Equilateral Triangular Cylinder Research Articles

COMBINED FORCED AND NATURAL CONVECTION FROM A SINGLE TRIANGULAR CYLINDER

Unsteady laminar confined and unconfined fluid flow and mixed (forced and free) convection heat transfer around equilateral triangular cylinders are investigated numerically. The computation model is a two-dimensional domain with blockage ratios of BR=0.5, 0.25, 0.2, 0.1, 0.05, and 0.0333, with the Reynolds numbers ranging from 100 to 200. The working fluid is water (Pr = 7). The effects of aiding and opposing thermal buoyancy are incorporated into the Navier-Stokes equations using the Boussinesq approximation. The Richardson number, which is a relative measure of free convection, is varied in the range -2 ≤ Ri ≤ 2. The governing equations are solved by using the Finite Volume Method with a second-order upwind scheme used for differencing of the convection terms, and the SIMPLE algorithm is used for the velocity-pressure coupling. A discussion of the effect of the blockage ratio on the mean drag, mean rms lift coefficients, the Strouhal number, and the mean Nusselt number is also presented. The iso-vorticity contours and dimensionless temperature field are generated to interpret and understand the underlying physical mechanisms. The results reveal that, in addition to the Richardson and Reynolds numbers, the blockage rate is effective in the vortex distribution in the channel. It has been determined that the vortices formed behind the cylinder spread to the channel with a decreasing blockage rate. Especially at high Reynolds numbers, both the drag coefficient and the mean Nusselt number are significantly affected by the blockage ratio. For Ri=0, the drag coefficients for BR=0.25 in comparison to the BR=0.05 case are about 9% and 29% larger for Re= 100 and 200, respectively. For BR

FIV and energy harvesting using bluff body piezoelectric water energy harvester with different cross-sections

Research utilizing piezoelectric fiber composites to power network nodes or micro-sensors by capturing energy from the surrounding environment is becoming a hot spot, and the structural design to efficiently improve the performance of energy harvesting is very important. The performance of a vertical cantilever piezoelectric water energy harvester (PWEH) with three different cross-sections including circular, square and equilateral triangle, each with a mass ratio of 4.8, was investigated at Reynolds number within 770–8800. Emphasis is placed on the effects of the bluff body cross-section, load resistance, and flow velocity on the flow-induced vibration (FIV) and energy response of the vertical cantilever beam of the PWEH. Except for the decreasing amplitude in the lower branch of the circular cylinder water energy harvester (CWEH), there is no distinction in the vibration response branches compared to the classical elastically supported circular cylinder. The resistance has little effect on the vibration response, while it has a significant effect on the voltage and power response. The maximum amplitude and pendulum angle of the square cylinder water energy harvester (SWEH) are slightly larger than those of the CWEH. The maximum voltage and power are smaller for the SWEH than for the CWEH. The equilateral triangular cylinder water energy harvester (TWEH) demonstrates excellent performance. It has a maximum amplitude of 3.8 D, 3.4 times that of the CWEH. The peak pendulum angle of TWCH is 13.9°, 3.2 times that of CWEH. It has a voltage of 0.057 V at a resistance of ∞, which is 3.4 times that of CEWH. In addition, the TWCH has an output power of 0.38 nW at a resistance of 106Ω, which is 9.5 times that of the CWEH. This study suggests that the best energy efficiency of TWEH is achieved by coupling vortex-induced vibration (VIV) and galloping excitation.

Deciphering the influence of shape on vortex-induced vibrations: Insight from diamond and equilateral triangle cylinder simulations

In this study, we present a comprehensive numerical investigation on the impact of geometric shapes on vortex-induced vibrations (VIV). We deploy the OpenFOAM computational fluid dynamics toolbox to simulate undamped transverse flow-induced vibrations in diamond and equilateral triangular cylinders, operating at a Reynolds number of 100 in a uniform flow. Both cylinders possess an identical mass ratio of 10 and operate within a reduced velocity range of 1–13. Our findings reveal a substantial shift in VIV branching behavior when transitioning from a diamond to a triangular geometry, with both cylinders exhibiting solely VIV responses. Intriguingly, the triangular cylinder does not exhibit a lock-out feature. Furthermore, the triangular cylinder showcases rich dynamical behavior, the occurrence of beating. Coinciding with this geometric transition is a surge in fluid forces and heightened flow asymmetry. While the diamond cylinder predominantly exhibits the P + S mode of vortex shedding, the triangular cylinder displays an unconventional 2P vortex arrangement, contributing to the observed asymmetry. As the geometry transitions from diamond to triangular, we note a phase alignment between the lift and transverse displacement. Remarkably, the triangular cylinder exhibits a higher energy conversion efficiency than its diamond counterpart. This research underscores the significant influence of geometry on vortex-induced vibrations, providing pivotal insight for optimizing the design and performance of structures subjected to fluid flows.

