Upscaling of superfluid helium flow in porous media

A PISO-like algorithm to simulate superfluid helium flow with the two-fluid model

“…This can be used to significantly reduce the CPU time and, more fundamentally, this suggests also that some kind of decomposition technique in terms of macro-scale variables and deviations can be performed in the context of upscaling. This has already been used in the paper by Allain et al (2010) in the Landau regime, our results indicate that this can be extended to more inertial flows with also significant Gorter-Mellink effects.…”

“…For coupled, non-linear equations, developing a macro-scale theory may benefit strongly of the quantitative view offered by direct pore-scale numerical results, which point in the right direction for performing necessary approximation. Such an illustration of this kind of approximation can be found in the paper by Allain et al (2010) We can notice in Fig. 13 that the temperature increase is much higher (30 times) than in the case of a straight capillary tube.…”

Experimental investigation of heat transfer through porous media in superfluid helium

“…The equations valid in a particular phase are spatially smoothed in order to obtain a set of equations valid everywhere. The volume averaging method has been applied to the superfluid helium two-fluid model [20]. This method was applied considering the equations in the Landau regime with no heat transfer between the solid and the superfluid.…”

“…More details can be found in [20]. The principle of the experimental set-up is presented in Figure 3.…”

Technical Notes on Volume Averaging in Porous Media I: How to Choose a Spatial Averaging Operator for Periodic and Quasiperiodic Structures

“…This approach has proven successful in studying many different problems in porous media sciences, from Darcy's law (Whitaker 1986) in geological formations to superfluid flow in engineering structures (Allain et al 2010), the formulation of macroscale boundary conditions between porous and fluid media (OchoaTapia and Whitaker 1995;Valdés-Parada et al 2007) or even mass transport in communities of microorganisms (Davit et al 2013;Wood and Whitaker 1998). The contributions of many authors over a time span of several decades have led to significant evolutions of the original approach.…”