Equilateral Triangular Cross-section Research Articles

Optimal aquarium shape for rearing male Siamese fighting fish (Betta splendens)

The aggressive behavior of male Siamese fighting fish (Betta splendens) necessitates their rearing in isolation in small aquaria. For intensive production, the major concerns are growth promotion and feed utilization. The small aquaria are connected to save space but little is known about the suitable characteristics of aquaria for this species. In this study, solid-red male Siamese fighting fish (0.57–0.58 g body weight) were individually housed in aquaria that had square (SQ), rectangular (RE), equilateral triangular (ET), or right triangular (RT) cross sections. The water in the aquaria had the same depth (6 cm) and volume (180 mL). At the end of the eight-week trial, fish housed in the ET and RT aquaria exhibited superior growth rate and feed utilization to fish housed in SQ or RE aquaria (P < 0.05). No differences in morphometrics, skin coloration, muscle quality, and whole-body composition were observed. Protein- and lipid-digesting enzyme activities, as well as amylase/trypsin ratios, indicated differences in feed utilization that were correlated with aquarium shape. The findings of our study indicated that the triangular aquaria were more suitable for rearing this fish in isolation. This study could be used as an animal protocol for experimental set-up, to improve betta fish farm management, and also for the development of intensive farming systems for this species.

On the flow of viscoplastic fluids in non-circular tubes

Steady flow of the viscoplastic Bingham and Herschel–Bulkley (H–B)​ fluids in tubes of non-circular cross-section is investigated analytically. The solution methodology is general in scope, does not put any restrictions on the Bingham number and thus allows the mapping of the flow field for high Bingham numbers in straight tubes with non-circular axially-symmetric but otherwise arbitrary cross-sectional contours. The circular tube contour is mapped onto an arbitrary non-circular contour on which the no-slip condition is satisfied via a one-to-one and continuous mapping. Governing equations are solved for the full spectrum of axially symmetrical cross-sectional shapes and a specific example is developed for the viscoplastic H–B fluid flow in a tube with an equilateral triangular cross-section. The shape and the extent of the plug zones centered on the tube axis and the stagnant zones in the corners are predicted for both Bingham and H–B fluids. The effect of the shear rate dependent viscosity of the H–B fluids, leading to either shear-thickening or shear-thinning behavior, on the formation of the plug and stagnation zones is examined.

Influence of cross-section shape on granular column collapses

We investigate granular column collapses with different column cross-sections and associate the cross-section shape influence with a finite-size analysis. Previous research, confined to initially circular configurations, reviewed the importance of granular column collapse studies and concluded that the run-out distance scales with the initial aspect ratio. In this work, granular columns with three different types of initial column cross-sections (square, equilateral triangular, and rectangular cross-sections) are simulated using the discrete element method (DEM). We explore how non-circular cross-sections lead to different run-out distances. Based on the previously obtained finite-size analysis, we further link the initial radius in different directions to the relative size of a column and perform the finite-size analysis to explain the cross-section influence. In the end, a universal relationship, which includes frictional properties, relative sizes, and the cross-section influence, is proposed. Our results are shown to have direct relevance to various natural and engineering systems.

Prediction of behavior of triangular solar air heater duct using V-down rib with multiple gaps and turbulence promoters as artificial roughness: A CFD analysis

In the current study, duct of equilateral triangular cross section having V-down ribs with multiple gaps and turbulence promoters as artificial roughness is analyzed and thermo-hydraulic response of duct is measured. For in depth analysis computational fluid dynamics analysis has been carried out using ANSYS FLUENT 19.0. Under the parametric variation part, effect of change in roughness parameters, viz., relative roughness pitch and angle of attack on thermohydraulic performance has been explored. Flow Reynolds number (Re) is systematically varied from 4,000 to 20,000. Proposed roughness proves its worth as its attachment over the absorber leads to an enhancement in Nusselt number and friction factor both, because of enhanced level of interaction among the fluid particles. Study reveals that upon varying the relative roughness pitch (P/e) from 8 to 14 and angle of attack from 45⁰ to 60⁰, maximum heat transfer rate is attained at P/e = 10 and α = 45⁰, respectively, irrespective of Reynolds number. Performance of the SAH with proposed roughness is found to be better than other type of roughness elements studied in recent past.

