Equilateral Triangle Arrangement Research Articles

Vortex-induced vibrations of three rigidly coupled circular cylinders in an equilateral-triangular arrangement

A three-cylinder system in an equilateral-triangular arrangement is a common, basic structure in the engineering field, and the rigid connection of multiple cylinders has been applied in some practical projects. In this paper, three cylinders in an equilateral triangle arrangement for a spacing ratio of 4 at Reynolds number of 200 are studied by means of numerical simulation. The vibration modes are divided into single cylinder vibration, three freely vibrating vibration and three rigidly coupled vibration. The vortex-induced vibration characteristics and aerodynamic forces and fluid–structure-interaction mechanisms are analyzed. The results show that the vibration velocity regions and the amplitude of three freely vibrating cylinders in the transverse and streamwise directions are obviously larger than that of a single cylinder. The rigid connection measures can effectively suppress the vibration velocity region and amplitude. However, this suppression effect is no better than the single cylinder. In the lock-in region, the trajectories of three rigidly coupled cylinders are regular closed shapes. The Strouhal numbers of the three cylinders are synchronous in the natural frequency in the lock-in region. The wake vortices from the upstream cylinders affect the downstream cylinders, which depends on different case and reduced velocity. The complex aerodynamic interference and parallel vortices of the wake enhance the vibration of the structure in some cases.

Integrated Impacts of Building Space Ratio and Wind Direction on Pedestrian-level Wind Environment around High-rise Buildings with Equilateral Triangle Arrangement

Integrated Impacts of Building Space Ratio and Wind Direction on Pedestrian-level Wind Environment around High-rise Buildings with Equilateral Triangle Arrangement

Research on Optimization Design of Heliostat Field Based on Ray Tracing

In tower-type solar thermal power generation systems, the optical efficiency of the mirror field is the primary factor determining the overall system's power generation efficiency. In order to meet the requirement of a rated power of 60MW with different heliostat sizes and installation heights, optimize the various parameters of the heliostat field, establish a tower-type solar thermal power generation system model, and evaluate the model. Taking the maximum annual average output power per unit mirror area as the optimization objective, through simulation, it is found that the heliostat with a side length of 6 meters, a gradient design of installation height, a regular triangular layout, and the use of ray tracing technology can efficiently capture solar energy. The average optical efficiency, average cosine efficiency, average shadow blocking efficiency, average truncation efficiency, and average thermal power factor per unit area mirror are analyzed. The research results show that there is an optimal combination of absorber northward movement, heliostat size, equilateral triangle arrangement, installation height gradient design, and solar trajectory, which enables the annual average output thermal power to reach or even exceed the rated power of 60MW.This model and algorithm compared and analyzed genetic, greedy, and simulated annealing algorithms on the same dataset. The runtime is approximately 8-10 minutes, with CPU utilization around 60%.

Vortex interaction in triple flickering buoyant diffusion flames

Triple flickering buoyant diffusion flames of methane gas in equilateral triangle arrangement, as a nonlinear dynamical system of coupled oscillators, were computationally investigated. The four distinct dynamical modes (in-phase, death, rotation, and partially in-phase), that were originally observed in candle-flame experiments, were computationally reproduced for the first time. The four modes were interpreted from the perspective of vortex interaction and particularly of vorticity reconnection and vortex-induced flow. Specifically, the in-phase mode is caused by the periodic shedding of the trefoil vortex formed by the reconnection of three toroidal vortices; the death mode is due to the suppression of vortex shedding at small Reynolds numbers; the rotation mode appears as three toroidal vortices alternatively shed off with a constant phase difference; the partially in-phase model is caused by the vorticity reconnection of two toroidal vortices leaving another one shedding off in anti-phase. This work well establishes a bridge between the vortex dynamics and the nonlinear dynamics of the triple-flame system, which is believed to play a key role in understanding larger dynamical systems of multiple flickering flames.

Investigation on heat transfer and flow-induced vibration of three cylinders in equilateral triangle arrangement

Flow-induced vibration (FIV) and heat transfer of three circular cylinders were numerically investigated in the reduced velocity range of 3 ≤ U⁎ ≤ 15. To obtain the vibration and heat transfer characters, the influence of FIV and Richardson number (0 ≤ Ri ≤ 1) on the heat transfer performance are studied. It's found that the rise of Ri can lead to the suppression of FIV and narrow the reduced velocity (U⁎) range of lock-in. The amplitude and lift coefficient of two downstream cylinders are higher than that of 1st cylinder (upstream one) for most of U⁎. The FIV can significantly enhance the heat transfer of 2nd and 3rd cylinders (downstream cylinders), the highest increments of averaged Nusselt number are 9.74% (2nd cylinder) and 9.78% (3rd cylinder), which can be obtained when Ri = 0.5 and U⁎ = 5. Meanwhile, the distribution of local Nusselt number shows that the heat transfer mainly occurs at the upstream side of each oscillator. The heat transfer characteristics on the surface of each cylinder are closely influenced by the thickness of thermal boundary, which determines the gradient of temperature around cylinders.

