Abstract In wind tunnel experiments, one approach to reproducing the representative flow environment around test bodies is the use of obstacles, which necessitates longer test sections. As an alternative, an active grid system, consisting of motor-driven rods with attached winglets, was introduced by Makita (1991). Since then, numerous studies have investigated the effects of synchronized and independent rod motions, the influence of input parameters on the resulting flow characteristics, and the ability to generate desired profiles through parameter adjustments. The present study explores a potential method for determining the input parameters required to produce specified mean velocity and turbulence intensity profiles. To this end, a mini wind tunnel equipped with an active grid system was designed, and various combinations of input parameters were tested to generate training data for artificial neural networks (ANNs). The results were consistent with previous findings, indicating that mean velocity profiles depend primarily on the flow restriction created by the collective winglet positions, while turbulence intensity profiles are influenced by both the restricted flow areas and the rotational speeds of the rods. The ANN successfully learned to predict input parameters for target mean velocity profiles, although achieving similar performance for turbulence intensities proved more challenging. Consequently, the turbulence intensity part of the study focuses on assessing the learning potential of ANNs for turbulence intensities and provides recommendations for future research.
Abstract The study of convective transport phenomena in the presence of internal heat and mass sources is of considerable significance in understanding various natural and industrial processes. In this work, we investigate a problem where an incompressible and viscous Newtonian fluid is subjected to an internal heat source ( R i ) along with two internal mass sources ( R j , R l ) in opposite sense, under isothermal and iso-solutal boundary conditions. Employing weakly nonlinear theory, the critical thermal Rayleigh number is obtained, and the corresponding Nusselt and Sherwood numbers are evaluated. Further, the Ginzburg–Landau equation is derived to describe the amplitude dynamics of the system. The resulting amplitude equation is solved numerically using MATHEMATICA, and the effects of various governing parameters on the thermal Rayleigh number ( R a T 0 ) , Nusselt number ( N u ) , and the two Sherwood numbers ( S h 1 , S h 2 ) are systematically analyzed. It is found that the parameters R i and R l faster the onset, while R j delays it. Additionally, an increase in Lewis number ( L e 1 ) leads to a rise in the Nusselt number ( N u ) and the first Sherwood number ( S h 1 ), whereas a decrease is observed in the second Sherwood number ( S h 2 ). The outcomes provide valuable insights into the stability behavior and transport characteristics of multi-component convection systems influenced by internal sources. The present study is not only theoretically significant but can also be useful in various industrial and experimental applications.
This study presents a novel, energy-free strategy for unidirectional liquid transport using a bionic anisotropic wetting surface inspired by<^> fish scale arrays. Unlike traditional systems that rely on external energy sources, this design achieves directional flow through cross-scale coupling without external actuation. Laser etching was used to fabricate asymmetric wetting gradient structures on silicon wafers, guided by the imbricate geometry of fish scales. Key laser parameters (scanning speed: 50 mm s-1, scans: 3, spacing: 50 mu m) and structural features (outer radius r1 = 1.25 mm, inner radius r2 = 0.65 mm, height h= 1.25 mm, stacking coefficient z = 0.2, array spacing d = 0.5 mm) were tested and selected to create regular, high-performance surfaces. The PET-assisted process effectively controlled heat-affected zones. At an injection volume of 1300 mu l, the rectification coefficient reached 23.3, indicating excellent unidirectional transport. This design provides a promising, low-energy solution for applications in microfluidics, water collection, and thermal management.
High-fidelity reconstruction and prediction of flow fields from sparse observations present a persistent challenge in computational fluid dynamics and ocean engineering. This study introduces a two-stage physics-informed Fourier neural operator (FNO) framework designed for super-resolution reconstruction and prediction of flow fields under low-resolution conditions. To mitigate the spectral bias of FNOs and the optimization instability inherent in standard physics-informed learning, we employ a decoupled 'Global Capture + Local Correction' strategy. Stage 1 utilizes low-resolution data to efficiently capture dominant global dynamics, ensuring rapid convergence to a stable solution manifold. Stage 2 enforces high-resolution physical constraints via spectral differentiation, enabling the unsupervised recovery of fine-scale structures and ensuring physical consistency without reliance on high-resolution labels. The method is validated across three benchmarks of increasing complexity: the 1D viscous Burgers equation (16)& times; super-resolution, 1.19% relative L2 error), 2D Kolmogorov flow (4 & times; super-resolution, 5.44%), and 2D tandem cylinder wake flow at Re=2.2 & times;104 (4 & times; super-resolution, 5.39%). Results demonstrate that the framework consistently outperforms standard FNO, physics-informed neural operator, and convolutional neural network-based super-resolution models, accurately recovering multiscale features with physical fidelity confirmed by proper orthogonal decomposition analysis and turbulence statistics. Furthermore, the framework demonstrates cross-geometry generalization to unseen cylinder spacing ( L/D=2) and maintains high predictive accuracy under measurement noise up to 5%. By harmonizing inference efficiency with physical rigor, this framework offers a robust, physics-consistent surrogate model for super-resolution reconstruction and prediction, enabling real-time hydrodynamic analysis in future digital twins.
