Search

This study investigates the effect of vibration on the flow structure transitions in thermal vibrational convection (TVC) systems, which occur when a fluid layer with a temperature gradient is excited by vibration. Direct numerical simulation (DNS) of TVC in a two-dimensional enclosed square box is performed over a range of dimensionless vibration amplitudes $0.001 \le a \le 0.3$ and angular frequencies $10^{2} \le \omega \le 10^{7}$ , with a fixed Prandtl number of 4.38. The flow visualisation shows the transition behaviour of flow structure upon the varying frequency, characterising three distinct regimes, which are the periodic-circulation regime, columnar regime and columnar-broken regime. Different statistical properties are distinguished from the temperature and velocity fluctuations at the boundary layer and mid-height. Upon transition into the columnar regime, columnar thermal coherent structures are formed, in contrast to the periodic oscillating circulation. These columns are contributed by the merging of thermal plumes near the boundary layer, and the resultant thermal updrafts remain at almost fixed lateral position, leading to a decrease in fluctuations. We further find that the critical point of this transition can be described nicely by the vibrational Rayleigh number ${{Ra}}_{vib}$. As the frequency continues to increase, entering the so-called columnar-broken regime, the columnar structures are broken, and eventually the flow state becomes a large-scale circulation (LSC), characterised by a sudden increase in fluctuations. Finally, a phase diagram is constructed to summarise the flow structure transition over a wide range of vibration amplitude and frequency parameters. [ABSTRACT FROM AUTHOR]

We experimentally study the heat transfer and flow characteristics of thermal convection in a rectangular cell with built-in lattice channels. The working fluid used is water with a Prandtl number of 5.5, and the Rayleigh number ranges from 2.5 × 10 8 to 6.9 × 10 9 . Three proposed models with different channel sizes and positions and the classical Rayleigh–Bénard convection (RBC) are studied, and the heat transfer and flow structure characteristics are analyzed using measured temperature signals. The first model included two short channels placed near the top and bottom plates, which disrupt the mixing zone and enhance heat transport. The second model involves relatively long channels positioned at the center of the cell, but far from the thermal boundary layer, resulting in a more coherent bulk flow that also enhances heat transport. For these two configurations, the heat transfer enhancement rate is approximately 20% compared to standard RBC. The third model uses long lattice channels that almost touches the top and bottom plates. This configuration results in a maximum heat transfer enhancement of about 138% due to the organized boundary layer and bulk flow induced by lattice channels. The presence of channels also results in a two-order smaller standard deviation of temperature, indicating a significant reduction in fluctuations. However, the average temperatures in the center of some channels were significantly different from the mean system temperature, suggesting the existence of cold or hot fluid flow through the channel. Our experimental results show that the inclusion of channels with appropriate lengths and positions can effectively regulate the flow near the boundary layer and in the bulk, leading to significant enhancements in heat transfer. [ABSTRACT FROM AUTHOR]

Thermal convection in nature and industrial applications usually encounters time-varying internal heating (IH); however, the effect of temporal modulation on temperature responses and heat fluxes of the system has been rarely explored. Here, we numerically studied the IH convection with a temporally periodic heating source. We conducted direct numerical simulations over Rayleigh number (Ra) range 10 5 ≤ R a ≤ 10 9 at fixed Prandtl number Pr = 1 with dimensionless modulation frequency 4 × 10 − 5 ≤ f ≤ 10 − 1 and amplitude fixed at Ω = 1. We first find that the introduction of periodic modulation has a slight effect on the heat transport over the individual plates and flow strength except for the lowest Ra. We then focus on the characteristics of the amplitude A and phase lag Δ ϕ of the globally averaged temperature response to the periodic modulation. Three regimes of the phase response are identified: (i) in-phase regime, where synchronous response is found at small frequencies with the vanished phase lag Δ ϕ and A keeping at constant value; (ii) transition regime, where both Δ ϕ and A decrease with increasing f for moderate frequencies; and (iii) half anti-phase regime, where Δ ϕ attains the minimal value − π / 2. We also find that the transition behavior between three regimes can be well described using the normalization of the Ra-dependent critical frequency with the scaling R a − 0.30 . To explain the regime transition, we further theoretically deduce an analytical solution for A and Δ ϕ , which agrees well with the numerical results. This solution can explain why f R a 0.30 gives a good description of the transition behavior. Our present findings provide a fundamental understanding of the underlying mechanism of temporal modulation on IH systems and have substantial implications for the investigation of convective system with periodic heating source. [ABSTRACT FROM AUTHOR]

