Seal surface topography typically consists of global-scale geometric features as well as local-scale roughness details and homogenization-based approaches are, therefore, readily applied. These provide for resolving the global scale (large domain) with a relatively coarse mesh, while resolving the local scale (small domain) in high detail. As the total flow decreases, however, the flow pattern becomes tortuous and this requires a larger local-scale domain to obtain a converged solution. Therefore, a classical homogenization-based approach might not be feasible for simulation of very small flows. In order to study small flows, a model allowing feasibly-sized local domains, for really small flow rates, is developed. Realization was made possible by coupling the two scales with a stochastic element. Results from numerical experiments, show that the present model is in better agreement with the direct deterministic one than the conventional homogenization type of model, both quantitatively in terms of flow rate and qualitatively in reflecting the flow pattern.
During operation, the mating surfaces of a metal-to-metal seal typically undergo significant plastic deformation, which in turn can have beneficial effect on its performance. In previous studies, it has, for instance, been shown that plastic deformation can provide for better sealing during unloading. Those studies did, however, only consider flow through unrealistically small domains. Therefore, it is possible that this might be a size effect, which would not be apparent in a real situation with a much larger domain. In this paper, we develop a model which can handle real-sized seal domains at the same time as fine details of the surface topography. More precisely, we construct a two-scale model, in which the global scale represents the seal domain and where the influence of the fine details at the local scale are represented by a stochastic element. By means of this stochastic two-scale model, we show that the beneficial effect associated with the plastic deformation persists also when real-sized seal domains are considered.
This study considers flow through the gap left between two surfaces during unloading, in other words, when an applied load is gradually reduced after loading to a state where plastic deformation occurs. In particular, the permeability of the gap is studied. It was found that a substantial reduction of the applied load is required before the permeability starts to increase significantly. The explanation for this phenomenon is given by the combination of components with different wavelengths present in the surface. Components with long wavelengths deform elastically and those with shorter wavelengths may also deform plastically. We found that plastic deformation acts to keep the permeability nearly constant at the beginning of the unloading and elastic spring-back is responsible for the rapid increase at lower loads. This principle constitutes a basis for the strategy that was developed in order to predict the load at which the rapid increase of permeability starts.
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