Computations of Newtonian fluid flow around a square cylinder near an adiabatic wall at low and intermediate Reynolds numbers: Effects of cross-buoyancy mixed convection

ABSTRACT

The effects of cross-buoyancy mixed convection from a square cylinder in the proximity of a plane wall are studied for Reynolds number (Re) = 1–100, Richardson number (Ri) = 0–2, and gap ratio (G) = 0.25–1 at Prandtl number (Pr) = 0.7. The flow observed is steady for G = 0.25 and 0.5. The transition from a steady to a time-periodic system is observed for G = 1, and it is found at Re = 56, 60, and 74 for Ri = 0, 1, and 2, respectively. With increasing G and/or Ri, the drag coefficient and average Nusselt number increase for all Re values studied and the lift coefficient decreases with increasing Ri except at Re = 1. Maximum heat transfer augmentation is found about 89% at G = 0.5 (Re = 20, Pr = 0.7, Ri = 0) with respect to the corresponding value at G = 0.25 (Re = 20, Pr = 0.7, Ri = 0). Lastly, the correlations of drag coefficient and heat transfer have been obtained.     

Mixed convection flow and heat transfer across a square cylinder under the influence of aiding buoyancy at low Reynolds numbers

In this paper, mixed convection flow and heat transfer around a long cylinder of square cross-section under the influence of aiding buoyancy are investigated in the vertical unconfined configuration (Reynolds number, Re = 1–40 and Richardson number, Ri = 0–1). The semi-explicit finite volume method implemented on the collocated grid arrangement is used to solve the governing equations along with the appropriate boundary conditions. The onset of flow separation occurs between Re = 1–2, between Re = 2–3 and between Re = 3–4 for Ri = 0, 0.5 and 1, respectively. The flow is found to be steady for the range of conditions studied here. The friction, pressure and total drag coefficients are found to increase with Richardson number, i.e., as the influence of aiding buoyancy increases drag coefficients increase at the constant value of the Reynolds number. The temperature field around the obstacle is presented by isotherm contours at the Prandtl number of 0.7 (air). The local and average Nusselt numbers are calculated to give a detailed study of heat transfer over each surface of the square cylinder and an overall heat transfer rate and it is found that heat transfer increases with increase in Reynolds number and/or Richardson number. The simple expressions for the wake length and average cylinder Nusselt number are obtained for the range of conditions covered in this work.     

Wall–bounded flow and heat transfer around a circular cylinder at low Reynolds and Hartmann numbers

A two–dimensional numerical simulation is performed following a finite volume approach to analyze the forced convection heat transfer for the hydromagnetic flow around a circular cylinder at low Reynolds numbers. The cylinder is placed within a rectangular channel subjected to externally applied magnetic fields and acted upon by the magnetohydrodynamic (MHD) flow of a viscous incompressible and electrically conductive fluid. The magnetic field is applied either along the streamwise or transverse directions. The simulation is carried out for the range of Reynolds number 10 ≤ Re ≤ 80 with Hartmann number 0 ≤ Ha ≤ 10 and for different Prandtl numbers, Pr = 0.02 (liquid metal), 0.71 (air), and 7 (water) for a blockage ratio β = 0.25. The flow is steady for the above range of conditions. Apart from the channel wall, the magnetic field provides additional stability to the flow as a result of which the recirculation region behind the obstacle reduces with increasing magnetic field strength for a particular Reynolds number. The rate of heat transfer is found almost invariant at low Re whereas it increases slightly for higher Re with the applied magnetic field. The heat transfer increases as usual with the Reynolds number for all Hartmann numbers. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21025     

Effect of thermal buoyancy on vortex shedding past a circular cylinder in cross-flow at low Reynolds numbers

This paper demonstrates the vortex shedding process behind a heated cylinder in a cross-flow at low Reynolds numbers under the influence of thermal buoyancy. The simulations were performed using an SUPG-based finite element technique. The range of Reynolds numbers was chosen to be 10–45. The flow was steady in the absence of thermal buoyancy. The eddy length and the separation angle were computed for the steady separated flow in the above range of Reynolds numbers. The results were in agreement with those reported in the literature. The Nusselt number distribution around the heated cylinder was also computed in the above range of Reynolds numbers for forced convective flows. The results compared fairly well with available experimental results. The effect of superimposed thermal buoyancy in the same range of Reynolds numbers was studied for various Richardson numbers. The steady separated flows become unsteady periodic in the presence of superimposed thermal buoyancy. For the unsteady periodic flows, the Strouhal numbers were computed. The separation angles and average Nusselt number for such unsteady flows were found to vary with time.     

