Two-scale stochastic modelling and analysis of leakage through metal-to-metal seals

A seal is a commonly used machine element whose function is to preventthe flow of a fluid from a high to a low pressure region. Metal-to-metalseals, in particular, are used whenever extreme conditions prevent theuse of less expensive rubber seals. Situations where such extreme condi-tions may be encountered are found, for example, in oil wells and nuclearpower plants. In such applications, the failure of a metal-to-metal sealcan become catastrophic, as it might mean the leakage of hazardousfluids to the environment. In order to minimize the risk, it is critical tounderstand the mechanisms controlling the seal’s performance and,if possible, be able to predict capability to prevent leakage on before-hand. Not surprisingly, the surface topography plays a crucial role hereand therefore requires careful consideration when conducting studies ofthis kind. Indeed, it has been shown that even very small details in thetopography (of size of the order of micrometres) can have a large effecton the performance of the whole seal (of size of the order of centimetresor larger). Another complicating factor is the topography’s stochas-tic nature, which makes even the identification of the relevant detailschallenging. Modelling is, in this context, a desirable approach, as itprovides the possibility to easily zoom in those fine details as well asisolate individual parameters. Moreover, it can provide for a predictionon the expected leakage.This work focuses primarily on the development of a model suitablefor studying the mechanisms controlling the performance of metal-to-metal seals and to enable prediction of leakage. To accomplish this, amodel that follows a two-scale approach is proposed. More precisely,the small details in the topography are considered in a local problemconnected to a highly resolved local-scale domain, while the componentlevel features are considered in a global problem allowing for a coarsegrid discretisation of the corresponding global-scale domain. During the present work it was also found that realistic results can only be obtainedif the model explicitly considers the surface topography’s stochastic na-ture. The model was first developed for liquids and was based on theassumption of incompressible and iso-viscous flow. Further work, withthe objective to enable studies of more complex type of flow situations,resulted in a versatile transformation translating results for incompress-ible and iso-viscous to compressible and piezo-viscous fluids and viceversa. This means that, the flow of gases and other more complex fluidscan be studied by combining the model for the simplistic incompressibleand iso-viscous flow with this newfound transformation.Using the model developed, the sealing performance of metal-to-metal seals during load cycling, i.e., by gradually increasing the load toa certain value and then releasing it again, is studied. The scope of thisstudy is to assess how the plastic deformation that the metal surfacesundergoes during the loading phase can affect the leakage during unload-ing. It is shown that this results in a change of the original topographythat may lead to a better sealing performance during unloading. Themain result obtained is, however, that given the right conditions, the ap-plied load can be released considerably (even down to half of the reachedbefore starting the unloading) with only a small increase in leakage asa result. This shows the seal’s capability to prevent leakage evenif an unexpected reduction of load occurs and is therefore is a valuabledescription of the robustness of the seal