Infinite Aspect Ratio Research Articles

Recycle waste PET yarn on site by feeding waste yarn as grinded powder to improve product quality, increase energy efficiency and reduce environmental impact

A technical approach was proposed to recycle waste PET yarn on site with the aim of building green manufacturing plant with no waste accumulation. In the recycling process, the waste PET yarn with almost infinite aspect ratio was first treated with custom-designed grinder prior to recycling, which breaks the yarn into small pieces and produce powder-like final product (waste yarn/fiber powder, WYP/WFP). Then it could be mixed with PTA and EG to form slurry and fed into manufacturing unit using well-established method rather than be fed as melt by screw-extruder that is known for its high energy intensity. Furthermore, the wetting of WYP by EG during slurry formation facilitates the de-oxygenation process and is beneficial to improve the quality of product, which produces higher quality products with lower cost compared to conventional methods. PET containing 20 wt.% WYP addition using the proposed technical approach could give best balance between performance and profit margin. The properties of the produced PET products (20% WYP addition) were found similar to that of virgin counterparts and meet the specs for various commercial application. With the help of energy benign treatment and feeding processes, the energy intensity and CO2 emission of this method compared to conventional method were reduced by 78.96% and 62.02%, respectively. The method proposed a novel energy efficient and cost-effective approach to reliably recycle waste PET to high quality PET products on site. It partially solves the problems that the industry currently encountered, such as high recycle cost, relatively low product quality, high energy intensity and low economic benefit. It moves one step forward to the greening of the manufacturing process and may help on the sustainable development of the PET industry.

INTERACTIONS BETWEEN TWO FLETTNER ROTORS USED FOR WIND SHIP ASSISTED PROPULSION

Wind tunnel tests are carried out at the Aerodynamics Laboratory of the Ecole Nationale des Arts et Métiers (ENSAM) in Paris on 50 mm and 130 mm diameter rotating circular cylinder in infinite aspect ratio or finite aspect ratio of 3 to 6, with or without rotating endplates. Aerodynamic forces are measured by a 5-components balance and by integrating pressures over three sections along the span of the rotating cylinder. The tests carried out at Reynolds numbers between 13,500 and 70,000 are significant and make it possible to dispense tests at high flow speeds. The results, based on pressure measurements, indicate that the rotation of the cylinder drives the fluid in a spiral motion along the span, winding the flow, accompanied by a very strong increase in the drag coefficient between the middle and the top of the cylinder. The interaction between two rotating cylinders, spaced out by 6 diameters, decreases the ratio CL / CD of the thruster reducing its propulsive performance at close wind angles (30° <β <70°).

Nonlinear emergent macroscale PDEs, with error bound, for nonlinear microscale systems

Many multiscale physical scenarios have a spatial domain which is large in some dimensions but relatively thin in other dimensions. These scenarios includes homogenization problems where microscale heterogeneity is effectively a ‘thin dimension’. In such scenarios, slowly varying, pattern forming, emergent structures typically dominate the large dimensions. Common modelling approximations of the emergent dynamics usually rely on self-consistency arguments or on a nonphysical mathematical limit of an infinite aspect ratio of the large and thin dimensions. Instead, here we extend to nonlinear dynamics a new modelling approach which analyses the dynamics at each cross-section of the domain via a multivariate Taylor series (Roberts and Bunder in IMA J Appl Math 82(5):971–1012, 2017. https://doi.org/10.1093/imamat/hxx021). Centre manifold theory extends the analysis at individual cross-sections to a rigorous global model of the system’s emergent dynamics in the large but finite domain. A new remainder term quantifies the error of the nonlinear modelling and is expressed in terms of the interaction between cross-sections and the fast and slow dynamics. We illustrate the rigorous approach by deriving the large-scale nonlinear dynamics of a thin liquid film on a rotating substrate. The approach developed here empowers new mathematical and physical insight and new computational simulations of previously intractable nonlinear multiscale problems.

Recirculation regions in wakes with base bleed

The appearance of detached recirculation regions in wakes with base bleed determines the aerodynamic properties of many natural organisms and technological applications. In this work we introduce an analytical model which captures certain key dimensions of the recirculation region in the wake of porous plates of infinite aspect ratio, along with the porosity range \ks{over which} it exists, when vortex shedding is absent or suppressed. The model is used to interpret why the recirculation region (i) emerges, (ii) migrates away from the body with increasing base bleed, (iii) disappears at a critical bleed and (iv) is partially insensitive to variations in the Reynolds number. The model predictions show considerable agreement with data from laboratory experiments and numerical simulations. exists. The predictions show considerable agreement with data from laboratory experiments and numerical simulations.

