Scholarly article on topic 'Deformation Characteristics and Sealing Performance of Metallic O-rings for a Reactor Pressure Vessel'

Deformation Characteristics and Sealing Performance of Metallic O-rings for a Reactor Pressure Vessel Academic research paper on "Mechanical engineering"

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{"Deformation Characteristic" / "Inconel 718" / "Metallic O-Ring" / "Reactor Pressure Vessel" / "Sealing Performance"}

Abstract of research paper on Mechanical engineering, author of scientific article — Mingxue Shen, Xudong Peng, Linjun Xie, Xiangkai Meng, Xinggen Li

Abstract This paper provides a reference to determine the seal performance of metallic O-rings for a reactor pressure vessel (RPV). A nonlinear elastic-plastic model of an O-ring was constructed by the finite element method to analyze its intrinsic properties. It is also validated by experiments on scaled samples. The effects of the compression ratio, the geometrical parameters of the O-ring, and the structure parameters of the groove on the flange are discussed in detail. The results showed that the numerical analysis of the O-ring agrees well with the experimental data, the compression ratio has an important role in the distribution and magnitude of contact stress, and a suitable gap between the sidewall and groove can improve the sealing capability of the O-ring. After the optimization of the sealing structure, some key parameters of the O-ring (i.e., compression ratio, cross-section diameter, wall thickness, sidewall gap) have been recommended for application in megakilowatt class nuclear power plants. Furthermore, air tightness and thermal cycling tests were performed to verify the rationality of the finite element method and to reliably evaluate the sealing performance of a RPV.

Academic research paper on topic "Deformation Characteristics and Sealing Performance of Metallic O-rings for a Reactor Pressure Vessel"

Nucl Eng Technol xxx (2016): 1-12

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Original Article

Deformation Characteristics and Sealing Performance of Metallic O-rings for a Reactor Pressure Vessel

Mingxue Shen a'*, Xudong Peng a, Linjun Xie a, Xiangkai Meng a, and Xinggen Li b

a Engineering Research Center of Process Equipment and Its Remanufacture, Ministry of Education, Zhejiang University of Technology, 18 Chaowang Road, Xiacheng District, Hangzhou 310032, People's Republic of China

b Ningbo Tiansheng Sealing Packing Co., Ltd., 418 Gaoke Avenue, Cixi District, Ningbo 315302, People's Republic of China

ARTICLE INFO

ABSTRACT

Article history:

Received 7 September 2015 Received in revised form 5 November 2015 Accepted 6 November 2015 Available online xxx

Keywords:

Deformation Characteristic Inconel 718 Metallic O-Ring Reactor Pressure Vessel Sealing Performance

This paper provides a reference to determine the seal performance of metallic O-rings for a reactor pressure vessel (RPV). A nonlinear elastic-plastic model of an O-ring was constructed by the finite element method to analyze its intrinsic properties. It is also validated by experiments on scaled samples. The effects of the compression ratio, the geometrical parameters of the O-ring, and the structure parameters of the groove on the flange are discussed in detail. The results showed that the numerical analysis of the O-ring agrees well with the experimental data, the compression ratio has an important role in the distribution and magnitude of contact stress, and a suitable gap between the sidewall and groove can improve the sealing capability of the O-ring. After the optimization of the sealing structure, some key parameters of the O-ring (i.e., compression ratio, cross-section diameter, wall thickness, sidewall gap) have been recommended for application in megakilowatt class nuclear power plants. Furthermore, air tightness and thermal cycling tests were performed to verify the rationality of the finite element method and to reliably evaluate the sealing performance of a RPV.

Copyright © 2016, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society.

1. Introduction

Seals are vital components in pressure vessels, especially in a reactor pressure vessel (RPV), which prevents the leakage of radioactive substances with a high pressure and high temperature [1]. To operate under such severe working conditions, two metallic self-tightening seals such as O-rings or C-rings are used between the flange of the head and

the flange of the barrel in a RPV [2,3], as shown in Fig. 1. The RPVs belong to the "normal operating system", seismic Class I. Previous RPVs were designed to operate for 40 years but the newer RPVs are designed to operate for more than 60 years. However, if the metallic seals degrade because of severe working conditions (e.g., temperature alternation, pressure fluctuation, radiation, and accidents), their operational lifetime may be limited [4-6]. The system's sealing

* Corresponding author. E-mail address: shenmingxue@126.com (M. Shen).

