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The interaction between droplets and a liquid pool is a widely observed fluid phenomenon with significant relevance to various industrial applications. This study numerically investigates the impact of both a single droplet and two successive droplets on a liquid pool with a fixed thickness. Particular emphasis was focused on the evolution of cavity depth and width during the deformation process. For single droplet impacts, the cavity depth exhibits linear growth with time in the early stage, consistent with predictions based on energy balance. This growth is independent of the Weber number (We) within the explored range of 96 < We < 345. Similarly, the cavity width shows weak dependence on the Weber number during early development, deviating and reaching a maximum width at later times. The maximum cavity width follows a power-law relationship with the Weber number, with a 0.5 exponent. In the case of successive droplet impacts with small initial separation, cavity depth also evolves linearly with time in the early stage but over an extended period. This prolonged growth is attributed to droplet merging, resulting in an effectively larger merged droplet. However, for successive droplets with large separation, the two linear growth stages exhibit intermittent interruptions due to the second impact occurring at a later time. The variation in cavity width due to different initial spacings between two successive droplets still exhibits similarity until a larger spacing causes a change in the rate of cavity width development. [ABSTRACT FROM AUTHOR]

In this paper, we introduce WindFormer, an innovative transformer-based model engineered for short-term wind speed forecasting, leveraging multivariate time series data. Unlike traditional approaches, WindFormer excels in processing diverse meteorological features—temperature, humidity, and power—to intricately map their spatiotemporal interdependencies with wind speeds. Utilizing a novel unsupervised pre-training strategy, WindFormer initially learns from vast volumes of unlabeled data to capture generalized feature representations. This foundation enhances the subsequent fine-tuning phase on labeled wind speed data, in which our model demonstrates exceptional predictive accuracy. Empirical evaluations across various public datasets illustrate that WindFormer markedly surpasses both conventional statistical models and contemporary deep learning techniques. The model not only achieves superior accuracy in forecasting wind speeds but also reveals a significant enhancement in handling complex spatiotemporal data dynamics. These advancements facilitate more effective wind farm management and power grid scheduling, making a substantial impact on operational efficiencies and renewable energy utilization. Our findings confirm the robustness of WindFormer in a real-world setting, underscoring its potential as a pivotal tool in meteorological and energy sectors. The integration of unsupervised pre-training with multi-task fine-tuning establishes a new benchmark for short-term wind speed prediction. [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]

The vortex dynamics of a supersonic flow past an impulsively started circular cylinder are studied numerically. A well-developed high-order finite difference method is adopted to solve the two-dimensional Navier–Stokes equations. In particular, Ma = 1.1 and Re = 2.2 × 104 are selected to report the vortex evolution process. The results confirm that the α-, β-, sub-α-, and sub-β-phenomena observed in incompressible flow in the separated region do exist in the supersonic regime. In addition, the influence of Mach number and Reynolds number on the vortex is also studied, and the vortex changes are compared at Ma = 1.1, 1.7 and Re = 1 × 104, 2 × 104, 2.5 × 104, 3 × 104, 5 × 104, and 1 × 105. [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]

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]