Session J12: Convection and Buoyancy-Driven Flows: Free Convection

Effect of a single sidewall cooling on Rayleigh-Bénard convection

Rayleigh-Bénard conveciton is a canonic scenario for studying the thermal convection phenomenon. We explored this probelm with a single sidewall cooling in a rectangular tank. The fluid was heated from the bottom and cooled at the top, and one sidewall had the same temperature as the top cooling; the other sidewalls kept adiabatic conditions. The flow field was characterized using particle image velocimetry at various vertical planes parallel and perpendicular to the cooling sidewall. A canonic RB convection without lateral cooling was also studied to aid insight into the modulation of lateral cooling at Rayleigh-number of Ra = 1.6×10¹⁰ and Prandtl number of Pr = 5.4. Results show that the single sidewall cooling induced flow asymmetry with strong descending motions near the cooling wall, modulating the spatial features of the large-scale circulation (LSC). The asymmetry in the system prevented LSC reversal. It also redistributed thermal diffusion and buoyancy effects, represented by an effective Ra. Flow statistics departed from the canonical case, with reduced impact relatively farther from the sidewall cooling. Velocity spectra showed two scalings, Kolmogorov and Bolgiano types. Inspection of the LSC core motions allowed us to identify a distinct mode with a characteristic timescale on the order of vortex turnover time, which can be associated with different vortex modes. The velovity spectra of the vortex core oscillation along its principal axis showed a -5/3 spectral scaling for the single sidewall cooling, which was dominant closer to the side cooling.    

Multi-alpha analysis of the mean-field Boussinesq equations

The quasilinear (QL) approximation, in which fluctuation/fluctuation nonlinearities are suppressed except where they feed back upon a suitably defined mean field, has a long history in fluid mechanics, dating back at least to the work of Stuart (1958) and Herring (1963, 1964) in their investigations of shear and convective turbulence. Interestingly, the Euler--Lagrange equations arising from variational analyses that yield rigorous bounds on the achievable momentum and heat transport in these flows have a similar QL form. Busse (1969, 1970, 1978) leveraged this mathematical structure to construct optimal momentum and heat transporting fields that include a hierarchy of horizontal wavenumbers. The resulting 'multi-alpha' optimal solutions exhibit nested boundary layers, reminiscent of Townsend's attached eddies. Here, we investigate the extent to which Busse's innovative multi-alpha asymptotic analysis can be adapted to obtain multiscale solutions of QL dynamical models. We pursue this investigation in the context of Rayleigh--Benard convection between stress-free isothermal boundaries, thereby extending an analysis by Howard (1965), who constructed steady single-wavenumber solutions to the mean-field (QL) Boussinesq equations in the large Rayleigh number limit.   

Wall modes and bulk convection in rapidly rotating Rayleigh-Bénard convection

We characterize the first transition to convection via wall mode instability and the nonlinear growth and instability of the resulting wall mode states including a secondary transition to time dependence. We describe how the transition to a state of bulk convection is influenced by the presence of the wall mode states and use temporal and spatial scales as measures of the local state of convection and heat transport Nu and momentum Re as representative of global transport. Our results elucidate the evolution of the wall state of rotating convection and confirm that wall modes and the BZF are strongly linked with the BZF being the robust remnant of nonlinear wall mode states. We also show how the heat transport Nu contributions of wall modes and bulk modes are related and how to disentangle their relative contributions.

[1] R.E. Ecke, X. Zhang, and O. Shishkina, Physical Review Fluids 7, L011501 (2022).

    

Heat flux enhancement by regular surface protrusions in turbulent thermal convection

We performed two-dimensional numerical simulations in a square Rayleigh-B\'{e}nard (RB) convection enclosure with equally spaced protrusions in the top and bottom conduction plates for the range of Rayleigh number $10^6$ to $10^8$ and at a fixed Prandtl number of $1$. The protrusions are in the form of a parallelepiped base and triangular top with vertex angle $90^o$. We have varied the protrusion height from $10\%$ to $25\%$ of enclosure height and found an increase in heat flux approximately up to $1.38$ times of classical square RB. The enhancement in heat transport up to a certain protrusion height and the heat transport decreases with a further increase in protrusion height. As protrusion height increases, the large-scale circulation can not thoroughly wash out the cavity between two consecutive protrusions.   

