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Mar 2008

Volume 20, Issue 3, Articles (03xxxx)

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Phys. Fluids 20, 035102 (2008); http://dx.doi.org/10.1063/1.2840200 (11 pages)

Karthik Duraisamy and Sanjiva K. Lele
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back to top Instability and Transition

Frictional drag reduction in bubbly Couette–Taylor flow

Yuichi Murai, Hiroshi Oiwa, and Yasushi Takeda

Phys. Fluids 20, 034101 (2008); http://dx.doi.org/10.1063/1.2884471 (12 pages) | Cited 8 times

Online Publication Date: 3 March 2008

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Frictional drag reduction due to the presence of small bubbles is investigated experimentally using a Couette–Taylor flow system; i.e., shear flow between concentric cylinders. Torque and bubble behavior are measured as a function of Reynolds number up to Re = 5000 while air bubbles are injected constantly and rise through an array of vortical cells. Silicone oil is used to avoid the uncertain interfacial property of bubbles and to produce nearly monosized bubble distributions. The effect of drag reduction on sensitivity and power gain are assessed. The sensitivity exceeds unity at Re<2000, proving that the effect of the reduction in drag is greater than that of the reduction in mixture density. This is due to the accumulation of bubbles toward the rotating inner cylinder, which is little affected by turbulence. The power gain, which is defined by the power saving from the drag reduction per the pumping power of bubble injection, has a maximum value of O(10) at higher Re numbers around 2500. An image processing measurement shows this is because of the disappearance of azimuthal waves when the organized bubble distribution transforms from toroidal to spiral modes. Moreover, the axial spacing of bubble clouds expands during the transition, which results in an effective reduction in the momentum exchange.
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47.55.dd Bubble dynamics
47.15.Fe Stability of laminar flows
47.15.ki Inviscid flows with vorticity
47.80.Jk Flow visualization and imaging
47.27.N- Wall-bounded shear flow turbulence

Spatially localized states in natural doubly diffusive convection

A. Bergeon and E. Knobloch

Phys. Fluids 20, 034102 (2008); http://dx.doi.org/10.1063/1.2837177 (8 pages) | Cited 17 times

Online Publication Date: 3 March 2008

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Numerical continuation is used to compute a multiplicity of stable spatially localized steady states in doubly diffusive convection in a vertical slot driven by imposed horizontal temperature and concentration gradients. The calculations focus on the so-called opposing case, in which the imposed horizontal thermal and solutal gradients are in balance. No-slip boundary conditions are used at the sides; periodic boundary conditions with large spatial period are used in the vertical direction. The results demonstrate the presence of homoclinic snaking in this system, and can be interpreted in terms of a pinning region in parameter space. The dynamics outside of this region are studied using direct numerical simulation.
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44.27.+g Forced convection
47.27.te Turbulent convective heat transfer
47.55.pb Thermal convection
47.60.Dx Flows in ducts and channels

Modeling of transitional channel flow using balanced proper orthogonal decomposition

Miloš Ilak and Clarence W. Rowley

Phys. Fluids 20, 034103 (2008); http://dx.doi.org/10.1063/1.2840197 (17 pages) | Cited 33 times

Online Publication Date: 6 March 2008

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We study reduced-order models of three-dimensional perturbations in linearized channel flow using balanced proper orthogonal decomposition (BPOD). The models are obtained from three-dimensional simulations in physical space as opposed to the traditional single-wavenumber approach, and are therefore better able to capture the effects of localized disturbances or localized actuators. In order to assess the performance of the models, we consider the impulse response and frequency response, and variation of the Reynolds number as a model parameter. We show that the BPOD procedure yields models that capture the transient growth well at a low order, whereas standard POD does not capture the growth unless a considerably larger number of modes is included, and even then can be inaccurate. In the case of a localized actuator, we show that POD modes which are not energetically significant can be very important for capturing the energy growth. In addition, a comparison of the subspaces resulting from the two methods suggests that the use of a nonorthogonal projection with adjoint modes is most likely the main reason for the superior performance of BPOD. We also demonstrate that for single-wavenumber perturbations, low-order BPOD models reproduce the dominant eigenvalues of the full system better than POD models of the same order. These features indicate that the simple, yet accurate BPOD models are a good candidate for developing model-based controllers for channel flow.
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47.60.Dx Flows in ducts and channels
47.85.L- Flow control
47.11.-j Computational methods in fluid dynamics
02.10.Ud Linear algebra

Directional effect of a magnetic field on oscillatory low-Prandtl-number convection

D. Henry, A. Juel, H. Ben Hadid, and S. Kaddeche

Phys. Fluids 20, 034104 (2008); http://dx.doi.org/10.1063/1.2856125 (12 pages) | Cited 3 times

Online Publication Date: 7 March 2008

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The directional effect of a magnetic field on the onset of oscillatory convection is studied numerically in a confined three-dimensional cavity of relative dimensions 4:2:1 (length:width:height) filled with mercury and subject to a horizontal temperature gradient. The magnetic field suppresses the oscillations most effectively when it is applied in the vertical direction, and is the least efficient when applied in the longitudinal direction (parallel to the temperature gradient). In all cases, however, exponential growths of the critical Grashof number, Grc (Gr, ratio of buoyancy to viscous dissipation forces) with the Hartmann number (Ha, ratio of magnetic to viscous dissipation forces) are obtained. Insight into the damping mechanism is gained from the fluctuating kinetic energy budget associated with the time-periodic disturbances at threshold. The kinetic energy produced by the vertical shear of the longitudinal basic flow dominates the oscillatory transition, and when a magnetic field is applied, it increases in order to balance the stabilizing magnetic energy. Moreover, subtle changes in the spatial distribution of this shear energy are at the origin of the exponential growth of Grc. The destabilizing effect of the velocity fluctuations strongly decreases when Ha is increased (due to the decay of the velocity fluctuations in the bulk accompanied by the appearance of steep gradients localized in the Hartmann layers), so that an increase of the shear of the basic flow at Grc is required in order to sustain the instability. This yields an increase in Grc, which is reinforced by the fact that the shear of the basic flow naturally decreases at constant Gr with the increase of Ha, particularly when the magnetic field is applied in the vertical direction. For transverse and longitudinal fields, the decay of the velocity fluctuations is combined with an increase of the shear energy term due to a sustained growth in stabilizing magnetic energy with Ha.
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47.55.P- Buoyancy-driven flows; convection
47.65.-d Magnetohydrodynamics and electrohydrodynamics

