Liquid oil painting: Free and forced convection in an enclosure with mechanical and thermal forcing

A fluid dynamics video is linked to this article, which have been submitted to the Gallery of Fluid Motion as part of the 65th American Physical Society meeting of the Division of Fluid Dynamics, held in San Diego, California, USA, over 17-20 November 2012. The video serves to visualize flows generated in a rectangular enclosure that are subjected to both mechanical and thermal forcing through a common horizontal boundary. This system exhibits features consistent with either horizontal convection or lid-driven cavity flows depending on the ratio between thermal and mechanical stirring, and three different cases are visualized in the linked videos.Comment: 2 video files attached, 4 pages, 1 figure. This article is submitted accompanying a video submitted to the Gallery of Fluid Motion as part of the 65th Division of Fluid Dynamics meeting of the American Physical Society (17-20 November, San Diego, CA, USA

Cylinders with Square Cross Section: Paths to Turbulence with Various Angles of Incidence

The path to turbulence in the wake of cylinders with square crosssection is investigated by means of direct numerical simulation, employing a two-dimensional spectral element method and Floquet linear stability analysis. The critical Reynolds number for the onset of the three-dimensional instability modes A, B, C and QP are reported for cylinder incidence angles between 0° and 45°. The Strouhal—Reynolds number relationship, and lift and drag coefficients are also investigated for these incidence angles. Reynolds numbers (based on the side length of the square) up to Re=300 are considered, and a significant variation in bifurcation scenarios are observed for the various incidence angles. At Reynolds numbers greater than Re ≈ 225 for an incidence angle of 45°, a previously unreported asymmetry is detected in the von Kármán vortex street. The cause of this asymmetry is investigated as it presents a possible alternative path to turbulence to that reported in the wakes of other bluff bodies

Linear stability of horizontal, laminar fully developed, quasi-two-dimensional liquid metal duct flow under a transverse magnetic field and heated from below

This study considers the linear stability of Poiseuille-Rayleigh-B\'enard flows, subjected to a transverse magnetic field to understand the instabilities that arise from the complex interaction between the effects of shear, thermal stratification and magnetic damping. This fundamental study is motivated in part by the desire to enhance heat transfer in the blanket ducts of nuclear fusion reactors. In pure MHD flows, the imposed transverse magnetic field causes the flow to become quasi-2D and exhibit disturbances that are localised to the horizontal walls. However, the vertical temperature stratification in Rayleigh-B\'enard flows feature convection cells that occupy the interior region and therefore the addition of this aspect provides an interesting point for investigation. The linearised governing equations are described by the \qtwod\ model proposed by Sommeria and Moreau (1982) which incorporates a Hartmann friction term, and the base flows are considered fully developed and 1D. The neutral stability curves for critical Reynolds and Rayleigh numbers, $Re_c$ and $Ra_c$, respectively, as functions of Hartmann friction parameter $H$ have been obtained over $10^{-2}\leq H\leq10^4$. Asymptotic trends are observed as $H\rightarrow\infty$ following $Re_c\propto H^{\,1/2}$ and $Ra_c\propto H$. The linear stability analysis reveals multiple instabilities which alter the flow both within the Shercliff boundary layers and the interior flow, with structures consistent with features from plane Poiseuille and Rayleigh-B\'enard flows

Subcritical transition to turbulence in quasi-two-dimensional shear flows

The transition to turbulence in ducts, pipes or other conduits is a crucial phenomenon. It determines the energy consumption and heat or mass exchange in countless processes: whether cooling circuits of heat exchangers, pipelines or chemical reactors to cite but a few. The transition occurs at relatively low flow rates as a response to perturbations exceeding a critical amplitude (such transitions are subcritical) through an intrinsically three-dimensional (3D) mechanism. However, fluid motion can be restricted to two dimensions, if it is stratified, subject to rapid rotation or intense magnetic fields, for example in rotating machines or in the liquid metal cooling circuits of nuclear fusion reactors. Subcritical turbulence has yet to be observed in 2D or quasi-2D flows, let alone a transition to it. Here we use stability analysis and direct numerical simulations on the example of a duct flow driven by the motion of its lateral walls to provide the first evidence of turbulence in subcritical quasi-2D shear flows. We further show that the scenario leading to turbulence mostly relies on the nonlinear dynamics of so-called Tollmien-Schlichting waves, rather than on perturbations experiencing fast, transient growth. Although the transition is subcritical, it cannot take place at such low flow rates as in 3D flows, because these waves are severly damped. This alternative scenario opens a new route to turbulence that calls for exploration. This new landscape may reset current strategies to promote or to hinder quasi-2D turbulence in practical applications, including in fusion reactors.Comment: Combined main paper (7 pages, 5 figures) and supplementary information (16 pages, 6 figures, 5 tables), submitted for consideration to Nature Physic

From three-dimensional to quasi-two-dimensional:Transient growth in magnetohydrodynamic duct flows

This study seeks to elucidate the linear transient growth mechanisms in a uniform duct with square cross-section applicable to flows of electrically conducting fluids under the influence of an external magnetic field. A particular focus is given to the question of whether at high magnetic fields purely two-dimensional mechanisms exist, and whether these can be described by a computationally inexpensive quasi-two-dimensional model. Two Reynolds numbers of $5000$ and $15\,000$ and an extensive range of Hartmann numbers $0 \leq Ha \leq 800$ were investigated. Three broad regimes are identified in which optimal mode topology and non-modal growth mechanisms are distinct. These regimes corresponding to low, moderate and high magnetic field strengths are found to be governed by the independent parameters, Hartmann number, Reynolds number based on the Hartmann layer thickness $R_H$, and Reynolds number built upon the Shercliff layer thickness $R_S$, respectively. Transition between regimes respectively occurs at $Ha \approx 2$ and no lower than $R_H \approx 33.\dot{3}$. Notably for the high Hartmann number regime, quasi-two-dimensional magnetohydrodynamic models are shown to be an excellent predictor of not only transient growth magnitudes, but also the fundamental growth mechanisms of linear disturbances. This paves the way for a precise analysis of transition to quasi-two-dimensional turbulence at much higher Hartmann numbers than is currently achievable.Comment: Accepted for publication in Journal of Fluid Mechanics (2018

Quasi-two-dimensional MHD duct flow around a 180-degree sharp bend in a strong magnetic field

This study considers the quasi-two-dimensional flow of an electrically conducting fluid subjected to a strong out-of-plane magnetic field in a rectangular duct. The effect of Hartmann number on flow features such as the length of the downstream recirculation bubbles and the threshold Reynolds numbers between steady-state and unsteady flow regimes for values of the ratio between the throat of the bend and the duct height, β = 1 are identified. The simulations reveal that the primary recirculation bubble length decreases with increasing Hartmann number, and simultaneously the secondary recirculation bubble is significantly damped compared to the corresponding non-MHD case. The critical Reynolds number where the transitions from steady to unsteady flow occurs was found to increase with increasing of Hartman number. This study provides information that will be useful for refining the design of heat exchanger ducting in MHD systems to maximise the useful mass transport adjacent to the duct walls where heating is applied

Linear stability of confined flow around a 180-degree sharp bend

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number Re < 1150 and bend opening ratio (ratio of bend width to inlet height) 0.26β 65. This range of Re and β captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For 0.2 6 β 6 1, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as β increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for β = 0.2 and a spanwise synchronous mode for β > 0.3. The critical Reynolds number and the spanwise wavelength of perturbations increase as β increases. For 1 < β 6 2 both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as β increases. Finally, for 2 < β 6 5, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubbl