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MATHEMATICAL MODELS. Helium flow modelling
The core of the program consists in the description of the helium flow in channels, possibly coupled (exchange of mass and energy), also possibly coupled with walls (or conductors) which can also be coupled to each other. The helium flow model channel simulates transient parameters of a compressible helium flow inside a channel. Channel is described by a set of 1-D equations of continuity, momentum and energy conservation laws completed with the transverse mass, momentum and energy transfer terms to take into account the thermal-hydraulic coupling with different flows and solid materials. Generally, the helium flow in a channel can simultaneously have a thermal contact with some various solid materials and helium in other channels. Besides, different helium flows inside channels can be hydraulically coupled between themselves in the longitudinal direction (due to the transverse holes) as, for example, in the Cable-In-Conduit Conductor (CICC) with a central channel. The final set of equations describing a transient process for helium flow in the i channel in terms of interaction with flows in k channels and m conductors has a form:
To determine a transverse mass flux it is assumed that the pressure difference between coupled flows is small enough. In such approach the local transverse mass and enthalpy flux from k to i flow can be obtained in the following simple form:
where Ski is a coefficient with the dimensionality of cross-section area per unit of length between k and i flows. As the transverse mass flux from k flow is suggested to be normal to i flow, the momentum transport term is negligible (i.e.  ).
Such description of the transfer processes between flows is applicable to modelling mass and energy exchange if an assumption of a small pressure drop between flows is valid (transverse cross area is large enough). The advantage of this model is a possibility to analyze the influence of transverse coupling on thermal and hydraulic parameters of coupled flows and to estimate the transverse mass and energy transport term.
The following boundary conditions are used to close the system (1)-(3). The helium pressures at the ends of the channel are supposed to be identical to pressures in joined collectors. When helium enters the channel, the helium enthalpy at an appropriate end of the channel is assumed to be equal to the enthalpy in the joined collector. At the closed end of the tube the helium velocity assumed to be zero.
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