Vertical convection (VC) under the action of vertical vibration in a square cavity has been investigated using direct numerical simulation. The simulations are conducted with Prandtl number Pr fixed at 4.38 and Rayleigh number Ra ranging from 10 8 to 10 10 . To examine the influence of vertical vibration, the dimensionless vibration frequency is varied in the range of 0 ≤ ω ≤ 1000 and a small dimensionless amplitude is fixed at a = 1.52 × 10 − 3 . First, for low vibration frequency, trivial results are obtained where flow structures and the scalings of Nu and Re resemble that of the standard VC cases. In contrast, when the vibration frequency ω increases beyond a critical value ω * , a strong shearing effect from vibration leads to abundant eruptions of thermal plumes from sidewalls, and thus a laminar-turbulent transition of the bulk flow. As a result, heat-transport is greatly enhanced and the scaling exponent β of N u ∼ R a β substantially increases in such the vibration-dominated regime. In specific, the scaling relations obtained transit from N u ∼ R a 0.25 and R e ∼ R a 0.37 at ω = 0 in the laminar regime to N u ∼ R a 0.42 and R e ∼ R a 0.52 at ω ≳ 300 in the turbulent regime. Analysis of the mean flow field shows that the vibration thins the thermal boundary layer and enhances the thermal dissipation rate in the bulk region. Furthermore, we found that the trend of Nu and Re can be well described by the vibrational Rayleigh number R a vib . In particular, Nu is insensitive to R a vib for R a vib ≤ R a vib * , whereas N u (ω) / N u (0) ∼ (R a vib / R a vib *) 0.42 for R a vib > R a vib * , where the critical vibrational Rayleigh number exhibits a scaling relation R a vib * ∼ R a 0.68 obtained from numerical results. [ABSTRACT FROM AUTHOR]

We investigate the flow characteristics and kinetic behaviors of particles in turbulent Rayleigh–Bénard convection particulate flows. Direct numerical simulations combined with a Lagrangian point-particle strategy were carried out in the range of Stokes numbers 2 × 10 − 4 ≤ S t L ≤ 7.3 × 10 − 2 for Rayleigh numbers from 2 × 10 6 to 10 8 at the Prandtl number P r = 0.678. A two-way coupling model is employed in which the momentum exchange between the dispersed particles and the carrier fluid is taken fully into account. Based on various patterns of particle motion, we find three transport modes of inertial particles which are labeled as the circling transport (CCT) mode, the channel transport (CNT) mode, and the downpour transport (DPT) mode, respectively. These modes can switch to each other when Stokes numbers and Rayleigh numbers vary and exhibit different effects of particle motions on the flow field and heat transfer. For the CCT and DPT modes, compared with the CNT, a weakening alteration of flow structures and thermal plumes leads to no significant effect on the transport of momentum and heat. For the CNT mode, a pronounced effect of particles on enhancements of the turbulent momentum transport and heat transfer relates to the strong interaction between the particle clusters and the chaotic structures of eddies. What is more, the particles tend to homogeneously distribute for the CCT and DPT modes, although the particles exhibit different transport states. As for the CNT mode, under both preferential sweeping and centrifugal effects, particles accumulate into clusters that hover toward the region of high strain rate and the edges of eddies. We found that the averaged particle settling speeds are almost proportional to the Stokes number. The particle settling speeds are larger than the terminal velocity of Stokesian particles for the CCT and CNT modes as particles tend to settle in the downward fluid. In contrast, it becomes smaller than the terminal velocity for the DPT mode due to the drag of the upward fluid. [ABSTRACT FROM AUTHOR]

We investigate the dynamic couplings between particles and fluid in turbulent Rayleigh–Bénard (RB) convection laden with isothermal inertial particles. Direct numerical simulations combined with the Lagrangian point-particle mode were carried out in the range of Rayleigh number $1\times 10^6 \le {Ra}\le 1 \times 10^8$ at Prandtl number ${Pr}=0.678$ for three Stokes numbers ${St_f}=1 \times 10^{-3}$ , $8 \times 10^{-3}$ and $2.5 \times 10^{-2}$. It is found that the global heat transfer and the strength of turbulent momentum transfer are altered a small amount for the small Stokes number and large Stokes number as the coupling between the two phases is weak, whereas they are enhanced a large amount for the medium Stokes number due to strong coupling of the two phases. We then derived the exact relation of kinetic energy dissipation in the particle-laden RB convection to study the budget balance of induced and dissipated kinetic energy. The strength of the dynamic coupling can be clearly revealed from the percentage of particle-induced kinetic energy over the total induced kinetic energy. We further derived the power law relation of the averaged particles settling rate versus the Rayleigh number, i.e. $S_p/(d_p/H)^2{\sim} Ra^{1/2}$ , which is in remarkable agreement with our simulation. We found that the settling and preferential concentration of particles are strongly correlated with the coupling mechanisms. [ABSTRACT FROM AUTHOR]