This article reviews our research progress on developing machine-learning-enhanced large-eddy simulation (LES) methods, with a focus on neural-network-based (NN-based) subgrid-scale (SGS) modeling, wall modeling, and LES-enabled shape optimization. We first identify the limitations of the eddy viscosity (EV) SGS models, which over-predict the space-time correlations due to the absence of random forcing (RF). Therefore, an NN-based SGS model is proposed to represent the coupled effects of the EV model and RF for the correct prediction of space-time correlations in turbulent channel flows. Furthermore, we introduce the knowledge-integrated additive (KIA) learning wall model, a physics-based modeling architecture built upon the simplified boundary-layer equations with NN-based forcing terms. The KIA model is designed to respect the law of the wall and enable continual learning without catastrophic forgetting. Finally, a self-adaptive ensemble Kalman method is proposed for LES-based shape optimization with the aim of aeroacoustic shape optimization. The ensemble-based sensitivity analysis is shown to effectively provide accurate sensitivity for chaotic Lorenz systems and demonstrates its utility in optimizing the trailing-edge shape of an airfoil. The synergy of these NN-based SGS and wall models is expected to enable time-accurate LES and LES-based shape optimization for complex turbulent flows.
Abstract This paper aims to regularize complex flows characterized by a singularity in the orifice region of a zero-thickness plate using the patching method. The entire flow field is divided into three regions: the I -region, which is a sphere sharing the same origin and radius as the orifice; and the O u and O d regions, which represent the upstream and downstream half-infinite domains outside the sphere, respectively. The solution in each region is obtained in closed form. These solutions are subsequently patched over their common hemisphere using the relationship between pressure drop and volumetric flow rate from the Sampson solution. Matching the pressure gradients enables the determination of unknown coefficients in the solution. Consequently, the regularized flows allow for the practical application of the Sampson solution to actual flow problems, such as biofluid flow. The resulting complex velocity field is qualitatively compared with a computational fluid dynamics (CFD) simulation for a rounded orifice edge, which was conducted using the finite volume method.
This experimental study examines the water-entry dynamics of cylindrical projectiles with longitudinal groove configurations of 0, 4, 8, and 12 equally spaced semicircular grooves across Froude numbers Fr ranging from 8.16 to 21.60, corresponding to impact velocities of 1.98-5.24 m s-1, achieved by varying release heights Hr = 20-140 cm. Using high-speed photography, we systematically analyze cavity formation dynamics and projectile kinematics, showing that ballistic performance-characterized by vertical acy, angular alpha, and horizontal acx accelerations and displacements-is primarily governed by cavity evolution and wetted surface features. Our results indicate that surface grooves enhance ballistic performance through three key mechanisms: viscous drag reduction, improved cavity symmetry, and optimized bubble shedding. Notably, grooves actively regulate cavity closure processes, with intermediate and high Froude numbers of Fr >= 11.54 exhibiting water jet formations that affect ballistic stability. We identify two critical Froude numbers Frd1 approximate to 9.70 and Frd2 approximate to 13.28 that demarcate groove effects on cavity and splash crown dynamics. Additionally, a transitional range between 4 and 8 grooves exists for high-Fr >= 19.17 symmetry stabilization reversal, whereas fewer grooves amplify trajectory deviations due to flow asymmetry. These findings offer new insights into the design of water-entry projectiles through strategic surface feature engineering.
