Search Results (60)

This paper presents a theoretical framework for predicting molten jet breakup at the outlet of a rotating granulation system operating without forced excitation. The study focuses on the critical regime in which mechanical excitation is absent, and jet disintegration is governed solely by intrinsic hydrodynamic instabilities. The analysis is based on the linear stability theory of viscous liquid jets, employing the Rayleigh–Plateau and Tomotika approaches adapted to melt conditions typical of industrial granulation processes. The Navier–Stokes equations are formulated in a cylindrical coordinate system for an axisymmetric, incompressible viscous jet with appropriate kinematic and dynamic boundary conditions at the free surface. The breakup mechanism is characterized using key dimensionless parameters, including the Ohnesorge, Weber, Reynolds, and Capillary numbers, enabling identification of the dominant instability regime. Analytical expressions are derived for the most unstable wavelength, perturbation growth rate, breakup time, and characteristic droplet diameter. These relationships are evaluated for representative thermophysical properties of molten urea. Theoretical predictions obtained from classical Rayleigh theory, viscosity-corrected models, and modern empirical correlations show strong agreement, with deviations not exceeding 7%. Sensitivity analysis indicates limited dependence of the predicted droplet diameter on moderate variations in viscosity, surface tension, and jet velocity. The proposed model provides a physically grounded basis for predicting and controlling granule size distribution in rotating granulation systems operating without external mechanical excitation. Full article

The stability analysis for isothermal three-component gas mixtures, in which one of the components exhibits real properties in the considered pressure range, is performed. The system of Navier–Stokes and diffusion equations in the Boussinesq approximation is considered, taking into account analogs of buoyancy effects in a density-stratified medium. The presented solution is obtained by the small-perturbation method using the principle of diffusion independence, while maintaining the condition of neutrality of convective perturbations. Expressions for the boundary between the “diffusion–gravitational convection” regimes are obtained in terms of partial Rayleigh numbers that account for the compressibility factor of the mixing components. The stability cartograms show that on the stability maps, the position of the boundary of the regimes change depends on the variation in the compressibility factor with a pressure change. When the compressibility factor changes, the values of the critical Rayleigh numbers, which are the intersection points of the boundary of the regimes change and the coordinate axes, decrease. It is established that the behavior of the partial Rayleigh numbers on the plane (Ra₁, Ra₂) is nonlinear for isothermal ternary mixtures, which have the general form H₂ + N₂O–N₂ and He + CO₂–N₂, He + R12–Ar, at T = 298.0 K and elevated pressures. It is revealed that when taking into account the compressibility factor of the components, the partial Rayleigh numbers of the components decrease. Full article

This article examines the thermohaline stability of a power-law fluid saturating a porous layer in the presence of a magnetic field. The system stability is analyzed using both linear and weakly nonlinear instability theories. Within the linear framework, the Galerkin method is employed to derive analytical expressions for the Rayleigh number corresponding to steady and oscillatory modes of instability. Takens–Bogdanov and Hopf bifurcation points are identified, highlighting the transition mechanisms between different instability regimes. An increase in the Hartmann number delays the onset of convection. The critical Rayleigh number is a monotonic increasing function of the solute Rayleigh number, whereas it is a non-monotonic function of the Peclet number. To investigate heat and mass transport characteristics, an amplitude equation is derived in the weakly nonlinear regime. The results reveal that increasing the Hartmann, Lewis, and Peclet numbers enhances both heat and mass transport, whereas an opposite trend is observed with increasing the solute Rayleigh number. Full article