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http:// creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. http://dx.doi.org/10.1016/j.net.2015.11.009

1738-5733/Copyright © 2016, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society.

Nucl Eng Technol xxx (2016): 1-12

Fig. 1 - Diagram of a typical reactor pressure vessel and its sealing element.

performance is determined by the rings' intrinsic properties and their deformation behaviors in the RPV. The compression-resilience property and linear load are basic information used to evaluate the performance of a well-designed O-ring [7]. As shown in Fig. 2, when the O-ring is compressed to a predetermined load, plastic deformation of the metallic ring occurs in the tightening process, and the compressed O-ring must have sufficient resilience and sealing contact specific pressure. The sealing performance is then determined by the reaction forces between the flanges and metallic ring, and good sealing performance can be obtained with a comparatively low tightening force. Thus, the reactor pressure vessel employs auto-tightening sealing, which can ensure sealing reliability when the pressure and temperature fluctuate [8]. However, for a long time, the aforementioned key sealing technologies in RPVs

Fig. 2 - Sealing mechanism of a metallic O-ring [8].

have been monopolized by only a few enterprises such as Garlock Sealing in the United States of America [9]. Nearly all existing studies in this area have focused primarily on the flanges' deformation, but have neglected or oversimplified the metallic rings. Few studies have reported on metallic rings in RPVs [1,10,11].

In China, the unit capacities of nuclear power plants are gradually increasing with the rapid development of the nuclear industry. This factor will inevitably make the dimensions of the RPV and its sealing ring increase further [12,13]. For the key sealing design of megakilowatt class nuclear power plants, a theoretical reference basis is still lacking [14,15]. In particular, the structure size of O-rings and geometric dimensions of grooves for installing such rings (including the groove depth on the flange face and the fit-up gap between the groove and O-ring) are important design parameters that can determine the sealing pressure. The reasons are as follows: the structure size of the O-ring has a direct impact on the distribution of the stress field and the size of the contact zone on the sealing surface; a suitable sidewall gap can prevent radial slippage of the O-ring under internal pressure, and more importantly, it can greatly improve the sealing specific pressure of the O-ring on the sealing surface with the help of the blocking effect of the groove sidewall. However, in practical industrial application, these critical design factors are usually estimated and determined only by a traditional empirical method. Kobayashi et al [10] analyzed the impact of the sidewall gap on the deformation linear load of O-rings. The results were that, compared to an O-ring without sidewall groove, the linear load of an O-ring with a sidewall groove increased significantly when the sidewall gap was 0 mm or 0.07 mm. Other researchers [16] also mention that the groove precision requirements of a metallic O-ring are much stricter than those of an elastomer O-ring. In summary, for a RPV, the sealing performance of flange connections with metallic O-rings has not been sufficiently examined and needs to be studied.

In this paper, the deformation characteristics of an Inconel 718 alloyed O-ring for RPV were analyzed by the finite element method, based on the nonlinear elastic-plastic model. First, the impact of geometrical parameters (e.g., cross-section diameter, d; wall thickness, t; and outer diameter, D) of the O-ring on the deformation characteristics is discussed. To examine the effect of the groove in a flange, a sidewall was considered, and the structure parameters of the groove on the flange face (e.g., the sidewall gap, 5, between the sidewall and the O-ring and the groove depth, h, as shown in Fig. 1B) were also studied. The leakage rate of the O-ring under different compression ratios and different sidewall gaps were determined using helium leak test techniques to verify the reasonability of the finite element analysis. Based on the parameter optimization by numerical simulation, a thermal cycling test was performed to further verify the reliability of the designed O-ring and its sealing structure. This is expected to provide a theoretical reference for the development of metallic O-rings and for the design of flange faces for RPVs so that key sealing technology in nuclear power plants can be promoted in China.

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2. Methods and experiments

2.1. Material properties and sample sizes

The O-rings used in the experiments were produced by Ningbo Tiansheng Sealing Packing Co., Ltd (Ningbo, China). The base material was Inconel 718 alloy. The chemical composition and mechanical properties are shown in Tables 1 and 2, respectively. In Table 2, E is the Young's modulus, H is the strain-hardening parameter, ffp0.2 is the material's yield strength, and sb is the material's tensile strength. In general, the outer diameter of an O-ring, which is used in a megakilowatt class nuclear power unit, is approximately 4 m. Therefore, in this paper, the outer diameter of the O-ring for finite element modeling was D = 4,002 mm and the outer diameter of the O-ring for experiments was D = 650 mm, unless otherwise stated.

