Abstract This paper presents computational results for the viscous instability of a vortex with azimuthal velocity profile V ¯ = [ 1 − ( 1 − ε r 2 ) e − r 2 ] / r . When ɛ = 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 ɛ > 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 ɛ 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 → ∞ . Stability characteristics are presented for a large range of the parameters ɛ and Re and critical Reynolds numbers are determined for 0 < ε ⩽ 1.0 .

Abstract 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.

Abstract This paper presents a new sensitivity analysis for aerodynamic inverse design problems. Both incompressible and compressible flows are considered. The objective of inverse design problem considered here is to infer the airfoil shape that produces a desired pressure distribution. Based on an idea of considering significant sensitivity coefficients only as well as partial differentiation, a sensitivity matrix is formed which enables us to compute all sensitivity coefficients at each iteration during the minimization process with no need to additional flow solutions or adjoint equation solution to calculate the derivative of objective function with respect to design variables. We show by considering a few test cases that the proposed method is very efficient, accurate, robust, and easy to implement.

Abstract Efficient fluidic mixing is crucial for various applications, including chemical synthesis and biological assays. This study numerically investigates the effect of vortex generators (barriers) on the mixing performance of a T-micromixer. We conducted over 120 simulations to examine the impact of key parameters, including the number of vortex generator sets, the spacing between barriers, and the barrier gap ratio, across a range of Reynolds numbers. Our findings, validated against existing numerical and experimental data, demonstrate that the vortex generator design consistently outperforms a simple T-micromixer, achieving up to 100% mixing efficiency due to the vortices generated by the barriers. While configurations with three sets of vortex generators show a higher mixing index and pressure drop, we found that two and three-set configurations can achieve the same mixing efficiency by adjusting the gap ratio and barrier spacing. We further determined the optimal gap ratio for different configurations and Reynolds numbers. These results underscore the importance of our proposed model for designing and creating highly efficient fluidic micromixers with short mixing distances.

Abstract This study investigates the prediction of two-dimensional lid-driven cavity fluid flow in a square domain using supervised machine learning techniques. The classical problem of lid-driven cavity flow is utilized to demonstrate the integration of the mesoscopic Lattice Boltzmann Method (LBM) with machine learning algorithms. The LBM is employed to generate macroscopic velocity and pressure data for varying Reynolds numbers (Re = 2000, 3200, 5000, and 7500). Machine learning-based regression models are then applied to forecast key macroscopic variables, including density, pressure, and velocity based on directional coordinate measurements. For all datasets, the Random Forest regressor consistently predicted velocity with high precision, with R² scores of 0.9998 (Re = 2000), 0.9997 (Re = 3200), 0.9996 (Re = 5000), and 0.9996 (Re = 7500), and RMSE values ranging between 0.0032–0.0042. For pressure prediction, XGBoost outperformed others with an R² score of 0.9250 and RMSE of 1.04×10⁻⁴, while Random Forest followed closely with R² = 0.9063 and RMSE = 1.02×10⁻⁴. On the other hand, Decision Tree (R² = 0.112) and Linear Regression (R² = 0.064) performed badly in terms of prediction, underscoring the superiority of ensemble-based approaches. The study further demonstrates that ensemble-based approaches like Random Forest and XGBoost outperform traditional regression methods, showing significant capability for accelerating the parametric research and enhancing design optimization in engineering domain.

Abstract The nonequilibrium behaviors in the collisional coalescence of off-center bubbles are investigated using a discrete Boltzmann model. Based on the tendency of surface energy, the physical process can be categorized into three distinct stages: approach, coalescence, and oscillation. The influence of the relative position of bubble centers, the initial velocity, and the surface tension on the nonorganized momentum flux and the nonorganized energy flux is explored. The results show that the relative position of bubble centers has a minimal impact on both the nonequilibrium momentum and energy fluxes. Higher initial velocities enhance nonequilibrium behaviors, while increased surface tension accelerates coalescence and suppresses oscillations. In addition, the angular momentum of the system is analyzed. It is found to vary linearly with both the relative position and initial velocity, but not with surface tension. However, the associated energy dissipation can be interpreted through further analysis. These findings offer valuable insights into the kinetics of bubble coalescence.