Lumped Parameter Description of Thermoviscous Acoustics in Tubes with Equilateral Triangular Cross-Sections

An accurate acoustic model of a tube in the millimeter or sub-millimeter size should include the losses that occur due to viscosity and thermal conduction, collectively termed thermoviscous losses. These losses are prominent in a boundary layer near the tube walls. Under the assumption that the boundary layer is thick compared to a characteristic geometry length, such as the radius for a circular cross-section, and fills out the entire cross-section, the tube can be described via a lumped parameter model. The lumped parameters have been known for several decades for a tube with circular cross-section, but the equilateral triangular tube has only been investigated in terms of transmission line parameters. The lumped parameters have here been established for the equilateral triangular tube as a truncated series solution of the transmission line parameters. One result observed is that the lumped parameter model for a triangular tube has 38% more viscous loss than a circular tube for a given area.

Analytical expressions of the Q ‐factor for the complete resonant mode spectrum of the equilateral triangular waveguide cavity

This Letter presents the closed-form expressions of the unloaded Q -factor in metallic cavities with equilateral triangular cross section, computed from its analytical resonant mode solutions. The obtained analytical formulas for the Q -factor extend the very restricted range of problems with closed-form solutions, complementing the classic cases of the rectangular and circular cavities found in the literature. The presented derivation provides extremely rapid reference solutions for diverse applications such as filter design by test cases for microwave characterisation systems or numerical full-wave solvers. A universal Q -chart, valid for any aspect ratio, is given and the achieved analytical results for the first resonant modes are tested with numerical commercial software, showing excellent agreement.

Simulating imbibition process using interacting capillary bundle model with corner flow: The role of capillary morphology

Interacting capillary bundle model has been much attended for modeling of imbibition process, however, how the tube morphology controls the front displacement is not well discussed in the available literature, especially when corner flow of wetting phase is considered. Tubes with non-circular cross-sections were used for simulating imbibition process performed on drained bundle of tubes. Different combinations of the interacting tubes with equilateral triangular, square, and circular cross sections were used in the bundle model to explore the role of capillary morphology. The evolution of displacement front, as well as transient water saturation profiles along the model, were obtained for oil-water two phase system. The results showed that the position of displacement front is controlled by the shape factor of tubes. The cylindrical capillaries present the highest front velocity while the equilateral triangular tubes indicate the lowest one, and the square tubes falls in between. It has been observed when the water injection rate is low, the displacement interfaces in the cylindrical model may advance slower than those of in non-circular tubes, especially at early times. The gravity force was also considered in a vertical interacting bundle model, which has been rarely attended in previous studies, and it is found that the behavior of dimensionless differences between front positions in presence and absence of gravity forces versus dimensionless time is linear. Results of this work help to better understand the role of tube morphology on displacement efficiency in imbibition process when wetting phase is present in the corner of drained angular tubes.

An Experimental and Numerical Investigation of Heat Transfer Enhancement Using Annular Ribs in a Tube

In this study, heat transfer and fluid flow features were numerically and experimentally studied in a circular steel passage of length 50 cm with an outer diameter of 40 mm and inner diameter of 37 mm under a constant surrounding temperature of 673 K for Reynolds numbers Re=10,800, 12,900, and 15,700, in order to simulate a gas turbine blade cooling passage. Turbulence was simulated using ANSYS - FLUENT (version 16.1), and the (k-ε) turbulence model was utilised. The rib constructions (of 5 × 10 mm equilateral triangular cross-section) were fixed inside the circular passage and diverged by 5 cm. The results of temperature and velocity distribution along the circular passage’s centreline for the smooth passage were compared with those of a circular passage fitted with these enclosed ribs. An improvement in the rate of heat transfer, especially at Re=12,900, was observed in the tube with ribs, with a rate of heat transfer increase of 84.3% compared to the smooth case; the ribbed tube was also observed to have a greater performance factor for turbulent flow.

