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This article is originally published on the WeChat official account \"ANSYS Analysis and Design Professionals\". We respect original works; for more content, please follow the official account. 1. Background introduction? Sealing reliability is an important guarantee for the safe operation of pressure vessels, and a rational and reliable sealing structure design is a crucial aspect of pressure vessel design. Compared to medium and low-pressure vessels, high-pressure vessels present greater challenges in terms of sealing. To address this issue, various high-pressure sealing structures have been developed, which can be divided into forced-sealing and self-tightening types. These include flat gasket seals, octagonal gasket seals, double-cone seals, Karrari seals, Wood seals, etc. Among them, flat gasket seals, Karrari seals, and octagonal gasket seals belong to the forced-sealing category, while double-cone seals and Wood seals fall under the self-tightening category. Although the commonly used octagonal gasket sealing structure possesses certain self-sealing properties, the height of the annular gasket used is relatively small, and the gasket lacks the ability to compress radially or rebound, resulting in very limited self-sealing effect; therefore, such structures are currently designed as forced-sealing types. 2. Forced octagonal gasket + double-cone sealing principle = self-tightening octagonal gasket sealing structure? The self-tightening octagonal gasket sealing structure is similar to an octagonal gasket, and its sealing principle is akin to that of a double-cone sealing structure. The sealing structure is shown in Figures 1 and 2: https://pic4.zhimg.com/80/v2-99d986ca8ae551049dff72c11646c09e_hd.jpg Figure 1: Structure of the self-tightening octagonal gasket and the sealing groove; https://pic3.zhimg.com/80/v2-ea1058aa851268eca0297171e6acabcd_hd.jpg Figure 2: Schematic diagram of the assembly of the self-tightening octagonal gasket with the flange. Features of the self-tightening octagonal gasket structure: [1] The inner and outer half-cone angles of both the self-tightening octagonal gasket and the sealing groove are 23° ； 【2】The self-tightening octagonal gasket and the conical surface on the outside of the sealing groove form a sealing surface; this is a sealing structure similar to the double-cone sealing structure. Soft metal gaskets can be inserted between this sealing surface of the octagonal gasket and the sealing groove, or graphite can be bonded to the outer conical surface of the octagonal gasket ； 【3】The conical surface on the inner side of the sealing groove serves as the supporting conical surface for the octagonal gasket, and is used to control the maximum allowable radial deformation of the octagonal gasket ； 【4】There is a radial gap between the center line of the octagonal gasket cross-section and the center line of the seal groove cross-section. Once the sealing structure is pre-tightened, the octagonal gasket is radially elastically compressed until it presses against the inner conical surface of the sealing groove, as shown in Figure 3 below. This radial clearance is equivalent to the clearance between the biconical ring and the supporting end face in the biconical seal structure. 【5】Compared to the commonly used forcibly sealed octagonal gaskets, self-tightening octagonal gaskets have a larger height dimension in order to meet the requirement for sufficient self-tightening force and ensure sealing performance. https://pic3.zhimg.com/80/v2-4433443d1c4b60cac173f9aa55faaf33_hd.jpg Figure 3 shows the elastic compression deformation of the self-tightening octagonal gasket before and after bolt pre-tensioning. As shown in Figure 3, in the assembled state before bolt pre-tensioning, there is a gap between the center circle of the octagonal gasket and the center circle of the sealing groove; this is the radial gap g indicated in the figure. After the bolts are pre-tensioned, the centers of these two circles align, and the internal conical surface of the gasket comes into contact with the internal conical surface of the sealing groove. 3. Comparison of the differences among the three high-pressure sealing structures? The self-tightening octagonal gasket sealing structure combines the advantages of both double-cone sealing and traditional octagonal gasket sealing, and is a type of self-tightening sealing structure. The differences in the main structural parameters and sealing characteristics between it and traditional octagonal gaskets as well as biconical sealing structures are shown in Table 1. https://pic4.zhimg.com/80/v2-bf4b4ef1e919542b1a40b4b0ed8dfd3f_hd.jpg Table 1: Elastic compression deformation of self-tightening octagonal gaskets before and after bolt pre-tensioning. 4. Verification through finite element analysis of the self-tightening octagonal gasket model? 