Finite element model

A commercial finite element analysis program ABAQUS version 6.10 (Hibbit, Karlsson and Sorensen Inc. USA, 2010) was employed throughout. An axisymmetric structure was modeled while taking into account the symmetrical characteristics of both models and the boundary condition (see Fig. 3). For the sake of simplicity, it was assumed that the upper and lower flanges were rigid bodies and the O-ring was defined as a deformable elastic-plastic body because the flanges have a much higher stiffness than the O-ring. Furthermore, the effect of the surface silver coating was ignored. The material of the O-ring was assumed to be elastic-plastic with linear strain-hardening. The constitutive equation can be written as:

Eee in the elastic zone ss + Hep in the plastic zone

in which ee is the elastic strain and ep is the plastic strain.

Fig. 3 shows the mesh divisions of the O-ring used in the analysis. The local mesh is densified near the contact area of the O-ring and the cylinder, compared to the other parts of the O-ring. There were 13,020 nodes and 12,600 four-node bilinear axisymmetric quadrilateral elements in the model. In ABA-QUS/Standard, the contacting surfaces were created first, the

Table 1 - Chemical composition of the materials.

Material Chemical elements

C Mn Ni Cr Co Si Ti Nb + Ta

Inconel 718 0.03 0.08 52.9 19.1 0.1 0.12 1.06 5.2

Material Chemical elements

Cu Mo Al S B P Fe

Inconel 718 0.07 3.0 0.58 0.001 0.005 0.009 Balance

The data are presented as mass %.

Al, aluminum; B, boron; C, carbon; Co, cobalt; Cr, chromium; Cu, copper; Fe, iron; In, indium; Mn, manganese; Mo, molybdenum; Nb, niobium; Ni, nickel; P, phosphorus; S, sulfur; Si, silicon; Ta, tantalum; Ti, titanium.

Table 2 - Main mechanical properties of the materials.

Material E H (GPa) (MPa) sp0.2 (MPa) Sb (MPa) Poisson's ratio

Inconel 718 209 10,854 1,087 1,306 0.3

contact pairs were then defined, and the mechanical model was finally created to control the behavior of the contacting surfaces. In the finite element model, two contact pairs were defined: (1) the contact between the upper flange and the O-ring and (2) the contact between the lower flange and the O-ring. The sides of the upper and lower flanges were the master side and the O-ring side was the slave side. Furthermore, finite sliding formulation was used for the two contact pairs. In general, under water lubrication, the friction coefficient between the friction pair of metals was approximately 0.1-0.3 [17]. Therefore, the value of the friction coefficient between the contact surfaces is 0.15. A reference point, RP-1, was created in the center of the upper flange, and the upper flange was constrained with RP-1 by a coupling constraint. The coupling constraint is to make one or more freedom degrees of two bodies have the same value. This model is used in all directions. In addition, a reference point, RP-2, was created at the center of the lower flange. The lower flange is constrained with RP-2 by using a coupling constraint. This coupling constraint is also used in all directions. The two reference points were fixed at the initial step. To avoid singularity in the numerical analysis when a slip occurs between the contact surfaces, the first step applied a small displacement amplitude at RP-1 in the y direction. The displacement amplitude at RP-1 was changed from 0 mm to -0.0001 mm in this step. To simulate the loading process, the next step changed the displacement amplitude at RP-1 from -0.0001 mm to -2.0432 mm (taking the compression ratio of C = 16% as an example). Furthermore, the displacement amplitude was changed to 0 mm in the last step, which was used to simulate the unloading process.

Fig. 3 - Geometrical parameters and finite element mesh divisions of the contact pairs.

