ABSTRACT Active cooling is resorted to enhance the heat removal from hot bodies when the ambient temperature is relatively high. The current problem benefits the fluid–structure interaction by introducing a flexible fin to modulate the non‐Newtonian coolant entering into a trapezoidal vented cavity, and investigates the roles of various Prandtl numbers (Pr = 2–10) and different fin specifications (based on inlet width H) such as its thickness ( ξ = 0.1–0.2), elasticity ( E = 10 4 –10 15 ), and proximity ( L = 1–2) to the coolant inlet. The numerical solution of the problem is conducted by FEM and supported by two numerical verifications. Power law model is adopted for the non‐Newtonian fluid ( n = 0.5, 1, 1.5) and laminar flow regime (Re = 100–500). The results show that the use of flexible fin modulates and guides the flow and promotes the average Nusselt number better than it was not used. The gain in Nu av number is about 17.6% for pseudoplastic fluid and 20.7% for Newtonian fluid, while for the dilatant fluid, the flexible fin is less beneficial. For better heat transfer, we propose a fin thickness of 0.1H and a fin location as close as 1H to the inlet port, where H is the width of the inlet and outlet ports. Also, the dimensionless elasticity property of the fin should be as low as 10 4 to obtain better convective heat transfer.
ABSTRACT Turbomachinery features complex geometry and flow‐field characteristics, which impose strict requirements on mesh generation. This study proposes a periodic boundary‐layer mesh generation scheme for turbomachinery. Semi‐structured prismatic mesh is widely used to resolve boundary‐layer flows in viscous flow simulations. However, ensuring the periodicity of the boundary‐layer mesh during the mesh generation process remains a challenging and underexplored problem. To address this issue, a feature recognition method based on periodic affine transformation is first developed. Using the resulting periodic transformation function, a bottom‐up periodic boundary‐layer mesh generation framework is developed, including periodic surface meshing, calculation of periodic marching directions and distances, invalid element removal, transition element correction, and compatible far‐field tetrahedral mesh generation. Validations on typical turbomachinery benchmarks, including NASA Stage 35, NASA C3X, and Rolls‐Royce ACE, show that the simulation results agree well with experimental data and results obtained using commercial software. These results verify the dependability of the developed approach and its practical value in turbomachinery analysis.
ABSTRACT In computational fluid dynamics (CFD), obstacle flows are a pivotal benchmark, providing essential insights into complex fluid dynamics phenomena. CFD frameworks extensively employ these flows to analyze boundary conditions, offering a comprehensive understanding of fluid‐structure interactions. Throughout the development of CFD over the last decades, the stationary circular cylinder has been one of the most frequently simulated obstacle flows, combining simplicity for methodological work and similarity as well as transferability to practical applications. Despite its prevalence, published results exhibit significant and sometimes unexplained variations. This study addresses this issue by conducting a thorough investigation into how sensitive simulations are to system and model parameters, using the example of the lattice Boltzmann method. We summarize the state of the art and conduct additional parameter studies to examine the sensitivities of essential metrics such as force coefficients, Strouhal number, average velocity, and Reynolds stress profiles across a range of Reynolds numbers encompassing laminar and turbulent flows. Our findings indicate non‐monotonous convergence and fluctuations in response to grid resolution changes, with parameter choices becoming increasingly critical at higher Reynolds numbers. Furthermore, we captured the transition from two‐dimensional periodic to inherently three‐dimensional flow, underlining the necessity of 3D simulations even in a geometrically 2D environment for Reynolds numbers at or above the transition regime.
ABSTRACT We present a formulation of the immersed boundary method for incompressible flows over bodies with surface slip described by the Navier boundary condition. In the present method, the wall slip velocity and the boundary force are implicitly determined through a projection that enforces both the boundary conditions and the divergence‐free constraint of the velocity field. The present method is first‐order accurate in space and fourth‐order accurate in time, providing a consistent way to evaluate the velocity gradient on the boundary, which is challenging in conventional continuous forcing approaches. The validation results from the simulation of the flow past two‐dimensional stationary and moving bodies are in good agreement with previous experimental and numerical results for a wide range of slip lengths on the surface, including the no‐slip case. The spatial resolution required to reproduce the body‐fitted mesh solution is numerically evaluated for Reynolds numbers below 100, where the wall slip velocity plays an important role.
