Cylinder Of Square Cross-section Research Articles

Pressure gradient and an upstream cylinder on nanofluid flow around a heated cylinder: Heat transfer and entropy analysis

This study numerically investigates the nanofluid flow around a long heated cylinder of square cross-section (DSC) with height placed parallel to a cold wall at a fixed gap height The incident flow is Couette–Poiseuille (C–P) flow. Another cylinder of rectangular cross section (UREP) is placed on the upstream side in an inline arrangement with different gap spacings between the cylinders. The base fluid is chosen as the water and ethylene glycol–water mixture. Numerical experiments are made using staggered grid arrangement on non–uniform grid, finite volume methods, and Semi–Implicit Method for Pressure Linked Equations algorithm. Impact of pressure gradient at the inlet (due to C–P flow), position and shape (square/rectangular) of the UREP, nanoparticle concentration, and base fluid on the crowding of isotherms around edges of the DSC and hence to the heat transfer characteristics (Nusselt number and entropy generation rate density) is investigated. Bejan number is used to ratify that the irreversibility due to heat transfer is the major constituent of the total system irreversibility here. A reduction of heat transfer and entropy generation from the values of an isolated DSC is natural here due to the inline arrangement. An effort is made to improve the heat transfer by reducing the height of the UREP or/and by generating unsteadiness in the incoming flow to the DSC using a bluffer UREP or/and an increased pressure gradient. Finally, some scenarios are reported where the heat transfer decrement is less in comparison to that of the total system irreversibility.

Roles of Nanofluids, Temperature of Base Fluids, and Pressure Gradient on Heat Transfer Enhancement From a Cylinder: Uniformly Heated/Heat Flux

Heat transfer from a cylinder of square cross section (either dissipating constant heat flux (qW) or maintaining at a constant temperature (TW)) placed near a plane wall under the incidence of nonuniform linear/nonlinear velocity profile is studied numerically (finite volume method (FVM), quadratic upstream interpolation for convective kinematics (QUICK), and SIMPLE). The conventional fluids are chosen as water, and ethylene glycol–water mixture. The nanoparticles are selected as Al2O3 and CuO. Roles of pressure gradient P (at the inlet), temperature of base fluids, thermal conditions (TW or qW), and nanofluids' parameters (nanoparticle concentrations (ϕ), diameter, materials, and base fluids) on the heat transfer (Nusselt number (Nu¯M)) of the cylinder are investigated here. Nu¯M enhancement from the cylinder together with its drag coefficient reduction/increment due to addition of nanomaterials in both fluids at two different temperatures is assessed under the Couette flow. Classical fluid dynamics relationship among Nu¯M, Reynolds number (Re), and Prandtl number is discussed through Colburn j–factor, and hence the utility of proposed correlation between j–factor and Re toward engineering problems is also explored. The graphical observations of dependency of Nu¯M on the aforesaid parameters are reconfirmed by proposed functional forms of Nu¯M=Nu¯M(P), Nu¯M=Nu¯M(ϕ) and hence Nu¯M=Nu¯M(P,ϕ). An effort is made to examine the effectiveness of the aforementioned parameters on the heat transfer enhancement rate.

From steady to unsteady laminar flow in model porous structures: an investigation of the first Hopf bifurcation

This work focuses on the occurrence of the first Hopf bifurcation, corresponding to the transition from steady to unsteady flow conditions, on 2D periodic ordered and disordered non-deformable porous structures. The structures under concern, representative of real systems for many applications, are composed of cylinders of square cross section for values of the porosity ranging from 15% to 96%. The critical Reynolds number at the bifurcation is determined for incompressible isothermal Newtonian fluid flow by Direct Numerical Simulations (DNS) based on a finite volume discretization method that is second order accurate in space and time. It is shown that for ordered square periodic structures, the critical Reynolds number increases when the porosity decreases and strongly depends on the choice of the Representative Elementary Volume on which periodic boundary conditions are employed. The flow orientation with respect to the principal axes of the structure is also shown to have a very important impact on the value of the Reynolds number of the bifurcation. When structural disorder is introduced, the critical Reynolds number decreases very significantly in comparison to the ordered structure having the same porosity. Correlations between the critical Reynolds number and the porosity are obtained on both ordered and disordered structures over wide ranges of porosities. A frequency analysis is performed on one of the velocity components to investigate pre- and post-bifurcation flow characteristics.

