Normal Coefficient Research Articles

Extremely fast vortex dynamics in Bi2Sr2Ca2Cu3O10+δ crystalline nanostrip

The maximum velocity of a mobile vortex in movement is generally limited by the phenomenon of flux-flow instability (FFI), which necessitates weak vortex pinning and fast heat removal from non-equilibrium electrons. We here demonstrate exfoliations and nano-fabrications of Bi2Sr2Ca2Cu3O10+δ crystalline nanostrips, which possess a rather weak pinning volume of vortices, relatively low resistivity, and large normal electron diffusion coefficient. The deduced vortex velocity in Bi2Sr2Ca2Cu3O10+δ crystalline nanostrips can be up to 300 km/s near the superconducting transition temperature, well above the speed of sound. The observed vortex velocity is an order of magnitude faster than that of conventional superconducting systems, representing a perfect platform for exploration of ultra-fast vortex matter and a good candidate for fabrications of superconducting nanowire single photon detectors or superconducting THz modulator.

Analytical bifurcation and strong resonances of a discrete Bazykin–Berezovskaya predator–prey model with Allee effect

This paper investigates multiple bifurcations analyses and strong resonances of the Bazykin–Berezovskaya predator–prey model in depth using analytical and numerical bifurcation analysis. The stability conditions of fixed points, codim-1 and codim-2 bifurcations to include multiple and generic bifurcations are studied. This model exhibits transcritical, flip, Neimark–Sacker, and [Formula: see text], [Formula: see text], [Formula: see text] strong resonances. The normal form coefficients and their scenarios for each bifurcation are examined by using the normal form theorem and bifurcation theory. For each bifurcation, various types of critical states are calculated, such as potential transformations between the one-parameter bifurcation point and different bifurcation points obtained from the two-parameter bifurcation point. To validate our analytical findings, the bifurcation curves of fixed points are determined by using MatcontM.

Acoustic transmission characteristics based on coiled-up space metamaterials

Coiled-up metamaterials with solid plate (SC) and with micro-perforated plate (MPC) are proposed for broadband low-frequency acoustic insulation and absorption. Firstly, the sound transmission theory of the double-layer plate and the impendence of the micro-perforated plate coupled with the coiled-up channel are introduced to obtain the dependence of structural parameters on the acoustic characteristics. Then, the acoustic performances of SC and MPC are investigated numerically and verified by experiments, and the effects of geometry parameters are analysed to predict the acoustic performance of SC and MPC. The minimum sound transmission loss (STL) of SC with a thickness of less than 2 cm is higher than 20 dB and the average STL reaches 45 dB at [0, 1600] Hz. The multi-order resonances of coiled-up space induce STL valleys but provide 10 dB improvement at valleys compared with double-layer plates. The MPC achieves narrow absorption at 422 Hz and 1232 Hz, which are induced by the resonances of coiled-up channels and 99.99 % of total energy dissipation is viscous dissipation mainly occurring in MPP. Coiled-up space with embedded porous materials (PTM) achieves above 0.9 absorption coefficient at [700, 1600] Hz. The optimized MPTMs, which consists of three parallel MPCs guided by the genetic algorithm (GA) and a single PTM unit, can reach a normal incident average absorption coefficient of 0.80 at [342–2000] Hz and a random incident absorption coefficient above 0.5 at [352–1862] Hz.

Verification, calibration, and validation of stall delay models using NREL phase VI and MEXICO data

An accurate estimation of rotational effects is critical during the preliminary design of wind turbines. For this purpose, different stall delay models were developed based on the centrifugal pumping mechanism. However, their generality is not yet thoroughly evaluated. In this work, we investigated the causal relationship between the radial flow, the pressure reduction, and forces augmentation. Three stall delay models, which represent different solutions of the centrifugal pumping mechanism, were verified and modified to accurately predict the radial flow, the pressure coefficient, and normal and tangential force coefficients. Then, the three modified stall delay models were calibrated using radial flow data available from the literature. Finally, they were validated against the experimental data of the NREL phase VI and MEXICO rotors. The results showed that the centrifugal pumping produces a small chordwise pressure gradient in the separated boundary layer, which produces a small augmentation in the normal and tangential force coefficients. In contrast, the measured pressure coefficient and the normal and tangential force coefficients showed a large augmentation compared to the three modified stall delay models. Consequently, the lack of generality of current stall delay models is mainly due to the centrifugal pumping assumption. Furthermore, the verification and calibration of these stall delay models allowed us to isolate large errors in the model's output due to the model's assumptions. Thus, the importance of a rigorous verification and calibration before performing the validation.

