A Multi‐Phase Heat Transfer Model for Water Infiltration Into Frozen Soil

In many regions, water infiltration into frozen soil is a critical process. Frozen soil is known to have a substantially reduced infiltration capacity, resulting in surface water runoff. This surface runoff is often associated with erosive behavior posing a potential natural hazard as it facilitates snow avalanches and debris flow, especially in springtime when rainfall and snowmelt coincide. As infiltration capacity depends on the ice content within the porous soil, thermal and hydraulic processes are strongly coupled. The involved phases during water infiltration into frozen soil are initially not in a local thermal equilibrium as the infiltrated water is warmer than the frozen soil. The duration of the temperature differences is yet to be determined. To adequately describe this thermal state, a local thermal non‐equilibrium (LTNE) model needs to be applied, which accounts for separate phase temperatures and describes the heat transfer between the phases explicitly. While LTNE models are common in more simple setups of saturated porous media flow, in this work, a multi‐phase LTNE model for water infiltration into a partly saturated, frozen soil is presented. All required parameters, such as heat transfer area and heat transfer coefficient are discussed and derived based on a capillary tube model. The theoretical model is implemented into a numerical model and compared to experimental data available from literature. Substantial differences of up to 0.5 ° C between phase temperatures during freezing and melting are observed after hours of infiltration and are especially pronounced around the freezing front.