Natural convection in enclosures heated from both sides is a topic of interest in various space and safety applications in nuclear power reactors. The transient dynamics during natural convection in enclosures is critically dependent on micro-scaled boundary layers and also the timescales of micromixing. In the present work, a square enclosure operating at two high Rayleigh numbers (Ra = 3.27 × 10¹⁰ and Ra = 6.55 × 10¹⁰, with water as the working fluid) have been chosen for study. First, the velocity and timescales were found using Computational Fluid Dynamic (CFD) simulations for the square enclosure with Ra 3.27 × 10¹⁰ and compared with scaling laws that presently define them. An empirical correlation for heat transfer is then developed for the Ra range (1.3 × 10¹⁰ < Ra < 6.55 × 10¹⁰). Then, an existing DL framework (Proper Orthogonal Decomposition and Long Short-Term Memory (POD-LSTM)) network) is compared qualitatively and quantitatively with the CFD data. The transient data Ra = 6.55 × 10¹⁰ was chosen for this purpose. The scaling laws show a 30% deviation for the predictions of the transient length and time scales as compared to CFD and DL model predictions. Further, accurate results up to 99.6% have been obtained by the DL model when compared with the CFD model. The DL model is also found to require an order of magnitude less time than the one required for a CFD simulation. Full article

The strategic positioning of heating and cooling segments within complex non-rectangular geometries has emerged as a critical engineering challenge across multiple industries in thermal management systems for electronic components. This analysis presents a numerical inspection of buoyancy-driven convective flow and thermal transport mechnisms of nanofluids in a parallelogrammic porous geometry. A single discrete heating–cooling segment has been placed along the slanting surfaces of the geometry. The mathematical model is formulated utilizing Darcy’s law, incorporating the Tiwari and Das approach to characterize the thermophysical properties of the nanofluid. The governing model equations corresponding to the physical process are solved numerically using finite-difference-based alternating direction implicit (ADI) and successive line over-relaxation (SLOR) techniques. Computational simulations are performed for various parametric conditions, including different nanoparticle volume fractions ($\varphi =0$–$0.05$), Rayleigh numbers ($Ra={10}^1$–${10}^3$), and parallelogram geometry ($\alpha$) and sidewall ($\gamma$) tilting angles ($-{45}^{°}\le \alpha \le +{45}^{°}$ and $-{45}^{°}\le \gamma \le +{45}^{°}$), while examining the effect of discrete thermal locations. The results reveal a significant decrement in thermal transfer rates with an increasing nanoparticle concentration, particularly at higher Rayleigh numbers. The skewness of the parallelogrammic boundaries is found to substantially influence flow patterns and thermal transport characteristics compared to conventional rectangular enclosures. Further, the discrete placement of heating and cooling sources creates unique thermal plumes that modify circulation patterns within the domain. The predictions suggest profound insights for optimizing thermal management systems by employing nanofluids in non-rectangular porous configurations, with potential applications in geothermal energy extraction, electronic cooling systems, and thermal energy storage devices. Full article

We investigate the linear onset of thermal convection in rotating spherical shells with a focus on the influence of mechanical boundary conditions and thermal driving modes. Using a spectral method, we determine critical Rayleigh numbers, azimuthal wavenumbers, and oscillation frequencies over a wide range of Prandtl numbers and shell aspect ratios at moderate Ekman numbers. We show that the preferred boundary condition for convective onset depends systematically on both aspect ratio and Prandtl number: for sufficiently thick shells or for large Pr, the Ekman boundary layer at the outer boundary becomes destabilising, so that no-slip boundaries yield a lower ${\mathrm{Ra}}_c$ than stress-free boundaries. Comparing differential and internal heating, we find that internal heating generally raises ${\mathrm{Ra}}_c$, shifts the onset to larger wavenumbers and frequencies, and relocates the critical column away from the tangent cylinder. Mixed boundary conditions with no-slip on the inner boundary behave similarly to purely stress-free boundaries, confirming the dominant influence of the outer surface. These results demonstrate that boundary conditions and heating mechanisms play a central role in controlling the onset of convection and should be carefully considered in models of planetary and stellar interiors. Full article

