arXiv subjects

Heng-Dong Xi

Publications and source records attributed to Heng-Dong Xi.

At least 19 recordsLinked to original sources

arXiv2026

Buoyancy-induced velocity dip in turbulent open Poiseuille--Rayleigh--Bénard convection

We investigate buoyancy-induced transitions in flow structure and the associated velocity dip in turbulent mixed convection. Numerical simulations are performed for an open Poiseuille--Rayleigh--Bénard system with a heated no-slip lower wall and a cooled free-slip upper boundary over $10^5 \leq Ra \leq 10^8$, $90 \leq Re_b \leq 5700$, $Pr=0.71$, and $0.013 \leq Ri_b \leq 17$. The flow organisation is governed primarily by the bulk Richardson number $Ri_b$. As buoyancy increases, the flow changes from a shear-dominated state to streamwise-oriented large-scale rolls and then to fragmented rolls. Roll formation coincides with a reorganisation of the velocity statistics about the channel midplane and a displacement of the maximum mean streamwise velocity from the upper boundary into the channel interior, producing a velocity dip. The mean momentum balance shows that spatially uniform streamwise forcing imposes a linear total-stress profile. Wherever the Reynolds shear stress exceeds the local total stress, the viscous stress and mean velocity gradient must be negative. A triple decomposition attributes most of the Reynolds-stress excess in the roll states to slowly varying, roll-associated motions. The roll-associated stress and dip strength vary non-monotonically with $Ri_b$. Quadrant analysis shows that ejections and sweeps sustain the net roll-associated stress, whereas roll fragmentation strengthens the cancellation between positive and negative contributions and weakens the dip. The turbulent kinetic energy (TKE) budget shows a corresponding shift from near-wall shear production to bulk buoyancy production, with shear production becoming negative above the velocity maximum. Finally, a case-specific \textit{a posteriori} simplification of the core-region TKE budget yields an approximate velocity profile that captures the gradient reversal.

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arXiv2026

Learning to traverse convective flows at moderate to high Rayleigh numbers

We study the navigation of a self-propelled inertial particle in two-dimensional Rayleigh-Bénard convection at Prandtl number $Pr=0.71$ and cell aspect ratio $Γ=4$ for Rayleigh numbers $Ra$ ranging from $10^7$ to $10^{11}$. A reinforcement-learning (RL) controller selects the propulsive acceleration, subject to an upper bound $\mathcal{A}_{\max}$, to achieve a prescribed horizontal displacement. We find that the success rate increases abruptly with $\mathcal{A}_{\max}$ at moderate $Ra$, whereas at higher $Ra$ the transition becomes more gradual and shifts to larger $\mathcal{A}_{\max}$. Moreover, although the completion time increases with $Ra$, the propulsion energy required for successful traversal decreases. Proper orthogonal decomposition indicates that these performance differences are associated with reorganisation of the carrier flow. At moderate $Ra$, the dominant large-scale circulation partitions the domain through persistent transport barriers, requiring a finite thrust surplus to cross them; at higher $Ra$, energy is distributed across many modes, the barriers fragment and transient plume-assisted pathways emerge. Compared with a constant-heading baseline, the learned policy aligns with local currents and consumes significantly less energy. Lagrangian coherent structure analysis further suggests that the RL agent tends to cross repelling barriers and surf along attracting pathways. Finally, by mapping these behaviours onto the local Eulerian flow topology using Voronoi tessellation and the $Q$-criterion, we distil an interpretable, physics-based heuristic strategy that retains robust navigability. These results connect turbulent-flow organisation with autonomous navigation under bounded actuation.