【Design Conditions】: The structural parameters for the finite element simulation of the self-tightening octagonal gasket seal are shown in Table 2. https://pic3.zhimg.com/80/v2-b6b210fbc123dc94718b9c2c8e765b42_hd.jpg Table 2: Main geometric dimensions of the sealing structure. [Material and performance parameters]: According to GB/T150-2011 \"Pressure Vessels\", the gasket pressure ratio for metal gaskets is 124.1 MPa, and the gasket coefficient m = 5.5; the pre-tightening load per bolt is calculated to be 131542 N. The material and performance parameters of the various components of the sealing structure are shown in Table 3. https://pic1.zhimg.com/80/v2-77b27a763056b3040552d3d1efdca6f7_hd.jpg Table 3: Materials and performance parameters of various components in the sealing structure. [Model establishment and element selection]: To reduce the amount of computation, and taking into account the periodic symmetry of the geometric structure, loads, and boundary conditions, a 1/20 scale model was used to create the finite element model. This model uses Solid185 solid elements and PRETS179 pre-tensioning elements for mesh generation; all volumes are meshed using hexahedra, while the gasket and the areas in direct contact with it have a finer mesh to ensure the convergence of the structure and the accuracy of the solution results. All components in the model are assumed to be linearly elastic materials. The 3D model of the structure and its meshing are shown in Figures 4 and 5. https://pic2.zhimg.com/80/v2-a1c8e0208c282414c9ae24f75a974962_hd.jpg Figure 4: 1/20 scale 3D finite element model https://pic2.zhimg.com/80/v2-9a42bb399baeb22e1542a91acfffc948_hd.jpg Figure 5: Fine-grained meshing 【Application of loads and boundary conditions】: 【Internal pressure and equivalent loads】 A uniform pressure of 15 MPa is applied to the inner surface of the structure, while an equivalent pressure of -65.44 MPa is applied to the upper end face of the cylinder ； 【Pre-tightening load】A pre-tightening load is applied to the nodes of the pre-tightening unit, with the bolt pre-tightening force increasing from zero to the specified value ； [Rigid body displacement restriction] To prevent axial displacement of the model, the Z-direction displacement of the end face of the lower cylinder is constrained ； 【Symmetry constraint】Apply a symmetry constraint on the symmetry plane of the 1/20 model ； [Contact Pair Settings] In the analysis, the Contact174 contact element and the Targe170 target element are used to define the contact pairs; a total of 6 pairs of contacts between planes are established in the model, namely the contact between the nut and the upper flange, the contact between the nut and the lower flange, and 4 pairs of contacts between the 4 conical surfaces of the gasket and the sealing groove ； 【Application of load steps】Since contact nonlinear analysis is involved in the simulation process, to ensure the convergence and accuracy of the calculation results, the load is applied in multiple steps; the contact constraint algorithm used in the analysis is the augmented Lagrangian method. The application of detailed loads and boundary conditions is shown in Figure 6. https://pic4.zhimg.com/80/v2-3da35a6982c93cceeae1003a3e63c130_hd.jpg Figure 6 Load and boundary conditions 5. Analysis of finite element simulation results? The equivalent stress maps for the overall structure and the gaskets are shown in Figures 7 and 8 respectively: https://pic3.zhimg.com/80/v2-7654aeee90b33482fbe371572708ea57_hd.jpg Figure 7: Stress distribution map of the overall structure. https://pic4.zhimg.com/80/v2-811f379510256ccbe49f708f98adb6e5_hd.jpg Figure 8: Equivalent stress distribution map of the gaskets. As can be seen from Figure 7, the maximum equivalent stress in the structure is 287.834 MPa, and it occurs at the contact surface between the gasket and the flange; this value is below the material’s yield strength ； Due to the internal pressure, the stress in the bolts is unevenly distributed ； As can be seen from Figure 8, the maximum equivalent stress of the gasket is 83.64 MPa, which is below the yield strength of the gasket material, and the maximum stress occurs on the sealing surface side of the gasket. https://pic3.zhimg.com/80/v2-0d98b1853e53b3b6d92206fd68ff1a08_hd.jpg Figure 9: Curve of bolt axial force versus internal pressure. https://pic2.zhimg.com/80/v2-3f8cc3290bd53ce4d7dc13c78a892487_hd.jpg Figure 10: Curve of gasket stress versus internal pressure. Figure 9 shows the curve of bolt axial force as a function of the applied internal pressure, and it is compared with the results obtained from theoretical calculations. It can be seen that the finite element simulation results are in good agreement with the theoretical calculation results ； Figure 10 shows the graph of compressive stress on the gasket sealing side versus internal pressure. During the initial stage of pressurization, the stress on the gasket sealing surface decreases as the internal pressure increases; once the internal pressure reaches a certain value, the stress on that surface increases linearly with further increases in pressure. The stress on the sealing surface side of the model gasket is always greater than the operating sealing pressure, indicating that the sealing performance of the gasket is reliable during the pressurization process.