Comments on the paper by M. F. Letelier and D. A. Siginer : On the flow of a class of viscoinelastic–viscoplastic fluids in tubes of non-circular contour. International Journal of Engineering Science, Vol. 45 (2007), 873–881

It is shown that the solution to the steady flow of a Newtonian fluid in a pipe of equilateral triangular cross-section is wrong, for it is based on an inappropriate choice of a parameter and the incorrect use of trigonometry. Secondly, the assumption that the shear stresses in a steady flow in a pipe are given by the gradient of a scalar function is also incorrect, since it depends on the equality between directional and partial derivatives everywhere.

Experimental investigation on heat transfer enhancement in a circular tube with equilateral triangle cross sectioned coiled-wire inserts

The thermo-hydraulic performance of coiled-wire inserted in a tube was experimentally investigated. The wire inserts have equilateral triangular cross-sections; they were coiled in a specific way to ensure that a vertex of the triangle was oriented to face the incoming air flow. The coiled-wires were installed with a 1 mm separation from the inner tube wall so that the heat transfer enhancement due to the viscous sublayer disturbance could be investigated. In total, six different coiled-wire configurations (three different pitch-to-diameter ratios: P/D = 1, P/D = 2 and P/D = 3 and two different ratios of triangle side-length to tube diameter: e/D = 0.0714 and e/D = 0.0892) were chosen for the experiment. To determine the effect of triangle position on thermal performance, the results of present study were compared with a previous study results. The maximum thermal performance is approximately 1.67 times that for a smooth tube was observed for a wire with ratios of e/D = 0.0892, P/D = 1 and 11–18% more heat transfer enhancement was achieved than the previous work results. In conclusion, to enhance heat transfer, a coiled-wire that a vertex of the triangle is oriented to face the flow can be widely applied wherever heat exchangers with tubes are used.

Entropy generation analysis for a circular tube with equilateral triangle cross sectioned coiled-wire inserts

This experimental study addresses the entropy generation in a circular tube with coiled-wire inserts. The wire inserts were manufactured with an equilateral triangular cross-section and were coiled using a method so that an edge of the triangle was oriented to face the flow direction. The triangle side length of 4, 5 and 6 mm were chosen for the experiment. The coiled-wire inserts were installed with 1, 1.5 and 2 mm separations from the inner tube wall and coiled with three different pitch-to-diameter ratios: P/D = 1, P/D = 2 and P/D = 3. A uniform heat flux was applied to the outer surface of the tube. Experiments were performed for a range of Reynolds numbers from 2731 to 27,732. The effect of several conditions on entropy generation were studied. The experimental results revealed that entropy generation number increases with increasing of Reynolds number and decreases with increasing pitch ratio. The thinner wire configuration's entropy generation numbers were lower than the other models. The entropy generation number was quite closer to each other in terms of separation between inner wall of the tube and the wire inserts. The minimum entropy generation was obtained for the tube-and-insert combination with s = 2 mm, e = 4 mm and P/D = 3.

Bingham fluids: deformation and energy dissipation in triangular cross section tube flow

Flow of Bingham plastics through straight, long tubes with non-circular cross-sections is studied by means of an analytical method that allows to model a wide spectrum of tube geometries. Shear stress normal to equal velocity lines, velocity field and plug zones are explored, in particular in a tube with equilateral triangular cross-section for small values of the Bingham number Bi, and they are compared with corresponding numerical solutions. We show that a circular plug is present at the center of the triangular tube cross-section, consistent with numerical simulations as well as with previous results in the literature, if calculations up to and including first order in the shape perturbation parameter $$\epsilon$$ are taken into account. However with the inclusion of the second order terms in the algorithm this structure is no longer present and no plug zone is predicted for the same pressure drop. We find that in that case normal shear stresses are always greater than the yield stress of the fluid. As a result, the central region becomes a pseudo-plug since it presents small but non-vanishing relative deformations and does not move as a rigid core. The energy dissipation function for the Bingham fluid flow is written in terms of natural coordinates. Its distribution depends only on the normal shear stress at any point with Bingham number as a parameter.