ABSTRACT Particle deposition poses a significant challenge in the application of nanofluids within microchannels. This study provides an angle‐ and radius‐resolved numerical analysis of nanoparticle deposition in bent microchannels and clarifies how microchannel geometry regulates deposition through curvature‐induced acceleration, secondary flow, and particle‐wall encounter mechanisms. The results demonstrate that the particle deposition number per unit area decreases from 28.612 to 8.941 as the bending angle increases from 30° to 120°. Furthermore, particle deposition per unit area decreases from 11.922 to 4.769 as the bending radius increases from 0.2 mm to 0.4 mm. The inlet and curved segments exhibit significantly higher particle deposition than the other segments. Specifically, deposition in the inlet segment is approximately 10 times higher than that in the other segments, while deposition in the curved segment is approximately three times higher. The Reynolds number and Dean number are identified as critical parameters for linking primary flow, curvature‐induced secondary vortices, and deposition risk. These findings provide quantitative insights and a mechanistic framework for the rational design and optimization of nanofluid microchannel cooling systems.
This study presents a validated numerical framework for predicting unsteady aerodynamic loads induced by prescribed moving boundaries using a single-phase computational fluid dynamics (CFD) approach. Rather than explicitly resolving an air-water interface, wave-induced effects are represented through time-dependent deformation of a solid lower boundary within an incompressible air-only domain. The methodology is implemented in OpenFOAM using dynamic mesh motion and is evaluated for an airfoil operating in ground effect above mechanically generated waves. Numerical predictions are compared against experimental force measurements from the DARPA Wing Over Water campaign and against corresponding two-phase volume-of-fluid simulations. Results show that the single-phase dynamic-boundary approach accurately captures the dominant unsteady lift and drag trends, including frequency and phase behavior, while providing improved numerical robustness and substantially reduced computational cost. Although localized nonlinear effects and force amplitudes are attenuated under steep wave conditions, the framework offers a practical and scalable surrogate for fully coupled multiphase simulations. The study provides quantitative guidance on the applicability and limitations of dynamic-boundary single-phase CFD for wave-influenced aerodynamic flows, supporting its use in engineering analysis and parametric studies.
A new technique based on the finite element method (FEM) is introduced that couples the fluid flow and heat transfer processes within a gas-filled porous medium, such as closed-cell polymeric foam. For such an analysis the classic FEM relies on a mesh fitting the solid-fluid boundaries; however, the new approach requires a fixed background mesh independent of the foam morphology. We term the method the moving least-squares aided finite element method (MLS-FEM), as it employs moving least-squares interpolants to enhance the pressure, velocity, and temperature shape functions in the active elements or the elements intersected by the solid-fluid interface. The accuracy of the MLS-FEM for a single-void foam patch is assessed against a classical boundary-fitted FEM, showing that the field variables, such as velocity components and temperature, are in close agreement across different mesh resolutions. The comparison is then extended to multivoid patches, with similarly close agreement between the two approaches. Notably, the MLS-FEM reuses the same background mesh regardless of geometry, whereas the classical FEM requires remeshing whenever the foam morphology changes.
ABSTRACT We consider a dual‐mixed method for the generalized Oseen equations, where the velocity and pseudo‐stress are treated as the primary unknowns. A stabilized discrete scheme is obtained by augmenting the dual‐mixed approach with suitable least‐squares terms derived from the physical equations. We prove that the scheme is well‐posed using the Lax‐Milgram Lemma. To approximate the unknowns, we propose using continuous piecewise polynomials for the velocity field and Raviart Thomas elements for each row of the pseudo‐stress. We prove optimal a priori error estimates for this choice. We also provide a residual‐based a posteriori error analysis. We derive a simple a posteriori error indicator and prove it is reliable and locally efficient. Finally, we supply some numerical experiments that confirm the theoretical results.
Nonlinear shallow-water modeling for tsunamis, river flooding, and storm surges faces persistent challenges in computational speed and numerical stability near wet/dry fronts. To address these issues, this study develops Systematic Grid, an object-oriented simulation framework that integrates 1D 2D coupling and hp-adaptive methods to accelerate computations while incorporating stabilization techniques for the Discontinuous Galerkin (DG) method. Systematic Grid provides a hierarchical structure consisting of Domains, Blocks, SubBlocks, and Elements. This organization allows flexible control of dimensions, polynomial orders, and spatial resolutions at each level. Object-oriented programming further allows consistent treatment of elements with different shapes and polynomial orders, naturally supporting hp-adaptive refinement on arbitrary grids. The paper first describes the design of Systematic Grid and the implementation of each numerical technique. It then introduces the stabilization methods and explains how they are applied near wet/dry fronts. Finally, the proposed framework is validated through the Carrier Greenspan problem, the dam-break flow in an L-shaped channel, and the Okushiri benchmark for the 1993 Hokkaido Southwest Offshore Earthquake tsunami. The results demonstrate clear improvements in both computational efficiency and numerical stability.