Abstract The study aims to enhance the aerodynamic performance of a NACA0012 profile by utilizing backward-facing steps inclined forward, inspired by shark denticles known for delaying boundary layer separation. The turbulent and steady-in-the-mean flow around the airfoil fitted with inclined backward-facing steps (IBFSs) is numerically investigated via Ansys Fluent. In this work, the effects of characteristic geometrical parameters of the IBFSs like the step height, the inclination angle and the layout of the steps along the airfoil suction surface on the lift and drag coefficients are brought to light. The results demonstrate a notable enhancement in aerodynamic finesse, showing an improvement of up to 4.53% compared to the standard NACA0012. This improvement is affected by the different geometrical parameters tested. Specifically, fitting IBFSs on 80% of the suction surface and decreasing the steps height and inclination angle contributed to increased performance. The impact of IBFSs is more noticeable at high angles of attack (AOAs), where lift is significantly influenced compared to drag, while the opposite occurs at low AOA. These findings highlight the potential of the use of IBFSs for optimizing aerodynamic efficiency, particularly in scenarios characterized by high AOA.

Abstract A semi-analytical study of coupled translation and rotation of a composite spherical particle (a hard sphere core coated with a permeable porous layer) in a viscous fluid inside an eccentric spherical cavity normal to their common diameter is presented in the quasi-steady limit of low Reynolds number. To solve the Stokes and Brinkman equations for the flow fields outside and inside the porous layer, respectively, a general solution is constructed from the fundamental solutions in the two spherical coordinate systems based on both the composite particle and the cavity. The boundary conditions at the cavity wall and inner and outer surfaces of the porous layer are satisfied by a collocation method. Numerical results for the force and torque exerted on the particle by the fluid are obtained with good convergence for various values of the relevant parameters in practical applications. For the translation and rotation of a composite sphere inside a concentric cavity, our force and torque results agree well with the available solutions in the literature. The force and torque on a translating and rotating particle increase monotonically with increases in the ratios of particle radius to porous layer permeation length, core-to-particle radii, and particle-to-cavity radii. In general, they also increase with an increase in the relative distance between the particle and cavity centers. The boundary effect of the cavity on the translation of the particle is much more pronounced than that on the rotation. The coupling effect in the simultaneous translation and rotation inside an eccentric spherical cavity is complicated and not a monotonic function of the particle-to-cavity radius ratio.

Abstract This article explores the steady and uniform motion of two spherical particles submerged in an infinite fluid with Brinkman-couple stress properties, where the particles are entirely immersed and surface slippage is disregarded. While the particles may vary in size, they are composed of the same material and move along the line that connects their centers, influenced by different velocities or external forces. The analysis is performed under low Reynolds number conditions, which signify laminar flow dominated by viscous forces. Using boundary collocation methods, semi-analytical solutions to the governing differential equations are derived, facilitating a thorough investigation of the system. The study employs normalized drag force to evaluate the effects of particle interactions, presenting calculated values graphically and discussing them with several key factors, such as particle size and separation distance, thereby enhancing the understanding of particle dynamics in complex fluid environments. The analysis of how varying the permeability parameter affects flow patterns around two spheres in a couple of stress fluids is shown.

Abstract The effects of pivot location ( x p / c ) and spacing ratio ( λ = d s / c ) on enhancing the lift generated by rigid biplane NACA 0012 airfoils at R e = 1.35 × 10 5 are studied through the numerical method. SST k − ω turbulence model is adopted to solve URANS equations with overset grids. Results reveal that C L hysteresis exist phase lag under five fixed pivot locations x p / c = 0 , 0.25, 0.5, 0.75 and 1 when biplane airfoils tilt just like pitching stroke. C M curves drop regularly as the pivot point moves towards the spacing direction. However, λ decreasing plays a important role in aerodynamics: C L , lower curve family significantly collapse and C L , upper hysteresis rise overall owing to intensified low-pressure distribution in the gap. Additionally, these performances can be explained from the view of vorticity evolution, particularly, high angles of attack around the stall induce violent turbulence structures. With rearward movement of the pivot point, resemble vortex details appear in the further upstream, indicating aerodynamic characteristics have high similarity under different x p / c regardless of λ. And thus a concept of effective angle of attack for biplane airfoils is proposed where a new factor λ must be introduced. Data assimilation results and vorticity contours are exhibited to prove the feasibility of α eff .