Nils Tilton, Denis Martinand. Taylor–Couette–Poiseuille flow with a weakly permeable inner cylinder: absolute instabilities and selection of global modes. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 849, pp.741 - 776. ⟨10.1017/jfm.2018.437⟩. ⟨hal-02116002⟩ Plus de détails...
Variations in the local stability of the flow in a Taylor-Couette cell can be imposed by adding an axial Poiseuille flow and a radial flow associated with one or both of the cylinders being permeable. At a given rotation rate of the inner cylinder, this results in adjacent regions of the flow that can be simultaneously stable, convectively unstable, and absolutely unstable, making this system fit for studying global modes of instability. To this end, building on the existing stability analysis in absolute modes developing over axially invariant base flows, we consider the case of axially varying base flows in systems for which the outer cylinder is impermeable, and the inner cylinder is a weakly permeable membrane through which the radial flow is governed by Darcy's law. The frameworks of linear and nonlinear global modes are used to describe the instabilities and assess the results of direct numerical simulations using a dedicated pseudospectral method. Three different axially evolving set-ups are considered. In the first, fluid injection occurs along the full inner cylinder. In the second, fluid extraction occurs along the full inner cylinder. Besides its fundamental interest, this set-up is relevant to filtration devices. In the third, fluid flux through the inner cylinder evolves from extraction to injection as cross-flow reversal occurs. In agreement with the global mode analyses, the numerical simulations develop centrifugal instabilities above the predicted critical rotation rates and downstream of the predicted axial locations. The global mode analyses do not fully explain, however, that. the instabilities observed in the numerical simulations take the form of axial stacks of wavepackets characterized by jumps of the temporal frequency.
Nils Tilton, Denis Martinand. Taylor–Couette–Poiseuille flow with a weakly permeable inner cylinder: absolute instabilities and selection of global modes. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 849, pp.741 - 776. ⟨10.1017/jfm.2018.437⟩. ⟨hal-02116002⟩
Eunok Yim, Jean-Marc Chomaz, D. Martinand, E. Serre. Transition to turbulence in the rotating disk boundary layer of a rotor–stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 848, pp.631-647. ⟨10.1017/jfm.2018.239⟩. ⟨hal-02354169⟩ Plus de détails...
The transition to turbulence in the rotating disk boundary layer is investigated in a closed cylindrical rotor-stator cavity via direct numerical simulation (DNS) and linear stability analysis (LSA). The mean flow in the rotor boundary layer is qualitatively similar to the von Kármán self-similarity solution. The mean velocity profiles, however, slightly depart from theory as the rotor edge is approached. Shear and centrifugal effects lead to a locally more unstable mean flow than the self-similarity solution, which acts as a strong source of perturbations. Fluctuations start rising there, as the Reynolds number is increased, eventually leading to an edge-driven global mode, characterized by spiral arms rotating counterclockwise with respect to the rotor. At larger Reynolds numbers, fluctuations form a steep front, no longer driven by the edge, and followed downstream by a saturated spiral wave, eventually leading to incipient turbulence. Numerical results show that this front results from the superposition of several elephant front-forming global modes, corresponding to unstable azimuthal wavenumbers m, in the range m ∈ [32, 78]. The spatial growth along the radial direction of the energy of these fluctuations is quantitatively similar to that observed experimentally. This superposition of elephant modes could thus provide an explanation for the discrepancy observed in the single disk configuration, between the corresponding spatial growth rates values measured by experiments on the one hand, and predicted by LSA and DNS performed in an azimuthal sector, on the other hand.
Eunok Yim, Jean-Marc Chomaz, D. Martinand, E. Serre. Transition to turbulence in the rotating disk boundary layer of a rotor–stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 848, pp.631-647. ⟨10.1017/jfm.2018.239⟩. ⟨hal-02354169⟩
Eunok Yim, J.-M. Chomaz, Denis Martinand, Eric Serre. Transition to turbulence in the rotating disk boundary layer of a rotor–stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 848, pp.631 - 647. ⟨10.1017/jfm.2018.239⟩. ⟨hal-02116221⟩ Plus de détails...