In this work, a multiscale, zonal-coupled physics-informed neural network (PINN) framework, termed BL-NS-PINNs, is proposed for accurately predicting steady laminar near-wall flow fields at high Reynolds numbers without requiring near-wall data. The framework ensures physical continuity across flow regions by solving the Blasius and Navier-Stokes equations in the inner and outer zones, respectively, while enforcing velocity consistency within the matching region. Numerical experiments demonstrate that BL-NS-PINNs significantly outperform conventional PINNs trained with data supervision, accurately capturing near-wall flow features and sharp gradients in high-Reynolds-number laminar boundary layers. The method is further extended to wedge flows with self-similar solutions, offering both a theoretical foundation and a practical pathway for integrating wall functions into data-driven boundary-layer modeling. Overall, BL-NS-PINNs effectively overcome the limitations of conventional PINNs in resolving sharp near-wall velocity gradients and show strong potential for efficient, high-fidelity modeling of high-Reynolds-number flows.
This study examines the influence of the thermophysical properties of various partition materials on heat transfer processes in a cavity filled with liquid. To achieve this goal, both direct computational fluid dynamics (CFD) and machine learning (ML) methods were applied. Direct CFD simulations were performed to obtain a detailed understanding of the temperature distribution within the cavity for different septum materials. Subsequently, machine learning methods were applied to create regression models capable of predicting changes in the temperature value inside the cavity based on different septum materials. The best results were achieved using third-degree polynomial regression, achieving a coefficient of determination (R 2) of 0.816. This indicates that the model is well adapted to the data and is able to explain the variability of the target variable. Additionally, random forest regression models were examined, but their results were slightly less accurate compared to polynomial regression. The study demonstrates that integrating machine learning techniques into computational fluid dynamics can significantly improve the analysis and prediction of thermal processes.
ABSTRACT We investigate multi‐physical topology optimization for microfluidic mixers. Starting from the Ising model, we derive a thermodynamically consistent Ginzburg–Landau free energy functional that incorporates the objective functional as an effective external field, providing a physically interpretable framework for phase‐field topology optimization. To eliminate fluid blockage in microfluidic mixers, we incorporate the coupled Navier–Stokes, convection–diffusion, and Poisson–Boltzmann equations. An Allen–Cahn type gradient flow method is proposed based on sensitivity analysis. The algorithm is validated for its computational effectiveness through numerical simulations of benchmark problems in 2D and 3D.
In this work, the droplet impact on a sinusoidally oscillating hydrophobic substrate is numerically simulated using the lattice Boltzmann method. We focus particularly on energy transfer and the maximum droplet spreading diameter () as functions of substrate oscillation parameters, the Weber number, and the wettability of the substrate. Our analysis shows that the maximum spreading diameter scales linearly with the tangential Weber number (), calculated from the substrate velocity amplitude. Notably, the spreading dynamics exhibit a nonmonotonic, resonance-like response, peaking when the spreading time coincides with half the oscillation period. Additionally, decreasing the contact angle strengthens interfacial adhesion to amplify horizontal migration, whereas superhydrophobic surfaces severely attenuate this tangential momentum exchange through inherent slip. Furthermore, the analysis of the normal Weber number () uncovers a "forgetting" mechanism, whereby the droplet ultimately converges to a consistent dynamic response across different as the initial kinetic energy dissipates. The study further elucidates the distinct regulatory effects of amplitude and period: amplitude primarily shifts the overall - scaling relation, while period significantly alters its slope. Based on these insights, we propose a universal scaling law that decomposes the maximum spreading factor into a normal-inertia-dominated term and a tangential vibration-coupling term. A semi-empirical correlation is subsequently derived, which quantifies the significant spreading enhancement induced by long-period oscillations and captures the attenuation of this gain at high .