Propagation properties of ring Airy beams array in a nonlinear media

The control of lasers is one of the most important subjects in optics. In this paper, we investigate the propagation behavior of three ring Airy beams (RABs) with an equilateral triangle arrangement. The visualized intensity distribution of RABs array exhibits two types of autofocus: 1. sudden autofocus, which can be applied in producing laser bullets; 2. triangle autofocus, which can be used as laser-tweezers. The properties of laser bullets are investigated. The results reveal that the center intensity (position) of laser bullets increases (decreases) in a power-law way versus initial RABs' intensity. Moreover, we discuss the range of parameters to produce laser-tweezers with the best quality. Since the position and power of the RABs-bullet and RABs-tweezers can be controlled with high precision, it has important application value in many fields such as laser targeted therapy of cancers, manipulation of microscopic objects, photoresist technology in chips and so on.

Deformation and Aspect Ratio of Bubbles Continuously Rising in Shear-Thinning Fluids

The shape deformation of three bubbles with equilateral triangle arrangement continuously rising in shear-thinning non-Newtonian fluids was numerically investigated using the three-dimensional volume of fluid method (3D-VOF). The shape deformation of three continuously rising bubbles was compared with that of a single bubble under consistent operations to analyze the effect of interaction between bubbles. The influences of bubble diameter, initial bubble distance, bubble formation frequency, and liquid rheological property on the aspect ratio of the bubble were investigated. The results indicate that the aspect ratio of the bubble for multi-bubble systems with greater bubble diameter, initial bubble distance, and more intense shear-thinning effect of the liquid decreases, and the shape of the bubble deforms flatter. However, as the bubble formation frequency increases, the deformation of the bubble weakens, and the bubble aspect ratio increases. In comparison with the single bubble rising freely, the aspect ratio of the bubble for the multi-bubble systems is larger. Moreover, a modified model of the aspect ratio of the bubble was proposed by considering the interaction between bubbles for the multi-bubble system.

Derivatization of Protein Crystals with I3C using Random Microseed Matrix Screening.

Protein structure elucidation using X-ray crystallography requires both high quality diffracting crystals and computational solution of the diffraction phase problem. Novel structures that lack a suitable homology model are often derivatized with heavy atoms to provide experimental phase information. The presented protocol efficiently generates derivatized protein crystals by combining random microseeding matrix screening with derivatization with a heavy atom molecule I3C (5-amino-2,4,6-triiodoisophthalic acid). By incorporating I3C into the crystal lattice, the diffraction phase problem can be efficiently solved using single wavelength anomalous dispersion (SAD) phasing. The equilateral triangle arrangement of iodine atoms in I3C allows for rapid validation of a correct anomalous substructure. This protocol will be useful to structural biologists who solve macromolecular structures using crystallography-based techniques with interest in experimental phasing.

Derivatization of Protein Crystals with I3C using Random Microseed Matrix Screening

Protein structure elucidation using X-ray crystallography requires both high quality diffracting crystals and computational solution of the diffraction phase problem. Novel structures that lack a suitable homology model are often derivatized with heavy atoms to provide experimental phase information. The presented protocol efficiently generates derivatized protein crystals by combining random microseeding matrix screening with derivatization with a heavy atom molecule I3C (5-amino-2,4,6-triiodoisophthalic acid). By incorporating I3C into the crystal lattice, the diffraction phase problem can be efficiently solved using single wavelength anomalous dispersion (SAD) phasing. The equilateral triangle arrangement of iodine atoms in I3C allows for rapid validation of a correct anomalous substructure. This protocol will be useful to structural biologists who solve macromolecular structures using crystallography-based techniques with interest in experimental phasing.

Laminar flow and heat transfer of water/NDG nanofluid on tube banks with rhombic cross section with different longitudinal arrangements

In present numerical study, water/NDG (nitrogen-doped graphene) nanofluid flow in different arrangements of rhombic tube banks is investigated in a two-dimensional space. Water/NDG nanofluid is considered in mass fractions of 0, 1, 2, 4 and 6% and Re numbers of 10, 100 and 450 as cooling fluid. The arrangements of tube banks are considered as ET (equilateral triangle), RS (rotated square) and ES (equal spacing) arrangements. Results revealed that the enhancement of mass fraction causes heat transfer enhancement which is due to the increase in thermal conductivity coefficient of cooling nanofluid compared to base fluid. The increase in Re causes the enhancement of average Nu which is due to better mixture of fluid layers with the enhancement of fluid velocity in higher Re which causes the reduction in temperature gradients among fluid layers away from tubes and homogeneous temperature distribution in these areas. Among investigated arrangements, RS has the highest Nu. Also, ET arrangement, compared to ES arrangement, has higher Nu. In all of the studied arrangements, the increase in Re causes the reduction in friction factor and the maximum values of friction factor are related to RS and ET arrangements, respectively.

