H. Marschall | Searcharxiv

arXiv2021

Large eddy simulation of flow in porous media: Analysis of the commutation error of the double-averaged equations

The continuum approach employing porous media models is a robust and efficient solution method in the area of the simulation of fixed-bed reactors. This paper applies the double-averaging methodology to refine the continuum approach, opening a way to alleviate its main limitations: space-invariant averaging volume and inaccurate treatment of the porous/fluid interface. The averaging operator is recast as a general space-time filter allowing for the analysis of commutation errors in a classic large eddy simulation (LES) formalism. An explicit filtering framework has been implemented to carry out an a posteriori evaluation of the unclosed terms appearing in the double-averaged Navier-Stokes (DANS) equations, also considering a space-varying filter width. Two resolved simulations have been performed. First, the flow around a single, stationary particle has been used to validate derived equations and the filtering procedure. Second, an LES of the turbulent flow in a channel partly occupied with a porous medium has been realized and filtered. The commutation error at the porous-fluid interface has been evaluated and compared to the prediction of two models. The significance of the commutation error terms is also discussed and assessed. Finally, the solver for DANS equations has been developed and used to simulate both of the studied geometries. The magnitude of the error associated with neglecting the commutation errors has been investigated, and an LES simulation combined with a porous drag model was performed. Very encouraging results have been obtained indicating that the inaccuracy of the drag closure overshadows the error related to the commutation of operators.

physics.flu-dyn↗

arXiv2019

Capillary Rise -- A Computational Benchmark for Wetting Processes

Four different numerical approaches are compared for the rise of liquid between two parallel plates. These are an Arbitrary Lagrangian-Eulerian method (OpenFOAM solver interTrackFoam), a geometric volume of fluid code (FS3D), an algebraic volume of fluid method (OpenFOAM solver interFoam), and a level set approach (BoSSS). The first three approaches discretize the bulk equation using a finite volume method while the last one employs an extended discontinuous Galerkin discretization. The results are compared to ODE models which are the classical rise model and an extended model that incorporates a Navier slip boundary condition on the capillary walls and levels at a corrected stationary rise height. All physical parameters are based on common requirements for the initial conditions, short simulation time, and a non-dimensional parameter study. The comparison shows excellent agreement between the different implementations with minor quantitative deviations for the adapted interFoam implementation. While the qualitative agreement between the full solutions of the continuum mechanical approach and the reference model is good, the quantitative comparison is only reasonable, especially for cases with increasing oscillations. Furthermore, reducing the slip length changes the solution qualitatively as oscillations are completely damped in contrast to the solution of the ODE models. To provide reference data for a full continuum simulation of the capillary rise problem, all results are made available online.

math.NA↗