Stability of the boundary layer flow on a long thin rotating cylinder

M. A. Herrada, C. Del Pino, and R. Fernandez-Feria

Phys. Fluids 20, 034105 (2008); http://dx.doi.org/10.1063/1.2885330 (11 pages) | Cited 2 times

Online Publication Date: 14 March 2008

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The development and stability of the boundary layer flow over a long thin cylinder aligned with the main flow and which rotates around its axis is considered. Numerical results show that the introduction of rotation has an important effect on the behavior of the basic flow. When the swirl increases, the shear stress at the wall also increases due to the changes in the pressure distribution along the cylinder surface. A nonparallel linear stability analysis of the basic flow is performed using parabolized stability equations. Even at moderately low rotation, we find the existence of unstable centrifugal modes, in addition to the shear ones found in previous stability analysis of the boundary layer flow on a cylinder with no rotation. These centrifugal instabilities develop at Reynolds numbers, based on the cylinder radius and external axial velocity, much smaller than those required for the growing of the shear instabilities. Our analysis shows that nonparallel effects play a key role in the onset and development of these instabilities, being the spiral mode with azimuthal wavenumber n = 1, the first to become unstable as the Reynolds number is increased in most cases of interest. We characterize the critical Reynolds number for convective instability as a function of the axial distance to the leading edge for several values of the swirl parameter.
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47.15.Cb Laminar boundary layers
47.15.Fe Stability of laminar flows
47.20.Ib Instability of boundary layers; separation
47.20.-k Flow instabilities
47.32.C- Vortex dynamics

Stability of Taylor–Couette flow in a finite-length cavity with radial throughflow

Eric Serre, Michael A. Sprague, and Richard M. Lueptow

Phys. Fluids 20, 034106 (2008); http://dx.doi.org/10.1063/1.2884835 (10 pages) | Cited 5 times

Online Publication Date: 18 March 2008

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Linear stability analysis predicts that a radial throughflow in a Taylor–Couette system will alter the stability of the flow, but the underlying physics for the stabilization of the flow is unclear. We investigate the impact of radial inflow and outflow on Taylor vortex flow and wavy vortex flow in a finite-length cavity via direct numerical simulation using a three-dimensional spectral method. The numerical simulations are consistent with linear stability predictions in that radial inflow and strong radial outflow have a stabilizing effect, while weak radial outflow destabilizes the system slightly. A small radial outflow velocity enhances the strength of the Taylor vortices resulting in destabilization of the base flow, whereas strong radial outflow and radial inflow reduce vortex strength, thus stabilizing the system. The transition to wavy vortex flow is unaffected by small radial outflow, but is stabilized for radial inflow. For strong radial outflow the wavy vortex flow includes localized dislocations in the vortex structure.
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47.11.-j Computational methods in fluid dynamics
47.20.-k Flow instabilities
47.32.C- Vortex dynamics
47.32.-y Vortex dynamics; rotating fluids

Dispersion enhancement and damping by buoyancy driven flows in two-dimensional networks of capillaries

Maria Veronica D’Angelo, Harold Auradou, Catherine Allain, Marta Rosen, and Jean-Pierre Hulin

Phys. Fluids 20, 034107 (2008); http://dx.doi.org/10.1063/1.2899635 (9 pages) | Cited 6 times

Online Publication Date: 31 March 2008

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The influence of a small relative density difference (Δρ/ρ ≃ 3×10−4) on the displacement of two miscible Newtonian liquids is studied experimentally in transparent two-dimensional square networks of microchannels held vertically; the channel width distribution is log normal with a mean value of a = 0.33 mm. Maps of the local relative concentration are obtained by an optical light absorption technique. Both stable displacements in which the denser fluid enters at the bottom of the cell and displaces the lighter one and unstable displacements in which the lighter fluid is injected at the bottom and displaces the denser one are realized. Except at the lowest mean flow velocity U, the average C(x,t) of the relative concentration satisfies a convection-dispersion equation. The relative magnitude of ∣U∣ and of the velocity Ug of buoyancy driven fluid motions is characterized by the gravity number Ng = Ug/∣U∣. At low gravity numbers ∣Ng∣<0.01 (or equivalently high Péclet numbers Pe = Ua/Dm>500), the dispersivities ld in the stable and unstable configurations are similar to ld∝Pe0.5. At low velocities such that ∣Ng∣>0.01, ld increases like 1/Pe in the unstable configuration (Ng<0), while it becomes constant and close to the length of individual channels in the stable case (Ng>0). Isoconcentration lines c(x,y,t) = 0.5 are globally flat in the stable configuration, while in the unstable case, they display spikes and troughs with a rms amplitude σf parallel to the flow. For Ng>−0.2, σf increases initially with the distance and reaches a constant limit, while it keeps increasing for Ng<−0.2. A model taking into account buoyancy forces driving the instability and the transverse exchange of tracer between rising fingers and the surrounding fluid is suggested and its applicability to previous results obtained in three-dimensional media is discussed.
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47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.56.+r Flows through porous media
46.65.+g Random phenomena and media
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