Effect of a wall on the wake dynamics of an infinite square cylinder

The present study investigates the influence of a solid wall on the wake structure of an infinite cylinder of square cross-section when it is placed in proximity to the wall. Three different values of the gap ratio were considered, i.e. g/D=0,0.5and1, in addition to the reference case of a cylinder in a free stream with no wall. The Reynolds number based on the cylinder width and free stream velocity was Re=500. A coarse-grid Large Eddy Simulation was used to predict the resolved-scale velocity and pressure fields, and also generate the input data for the Proper Orthogonal Decomposition (POD) analysis. When the cylinder was in close proximity to the wall, it introduced strong asymmetry into the near-wake, which was manifest in the reorientation of the upper and lower recirculation cells, as well as the development of a secondary recirculation zone on the bottom wall itself. For the case of the cylinder resting directly on the bottom wall, the wake was dominated by a single large, elevated recirculation zone, and vortex shedding was entirely suppressed. For each gap ratio, the coherent structures associated with the first three POD modes were identified and the results compared with the case of an infinite cylinder in a free stream. Both the energy distribution among the POD modes and the flow pattern associated with the coherent structures for each mode were strongly influenced by the presence of the wall for the two smallest gap ratios.

Cross-flow and heat transfer of porous permeable cylinder

Non-isothermal flow around the porous permeable cylinder of square cross section by a viscous incompressible fluid is considered. The motion and energy equations is solved numerically using the finite volume method. The character of the fluid flow, change of the cylinder drag coefficient and Nusselt number as a function of Reynolds and Darcy numbers is analyzed.

On the formation of axial corner vortices during spin-up in a cylinder of square cross-section

We present experimental and theoretical results for the adjustment of a fluid (homogeneous or linearly stratified), which is initially rotating as a solid body with angular frequency ${\it\Omega}-{\rm\Delta}{\it\Omega}$, to a nonlinear increase ${\rm\Delta}{\it\Omega}$ in the angular frequency of all bounding surfaces. The fluid is contained in a cylinder of square cross-section which is aligned centrally along the rotation axis, and we focus on the $O(\mathit{Ro}^{-1}{\it\Omega}^{-1})$ time scale, where $\mathit{Ro}={\rm\Delta}{\it\Omega}/{\it\Omega}$ is the Rossby number. The flow development is shown to be dominated by unsteady separation of a viscous sidewall layer, leading to an eruption of vorticity that becomes trapped in the four vertical corners of the container. The longer-time evolution on the standard ‘spin-up’ time scale, $E^{-1/2}{\it\Omega}^{-1}$ (where $E$ is the associated Ekman number), has been described in detail for this geometry by Foster & Munro (J. Fluid Mech., vol. 712, 2012, pp. 7–40), but only for small changes in the container’s rotation rate (i.e. $\mathit{Ro}\ll 1$). In the linear case, for $\mathit{Ro}\ll E^{1/2}\ll 1$, there is no sidewall separation. In the present investigation we focus on the fully nonlinear problem, $\mathit{Ro}=O(1)$, for which the sidewall viscous layers are Prandtl boundary layers and (somewhat unusually) periodic around the container’s circumference. Some care is required in the corners of the container, but we show that the sidewall boundary layer breaks down (separates) shortly after an impulsive change in rotation rate. These theoretical boundary-layer results are compared with two-dimensional Navier–Stokes results which capture the eruption of vorticity, and these are in turn compared to laboratory observations and data. The experiments show that when the Burger number, $S=(N/{\it\Omega})^{2}$ (where $N$ is the buoyancy frequency), is relatively large – corresponding to a strongly stratified fluid – the flow remains (horizontally) two-dimensional on the $O(\mathit{Ro}^{-1}{\it\Omega}^{-1})$ time scale, and good quantitative predictions can be made by a two-dimensional theory. As $S$ was reduced in the experiments, three-dimensional effects were observed to become important in the core of each corner vortex, on this time scale, but only after the breakdown of the sidewall layers.

