Anne Juel

Scaling of the Turbulence Transition Threshold in a Pipe

We report the results of an experimental investigation of the transition to turbulence in a pipe over approximately an order of magnitude range in the Reynolds number Re. A novel scaling law is uncovered using a systematic experimental procedure which permits contact to be made with modern theoretical thinking. The principal result we uncover is a scaling law which indicates that the amplitude of perturbation required to cause transition scales as O(Re-1).

Magnetohydrodynamic convection in molten gallium

We present the results of an experimental and numerical study of the effects of a steady magnetic field on sidewall convection in molten gallium. The magnetic field is applied in a direction which is orthogonal to the main flow which reduces the convection and good agreement is found for the scaling of this effect with the relevant parameters. Moreover, qualitatively similar changes in the structure of the bulk of the flow are observed in the experiment and the numerical simulations. In particular, the flow is restricted to two dimensions by the magnetic field, but it remains different to that found in two-dimensional free convection calculations. We also show that oscillations found at even greater temperature gradients can be suppressed by the magnetic field.

Three-dimensional free convection in molten gallium

Convective flow of molten gallium is studied in a small-aspect-ratio rectangular, dierentially heated enclosure. The three-dimensional nature of the steady flow is clearly demonstrated by quantitative comparison between experimental temperature measurements, which give an indication of the strength of the convective flow, and the results of numerical simulations. The three-dimensional flow structure is characterized by cross-flows which are an order of magnitude smaller than the main circulation, and spread from the endwall regions to the entire enclosure when the Grashof number is increased beyond Gr =1 0 4 . The mergence of these eects in the centre of the enclosure leads to a complex central divergent flow structure which underpins the observed transition to oscillatory convection.

Free convection in liquid gallium

Free convection in liquid metals is of significant practical interest to the crystal-growing community since the adverse effects of convective instabilities in the melt phase can be frozen into the solid product. Here, we present the results of a combined numerical and experimental study of steady convective flows in a sample of liquid gallium which is heated at one end and cooled at the other. Experimental measurements of temperature distributions in the flow are compared with the standard Hadley-cell solution and with the numerical results obtained from a two-dimensional model. Excellent quantitative agreement is found between all three for low Grashof numbers but a systematic divergence between the results is seen as this parameter is increased.

The Steady Propagation of an Air Finger into a Rectangular Tube

The steady propagation of an air finger into a fluid-filled tube of uniform rectangular cross-section is investigated. This paper is primarily focused on the influence of the aspect ratio, α, on the flow properties, but the effects of a transverse gravitational field are also considered. The three-dimensional interfacial problem is solved numerically using the object-oriented multi-physics finite-element library oomph-lib and the results agree with our previous experimental results (de Lo´ zar et al. Phys. Rev. Lett. vol. 99, 2007, article 234501) to within the ±1% experimental error. At a fixed capillary number Ca (ratio of viscous to surface-tension forces) the pressure drops across the finger tip and relative finger widths decrease with increasing α. The dependence of the wet fraction m (the relative quantity of liquid that remains on the tube walls after the propagation of the finger) is more complicated: m decreases with increasing α for low Ca but it increases with α at high Ca. Our results also indicate that the system is approximately quasi-two-dimensional for α 8, when we obtain quantitative agreement with McLean & Saffman’s two-dimensional model for the relative finger width as a function of the governing parameter 1/B =12α2Ca. The action of gravity causes an increase in the pressure drops, finger widths and wet fractions at fixed capillary number. In particular, when the Bond number (ratio of gravitational to surface-tension forces) is greater than one the finger lifts off the bottom wall of the tube leading to dramatic increases in the finger width and wet fraction at a given Ca. For α 3 a previously unobserved flow regime has been identified in which a small recirculation flow is situated in front of the finger tip, shielding it from any contaminants in the flow. In addition, for α 2 the capillary number, Cac, above which global recirculation flows disappear has been observed to follow the simple empirical law: Ca2/3 c α =1.21.

On the onset of oscillatory convection in molten gallium

The results of experimental and numerical investigations of the onset of oscillatory convection in a sidewall heated rectangular cavity of molten gallium are reported. Detailed comparisons are made between experimental observations and calculations from numerical simulations of a three-dimensional Boussinesq model. The onset of time-dependence takes place through supercritical Hopf bifurcations and the loci of critical points in the (Gr, Pr)-plane are qualitatively similar with excellent agreement between the frequencies of the oscillatory motion. This provides a severe test of the control of the experiment since the mode of oscillation is extremely sensitive to imperfections. Detailed numerical investigations reveal that there are a pair of Hopf bifurcations which exist on two asymmetric states which themselves arise at a subcritical pitchfork from the symmetric state. There is no evidence for this in the experiment and this qualitative difference is attributed to non-Boussinesq perturbations which increase with Gr. However, the antisymmetric spatial structure of the oscillatory state is robust and is present in both the experiment and the numerical model. Moreover, the detailed analysis of the numerical results reveals the origins of the oscillatory instability.

