal geometry and the improved design of seal holder. The robustness of the designs is demonstrated numerically with respect to the possible variations in friction coefficient and seal dimensional tolerances. Experimental validation of the recommended seal geometry and the holder design is being taken up shortly.