Session F06: Free and Rayleigh-Benard Convection II

Computational study of Rayleigh-Bernard convection in a cylindrical pressurized cryogenic tank

This research discussed a joint CFD-nodal computational approach for flow modeling inside a closed pressurized cryogenic tank. The effect of the tank’s physic on the Rayleigh-Bernard convection is explored. Our primary goal is to alleviate the drawback of pure nodal approaches for capturing the flow physics and thermodynamics of cryogenic flows in storage vessels and reduce the expensive computational cost of full CFD simulations through the employment of coupled nodal and CFD approaches. The proposed algorithm is tested for a cryogenic fuel tank with the assumption that the exchange between the phases is due to the thermal and mass boundary conditions at the liquid/gas interface. The Nodal and CFD models are coupled through a 0D/3D interface coupling wherein the CFD approach is employed for the liquid domain. We show that the presented 0D/3D connection of the CFD and Nodal with proper temporal coupling at their interfaces can be employed to efficiently study the flow and thermal physics of storage tanks. The role of the tank’s aspect ratio, Rayleigh number, and the volume ratio of gas to liquid parts on the circulation patterns and thermal stratification in tanks will be discussed.

 

Grant support (80NSSC20K0352) from the National Aeronautics and Space Administration (NASA) is gratefully acknowledged.   

Quasi-static magnetoconvection with a tilted magnetic field

A numerical study of convection with stress-free boundary conditions in the presence of an imposed magnetic field that is tilted with respect to the direction of gravity is carried out in the limit of small magnetic Reynolds number. The dynamics are investigated over a range of Rayleigh number Ra and Chandrasekhar numbers up to Q = 2×10⁶, with the tilt angle between the gravity vector and imposed magnetic field vector fixed at 45^°. Heat and momentum transport, as characterized by the Nusselt and Reynolds numbers, are quantified and compared with the vertical field case. Ohmic dissipation dominates over viscous dissipation in all cases investigated. 

Provided Ra is sufficiently large, all investigated values of Q exhibit an inverse kinetic energy cascade that yields large scale flows. The interaction of these mean flows with the imposed field results in the formation of Hartmann boundary layers.

For fixed Q the mean flow is initially stronger in the direction perpendicular to the imposed magnetic field, but as Ra is increased we observe relaxation oscillations in which both along-field and cross-field mean flows are comparable in magnitude. Our findings suggest that both field direction and magnitude are critical factors in nonlinear magnetoconvection dynamics.   

Quantifying differences between chaotic Rayleigh-Bénard convection experiments and simulations using plumes detected by persistent homology 10.1.3

Persistent homology is a data analysis technique that can be used to quantify the topological information of image data. In the spatio-temporally chaotic flow known as spiral defect chaos in Rayleigh-Benard convection, we explore the difference between convective plume statistics, detected using persistent homology, over long time-series of convection experiments and simulations of the Boussinesq equations with constant temperature boundary conditions.   We find that such simulations produce plume statistics that are different from experiments.  We describe a model of the thermal conduction in the experimental cell that produces temperature boundary conditions that are constant in time but vary in space while accounting for the finite thickness and thermal conductivity of the heating and cooling plates in experiments.  We demonstrate that simulations that employ these improved boundary conditions produce total plume statistics that are more similar to experiments.  However, we demonstrate that in order to account for a discrepancy in cold and hot experimental plume rates, simulations that include non-Boussinesq effects are necessary.

 

Heat transfer in turbulent Rayleigh-Bénard convection with two immiscible fluid layers

We numerically investigate turbulent Rayleigh-Bénard convection with two immiscible fluid layers, aiming to understand how the layer height and fluid properties affect the heat transfer (characterized by the Nusselt number Nu) in two-layer systems. Both two- and three-dimensional simulations are performed at fixed global Rayleigh number Ra = 10⁸, Prandtl number Pr = 4.38 and Weber number We = 5. We vary the thickness of the upper layer 0.01 < α <  0.99 and the thermal conduction coefficient ratio 0.1 < λ_k < 10 of the two layers. Two flow regimes are observed: In the first regime at 0.02 < α < 0.98, convective flows appear in both layers and Nu is not sensitive to α. In another regime at α < 0.02 or α > 0.98, convective flow only exists in the thicker layer, while the thinner layer is dominated by pure conduction. In this regime, Nu is sensitive to α. To predict Nu in the two-layer system with the interface between the two layers does not break up, we apply the Grossmann-Lohse theory in the individual layers, imposing heat flux conservation at the interface. The predictions for Nu and for the temperature at the interface well agree with our numerical results and previous experimental data.   

Impact of convective flows in melting and thermal energy storage of Phase Change Materials

Phase change materials (PCMs) use the latent heat of the solid/liquid phase change to store or release large amounts of thermal energy, allowing for compact thermal management and energy storage systems.

We  show the dynamic regimes occurring during the melting of an organic PCM  up to  Ra~10^9: (i)  base state, (ii)  plumes, (iii) plume coarsening, and (iv) turbulence.  Each one of these creates a distinctive melting front visible in experiments.  The transition to turbulence occurs through a secondary instability that forces the coarsening of the thermal plumes. By inclining the domain,   above a critical tilting only exists a laminar flow at the melted phase, irrespective of the Rayleigh number. The Nusselt, Reynolds numbers, and boundary layers follow power laws whose exponents agree with the high Rayleigh convection literature.  However, some striking differences appear as the stabilization of turbulent states further increasing the Rayleigh number.  

We show as well how thermocapillary enhances the heat transfer performance of  PCMs.  The interplay between conduction and convection-dominated regions in the liquid phase determines the melting dynamics.   Magnitudes as the position of the melting front, time to total melting, or stored energy follow power laws.   

Plume dynamics across scales: from laminar flow, instability to turbulent flow

Buoyant plumes generated from localised sources arise throughout the natural world and across a wide variety of scales. The Prandtl number (Pr) in particular varies from ~10^{-4} in planetary applications to ~10^{20} in geological flows. We use direct numerical simulation based on a spectral element method combined with scaling/asymptotic analysis to investigate the full life cycle of evolving plumes in both unstratified and stratified environments, spanning initially laminar to turbulent flow. We thereby explore the general effects of viscosity and thermal diffusivity on the dynamics of plumes. Our numerical simulations reveal characteristics of plumes without reference to simplified models, thereby allowing us to scrutinise these simplified descriptions of plume dynamics. Further, they yield insight into the conditions necessary for direct numerical solutions (typically limited to Re < O(10⁴)) to effectively simulate flow in large-scale phenomena such as volcanic eruptions (where Re ~ O(10¹²)).

By considering intrinsic scales derived directly from the Navier-Stokes equations, we find that all plumes can be fully classified in terms of a spectrum of Pr alone. Through a systematic analysis of solutions across this spectrum, we determine the transition length on which laminar to turbulent flow occurs, separating the plume into three regions - the laminar, the turbulent and an intervening transition zone - and explore the relative size and growth rate of these regions.

In the stratified case, an additional dimensionless number is introduced, Re, representing the relative importance of viscosity. Remarkably, the rise height of a plume varies non-monotonically with this parameter, reaching a global maximum for Re ≈ 700. As Re is increased beyond this maximal value, the rise height decreases slowly towards an asymptote of 4.3 as Re → ∞, recovering the limit in which the plume becomes independent of both viscosity and thermal diffusivity.