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arXiv2026

Triggering of extreme events and coherent-structure modulation in wall-turbulence under cyclostationary forces

Atmospheric gusts expose wall-bounded turbulence to severe unsteady forcing, triggering complex non-equilibrium dynamics and extreme aerodynamic loads. In this study, direct numerical simulations are performed to investigate the spatiotemporal modulation of turbulent structures and the triggering mechanisms of near-wall extreme events under Gaussian-type transient forcing. The results reveal that high-amplitude gusts inject energy primarily into the streamwise velocity component, inducing a pronounced non-equilibrium phase lag during turbulent energy redistribution. This process produces hysteresis in wall friction and extends the relaxation time. Spectral and continuous wavelet analyses demonstrate that intense gust forcing suppresses high-frequency random fluctuations and reorganizes turbulent kinetic energy into low-frequency coherent structures. The characteristic frequency of these energetic structures locks onto the gust driving frequency, with a relative deviation of only $2.4\%$. Furthermore, the occurrence probability of extreme near-wall events, including extreme positive (EP) wall-shear-stress events and rare backflow (BF) events, increases by up to an order of magnitude under severe forcing. Using a two-step conditional averaging technique, we demonstrate that BF events are actively driven by intense, localized adverse pressure gradients and energetic ejections, which promote spanwise vortex roll-up in the buffer layer. By contrast, EP events are governed by energetic sweeps of high-speed fluid that compress intense spanwise vorticity into the immediate vicinity of the wall. These findings provide physical insights into non-equilibrium energy transfer and offer theoretical guidance for load alleviation and robust flow control of unmanned aerial vehicles operating in unsteady atmospheric environments.

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arXiv2026

Measured multiple flow states in turbulent thermal convection with aspect ratio 10

We report an experimental investigation of turbulent Rayleigh-Benard convection in a rectangular cell of large aspect ratio ($Γ= 10$) over the Rayleigh number range $5.4\times10^7 \le Ra \le 7.2\times10^9$ and Prandtl number range $4.3 \le Pr \le 67.3$. Planar particle image velocimetry measurements show that the flow self organises into several horizontally stacked convection rolls, and repeated experiments under identical parameters (both $Ra$ and $Pr$) reveal that the number of rolls varies within the range of 3 to 7 with 6 being the most probable, which demonstrates the presence of multiple flow states. When $Pr$ is increased to 67.3, the number of roll like structures increases significantly, indicating a structural transition from a roll dominated to a plume dominated flow. This transition is reflected in the global momentum transport, for $Pr \leq 18.3$ the Reynolds number scales as $Re \sim Ra^{0.58}Pr^{-0.97}$, whereas the scaling is changed to $Re \sim Ra^{0.72}$ when $Pr$ reaches 67.3. Within individual rolls, we further examine the Reynolds numbers based on horizontal and vertical velocity components, $Re_{u,\text{roll}}$ and $Re_{w,\text{roll}}$, and find that the former increases while the latter decreases with roll size (quantified as the aspect ratio of the roll $Γ_\text{roll}$) due to continuity constraints, with their ratio following $Re_{w,\text{roll}}/Re_{u,\text{roll}} \sim Γ_\text{roll}^{-0.61}$. We impose different initial flow conditions (roll structures) with controlled perturbations, and demonstrate that the initial condition can influence the final turbulent state. We show that the number of horizontally stacked rolls regulates the global transport, larger number of rolls induces greater vertical momentum and heat transfer.

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arXiv2026

Super-resolution reconstruction of turbulent flows from a single Lagrangian trajectory

We studied the reconstruction of turbulent flow fields from trajectory data recorded by actively migrating Lagrangian agents. We propose a deep-learning model, track-to-flow (T2F), which employs a vision transformer as the encoder to capture the spatiotemporal features of a single agent trajectory, and a convolutional neural network as the decoder to reconstruct the flow field. To enhance the physical consistency of the T2F model, we further incorporate a physics-informed loss function inspired by the framework of physics-informed neural network (PINN), yielding a variant model referred to as T2F+PINN. We first evaluate both models in a laminar cylinder wake flow at a Reynolds number of $Re = 800$ as a proof of concept. The results show that the T2F model achieves velocity reconstruction accuracy comparable to that of existing flow reconstruction methods, while the T2F+PINN model reduces the normalised error in vorticity reconstruction relative to the T2F model. We then apply the models in a turbulent Rayleigh-Bénard convection at a Rayleigh number of $Ra = 10^8$ and a Prandtl number of $Pr = 0.71$. The results show that the T2F model accurately reconstructs both the velocity and temperature fields, whereas the T2F+PINN model further improves the reconstruction accuracy of gradient-related physical quantities, such as temperature gradients, vorticity and the Q value, with a maximum improvement of approximately 60 % compared to the T2F model. Overall, the T2F model is better suited for reconstructing primitive flow variables, while the T2F+PINN model provides advantages in reconstructing gradient-related quantities. Our models open a promising avenue for accurate flow reconstruction from a single Lagrangian trajectory.