Two-dimensional mixed convection heat transfer from confined tandem square cylinders in cross-flow at low Reynolds numbers

A two-dimensional numerical simulation is carried out to understand the effects of thermal buoyancy and Prandtl number on flow characteristics and mixed convection heat transfer over two equal isothermal square cylinders placed in a tandem arrangement within a channel at low Reynolds numbers. The spacing between the cylinders is fixed with four widths of the cylinder. The numerical results are presented for the range of conditions as: 1 ≤ Re ≤ 30, 0.7 ≤ Pr ≤ 100 (the maximum value of Peclet number being 3000) and 0 ≤ Ri ≤ 1 for a fixed blockage parameter B = 10%. The unsteady numerical simulations are performed with a finite volume code based on the PISO algorithm in a collocated grid system. The representative streamlines, vortex structures and isotherm patterns are presented and discussed. In addition, the overall drag and lift coefficients, recirculation length and average Nusselt numbers are determined to elucidate the role of Reynolds, Prandtl and Richardson numbers on flow and heat transfer. It is found that the flow is completely steady for the chosen ranges of the parameters.     

Mass transport around two spheres at low Reynolds numbers

A relaxation technique has been used to solve the conservation of species equation to obtain mass-transfer rates around two equally sized spheres placed parallel to their line of centers in Stokes' flow. Four different sphere spacings were studied in the Peclét number range of 0–50. It was found that the overall Sherwood number for either sphere was always less than that of a single isolated sphere, and at low Peclét numbers, overall Sherwood numbers of less than 2 were obtained.     

Large eddy simulation of flow over square cylinder arrays in an octagonal configuration at subcritical Reynolds numbers

In this study, fluid flow over an array of eight, 0.029 m × 0.029 m, square cross‐section cylinders in an octagonal configuration is studied numerically. The mean force coefficients (drag and lift) and the vortex formation characteristics of the array are calculated numerically by utilizing a three‐dimensional large eddy simulation mathematical model for turbulence. The numerical simulation is performed with commercial software ANSYS Fluent 19R1. To investigate the parametric influences, three spacings between the cylinders (0.07, 0.14, and 0.2 m), two array attack angles (0° and 15°), and two Reynolds numbers (4060 and 45 800) are considered. The results comprise flow patterns and force coefficients' variations with Reynolds numbers. The lift force of the downstream cylinder reaches its maximum at α = 15°, and the drag force of the upstream cylinders finds its peak at α = 0°. It is observed through velocity and viscosity contour plots that vortex formation length near the cylinder increases at higher Reynolds number. Velocity vector plots are also presented to show fluid flow behavior near the cylinder. Furthermore, the predicted mean forces on the cylinders are slightly different for different Reynolds numbers, spacings, and angles of attack.     

Effects of Reynolds and Prandtl numbers on heat transfer from a square cylinder in the unsteady flow regime

The effects of the Reynolds and Prandtl numbers on the rate of heat transfer from a square cylinder are investigated numerically in the unsteady two-dimensional periodic flow regime, for the range of conditions 60 ? Re ? 160 and 0.7 ? Pr ? 50 (the maximum value of Peclet number being 4000). A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. Using the present numerical results, simple heat transfer correlations are obtained for the constant temperature and constant heat flux conditions on the solid square cylinder. In addition, the variation of the time averaged local Nusselt number on the each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number on heat transfer in the unsteady flow regime.     

Unconfined laminar nanofluid flow and heat transfer around a square cylinder

The momentum and forced convection heat transfer for a laminar and steady free stream flow of nanofluids past an isolated square cylinder have been studied numerically. Different nanofluids consisting of Al₂O₃ and CuO with base fluids of water and a 60:40 (by mass) ethylene glycol and water mixture were selected to evaluate their superiority over conventional fluids. Recent correlations for the thermal conductivity and viscosity of nanofluids, which are functions of particle volumetric concentration as well as temperature, have been employed in this paper. The simulations have been conducted for Pe = 25, 50, 100 and 200, with nanoparticle diameters of 30 and 100 nm and particle volumetric concentrations ranging from 0% to 4%. The results of heat transfer characteristics of nanofluid flow over a square cylinder showed marked improvement comparing with the base fluids. This improvement is more evident in flows with higher Peclet numbers and higher particle volume concentration, while the particle diameter imposes an adverse effect on the heat transfer characteristics. In addition, it was shown that for any given particle diameter there is an optimum value of particle concentration that results in the highest heat transfer coefficient.     

