This benchmark is testing the extended version of a classical heat conduction equation termed ‘heat conduction equation with phase change’ (with a slight abuse of notations, we also call it simply ‘T+freezing’ equation). The initialboundary value problem (IBVP) for this equation models such processes as ice formation and ice melting in watersaturated porous medium. Since the equation is strongly nonlinear in the temperature variable $T$ to be solved for and contains multiple parameters which may affect accuracy of finite element discretization, a carefully designed model and code verification must be performed.
Below, we model heat transfer process – focusing specifically on ice formation – in a cylindrical soil specimen around a borehole heat exchanger (BHE) which contains a refrigerant of subzero temperature. This (negative) temperature is used to prescribe a Dirichlet boundary condition on the specimen boundary adjacent to the BHE, what triggers cooling and consequent freezing of watersaturated soil whose initial temperature is positive.
Simulations are performed using both our OpenGeoSys platform and the FreeFem++ open source finite element code (in the following, simply termed OGS and FF++, respectively), thus enabling crossverification of the numerical codes.
The detailed IBVP problem description for the T+freezing equation, geometric setup, material and model parameters used in the implementation can be found in this document this PDF document. The figures below are taken from this documentation and serve for illustrative purposes to give a hint about the modeled process and simulations outcome.
In the corresponding OGS project file m16m15projectB.prj
the time discretization is different for the “real case study” whose results are presented in the documentation and for the ctest
case, and must be altered manually.
This article was written by Tymofiy Gerasimov. If you are missing something or you find an error please let us know.
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