Multi-objective optimization of wave break forest design through machine learning

Abstract Planting trees on a floodplain along a river is a practical and ecological method for embankment protection. Optimization of wave break forest is also a new concept on wave attenuation studies. In this study, we carried out physical experiments to obtain fundamental data and proposed the Cluster Structure Preserving Based on Dictionary Pair for Unsupervised Feature Weighting model (CDUFW) for multi-objective wave break forest design. Physical experiments were designed with considering the effects of different planting configurations on wave attenuation in three scenarios: (1) the equilateral triangle arrangement with different row spacings; (2) different arrangements with the same density; (3) different tree shapes with the same row spacing. The physical experiment condition was typically defined according to the field research of the study area. Then, a multi-objective weighting model for wave break forest design optimization was based on the scheme set of physical experiment outputs using the proposed CDUFW model. Physical experiments showed that different arrangement modes take advantage of the wave attenuation effect of different forest widths. The CDUFW model performed well in finding the effective, economic and reasonable scheme. The proposed model is excellent in data mining and classification, and can be applied to many decision-making and evaluation fields.

Numerical simulation of flow-induced motion of three rigidly coupled cylinders in equilateral-triangle arrangement

Numerical simulation of flow-induced motion of three rigidly coupled cylinders in equilateral-triangle arrangement

3D simulation of interaction and drag coefficient of bubbles continuously rising with equilateral triangle arrangement in shear-thinning fluids

Numerical simulations by the volume of fluid model (3D-VOF) were performed for the dynamical behavior of bubbles with equilateral triangle arrangement continuously rising in shear-thinning fluids. The influences of bubble diameter, bubble formation frequency, initial bubble distance and liquid rheological property on the interaction between bubbles and drag coefficient were studied systematically. With the increase of bubble diameter, bubble formation frequency and the decrease of initial bubble distance, both the horizontal attractive effect and vertical wake effect of bubbles strengthened, resulting in the decrease of drag coefficient. The intensified liquid shear-thinning property for the lower flow index could also enhance these two effects, and accordingly lead to a decrease of bubble drag coefficient. To characterize the interaction within multi-bubble systems, the bubble interaction coefficient Ψ was introduced, and an empirical correlation of Ψ was proposed. Based on the Magnaudet model, a new bubble drag coefficient relationship for the multi-bubble system was proposed by Ψ with an average deviation of 5%.

Flow structures around an equilateral triangle arrangement of three spheres

This paper represents the results of an experimental study on the flow structure around a single sphere and three spheres in an equilateral-triangular arrangement. Flow field measurements were performed using a Particle Image Velocimetry (PIV) technique and dye visualization in an open water channel for a Reynolds number of Re=5×103 based on the sphere diameter. The distributions and flow features at the critical locations of the contours of the velocity fluctuations, the patterns of sectional streamlines, the vorticity contours, the turbulent kinetic energy, the Reynolds stress correlations and shedding frequency are discussed. The gap ratios (G/D) of the three spheres were varied in the range of 1.0⩽G/D⩽2.5 where G was the distance between the sphere centers, and D was the sphere diameter which was taken as 30mm. Due to the interference of the shedding shear layers and the wakes, more complex features of the flow patterns can be found in the wake region of the two downstream spheres behind the leading sphere. For G/D=1.25, a jet-like flow around the leading sphere through the gap between the two downstream spheres occurred, which significantly enhanced the wake region. It was observed that a continuous flow development involving shearing phenomena and the interactions of shedding vortices caused a high rate of fluctuations over the whole flow field although most of the time-averaged flow patterns were almost symmetric about the two downstream spheres.

Comparison of Flow Characteristics of Different Sphere Geometries Under the Free Surface Effect

Comparison of the experimental results of turbulent flow structures between a smooth sphere and a sphere with a vent hole, roughened, and o-ring is presented in the presence of a free-surface. Dye visualization and particle image velocimetry (PIV) techniques were performed to examine effects of passive control methods on the sphere wake for Reynolds number Re = 5000 based on the sphere diameter with a 42.5mm in an open water channel. Instantaneous and time-averaged flow patterns in the wake region of the sphere were examined from point of flow physics for the different sphere locations in the range of 0≤h/D ≤2.0 where h was the space between the top point of the sphere and the free surface. The ratio of ventilation hole to sphere diameter was 0.15, o-ring was located at 55 o with a 2 mm from front stagnation point of the sphere and roughened surface was formed by means of totally 410 circular holes with a 3 mm diameter and around 2 mm depth in an equilateral triangle arrangement. The flow characteristics of instantaneous velocity vectors, vorticity contours, time-averaged streamline patterns, Reynolds stress correlations and streamwise and cross-stream velocity fluctuations for both the smooth and passively controlled sphere were interpreted.