Numerical investigation of two-dimensional unsteady flow and heat transfer from rounded equilateral isothermal triangular cylinders in cross flow

Numerical investigation of two-dimensional unsteady flow and heat transfer from rounded equilateral isothermal triangular cylinders in cross flow

Numerical simulations of flow around three cylinders using momentum exchange-based immersed boundary-lattice Boltzmann method

Wake flow behind multiple bluff bodies is of critical significance in ocean engineering and has important scientific significance in fluid mechanics and dynamics. Three cylinders arranged in side-by-side, tandem, equilateral-triangular, and staggered arrangements were extensively researched in the previous study. In this study, the flow passing through three cylinders in staggered and equilateral-triangular arrangement were numerical calculated using a momentum exchange-based immersed boundary-lattice Boltzmann method. The numerical investigations for staggered arrangement were carried out by changing the Reynolds number (Re) from 10 to 200 with an increment of 1, and varying the gap ratio (δ = ΔP/D) from 0.1 to 8.0 with an increment of 0.1. The flow patterns of three equilateral-triangular cylinders with different gap ratios at Re = 100 were also numerical studied. The numerical results identified various flow patterns, and the variations of the above two parameters have a decisive influence on the vortex shedding patterns and flow properties. The drag coefficient, lift coefficient, and Strouhal number (St) were also surveyed to demonstrate the relationship among flow pattern, parameters δ and Re. The outcomes in this paper provide a relatively comprehensive understanding to the vortex shedding patterns and flow properties of three circular cylinders with different gap ratios and Reynolds number.

Examining of the Effect of Geometric Objects on SLAM Performance Using ROS and Gazebo

Development effort on Autonomous mobile robots that can operate in unknown environments are ongoing in order to extend the application area of the robots. In order to navigate, an autonomous mobile robot needs a map of the environment and location information relative to the map. Simultaneous Localization and Mapping (SLAM) is a prediction process in which the autonomous mobile robot can use this map to determine its position while building a consistent map. The purpose of this study is to examine the effect of geometric objects on SLAM performance. In this direction, three different experimental areas including equilateral triangular prisms, square prisms and cylinders are designed in a Gazebo. The fourth experiment area includes all three geometric objects used in the study. SLAM algorithm was tested by using the TurtleBot3 Waffle Pi robot. When the mapping times of the four experimental areas were compared, it was seen that the fastest scenario is achieved within triangular-only objects and the slowest within mixed prism. In terms of measures, the map including the triangular prisms is the closest to the actual measures of the simulated area. The obtained results show that the shapes of the geometric objects directly affect the performance of SLAM.

Assessment of algebraic subgrid scale models for the flow over a triangular cylinder at Re = 45000

The turbulent separated flow over an equilateral triangular cylinder at a Reynolds number 45000 (based on the triangle edge) is studied by means of large-eddy simulation (LES). The moderate Reynolds number is chosen in order to replicate available experimental data (Laser Doppler Anemometry measurements at the Volvo test rig). The OpenFoam CFD toolbox is used for the present numerical simulations. Several algebraic subgrid scale (SGS) closures, including the conventional Smagorinsky model (Cs=0.1 and Cs=0.053), the model by Vreman (Cs=0.1) and the dynamic version of the k-equation model are investigated. The spectral analysis of the vortex shedding and the convective instabilities as well as the turbulence kinetic energy dissipation rate is presented. Some aspects of the blockage effects are investigated and compared to experimental data available in the literature. It was shown that blockage affects significantly the mean drag and pressure coefficients of the triangular cylinder. At the same time the mean velocity field is tending to similarity. Overall, all SGS models reproduced most important aspects of the flow physics of the separated bluff-body flow, including integral flow parameters and spectral characteristics with dispersion about 10%, showing a reasonable consistency with the experimental data.