The heat transfer enhancement achieved by the additional electric field in Rayleigh–Bénard convection (RBC) of a dielectric fluid is numerically studied beyond the Rayleigh number Ra = 105. We carried out direct numerical simulations of RBC in a rectangular enclosure under the strong injection condition with a fixed non-dimensional injection parameter C = 10, a fixed mobility number M = 10, two Rayleigh numbers Ra = 105 and Ra = 106, and two Prandtl numbers Pr = 1 and Pr = 10 to investigate the characteristics of flow structure and heat transfer and evaluate the dependence on these parameters. It is observed that the flow structure exhibits multiple states with various steady or unsteady flow patterns such as four cells, three cells, and two cells (up/down). It is found that the introduction of an electric field is an effective way to achieve heat transfer enhancement. The heat flux is augmented more efficiently for a large Prandtl number and a low Rayleigh number, where the electric field has a strong effect relative to buoyancy. It is also found that heat transfer is most efficient when the flow pattern is in a three cells flow state. [ABSTRACT FROM AUTHOR]

Thermal convection in a tilted three-dimensional rectangular box has been systematically investigated by direct numerical simulation. The Rayleigh number Ra varies from 107 to 109, the Prandtl number Pr is set to 0.7, and the tilted angle β ranges from 0° to 90°. The effects of tilting on large-scale circulation (LSC), Nusselt number (Nu), Reynolds number (Re), and boundary layers (BLs) and the Ra-dependency are investigated. For large β exceeding certain values, say 45°, the stable temperature stratification forms in the bulk, resulting in low Re and Nu. It is found that the tilting leads to a distinct trend for Nu and Re: Nu first increases to some extent for small β, then nearly stays unchanged for moderate β, and finally decreases for large β, while Re initially increases for small β and then directly declines with increasing β. Based on the analysis of flow structures, with increasing β, it is found that the volume of the high-velocity tube (HVT) initially increases for 107 ≤ Ra ≤ 108 but decreases for Ra = 109, which is responsible for the variation in Nu at small β. The probability density functions of instantaneous convective heat transport within the HVT show higher probabilities for large values when β increases, implying that LSC tends to be more coherent and causing different tilting behaviors between Nu and Re. Finally, we find that, except for β = 90°, the normalized profiles of viscous and thermal BLs tend to have universal profiles, deviating from the BL of the Prandtl–Blasius–Pohlhausen (PBP) type to some extent regardless of β. Only the thermal BL for β = 90° is found to be in good agreement with the classic PBP laminar BL profile. [ABSTRACT FROM AUTHOR]

We carry out direct numerical simulations of turbulent Rayleigh–Bénard convection in a square box with rough conducting plates over the Rayleigh number range $10^7\leqslant Ra\leqslant 10^9$ and the Prandtl number range $0.01\leqslant Pr\leqslant 100$. In Zhang et al. (J. Fluid Mech., vol. 836, 2018, R2), it was reported that while the measured Nusselt number $Nu$ is enhanced at large roughness height $h$ , the global heat transport is reduced at small $h$. The division between the two regimes yields a critical roughness height $h_c$ , and we now focus on the effects of the Prandtl number ($Pr$) on $h_c$. Based on the variations of $h_c$ , we identify three regimes for $h_c(Pr)$. For low $Pr$ , thermal boundary layers become thinner with increasing $Pr$. This makes the boundary layers easier to be disrupted by rough elements, leading to the decrease of $h_c$ with increasing $Pr$. For moderate $Pr$ , the corner-flow rolls become much more pronounced and suppress the global heat transport via the competition between the corner-flow rolls and the large-scale circulation (LSC). As a consequence, $h_c$ increases with increasing $Pr$ due to the intensification of the corner–LSC competition. For high $Pr$ , the convective flow transitions to the plume-controlled regime. As the rough elements trigger much stronger and more frequent plume emissions, $h_c$ again decreases with increasing $Pr$. [ABSTRACT FROM AUTHOR]

