A second-order dynamic subgrid-scale stress model

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The formation of vortex rings in a strongly forced round jet

The periodic formation of vortex rings in the developing region of a round jet subjected to high-amplitude acoustic forcing is investigated with High-Speed Particle Image Velocimetry. Harmonic velocity oscillations ranging from 20 to 120% of the mean exit velocity of the jet was achieved at several forcing frequencies determined by the acoustic response of the system. The time-resolved history of the formation process and circulation of the vortex rings are evaluated as a function of the forcing conditions. Overall, high-amplitude forcing causes the shear layers of the jet to breakup into a train of large-scale vortex rings, which share many of the features of starting jets. Features of the jet breakup such as the roll-up location and vortex size were found to be both amplitude and frequency dependent. A limiting time-scale of t/T ≈ 0.33 based on the normalized forcing period was found to restrict the growth of a vortex ring in terms of its circulation for any given arrangement of jet forcing conditions. In sinusoidally forced jets, this time-scale corresponds to a kinematic constraint where the translational velocity of the vortex ring exceeds the shear layer velocity that imposes pinch-off. This kinematic constraint results from the change in sign in the jet acceleration between t = 0 and t = 0.33T. However, some vortex rings were observed to pinch-off before t = 0.33T suggesting that they had acquired their maximum circulation. By invoking the slug model approximations and defining the slug parameters based on the experimentally obtained time- and length-scales, an analytical model based on the slug and ring energies revealed that the formation number for a sinusoidally forced jet is L/D ≈ 4 in agreement with the results of Gharib et al. (J Fluid Mech 360:121–140, 1998).     

Simulation of conjugate radiation–forced convection heat transfer in a porous medium using the lattice Boltzmann method

In this paper, a lattice Boltzmann method is employed to simulate the conjugate radiation–forced convection heat transfer in a porous medium. The absorbing, emitting, and scattering phenomena are fully included in the model. The effects of different parameters of a silicon carbide porous medium including porosity, pore size, conduction–radiation ratio, extinction coefficient and kinematic viscosity ratio on the temperature and velocity distributions are investigated. The convergence times of modified and regular LBMs for this problem are 15 s and 94 s, respectively, indicating a considerable reduction in the solution time through using the modified LBM. Further, the thermal plume formed behind the porous cylinder elongates as the porosity and pore size increase. This result reveals that the thermal penetration of the porous cylinder increases with increasing the porosity and pore size. Finally, the mean temperature at the channel output increases by about 22% as the extinction coefficient of fluid increases in the range of 0–0.03.

     

Experimental and theoretical investigation of superharmonic resonances in a planar oscillator under angular base excitation

This paper explores the complicated dynamic behavior of a mechanical oscillator under harmonic angular excitation. The motivation behind this work comes from the nature of the actuation produced by high-performance dither motors. A lumped-mass model, which captures the primary and the 1 : 2 superharmonic resonances observed on an analogous experimental test setup, is put forward. The equations of motion governing the dynamics of the model are derived and are found to comprise both parametric and direct forcing terms. The governing equations are solved analytically using the generalized harmonic balance method and numerical integration. The method of multiple scales is utilized to obtain closed-form expressions that relate the system parameters to the oscillation amplitudes in the vicinity of the direct and the 1 : 2 superharmonic resonances. It is found that eccentricity plays a vital role in the occurrence of the resonances. Besides, the relationship between the excitation amplitudes and the resulting oscillations for the direct and the superharmonic resonances are dissimilar. A few salient differences between classical (rectilinear) and angular base excitation mechanisms are pointed out.

     

Experimental study on the effect of pulsating inflow to an enclosure for improved mixing

Optimal control of inlet jet flows is of broad interest for enhanced mixing in ventilated rooms. The general approach in mechanical ventilation is forced convection by means of a constant flow rate supply. However, this type of ventilation may cause several problems such as draught and appearance of stagnation zones, which reduces the ventilation efficiency. A potential way to improve the ventilation quality is to apply a pulsating inflow, which has been hypothesised to reduce the stagnation zones due to enhanced mixing. The present study aims at testing this hypothesis, experimentally, in a small-scale two-dimensional water model using Particle Image Velocimetry with an in-house vortex detection program. We are able to show that for an increase in pulsation frequency or alternatively in the flow rate the stagnation zones are reduced in size and the distribution of vortices becomes more homogeneous over the considered domain. The number of vortices (all scales) increases by a factor of four and the swirl-strength by about 50% simply by turning on the inflow pulsation. Furthermore, the vortices are well balanced in terms of their rotational direction, which is validated by the symmetric Probability Density Functions of vortex circulation (Γ) around Γ = 0. There are two dominating vortex length scales in the flow, namely 0.6 and 0.8 inlet diameters and the spectrum of vortex diameters become broader by turning on the inflow pulsation. We conclude that the positive effect for enhanced mixing by increasing the flow rate can equally be accomplished by applying a pulsating inflow.     