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arXiv2025

Statistics of velocity gradient and vortex sheet structures in polymeric turbulent von K{á}rm{á}n swirling flow

Investigations into the effects of polymers on small-scale statistics and flow patterns were conducted in a turbulent von Karman swirling (VKS) flow. We employed the tomographic particle image velocimetry (Tomo-PIV) technique to obtain full information on three-dimensional velocity data, allowing us to effectively resolve dissipation scales. Under varying Reynolds numbers ($R_λ=168 - 235$) and polymer concentrations ($ϕ=0 -25~\rm ppm$), we measured the velocity gradient tensor (VGT) and related quantities. Our findings reveal that the ensemble average and probability density function (PDF) of VGT invariants, which represent turbulent dissipation and enstrophy along with their generation terms, are suppressed as polymer concentration increases. Notably, the joint PDFs of the invariants of VGT, which characterize local flow patterns, exhibited significant changes. Specifically, the third-order invariants, especially the local vortex stretching, are greatly suppressed, and strong events of dissipation and enstrophy coexist in space. The local flow pattern tends to be two-dimensional, where the eigenvalues of the rate-of-strain tensor satisfy a ratio $1:0:-1$, and the vorticity aligns with the intermediate eigenvector of the rate-of-strain tensor while is perpendicular to the other two. We find that these statistics observations can be well described by the vortex sheet model. Moreover, we find that these vortex sheet structures align with the symmetry axis of the VKS system and orient randomly in the horizontal plane. Further investigation, including flow visualization and conditional statistics on vorticity, confirms the presence of vortex sheet structures in turbulent flows with polymer additions. Our results establish a link between single-point statistics and small-scale flow topology, shedding light on the previously overlooked small-scale structures in polymeric turbulence.

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arXiv2025

Temporal modulation on mixed convection in turbulent channels

We studied flow organization and heat transfer properties in mixed turbulent convection within Poiseuille-Rayleigh-Bénard channels subjected to temporally modulated sinusoidal wall temperatures. Three-dimensional direct numerical simulations were performed for Rayleigh numbers in the range $10^6 \leq Ra \leq 10^8$, a Prandtl number $Pr = 0.71$ and a bulk Reynolds number $Re_b \approx 5623$. We found that high-frequency wall temperature oscillations had minimal impact on flow structures, while low-frequency oscillations induced adaptive changes, forming stable stratified layers during cooling. Proper orthogonal decomposition (POD) analysis revealed a dominant streamwise unidirectional shear flow mode. Large-scale rolls oriented in the streamwise direction appeared as higher POD modes and were significantly influenced by lower-frequency wall temperature variations. Long-time-averaged statistics showed that the Nusselt number increased with decreasing frequency by up to 96\%, while the friction coefficient varied by less than 15\%. High-frequency modulation predominantly influenced near-wall regions, enhancing convective effects, whereas low frequencies reduced these effects via stable stratified layer formation. Phase-averaged statistics showed that high-frequency modulation resulted in phase-stable streamwise velocity and temperature profiles, while low-frequency modulation caused significant variations due to weakened turbulence. Turbulent kinetic energy (TKE) profiles remained high near the wall during both heating and cooling at high frequency, but decreased during cooling at low frequencies. A TKE budget analysis revealed that during heating, TKE production was dominated by shear near the wall and by buoyancy in the bulk region; while during cooling, the production, distribution and dissipation of TKE were all nearly zero.