The transition to turbulence in the rotating disk boundary layer is investigated in a closed cylindrical rotor-stator cavity via direct numerical simulation (DNS) and linear stability analysis (LSA). The mean flow in the rotor boundary layer is qualitatively similar to the von Karman self-similarity solution. The mean velocity profiles, however, slightly depart from theory as the rotor edge is approached. Shear and centrifugal effects lead to a locally more unstable mean flow than the self-similarity solution, which acts as a strong source of perturbations. Fluctuations start rising there, as the Reynolds number is increased, eventually leading to an edge-driven global mode, characterized by spiral arms rotating counter-clockwise with respect to the rotor. At larger Reynolds numbers, fluctuations form a steep front, no longer driven by the edge, and followed downstream by a saturated spiral wave, eventually leading to incipient turbulence. Numerical results show that this front results from the superposition of several elephant front-forming global modes, corresponding to unstable azimuthal wavenumbers m, in the range m is an element of [32, 78 ]. The spatial growth along the radial direction of the energy of these fluctuations is quantitatively similar to that observed experimentally. This superposition of elephant modes could thus provide an explanation for the discrepancy observed in the single disk configuration, between the corresponding spatial growth rates values measured by experiments on the one hand, and predicted by LSA and DNS performed in an azimuthal sector, on the other hand.
Eunok Yim, J.-M. Chomaz, Denis Martinand, Eric Serre. Transition to turbulence in the rotating disk boundary layer of a rotor–stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 848, pp.631 - 647. ⟨10.1017/jfm.2018.239⟩. ⟨hal-02116221⟩
Eunok Yim, J.-M Chomaz, Denis Martinand, Eric Serre. Transition to turbulence in the rotating disk boundary layer of a rotor-stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 836, pp.43-71. ⟨10.1017/jfm.2017.771⟩. ⟨hal-02121890⟩ Plus de détails...
This paper proposes a resolution to the conundrum of the roles of convective and absolute instability in transition of the rotating-disk boundary layer. It also draws some comparison with swept-wing flows. Direct numerical simulations based on the incompressible Navier–Stokes equations of the flow over the surface of a rotating disk with modelled roughness elements are presented. The rotating-disk flow has been of particular interest for stability and transition research since the work by Lingwood (J. Fluid Mech., vol. 299, 1995, pp. 17–33) where an absolute instability was found. Here stationary disturbances develop from roughness elements on the disk and are followed from the linear stage, growing to saturation and finally transitioning to turbulence. Several simulations are presented with varying disturbance amplitudes. The lowest amplitude corresponds approximately to the experiment by Imayama et al. (J. Fluid Mech., vol. 745, 2014a, pp. 132–163). For all cases, the primary instability was found to be convectively unstable, and secondary modes were found to be triggered spontaneously while the flow was developing. The secondary modes further stayed within the domain, and an explanation for this is a proposed globally unstable secondary instability. For the low-amplitude roughness cases, the disturbances propagate beyond the threshold for secondary global instability before becoming turbulent, and for the high-amplitude roughness cases the transition scenario gives a turbulent flow directly at the critical Reynolds number for the secondary global instability. These results correspond to the theory of Pier (J. Engng Maths, vol. 57, 2007, pp. 237–251) predicting a secondary absolute instability. In our simulations, high temporal frequencies were found to grow with a large amplification rate where the secondary global instability occurred. For smaller radial positions, low-frequency secondary instabilities were observed, tripped by the global instability. The transition to turbulence in the rotating disk boundary layer is investigated in a closed cylindrical rotor-stator cavity via direct numerical simulation (DNS) and linear stability analysis (LSA). The mean flow in the rotor boundary layer is qualitatively similar to the von Kármán self-similarity solution. The mean velocity profiles, however, slightly depart from theory as the rotor edge is approached. Shear and centrifugal effects lead to a locally more unstable mean flow than the self-similarity solution, which acts as a strong source of perturbations. Fluctuations start rising there, as the Reynolds number is increased, eventually leading to an edge-driven global mode, characterized by spiral arms rotating counterclockwise with respect to the rotor. At larger Reynolds numbers, fluctuations form a steep front, no longer driven by the edge, and followed downstream by a saturated spiral wave, eventually leading to incipient turbulence. Numerical results show that this front results from the superposition of several elephant front-forming global modes, corresponding to unstable azimuthal wavenumbers m, in the range m ∈ [32, 78]. The spatial growth along the radial direction of the energy of these fluctuations is quantitatively similar to that observed experimentally. This superposition of elephant modes could thus provide an explanation for the discrepancy observed in the single disk configuration, between the corresponding spatial growth rates values measured by experiments on the one hand, and predicted by LSA and DNS performed in an azimuthal sector, on the other hand.
Eunok Yim, J.-M Chomaz, Denis Martinand, Eric Serre. Transition to turbulence in the rotating disk boundary layer of a rotor-stator cavity. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 836, pp.43-71. ⟨10.1017/jfm.2017.771⟩. ⟨hal-02121890⟩
Denis Martinand, Eric Serre, Richard M. Lueptow. Linear and weakly nonlinear analyses of cylindrical Couette flow with axial and radial flows. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2017, 824, pp.438 - 476. ⟨10.1017/jfm.2017.351⟩. ⟨hal-01592948⟩ Plus de détails...