This work presents an investigation into the unsteady thermal flow behavior of a tempered fractional Maxwell viscoelastic fluid over a moving plate. To accurately characterize the fluid behavior, the classical Maxwell constitutive relation is extended by incorporating a tempered fractional derivative, which is shown to be both physically meaningful and significant in capturing the viscoelastic properties of the fluid. The newly developed fractional Maxwell constitutive model is incorporated into both the momentum equation and the energy equation, forming a coupled system that describes the fluid dynamics and heat transfer. To numerically solve this tempered fractional coupled model, we employ the scheme with the finite difference method. However, due to the high computational cost associated with small time steps, we propose an efficient fast algorithm based on the sum-of-exponential (SOE) approximation to significantly reduce computation time. To verify the efficiency of the numerical scheme and fast algorithm, a specific example is examined. Furthermore, we analyze the influence of key parameters on fluid motion and thermal characteristics, offering deeper insights into the system's behavior. The study demonstrates that the tempered fractional coupled model is a viable and efficient tool to model flow and heat transfer in Maxwell fluids, offering valuable contributions to the study of complex systems.
The nonlinear collisional fragmentation equation is valuable for studying particle collisions and can model the evolution of raindrops, liquid-liquid dispersion, bubble columns, astrophysical planetary phenomena, and granulation processes in the pharmaceutical industry. Solving this equation analytically is highly tedious due to the complex structures of rate kernels, along with the nonlinear nature of the equation. This work aims to develop a generalised and efficient semi-analytical method that combines the Laplace decomposition method with Pad & eacute; approximation to solve multidimensional nonlinear integro-partial differential equations. The Laplace decomposition method yields a series solution that represents the collisional fragmentation process over short time periods, while the combined Laplace decomposition with Pad & eacute; approximation approach effectively captures the long-term dynamics. The mathematical formulation is validated through a detailed convergence analysis in a Banach space. Several examples including binary, Austin's and a gelling kernel are examined to demonstrate its accuracy and robustness. Most of the cases analysed in one-dimension, explicit (closed-form) solutions for the number density functions are derived for the first time. For the remaining multidimensional cases, accuracy is evaluated by comparison with the finite volume scheme [Das et al. (2020), SIAM J. Sci. Comput. 42, B1570-B159], the homotopy perturbation method [Yadav et al. (2023), Proceedings of the Royal Society A, 479(2279), 20230567] and the blues function method [Hussain et al. (2024), Physics of Fluids, 36, 103359]. The new approach captures both number density functions and their integral moments with high precision. Errors in number density functions are computed using various series solutions.
Mitigating aerodynamic heating while reducing drag is a critical challenge in the development of high-speed vehicles. A modified aerospike (MAS) configuration integrating a flat spike with stepped-ramp geometries is proposed to improve the aerodynamic performance of blunt-nosed bodies. Two-dimensional axisymmetric simulations were performed by solving the Reynolds-averaged Navier-Stokes (RANS) equations with the SST k-omega turbulence model at Mach 2.23, zero angle of attack, static pressure of 28,554.2 Pa, and free stream temperature of 300 K. Grid independence and validation against available experimental and computational results established the reliability of the numerical framework. Comparative analysis revealed that stepped-ramp aerospikes significantly outperformed conventional aerospike designs. The three-stepped configuration (MAS1) achieved a drag reduction of approximately 39%, while the four-stepped configuration (MAS2) provided the maximum reduction of nearly 47% relative to the baseline blunt body and up to 30% compared to a conventional aerospike. Thermal analysis showed a marked decrease in surface heat flux on the aft section, enhancing thermal protection and reducing material degradation risks. The results demonstrate that stepped-ramp aerospikes effectively control shock-boundary layer interactions, reduce both pressure drag and aerodynamic heating, and offer a promising solution for integration into next generation supersonic vehicle designs.
Fully nonlinear wave-structure interaction in real sea states is complex to simulate, though important for load estimations. While Navier-Stokes equation-based CFD solvers have proven to be capable of modelling these physics, their computational costs are often a limiting factor for their applicability. An alternative is given by FDM-based fully nonlinear potential flow solvers, which have been under constant development in the recent years and have proven to be capable of simulating irregular nonlinear real sea states at a fraction of the computational costs needed by CFD. Most of the current fully nonlinear potential flow solvers are utilising a -grid domain to represent the unsteady free surface boundary, which significantly hinders the representation of structures inside the domain. In the presented work, a fixed-grid potential flow solver utilising parallel computation on a multi-core infrastructure is developed to allow for the implementation of structures directly in the domain. Therefore, new methods for enforcing the free surface boundary conditions inside the fixed-grid domain are derived. Different approaches are introduced and tested to determine the most accurate one. The presented work thereby puts emphasis on building a fixed-grid solver that can model complex wave transformations, as well as irregular real sea states in time domain with an accuracy on par with a -grid solver, while not limiting its flexibility with a -grid. The presented solver's accuracy is tested for various two- and three-dimensional nonlinear wave propagation and transformation cases by comparing to nonlinear wave theory and experimental results. The results show that the solver is capable of modelling real sea states and nonlinear wave transformation and that it is of comparable accuracy to fully nonlinear potential flow solvers utilising a -grid.