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arXiv2024

Global drag reduction and local flow statistics in Taylor-Couette turbulence with dilute polymer additives

We present an experimental study on the drag reduction by polymers in Taylor-Couette turbulence at Reynolds numbers ($Re$) ranging from $4\times 10^3$ to $2.5\times 10^4$. In this $Re$ regime, the Taylor vortex is present and accounts for more than 50\% of the total angular velocity flux. Polyacrylamide polymers with two different average molecular weights are used. It is found that the drag reduction rate increases with polymer concentration and approaches the maximum drag reduction (MDR) limit. At MDR, the friction factor follows the $-0.58$ scaling, i.e., $C_f \sim Re^{-0.58}$, similar to channel/pipe flows. However, the drag reduction rate is about $20\%$ at MDR, which is much lower than that in channel/pipe flows at comparable $Re$. We also find that the Reynolds shear stress does not vanish and the slope of the mean azimuthal velocity profile in the logarithmic layer remains unchanged at MDR. These behaviours are reminiscent of the low drag reduction regime reported in channel flow (Warholic et al., Exp. Fluids, vol. 27, issue 5, 1999, p. 461-472). We reveal that the lower drag reduction rate originates from the fact that polymers strongly suppress the turbulent flow while only slightly weaken the mean Taylor vortex. We further show that polymers steady the velocity boundary layer and suppress the small-scale Görtler vortices in the near-wall region. The former effect reduces the emission rate of both intense fast and slow plumes detached from the boundary layer, resulting in less flux transport from the inner cylinder to the outer one and reduces energy input into the bulk turbulent flow. Our results suggest that in turbulent flows, where secondary flow structures are statistically persistent and dominate the global transport properties of the system, the drag reduction efficiency of polymer additives is significantly diminished.

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arXiv2024

Particle transport and deposition in wall-sheared thermal turbulence

We studied the transport and deposition behaviour of point particles in Rayleigh-Bénard convection cells subjected to Couette-type wall shear. Direct numerical simulations (DNSs) are performed for Rayleigh number ($Ra$) in the range $10^7 \leq Ra \leq 10^9$ with a fixed Prandtl number $Pr = 0.71$, while the wall-shear Reynolds number ($Re_w$) is in the range $0 \leq Re_w \leq 12000$. With the increase of $Re_w$, the large-scale rolls expanded horizontally, evolving into zonal flow in two-dimensional simulations or streamwise-oriented rolls in three-dimensional simulations. We observed that, for particles with a small Stokes number ($St$), they either circulated within the large-scale rolls when buoyancy dominated or drifted near the walls when shear dominated. For medium $St$ particles, pronounced spatial inhomogeneity and preferential concentration were observed regardless of the prevailing flow state. For large $St$ particles, the turbulent flow structure had a minor influence on the particles' motion; although clustering still occurred, wall shear had a negligible influence compared with that for medium $St$ particles. We then presented the settling curves to quantify the particle deposition ratio on the walls. Our DNS results aligned well with previous theoretical predictions, which state that small $St$ particles settle with an exponential deposition ratio and large $St$ particles settle with a linear deposition ratio. For medium $St$ particles, where complex particle-turbulence interaction emerges, we developed a new model describing the settling process with an initial linear stage followed by a nonlinear stage. Unknown parameters in our model can be determined either by fitting the settling curves or using empirical relations. Compared with DNS results, our model also accurately predicts the average residence time across a wide range of $St$ for various $Re_w$.