Dispersion and deposition of nanoparticles in microchannels with arrays of obstacles

Air pollutants are among the hazardous materials for human health. Therefore, many scientists are interested in removing particles from the carrier gas. In this study, flow of air and airborne particles through the virtual multi-fibrous filters that consist of different fiber cross-sectional shapes and arrangements is simulated where particle deposition and filtration performance are studied. Regular and irregular arrangements of fibers with the circular, elliptical, and equilateral triangular cross sections have been considered. Effects of important parameters such as solid volume fraction, internal structure, and filter thickness on particle collection efficiency and pressure drop are investigated, and the best internal structure of the multi-fiber filters for the collection of particles is obtained. Results indicate that an increase in the ratio of the vertical distances between fibers to fiber diameter and the solid volume fraction would result in a dramatic reduction of filtration. Collection efficiency of multi-fiber filters is validated with the available numerical studies.

Equivalent surface impedance of a slot impedance load on the basis of a cavity with an equilateral triangular cross section

The problem of plane-wave excitation of an impedance load on the basis of a slot in an infinite perfectly conducting screen closed from one side by a cavity with an equilateral triangular cross section is considered. The problem is solved by the integral equation method. The numerical solution of the integral equation is performed by the Krylov–Bogolyubov method. For an H-polarized incident wave, the impedance as a function of the slot and cavity sizes and the angle of incidence of a plane wave is calculated.

On the physics of viscoplastic fluid flow in non-circular tubes

Flow of Bingham plastics through straight, long tubes is studied by means of a versatile analytical method that allows extending the study to a large range of tube geometries. The equation of motion is solved for general non-circular cross-sections obtained via a continuous and one-to-one mapping called the shape factor method. In particular the velocity field and associated plug and stagnant zones in tubes with equilateral triangular and square cross-section are explored. Shear stress normal to equal velocity lines, energy dissipation distribution and rate of flow are determined. Shear-thinning and shear-thickening effects on the flow, which cannot be accounted for with the Bingham model, are investigated using the Hershey-Bulkley constitutive formulation an extension of the Bingham model. The existence and the extent of undeformed regions in the flow field in a tube with equilateral triangular cross-section are predicted in the presence of shear-thinning and shear-thickening as a specific example. The mathematical flexibility of the analytical method allows the formulation of general results related to viscoplastic fluid flow with implications related to the design and optimization of physical systems for viscoplastic material transport and processing.

Experimental investigation on heat transfer enhancement of a tube with coiled-wire inserts installed with a separation from the tube wall

An experimental investigation was conducted for the thermo-hydraulic performance of a circular tube with coiled-wire inserts which were installed with a small separation from the inner wall of the tube. The wire inserts had an equilateral triangular cross-sections with a constant side length of e=6mm and they were coiled with three different pitch-to-diameter ratios: P/D=1, P/D=2, P/D=3. A specific method was employed to coil the wires so that an edge of the triangle was oriented to face the incoming air flow. The coiled-wire inserts were installed with 1 and 2mm separation from the inner tube wall so that the heat transfer enhancement due to the laminar boundary layer disturbance could be investigated. Experiments were performed for Reynolds numbers from 3429 to 26,663. The coiled-wire inserts led to a significant increase in both the heat transfer rate and friction factor over the smooth tube based on coil pitches and clearance. The maximum thermal performance was observed around 1.82 for the P/D=1, s=1 type at a Reynolds number of 3429. In conclusion, the laminar boundary layer disturbance can be effectively enhanced by using these types of coiled-wire inserts.

Modulating wall shear stress gradient via equilateral triangular channel for in situ cellular adhesion assay.

