Session HH: Convection and Buoyancy Driven Flows V

Lagrangian particle tracking in turbulent convection

The dispersion of inertial particles in turbulent convection has direct relevance for many industrial and environmental applications, where the fluid heat transfer can be modified by the presence and the deposition of particles at the walls (e.g. nuclear power plants, petrochemical multiphase reactors, cooling systems for electronic devices, pollutant dispersion in the atmospheric boundary layer, aerosol deposition etc.). A high resolution numerical technique coupled with Lagrangian particle tracking is employed, in this work, to investigate the behaviour of inertial particles in a periodic turbulent Rayleigh-Benard convection cell. In particular, we focus on the effects of different flow regimes, obtained varying the Rayleigh number, on particle dispersion/resuspension. Different Stokes numbers are considered to evaluate the influence of inertia on particle clustering and consequently, on the heat exchange modification between the two walls. Single and two particle statistics are used to estimate the level of mixing and the role of turbulent structures in particle transport. Mean and higher order statistics on particle and fluid velocity and temperature fields are also presented.   

An Experimental Study of Lagrangian Statistics in Rayleigh-B\'enard Convection

We present an experimental study of Lagrangian statistics in Rayleigh-B\'enard convection, using water as the working fluid. The tracking volume is (5 cm)$^{3}$ in the centre of a cylindrical shaped convection cell of aspect ratio one and 20 cm in height. Three cameras were used to identify the 3-dimensional positions of the tracer particles, which were evenly suspended in the cell. Detailed properties of the particle velocity, acceleration and dispersions along different directions have been investigated. We also studied the dependency of pair dispersion properties on the initial pair separation. All these properties have been examined with Rayleigh number spanning from $10^8$ to $10^{10}$ and Prandtl number around 6.2.   

An alternative Lagrangian approach to laminar heat transfer

Heat transfer in essence is the transport of thermal energy along certain paths in a similar way as fluid motion is the transport of fluid parcels along fluid paths. This similarity in principle admits Lagrangian heat-transfer analyses in terms of the geometry of such ``thermal paths'' analogous to the well-known Lagrangian analyses on chaotic mixing in viscous flows and micro-fluidics. To date such Lagrangian approaches towards laminar heat transfer represent convective heat transfer by the enthalpy flux. However, though conceptually entirely correct, this ansatz hampers physical interpretation of Lagrangian heat-transfer analyses, as the enthalpy is determined only up to a uniform background state. An alternative approach is proposed that may resolve this indeterminacy. This approach is outlined and demonstrated for the laminar heat transfer in a simple 2D unsteady flow.   

A variational principle for solute fluxes in mushy-layer convection

The utility of variational principles to describe nonlinear dissipative systems has been a topic of long-standing debate. We apply a variational principle to describe nonlinear convection in a \textit{mushy layer}: a reactive porous medium formed during solidification of a binary alloy. Convection drives the formation of channels of zero solid fraction, or chimneys, which are the principle conduits through which solute drains from the mushy layer. By optimizing the rate of removal of stored potential energy, our numerical model predicts scalings for solute fluxes and chimney spacings consistent with previous simulations and laboratory experiments. This leads to predictions of solute fluxes from growing sea ice.   

The Steepling of Mushy Layers

The rapid solidification of a binary alloy leads to the formation of a mushy layer, comprised of a dendritic solid phase and a concentrated interstitial fluid phase. When freezing from below, such that the mean density field is statically stable, a phenomenon known as ``steepling'' has been observed, whereby the mushy layer becomes domed. In experiments, the degree of steepling has been shown to increase with a decreased rate of solidification and the lateral extent of the steeple is comparable to the size of the container. It was reasoned that steepling is the cause of an instability of a planar front induced by convection within a perturbed compositional boundary layer at the top of the mushy layer in an otherwise stable solute field. We explore this possibility using a linear stability analysis of the mush-liquid interface and compare the results to unidirectional solidification experiments using aqueous NaCl solutions.   

