Application of wake oscillators to two-dimensional vortex-induced vibrations of circular cylinders in oscillatory flows

A nonlinear time-domain simulation model for predicting two-dimensional vortex-induced vibration (VIV) of a flexibly mounted circular cylinder in planar and oscillatory flow is presented. This model is based on the utilization of van der Pol wake oscillators, being unconventional since wake oscillators have typically been applied to steady flow VIV predictions. The time-varying relative flow–cylinder velocities and accelerations are accounted for in deriving the coupled hydrodynamic lift, drag and inertia forces leading to the cylinder cross-flow and in-line oscillations. The system fluid–structure interaction equations explicitly contain the time-dependent and hybrid trigonometric terms. Depending on the Keulegan–Carpenter number (KC) incorporating the flow maximum velocity and excitation frequency, the model calibration is performed, entailing a set of empirical coefficients and expressions as a function of KC and mass ratio. Parametric investigations in cases of varying KC, reduced flow velocity, cylinder-to-flow frequency ratio and mass ratio are carried out, capturing some qualitative features of oscillatory flow VIV and exploring the effects of system parameters on response prediction characteristics. The model dependence of hydrodynamic coefficients on the Reynolds number is studied. Discrepancies and limitations versus advantages of the present model with different feasible solution scenarios are illuminated to inform the implementation of wake oscillators as a computationally efficient prediction model for VIV in oscillatory flows.     

A fluid–structure interaction solver for the study on a passively deformed fish fin with non-uniformly distributed stiffness

Research on fish locomotion has made extensive progress towards a better understanding of how fish control their flexible body and fin for propulsion and maneuvering. Although the biologically flexible fish fins are believed to be one of the most important features to achieve optimal swimming performance, due to the limitations of the existing numerical modeling tool, studies on a deformable fin with a non-uniformly distributed stiffness are rare. In this work, we present a fully coupled fluid–structure interaction solver which can cope with the dynamic interplay between flexible aquatic animal and the ambient medium. In this tool, the fluid is resolved by solving Navier–Stokes equations based on the finite volume method with a multi-block grid system. The solid dynamics is solved by a nonlinear finite element method. A sophisticated improved IQN-ILS coupling algorithm is employed to stabilize solution and accelerate convergence. To demonstrate the capability of the developed Fluid–Structure-Interaction solver, we investigated the effect of five different stiffness distributions on the propulsive performance of a caudal peduncle-fin model. It is shown that with a non-uniformly distributed stiffness along the surface of the caudal fin, we are able to replicate similar real fish fin deformation. Consistent with the experimental observations, our numerical results also indicate that the fin with a cupping stiffness profile generates the largest thrust and efficiency whereas a heterocercal flexible fin yields the least propulsion performance but has the best maneuverability.     

The effect of vertical vibration on the onset of thermocapillary convection in a horizontal liquid layer

The effect of vertical vibration on the onset of Marangoni convection in a horizontal layer of a viscous incompressible uniform liquid with a free surface and a hard (solid) or soft (impermeable and stress-free) wall is investigated. In the case of harmonic vibration, a dispersion relation is constructed in explicit form using continued fractions. From this, equations are obtained for determining the critical values of the parameters for all three main types of loss of stability. Neutral curves of the monotonic and oscillatory instability are constructed, for fixed frequency and amplitude of the vibration, in the form of a graph of the Marangoni number against the wave number. The regions of parametric resonances, corresponding to synchronous and subharmonic modes are determined. The frequency values for which a high-frequency asymptotic form is reached are obtained. The long-wave Marangoni oscillatory instability is investigated, and it is shown that in this case the Marangoni numbers are negative and depend only on the Prandtl and Biot numbers.     

A numerical investigation of the resonance of gas-filled microbubbles: resonance dependence on acoustic pressure amplitude

The general Keller–Herring equation for free gas bubbles is augmented by specific terms to describe the elasticity, viscosity and thickness of the encapsulating shell in ultrasound contrast agent microbubbles. A numerical investigation that analyses the acoustic backscatter from bubbles is employed to identify resonance frequencies that can be compared, for increasing driving pressure amplitude, with linear approximations obtained via analytical considerations. Calculations for bubbles of the size employed in diagnostic ultrasound, between 2 and 6 μm diameter, that are immersed in water and blood and exposed to monochromatic insonation, causing the bubbles to undergo stable cavitation, reveal that the resonance frequency diverges from the linear approximation as the pressure amplitude is increased. The shift in resonance, to lower frequency values, is found to be more pronounced for larger bubbles with the calculated value differing by up to 40% from the linear approximation. The results of this simulation might be potentially useful in preparation of formulations of ultrasound contrast agents with the specifically desired features, such as for instance resonance frequency.     