Hysteresis Impacts in Steady Flow Transitions of the Rayleigh Bénard Problem

Policymakers are searching for conscious solutions to the global threat of climate change and nuclear power is an unavoidable part of any combatting strategy. Public perception of nuclear safety was eroded by the Fukushima Daiichi accident in the spring of 2011. Research programs after the accident have focused on safety improvements of modern reactor designs. Important to these efforts is the refinement of Severe Accident Management strategies, such as External Reactor Vessel Cooling. This strategy relies on a low enough outward facing heat flux to prevent failure of the submerged reactor vessel lower head when under thermal assault from the naturally circulating molten reactor core. Correlations used to predict the subject heat transfer problem have low confidence in applicability, being derived from simplified, steady-flow experiments. We will present transient direct numerical simulations of the Rayleigh Bénard problem with internally heated convection using a scalable, in-house Navier-Stokes solver, with optimal concervation properties.  We will showcase the presense of a hysteresis effect to the subject heat transfer problem. The observed transition Nusselt numbers are under-predicted by the steady value by more than the thermal margin available in published safety analyses in some cases. This transition is brief and may likely abated by the heat capacity of the reactor vessel.

    

Effect of Sierpinski carpet geometry on the distribution of the convection heat transfer coefficient in cooling fins

Different approaches have been studied to improve the heat exchange capacity of the fins. One of these, involves manufacturing windows in rectangular fins according to the fractal Sierpinski carpet. In this research field the main efforts have been focused on the global heat transfer per unit of mass of the fin, showing promising results. The present work is aimed to study the effect of window patterns on the local heat transfer coefficient. Each fin consists of a copper-squared plate of 10 cm per side and 3.14 mm of thickness. The window patterns were manufactured on the fins according to the first, second and third step of the Sierpinski carpet respectively. A fourth fin with no windows was used as a benchmark case. The inverse heat transfer problem was used to compute the local heat transfer coefficients. This method requires the temperature distribution on the fin surface as a reference data set, which was measured using an infrared camera. Computations of the tridimensional heat conduction problem for each fin were performed using ANSYS and applying similar boundary conditions of the experiments. The local heat transfer coefficient was estimated using the steepest descent method. Results shown the local heat transfer is strongly affected by the windows, mainly in its tip.

    

Oscillations of the large-scale circulation in experimental liquid metal convection at aspect ratios 1.4–3

We investigate the scaling properties of the primary flow modes and their sensitivity to aspect ratio in a liquid gallium convection system through combined laboratory experiments and numerical simulations. We survey cylindrical aspect ratios 1.4 ≤ Γ ≤ 3 and Rayleigh numbers 10⁴ <∽ Ra <∽ 10⁶. In this range the flow is dominated by a large-scale circulation (LSC) subject to low-frequency oscillations. In line with previous studies, we show robust scaling of the Reynolds number (Re) with Ra and we confirm that the LSC flow is dominated by a jump rope vortex (JRV) mode whose signature frequency is present in velocity and temperature measurements. 

We further show that both Re and JRV frequency scaling trends are relatively insensitive to container geometry. The temperature and velocity spectra consistently show peaks at the JRV frequency, its harmonic, and a secondary mode. The relative strength of these peaks changes, and the presence of the secondary peak depends highly on aspect ratio, indicating that, despite having a minimal effect on typical velocities and frequencies, the aspect ratio has a significant effect on the underlying dynamics. Applying a bandpass filter at the secondary frequency to velocity measurements reveals that a clockwise twist in the upper half of the fluid layer coincides with a counterclockwise twist in the bottom half, indicating a torsional mode. For aspect ratio Γ = 3, the unified LSC structure breaks down into multiple rolls in both simulation and experiment.   