Hydrogen-air combustion in confined geometries is critical for aerospace propulsion systems, energy technologies, and safety assessments. A notable phenomenon in such environments is the formation of tulip flames, where the flame front inverts due to interactions with pressure waves and hydrodynamic instabilities. Planar laser-induced fluorescence (PLIF), particularly OH-PLIF, is widely used to visualize flame structures, but its application to tulip flame analysis remains limited due to experimental challenges and complex signal interpretation. This study presents a numerical OH-PLIF model for hydrogen-air combustion in a confined duct, coupling detailed chemical kinetics with a comprehensive fluorescence simulation framework. Synthetic PLIF images are generated for excitation wavelengths of 266, 282, and 307 nm, accounting for collisional quenching, laser-sheet attenuation, and radiative transitions. A novel temperature-dependent OH partition function is developed and implemented, which enhances model robustness and reproduces the HITRAN (High-Resolution Transmission) database with a mean error of 0.2% across 273-3000 K. Synthetic OH-PLIF images are analyzed with the evolving flame dynamics, revealing fluctuations in pressure, OH concentration, and fluorescence intensity near tulip flame formation and at the domain center. The results demonstrate that numerical OH-PLIF modeling, incorporating the new partition-function formulation, is a valuable tool for diagnostics and predictive analysis of hydrogen-air combustion in aerospace propulsion systems.
In order to address the difficulty of Reynolds-averaged Navier-Stokes (RANS) to simulate unsteady flows with massive separations and the high computational cost of large-eddy simulation (LES), some hybrid RANS/LES methods have been proposed. The scale adaptive simulation (SAS) is one of the most promising methods. The RANS/LES interface of SAS is determined by von Karman length scale. Since the von Karman length scale is dynamically solved using flow information, SAS significantly reduces the impact of grid-resolution. However, the small-scale turbulent flow of the inner layer might be suppressed by RANS, which could lead to an underestimated prediction of the resolved Reynolds stress. To address this problem, the present study proposes an improved SAS technique, i.e. the Reynolds-stress-compensated SAS (RSC-SAS) method. The RSC-SAS provides compensations for Reynolds stresses and turbulent heat flux, as inspired by constrained LES (CLES). In addition, the length scale of RSC-SAS has been replaced with dissipation-adaptive length scale. To evaluate the performance of RSC-SAS, three test cases are conducted, including compressible flow past a circular cylinder at high Reynolds number, high subsonic flow past a wing-body configuration and supersonic flow past an axisymmetric slender body. The a posteriori tests show that RSC-SAS can achieve satisfactory results including mean flow information and turbulence statistics. The coherent structures and flow visualization suggest that the RSC-SAS effectively promotes the generation of small-scale structures and captures turbulent fluctuations. Furthermore, the analysis of turbulence anisotropy suggests that RSC-SAS may be essentially closer to LES and is a more promising hybrid RANS/LES approach.
Inertial microfluidics offers an effective approach for high-throughput manipulation of biological microparticles. However, it remains highly challenging to achieve real-time and precise control over the equilibrium positions in the inertial focusing of deformable particles at the microscale. In this paper, a numerical model based on the lattice Boltzmann method is developed. By coupling the immersed boundary method with a slip boundary condition, the model accurately captures the two-way interaction between the deformable particle and the fluid. Simulations are performed by varying parameters such as particle deformability, Reynolds number, blockage ratio, and slip length to investigate the behavior and underlying mechanisms of inertial focusing for deformable particles. Numerical results reveal that the boundary slip effect is the key factor influencing the particle's equilibrium position and exhibits the most significant regulatory role, followed by the blockage ratio and particle deformability. In contrast, the Reynolds number has the weakest influence on controlling the equilibrium position although higher Reynolds number substantially accelerate the focusing process. Building on these insights, an effective scheme is proposed for real-time, directional, and precise control of the particle's equilibrium position by utilizing boundary slip. This study can provide theoretical support and an effective numerical tool for the precise separation and transport of biological particles, such as cells and vesicles, in microfluidic systems.
This study examines the linear stability of convection in a horizontal porous channel with uniform cross-flow and wall velocity slip. The above system is subjected to non-uniform internal heat generation, modeled using linear and quadratic spatial distributions. While convection in porous media is often modeled using Darcy's law, our study employs the Navier-Stokes-Brinkman flow model, along with the energy equation. The resulting eigenvalue problem, representing the growth rate of small perturbations, is solved numerically using the Chebyshev spectral collocation method. Results show that increasing slip length advances the onset of convection. The upper cross-flow delays convective instability, while downward cross-flow promotes it. The critical Rayleigh number decreases with stronger internal heating, which promotes convective instability early on. Depending on the nature of the internal heat source, the resulting thermal gradient can either intensify or suppress temperature disturbances near the boundary. In the linear case, a gradient that increases with distance from the center leads to destabilization and promotes convection, while one that decreases in that direction exerts a stabilizing influence. However, the quadratic spatial configuration shows no significant change in stability behavior with varying gradients.