Adaptive Remodeling in the Elastase-Induced Rabbit Aneurysms

Background

Rupture of brain aneurysms is associated with high fatality and morbidity rates. Through remodeling of the collagen matrix, many aneurysms can remain unruptured for decades, despite an enlarging and evolving geometry.

Objective

Our objective was to explore this adaptive remodeling for the first time in an elastase induced aneurysm model in rabbits.

Methods

Saccular aneurysms were created in 22 New Zealand white rabbits and remodeling was assessed in tissue harvested 2, 4, 8 and 12 weeks after creation.

Results

The intramural principal stress ratio doubled after aneurysm creation due to increased longitudinal loads, triggering a remodeling response. A distinct wall layer with multi-directional collagen fibers developed between the media and adventitia as early as 2 weeks, and in all cases by 4 weeks with an average thickness of 50.6?±?14.3 μm. Collagen fibers in this layer were multi-directional (AI?=?0.56?±?0.15) with low tortuosity (1.08?±?0.02) compared with adjacent circumferentially aligned medial fibers (AI?=?0.78?±?0.12) and highly tortuous adventitial fibers (1.22?±?0.03). A second phase of remodeling replaced circumferentially aligned fibers in the inner media with longitudinal fibers. A structurally motivated constitutive model with both remodeling modes was introduced along with methodology for determining material parameters from mechanical testing and multiphoton imaging.

Conclusions

A new mechanism was identified by which aneurysm walls can rapidly adapt to changes in load, ensuring the structural integrity of the aneurysm until a slower process of medial reorganization occurs. The rabbit model can be used to evaluate therapies to increase aneurysm wall stability.

     

Shear deformable bars of doubly symmetrical cross section under nonlinear nonuniform torsional vibrations—application to torsional postbuckling configurations and primary resonance excitations

In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross section, taking into account the effects of geometrical nonlinearity (finite displacement—small strain theory) and secondary twisting moment deformation. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are subjected to the most general axial and torsional (twisting and warping) boundary conditions. The resulting coupling effect between twisting and axial displacement components is also considered and a constant along the bar compressive axial load is induced so as to investigate the dynamic response at the (torsional) postbuckled state. The bar is assumed to be adequately laterally supported so that it does not exhibit any flexural or flexural–torsional behavior. A coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an independent warping parameter is formulated. The resulting equations are further combined to yield a single partial differential equation with respect to the angle of twist. The problem is numerically solved employing the Analog Equation Method (AEM), a BEM based method, leading to a system of nonlinear Differential–Algebraic Equations (DAE). The main purpose of the present contribution is twofold: (i) comparison of both the governing differential equations and the numerical results of linear or nonlinear free or forced vibrations of bars ignoring or taking into account the secondary twisting moment deformation effect (STMDE) and (ii) numerical investigation of linear or nonlinear free vibrations of bars at torsional postbuckling configurations. Numerical results are worked out to illustrate the method, demonstrate its efficiency and wherever possible its accuracy.

     

Simple shear in nonlinear Cosserat elasticity: bifurcation and induced microstructure

We discuss the simple shear problem for a geometrically exact Cosserat model. In contrast to linear Cosserat elasticity, where the unique solution is available in closed form we exhibit a multitude of solutions to the nonlinear problem, even if the two fields of deformations φ and microrotations remain homogeneous. This motivates a search for new conditions on the microrotations which single out a unique, physically reasonable, response. The influence of material parameters, notably the Cosserat couple modulus μ _c and the internal length scale L _c on the response is also studied. For small Cosserat couple modulus μ _c  > 0 we observe a pitchfork bifurcation of the homogeneous response and for vanishing internal length L _c  = 0 and zero Cosserat couple modulus μ _c  = 0 the Cosserat model may show highly oscillating “microstructure” solutions which are energetically better than the homogeneous response. Thus, the large scale nonlinear Cosserat limit is not necessarily a classical limit.      