4 Nucl Eng Technol xxx (2016) : 1-12

2.3. Experiment details

Fig. 4 shows a diagram of the multifunctional test rig, which was used to examine the compression characteristics of the metallic O-ring. The air tightness tests were performed in air condition. To complete the air tightness test, special tooling should be added (Fig. 4). In this paper, the sidewall gap, 5, which exists when the O-ring is installed in the groove, was controlled by the inner diameter of the retaining ring. The groove depth, h, is obtained by controlling the height of the retaining ring. Furthermore, the height of the retaining ring is slightly higher than the height of the lower flange. The surface roughness of the sealing faces on the flange and retaining ring was determined by using a profil-ometer (Dektak XT; Bruker, Billerica, MA, USA) before the test, as required in ISO 4287. The surface roughness of the inner side of the retaining ring was Ra = 0.4 and the surface roughness of the upper flange and the lower flange was Ra = 0.2. Before the test, the O-ring was placed between the two flanges. During the test, a compressive load was applied to the test rig through a spherical bearing to avoid an inclined compression. The deformation of the O-ring was measured at three points by a dial gauge, and the compressive load was measured with a load cell. The deformation and the load were recorded by a data acquisition and control system. The negative pressure helium leak detection method was used. The test can accurately determine the leakage rate of the O-ring. The leakage rate and purity (99.9%) of the helium for the test were meanwhile detected with a helium mass spectrometer leak detector (SFJ-211; Anhui Wayee Technology Co., Ltd., Hefei, China; resolution ratio, 1.10 x 10~12 Pam3/s).

More importantly, to simulate the working conditions with cold and hot alternation of the reactor pressure vessel, a realistically scaled sealing system test rig was specially designed. Fig. 5 shows the thermal cycling test system in which the design pressure reaches 18 MPa and the design temperature is 360 °C. A thermal cycling simulation

experiment was performed on the test rig under high temperature and high pressure conditions. The test medium was deionized water. In addition, after the test, the morphology characterization of the indentation surface for part of the O-ring was measured by a three-dimensional surface profiler (Contour GT-K; Bruker, Billerica, MA, USA).

3. Results and discussion

3.1. Reliability verification of the finite element analysis

The external surface of an O-ring in service is usually plated with silver (generally with a thickness of 0.15-0.22 mm [1]). The silver coating has lower stiffness; therefore, the microirregularities of the mating surface and microdefects on the flange face can be easily recovered to prevent leakage effectively. The aforementioned theoretical proposed model ignores the influence of the silver coating on the O-ring surface, but it has great significance for the static sealing performance of metallic sealing rings. Fig. 6 shows the loading displacement curves of O-rings with and without a silver plating layer (with a thickness of 0.2 ± 0.01 mm) and finite element compression-resilience curves of O-rings (without silver coatings) with different diameters. Under the same compression load, the compression-resilience curve of O-rings without silver plating was approximately 0.2 mm deformation hysteresis. The value of the deformation hysteresis is close to the thickness of the silver coating. This showed that the silver coating has no substantial impact on the compression-resilience performance of the O-ring. Therefore, the silver coating can be ignored by the finite element model. In addition, without regard to the silver plating layer, the three curves that were obtained through the modeling experiment, based on the same compression ratio were rather consistent. In this paper, if the curve of the elastic stage and the curve of plastic stage were extended in

Fig. 4 - Diagram of the multifunctional test rig.

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Fig. 5 - The thermal cycling test system. (A) Internal structure. (B) External view. (C) Data acquisition and analysis. The compressed O-ring (D) during and (E) after the experiment.

the stress-strain curve, the point at which they intersect would be defined as the yield stress. The line specific pressure of an O-ring with silver plating at the beginning of the plastic stage was 485 N/mm. At this time, the corresponding compression displacement was 0.85 mm. Therefore, the compression rate of the O-ring was 6.69%.

Generally speaking, for static sealing, the sealing element can be compressed to make the maximum displacement correspond to the displacement when totally unloaded; this is the resilience value. When the compression ratio is 16%, the resilience value for removing the O-ring is 0.43 mm (Fig. 6). Furthermore, the bending equations of an O-ring can be expressed as follows:

Fig. 6 - Comparison of the loading-displacement curve of the O-rings between the experiment and finite element method without and with silver coating and different outer diameters.

dqu+u=MR?/1

in which

M = M0 + PRj(1 - cos 6)/2

I = Et3/12(1 - g2)

The following equation can then be inferred from the previous equation:

PR3 /4

U=---6 Sin 6 - cos 6

In the elastic stage, the relationship between the bending stress and the line specific pressure is accordingly given by:

3PR / 2

s = 3pR l1 - P

In which R is the inner radius and t is the thickness of the O-ring. The geometric parameters can be inserted into the equation:

s = 3P

Therefore, Pa—the point on the curve for the line specific pressure versus the bending stress at which the curve levels off and nonlinear deformation begins to occur—can be computed by

in which ss is the stress value at which the material of the O-

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Fig. 7 - Comparison of the deformation characteristics of O-ring, based on numerical simulation and flattening test. (A) C = 7.0%; (B) C = 12%; (C) C = 16%; (D) C = 20%.