This study introduces an equilateral triangular channel (ETRIC), a novel microfluidic channel with an equilateral triangular cross-section, for cell adhesion assay by modulating the wall shear stress (WSS) gradient. The channel can generate a parabolic WSS gradient perpendicular to the flow direction at a single flow rate, and cell detachment can be in situ screened in response to spatially different levels of WSS. The existence of a simple form of exact solution for the velocity field inside the entire ETRIC region enables the easy design and modulation of the WSS levels at the bottom surface; therefore, the detachment of the cells can be investigated at the pre-defined observation window in real time. The exact solution for the velocity field was validated by comparing the analytical velocity profile with those obtained from both numerical simulation and experimental particle image velocimetry. The parabolic WSS gradient can be generated stably and consistently over time at a steady-state condition and easily modulated by changing the flow rate for the given ETRIC geometry. The WSS gradient in the ETRIC is in a symmetric parabolic form, and this symmetry feature doubles the experimental data, thereby efficiently minimizing the number of experiments. Finally, a WSS gradient ranging from 0 to 160 dyn/cm2 was generated through the present ETRIC, which enables not only to measure the adhesion strength but also to investigate the time-dependent detachment of NIH-3T3 cells attached on the glass.

Shape effect of nanochannels on water mobility

Confinement can induce unusual behaviors of water. Inspired by the fabrication of carbon nanotubes with noncircular cross sections, we performed molecular dynamics simulations to investigate the mobilities of water confined in carbon nanochannels with circular, square, and equilateral triangular cross sections over a variety of dimensions. We find that water exhibits disparate mobilities across different types of channels below 0.796 nm2. Notably, compared with the other two channels, water in equilateral triangular channels displays the greatest mobilities. Moreover, at 0.425 nm2, different ordered structures are found in the three channels, and water inside the square channel exhibits an extremely low mobility. It is also found that above 0.796 nm2, the mobilities along the tube axis of water converge to that of the bulk. These phenomena are understood by analyzing the structure, dynamics, and hydrogen bonding of water. Our work explores the mobilities of water across noncircular carbon nanochannels, which may expand the prospect of noncircular nanochannels in scientific studies and practical applications, such as desalination and drug delivery.

Two-dimensional wake dynamics behind cylinders with triangular cross-section under incidence angle variation

The wakes behind cylinders having an equilateral triangular cross-section are studied numerically for various cylinder inclinations and Reynolds numbers. For steady flows, the development of the recirculation region near the onset of flow separation is described, and the separation Reynolds numbers mapped for different cylinder inclinations. Cylinder inclinations that are not reflection symmetric about the horizontal centreline produce asymmetric recirculation regions which persist until the flow becomes unstable. Flow separation is observed to initiate on the rear-face of the cylinder and develops in size with increasing Reynolds numbers until the separation points become defined at the triangular cross-section's vertices where they remain even at higher Reynolds numbers. Using the Stuart–Landau equation, the critical Reynolds numbers of the different flow cases are quantified. The inclination of the cylinder is seen to strongly affect the location of the separation points, the dimensions of the recirculation region, and ultimately the critical Reynolds numbers. Increasing the Reynolds number past the instability threshold, a Bénard–von Kármánvortex street is initially observed before the downstream region of the wake re-aligns to a bi-layered vortex structure. Beyond this regime, the vortex street is observed to develop variously. At most cylinder inclinations (α<30° and α≳42°), the bi-layered wake re-assembles into a secondary vortex street further downstream. For a small range of cylinder inclinations (30°≤α≲38°), the shedding vortices interact to form a vortex street similar to that produced by the 2P shedding mode for oscillating circular cylinders, while inclinations 38°≲α<54° describe the development of a P+S-like vortex street. The formation of these unsteady wakes are attributed to vortex interactions in the wake. The drag and lift force coefficients for various cylinder inclinations and Reynolds numbers are also summarised. Phase trajectories of the force coefficients reveal that the transition from the bi-layered wake to the 2P-like wake alters its profile significantly, while the transitions to the other vortex streets observed did not incur such changes.

A study of dislocation transmission through a grain boundary in hcp Ti–6Al using micro-cantilevers

Micro-cantilevers with an equilateral triangular cross-section and an apex at the bottom were machined across grain boundaries in a Ti–6Al alloy sample using a focused ion beam (FIB). A nano-indenter was used to deform the micro-cantilevers. An <a> prism slip system was selectively activated in the upper grain by controlling the crystal orientation along the micro-cantilever. Specimens for transmission electron microscopy (TEM) were prepared from the deformed micro-cantilevers using dual-beam FIB. Bright field scanning transmission electron microscopy was used to investigate the process of slip propagation through the grain boundary.