Control of vortex shedding and drag reduction through dual splitter plates attached to a square cylinder

In this paper we have made a numerical study on the control of vortex shedding and drag reduction of a cylinder by attaching thin splitter plates. The wake structure of the cylinder of square cross-section with attached splitter plates is analyzed for a range of Reynolds number, based on the incident stream and height of the cylinder, in the laminar range. The Navier-Stokes equations governing the flow are solved by the control volume method over a staggered grid arrangement. We have used the semi-implicit method for pressure-linked equation (SIMPLE) algorithm for computation. Our results show that the presence of a splitter plate upstream of the cylinder reduces the drag, but it has a small impact on the vortex shedding frequency when the plate length is beyond 1.5 time the height of the cylinder. The presence of a downstream splitter plate dampens the vortex shedding frequency. The entrainment of fluid into the inner side of the separated shear layers is obstructed by the downstream splitter plate. Our results suggest that by attaching in-line splitter plates both upstream and downstream of the cylinder, the vortex shedding can be suppressed, as well as a reduction in drag be obtained. We made a parametric study to determine the optimal length of these splitter plates so as to achieve low drag and low vortex shedding frequency.

Lock-exchange gravity currents propagating in a channel containing an array of obstacles

AbstractLarge eddy simulation (LES) is used to investigate the evolution of Boussinesq gravity currents propagating through a channel of height$H$containing a staggered array of identical cylinders of square cross-section and edge length$D$. The cylinders are positioned with their axes horizontal and perpendicular to the (streamwise) direction along which the lock-exchange flow develops. The effects of the volume fraction of solids,${\it\phi}$, the Reynolds number and geometrical parameters describing the array of obstacles on the structure of the lock-exchange flow, total drag force acting on the gravity current, front velocity and global energy budget are analysed. Simulation results show that the currents rapidly transition to a state in which the extra resistance provided by the cylinders strongly retards the motion and dominates the dissipative processes. A shallow layer model is also formulated and similarity solutions for the motion are found in the regime where the driving buoyancy forces are balanced by the drag arising from the interaction with the cylinders. The numerical simulations and this shallow layer model show that low-Reynolds-number currents transition to a drag-dominated regime in which the resistance is linearly proportional to the flow speed and, consequently, the front velocity,$U_{f}$, is proportional to$t^{-1/2}$, where$t$is the time measured starting at the gate release time. By contrast, high-Reynolds-number currents, for which the cylinder Reynolds number is sufficiently high that the drag coefficient for most of the cylinders can be considered constant, transition first to a quadratic drag-dominated regime in which the front speed determined from the simulations is given by$U_{f}\sim t^{-0.25}$, before undergoing a subsequent transition to the aforementioned linear drag regime in which$U_{f}\sim t^{-1/2}$. Meanwhile, away from the front, the depth-averaged gravity current velocity is proportional to$t^{-1/3}$, a result that is in agreement with the shallow water model. It is suggested that the difference between these two is due to mixing processes, which are shown to be significant in the numerical simulations, especially close to the front of the motion. Direct estimation of the drag coefficient$C_{D}$from the numerical simulations shows that the combined drag parameter for the porous medium,${\it\Gamma}_{D}=C_{D}{\it\phi}(H/D)/(1-{\it\phi})$, is the key dimensionless grouping of variables that determines the speed of propagation of the current within arrays with different$C_{D},{\it\phi}$and$D/H$.

Deformation of a long, current-carrying elastic cylinder of square cross-section: numerical solution by boundary integrals

The static, plane uncoupled problem of thermo-magnetoelasticity for a long elastic cylinder of square cross-section carrying a steady, axial electric current is investigated numerically by a boundary integral method. The lateral surface of the cylinder may be subjected, additionally, to an external distribution of pressures. The deformation is induced by the combined action of Joule heat, the magnetic forces due to the current and the external pressure. Following a smoothing process of the boundary, the applied numerical method yields the values of all quantities of practical interest at the boundary. The corresponding values in the bulk and the magnetic field in the space surrounding the conductor may be easily determined by quadrature. The results are represented graphically and discussed.

Laminar forced convection heat transfer from a heated square cylinder in a Bingham plastic fluid

In this work, the momentum and heat transfer characteristics of a heated cylinder of square cross-section immersed in a streaming Bingham plastic medium have been studied. The governing differential equations (continuity, momentum and thermal energy) have been solved numerically over wide ranges of conditions as: plastic Reynolds number, 0.1⩽Re⩽40, Prandtl number, 1⩽Pr⩽100 and the Bingham number, 0⩽Bn⩽100. Over this range of conditions, the flow is expected to be symmetric and steady. The detailed flow and temperature fields in the vicinity of the cylinder surface are examined in terms of streamline and isotherm profiles respectively. In particular, owing to the presence of the yield stress, the so-called yielded (fluid-like) and unyielded (solid-like) regions are delineated in the flow domain as functions of the Reynolds and Bingham numbers. This objective is accomplished by a detailed examination of the velocity profiles and shear rate profiles along the center planes. Further insights are developed in terms of the distribution of the pressure and local Nusselt number along the cylinder surface together with their average values in terms of drag coefficients and mean Nusselt number. The present numerical results on drag and Nusselt number (in the form of j-factor) have been correlated to the modified Bingham and Reynolds numbers via simple expressions thereby enabling their interpolation for the intermediate values of these dimensionless parameters.