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arXiv2023

Pore-scale statistics of temperature and thermal energy dissipation rate in turbulent porous convection

We report pore-scale statistical properties of temperature and thermal energy dissipation rate in a two-dimensional porous Rayleigh-Bénard (RB) cell. High-resolution direct numerical simulations were carried out for the fixed Rayleigh number ($Ra$) of $10^{9}$ and the Prandtl numbers ($Pr$) of 5.3 and 0.7. We consider sparse porous media where the solid porous matrix is impermeable to both fluid and heat flux. The porosity ($ϕ$) range $0.86 \leq ϕ\le 0.98$, the corresponding Darcy number ($Da$) range $10^{-4}<Da<10^{-2}$ and the porous Rayleigh number ($Ra^{*}=Ra\cdot Da$) range $10^{5} < Ra^{*} < 10^{7}$. Our results indicate that the plume dynamics in porous RB convection are less coherent when the solid porous matrix is impermeable to heat flux, as compared to the case where it is permeable. The averaged vertical temperature profiles remain almost a constant value in the bulk, while the mean-square fluctuations of temperature increases with decreasing porosity. Furthermore, the absolute values of skewness and flatness of the temperature are much smaller in the porous RB cell than in the canonical RB cell. We found that intense thermal energy dissipation occurs near the top and bottom walls, as well as in the bulk region of the porous RB cell. In comparison with the canonical RB cell, the small-scale thermal energy dissipation field is more intermittent in the porous cell, although both cells exhibit a non-log-normal distribution of thermal energy dissipation rate. This work highlights the impact of impermeable solid porous matrices on the statistical properties of temperature and thermal energy dissipation rate, and the findings may have practical applications in geophysics, energy and environmental engineering, as well as other fields that involve the transport of heat through porous media.

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arXiv2023

Wall-sheared thermal convection: heat transfer enhancement and turbulence relaminarization

We studied the flow organization and heat transfer properties in two-dimensional and three-dimensional Rayleigh-Bénard cells that are imposed with different types of wall shear. The external wall shear is added with the motivation of manipulating flow mode to control heat transfer efficiency. We imposed three types of wall shear that may facilitate the single-roll, the horizontally stacked double-roll, and the vertically stacked double-roll flow modes, respectively. Direct numerical simulations are performed for fixed Rayleigh number $Ra = 10^{8}$ and fixed Prandtl number $Pr = 5.3$, while the wall-shear Reynolds number ($Re_{w}$) is in the range $60 \le Re_{w} \le 6000$. Generally, we found enhanced heat transfer efficiency and global flow strength with the increase of $Re_{w}$. However, even with the same magnitude of global flow strength, the heat transfer efficiency varies significantly when the cells are under different types of wall shear. An interesting finding is that by increasing the wall-shear strength, the thermal turbulence is relaminarized, and more surprisingly, the heat transfer efficiency in the laminar state is higher than that in the turbulent state. We found that the enhanced heat transfer efficiency at the laminar regime is due to the formation of more stable and stronger convection channels. We propose that the origin of thermal turbulence laminarization is the reduced amount of thermal plumes. Because plumes are mainly responsible for turbulent kinetic energy production, when the detached plumes are swept away by the wall shear, the reduced number of plumes leads to weaker turbulent kinetic energy production. We also quantify the efficiency of facilitating heat transport via external shearing, and find that for larger $Re_{w}$, the enhanced heat transfer efficiency comes at a price of a larger expenditure of mechanical energy.

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arXiv2023

Long-distance migration with minimal energy consumption in a thermal turbulent environment

We adopt the reinforcement learning algorithm to train the self-propelling agent migrating long-distance in a thermal turbulent environment. We choose the Rayleigh-Bénard turbulent convection cell with an aspect ratio ($Γ$, which is defined as the ratio between cell length and cell height) of 2 as the training environment. Our results showed that, compared to a naive agent that moves straight from the origin to the destination, the smart agent can learn to utilize the carrier flow currents to save propelling energy. We then apply the optimal policy obtained from the $Γ=2$ cell and test the smart agent migrating in convection cells with $Γ$ up to 32. In a larger $Γ$ cell, the dominant flow modes of horizontally stacked rolls are less stable, and the energy contained in higher-order flow modes increases. We found that the optimized policy can be successfully extended to convection cells with a larger $Γ$. In addition, the ratio of propelling energy consumed by the smart agent to that of the naive agent decreases with the increase of $Γ$, indicating more propelling energy can be saved by the smart agent in a larger $Γ$ cell. We also evaluate the optimized policy when the agents are being released from the randomly chosen origin, which aims to test the robustness of the learning framework, and possible solutions to improve the success rate are suggested. This work has implications for long-distance migration problems, such as unmanned aerial vehicles patrolling in a turbulent convective environment, where planning energy-efficient trajectories can be beneficial to increase their endurance.