Size effects on tensile and compressive strengths in metallic glass nanowires

Shear localization induced brittleness is the main drawback of metallic glasses which restricts their practical applications. Previous experiments have provided insights on how to suppress shear localization by reducing the sample size of metallic glasses to the order of 100 nm. In order to reveal the size effects and associated deformation mechanisms of metallic glasses in an even finer scale, we perform large-scale atomistic simulations for the uniaxial compression and tension of metallic glass nanowires. The simulation results show that, as the diameter of metallic glass samples decreases from 45 nm to 8 nm, the tensile yield strength increases while the compressive yield strength decreases. Homogeneous flow is observed as the governing deformation mechanism in all simulated metallic glass samples, where plastic shearing tends to initiate on the sample surface and propagate into the interior. To rationalize the size dependence of yield strengths, we propose a theoretical model based on the concept of surface stress and Mohr–Coulomb criterion. The theoretical predictions agree well with the simulation results, implying the important role of surface stress on the yielding of MGs below 100 nm. Finally, a discussion about the size effects of strength in metallic glasses at different length scales is provided. Our results suggest that the shear band energy and surface stress might be the two crucial parameters in determining the critical size required for the transition from shear localization to homogeneous deformation in MGs.     

Two-fluid modeling of Geldart A particles in gas-fluidized beds

We have investigated the effect of cohesion and drag models on the bed hydrodynamics of Geldart A particles based on the two-fluid （TF） model. For a high gas velocity U0 = 0.03 m/s, we found a transition from the homogeneous fluidization to bubbling fluidization with an increase of the coefficient C1, which is used to account for the contribution of cohesion to the excess compressibility. Thus cohesion can play a role in the bed expansion of Geldart A particles. Apart from cohesion, we have also investigated the influence of the drag models. When using the Wen and Yu drag correlation with an exponent n = 4.65, we find an under-prediction of the bed expansion at low gas velocities （U0 = 0.009 m/s）. When using a larger exponent （n = 9.6）, as reported in experimental studies of gas-fluidization, a much better agreement with the experimental bed expansion is obtained. These findings suggest that at low gas velocity, a scale-down of the commonly used drag model is required. On the other hand, a scale-up of the commonly used drag model is necessary at high gas velocity （U0 = 0.2 and 0.06 m/s）. We therefore conclude that scaling the drag force represent only an ad hoc way of repairing the deficiencies of the TF model, and that a far more detailed study is required into the origin of the failure of the TF model for simulating fluidized beds of fine powders.     

Numerical investigation of turbulent flow,heat transfer and entropy generation in a helical coiled tube with larger curvature ratio

Three-dimensional turbulent forced convective heat transfer and flow characteristics, and the non-dimensional entropy generation number in a helical coiled tube subjected to uniform wall temperature are simulated using the k–ε standard turbulence model. A finite volume method is employed to solve the governing equations. The effects of Reynolds number, curvature ratio, and coil pitch on the average friction factor and Nusselt number are discussed. The results presented in this paper cover a Reynolds number range of 2 × 10⁴ to 6 × 10⁴, a pitch range of 0.1–0.2 and a curvature ratio range of 0.1–0.3. The results show that the coil pitch, curvature ratio and Reynolds number have different effects on the average friction factor and Nusselt number at different cross-sections. In addition, the flow and heat transfer characteristics in a helical coiled tube with a larger curvature ratio for turbulent flow are different from that of smaller curvature ratio for laminar and turbulent flow in certain ways. Some new features that are not obtained in previous researches are revealed. Moreover, the effects of Reynolds number, curvature ratio, and coil pitch on the non-dimensional entropy generation number of turbulent forced convection in a helical coiled tube are also discussed.     

In-plane Operating Deflection Shape Measurement of an Aluminum Plate Using a Three-dimensional Continuously Scanning Laser Doppler Vibrometer System

Background

In-plane vibration is significant to a structure and has been accurately solved by many numerical methods; however, there are still not enough studies on its experimental measurement.

Objective

This work aims to propose a non-contact and fast way to measure dense full-field in-plane vibration of a plate structure, which has high frequencies and low response magnitudes.

Methods

A novel three-dimensional (3D) continuously scanning laser Doppler vibrometer (CSLDV) system that contains three CSLDVs is developed to conduct full-field scanning of a plate with free boundary conditions under sinusoidal excitation to measure its 3D vibrations. Calibration among the three CSLDVs in the 3D CSLDV system based on the geometrical model of its scan mirrors is conducted to adjust their rotational angles to ensure that three laser spots can continuously and synchronously move along the same two-dimensional scan trajectory on the plate. The demodulation method is used to process the measured response to obtain in-plane operating deflection shapes (ODSs) of the plate.