The linear spin-up of a stratified, rotating fluid in a square cylinder

AbstractHere we present experimental and theoretical results for how a stratified fluid, initially rotating as a solid body with constant angular velocity, $\Omega $, within a closed cylinder of square cross-section, is spun up when subject to a small, impulsive increase, $ \mrm{\Delta} \Omega $, in the cylinder’s rotation rate. The fluid’s adjustment to the new state of solid rotation can be characterized by: (a) an inviscid, horizontal starting flow which conserves the vorticity of the initial condition; (b) the eruption of Ekman layer fluid from the perimeter region of the cylinder’s base and lid; (c) horizontal-velocity Rayleigh layers that grow into the interior from the container’s sidewalls; and (d) the formation and decay of columnar vortices in the vertical corner regions. Asymptotic results describe the inviscid starting flow, and the subsequent interior spin-up that occurs due to the combined effects of Ekman suction through the base and lid Ekman layers, and the growth of the sidewall Rayleigh layers. Attention is focused on the flow development over the spin-up time scale ${T}_{s} = {E}^{\ensuremath{-} 1/ 2} {\Omega }^{\ensuremath{-} 1} $, where $E$ is the Ekman number. (The spin-up process over the much longer diffusive time scale, ${T}_{d} = {E}^{\ensuremath{-} 1} {\Omega }^{\ensuremath{-} 1} $, is not considered here.) Experiments were performed using particle imaging velocimetry (PIV) to measure horizontal velocity components at fixed heights within the flow interior and at regular stages during the spin-up period. The velocity data obtained are shown to be in excellent agreement with the asymptotic theory.

Influence of defect states on band gaps in the two-dimensional phononic crystal of 4340 steel in an epoxy

The band structures of a new two-dimensional triangle-shaped array geometry of 4340 steel cylinders of square cross section in an epoxy resin were studied by the plane-wave expansion and supercell calculation method. The band gaps of this type of phononic crystals with different defects were calculated such as defect-free, 60° crystal linear defect states, 120° crystal linear defect states, and 180° crystal linear defect states. It was found that the band gap will emerge in different linear defects of the phononic crystals and the bandwidth of linear defect states is larger than that of the free-defect crystal by about 2.14 times within the filling fraction F = 0.1–0.85. In addition, the influence of the filling fraction on the relative width of the minimum band gap is discussed.

Effect of Thermal Buoyancy on the Two-Dimensional Upward Flow and Heat Transfer Around a Square Cylinder

The effect of aiding/opposing buoyancy on the two-dimensional upward flow and heat transfer around a heated/cooled cylinder of square cross section is studied in this work. The finite-volume-based commercial computational fluid dynamics (CFD) software FLUENT is used for the numerical simulation. The influence of aiding/opposing buoyancy is studied for Reynolds and Richardson numbers ranges of 50 to 150 and –1 to 1, respectively, and the blockage parameters of 2% and 25%. The flow exhibits unsteady periodic characteristics in the chosen range of Reynolds numbers (except for Reynolds number of 50 and blockage parameter of 25%) for the forced convective cases (Richardson number of 0). However, the vortex shedding is observed to stop completely at some critical value of Richardson number for a particular Reynolds number, below which the shedding of vortices into the stream is quite prominent. Representative streamlines and isotherm patterns for different blockage parameters are systematically presented and discussed. The critical Richardson and average Nusselt numbers are plotted against the Reynolds and Richardson numbers, respectively, to elucidate the role of thermal buoyancy on flow and heat transfer characteristics. It is observed that the vortex shedding frequency (Strouhal number) increases with increased heating and suddenly reduces to zero at the critical Richardson number. The critical Richardson number is again found to increase with Reynolds number for a particular blockage ratio, and the higher the blockage ratio, the less is the critical Richardson number. The results obtained from the commercial solver are extensively validated with the available numerical results in the literature and an excellent agreement is observed.