Data-Driven Modeling of Rayleigh-Bernard & Vertical Convection in a Two-Phase Cryogenic Fuel Storage Tank Using Sparse Identification of Nonlinear Dynamics

A novel data-driven approach was developed and applied in this study in order to investigate Rayleigh-Bernard and vertical convection in a two-phase cryogenic fuel tank with varying gravity levels. Initially, a pressurized cryogenic tank was simulated using a joint CFD-multinodal technique (CMT), with the gas section developed by a multinode model and the fuel section developed by an axisymmetric CFD solver. As the direct numerical simulation of the liquid part would be computationally expensive, a new data-driven technique called Sparse Identification of Nonlinear Dynamics (SINDy) was utilized to reduce the order of the CFD model. By using the appropriate orthogonal decomposition modes based upon the high-fidelity simulation, SINDy determines the reduced-order model of governing equations. We will link the determined nonlinear compact ordinary differential equations to the multinodal ODE equations for the gas section. We will demonstrate how the SINDy-based CMT overcomes the liability of pure multinodal approaches for capturing the complexity of cryogenic flow dynamics in a two-phase fuel tank under various gravity levels for long-duration investigation.   

Not Participating

Natural convection continues to be an interesting research topic since a variety of fundamental questions are not fully addressed, and new and exciting experimental techniques offer opportunities to cast further light on the topic. In this study, the three-dimensional convection is generated in octagonal water tank with diameter of 33cm and aspect ratio of 0.753, with heating from the bottom and cooling from the top. The nonintrusive measurement of velocity and acceleration are performed with our Lagrangian Particle Tracking system. Simultaneously, color signals of thermochromic liquid crystals (TLCs) are recorded to perform temperature measurements in the illumination plane. The main reason why TLCs are used for temperature measurement is that they display a definite color at different temperatures. Calibration, which correlates temperature and colors of TLCs, is the essential step of this methodology. The calibration process presents the challenge of correlating 3 channel color information (RGB) with a scalar, temperature. To overcome this challenge, proper orthogonal decomposition (POD) is applied to the RGB data. As a result, statistics of velocity, acceleration and temperature measurements are obtained for different Rayleigh numbers.   

An extension to the problem of natural convection of a newtonian fluid in a rectangular cavity

The convection in a cavity filled with a newtonian fluid and heated from below has been extended to consider the thermal properties of the walls. The theoretical hyrodynamics of a confined fluid in a cavity has been studied for thermal insulating (TI) or perfect thermal conducting (PTC) walls. Thus, the known 2D problem of the Rayleigh convection has been reworked with thermal boundary conditions incluidng the Biot number (Bi). Previous theoretical results for situations with TI walls, with PTC walls or even combinations of those type of walls were bridged so that a more detailed picture of the hydrodynamics could be obtained. The study was constrained to the onset of convection in steady conditions so that only the Rayleigh number (Ra) was computed. Results shall be presented as plots of the Ra against aspect ratio of the cavity for fixed values of the Bi. Since the TI and PTC extreme cases were bridged by using small Bi steps results were taken as valid. However, the plots of the Ra against the aspect ratio are quite similar to those previously reported with differences in the magnitudes of the Ra which smoothly changes between the two extreme cases. Further discussion on the the heat transport physical mechanism and changes in the number of rolls shall be given.   

Interpretable Deep Learning for Turbulent Heat Transfer with Prandtl Number Effect

We investigate the prediction and interpretation of Prandtl number effect in turbulent heat transfer using deep learning. Turbulent heat transfer is an important physical phenomenon observed in industries such as heat exchangers and gas turbines, and its prediction is very important. However, the distribution of heat transfer is very different according to Prandtl number (Pr), and this nonlinearity makes it difficult to predict heat transfer. In this study, the turbulent heat transfer was considered for the analysis of the Prandtl effect. First, conditional generative adversarial networks (cGAN) predicted the surface heat flux for Pr = 0.1-7 from wall information, streamwise and spanwise shear stresses. Our model was able to generate heat flux well reflecting the characteristics for Pr. Furthermore, we analyzed the nonlinear relationship between input and output for Pr using a gradient map and decomposition algorithm. Through these methods, we find that the model learns spatially shifting characteristics for strong local heat fluxes for Pr from the same wall shear stresses in predicting heat fluxes.