On the combined influence of Reynolds number and cylinder spacing for flow around a row of heated square cylinders

The characteristics of forced convection heat transfer across a row of heated square cylinders kept in side-by-side arrangement are numerically investigated to examine the combined effects of Reynolds number and cylinder spacing for Ri = 0, 60 ≤ Re ≤ 160, Pr = .71, and s/d = 1.0–8.0, where the space between cylinder surfaces is s and the cylinder size is d. A numerical study was carried out using the thermal lattice Boltzmann method. The goal of this work is to explore the transitions in heat transfer phenomenon that occurs behind the cylinder and to report the corresponding regimes for heat transfer namely synchronous, quasiperiodic, and chaotic. The proposed regime of heat flow is a function of Reynolds number and spacing. The synchronous heat regime is obtained for s/d ≥ 5.0 and quasiperiodic, chaotic regimes are observed for 3.0 ≤ s/d < 5.0, s/d < 3.0, respectively at Re = 100. The instantaneous isotherms, the power spectra of the corresponding Nusselt number signals, and the significance of cylinder Nusselt number frequency are used to examine these heat flow regimes. The heat transfer regimes for a row of heated cylinders and flow regimes for a row of unheated cylinders both have comparable appearances except for the fact that the heat transfer regime is synchronous at s/d ≥ 5.0 and flow is synchronous at s/d ≥ 4.0. The chaotic or quasiperiodic heat transfer regimes occur due to merging and strong interactions between thermal blobs shed from the cylinders. Heat transfer is synchronous at a higher spacing and characterized by independent thermal blobs shedded from the cylinders. It is reported that as spacing reduces and Reynolds number increases, the mean value of the Nusselt number experienced by all cylinders increases. The important outcome of the present numerical work is that for understanding heat transfer from bluff body, the transitions that occur in heat transfer are useful.     

Fluid flow and mass transfer in a sinusoidal wavy‐walled tube at moderate Reynolds numbers

Fluid flow and mass transfer characteristics in an axisymmetric sinusoidal wavy‐walled tube are experimentally investigated in the Reynolds number range of 50 to 1000. Attention is paid to the transitional flow, which is observed in the Reynolds number range of 160 to 200. In the laminar flow regime, wall shear stress and mass transfer rate increase with the slopes of 1 and 1/3, respectively, whereas in the turbulent flow regime they increase with the slopes of 3/2 and 3/5, respectively. In the transitional flow regime they increase dramatically, with a sharp slope. It is found that in this flow regime, laminar‐like motion and turbulent‐like motion alternatively take place at different time intervals. This is quite different from the flow instability for the wavy‐walled channel, where Tollmien‐Schlichting waves are observed. The flow instability in the wavy‐walled tube in the transitional flow regime is considered to be responsible for a significant increase in the wall shear stress and mass transfer rate. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 650–661, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10121     

Heat transfer downstream of a 3D confined square cylinder under flow pulsation

Abstract

This 3D study deals with the effect that a low Reynolds number (Re) pulsating water flow has on both the heat transfer to the walls of a square section channel in which a square section prism was located, and the associated pumping power. The prism blockage ratio was 2.5/1. Re, based on the prism cross-section height, varied from 100 up to 200. The inflow velocity profile was sinusoidal. Taking St₀ as the Strouhal number of the vortex shedding downstream of the prism at Re 100, the inflow Strouhal of the pulsating cases varied between 0.125 St₀ and 4 St₀. The results show that, for this particular geometry and parametric space, flow pulsation generally enhances heat transfer although its extent depends on Re and pulsation frequency. In the most favorable case, heat transfer doubles as compared to the clean channel case at the expense of tripling the pumping power.     

Characteristics for flow and heat transfer around a circular cylinder near a moving wall in wide range of low Reynolds number

The present study numerically investigates two-dimensional laminar fluid flow and heat transfer past a circular cylinder near a moving wall. Numerical simulations to calculate the fluid flow and heat transfer past a circular cylinder are performed for different Reynolds numbers varying in the range of 60–200 and a fixed Prandtl numbers of 0.7 (air) in the range of 0.1 ? G/D ? 4, where G/D is the ratio of the gap between the cylinder and a moving wall, G and the cylinder diameter, D. The flow and thermal fields become the steady state below the critical gap ratios of 0.8, 0.4 and 0.2 for the Reynolds numbers of 60, 80 and 100, respectively. As the gap ratio decreases, the magnitude of lift coefficient for all Reynolds numbers increased significantly with diminishing G/D due to the ground effect. The cases of Reynolds numbers of 60, 80 and 100 revealed the sharp slope of drag coefficient in the range of the gap ratio where the flow transfers from the unsteady state to the steady state. As the Reynolds number decreases, the variation of Nusselt is much significant and increases considerably with decreasing G/D.     