ring begins to deform plastically. For the Inconel 718 alloy, the value of ss is 980 MPa. Therefore, the value of is given by

Pi = 326.7Nmm-1

In addition, P2—the point on the curve for the line-specific pressure versus the bending stress at which the curve changes into a straight line again—can be given by

P2 = 1.5pa = 490 Nmm-1

The finite element analysis results consequently showed good agreement between the experimental results and the theoretical results, as shown in Fig. 6.

Figs. 7A-7D show the cross-section deformation and the equivalent plastic strain nephograms obtained by numerical simulation and flattening tests under different compression ratios. The values of width, w, and height, h, of the deformed cross-sections are listed in Table 3. Thus, the numerical simulations were in good agreement with the experimental tests. Therefore, the deformation behaviors of a metallic O-ring can be simulated by the finite element model.

parameters such as the groove depth (h). The compression ratio (C) is calculated as follows:

d-d' d - h C = x 100% = d-r-h x 100% dd

In which d (mm) is the initial cross-section diameter of the O-ring, d' (mm) is the diameter of the cross-section of the O-ring after it is compacted, and h (mm) is the depth of the installing groove on the flange.

The contact stress on the seal surface is the main factor that affects the sealing performance of a static seal. The initial contact stress was provided by the resilience force generated after the O-ring was compacted to a predetermined compression amount when it was installed into the flange. This factor also ensures that the O-ring has a sufficient resilience margin and a suitable sealing specific pressure during service.

The contact pressure between the O-ring and the mating surface should certainly be more than the differential pressure across the seal; otherwise, the seal will fail.

3.2. Parameter optimization, based on finite element analysis

3.2.1. Compression ratio C

In general, the compression ratio of an O-ring is guaranteed by controlling the depth of its sealing groove [16]. Therefore, the compression ratio of an O-ring can be expressed by

■ 1.5 -1.0 -0.5 o 0.5 1.0 1.5 Distance to the contact center (mm)

Fig. 8 - Contact stress distributions on the sealing interface under different compression ratios.

Table 3 - Width and height dimensions of the deformed cross-sections.

Compression ratio (%) 7.0 12.0 16.0 20.0

Width (mm) Simulation results 13.20 13.70 14.10 14.50

Experiment results 13.19 13.71 14.10 14.48

Height (mm) Simulation results 12.25 11.60 11.10 10.65

Experiment results 12.25 11.63 11.13 10.63

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Fig. 9 - Comparison of the simulation and experimental results, (A) Von Mises stress nephogram. (B) Deformation nephogram. (C) Surface three-dimensional profile (corresponding to Fig. 5E), C = 20%.

Fig. 8 displays the contact stress distribution on the sealing interface under different compression ratios. The maximum contact stress on the sealing interface increases as the compression ratio increases, and the contact width widens. Furthermore, the maximum contact stress always appears on two sides of the contact zone, but the contact stress is relatively lower in the contact center. When the compression ratio, C, is 20%, the maximal contact stress can exceed 1,200 MPa, which exceeds the yield strength limit of the Inconel 718 alloy. Of course, this stress will actually be lower as the deformation of the flange is considered. The contact stress is zero within a range of approximately 1.0 mm from the contact center when the compression ratio C is 20%. This corresponds to the concave shape of the O-ring around the contact area (Fig. 9). At this point, the O-ring near the contact center is separated from the flange surface, and the number of actual contact zones increases from one to two (Fig. 9B). This concave phenomenon was again confirmed through the experiment test. Fig. 9C shows the three-dimensional profile of the O-ring surface when the compression ratio C is 20%. The actual measured concave depth of the O-ring was approximately 12 mm.

It is noteworthy that the concavity will inevitably cause the contact width on the sealing interface to decrease and permanent deformation to be aggravated, and thus reduce the sealing performance. Fig. 10 shows the contact width and resilience value with the change in the compression ratio. The contact width increases gradually with the increase in the compression ratio when the compression ratio is less than 18%. The contact width then rapidly decreases and gradually stabilizes when the compression ratio is greater than 18%. The resilience value gradually increases when the compression ratio is less than 20%. However, the increase in the resilience value is less obvious after the compression ratio exceeds 20%. This indicates better performance can be obtained when the

compression ratio of the O-ring is between 10% and 16%. When a metallic sealing ring with a wire diameter of 12.7 mm is used, an effective groove depth on flange face of 10.67-11.43 mm is preferred.