Dynamics of inverted flags: Experiments and comparison with theory

The study of the dynamics of cantilevered thin flexible plates in reverse axial flow – also known as inverted flags – has become of significant interest, partly due to their energy harvesting potential. This paper presents fresh experimental results, aiming to enhance our understanding of the dynamics of inverted flags, particularly concerning stability and global dynamics sensitivity to various system parameters, such as the aspect ratio (i.e. height-to-length ratio) and flag material. This is achieved through testing flags of various dimensions, made from different materials. The dynamics of the system is presented in the form of bifurcation diagrams in which the flag tip angle is shown as a function of the dimensionless flow velocity. The frequency content of oscillatory motions is presented in the form of spectrograms. Also, time-histories, phase-plane portraits, as well as power spectral density and probability density function plots are presented for different flow regimes. Interesting dynamical features, such as small- and large-amplitude flapping, static divergence, large-amplitude buckling, and chaotic motions, have been observed experimentally, some for the first time. It is shown that for flags of very low aspect ratio the undeflected static equilibrium is stable prior to a subcritical pitchfork bifurcation. For flags of large aspect ratio, on the other hand, the undeflected static equilibrium becomes unstable via a supercritical pitchfork bifurcation leading to static divergence (buckling) at a sufficiently high flow velocity; at higher flow velocities, past the pitchfork bifurcation, a supercritical Hopf bifurcation materializes leading to flapping motion around the deflected static equilibrium; at even higher flow velocities, flapping motion becomes symmetric around the undeflected static equilibrium. Interestingly, it is found that heavy flags may exhibit large-amplitude flapping right after the initial static equilibrium, provided that they are subjected to a sufficiently large disturbance. In addition to experiments, nonlinear analytical models for the two asymptotic cases of zero and infinite aspect ratios are outlined, the results of which are used for comparison with the experimental results. Theory and experiments are found to be in reasonably good agreement.

Combined effects of lateral heating and thermo-diffusion on convection bifurcations in a porous enclosure subject to vertical thermal and solutal gradients

The present study deals with double diffusive convection within a horizontal well packed porous layer of finite aspect ratio where thermo-diffusion has a predominant effect on the convective flow stability. The porous layer is subject to vertical thermal and solutal gradients and a lateral heating flux. The investigation is focused on a special situation where the lateral heat flux is balanced by the horizontally induced Soret mass flux, which allows a possible equilibrium state (motionless state) that becomes unstable under certain conditions. The aim of the present investigation is to study the flow stability and to develop some universal correlations for the flow intensity and heat transfer, which is valid for any aspect ratio independently of the governing parameters. The correlations were constructed from the parallel flow assumption valid for an infinite aspect ratio enclosure but can be used for a finite aspect ratio. To this end, numerical simulations are performed to support the investigation and to calibrate the correlations. By using a linear stability analysis, based on a finite element method, the onset conditions for the stationary convection and over stabilities are investigated with the focus on the effect of the lateral heating magnitude on the stability thresholds. In general, the thermo-diffusion problem balanced by a lateral heating effect is found to exhibit a rich variety of different bifurcation phenomena and complex unsteady flow patterns near criticality.

Shaping effects on scrape-off layer plasma turbulence: A rigorous validation of three-dimensional simulations against TCV measurements

The effect of plasma shaping on scrape-off layer (SOL) plasma turbulence is investigated through a rigorous validation exercise. Two- and three-dimensional simulations of the SOL plasma dynamics in three TCV limited discharges are carried out with the GBS code. These discharges realize an almost circular magnetic equilibrium, an elongated equilibrium, and an elongated equilibrium with negative triangularity. For the three plasma discharges, three simulations are performed, considering (i) a three-dimensional model with an explicit dependence on elongation, triangularity, and the inverse aspect ratio; (ii) a circular three-dimensional model in the infinite aspect ratio limit; and (iii) a two-dimensional model, which assumes a circular magnetic equilibrium in the infinite aspect ratio limit, cold ions, and interchange driven turbulence in the sheath limited regime. Ten validation observables common to simulations and experimental measurements from a reciprocating probe located at the TCV outer midplane are identified, and the agreement between experimental and numerical results relative to each observable is evaluated. The composite metric introduced by Ricci et al. [Phys. Plasmas 18, 032109 (2011)] is then used to assess the overall agreement between simulations and experimental measurements. It is found that the shaping model implemented in GBS improves the description of SOL plasma turbulence, taking into account the impact of elongation and triangularity.