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arXiv2022

Migration of self-propelling agent in a turbulent environment with minimal energy consumption

We present a numerical study of training a self-propelling agent to migrate in the unsteady flow environment. We control the agent to utilize the background flow structure by adopting the reinforcement learning algorithm to minimize energy consumption. We considered the agent migrating in two types of flows: one is simple periodical double-gyre flow as a proof-of-concept example, while the other is complex turbulent Rayleigh-Bénard convection as a paradigm for migrating in the convective atmosphere or the ocean. The results show that the smart agent in both flows can learn to migrate from one position to another while utilizing background flow currents as much as possible to minimize the energy consumption, which is evident by comparing the smart agent with a naive agent that moves straight from the origin to the destination. In addition, we found that compared to the double-gyre flow, the flow field in the turbulent Rayleigh-Bénard convection exhibits more substantial fluctuations, and the training agent is more likely to explore different migration strategies; thus, the training process is more difficult to converge. Nevertheless, we can still identify an energy-efficient trajectory that corresponds to the strategy with the highest reward received by the agent. These results have important implications for many migration problems such as unmanned aerial vehicles flying in a turbulent convective environment, where planning energy-efficient trajectories are often involved.

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arXiv2022

Production and transport of vorticity in two-dimensional Rayleigh-Bénard convection cell

We present a numerical study of vorticity production and transport in the two-dimensional Rayleigh-Bénard (RB) convection. Direct numerical simulations are carried out in the Rayleigh number ($Ra$) range $10^{5}\le Ra \le 10^{6}$, the Prandtl number ($Pr$) of 0.71, and the aspect ratio ($Γ$) of the convection cell range $0.75\le Γ\le 6$. We found that the flow structure and temperature distribution vary with $Γ$ greatly due to multiple vortices interaction. Further investigation on the vorticity production and transport reveals that, in the RB convection, in addition to the vorticity production due to wall shear stress, buoyancy produces significant vorticity in the bulk region. The produced vorticity is transported via advection and diffusion. An interesting finding is that the main vortices and the corner vortices can be visualized via the contour of buoyancy-produced vorticity. Although a vigorous definition of the vortex is still lacking in the community, our efficient vortex visualization approach in the RB convection may shed light on further research toward vortex identification. We also found that the spatial distribution of vorticity flux along the wall is positively correlated with that of the Nusselt number ($Nu$), suggesting the amount of vorticity that enters the flow is directly related to the amount of thermal energy that enters the flow.

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arXiv2021

Experimental observation of the elastic range scaling in turbulent flow with polymer additives

Minute amount of long chain flexible polymer dissolved in a turbulent flow can drastically change flow properties, such as reducing the drag and enhancing mixing. One fundamental riddle is how these polymer additives interact with the eddies of different spatial scales existing in the turbulent flow and in turn alter the turbulence energy transfer. Here we show how turbulent kinetic energy is transferred through deferent scales in the presence of the polymer additives. In particular, we observed experimentally the emerging of a new scaling range, referred to as the elastic range, where increasing amount of energy is transferred by the elasticity of the polymers. In addition, the existence of the elastic range prescribes the scaling of high-order velocity statistics. Our findings have important implications to many turbulence systems such as turbulence in plasmas or superfluids where interaction between turbulent eddies and other nonlinear physical mechanisms are often involved.