Fluctuations in viscous fingering.

Our experiments on viscous (Saffman-Taylor) fingering in Hele-Shaw channels reveal finger width fluctuations that were not observed in previous experiments, which had lower aspect ratios and higher capillary numbers Ca. These fluctuations intermittently narrow the finger from its expected width. The magnitude of these fluctuations is described by a power law, Ca(-0.64), which holds for all aspect ratios studied up to the onset of tip instabilities. Further, for large aspect ratios, the mean finger width exhibits a maximum as Ca is decreased instead of the predicted monotonic increase.

The effect of noise on pitchfork and Hopf bifurcations

We present the results of an experimental and numerical investigation into the effects of noise on pitchfork and Hopf bifurcations. Good quantitative agreement is found between calculations and experiment. In the case of the pitchfork we find that natural imperfections override the effects of the noise. However, novel noise amplification effects have been uncovered in the study of the Hopf bifurcation. These destroy the critical event found in the noise‐free case and could be of considerable practical importance in systems containing dynamic bifurcations.

The influence of viscosity on the frozen wave instability: theory and experiment

We present the results of an experimental and linear stability study of the influence of viscosity on the frozen wave (FW) instability, which arises when a vessel containing stably stratified layers of immiscible liquids is oscillated horizontally. Our linear stability model consists of two superposed fluid layers of arbitrary viscosities and infinite lateral extent, subject to horizontal oscillation. The effect of the endwalls of the experimental vessel is simulated by enforcing the conservation of horizontal volume flux, so that the base flow consists of counterflowing layers. We perform experiments with four pairs of fluids, keeping the viscosity of the lower layer (v(1)) constant, and increasing the viscosity of the upper layer (V-2) so that 1.02 x 10(2) <= N-1 = v(2)/v(1) <= 1.21 x 10(4). We find excellent quantitative agreement between theory and experiment despite the simple model geometry, for both the critical onset parameter and wavenumber of the FW We show that the model of Lyubimov & Cherepanov (Fluid Dyn. vol. 86, 1987, p. 849), which is valid in the limit of inviscid fluids, consistently underestimates the instability threshold for fluids of equal viscosity, but generally overestimates the threshold for fluids of unequal viscosity. We extend the experimental parameter range numerically to viscosity contrasts 1 <= N-1 <= 6 x 10(4) and identify four regions of N-1 where qualitatively different dynamics occur, which are reflected in the non-monotonic dependence of the most unstable wavenumber and the critical amplitude on N-1. In particular, we find that increasing the viscosity contrast between the layers leads to destabilization over a wide range of N-1, 10 <= N-1 <= 8 x 10(3). The intricate dependence of the instability on viscosity contrast is due to considerable changes in the time-averaged perturbation vorticity distribution near the interface.

The reopening of a collapsed fluid-filled elastic tube

We present an experimental study of the reopening mechanics of a collapsed liquid-filled elastic tube. The experiment is a simple mechanical model of pulmonary airway reopening and aims to assess the robustness of existing theoretical models. A metre-long horizontal elastic tube of inner radius Ri=4.88 ± 0.14mm is filled with silicone oil and is carefully collapsed mechanically. The injection of nitrogen at a constant flow rate results in the steady propagation of an air finger, after the decay of initial transients. This behaviour is observed over the realizable range of the capillary numbers Ca, which measures the ratio of viscous and capillary forces. With increasing Ca, the transition region between the collapsed and reopened sections of the tube shortens, and the height of the tube behind the bubble tip increases. We also find that air fingers can propagate in partially reopened tubes, in which the transmural pressure is negative far behind the finger tip. The effect of viscosity on the reopening dynamics was explored by performing experiments using three different grades of silicone oil, with kinematic viscosities of 1000cS, 200cS and 100cS. A direct comparison between the experimental pressure dependence on Ca and numerical simulations of the zero-gravity three-dimensional airway-reopening model of Hazel & Heil (Trans. ASME: J. Biomech. Engng, vol. 128, 2006, p. 473) highlights some significant differences. Within the experimental parameter range, gravity profoundly influences the reopening mechanics in several ways. The reopening tube is supported by a rigid base, which induces an asymmetry about the horizontal mid-plane of the collapsed tube, resulting in distinct phases of reopening as Ca increases. In addition, buoyancy forces act on the air finger, which is observed to propagate near the top of the cross-section of the tube, leaving a thicker fluid-lining below. In the limit of small Ca, the height of the reopened tube increases significantly with viscosity. Experimental evidence suggests that this increase in viscosity leads to significant changes in the film configuration behind the propagating finger, caused by the increased contribution of buoyancy forces. The altered film configuration changes the mechanical load on the tube walls and, hence, the shape of the reopened tube.