NATURAL CONVECTION HEAT TRANSFER INSIDE HORIZONTAL CIRCULAR ENCLOSURE WITH TRIANGULAR CYLINDER AT DIFFERENT ANGLES OF INCLINATION

Numerical simulation study by using Fluent CFD software has been carried out to investigate the steady. laminar natural convective heat transfer for air formed by heated inner equilateral triangular cylinder inside cold circular enclosure. The triangular cylinder was located at center of enclosure with four radius ratio RR=1.5, 2, 2.5, and 3; and four inclination angles, θ=0o (the base of triangle cylinder at bottom), 20o, 40o and 60o (the base of triangle at top). All numerical calculations were performed in the range of Rayleigh number extends from 103 to 107. The fluid and temperature fields were represented in the form of streamlines and isotherms. Results show that, As Rayleigh number increases, the streamlines become more concentrated next to the walls and the center of vortex displays upward towards the central plane of enclosure. Also, there is no effect for the inclination angle of triangular cylinder on the peak values of local Nusselt number along the inner surface of circular cylinder except the positions of these peaks due to turning of thermal plumes.

High Frequency Characteristics of the Near Wake and Vortex Past a Triangular Cylinder

Abstract The flow past a triangular cylinder is one of the fundamental flows and widely utilized in flame stabilization and heat transfer. In this study, the near wake and vortex characteristics of the flow past an equilateral triangular cylinder are experimentally measured by a high frequency particle image velocimetry (PIV) system at 3 kHz. The triangular cylinder is installed in a wind tunnel with Reynolds numbers ranging from 10,700 to 17,700. The Reynolds-averaged and phase-averaged methods are utilized to analyze the flow field. Based on the flow fields, the length of the vortex formation region is about 1.5 times of the length of the equilateral triangle side. The residence time of a vortex in the vortex formation region is equal to a vortex shedding period. The stream wise velocity of the vortex core center downstream the vortex formation is about 0.8 times of the freestream velocity, which is slightly larger than the value about 0.7 for the flow past a circular cylinder at the same Reynolds number. The maximum tangential velocity at the periphery of the vortex core maybe occurs slightly in advance of the vortex reaching the boundary of the vortex formation region. The normalized lengths of the recirculation zone of the triangular cylinder keep nearly unchanged and are about 1.55 to 1.9 times of those of the circular cylinder at the same Reynolds number. The normalized normal wise instead of stream wise turbulence intensity has stronger effects on the distribution of the normalized turbulent kinetic energy.

Mixed convection heat transfer from a triangular cylinder subjected to upward cross flow

Unsteady laminar mixed (forced and free) convection heat transfer and fluid flow over long horizontal equilateral triangular cylinder subjected to upward cross flow are investigated numerically. The computation model is a two-dimensional unconfined rectangular domain with an aspect ratio of 1.4. A second order upwind scheme was used for differencing of the convection terms, and SIMPLE algorithm was adopted. The working fluids are air (Pr = 0.7) and water (Pr = 7). The equilateral isothermal triangular cylinder is placed in a uniform stream. The effect of buoyancy is incorporated into the Navier-Stokes (NS) equations using the Boussinesq approximation. This study is a case of “assisting flow” where the buoyancy-induced flow and fluid motions have the same upward direction. The basic dimensionless simulation variables, Reynolds and Richardson numbers, are varied in the range 10 ≤ Re ≤ 200 and 0 ≤ Ri ≤ 10. The flow characteristics such as the mean drag, mean rms lift coefficients and the Strouhal number are computed for each simulation. The flow patterns and isotherms are generated to interpret and understand the underlying physical mechanism. The cylinder surface mean Nusselt number was computed for mixed as well as for forced and free convection conditions. The computational data were used to develop the several Nusselt number correlations for forced, free and mixed convection flow.

Comparison of flow characteristics around an equilateral triangular cylinder via PIV and Large Eddy Simulation methods

The flow structures around an equilateral triangular cylinder, which is commonly used as a vortex shedder in the vortex flowmeter, were investigated experimentally and numerically. Flow characteristics such as vorticity contours, patterns of sectional streamlines, velocity vectors, velocity fields, Reynolds stress correlations, Strouhal numbers and drag coefficients were examined using the Particle Image Velocimetry (PIV) technique and the Large Eddy Simulation (LES) turbulence model. Experimental studies were performed in an open water channel for Re=2.9×103, Re=5.8×103 and Re=1.16×104 based on the equilateral triangle edge. A sharp-tip corner of the cylinder with a triangle cross-section was exposed to the upstream side while the other two sharp-tip corners were placed on the downstream side. Numerical studies were also completed at Reynolds numbers in the range of 2.9×103≤Re≤1.16×105 to obtain the changes in the Strouhal numbers and drag coefficients. When the results of PIV and LES are considered in the same interval of Reynolds numbers, the maximum and minimum values of each flow pattern were nearly the same. The time-averaged patterns had considerable symmetry with respect to the axis line passing through the sharp-tip corner of the cross-section of the triangular cylinder. The Strouhal number was independent of the Reynolds number and was found to be approximately 0.22. The drag coefficient decreased with increasing Reynolds numbers while increasing the Power Spectral Density (PSD) and the vortex shedding frequency. For the same Reynolds numbers, the experimental and numerical results were in good agreement. Therefore, the LES turbulence model is recommended for applications of flow around this type of bluff body that is generally used in the design of vortex flowmeters to generate vortex shedding.