Numerical Study of Vortex-Induced Vibrations of Three Circular Cylinders in Equilateral-Triangle Arrangement

Vortex-induced vibrations (VIV) of three circular cylinders in equilateral-triangle arrangement are numerically investigated. The Reynolds number based on the free stream velocity D is 150. The gap spacing between the cylinders is set as 4 D and all cylinders are free to vibrate in both transverse and in-line directions. The incompressible Navier-Stokes equations in two dimensions are solved by a four-step fractional finite element method. Simulations are carried out for three typical flow incidence angles (i.e., α = 0°, 30°, and 60°) and a wide range of reduced velocities (3 ≤ Ur r ≤ 12). Numerical results show that the responses of these cylinders, including the vortex shedding frequencies, the vibration amplitudes, and the motion trajectories, are significantly affected by the flow incidence angle and the reduced velocity. Some typical vorticity fields are also shown to investigate the flow interference between the cylinders.

Influence of Electric Field Interference on Three Nozzles Electrospinning

The low production rate of electrospinning process may limit the industrial use of single needle system. To meet high yield requirement and uniform fibers, a bottom-up multiple jets electrospinning nozzle was designed. The influence of electric field interference on jet path, membrane shape and fiber morphology was investigated. Experiment finds that electrical field strength in the closer part of two nozzles is weakened due to electric field interference when the distance between two nozzles is close. Electric field, jet path, fiber web shape and fiber morphology of three nozzles electrospinning with linear arrangement, equilateral triangle arrangement and isosceles right triangle arrangement were also compared. Results show that electric field and spun fibers of three nozzles electrospinning with equilateral triangle arrangement is the most uniform.

Three-vortex configurations in trapped Bose-Einstein condensates

We report on the creation of three-vortex clusters in a $^{87}Rb$ Bose-Einstein condensate by oscillatory excitation of the condensate. This procedure can create vortices of both circulation, so that we are able to create several types of vortex clusters using the same mechanism. The three-vortex configurations are dominated by two types, namely, an equilateral-triangle arrangement and a linear arrangement. We interpret these most stable configurations respectively as three vortices with the same circulation, and as a vortex-antivortex-vortex cluster. The linear configurations are very likely the first experimental signatures of predicted stationary vortex clusters.

Numerical simulation of flow over three circular cylinders in equilateral arrangements at low Reynolds number by a second-order characteristic-based split finite element method

In this paper, two versions of a second-order characteristic-based split scheme are developed in the framework of incremental projection method for the solution of incompressible flow problem. After the demonstration of the good accuracy and effectiveness of the developed schemes, a flow over three equal circular cylinders arranged in equilateral-triangle arrangement is numerically investigated on unstructured mesh systems. The examined Reynolds number is 100 and the flow is supposed to be laminar. Computations by the developed algorithm are then performed for six gap spacings, s, ranging from 0.5 to 4.0, and for three incidence angles, α = 0°, 30° and 60°. Numerical results show that, at sufficiently small and large s, the range of which is different for different α, the flow interference is dominated by proximity and wake effect, respectively. And in the intermediate range of the spacing, the flow pattern is influenced by both of them. The mean force results are compared with the existing experimental measurements and that shows a similar trend in the variation of mean force with the spacing for different Reynolds number. It is also observed that the interference effect transitions plays an important role in the variation of the fluctuating forces and Strouhal number.

Coupling of gap plasmons in multi-wire waveguides

We investigate the coupling of gap plasmons in various configurations of neighboring metallic nanowires. Starting with the basic element defining a gap plasmon, consisting of two neighboring silver wires, we study the energy splitting and symmetry properties of hybridized plasmons resulting from the interaction of two wire pairs. The system is shown to display non-avoided crossings of hybridized modes, and it evolves at short distances towards a degenerate system consisting of four wires arranged in a square, where two new gap plasmons emerge from redshifted higher-energy modes. The gap modes of three neighboring wires are also described in a continuous transition from a coplanar configuration to an equilateral triangle arrangement. The interaction between wire pairs is shown to be weak enough to prevent efficient transfer of plasmon signal from a pair to the other one, which is beneficial to avoid crosstalking, but not to produce waveguide couplers. The coupling is significantly increased by placing a wire of rectangular cross section in between the wire pairs, thus allowing us to achieve large plasmon-signal transfers within propagation distances below the attenuation length. Our results can find application in the design of signal-processing devices based upon gap plasmons.