Results

Four in-plane ODSs are obtained in the frequency range of 0–5000 Hz. Modal assurance criterion (MAC) values between in-plane ODSs from 3D CSLDV and step-wise scanning laser Doppler vibrometer (SLDV) measurements are larger than 95%. MAC values between ODSs from 3D CSLDV measurements and corresponding mode shapes from the finite element model of the plate are larger than 91%.

Conclusions

Results from 3D CSLDV measurements have good accuracy compared to those from SLDV measurements and numerical calculation, and the 3D CSLDV system can scan much more measurement points in much less time than the SLDV system.

     

Oblique stagnation-point flow of a viscoelastic fluid with heat transfer

The two-dimensional forced convection stagnation-point flow and heat transfer of a viscoelastic second grade fluid obliquely impinging on an infinite plane wall is considered as an exact solution of the full partial differential equations. This oblique flow consists of an orthogonal stagnation-point flow to which a shear flow whose vorticity is fixed at infinity is added. The relative importance of these flows is measured by a parameter γ. The viscoelastic problem is reduced to two ordinary differential equations governed by the Weissenberg number W_e, two parameters α and β, the later being a free parameter β, introduced by Tooke and Blyth [A note on oblique stagnation-point flow, Physics of Fluids 20 (2008) 033101-1–3], and the Prandtl number Pr. The two cases when α=β and α≠β are, respectively, considered. Physically the free parameter may be viewed as altering the structure of the shear flow component by varying the magnitude of the pressure gradient. It is found that the location of the separation point x_s of the boundary layer moves continuously from the left to the right of the origin of the axes (x_s<0).     

Dynamic properties of interactional solutions for the (4 + 1)-dimensional Fokas equation

The internal resonances between the longitudinal and transversal oscillations of a forced Timoshenko beam with an axial end spring are studied in depth. In the linear regime, the loci of occurrence of 1 : ir, \(ir \in \mathbb {N}\), internal resonances in the parameters space are identified. Then, by means of the multiple time scales method, the 1 : 2 case is investigated in the nonlinear regime, and the frequency response functions and backbone curves are obtained analytically, and investigated thoroughly. They are also compared with finite element numerical simulations, to prove their reliability. Attention is paid to the system response obtained by varying the stiffness of the end spring, and it is shown that the nonlinear behaviour instantaneously jumps from hardening to softening by crossing the exact internal resonance value, in contrast to the singular (i.e. tending to infinity) behaviour of the nonlinear correction coefficient previously observed (without properly taking the internal resonance into account).

     

Numerical study on the resistance of rigid projectiles penetrating into semi-infinite concrete targets

A study on the resistance of rigid projectiles penetrating into semi-infinite concrete targets is performed in this paper. Experimental data are analyzed to examine the penetration resistance during various stages of the penetration process. A numerical tool using AUTODYN hydrocode is applied in the study. The numerical results on both deceleration-time history and depth of penetration of projectiles are in good agreement with experimental data, which demonstrate the feasibility of the numerical model in these conditions. Based on the numerical model with a two-staged pre-drilled hole, the rigid projectile penetration in tunneling stage is studied for concrete targets with different strengths in a wide range of impact velocities. The results show that the penetration in tunnel stage can be divided into two different cases in terms of initial impact velocity. In the first case, when the impact velocity is approximately less than 600 m/s, the deceleration depends on initial impact velocity. In the second case, when the impact velocity is greater than 600 m/s, the effect of target inertia becomes apparent, which agrees with commonly used concrete penetration resistance equations based on cavity expansion model.

Graphic abstract

A two-staged pre-drilled hole model was developed and the results show that the depth of entrance stage tends to decrease with the increase of impact velocity. The influence of the inertial term at low velocity range (approximately close to 600 m/s) is inconspicuous. With further increase of the penetration velocity, the effect of the target inertia becomes apparent as proposed by Forrestal. The effect of mass abrasion of projectiles, entrance phase and strain effect of concrete materials on the tendency of deceleration was clarified.

     

Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

A study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electro-mechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electro-mechanical coupling of the material.     