Impact of complex flow structures on the turbine blade tip region mixing

Mixing of the turbine blade tip leakage and mainstream flows causes considerable aerodynamic loss. Its understanding is crucial to raise a consequential improvement of the turbine performance. In the present paper, a typical high pressure turbine rotor flow is simulated by detached eddy simulation. The complex mixing in the blade tip region is assessed by the dilution index algorithm in the streamwise direction. Influences of typical parameters on mixing are consecutively identified and analyzed. Relating the influences to flow structures, the mixing mechanism is obtained. It is revealed that the normal effective diffusion coefficient is key in mixing and is correlated with the unsteady tip leakage flow stick vortices. The latter induced by the Kelvin–Helmholtz instability can significantly enhance the local mass and energy transfer and hence diffusion. As a result, mixing is strengthened. Furthermore, the tip region is knowingly divided into the juxtaposing near and far fields. The former contains the tip leakage vortex, leakage jet, mainstream flow, and two entrainment zones. Meanwhile, the latter contains the leakage jet, mainstream flow, and entrainment zone. It was found that the entrainment zone is mixed to a high-degree, whereas the leakage jet is barely mixed.

Rod-climbing rheometry revisited.

The rod-climbing or "Weissenberg" effect in which the free surface of a complex fluid climbs a thin rotating rod is a popular and convincing experiment demonstrating the existence of elasticity in polymeric fluids. The interface shape and steady-state climbing height depend on the rotation rate, fluid elasticity (through the presence of normal stresses), surface tension, and inertia. By solving the equations of motion in the low rotation rate limit for a second-order fluid, a mathematical relationship between the interface deflection and the fluid material functions, specifically the first and second normal stress differences, emerges. This relationship has been used in the past to measure the climbing constant, a combination of the first (Ψ1,0) and second (Ψ2,0) normal stress difference coefficients from experimental observations of rod-climbing in the low shear rate limit. However, a quantitative reconciliation of such observations with the capabilities of modern-day torsional rheometers is lacking. To this end, we combine rod-climbing experiments with both small amplitude oscillatory shear (SAOS) flow measurements and steady shear measurements of the first normal stress difference from commercial rheometers to quantify the values of both Ψ1,0 and Ψ2,0 for a series of polymer solutions. Furthermore, by retaining the oft-neglected inertial terms, we show that the "climbing constant"  = 0.5Ψ1,0 + 2Ψ2,0 can be measured even when the fluids, in fact, experience rod descending. A climbing condition derived by considering the competition between elasticity and inertial effects accurately predicts whether a fluid will undergo rod-climbing or rod-descending. Our results suggest a more general description, "rotating rod rheometry" instead of "rod-climbing rheometry", to be more apt and less restrictive. The analysis and observations presented in this study establish rotating rod rheometry combined with SAOS measurements as a prime candidate for measuring normal stress differences in complex fluids at low shear rates that are often below commercial rheometers' sensitivity limits.

Estimation of the Acoustic Properties of the Random Packing Structures of Granular Materials: Estimation of the Sound Absorption Coefficient Based on Micro-CT Scan Data

In this study, the sound absorption properties of randomly packed granular materials were estimated. Generally, it is difficult to construct a general mathematical model for the arrangement of randomly packed granular materials. Therefore, in this study, an attempt was made to estimate the sound absorption coefficient using a theoretical analysis by introducing data from computed tomography (CT) scans, as the tomographic images of CT scans correspond to the slicing and elemental division of packing structures. In the theoretical analysis, the propagation constants and characteristic impedances in the voids were obtained by approximating each tomographic image as a void between two parallel planes. The derived propagation constants and characteristic impedances were then treated as a one-dimensional transfer matrix in the propagation of sound waves, and the transfer matrix method was used to calculate the normal incident sound absorption coefficient. The theoretical value of the sound absorption coefficient was derived using the effective density to which the measured tortuosity was applied. As a result, for the theoretical values considering the tortuosity, in many cases, the theoretical values were close to the measured values. For the theoretical values, when both the surface area and tortuosity were considered, the peak sound absorption frequency moved to a lower frequency and was in general agreement with the measured values.