Extending previous linear stability analyses of the instabilities developing in permeable Taylor-Couette-Poiseuille flows where axial and radial throughflows are superimposed on the usual Taylor-Couette flow, we further examine the linear behaviour and expand the analysis to consider the weakly nonlinear behaviour of convective-type instabilities by means of the derivation of the fifth-order amplitude equation together with direct numerical simulations. Special attention is paid to the influence of the radius ratio eta = r(in)/r(out), and particularly to wide gaps (small eta) and how they magnify the effects of the radial flow. The instabilities take the form of pairs of counter-rotating toroidal vortices superseded by helical ones as the axial flow is increased. Increasing the radial inflow draws these vortices near the inner cylinder, where they shrink relative to the annular gap, when this gap is wide. Strong axial and radial flows in a narrow annular gap lead to a very large azimuthal wavenumber with steeply sloped helical vortices. Strong radial outflow in a wide annular gap results in very large helical vortices. The analytical and numerical saturated vortices match quite well. In addition, radial inflows or outflows can turn the usually supercritical bifurcation from laminar to vortical flow into a subcritical one. The radial flow above which this change occurs decreases as the radius ratio eta decreases. A practical motivation for this weakly nonlinear analysis is found in modelling dynamic filtration devices, which rely on vortical instabilities to reduce the processes of accumulation on their membranes.
Denis Martinand, Eric Serre, Richard M. Lueptow. Linear and weakly nonlinear analyses of cylindrical Couette flow with axial and radial flows. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2017, 824, pp.438 - 476. ⟨10.1017/jfm.2017.351⟩. ⟨hal-01592948⟩
Denis Martinand, Eric Serre, Richard M. Lueptow. Mechanisms for the transition to waviness for Taylor vortices. Physics of Fluids, American Institute of Physics, 2014, 26 (9), pp.094102. ⟨10.1063/1.4895400⟩. ⟨hal-01300402⟩ Plus de détails...
Building on the weakly nonlinear amplitude equation of the saturated Taylor vortices developing in a Taylor–Couette cell with a rotating inner cylinder and a fixed outer one, the physical mechanism underlying the destabilization of these vortices resulting in azimuthal waviness is addressed using Floquet analysis. For narrow gap configurations, analysis and direct numerical simulations together with existing experimental results support the idea that the waviness is generated by the axial shear in the azimuthal velocity due to the alternate advection by the Taylor vortices of azimuthal momentum between the cylinders. For wide gap configurations, this mechanism is no longer able to drive the azimuthal waviness and a different mechanism tends to select a subharmonic instability.
Denis Martinand, Eric Serre, Richard M. Lueptow. Mechanisms for the transition to waviness for Taylor vortices. Physics of Fluids, American Institute of Physics, 2014, 26 (9), pp.094102. ⟨10.1063/1.4895400⟩. ⟨hal-01300402⟩
Nils Tilton, Eric Serre, Denis Martinand, Richard M. Lueptow. A 3D pseudospectral algorithm for fluid flows with permeable walls. Application to filtration. Computers and Fluids, Elsevier, 2014, 93, pp.129-145. ⟨10.1016/j.compfluid.2014.01.003⟩. ⟨hal-01053339⟩ Plus de détails...
The present work proposes a Chebyshev-collocation Fourier-Galerkin pseudospectral method for simulating unsteady, three-dimensional, fluid flows in cylindrical geometries with pressure-driven flow through permeable boundaries. Such systems occur in diverse applications and are challenging to simulate due to an additional velocity-pressure coupling on the permeable walls through Darcy's law. The present work extends the projection method of Raspo et al. (2002) to assure Darcy's law is satisfied exactly. A multidomain solver allows the efficient treatment of open boundary conditions that necessitate permeability buffers and a sponge layer. The method is spectrally convergent, and we demonstrate that pressure-prediction is necessary to obtain second-order temporal accuracy. The ability of the method to simulate complicated physical systems is demonstrated by simulating subcritical and supercritical flows in rotating filtration in Taylor-Couette cells. For subcritical cases, numerical results show excellent agreement with analytical solutions. For supercritical cases, the numerical method accurately resolves convectively and absolutely unstable flows with traveling toroidal and helical vortical structures that are in good agreement with a local linear stability analysis and experimental observations.
