Modeling gas flow in a looped thermosyphon with a 1 D low-Mach number expansion

This article provides numerical results for a laminar gas flow at small velocities in the “looped thermosyphon”, or “natural circulation loop” : a closed configuration composed of two horizontal adiabatic pipes and two vertical pipes with different fixed wall temperature. To this extent, following Paolucci (1982; 1994) we construct a low-Mach number model capable of taking into account the periodicity and the discontinuities intrinsic to this configuration. This compressible model is richer than the Boussinesq model since it describes the pressure variation and is adapted to the description of flows driven by large temperature gradients. We settle averaged equations through the pipes of small radius compared to the length, this gives a one dimensional system of equations of mass, momentum and energy with two pressures, a dynamical one and a thermodynamical one only function of time. We construct a quasi-exact solution in a laminar and steady-state regime. We approach the low-Mach averaged 1D Model with a coupled numerical method based on the characteristics method considering the presence of the periodic conditions and the discontinuous gravity term with Dirac distributions as derivatives at the corners. The numerical results are confronted and validated by the aforementioned reference solution to determine their accuracy.