3.2.2. Diameter of the cross-section of the O-ring Fig. 11 shows the resilience value and line specific pressure (i.e., load on the seal divided by perimeter) with change in the cross-section diameter under the same compression amount (t = 1.35 mm, 5 = a>). The resilience value and line specific pressure of the O-ring showed a monotonic increase trend and a monotonic decrease trend with the increase in the cross-section diameter, respectively. Furthermore, the reduction of the cross-section diameter of the O-ring will cause the resilience value to be inadequate and the concavity to appear more easily under the same wall thickness. However, if the cross-section diameter is too small or the compression ratio is too

Fig. 10 - Change in the contact width and resilience value of the sealing surface with the compression ratio.

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Fig. 11 - Variation in the resilience value and linear specific pressure with the cross-section diameter.

Fig. 13 - Contact stress distribution on the sealing interface for different wall thicknesses: C = 16%.

large, the line specific pressure will be borne together by contact zone I and contact zone II (Fig. 9B), after concavity occurs. The value of the line specific pressure of a single side is approximately one-half the total line specific pressure. The total line specific pressure (Fig. 12) would be evenly divided between contact zone I and contact zone II in Fig. 9B, but it is less than the line specific pressure of the other two cross-section diameters, as shown in Fig. 12. Therefore, once concavity forms, sealing failure could result. To sum up, the O-ring has a rather high resilience value and line specific pressure when the cross-section diameter (d) is 12.7 mm. Therefore, the sealing performance is relatively better.

3.2.3. Wall thickness of the O-ring

Fig. 13 shows the contact stress distribution of O-rings with different wall thicknesses and the same compression ratio (C = 16%). It evident that (1) the contact stress of the contact center of the O-ring constantly increases with increasing wall thickness, (2) the value of the contact stress when t is 1.65 mm is close to the value of the contact stress when t is 1.80 mm, and (3) the contact stress of the contact center is zero when the wall thickness is 1.00 mm. This finding indicates that the wall thickness of the O-ring should not be too small; if it is, a

concavity in the contact center would be generated. With increasing wall thickness, the contact stress on the sealing face increases accordingly, but the resilience value of the O-ring decreases, as shown in Fig. 14. Therefore, for an O sealing ring with a cross-section diameter of 12.7 mm, the wall thickness should not be too large. The sealing performance of the O-ring is rather good when the wall thickness is between 1.35 mm and 1.65 mm.

3.2.4. Outer diameter of the O-ring

Fig. 15 shows the line specific pressure and resilience value with the change in the outer diameter (D) of the O-ring (d = 12.7 mm; t = 1.35 mm). The following can be concluded: the line specific pressure of the sealing face becomes insensitive once the outer diameter of the O-ring is more than 650 mm. However, the resilience value always remains the same. The effect of the external diameter on the stress field is substantially prevented because the circular stiffness of the O-ring is significantly decreased. The aforementioned conclusions further confirm that it is reasonable to conduct the experimental test by using an O-ring with a diameter of 650 mm to verify the results of finite element modeling. It is

Fig. 12 - Comparison of the linear pressures under different cross-section diameters and compression amounts.

Fig. 14 - Change in the resilience value with the wall thickness of the O-ring.

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Ê 0.4

A Compression ratio C = 12% ■ Compression ratio C = 16%

• Compression ratio C = 20% h

- :—

700 (1)

fi00 o

500 —I

50 100 200 350 650 2,500 4,000 Outer diameter (mm)

Fig. 15 - Evolution of the line specific pressure and resilience value with the outer diameter of the O-ring.

also reasonable to determine the performance of the sealing ring so as to predict the performance of a full-scale O-ring by reducing the outer diameter only in the test.

3.2.5. Sidewall gap on the flange

Fig. 16 shows the characteristic curve of the load displacement deformation of O-rings with and without 0.6-mm sidewall gaps. During the process of O-ring compression, the line specific pressure rapidly increases after the O-ring contacts the sidewall of the groove. The results indicate that, compared to an O-ring without a sidewall, the line specific pressure of the O-ring with a sidewall increased by at least 30% and its resilience was not weakened. Therefore, the sealing performance of the O-ring can be further improved by optimizing the structure parameters of the groove on the flange.