A comparison of pendulum experiments and discrete‐element simulations of oblique collisions of wet spheres

AbstractOblique collisions of two spherical particles coated with a thin layer of viscous liquid are considered. Experimental measurements are performed using particle tracking velocimetry and the results are compared to viscous force and capillary force models via numerical simulation using the discrete‐element method. Comprehensive experimental data for collisions with an impact angle between 0° and 60° are presented to ensure future models can be rigorously validated. Collisions are characterized by the normal Stokes' number (a dimensionless ratio of normal inertial forces to normal viscous forces), and the normal coefficient of restitution (a dimensionless ratio of postcollisional normal velocity to precollisional normal velocity). Good agreement was found between the models and the experiments at high Stokes' number, where the models are dominated by the normal components. As the tangential forces become more significant (i.e., at low to medium Stokes' number, and high collision angle), agreement between the simulations and experiments is poorer. Furthermore, the models predict a decreasing rotational velocity with increasing Stokes' number past some critical Stokes' number. A coefficient of friction term was implemented and found to improve agreement for the rotational velocity postcollision.

Complex dynamics of a discrete‐time seasonally forced SIR epidemic model

In this paper, a discrete‐time seasonally forced SIR epidemic model with a nonstandard discretization scheme is investigated for different types of bifurcations. Although many researchers have already suggested numerically that this model can exhibit chaotic dynamics, not much focus is given to the bifurcation theory of the model. We prove analytically and numerically the existence of different types of bifurcations in the model. First, one and two parameters bifurcations of this model are investigated by computing their critical normal form coefficients. Second, the flip, Neimark–Sacker, and strong resonance bifurcations are detected for this model. The critical coefficients identify the scenario associated with each bifurcation. The complete complex dynamical behavior of the model is investigated. The model is discretized by a novel technique, namely a nonstandard finite difference discretization scheme (NSFD). Some graphical representations of the model are presented to verify the obtained results.

Normal contact stiffness model for fractal surfaces considering scale dependence and friction behavior

The normal contact stiffness on rough surfaces has a significant impact on the interfacial dynamic characteristics of mechanical joints. Based on the fractal geometry theory, this work improves the contact stiffness modeling by considering the complete contact characteristics of multiple asperities and frictional factor. First, to include the property that the critical contact areas of asperities are scale-dependent, the model for the contact stiffness is formed on each scale and the relationship between total stiffness and load on rough surfaces is obtained by the summation of all length scale asperities. Second, friction factor is taken into account in the revised normal contact stiffness model, where a contact friction coefficient is introduced into the equation to incorporate the effects of friction force. Moreover, the influences of fractal dimension D and fractal roughness G on normal contact stiffness and friction coefficient are investigated. Through the comparison of numerical and experimental results, the revised model is shown to be more reasonable and presents higher consistency of the stiffness versus load curve than the original model. It is therefore concluded that a complete and more accurate model for normal contact stiffness is proposed in this work with precise modeling of scale-dependent contact characteristics and friction behavior taken into account, which is critical for exact estimation of rigidity of contact surfaces in industrial applications.

Dynamics and bifurcations of a discrete‐time Lotka–Volterra model using nonstandard finite difference discretization method

A newly disclosed nonstandard finite difference method has been used to discretize a Lotka–Volterra model to investigate the critical normal form coefficients of bifurcations for both one‐parameter and two‐parameter bifurcations. The discrete‐time prey–predator model exhibits a variety of local bifurcations such as period‐doubling, Neimark–Sacker, and strong resonances. Critical normal form coefficients are determined to reveal dynamical scenarios corresponding to each bifurcation point. We also investigate the complex dynamics of the model numerically by Matlab package using MatcotM based on numerical continuation technique. The numerical continuation validates the theoretical analysis, which is discussed from an ecological perspective.