This study investigates natural convection of liquid metal in an annular enclosure with a square cross-section using three-dimensional numerical simulations. Liquid metals, with low Prandtl numbers, exhibit oscillatory transitions at lower Rayleigh numbers than conventional fluids. While previous studies focused on full-circle domains where steady or irregular flows were observed, this work examines the effect of angular partitions on flow dynamics. The results reveal that periodic three-dimensional oscillatory flows arise in domains with specific angular sizes, such as quarter circles, whereas full-circle domains produce irregular or steady flows. Angular wave numbers vary spatially and temporally during transitional growth. The emergence of half-symmetric oscillatory modes highlights the role of symmetry constraints imposed by the geometry and boundary conditions. These transitions are closely tied to symmetry breaking and mode selection. A linear stability perspective helps clarify the critical factors that determine the transition type. These findings underscore that angular segmentation and periodic boundary conditions are essential for sustaining regular oscillatory convection. This study contributes to the understanding of symmetry-governed convection transitions in low-Prandtl-number fluids and has potential implications for industrial processes, such as semiconductor crystal growth, where flow uniformity and thermal stability are crucial. Full article

This paper addresses the critical gap in the existing literature regarding the combined buoyancy–Marangoni convection of power-law fluids in three-dimensional porous media with complex evaporation surfaces. Previous studies have rarely investigated the convective heat transfer mechanisms in such systems, and there is a lack of effective methods to accurately track fractal evaporation surfaces, which are ubiquitous in natural and engineering porous media (e.g., geological formations, industrial heat exchangers). This research is significant because understanding heat transfer in these complex porous media is essential for optimizing energy systems, enhancing thermal management in industrial processes, and improving the efficiency of phase-change-based technologies. For this scientific issue, a general model is designed. There is a significant temperature difference on the left and right sides of the model, which drives the internal fluid movement through the temperature difference. The upper end of the model is designed as a complex evaporation surface, and there is flowing steam above it, thus forming a coupled flow field. The VOF fractal reconstruction method is adopted to approximate the shape of the complex evaporation surface, which is a major highlight of this study. Different from previous research, this method can more accurately reflect the flow and phase change on the upper surface of the porous medium. Through numerical simulation, the influence of the evaporation coefficient on the flow and heat transfer rate can be determined. Key findings from numerical simulations reveal the following: (1) Heat transfer rates decrease with increasing fractal dimension (surface complexity) and evaporation coefficient; (2) As the thermal Rayleigh number increases, the influence of the Marangoni number on heat transfer diminishes; (3) The coupling of buoyancy and Marangoni effects in porous media with complex evaporation surfaces significantly alters flow and heat transfer patterns compared to smooth-surfaced porous media. This study provides a robust numerical framework for analyzing non-Newtonian fluid convection in complex porous media, offering insights into optimizing thermal systems involving phase changes and irregular surfaces. The findings contribute to advancing heat transfer theory and have practical implications for industries such as energy storage, chemical engineering, and environmental remediation. Full article

Medium- and large-scale heat sinks are critical for thermal load management in high-performance systems. However, their high heat flux densities and limited space complicate cooling, leading to risks of overheating, performance degradation, or failure. This study employs the Cascaded Lattice Boltzmann Method (CLBM) to enhance their thermal performance. This numerical approach is known for being stable, accurate when dealing with complex boundaries, and efficient when computing in parallel. The numerical code was validated against a benchmark configuration and an experimental setup to ensure its reliability and accuracy. While previous studies have explored mixed convection in cavities or heat sinks, few have addressed configurations involving side air injection and boundary conditions periodicity in the transition-to-turbulent regime. This gap limits the understanding of realistic cooling strategies for compact systems. Focusing on mixed convection in the transition-to-turbulent regime, where buoyancy and forced convection interact, the study investigates the impact of Rayleigh number values ($5\times {10}^7$ to $5\times {10}^8$) and Reynolds number values (${10}^3$ to $3\times {10}^3$) on heat transfer. Simulations were conducted in a rectangular cavity with periodic boundary conditions on the vertical walls. Two heat sources are located on the bottom wall ($T_h$ = 50 °C). Two openings, one on each side of the two hot sources, force a jet of fresh air in from below. An opening at the level of the cavity ceiling’s axis of symmetry evacuates the hot air. Mixed convection drives the flow, exhibiting complex multicellular structures influenced by the control parameters. Calculating the average Nusselt number (Nu) across the surfaces of the heat sink reveals significant dependencies on the Reynolds number. The proposed correlation between Nu and Re, developed specifically for this configuration, fills the current gap and provides valuable insights for optimizing heat transfer efficiency in engineering applications. Full article