Effect of splitter plate on fluid flow characteristics past a triangular cylinder

In the present numerical investigation, the effect of splitter plate length on fluid flow characteristics past an equilateral triangular cylinder apex facing the flow configuration is studied. Simulations are carried out by using in-house solver based on Streamline Upwind/Petrov-Galerkin (SUPG) finite element method in laminar regime. The range of Reynolds numbers (Re) based on side (b) of the triangular cylinder is varied from 50 to 200 and the splitter plate length (L) is varied from L/b = 0 to = 6. The effect of splitter plate length on parameters like lift and drag are studied. It is observed that drag decreases with the attachment of splitter plate. In addition, vortex shedding suppression is observed for Re = 50 − 150 whereas, for Re = 200 vortex shedding suppression is not observed even for plate length of L/b = 6. The obtained results indicate that for a specific value of Re drag is minimized at a particular splitter plate length. The drag is minimized approximately from 9% to 57% based on Re by attaching a splitter plate to the triangular cylinder.

Some Spectral Geometry Inequalities for Generalized Heat Potential Operators

In this paper we prove that the circular cylinder is a maximizer of the Schatten p-norm of generalized heat potential operators among all Euclidean cylindric domains of a given measure. We also show that the equilateral triangular cylinder has the largest Schatten p-norm among all triangular cylinders of a given measure. Cylindric analogues of the Rayleigh–Faber–Krahn inequalities are established in both cases as well. We also give an analogue of a Hong–Krahn–Szego type inequality.

The study of the wedge-shaped vibration-driven robot motion in a viscous fluid forced by different oscillation laws of the internal mass

A rectilinear motion of a two-mass system in a viscous incompressible fluid is considered. The system consists of a shell having the form of an equilateral triangular cylinder and a movable internal mass. The motion of the system as a whole is forced by longitudinal oscillations of the internal mass relative to the shell. This mechanical system simulates a vibration-driven robot, i.e. a mobile device capable to move in a resistive medium without external moving parts. Investigation of the system is carried out by a direct numerical simulation. A comparative analysis of the characteristics of the motion and flow regimes around the vibration-driven robot is carried out for different internal mass oscillation laws.

Electromagnetic Scattering by 2-D PEC Cylinder of General Cross Section Under <inline-formula> <tex-math notation="LaTeX">$\text {TM}^{z}$ </tex-math> </inline-formula> Illumination

A semianalytical method is presented for the evaluation of scattered fields from arbitrarily shaped 2-D Perfect Electric Conductor (PEC) scatterers under $\text {TM}^{z}$ wave incidence. Surface equivalence principle for scattered fields is used in conjunction with modal expansion of fields in terms of cylindrical eigenfunctions. It is assumed that no field variation exists in axial ( $z$ ) direction. Implementation of boundary conditions on scatterer surface leads to a system of linearly independent equations to solve for equivalent surface currents. Scattered fields are calculated by equivalent surface currents leading to evaluation of scattering widths (Radar Cross-Section of 2-D objects) for different observation angles. $\text {TM}^{z}$ polarized incident wave does not excite any $\text {TE}^{z}$ component. The novelty of proposed method is use of addition theorem of Bessel functions for representation of scattered fields in terms of equivalent surface currents, giving an integral equation with an analytic integrand and a well-behaved impedance matrix. Orthogonality of cylindrical modes results in excitation matrix to be a discrete function of mode numbers. Therefore, contrary to method of moments, there is no need for weighting functions. Four examples are considered, namely, line source and plane wave incidence on a 2-D PEC circular cylinder and also plane wave incidence on 2-D elliptical and equilateral triangular PEC cylinders.