Composite solid propellant slurry is a complex non-Newtonian fluid whose rheological properties critically affect grain molding quality and process safety. Prior simulations mostly focus on shear-thinning behavior using generalized non-Newtonian viscous models, while the potential influence of viscoelasticity remains underexplored. Herein, a linear viscoelastic constitutive model (Phan-Thin-Tanner) is employed to characterize and identify the rheological parameters of an (hydroxyl-terminated polybutadiene) propellant slurry. Validation is performed with numerical simple-shear simulations. Effects of dimensionless numbers and pipe geometry on flow in straight and sudden-expansion pipes are studied. Specifically, we examine the effects of the Reynolds number (Re) and Weissenberg number (Wi) on development length, velocity distribution, and pressure loss. The main findings show that both inertia and elasticity substantially restructure the flow field: increasing Re strengthens inertial effects and suppresses inlet velocity overshoot, whereas shear thinning suppresses the elastic response that would otherwise grow with increasing Wi, thus reducing overshoot magnitude. In expansion flows, larger Re and Wi both intensify recirculation; a higher expansion ratio enlarges the recirculation region, while reducing the expansion angle suppresses separation and mitigates elastic fluctuations. These findings provide a theoretical basis for understanding viscoelastic behavior of propellant slurry in complex flows and guide the optimization of casting parameters to improve grain quality.
The Marangoni flow with a soluble and diffusive surfactant in a deep layer of a non-Newtonian fluid is numerically analyzed. We have solved the momentum equations considering inertial effects and the components of the stress tensor based on the Carreau model using the modified vorticity-stream function formulation. A tangential stress balance at the interface relates the surface tension to the surface surfactant concentration using the Langmuir's non-linear equation. The convective-diffusion equations for surface and bulk surfactant concentrations, taking diffusive effects into account, were solved using the one-dimensional Crank-Nicolson method and the alternating-direction-implicit method, respectively. Due to solubility, the mass exchange between the interface and the bulk fluid is driven by adsorption-desorption kinetics, leading to a coupled system of highly nonlinear equations. The main parameters controlling the temporal evolution of the initial surfactant distribution on the interface are the following: the fluid behavior index ( n), the Carreau number ( Cu), the Biot number ( Bi), the solubility parameter ( beta) and the dimensionless surfactant depletion depth (alpha). Our findings indicate that, for a shear-thinning fluid, a decrease in the power-law index leads to a faster decrease in the surface surfactant concentration when soluble surfactants are present. The associated high strain rates amplify convective effects, which significantly enhance mass transport and diminish interfacial non-uniformities by reducing surface tension gradients. The surfactant is transported more effectively into the bulk phase, leading to a more homogeneous distribution and preventing localized accumulations within a shear-thinning fluid. In addition, under fully adsorptive conditions, the strain rates are sufficiently low that shear-thinning fluids exhibit their maximum Newtonian viscosity as predicted by the Carreau model, so the fluid rheology does not influence the relaxation process.
This paper presents computational results for the viscous instability of a vortex with azimuthal velocity profile V & strns; = [1 - (1 - epsilon r(2))e(-r2)]/r . When epsilon = 0, the Lamb-Oseen vortex model is recovered. Although the Lamb-Oseen vortex supports propagating waves known as Kelvin waves, these modes are stable according to Rayleigh's circulation criterion. However, in a recent paper by the author (Maslowe 2022 Fluid Dyn. Res. 54 015513), it was shown that for epsilon > 0 the modified vortex profile admits linearly unstable disturbances. According to these inviscid results, axisymmetric modes have the largest growth rates and their amplification rate grows monotonically as k, the axial wavenumber, increases. This large k behavior is at odds with what would be expected in a real fluid, because the effect of viscosity is usually to damp short waves. A principal motivation for the present study is to provide a more realistic description of the instability as k becomes large. The results presented herein confirm that for a given epsilon and Reynolds number, there is a value of k at which the amplification rate of an unstable perturbation reaches a maximum and it then decays to zero as k -> infinity. Stability characteristics are presented for a large range of the parameters epsilon and Re and critical Reynolds numbers are determined for 0 < epsilon <= 1.0.
