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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 22 Jun 2024 06:14:02 GMT2024-06-22T06:14:02ZModal and non-modal linear stability of Poiseuille flow through a channel with a porous substrate
http://hdl.handle.net/10985/18038
Modal and non-modal linear stability of Poiseuille flow through a channel with a porous substrate
GHOSH, Souvik; BREUGEM, Wim-Paul; BRANDT, Luca; LOISEAU, Jean-Christophe
We present modal and non-modal linear stability analyses of Poiseuille flow through a plane channel with a porous substrate modeled using the Volume Averaged Navier–Stokes (VANS) equations. Modal stability analysis shows the destabilization of the flow with increasing porosity of the layer. The instability mode originates from the homogeneous fluid region of the channel for all the values of porosity considered but the governing mechanism changes. Perturbation kinetic energy analysis reveals the importance of viscous dissipation at low porosity values while dissipation in the porous substrate becomes significant at higher porosity. Scaling analysis highlights the invariance of the critical wavenumber with changing porosity. On the other hand, the critical Reynolds number remains invariant at low porosity and scales as Rec ∼ (H/δ) 1.4 at high porosity where δ is the typical thickness of the vorticity layer at the fluid– porous interface. This reveals the existence of a Tollmien–Schlichting-like viscous instability mechanism at low porosity values, and Rayleigh analysis shows the presence of an inviscid instability mechanism at high porosity. For the whole range of porosities considered, the non-modal analysis shows that the optimal mechanism responsible for transient energy amplification is the lift-up effect, giving rise to streaky structure as in single-phase plane Poiseuille flow. The present results strongly suggest that the transition to turbulence follows the same path as that of classical Poiseuille flow at low porosity values, while it is dictated by the modal instability for high porosity values.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/180382019-01-01T00:00:00ZGHOSH, SouvikBREUGEM, Wim-PaulBRANDT, LucaLOISEAU, Jean-ChristopheWe present modal and non-modal linear stability analyses of Poiseuille flow through a plane channel with a porous substrate modeled using the Volume Averaged Navier–Stokes (VANS) equations. Modal stability analysis shows the destabilization of the flow with increasing porosity of the layer. The instability mode originates from the homogeneous fluid region of the channel for all the values of porosity considered but the governing mechanism changes. Perturbation kinetic energy analysis reveals the importance of viscous dissipation at low porosity values while dissipation in the porous substrate becomes significant at higher porosity. Scaling analysis highlights the invariance of the critical wavenumber with changing porosity. On the other hand, the critical Reynolds number remains invariant at low porosity and scales as Rec ∼ (H/δ) 1.4 at high porosity where δ is the typical thickness of the vorticity layer at the fluid– porous interface. This reveals the existence of a Tollmien–Schlichting-like viscous instability mechanism at low porosity values, and Rayleigh analysis shows the presence of an inviscid instability mechanism at high porosity. For the whole range of porosities considered, the non-modal analysis shows that the optimal mechanism responsible for transient energy amplification is the lift-up effect, giving rise to streaky structure as in single-phase plane Poiseuille flow. The present results strongly suggest that the transition to turbulence follows the same path as that of classical Poiseuille flow at low porosity values, while it is dictated by the modal instability for high porosity values.An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces
http://hdl.handle.net/10985/18775
An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces
GE, Zhouyang; TAMMISOLA, Outi; BRANDT, Luca; LOISEAU, Jean-Christophe
Aiming for the simulation of colloidal droplets in microfluidic devices, we present here a numerical method for two-fluid systems subject to surface tension and depletion forces among the suspended droplets. The algorithm is based on an efficient solver for the incompressible two-phase Navier–Stokes equations, and uses a mass-conserving level set method to capture the fluid interface. The four novel ingredients proposed here are, firstly, an interface-correction level set (ICLS) method; global mass conservation is achieved by performing an additional advection near the interface, with a correction velocity obtained by locally solving an algebraic equation, which is easy to implement in both 2D and 3D. Secondly, we report a second-order accurate geometric estimation of the curvature at the interface and, thirdly, the combination of the ghost fluid method with the fast pressurecorrection approach enabling an accurate and fast computation even for large density contrasts. Finally, we derive a hydrodynamic model for the interaction forces induced by depletion of surfactant micelles and combine it with a multiple level set approach to study short-range interactions among droplets in the presence of attracting forces.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/187752018-01-01T00:00:00ZGE, ZhouyangTAMMISOLA, OutiBRANDT, LucaLOISEAU, Jean-ChristopheAiming for the simulation of colloidal droplets in microfluidic devices, we present here a numerical method for two-fluid systems subject to surface tension and depletion forces among the suspended droplets. The algorithm is based on an efficient solver for the incompressible two-phase Navier–Stokes equations, and uses a mass-conserving level set method to capture the fluid interface. The four novel ingredients proposed here are, firstly, an interface-correction level set (ICLS) method; global mass conservation is achieved by performing an additional advection near the interface, with a correction velocity obtained by locally solving an algebraic equation, which is easy to implement in both 2D and 3D. Secondly, we report a second-order accurate geometric estimation of the curvature at the interface and, thirdly, the combination of the ghost fluid method with the fast pressurecorrection approach enabling an accurate and fast computation even for large density contrasts. Finally, we derive a hydrodynamic model for the interaction forces induced by depletion of surfactant micelles and combine it with a multiple level set approach to study short-range interactions among droplets in the presence of attracting forces.