Numerical simulation of the nitrogen boil-off recondensation in hybrid cooling devices for HPGe detectors

Abstract

This paper describes the results of a complex simulation of nitrogen boil-off recondensation in a hybrid cooling device for High Purity Germanium (HPGe) detectors. The OpenFOAM platform-based software was used. The proposed finite-volume axisymmetric 2D model combines cooling processes occurring in the considered three-phase medium, including a liquefier condenser (solid), nitrogen boil-off (gas) and the resulting condensate (liquid). At the beginning of the simulation condenser and gas temperatures are set above the condensation point while the end time is set such that the system reaches a quasi-steady state. For conical and hemispherical condensers, the energy consumption for the following processes occurring in the operating mode such as: condenser cooling; cooling of adjacent boil-off nitrogen vapors; their condensation; the gravity-driven flowing; condensate film subcooling and subsequent partial re-evaporation from its surface are compared. The visualizations of the temperature field of the finite-volume model and the velocity vectors of nitrogen vapors adjacent to the condenser are presented. The calculated integral mass recondensation rates were confirmed experimentally on a commercial hybrid cooling device, taking into account the actual equivalent characteristics of the liquefier on the Stirling cryocooler used.

Practical aspects of hybrid cooling devices engineering design for HPGe detectors

“…The research presented below is a continuation of the analysis of thermal processes in the hybrid cooling device, which was initiated by investigation of the 𝐿𝑁 2 boil-off recondensation [23], where the OpenFOAM software based on the Finite Volume Method was used. The proposed 2D axisymmetric computational model made it possible to simulate the recondensation process for condensers of various shapes and confirm the presence of a laminar-wave area in the flow of gravity driven condensate.…”

“…In recondensation mode, the cryocooler cools the condenser below the nitrogen boiling point. At the same time, in addition to the total heat flux determined by recondensation processes, there is a parasitic heat flux from the warmer walls of the bellows, which increases heat load on the cryocooler [23]. In the power interruption mode, the cryocooler turns into a passive component, the temperature of the condenser increases significantly and, as a rule, the heat flux is directed to the bellows wall, increasing heat gain into the Dewar.…”

“…The heat flux𝑄 recond depends on the difference between the temperature of the condenser 𝑇 cold and the nitrogen boiling point 𝑇 0 [25,26]. If 𝑄 recond ≤ 15 W, which is typical for hybrid cooling devices for HPGe detectors, the 𝑇 0 − 𝑇 cold difference does not exceed 1-2 K [23]. Therefore, it is permissible to accept 𝑇 cold 𝑇 0 which simplifies the expressions (3.8).…”