Permeability of microscale fibrous porous media using the lattice Boltzmann method

The permeabilities of microscale fibrous porous media were calculated using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Two models of the microscale fibrous porous media were constructed based on overlapping fibers (simple cubic, body-centered cubic). Arranging the fibers in skew positions yielded two additional models comprising non-overlapping fibers (skewed simple cubic, skewed body-centered cubic). As the fiber diameter increased, the fibers acted as granular inclusions. The effects of the overlapping fibers on the media permeability were investigated. The overlapping fibers yielded permeability values that were a factor of 2.5 larger than those obtained from non-overlapping fibers, but the effects of the fiber arrangement were negligible. Two correlations were obtained for the overlapping and non-overlapping fiber models, respectively. The effects of the rarefaction and slip flow are also discussed. As the Knudsen number increased, the dimensionless permeability increased; however, the increase differed depending on the fiber arrangement. In the slip flow regime, the fiber arrangement inside the porous media became an important factor.     

Numerical analysis of enhanced mixing in a Gallay tote blender

The mixing performance of a multi-bladed baffle inserted into a traditional Gallay tote blender is explored by graphic processing unit-based discrete element method software. The mixing patterns and rates are investigated for a binary mixture, represented by two different colors, under several loading profiles. The baffle effectively enhances the convective mixing both in the axial and radial directions, because of the disturbance it causes to the initial flowing layer and solid-body zone, compared with a blender without a baffle. The axial mixing rate is affected by the gap between the baffle and the wall on the left and right sides, and an optimal blade length corresponds to the maximum mixing rate. However, the radial mixing rate increases with the blade length almost monotonically.     

A comparative study of truly incompressible and weakly compressible SPH methods for free surface incompressible flows

In this paper, the performance of the incompressible SPH (ISPH) method and an improved weakly compressible SPH (IWCSPH) method for free surface incompressible flows are compared and analyzed. In both methods, the Navier–Stokes equations are solved, and no artificial viscosity is used. The ISPH algorithm in this paper is based on the classical SPH projection method with common treatments on solid boundaries and free surfaces. The IWCSPH model includes some advanced corrective algorithms in density approximation and solid boundary treatment (SBT). In density approximation, the moving least squares (MLS) approach is applied to re‐initialize density every several steps to obtain smoother and more stable pressure fields. An improved coupled dynamic SBT algorithm is implemented to obtain stable pressure values near solid wall areas and, thus, to minimize possible numerical oscillations brought in by the solid boundaries. Three representative numerical examples, including a benchmark test for hydrostatic pressure, a dam breaking problem and a liquid sloshing problem, are comparatively analyzed with ISPH and IWCSPH. It is demonstrated that the present IWCSPH is more attractive than ISPH in modeling free surface incompressible flows as it is more accurate and more stable with comparable or even less computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.     

Ultra-broadband piezoelectric energy harvesting via bistable multi-hardening and multi-softening

Nonlinear Dynamics - An electromechanical coupled distributed parameter model is derived for a broadband piezoelectric energy harvester with nonlinear magnetic interaction and...     

A modified model for isothermal homogeneous and heterogeneous reactions in the boundary-layer flow of a nanofluid

The homogeneous and heterogeneous reactions in the boundary-layer of a flat surface are considered. The autocatalysts are assumed to be of regular sizes, while the solution is a dilute nanofluid. The heat release due to the chemical reactions is taken into account. The Buongiorno's model is used to describe the behaviors of this reaction system. This configuration makes the current model be different from all previous publications. Multiple solutions are given numerically to the rescaled nonlinear system, whose stability is verified. The results show that the strength coefficients of the homogeneous and heterogeneous reactions are key factors to cause the appearance of the multiple solutions in the distribution of the chemical reactions. Nanofluids enhance the diffusion of heat and help maintain the stability of chemical reactions.