A moving frame of reference algorithm for fluid/structure interaction of rotating and translating bodies

A mathematical and numerical formulation is derived for fluid/structure interaction problems involving arbitrary geometries relevant to the simulation of bridge deck instabilities due to cross winds. A translating and rotating moving frame of reference is attached to the body to utilize an efficient fixed mesh spectral/hp element solver. The formulation is validated against experiments with flow simulations of circular cylinders at Reynolds numbers of 100–400 undergoing free and forced motion in the transverse and in‐line directions. The well‐documented phenomena of vortex lock‐in is captured. The formulation is then applied a rectangular body at Re=250 under forced and free motion the latter of which demonstrates torsional galloping. Copyright © 2002 John Wiley & Sons, Ltd.     

Derivation of a new free energy for biological membranes

A new free energy for thin biomembranes depending on chemical composition, degree of order and membranal-bending deformations is derived in this paper. This is a result of constitutive and geometric assumptions at the three-dimensional level. The enforcement of a new symmetry group introduced in (Deseri et al., in preparation) and a 3D--2D dimension reduction procedure are among the ingredients of our methodology. Finally, the identification of the lower order term of the energy (i.e. the membranal contribution) on the basis of a bottom-up approach is performed; this relies upon standard statistical mechanics calculations. The main result is an expression of the biomembrane free energy density, whose local and non-local counterparts are weighted by different powers of the bilayer thickness. The resulting energy exhibits three striking aspects:

Design of a quad-stable piezoelectric energy harvester capable of programming the coordinates of equilibrium points

In this study, a novel quad-stable energy harvester (QEH) is developed, in which its coordinates of equilibrium points can be user-defined like programming. This programmable feature distinguishes the proposed QEH from all reported magnet-type or buckling-type vibration energy harvesters. It has the advantage that it is easy to develop a high-performance QEH by appropriately programming these coordinate points and customizing a personalized QEH for different vibration environments. The dynamic model is established by the Ritz method and the Lagrange equation. The analytical steady periodic response is obtained by the average method. When the excitation acceleration is 2 m/s², the peak power is 575 μW at 8.5 Hz. Also, the influence of the coordinate arrangement of the equilibrium points on the energy harvesting performance is studied. A formula that can quickly determine the equilibrium point coordinates is given, and the QEH designed according to this formula has superior performance. At last, the performance of the designed QEH is compared with other reported vibration energy harvesters. It shows that the QEH has a high average output power (287 μW), high normalized power density (59.8 μW/cm³/g²), and wide operating frequency range (8.4 Hz) among these harvesters.

     

Extending the bounds of ‘steady’ RANS closures: Toward an instability-sensitive Reynolds stress model

The incapability of the conventional Unsteady RANS (Reynolds–Averaged Navier Stokes) models to adequately capture turbulence unsteadiness presents the prime motivation of the present work, which focuses on formulating an instability-sensitive, eddy-resolving turbulence model on the Second-Moment Closure level. The model scheme adopted, functioning as a ‘sub-scale’ model in the Unsteady RANS framework, represents a differential near-wall Reynolds stress model formulated in conjunction with the scale-supplying equation governing the homogeneous part of the inverse turbulent time scale ω_h (ω_h = ɛ_h/k). The latter equation was straightforwardly obtained from the model equation describing the dynamics of the homogeneous part of the total viscous dissipation rate ɛ, defined as ɛ_h = ɛ − 0.5ν∂²k/(∂x_j∂x_j) (Jakirlic and Hanjalic, 2002), by applying the derivation rules to the expression for ω_h. The model capability to account for vortex length and time scales variability was enabled through an additional term in the corresponding length-scale determining equation, providing a selective enhancement of its production, pertinent particularly to the highly unsteady separated shear layer region, modeled in terms of the von Karman length scale (comprising the second derivative of the velocity field) in line with the SAS (Scale-Adaptive Simulation) proposal (Menter and Egorov, 2010). The present model formulation, termed as SRANS model (Sensitized RANS), does not comprise any parameter depending explicitly on grid spacing. The predictive capabilities of the newly proposed length-scale determining model equation, solved in conjunction with Jakirlic and Hanjalic’s (2002) Reynolds stress model equation, are presently demonstrated by computing the flow configurations of increasing complexity featured by boundary layer separation from sharp-edged and continuous curved surfaces: backward-facing step flow, flow over a wall-mounted fence, flow over smoothly contoured periodically arranged hills and flow in a 3-D diffuser. The model performances are also assessed in capturing the natural decay of the homogeneous isotropic turbulence and the near-wall Reynolds stress anisotropy in a plane channel. In most cases considered the fluctuating velocity field was obtained starting from steady RANS results.