Journal
CANADIAN JOURNAL OF CHEMICAL ENGINEERING
Volume 100, Issue 12, Pages 3531-3547Publisher
WILEY
DOI: 10.1002/cjce.24598
Keywords
boundary slip; computational fluid dynamics; hydrodynamic eigenmodes; instationary channel flow
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Funding
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [B02 265191195-SFB 1194]
- Projekt DEAL
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This study proposes a fast, automated, and rigorously verified open-source solution for computing the hydrodynamic eigenmodes of a two-dimensional channel flow. The numerical results validate analytically derived asymptotic power laws for the leading hydrodynamic eigenmode in the limiting cases of small and large slip.
The transient start-up flow solution with slip is a useful tool to verify computational fluid dynamics (CFD) simulations. However, a highly accurate, open-source black box solution does not seem to be available. Our method provides a fast, automated, and rigorously verified open-source implementation that can compute the hydrodynamic eigenmodes of a two-dimensional channel flow beyond the standard floating-point precision. This allows for a very accurate computation of the corresponding Fourier series solution. We prove that all roots are found in all special cases for the general flow problem with different slip lengths on the channel walls. The numerical results confirm analytically derived asymptotic power laws for the leading hydrodynamic eigenmode and the characteristic timescale in the limiting cases of small and large slip. The code repository including test cases is publicly available (DOI: 10.5281/ zenodo.6806351). The Navier slip boundary condition for numerical simulations in OpenFOAM is also publicly available (DOI: 10.5281/zenodo.7037712).
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