Nils Tilton, Eric Serre, Denis Martinand, Richard M. Lueptow. A 3D pseudospectral algorithm for fluid flows with permeable walls. Application to filtration. Computers and Fluids, Elsevier, 2014, 93, pp.129-145. ⟨10.1016/j.compfluid.2014.01.003⟩. ⟨hal-01053339⟩
Nils Tilton, Denis Martinand, Eric Serre, Richard M. Lueptow. Incorporating Darcy's law for pure solvent flow through porous tubes: Asymptotic solution and numerical simulations. AIChE Journal, Wiley, 2012, 58 (7), pp.2030-2044. ⟨10.1002/aic.13823⟩. ⟨hal-01032148⟩ Plus de détails...
A generalized solution for pressure-driven, incompressible, Newtonian flow in a porous tubular membrane is challenging due to the coupling between the transmembrane pressure and velocity. To date, all analytical solutions require simplifications such as neglecting the coupling between the transmembrane pressure and velocity, assuming the form of the velocity fields, or expanding in powers of parameters involving the tube length. Moreover, previous solutions have not been validated with comparison to direct numerical simulation (DNS). We comprehensively revisit the problem to present a robust analytical solution incorporating Darcy's law on the membrane. We make no assumptions about the tube length or form of the velocity fields. The analytic solution is validated with detailed comparison to DNSs, including cases of axial flow exhaustion and cross flow reversal. We explore the validity of typical assumptions used in modeling porous tube flow and present a solution for porous channels in Supporting Information.
Nils Tilton, Denis Martinand, Eric Serre, Richard M. Lueptow. Incorporating Darcy's law for pure solvent flow through porous tubes: Asymptotic solution and numerical simulations. AIChE Journal, Wiley, 2012, 58 (7), pp.2030-2044. ⟨10.1002/aic.13823⟩. ⟨hal-01032148⟩
Matthieu J. Mercier, Denis Martinand, Manikandan Mathur, Louis Gostiaux, Thomas Peacock, et al.. New wave generation. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2010, 657, pp.308. ⟨10.1017/S0022112010002454⟩. ⟨hal-01139500⟩ Plus de détails...
We present the results of a combined experimental and numerical study of the generation of internal waves using the novel internal wave generator design of Gostiaux et al. (2007). This mechanism, which involves a tunable source comprised of oscillating plates, has so far been used for a few fundamental studies of internal waves, but its full potential has yet to be realized. Our studies reveal that this approach is capable of producing a wide variety of two-dimensional wave fields, including plane waves, wave beams and discrete vertical modes in finite-depth stratifications. The effects of discretization by a finite number of plates, forcing amplitude and angle of propagation are investigated, and it is found that the method is remarkably efficient at generating a complete wave field despite forcing only one velocity component in a controllable manner. We furthermore find that the nature of the radiated wave field is well predicted using Fourier transforms of the spatial structure of the wave generator.
Matthieu J. Mercier, Denis Martinand, Manikandan Mathur, Louis Gostiaux, Thomas Peacock, et al.. New wave generation. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2010, 657, pp.308. ⟨10.1017/S0022112010002454⟩. ⟨hal-01139500⟩
Matthieu J. Mercier, Denis Martinand, Manikandan Mathur, Louis Gostiaux, Thomas Peacock, et al.. New wave generation. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2010, 657, pp.308-334. ⟨hal-00516373⟩ Plus de détails...
Matthieu J. Mercier, Denis Martinand, Manikandan Mathur, Louis Gostiaux, Thomas Peacock, et al.. New wave generation. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2010, 657, pp.308-334. ⟨hal-00516373⟩
Nils Tilton, Denis Martinand, Eric Serre, Richard M. Lueptow. Pressure-driven radial flow in a Taylor-Couette cell. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2010, 660, pp.527-537. ⟨10.1017/S0022112010003228⟩. ⟨hal-01024690⟩ Plus de détails...
A generalized solution for pressure-driven flow through a permeable rotating inner cylinder in an impermeable concentric outer cylinder, a situation used commercially in rotating filtration, is challenging due to the interdependence between the pressure drop in the axial direction and that across the permeable inner cylinder. Most previous approaches required either an imposed radial velocity at the inner cylinder or radial throughflow with both the inner and outer cylinders being permeable. We provide an analytical solution for rotating Couette-Poiseuille flow with Darcy's law at the inner cylinder by using a small parameter related to the permeability of the inner cylinder. The theory works for suction, injection and even combined suction/injection, when the axial pressure drop in the annulus is such that the transmembrane pressure difference reverses sign along the axial extent of the system. Corresponding numerical simulations for finite-length systems match the theory very well.
Nils Tilton, Denis Martinand, Eric Serre, Richard M. Lueptow. Pressure-driven radial flow in a Taylor-Couette cell. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2010, 660, pp.527-537. ⟨10.1017/S0022112010003228⟩. ⟨hal-01024690⟩