Численные исследования особенностей обтекания крыла в режиме бафтинга

The numerical method validation using the Reynolds equations and calculations were made for the case of infinite aspect ratio rectangular wing, which is streamed by a transonic unbounded air flow in buffet regime. It is shown, that instead of 2D flow, a periodical flow along the lateral direction is realized. Furthermore, the oscillations in time along the longitudinal direction (buffet) take place. The presence of the side wind tunnel walls deforms this periodical structure and changes the buffet frequency. Calculations of the wing-body combination flow show that the oscillations take place inside the restricted wing area both along longitudinal and lateral directions.

End Effects on H2-Forced Convection in Rectangular Ducts of Large Aspect Ratios

The H2-forced convection in a rectangular duct of large aspect ratio (>10) is studied. It is found that the short ends have non-negligible effects on the Nusselt number and the temperature distribution. Even at infinite aspect ratios, the Nusselt number depends on the net heat addition from the ends, but not how they are distributed.

Analytical Solution of Water Vapor Condensation in Flow Channel of Battery Pack

The analytical solutions for condensation (and evaporation) rates of laminar humid air flow in the channels of a battery pack at both entrance and downstream regions are obtained/modeled. The effects of the entrance fluid velocity profile and the aspect ratio of the flow channel are taken into consideration. Initially, an analytical solution for laminar humid air flows' condensation at the flow channel with infinite aspect ratio and fully developed flow profile at the entrance is obtained. The solution is in good agreement with the simulation result obtained from a correlated fluent condensation model. After performing simulations of water vapor condensation and evaporation in the flow channel for different aspect ratios and entrance velocity profiles, the analytical solutions of condensation and evaporation rate of water vapor are presented in analytic forms by adding appropriate coefficients/correction factors to the solution for the flow in the channel with infinite aspect ratio. The resulting model accurately captures the effects of the entrance velocity profile and aspect ratio.

Numerical investigation of the effect of different working fluids on the pattern formation in a narrow rotating annulus

Fluid evolving in an annular gap between two coaxial cylinders, well known as Taylor–Couette flow, is one of the fundamental problems in fluid mechanics for the study of instabilities and the transition to turbulence. This flow system is typically a closed environment, where the working fluid is confined axially by end-plates and radially between the cylinders. In this work, we investigate, via CFD simulation, the influence of the working fluids confined inside an infinite aspect ratio Taylor–Couette system on the onset of cellular pattern. The inner cylinder rotates freely about a vertical axis through its centre, while the outer one, the upper and bottom end-caps are held at rest. The basic system is characterized by a height H = 150 mm, an annular gap d = 5 mm, a ratio of the inner to the outer cylinders radii η = 0.909, an aspect ratio corresponding to the cylinders height reported to the gap length Γ = 30 and a ratio of the gap to the radius of the inner cylinder δ = 0.1. The flow behaviour and the time-independent formation of axisymmetric vortices are investigated under steady-state condition. The main goal of this work is to show how the change in cellular pattern operates when changing the working fluid by simulating and comparing four different liquids, namely hydrogen, helium, lithium and water. Particular attention is given to the onset of Taylor vortices in the vicinity of the threshold of transition, i.e. from the laminar Couette flow to the occurrence of Taylor vortex flow. In addition, the flow patterns are presented in terms of distributions of wall shear stress, skin friction coefficient, streamlines and velocity components. The computed results show that the critical Taylor number for the different liquids is the same, Tac1 = 42.4. Interestingly, lithium and hydrogen exhibit quite different behaviours than other liquids. The shape and wavelength of Ekman cells and the Taylor vortices for lithium and hydrogen show significant changes compared to water and helium.

Anisotropy in electrical conductivity of films of aligned intersecting conducting rods.

Numerical simulations by means of the Monte Carlo method have been performed to study the electrical properties of a two-dimensional composite filled with rodlike particles. The main goal was to study the effect of the alignment of such rods on the anisotropy of its electrical conductivity. A continuous model was used. In this model, the rods have zero-width (i.e., infinite aspect ratio) and they may intersect each other. To involve both the low conductive host matrix and highly conductive fillers (rods) in the consideration, a discretization algorithm based on the use of a supporting mesh was applied. The discretization is equivalent to the substitution of rods with the polyominoes. Once discretized, the Frank-Lobb algorithm was applied to evaluate the electrical conductivity. Our main findings are (i) the alignment of the rods essentially affects the electrical conductivity and its anisotropy, (ii) the discrete nature of computer simulations is crucial. For slightly disordered system, high electrical anisotropy was observed at small filler content, suggesting a method to enable the production of optically transparent and highly anisotropic conducting films.