Dynamical Behaviors of an SIR Epidemic Model with Discrete Time

Analytically and numerically, the study examines the stability and local bifurcations of a discrete-time SIR epidemic model. For this model, a number of bifurcations are studied, including the transcritical, flip bifurcations, Neimark–Sacker bifurcations, and strong resonances. These bifurcations are checked, and their non-degeneracy conditions are determined by using the normal form technique (computing of critical normal form coefficients). We use the MATLAB toolbox MatcontM, which is based on the numerical continuation method, to confirm the obtained analytical results and specify more complex behaviors of the model. Numerical simulation is employed to present a closed invariant curve emerging from a Neimark–Sacker point and its breaking down to several closed invariant curves and eventually giving rise to a chaotic strange attractor by increasing the bifurcation parameter.

Study of the process of metal droplets with high surface tension impinging on wall

The behavior of aluminum droplets impacting a wall critically affects the operation of solid rocket motors. In the present study, the flow and rebound of aluminum droplets with a high surface tension are studied experimentally and numerically. In addition, the impact of aluminum droplets at different inclined angles is monitored experimentally. When the droplet is about to rebound away from the wall, it is stretched to its maximum length. An empirical correlation formula is proposed to predict the maximum length when a droplet is about to bounce off a flat plane. The velocity and pressure distributions of a droplet flowing over a flat plane and an inclined plane are compared by using the volume of fluid method. Furthermore, the restitution coefficient of the droplet is discussed in detail. When normal Weber number Wen ranges from 0 to 20, normal restitution coefficient en ranges from 0.3 to 0.6. When tangential Weber number Wet <10, tangential restitution coefficient et is subject to great uncertainty. When 10 < Wet < 80, et is maintained at 0.75. The formulas for the total restitution coefficient, normal restitution coefficient, and tangential restitution coefficient of the aluminum droplets are also presented. Based on the principle of conservation of energy, we calculate the remaining energy of the aluminum droplets impinging on a wall and provide the relationship between the restitution coefficient and the dissipated energy. The results elucidate the mechanisms at work when aluminum droplets collide with a wall.

Mean wake and aerodynamic forces for surface-mounted finite-height square prisms of very small aspect ratio

The mean flow field, aerodynamic forces, bending moment and Strouhal number (St) were investigated for isolated surface-mounted finite-height square prisms of very small aspect ratio (AR). The Reynolds number was Re =7.5×104 for the velocity measurements and 9×104 for the force, bending moment and St measurements. Prisms with AR = 0.5, 0.7 and 1 were considered, under two different boundary layer thicknesses of δ/D=0.7–0.8 (thin) and δ/D=1.3 (thick). For both boundary layers, the mean drag force coefficient showed a sharper increase with AR compared with taller prisms, and the mean normal force coefficient increased smoothly, with a lower magnitude than pressure-based normal force coefficients. An approximately constant point of action of the drag force was found for AR < 1. While the thick boundary layer caused the spectral peaks to weaken and St to decrease, some periodicity was still found for all AR. These features were connected to the changes in the mean wake of the prisms with AR and δ/D. A smaller AR and larger δ/D had similar effects, causing the wake to shorten, the probability and type of reattachment of the flow on the free end to change, and the mean wake structure to transition from a streamwise wake vorticity pattern to an inner vorticity pattern. The prism with AR = 1 showed a dipole wake structure similar to that of taller prisms, while the unique wake topology of prisms with AR < 1 was found to be responsible for the different force and St trends identified in this range of AR.

Discussion on dynamic characteristics of long journal bearings considering surface roughness

The hydrodynamic bearing is the key part of many rotating machines, and dynamic characteristics of the bearing would affect the operation performance of machines directly. Thus, this study focused on dynamic characteristics of long journal bearings and tried to illustrate the influence of surface roughness on dynamic performances of long bearings. Applying Christensen stochastic model and long bearing approximation, the modified Reynolds equation was established. To solve the modified Reynolds equation, the numerical integration method was applied. It is found that the surface roughness would significantly weaken the stability threshold speed, normal stiffness coefficients ([Formula: see text], [Formula: see text]), and crossed dampness coefficients ([Formula: see text] and [Formula: see text]) for the long bearing with a large eccentricity ratio. In summary, the influences of surface roughness cannot be ignored during discussing dynamic characteristics of long journal bearings.