Aerodynamic characteristics and thermal structure of nonpremixed reacting swirling wakes at low Reynolds numbers

The aerodynamic characteristics and thermal structure of uncontrolled and controlled swirling double-concentric jet flames at low Reynolds numbers are experimentally studied. The swirl and Reynolds numbers are lower than 0.6 and 2000, respectively. The flow characteristics are diagnosed by the laser-light-sheet-assisted Mie scattering flow visualization method and particle image velocimetry (PIV). The thermal structure is measured by a fine-wire thermocouple. The flame shapes, combined images of flame and flow, velocity vector maps, streamline patterns, velocity and turbulence distributions, flame lengths, and temperature distributions are discussed. The flow patterns of the no-control case exhibit an open-top, single-ring vortex sitting on the blockage disc with a jetlike swirling flow evolving from the central disc face toward the downstream area. The rotation direction and size of the near-disc vortex, as well as the flow properties, change in different ranges of annulus swirl number and therefore induce three characteristic flame modes: weak swirling flame, lifted flame, and turbulent reattached flame. Because the near-disc vortex is open-top, the radial dispersion of the fuel-jet fluids is not significantly enhanced by the annulus swirling flow. The flows of the reacting swirling double-concentric jets at such low swirl and Reynolds numbers therefore present characteristics of diffusion jet flames. In the controlled case, the axial momentum of the central fuel jet is deflected radially by a control disc placed above the blockage disc. This arrangement can induce a large near-disc recirculation bubble and high turbulence intensities. The enhanced mixing hence tremendously shortens the flame length and enlarges the flame width.     

Unsteady forced convection heat/mass transfer around two spheres in tandem at low Reynolds numbers

This paper presents a computational study of the forced convection heat/mass transfer from two spheres placed in a uniform viscous flow parallel to their line of centers. The temperature/concentration inside the spheres are assumed spatially uniform but not constant in time. Axisymmetric, slow, viscous flow (Stokes flow) around the spheres was considered. The appropriate energy/chemical species balance equations were solved numerically in bispherical coordinates. The finite difference method was used to discretize the mathematical model equations. Various spheres spacing, sizes and physical properties were considered at moderate Pe numbers.     

超临界雷诺数下旋转圆柱绕流的三维大涡

超临界雷诺数状态下,圆柱下游紊流边界层的分离会导致RANS算法在求解过程中遇到一定的困难,而在工程实际中,特别是在海洋能发电塔架、风力机钝尾缘处发生的钝头体绕流均处于超临界雷诺数状态。因此,文章基于Fluent模拟软件使用大涡模拟(LES)方法,对超临界雷诺数为3.5×106时,不同比转速的旋转圆柱进行三维数值模拟,并分析其水动力学特性。文章将模拟结果与相关文献的研究结果进行比较,验证了模拟结果的准确性。研究结果表明,由马格努斯效应产生的升力对旋转圆柱下游卡门涡街的发展具有抑制作用,当比转速大于10时,旋转圆柱下游不再发生有规律的卡门涡街。     

Effects of shear-thinning nature and opposing buoyancy from a square geometry in a confined framework

Numerical computations were brought up to study the effect of opposing buoyancy mixed convection (Ri?=?0 to ??1) flow of power law shear-thinning fluids past a confined cooled square bluff body at Prandtl numbers (Pr)?=?1, 50 and Reynolds numbers (Re)?=?1–40. Irrespective of the n, Ri, Pr, and Re, the flow separation is delayed with increasing confinement (β). The vortex shedding and flow separation start earlier for shear-thinning fluids than Newtonian fluid. For opposing buoyancy (Ri?Pr (except for n?=?0.2, Ri?=??1). Also, the periodic unsteady transition appears at some higher value of Re on increasing Ri for fixed Pr. The drag coefficient (C_D) value reduces with the decrease in n, whereas the maximum C_D is noted for Newtonian fluids. The maximum augmentation in the heat transfer was reached about 9 and 36% on comparing with Newtonian fluids and forced convection case, respectively, and also the corresponding maximum compression in heat transfer was found about 15 and 5%, respectively. The numerical results have also been correlated for C_D and the Colburn j_h factor values for various Re, Pr, Ri, and n. In surplus, the effects of wall confinement ranging from β?=?25 to 50% on flow separation and engineering output parameters were studied in a steady regime.     

Conjugate unsteady heat transfer from a spherical droplet at low Reynolds numbers

The phenomena of conjugate unsteady heat transfer from a spherical droplet or particle moving in a continuous fluid medium is numerically investigated. The energy equation is solved for a spherical droplet using the implicit, finite-difference method of alternating directions (ADI). In this study, the volumetric heat capacities of the two phases are of comparable magnitude but not necessarily equal to each other and the value of the thermal diffusivities of the two phases are set equal to each other. The range of Péclet numbers investigated are : 50⩽ Pe ⩽ 1000, with ratios of volumetric heat capacities, (interior to exterior) varying between 0.333 and 3.0. The velocities used in the convective terms are those corresponding to low Reynolds number flow. It was found that the dimensionless temperature profile asymptotically approaches a steady-state value that is independent of the initial profile in the droplet.