Natural convection in a square cavity with participating medium

The natural convective flow in a two dimensional square cavity filled with a material which has properties of an optical participating medium is theoretically analyzed. Radiant energy coming from an external heat source is assumed to fall on a small region of one of the lateral walls of the cavity, and as the working fluid is assumed to be participating, the incoming energy is absorbed in its volume, heating the material by conduction, convection and radiation. The simultaneous presence of temperature gradients and a body force generates a convective motion. We present a mathematical model for describing this phenomenon which includes the conservation equations of mass, momentum and energy. The integral term that describes the radiation heat transport is included in the energy conservation equation. The solution is obtained with a numerical method and representative cases are described. This study has potential applications in the design of heat exchangers in central solar towers.   

Time-periodic traveling solutions of localized convection cells and their collision in binary fluid mixture

We study the mathematical structure of localized convection cell solutions in a binary fluid mixture, some of which are not observed in Rayleigh-Benard convection in a pure fluid. In particular, a solution representing time-periodic traveling localized convection cells (periodic traveling pulse, PTP) has not been obtained even numerically because this solution requires two unknown variables to be determined: group velocity and temporal period in the comoving frame with the group velocity. We developed a new integrated numerical method to obtain the PTP solution as well as the steady, periodic, and traveling solutions. By using this method, a global bifurcation structure containing a variety of solutions including PTPs is obtained and the phase dependence of the collision of counter- propagating PTPs is investigated in detail.   

Convective instabilities in a ferrofluid with a viscoelastic carrier fluid

We report theoretical and numerical results on the convective instability for a ferrofluid in a viscoelastic carrier liquid. Such a system exhibits several features that are important for the onset and development of convective instabilities, like the Soret or thermodiffusive effect due to the binary mixture nature, shear thinning or thickening, stress retardation and normal stress generation due to the viscoelasticity of the carrier liquid, and the Kelvin force and magnetophoresis due to the ferromagnetic structure of the colloidal particles. Convective instabilities can be triggered by applying temperature (concentration) gradients and/or (homogeneous) magnetic fields. We systematically investigate the role of the various effects (and their mutual interplay) for the instability and bifurcation behavior. In particular, for oscillatory instabilities nonlinear magnetic and nonlinear viscoelastic properties are taken into account.   

Dynamical behavior of lean swirling premixed flame generated by change in gravitational orientation

The dynamic behavior of flame front instability in lean swirling premixed flame generated by the effect of gravitational orientation has been experimentally investigated in this work. When the gravitational direction is changed relative to the flame front, i.e., in inverted gravity, an unstably fluctuating flame (unstable flame) is formed in a limited domain of equivalence ratio and swirl number (Gotoda. H et al., Physical Review E, vol. 81, 026211, 2010). The time history of flame front fluctuations show that in the buoyancy-dominated region, chaotic irregular fluctuation with low frequencies is superimposed on the dominant periodic oscillation of the unstable flame. This periodic oscillation is produced by unstable large-scale vortex motion in combustion products generated by a change in the buoyancy/swirl interaction due to the inversion of gravitational orientation. As a result, the dynamic behavior of the unstable flame becomes low-dimensional deterministic chaos. Its dynamics maintains low-dimensional deterministic chaos even in the momentum-dominated region, in which vortex breakdown in the combustion products clearly occurs. These results were clearly demonstrated by the use of nonlinear time series analysis based on chaos theory, which has not been widely applied to the investigation of combustion phenomena.   

Three-dimensional simulations of burning thermals

Flame ignition in type Ia supernovae (SNe Ia) leads to isolated bubbles of burning buoyant fluid. As a bubble rises due to gravity, it becomes deformed by shear instabilities and transitions to a turbulent buoyant vortex ring. Morton, Taylor and Turner (1956) introduced the entrainment assumption, which can be applied to inert thermals. In this study, we use the entrainment assumption, suitably modified to account for burning, to predict the late-time asymptotic behaviour of these turbulent buoyant vortex rings in SNe Ia. The theory is validated against three- dimensional simulations with adaptive mesh refinement at effective resolutions up to 4096$^3$.