Plane strain formulations refer to elastically isotropic materials with plastic behavior governed by the von Mises criterion, which accounts for combined kinematic and isotropic hardening [18]. Fig. 17 shows the distribution nephograms of Mises stress of the O-ring when the compression ratio is 15.35% (which corresponds to a groove depth of 10.75 mm) and the sidewall gaps are 0 mm, 0.3 mm, 0.6 mm, and 0.9 mm. The results showed that the restraint

function of the sidewall with groove caused the O-ring to contact the sidewall and form local high-stress zones. Furthermore, the smaller the sidewall gap, the larger was the high-stress range and the stress value. In addition, when the sidewall gap increased to 0.9 mm, the O-ring and the sidewall were no longer in contact.

Fig. 18 shows the line specific pressure and resilience value of the O-ring with different sidewall gaps. As the sidewall gap increased, the line specific pressure showed a trend of gradual decline. More specifically, the line specific pressure became stable when the sidewall gap exceeded 0.7 mm. The resilience value gradually decreased with the increase in the sidewall gap when the sidewall gap was 0.0-0.4 mm. The resilience value rapidly increased and approached 0.40 mm when the sidewall gap was 0.4-0.6 mm. In general, the recommended resilience value in the nuclear power industry is 0.38 mm; therefore, the resilience value is higher than the recommended value.

The positions at which the maximum Mises stress appeared were different for the different sidewall gaps, as shown in Fig. 19. Under a small sidewall gap, the maximum Mises stress always appeared near the upper flange (point "A" in Fig. 19). However, with an increase in the sidewall gap, the positions where the maximum Mises stress appeared to shift to the lower flange (point "C" in Fig. 19) or near the sidewall (point "B" in Fig. 19). During this process, the maximum Mises stress had a large fluctuation. When the sidewall gap was approximately 0.5-0.6 mm, although the positions where the maximum Mises stress appeared were different for two different groove depths, the value of the stress was rather small, even lower than the value without a sidewall. This finding may be because the highest stress zones at A, B, and C produced a plastic hinge at the terminal points (e.g., B) of the major axis of the ellipsoid to allow rigid body-like movements for A-B and B-C along the plastic zone of the curve in Fig. 6. It reduced the assembly load, produced the differential pressure energized self-tightening effect, and created disengagement (in the vicinity of A and C) at higher compression ratios. However, if the sidewall gap is too small or too large, the maximum Mises stress of the O-ring will be higher, even greater than 1,700 MPa. This value is far more than the yield and tensile strengths of the Inconel 718 alloy. High von Mises stresses cause plastic deformation to increase and the line specific pressure to drop, and therefore probably results in sealing failure.

To summarize, a suitable sidewall gap can improve the sealing line-specific pressure of the O-ring through the blocking function of the sidewall. There is a strong correlation between the sidewall gap and the sealing performance of the O-ring. It undoubtedly makes strict demands on the installing process and the manufacturing process of the O-ring.

Experimental validation

Fig. 16 - The effect of the sidewall gap on the line specific pressure and deformation characteristics.

3.3.1. Air tightness test

On the basis of optimized structure parameters obtained through finite element analysis, a helium leakage detecting air tightness test was performed on an O-ring with a silver coating of approximately 0.2 mm thickness. Fig. 20A shows the leakage rate variation with the change of compression

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5 = 0.6 mm 5 = 0.9 mm

Fig. 17 - Von Mises stress distribution nephogram of the O-ring under different sidewall gaps.

ratio when the sidewall gap, <5, was 0.6 mm and 5 was m (i.e., no sidewall). The leakage rate gradually decreased with a gradual increase in the compression amount on the O-ring. However, a further increase in the compression amount can cause concavity of the O-ring on the sealing face (Fig. 9C), which increased the leakage rate. Therefore, the test results

Fig. 18 - The line specific pressure and the resilience value under different sidewall gaps.

were consistent with the results of the numerical simulation. Fig. 20B shows the change in the leakage rate with the change in the sidewall gap for three different groove depths. Within the recommended compression ratio range, the leakage rate remained at a low level when the groove depth (h) was 11.0 mm, and the leakage rate was lower than 1.10 x 10-12 Pa m3/s when the sidewall gap was more than 0.4 mm, which was beyond the resolution of the helium mass spectrometer. To compare the impact of different sidewall gaps on the leakage rate, the leakage rate analysis test was performed again under different sidewall gaps when the groove depth was 11.5 mm and 12.0 mm. The leakage rate of the O-ring could be effectively contained because of the blocking function of the sidewall. This implies that a reasonable sidewall gap can effectively improve the sealing performance of the O-ring.

