Explicit Numerical Modeling of Heat Transfer in Glacial Channels

Abstract:

Turbulent flow and heat transfer of water in englacial channels is explicitly modelelled and the numerical results are compared to the most commonly used heat transfer parameterization in glaciology, i.e. the Dittus–Boelter equation. The three-dimensional flow is simulated by solving the incompressible Navier–Stokes equations utilizing a variational multiscale method (VMS) turbulence model and the finite-element method (i.e. Elmer-FEM software), which also solves the heat equation. By studying a wide range of key parameters of the system, e.g. channel diameter, Reynolds number, water flux, water temperature and Darcy–Weisbach wall roughness (which is explicitly represented on the wall geometry), it is found that the Dittus–Boelter equation is inadequate for glaciological applications and a new, highly suitable heat transfer parameterization for englacial/subglacial channels will be presented. This new parameterization utilizes a standard combination of dimensionless numbers describing the flow and channel (i.e. Reynolds number, Prandtl number and Darcy–Weisbach roughness) to predict a suitable Nusselt number describing the effective heat transfer and thus can be readily used in existing englacial/subglacial hydrology models.