Evaluation of leakage rates of static seals based on elastic-plastic contact theories and seepage theories
LI Shunyang1, WAN Li1, GUI Nan1, YANG Xingtuan1, TU Jiyuan2, JIANG Shengyao1
1. Institute of Nuclear and New Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China; 2. School of Engineering, Royal Melbourne Institute of Technology University, Melbourne VIC 3083, Australia
Abstract：[Objective] The unintended leakage that occurs on the interface between the static seal and the flange leads to potential environmental pollution, economic loss, and safety accidents. The evaluation of leakage rates is a major concern in the industrial field. However, due to the problem's complexity, the leakage rates are usually calculated by a simplified or equivalent model, which deviates from the actual state of static seals.[Methods] In this study, a semi-analytical model is proposed to evaluate the leakage rates for static seals using the contacting model and seepage theory. The leakage rate is expressed as a function of working conditions, fluid properties, and leakage channel permeability. Working conditions, such as fluid pressure and fluid properties, including viscosity, are input parameters, while permeability needs to be inferred. Therefore, the deformation of asperities on the surfaces of static seals is calculated in advance by the elastic-plastic contact model. The porosity and permeability are calculated afterward. Several assumptions are made to simplify the calculations. First, the contacting process between the flange and the static seal is equivalent to the process of a rigid and rough surface. The distribution of asperity heights is then described using a Gaussian function, which is suitable for common materials. Finally, the leakage channel is assumed to be self-similar since the observation scale is much smaller than the characteristic scale of leakage channels. This assumption enables the relationship between permeability to porosity to be expressed explicitly.[Results] The deformation of asperities under different loads was investigated using this model. It was shown that the reduction of the dimensionless height of the leakage channel results in a lower porosity, and a larger load was required. During this process, the portion of the asperities subjected to plastic deformation also increased. The porosity of the leakage channel decreased rapidly under a lower load. However, the porosity decreased at a slower rate as the load further increased because the asperities became difficult to deform. The total deformation of the rough surface was less relative to the plasticity index compared to the pure elastic model because the former considers the rearrangement of local stress by interacting asperities and the displacement of the reference plane. The plasticity index was used to examine the deformation of the rough surface in relation to the surface topology. Although asperities with a higher plasticity index were more likely to undergo plastic deformation, the total surface deformation was reduced in this case. Several relationships between porosity and permeability were presented and validated. The relation under the assumption of self-similarity agreed well with the literature results, whereas the Kozeny-Carman relation was less accurate because it was based on an assumption deviating from the actual geometry of the leakage channel. When the load increased, the permeability of the leakage channel decreased, and thus the leakage rates reduced.[Conclusions] The value of leakage rates can be inferred by the model proposed in this study as long as the working condition and material properties are given. The model can explain the effects of load and surface topology. The model can be applied to various types of static seals, such as gaskets and rings, since it focuses on the contacting process, which is irrelevant to the structural design. However, the model's predictability decreases for seals with uneven stress or heavily worn surfaces.
李顺洋, 万力, 桂南, 杨星团, 屠基元, 姜胜耀. 基于弹塑性接触和渗流模型的静密封泄漏计算[J]. 清华大学学报（自然科学版）, 2023, 63(8): 1264-1272.
LI Shunyang, WAN Li, GUI Nan, YANG Xingtuan, TU Jiyuan, JIANG Shengyao. Evaluation of leakage rates of static seals based on elastic-plastic contact theories and seepage theories. Journal of Tsinghua University(Science and Technology), 2023, 63(8): 1264-1272.
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2023, Vol. 63 