Computational analysis of three blade vertical axis wind turbine

This paper discusses the performance of three blade vertical axis wind turbine. 2D computational flow analysis is carried out for different rotational speeds of the blades in a plane normal to wind turbine axis. It is implied that turbine blades have infinite aspect ratio. The selection is done based on the lift and drags generated by the various NACA series airfoil (NACA 0012, NACA 0015, NACA 0018, and NACA 0021) at a different angle of attacks, among them NACA 0015 airfoil is found to be most suitable one. A triangular meshed geometry is created and computational fluid dynamics (CFD) simulation is carried out. The computational analysis is performed at various speeds of VAWT blade rotation where the position of the airfoil is made with respect to the wind. Torques generated at different blade positions in a VAWT and the forces by the turbine over one full complete cycle were studied.

Subjamming transition in binary sphere mixtures.

We study the influence of particle-size asymmetry on structural evolution of randomly jammed binary sphere mixtures with varying large-sphere and small-sphere composition. Simulations of jammed packings are used to assess the transition from large-sphere dominant to small-sphere dominant mixtures. For weakly asymmetric particle sizes, packing properties evolve smoothly, but not monotonically, with increasing small-sphere composition, f. Our simulations reveal that at high values of ratio α of large- to small-sphere radii (α≥α_{c}≈5.75), evolution of structural properties, such as packing density, fraction of jammed spheres, and contact statistics with f, exhibit features that suggest a sharp transition, either through discontinuities in structural measures or their derivatives. We argue that this behavior is related to the singular, composition dependence of close-packing fraction predicted in infinite aspect ratio mixtures α→∞ by the Furnas model, but occurring for finite valued range of α above a critical value, α_{c}≈5.75. The existence of a sharp transition from small- to large-f values for α≥α_{c} can be attributed to the existence of a subjamming transition of small spheres within the interstices of jammed large spheres along the line of compositions f_{sub}(α). We argue that the critical value of finite-size asymmetry α_{c}≃5.75 is consistent with the geometric criterion for the transmission of small-sphere contacts between neighboring tetrahedrally close-packed interstices of large spheres, facilitating a cooperative subjamming transition of small spheres confined within the disjoint volumes.

Modulation of aerodynamic force on a 2D elliptic body via passive splitter pitching under high turbulence

The mean and fluctuating aerodynamic force on an elliptic body of infinite aspect ratio with hinged splitters were experimentally studied under high incoming turbulence for various angle of attack AoA of the body, Reynolds numbers and splitter length. High-resolution load cell was used to measure the mean and unsteady lift and drag forces of the body; whereas a hotwire anemometry was employed to characterize the incoming turbulence and get insight on the wake flow. Results show that the attached splitters reduce the lift and drag coefficients for AoA well beyond stall. Interestingly, the splitter length did not play a noticeable role on the mean aerodynamic force; this parameter just induced minor effects on the fluctuation counterpart. Such phenomenon appear to be inherently related to the background turbulence levels. Compared to the bare body, the force coefficients exhibit stronger dependence on Reynolds number due to the dynamics induced by the splitter pitching. In general, the force fluctuations are dominated by the natural frequency of the setup under the high turbulence. The joint distribution of the instantaneous lift and drag forces reveals that under sufficiently high AoA, the vortex shedding dominates the force fluctuations along the major axis of the body; whereas the splitters can efficiently dampen the vortex shedding and mitigate the overall force fluctuations.

Flow around a semicircular cylinder with passive flow control mechanisms

Wind tunnel experiments were performed to study the effect of passive flow control strategies on the wake and drag of a semicircular cylinder of infinite aspect ratio. High-resolution planar particle image velocimetry was used to obtain flow statistics around the semicircular cylinder at Reynolds number \(Re\approx 3.2\times 10^4\) based on the cylinder diameter. The control mechanisms under consideration include rigid flaps of various lengths placed at the edges of the structure and a small slot along the symmetry plane of the cylinder. Mean velocity fields reveal the distinctive effects of each passive mechanism on the flow, such as velocity recovery, size of the recirculation bubble and location of the reattachment point. The distributions of turbulence kinetic energy and kinematic shear stress show the modulation of each passive control mechanism on the wake, including the onset and location of the maximum turbulence levels. Instantaneous and mean fields of swirling strength further highlight the role of the passive mechanisms in the vortex dynamics. Drag coefficient for the various cases was estimated indirectly from the flow measurements using a momentum balance. This approach shows that long flaps and slot were able to reduce drag with respect to the base case. The rigid flaps with length coincident with the diameter of the cylinder offered the best performance with drag reduction of \(\sim\)25\(\%\).