3.3.2. Thermal cycling test

To further verify and evaluate the proposed approach, which was obtained in accordance with the results of the numerical analysis, a thermal cycling test was performed, based on the alternation of hot with cold. The geometrical parameters of

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Table 4 - Main geometrical parameters of the O-ring in the simulation experiment.

1 400 LJ-.-1-,-1-.-1-.-1-.-i_J

0.0 0.2 0.4 0.6 0.8 1.0

Sidewall gap (mm)

Fig. 19 - Maximum Mises stress and its location under different sidewall gaps.

the O-ring and structure parameters of the groove used in the experiment are listed in Table 4. During the aforementioned test, the O-ring sealing system experienced a complete cyclic process, from rising temperature and pressure to maintaining the temperature and pressure (2 hours, 15.5 MPa, respectively) to lowering the temperature and pressure. The cyclic process was repeated 20 times.

Figs. 21A and 21B illustrate the change curve of the test temperature and test pressure with time at the first cycle and the 20th cycle, respectively. The experiment results showed that the temperature of the medium was close to 345 °C when the pressure of the medium was approximately 15.5 MPa. During the whole test process, there was no leakage of the sealing system when the compression ratio was approximately 16%. However, failure occurred when the compression ratio increased to 25% and the leakage rate was approximately 2.3 L/h. This finding can be explained through the analysis of the surface morphology and simulation of the deformation in Fig. 9. In addition, numerical analysis showed that when the sidewall gap reached a suitable value (i.e., 5 = 0.5 mm), better sealing performance of the O-ring could be achieved. This indicated that the experiment results were consistent with the results of the numerical analysis.

Parameters Value

Compression ratio, C 16%, 25%

Outer diameter, D 650 ± 0.5 mm

Diameter of cross-section, d 12.7 ± 0.02 mm

Wall thickness 1.35 ± 0.01 mm

Sidewall gap 0.5 ± 0.01 mm

4. Conclusion

The major results and conclusions are as follows:

(1) Parameter optimization based on finite element analysis was conducted. When the compression ratio is controlled within 12% to 16%, the diameter of the cross-section (d) is approximately 12.7 mm, the wall thickness is 1.35-1.65 mm, the effective groove depth on the flange is approximately 11 ± 0.25 mm, the sidewall gap is approximately 0.5 mm, and the O-ring can obtain a better line specific pressure and sufficient resilience. Scaled samples with an outer diameter (D) no less than 650 mm can be used to perform a seal performance test in a verification experiment.

(2) By optimizing the geometrical parameters of the O-ring and structure parameters of the groove, the sealing performance was validated by the air tightness test and thermal cycling test on scaled samples with an outer diameter of 650 mm. In particular, the results of the thermal cycling test showed that an O-ring with optimized parameter design can meet the sealing requirements of the simulated operating conditions of RPV.

(3) If the compression ratio is too large or the diameter of the cross-section or sidewall gap is too small, a concavity at the sealing surface can occur and the sealingperformance will be reduced. Therefore, there are strict requirements for the installing process and the manufacturing process of the O-ring to obtain a better seal performance. This research could provide a reference for the deformation characteristics and sealing performance of metallic O-rings in a RPV. However, the theoretical proposed model

Fig. 20 - Change in the leakage rate. (A) At different compression ratios. (B) At different sidewall gaps.

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Fig. 21 - The change curve of the test temperature and test pressure with test time. (A) The first cycle. (B) The 20th cycle.

ignores the influence of the thermal and mechanical deformations of the RPV. Further investigations could be conducted based on this work.

Conflicts of interest

All authors have no conflicts of interest to declare. Acknowledgements

The authors would like to thank Dr J.H. Liu from Southwest Jiaotong University (Chengdu, China) for the helpful discussion and assistance. The authors are grateful for the financial support of the Public Projects of Zhejiang Province (Hangzhou, China; No. 2015C31120), the National Science Foundation of China (Beijing, China; No. 51305398).

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