Previous research has studied the evolution of patterns during the evaporation of sessile droplets of pure liquid, although there is a lack of reports focusing on the transition of flow regimes and flow stability of nanofluids. In this study, we investigate the evaporation of sessile droplets of Al₂O₃-ethanol nanofluid to elucidate the dynamic characteristics of the evaporation process from the perspective of internal convection. As the temperature increases, internal convection intensifies, significantly accelerating the evaporation rate. Three distinct convection flow patterns are observed under the combined influence of the Marangoni effect and buoyancy during evaporation: initially, two macroscopic convection cells form, followed by the periodic generation and propagation of hydrothermal waves (HTWs) near the contact line. Subsequently, Bénard–Marangoni (BM) convection cells gradually emerge and ultimately dominate the flow dynamics. The deposition patterns, which differ in part from the classic coffee-ring pattern, are closely related to the flow patterns of HTWs and BM convection cells during the pinning stage of droplet evaporation. Furthermore, the critical Marangoni (Ma) and Rayleigh (Ra) numbers for the onset of convection flow instability increase with rising substrate heating temperature. Full article

According to the Donnell–Mushtari shell theory, this work presents a closed-form solution procedure for free vibration of open laminated circular cylindrical shells with arbitrary homogeneous boundary conditions (BCs). The governing differential equations of free vibration are derived from the Rayleigh quotient and solved by the iterative separation-of-variable (iSOV) method. In addition, considering axial aerodynamic pressure, simulated by the linear piston theory, the exact eigensolutions for the flutter of open laminated cylindrical shells with simply supported circumferential edges and closed laminated cylindrical shells are also achieved. The governing differential equations of cylindrical shell flutter are derived from the Hamilton variational principle and solved by the separation-of-variable (SOV) method. The influence of circumferential dimension on flutter speed is investigated for open cylindrical shells, which reveals that the number of circumferential waves in critical flutter mode increases with circumferential length, and there exists an infimum for flutter speed that is an invariant independent of circumferential length. The present results agree well with those obtained by the Galerkin method, the finite element method, and other analytical methods. Full article

The straight part of the corrugated steel plate (CSP) pipe-arch structure in soil may cause local buckling instability due to insufficient load-bearing capacity. Recently, composite CSP pipe-arch has been widely utilized to enhance structural stability, and their stability needs to be thoroughly investigated. This paper studies the local buckling stability problem of the straight part of composite CSP pipe-arch in soil by simplifying the soil support and introducing the inter-layer bonding effect. Based on elastic stability theory, a theoretical mechanical model of composite CSP pipe-arch was proposed. The Rayleigh–Ritz method and the semi-combined composite structure stiffness approximation were used to derive the critical buckling conditions for the straight part of the composite CSP pipe-arch. Through numerical calculation and influencing factors analysis, it is concluded that the critical buckling load of the straight part of the composite CSP pipe-arch structure is affected by the elastic modulus, thickness, Poisson’s ratio, rotational restraint stiffness and side length of the straight part of the material. In particular, it is found that as the inter-layer bonding coefficient increases, the critical buckling load is improved, while the critical buckling wave number is mainly influenced by the width of the straight part, elastic modulus, and inter-layer bonding coefficient. Additionally, we discussed the coupling effect of several key parameters on the stability of the structure. The results of this study offer theoretical foundations and guidance for the application of composite CSP pipe-arch in soil engineering, such as culverts, tunnels, and pipeline transportation. Full article