Effect of Channel Confinement on Mixed Convective Flow Past an Equilateral Triangular Cylinder

The present work investigates the mixed convective flow and heat transfer characteristics past a triangular cylinder placed symmetrically in a vertical channel. At a representative Reynolds number, Re = 100, simulations are carried out for the blockage ratios β=1/3,1/4, and 1/6. Effect of aiding and opposing buoyancy is brought about by varying the Richardson number in the range -1.0≤Ri≤1.0. At a blockage ratio of 1/3, suppression of vortex shedding is found at Ri = 1, whereas von Kármán vortex street is seen both at β=1/4 and 1/6, respectively. This is the first time that such behavior of blockage ratio past a triangular cylinder in the present flow configuration is reported. Drag coefficient increases progressively with increasing Ri and a slightly higher value is noticed at β=1/3. For all β, heat transfer increases with increasing Ri. Flattening of Nuavg –Ri curve beyond Ri>0.75 is observed at β=1/3.

Flow past an Equilateral Triangular Bluff Obstacle: Computational Study of the Effect of Thermal Buoyancy on Flow Physics and Heat Transfer

The effect of thermal buoyancy on the wake dynamics and heat transfer characteristics of an isolated equilateral triangular cylinder in cross-flow configuration is considered here. Utilizing air (Pr = 0.71) as an operating fluid computations are carried out for wide ranges of the Reynolds number (80 ≤ Re ≤ 160) and the Richardson number (−1 ≤ Ri ≤ 1). In the range of conditions studied here, flow was found to be two-dimensional and unsteady. Detailed flow physics and temperature field are visualized in terms of the streamlines, vorticity, and isotherm contours in close proximity to the cylinder. Further insights are provided by analyzing the influence of buoyancy on the overall force coefficients, and the time-averaged Nusselt number.

Mixed Convection Heat Transfer From an Equilateral Triangular Cylinder in Cross Flow at Low Reynolds Numbers

A two-dimensional numerical study is undertaken to investigate the influences of cross buoyancy on the vortex shedding phenomena behind a long heated equilateral triangular cylinder for the low-Reynolds-number laminar regime. The flow is considered in an unbounded medium; however, fictitious confining boundaries are chosen on the lateral sides to make the problem computationally feasible. Numerical calculations are performed by using a finite-volume method based on the pressure-implicit with splitting of operators algorithm in a collocated grid system. The range of Reynolds number is chosen to be 10–100 with a fixed Prandtl number, 0.71. The mixed convection effect is studied for the Richardson number range of 0–1. The effects of superimposed thermal buoyancy on flow and isotherm patterns are presented and discussed. The global flow and heat transfer quantities such as the overall drag and lift coefficients, local and surface average Nusselt numbers, and Strouhal number are calculated and discussed for various Reynolds and Richardson numbers.

Forced Convection from a Heated Equilateral Triangular Cylinder in Bingham Plastic Fluids

The momentum and forced convection heat transfer characteristics of a heated equilateral triangular cylinder immersed in a Bingham plastic fluid have been studied numerically. The governing equations (continuity, momentum, and thermal energy) are solved for both vertex-upstream and vertex-downstream orientations, over wide ranges of the pertinent parameters, such as Reynolds number: 0.1 ≤ Re ≤30; Prandtl number: 1 ≤ Pr ≤100; and Bingham number: 0 ≤ Bn ≤200. Over the range of conditions, the flow is expected to be steady and symmetric. Detailed analysis of the flow and heat transfer phenomena in the vicinity of the cylinder is performed by a thorough inspection of the streamline and isotherm contours. Furthermore, due to the presence of the yield stress, the flow domain consists of yielded (or fluid-like) and unyielded (or solid-like) zones. The effect of Reynolds number and Bingham number on the shape and size of these zones has been thoroughly examined in terms of the detailed velocity and shear rate profiles. At the next level, the functional dependence of the drag and Nusselt number on the Reynolds number, Bingham number, and Prandtl number is explored and developed. The heat transfer results spanning the above-noted ranges of parameters are consolidated by developing a correlation in terms of the Colburn j h factor as a function of the modified Reynolds number.

Analysis of Heat Transfer and Flow Due to Natural Convection in Air Around Heated Triangular Cylinders of Different Sizes Inside a Square Enclosure

Heat transfer and flow due to natural convection in air around heated equilateral triangular cylinders of different sizes inside a square enclosure has been analyzed. The triangular cylinder is at higher temperature and the vertical walls of the enclosure are at lower temperature with insulated horizontal walls. The computational model is developed using Ansys Fluent 13 commercial CFD package. The Rayleigh number is varied from 104 to 106. For a given size of enclosure, cylinders of different size are taken corresponding to aspect ratios of 0.2, 0.3, 0.4 and 0.5. Results are presented in the form of contours of isotherm and stream function.