Computational Methods for Nonlinear Analysis of Hopf Bifurcations in Power System Models

Hopf bifurcations can occur in power systems when a system mode experiences low damping because of changes in system operating conditions and they can lead to the emergence of limit cycles and oscillations. There are two types of Hopf bifurcations, namely, supercritical and subcritical, and they are determined by the sign of a cubic normal form coefficient. This paper discusses the two types of Hopf phenomena in test power system models where both types could be seen under changes in system and control parameters. The paper proposes an efficient computational method for carrying out the higher-order center manifold and normal form calculations for a general power system model and discusses the implications of the normal form coefficients for power system dynamics. Distinguishing between subcritical versus supercritical is important since they lead to very different types of oscillatory phenomena, divergence versus sustained oscillations, respectively.

Effect of particle regularity on the shear response of geogrid-granular material interface under cyclic normal loading

The investigation of shear behaviour on geogrid-granular material interface under cyclic normal loading (CNL) is significant in seismic design of reinforcement structure. The cyclic shear mechanism about the effect of particle overall regularity on reinforced soil interface was analysed using dynamic direct shear apparatus. Five mixtures of round spherical media and crushed limestone with different percentages were selected to obtain various particle overall regularity. By comparing the shear behaviour under various overall regularity, the interface shear stress and vertical displacement under the CNL condition were smaller than those under the static loading condition. The decrement in interface shear stress of lower overall regularity was smaller than that of higher overall regularity. The interface peak shear stress, final vertical displacement decreased with the increase of cyclic normal loading amplitude and overall regularity. The effect of initial normal loading on ratio of strength reduction and energy consumption was reverse to that of the overall regularity. Based on the constant relative phase shift of the peak normal stress and friction coefficient for various overall regularity, the prediction formula was proposed. The test results improve the understanding on how normal loading perturbations and particle overall regularity affect the shear behaviour of reinforced soil interface.

Mathematical Models and Experiments on the Acoustic Properties of Granular Packing Structures (Measurement of Tortuosity in Hexagonal Close-Packed and Face-Centered Cubic Lattices).

In this study, the sound absorption characteristics of hexagonal close-packed and face-centered cubic lattices were estimated by theoretical analysis. Propagation constants and characteristic impedances were obtained by dividing each structure into elements perpendicular to the incident direction of sound waves and by approximating each element to a clearance between two parallel planes. Consequently, the propagation constant and the characteristic impedance were treated as a one-dimensional transfer matrix in the propagation of sound waves, and the normal incident sound absorption coefficient was calculated by the transfer matrix method. The theoretical value of the sound absorption coefficient was derived by using the effective density applied to the measured tortuosity. As a result, the theoretical value was becoming closer to the measured value. Therefore, the measured tortuosity is reasonable.

Odd viscosity in chiral passive suspensions

Prior studies have revealed that nonzero odd viscosity is an essential property for chiral active fluids. Here we report that such an odd viscosity also exists in suspensions of non-active or non-externally-driven but chirally-shaped particles. Computational simulations are carried out for monolayers of dense ratchets in simple shear and planar extensional flows. The contact between two ratchets can be either frictionless or infinitely-frictional, depending on their teeth and sliding directions at the contact point. Our results show that the ratchet suspension has the intermediate shear/extensional viscosity as compared with the suspensions of smooth and gear-like particles. Meanwhile, the ratchet suspensions show nonzero even and odd components of the first normal stress coefficient regarding the flow rate, which indicates the mixed feature of conventional complex fluids and chiral viscous fluids.

Drag coefficient estimation in FSI for PWR fuel assembly bowing

Assembly bowing in a PWR core can be a serious problem for managing the power during normal operation or for periodical maintenance. One of the causes of this phenomenon is the transverse flow in the core, generated by the non-uniformity of the axial flow. Modelling the mechanical behaviour of a PWR core is made difficult by the complex geometry and the numerous friction points that lead to non-linearities. A simple but efficient way to deal with these issues is the porous medium model proposed by Ricciardi et al. (2009). In this model, the equations used at the fluid–structure interface require empirical parameters such as the added mass, or axial and normal drag coefficients. Using a new experimental setup at CEA, Eudore, which hosts 3 half-scale fuel assemblies in a line, the forces acting on the assembly by a non-uniform flow profile were measured. An analytical model to retrieve the normal drag coefficient was then proposed. This coefficient is then used in FSCORE, a numerical software based on the porous medium approach. The experimental and numerical results are presented and show good agreement.