A vortex model for forces and moments on low-aspect-ratio wings in side-slip with experimental validation.

This paper studies low-aspect-ratio ([Formula: see text]) rectangular wings at high incidence and in side-slip. The main objective is to incorporate the effects of high angle of attack and side-slip into a simplified vortex model for the forces and moments. Experiments are also performed and are used to validate assumptions made in the model. The model asymptotes to the potential flow result of classical aerodynamics for an infinite aspect ratio. The [Formula: see text] → 0 limit of a rectangular wing is considered with slender body theory, where the side-edge vortices merge into a vortex doublet. Hence, the velocity fields transition from being dominated by a spanwise vorticity monopole ([Formula: see text] ≫ 1) to a streamwise vorticity dipole ([Formula: see text] ∼ 1). We theoretically derive a spanwise loading distribution that is parabolic instead of elliptic, and this physically represents the additional circulation around the wing that is associated with reattached flow. This is a fundamental feature of wings with a broad-facing leading edge. The experimental measurements of the spanwise circulation closely approximate a parabolic distribution. The vortex model yields very agreeable comparison with direct measurement of the lift and drag, and the roll moment prediction is acceptable for [Formula: see text] ≤ 1 prior to the roll stall angle and up to side-slip angles of 20°.

Three-dimensional instabilities in the wake of a flapping wing at low Reynolds number

We present a stability analysis of a plunging and pitching wing of infinite aspect ratio at low Reynolds number. Four cases are considered by varying the mean pitch angle and the phase shift between pitching and plunging. Each case is studied by performing two dimensional DNS and Floquet stability analysis. The four cases considered display different wake structures resulting in different mean aerodynamic forces. Two cases produce thrust and lift, one case only thrust (with symmetric plunging and pitching) and the remaining case mainly lift (with the highest mean pitch angle). In addition, the latter case displays a period doubling phenomenon, and it is found to be linearly unstable for long wavelengths, with an instability mode that resembles that of mode A found in the wake of cylinders. Other cases, although being linearly stable, present a convective instability at smaller wavelengths. Finally, the unstable case has been studied with a fully 3D DNS to evaluate the effect of the three-dimensionality on the forces. The resulting flow structure is consistent with the linear stability analysis in the near wake. Further downstream nonlinearities lead to a fully 3D wake. Despite this, the aerodynamic forces on the 3D wing are very similar to those obtained in the 2D simulation.

Capillary-induced deformations of a thin elastic sheet.

We develop a three-dimensional model for capillary origami systems in which a rectangular plate has finite thickness, is allowed to stretch and undergoes small deflections. This latter constraint limits our description of the encapsulation process to its initial folding phase. We first simplify the resulting system of equations to two dimensions by assuming that the plate has infinite aspect ratio, which allows us to compare our approach to known two-dimensional capillary origami models for inextensible plates. Moreover, as this two-dimensional model is exactly solvable, we give an expression for its solution in terms of its parameters. We then turn to the full three-dimensional model in the limit of small drop volume and provide numerical simulations showing how the plate and the drop deform due to the effect of capillary forces.

Aspect ratio effects in turbulent duct flows studied through direct numerical simulation

Three-dimensional effects in turbulent duct flows, i.e., sidewall boundary layers and secondary motions, are studied by means of direct numerical simulation (DNS). The spectral element code Nek5000 is used to compute turbulent duct flows with aspect ratios 1–7 (at Reb, c = 2800, Reτ, c ≃ 180) and aspect ratio 1 (at Reb, c = 5600, Reτ, c ≃ 330), in streamwise-periodic boxes of length 25h. The total number of grid points ranges from 28 to 145 million, and the pressure gradient is adjusted iteratively in order to keep the same bulk Reynolds number in the centreplane with changing aspect ratio. Turbulence is initiated via a trip forcing active during the initial stages of the simulation, and the statistical convergence of the data is discussed both in terms of transient approach and averaging period. Spanwise variations in wall shear, mean-flow profiles, and turbulence statistics are analysed as a function of aspect ratio, and also compared with the spanwise-periodic channel (as idealisation of an infinite aspect ratio duct). The computations show good agreement with experimental measurements carried out in parallel at the Illinois Institute of Technology (IIT) in Chicago, and highlight the relevance of sidewall boundary layers and secondary vortices in the physics of the duct flow. The rich array of secondary vortices extending throughout the upper and lower walls of the duct, and their dependence on Reynolds number and aspect ratio, had not been reported in the literature before.