This article investigates the behavior of two parallel layers of different miscible dielectric liquids enclosed and sandwiched between two electrodes. By applying an electric potential to one electrode while grounding the other, electro-convection occurs when the electric Rayleigh number exceeds a critical value, setting the fluid into motion and resulting in rapid mixing between the two liquids. A numerical model is developed to account for the varying ionic mobility and permittivity of the two liquids, considering their evolution based on the relative concentration field. The simulations confirm that electro-convection significantly enhances the mixing between the two liquids, as expected. Additionally, intriguing ripples are observed near the initial interface during the early stages of electro-convection instability growth. To explain and describe the flow dynamics in terms of stability analysis, a semi-analytical model is presented. This study provides insights into the mixing behavior and flow dynamics of miscible dielectric liquids under the influence of electro-convection. The findings contribute to a better understanding of the underlying mechanisms and can be valuable for applications such as microfluidics, energy conversion, and mixing processes. Further research is encouraged to explore additional parameters and optimize the control of electro-convection for practical applications. Full article

This study delves into the convective heat transfer phenomena within a square cavity that houses a porous medium, analyzing the effects of Darcy (Da) and Rayleigh (Ra) numbers on the thermal and fluid dynamic behavior within the system. Utilizing a combination of computational fluid dynamics (CFD) and the finite element method (FEM), the research focuses on steady-state, laminar flow conditions in two dimensions. The cavity, which is impermeable at its boundaries, contains a centrally located square region filled with a porous, isotropic material. The thermal environment is controlled with insulated horizontal walls and vertically positioned walls that experience sinusoidal temperature variations. The study examines how variations in the permeability of the porous medium (Da numbers ranging from 10⁻¹ to 10⁻⁴) and the buoyancy-driven flow strength (Ra numbers spanning from 10² to 10⁵) influence the velocity fields and heat transfer rates, with results expressed through Nusselt number (Nu) distributions. The findings reveal that higher Ra numbers, particularly at 10⁵, significantly intensify convection within the cavity, thereby boosting local rates of heat transfer, especially in the central vertical section. The research identifies that optimal flow resistance in the porous medium occurs within the Da number range of 10⁻³ to 10⁻⁴. These insights are critical for advancing thermal management techniques, particularly in the natural cooling of electronic devices and improving insulation methods. Full article

Cavitation phenomena in pumps are major determinants of the lifespan of both the impeller and the pump itself, causing significant vibration and noise, which are critical concerns for pump designers. This study focuses on the influence of various geometric factors of the impeller, including the shape of the blade leading edge, blade inlet angle, number and thickness of blades, surface roughness, wrap angle, impeller outlet width, inlet hub diameter, and tip clearance. The pump analyzed in this study, which exhibited issues of vibration and noise in actual industrial settings, was evaluated by varying only the shroud diameter based on Gulich’s theory, while keeping other parameters constant, to assess the effects on cavitation phenomena across five different impellers. Single-phase analysis was initially conducted to evaluate the performance of each pump model, with the reliability of the numerical analysis methods validated by comparison with experimental data. Furthermore, to analyze cavitation phenomena, a multiphase flow analysis was performed using the Rayleigh–Plesset model within a computational fluid dynamics framework. Quantitative analysis of cavitation occurrence, NPSH3% head-drop performance, and bubble volume was conducted. The results confirmed that the M1 model, featuring a shroud diameter of 560 mm, exhibited superior cavitation resistance. Variations in cavitation occurrence observed under three different flow conditions demonstrated a nonlinear trend, but overall, improvements were noted within a specific diameter range. This study offers valuable insights and data for pump design applicable in real-world industrial settings. Full article