This numerical study focuses on the development of secondary recirculation zones in viscous, incompressible, rotating flows. Two main objectives are pursued: extending Karl Buhler's reference cavity and analyzing the influence of upstream boundary conditions on the evolution of reverse flow. To this end, several spherical-bottom configurations are studied using a finite-volume approach in order to characterize the behavior of fully open flows under the combined effects of the radius ratio (1.48 <= alpha <= 2) and the Reynolds number (766 <= Re <= 2757). The results reveal that the size and the number of the recirculation region strongly depend on the imposed thermal gradient for the concentric hemispherical annular cavity. Specifically, a positive Rayleigh number () suppresses the reverse axial zone, while a negative Rayleigh number () reinforces it. Beyond these findings, a refined modeling framework is proposed, capable of accurately predicting both the onset and behavior of recirculating regions. Furthermore, the study provides a comprehensive analysis of vortex breakdown dynamics, offering new insights into their formation and evolution across different flow regimes. The reliability of the proposed model is further confirmed through validation against experimental data, demonstrating its robustness and applicability to real-world scenarios. These outcomes carry important implications for fluid mechanics, as they deepen the understanding of turbulence and contribute to the design of more efficient engineering systems as well as the optimization of industrial processes. Finally, the model shows strong potential for bioengineering applications by creating an environment with minimal cavity velocity that supports cell growth, while reducing energy consumption and preserving cell viability.
Predicting the microscopic distribution of remaining oil in chemical flooding is challenging due to the complex interplay of wettability, interfacial tension, and flow dynamics. Existing data-driven models often require extensive training data and lack physical consistency. To address this, we propose a physical-constrained deep learning framework for rapid and accurate prediction. Initially, a comprehensive dataset was generated using the lattice Boltzmann method, encompassing variations in wettability, interfacial tension, displacement velocity, and viscosity ratio. A regression model was derived to quantify the relationship between these parameters and the remaining oil characteristic. We then developed a hybrid loss function combining Dice loss with a physics-based regression loss. The network structure was established based on the U-Net structure and a normalization network. Then, the network underwent training with various loss functions and datasets. Finally, the method predicted the microscopic remaining oil under various conditions and classified the remaining oil to examine the change patterns. The prediction results were compared with and without constraints in the loss function, revealing that this method significantly reduces dataset establishment time and data volume required. Additionally, favorable findings were obtained even with displacement conditions not included in the training set. Prediction analysis under various conditions showed that a closer oil-wet rock ratio to water-wet rock ratio results in more network remaining oil and less cluster remaining oil. Higher displacement velocities or lower interfacial tensions correlate with a reduced proportion of network remaining oil. This study aids in swiftly analyzing the microremaining oil alterations in chemical flooding under different conditions and provides a foundation for further exploration of remaining oil postchemical flooding.
This paper presents a multidimensional free-surface detection method for Smoothed Particle Hydrodynamics (SPH) simulations aimed at highly dynamic flows. The approach combines density-guided candidate selection with an efficient seed-and-expand strategy: outermost-particle seeding is followed by breadth-first search (BFS) refinement, while local surface normal estimated via principal component analysis (PCA) guide adaptive sector/cone scanning to improve robustness in high-curvature and fragmented interfaces. To accelerate neighborhood queries, the method employs dimension-dependent spatial indexing (hash grids in 2D and an octree in 3D), reducing the practical cost of neighbor search compared with exhaustive scanning. The framework is validated on benchmark cases including 2D/3D tank sloshing and a 3D dam-break scenario. Results show improved interface identification accuracy over a standard density-ratio baseline (e.g., 12.7% higher interfacial precision in our tests) and substantially faster neighborhood-query performance (up to 72% reduction in the query stage), enabling reliable near-real-time free-surface detection for large-scale SPH simulations.