The investigation portrays the interrelationship between the stability variables, critical wavelength, and breakup length. To accomplish this objective, a temporal analysis of combined instability at the interface of a water sheet in a co-flowing air stream has been carried out in the Rayleigh breakup zone (Weg < 0.4). Two modes of disturbances, symmetric (dilatational) and asymmetric (sinusoidal), constitute the combined mode. Based on Kelvin-Helmholtz instability, the amplified Fourier modes of perturbation uniquely unveil the normal distribution of interfacial displacement rate as a function of wave number. Thereby, the critical wavelength can be theoretically extracted. By contrast, the breakup length measurements exploited high-speed flow visualization studies that discern the coexistence of low-frequency (primary) and high-frequency (intermediate) breakup events. The evolution of critical wavelength and breakup length data maintains approximately a constant offset value in the entire Rayleigh zone. That is, on average, the proportionality constant between breakup length and critical wave length is found to be 5.1-6.0. This numerical value is labeled as the stability factor at the interface of a liquid sheet in a co-flowing airstream. The theoretical critical wavelength data have been compared with the visualization results, which show very good harmony.
In this manuscript, we review the mathematical models and the numerical approaches used to perform direct numerical simulations of a variety of multiphase turbulent problems with the solver Fujin, developed in the Complex Fluids and Flows unit at the Okinawa Institute of Science and Technology.
This paper conducts a numerical analysis of the sedimentation dynamics of two-dimensional rigid circular particles suspended in a power-law fluid flow within a computational channel. The fluid dynamics are represented by the power-law model, encompassing three specific flow conditions: shear-thinning (n = 0.9), Newtonian (n = 1), and shear-thickening (n = 1.1). The finite element method (FEM) technique is integrated with the fictitious boundary method (FBM) to address the fluid-particle interaction issue. The particles, with radii R-1=0.2 and R-2=0.125, display intricate behaviors such as drafting, kissing, and tumbling during sedimentation. The research investigates the influence of particle size and initial particle placement on their behavior in the fluid. Principal findings reveal that shear-thinning fluids (n < 1) precipitate faster particle interactions, heightened instability, and expedited transitions into the tumbling phase, whereas shear-thickening fluids (n > 1) enhance wake stability, resulting in delayed interactions and more gradual settling. The research underscores the importance of the power-law index in ascertaining the overall particle dynamics and fluid-particle interaction. This research enhances the comprehension of particle movement in non-Newtonian fluids and has ramifications for diverse engineering applications, including sedimentation processes, fluid transport, and industrial processing. The simulations are performed using the FEATFLOW Software package which utilizes the FEM for the numerical solutions.
The dynamics of solid particles and fluid solid interaction in particulate flows with a power law model are examined. An Eulerian approach is employed to simulate this flow across a fixed computational grid, utilizing the fictitious boundary method (FBM) to efficiently handle complex geometries. The multigrid finite element solver FEATFLOW is extended to account for non-Newtonian fluids. Three types of rheological behavior are considered: (i) shear-thinning (n=0.9), (ii) Newtonian (n=1), and (iii) shear-thickening (n=1.1). Numerical experiments are conducted with two falling particles, focusing on the drafting, kissing, and tumbling phenomena in power-law fluids. Results from these experiments are presented and compared across shear-thinning, Newtonian, and shear-thickening fluids by varying the initial particle positions and the particle radii. The effects of particle-particle interactions on particle motion and the overall behavior of the fluid-particle system are analyzed. This study validates the FBM by comparing it with benchmark results and offers valuable insights into particle-fluid interactions.
We study the influence of the differential geometry of the flow domain on the motion of fluids on two-dimensional Riemannian manifolds, particularly on the elongation of material lines and vortices. We derive a formula for the second order time derivative of the square of the distance between close fluid particles and show that a curvature term appears. The elongation of a material line is accelerated by negative curvature. The use of this expression extends Haller's definition of hyperbolic domains to flows on curved surfaces. The need to consider curvature effects is illustrated by three examples. The example of a curved two-dimensional torus implies that the filamentation of vortices can be triggered by negative curvature.
Based on machine learning (ML) techniques, we propose a novel method to estimate flow fields using only floating sensor locations. This method does not require either ground-truth velocity fields or governing equations for fluid flows, which is attractive for practical applications. The ML model is supposed to generate accurate velocity fields so that the time variation of sensor motion is consistent with the given data of sensor locations. To validate the method, the estimation accuracy, the dependence on the number of sensors, the time intervals for the sensor location data, and the robustness to noise are investigated using three examples of two-dimensional flows: the flow around a circular cylinder, the forced homogeneous isotropic turbulence, and the ocean currents. These investigations demonstrate the performance and practicality of this method, revealing that the accuracy can be comparable to the state-of-the-art physics-informed neural networks-based method even without any assumption of governing equations. Moreover, we observe that the present method can estimate the major structures, such as periodic wakes behind a cylinder, coherent structures in the forced turbulence, and stable ocean currents, with only a few sensors. We believe the present method can provide effective utilization of floating sensor observations in various fields.
