Possible effect of flow velocity on thawing rock-water-ice systems under local thermal non-equilibrium conditions

摘要

Climate change causes thawing of many permafrost regions, increasing the rockfall and landslide hazard when the cementing ice melts and slopes become unstable. The thermo-hydro-mechanical processes are strongly coupled and complex to describe in those intrinsic multi-phase systems. So far, thermal models often utilize the local thermal equilibrium approach, assuming that all three phases (solid rock or soil, liquid water and ice) are in thermal equilibrium. While this approach is very tempting due to its easy implementation, there are situations especially during thawing in which temperature gradients exist between the involved phases. In such cases, the local thermal equilibrium approach has to be replaced by the more complex local thermal non-equilibrium approach in which the thermodynamic state of each phase is described by its own temperature. In those models, the heat transfer between the phases is described explicitly in dependence of the heat transfer coefficient and the contact area. Parameterization of the heat transfer coefficient is a challenging task and mostly relies on empirical values and relationships. Most models using the local thermal non-equilibrium approach utilize a constant heat transfer coefficient. However, experiments under geothermal temperature conditions prove that the heat transfer coefficient depends, among others, on flow velocity. This is of special interest as strong dynamics are characteristic for thawing system which impose a unique challenge to heat transfer models. For example, the volume fraction of the liquid domain increases significantly during thawing of rock-ice systems due to the melting of the ice phase. This again, directly influences flow velocity. In this work, the possible effect of a velocity dependent heat transfer coefficient on thawing rock-water-ice systems is investigated. With higher flow velocity, advection effects of the intruding fluid become more significant but also heat transfer is increased. When the intruding liquid water is colder than the surrounding rock, the melting rate is maximum for a specific flow velocity, as advection of cold water and heating from the rock counteract. While this is a purely synthetic study and no experimental data yet exists for validation of the proposed scheme, this study indicates the existence of a way more complex interaction between liquid fluid flow and melting processes as previously expected and way beyond state-of-the-art modeling.