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arXiv2021

Tristable flow states and reversal of the large-scale circulation in two-dimensional circular convection cells

We present a numerical study of the flow states and reversals of the large-scale circulation (LSC) in a two-dimensional circular Rayleigh-Bénard cell. Long-time direct numerical simulations are carried out in the Rayleigh number ($Ra$) range $10^{7} \le Ra \le 10^{8}$ and Prandtl number ($Pr$) range $2.0 \le Pr \le 20.0$. We found that a new, long-lived, chaotic flow state exists, in addition to the commonly observed circulation states (the LSC in the clockwise and counterclockwise directions). The circulation states consist of one primary roll in the middle and two secondary rolls near the top and bottom circular walls. The primary roll becomes stronger and larger, while the two secondary rolls diminish, with increasing $Ra$. Our results suggest that the reversal of the LSC is accompanied by the secondary rolls growing, breaking the primary roll and then connecting to form a new primary roll with reversed direction. We mapped out the phase diagram of the existence of the LSC and the reversal in the $Ra$-$Pr$ space, which reveals that the flow is in the circulation states when $Ra$ is large and $Pr$ is small. The reversal of the LSC can only occur in a limited $Pr$ range. The phase diagram can be understood in terms of competition between the thermal and viscous diffusions. We also found that the internal flow states manifested themselves into global properties such as Nusselt and Reynolds numbers.

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arXiv2020

Correlation of internal flow structure with heat transfer efficiency in turbulent Rayleigh-Bénard convection

To understand how internal flow structures manifest themselves in the global heat transfer, we study the correlation between different flow modes and the instantaneous Nusselt number ($Nu$) in a two-dimensional square Rayleigh-Bénard convection cell. High-resolution and long-time direct numerical simulations are carried out for Rayleigh numbers between $10^{7}$ and $10^{9}$ and a Prandtl number of 5.3. The investigated Nusselt numbers include the volume-averaged $Nu_{\text{vol}}$, the wall-averaged $Nu_{\text{wall}}$, the kinetic energy dissipation based $Nu_{\text{kinetic}}$, and the thermal energy dissipation based $Nu_{\text{thermal}}$. The Fourier mode decomposition and proper orthogonal decomposition are adopted to extract the coherent flow structure. Our results show that the single-roll mode, the horizontally stacked double-roll mode, and the quadrupolar flow mode are more efficient for heat transfer on average. In contrast, the vertically stacked double-roll mode is inefficient for heat transfer on average. The volume-averaged $Nu_{\text{vol}}$ and the kinetic energy dissipation based $Nu_{\text{kinetic}}$ can better reproduce the correlation of internal flow structures with heat transfer efficiency than that of the wall-averaged $Nu_{\text{wall}}$ and the thermal energy dissipation based $Nu_{\text{thermal}}$, even though these four Nusselt numbers give consistent time-averaged mean values. The ensemble-averaged time trace of $Nu$ during flow reversal shows that only the volume-averaged $Nu_{\text{vol}}$ can reproduce the overshoot phenomena that is observed in the previous experimental study. Our results reveal that the proper choice of $Nu$ is critical to obtain a meaningful interpretation.

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arXiv2020

Transport and deposition of dilute microparticles in turbulent thermal convection

We analyze the transport and deposition behavior of dilute microparticles in turbulent Rayleigh-Bénard convection. Two-dimensional direct numerical simulations were carried out for the Rayleigh number ($Ra$) of $10^{8}$ and the Prandtl number ($Pr$) of 0.71 (corresponding to the working fluids of air). The Lagrangian point particle model was used to describe the motion of microparticles in the turbulence. Our results show that the suspended particles are homogeneously distributed in the turbulence for the Stokes number ($St$) less than $10^{-3}$, and they tend to cluster into bands for $10^{-3} \lesssim St \lesssim 10^{-2}$. At even larger $St$, the microparticles will quickly sediment in the convection. We also calculate the mean-square displacement (MSD) of the particle's trajectories. At short time intervals, the MSD exhibits a ballistic regime, and it is isotropic in vertical and lateral directions; at longer time intervals, the MSD reflects a confined motion for the particles, and it is anisotropic in different directions. We further obtained a phase diagram of the particle deposition positions on the wall, and we identified three deposition states depending on the particle's density and diameter. An interesting finding is that the dispersed particles preferred to deposit on the vertical wall where the hot plumes arise, which is verified by tilting the cell and altering the rotation direction of the large-scale circulation.

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