Turbulent Rayleigh-Bénard convection in a square cavity with rough horizontal walls is investigated at a fixed Prandtl number Pr = 0.7 over the Rayleigh number range of 106 ≤ Ra ≤ 109. We have proposed five models with rough elements of the same height but different spatial distributions to evaluate their influences on the heat transport and flow structures of the system. It is found that the flow reversal can be promoted at a Rayleigh number around 107. In all the rough models, the heat transfer is impeded at a low Ra and enhanced at a Rayleigh number beyond a critical value. Interestingly, the heat transfer and flow structure can be clustered by the sparsity of the rough element distribution. Different scaling exponents for heat transfer are identified for sparsely distributed rough models and compactly distributed models. On the other hand, the spatial distribution of rough elements has little effect on the scaling of the Reynolds number. [ABSTRACT FROM AUTHOR]

We report an experimental study of turbulent Rayleigh-Bénard convection in a cylindrical cell of aspect ratio unity, focusing on the effects of the Prandtl number (Pr). Purified water was used as the convecting fluid. Five different Pr between 3.58 and 9.40 were achieved by changing the mean temperature of water, and the measurements were carried out over the Rayleigh number range 2.63 × 108 ≤ Ra ≤ 3.89 × 1010. Over the present parameter range, the measured Nusselt number Nu is found to scale as Nu ∼ Raβ with β = 0.30 and to be independent of Pr. Based on the oscillation period of the measured temperature, the Reynolds number Re scales as Re ∼ Ra0.47Pr−0.72. The local temperature fluctuations at the cell center and near the cell's sidewall were measured, and their relations with Ra and Pr were studied. Our results further reveal that the non-Oberbeck-Boussinesq effects of water have a relatively small influence on the measured scaling relation Nu ∼ Raβ. [ABSTRACT FROM AUTHOR]

Abstract: Rayleigh–Bénard convection under a low frequency traveling magnetic field (TMF) in a vertical cylinder is investigated by linear stability analysis. The cylinder with a adiabatic vertical wall is heated from below and cooled from above. The effects of traveling magnetic field on flow instability are studied for four aspect ratios (height/radius) A=1, 2, 3, 4 and three Prandtl numbers Pr=0.001, 0.02, 0.1. The critical Rayleigh number and corresponding critical frequency are evaluated as a function of TMF force Ft, and diversity profiles of stability curves are obtained under different control parameters. Moreover, stability properties for different Prandtl numbers are compared at fixed aspect ratios. The results obtained show that the magnetic force is able to either stabilize or destabilize the flow, which is determined by the effects of combination of the strength of the force, the aspect ratio and the Prandtl number. [Copyright &y& Elsevier]

In this study, we investigate the impact of spatial temperature modulation on vertical convection (VC) and analyze how the efficiency of heat transfer varies with modulation parameters. Our analysis focuses on the behavior of VC under sinusoidal temperature variations imposed on the hot wall, while maintaining a fixed temperature at the cold wall. The simulations are carried out in both two dimensions (2D) and three dimensions (3D), spanning a range of Rayleigh numbers, 10 6 ≤ R a ≤ 10 10 , and a dimensionless modulation wave number, 1 ≤ k ≤ 80 , while keeping the Prandtl number fixed at P r = 4.38. We identify three distinct regimes that exhibit different heat transfer behaviors. The first regime corresponds to an unperturbed state where the modulation effect does not penetrate the thermal boundary layer (BL). In the second regime, known as the weakly modulated regime, temperature modulation influences the thermal BL edge and strengthens the bulk stratification, resulting in an enhanced Nusselt number. Transitioning to the strongly modulated regime, which shows a higher heat transfer enhancement rate compared to the weakly modulated regime, the emergence of reverse flow allows for horizontal emission of thermal plumes that penetrate into the bulk, which provides a new way to strengthen bulk stratification. This phenomenon further promotes the flow strength and thus the heat transfer efficiency. We find that in strongly modulated regime, modifying the phase shift can change the position of reverse flow, modulate heat transfer mainly by changing the bulk stratification effect. This study on spatial temperature modulation in vertical convection allows us to uncover the underlying physics and mechanisms that govern heat transfer enhancement. This knowledge can be leveraged to develop more efficient and effective heat transfer systems in various practical applications. • Three different regimes are identified based on the relative importance of modulation layer to thermal boundary layer. • The heat transfer enhancement is caused by strengthening the bulk stratification through spatial modulation. • Emergence of reverse flow leads to a pronounced heat transfer enhancement rate via strengthening the bulk stratification. [ABSTRACT FROM AUTHOR]