Crossover between macroscopic and mesoscopic regimes of vortex interactions in type-II superconductors

In the present work we report the existence of a crossover between the macroscopic and mesoscopic regimes of vortex interactions in type-II superconductors. Our findings rely on a systematic procedure to determine this crossover, which is based on the influence of the surface on the vortex structure of small superconductors. An adjacent result that we have found is that near this regime transformation, the vortex lattice develops a progressive change of symmetry, from square to hexagonal, which is intimately related to the meso-to-macro crossover. Our numerical simulations have been done for a long superconducting cylinder of square cross section for a wide range of length scales and temperatures.

Effect of orientation on laminar natural convection from a heated square cylinder in power-law liquids

Extensive numerical results are reported on the steady laminar natural convection in power-law fluids from a heated horizontal cylinder of square cross-section tilted by 45° from the direction of gravity thereby resulting in an upward flow due to density difference. The governing differential equations describing the fluid flow and heat transfer have been solved numerically over wide ranges of dimensionless parameters, namely, Grashof number (10 ≤ Gr ≤ 105), Prandtl number (0.72 ≤ Pr ≤ 100) and power-law index (0.3 ≤ n ≤ 1.8). The detailed flow and temperature fields in the proximity of the cylinder surface are visualized in terms of streamline and isotherm profiles respectively. Further insights are provided in terms of the distribution of the local Nusselt number along the cylinder surface together with its average value. Broadly speaking, over the ranges of conditions spanned herein, the flow remains attached to the surface of the cylinder. Furthermore, all else being equal, shear-thinning fluid behaviour promotes heat transfer whereas shear-thickening somewhat impedes it. Indeed, it is possible to enhance the rate of heat transfer by up to 100% in shear-thinning fluids in comparison to the Newtonian fluids under appropriate conditions. The inclination of the cylinder (α = 45°) also enhances the rate of heat transfer in comparison to an untilted cylinder. Finally, the heat transfer results are correlated by using a simple analytical form which facilitates interpolation of the present results for intermediate values of the pertinent dimensionless parameters.

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.

On creeping flow of a Bingham plastic fluid past a square cylinder

In this work, the 2-D creeping flow of Bingham plastic fluids past a cylinder of square cross-section has been studied numerically. The governing differential equations (continuity and momentum) have been solved over a wide range of Bingham number as 1⩽Bn⩽105. Similar to the case of a circular cylinder, three zones of unyielded regions are seen to be present in the vicinity of the submerged cylinder, namely, caps attached to the top and bottom surfaces of the square cylinder, two sectors situated on the lateral sides undergoing rigid-body like motion and the usual far away unyielded regions. The influence of the Bingham number on their size and on the stress (normal and shear components) field in the vicinity of the cylinder is discussed in detail. In addition, the corresponding rate of strain, pressure and stress contours are also presented to facilitate the visualization of the structure of the flow field for scores of values of Bingham number. Also, the present numerical drag results have been correlated with the Bingham number via a simple expression thereby enabling their interpolation for the intermediate values of Bingham numbers.

Laminar natural convection from a heated square cylinder immersed in power-law liquids

Laminar natural convection heat transfer from a heated long cylinder of square cross-section submerged in stagnant power-law fluids has been investigated numerically. The governing differential equations (continuity, momentum and thermal energy) have been solved over wide ranges of the pertinent dimensionless parameters, namely, Grashof number ( 10 ⩽ Gr ⩽ 10 5 ), Prandtl number ( 0.72 ⩽ Pr ⩽ 100 ) and power-law index ( 0.3 ⩽ n ⩽ 1.8 ) thereby covering both shear-thinning and shear-thickening type fluid behaviours. Detailed structure of the flow is studied in terms of streamline and isotherm patterns while heat transfer characteristics are analyzed in terms of the local Nusselt number distribution over the surface of the cylinder as well as its surface averaged values. Broadly, the flow remains attached to the surface up to larger values of the Grashof number in shear-thinning fluids ( n < 1 ) than that in Newtonian media ( n = 1 ). Similarly, all else being equal, shear-thinning behaviour promotes heat transfer. Indeed, it is possible to enhance the rate of heat transfer by up to 100% under appropriate conditions, i.e., values of the Grashof number, Prandtl number and power-law index. Of course, shear-thickening fluid behaviour has an adverse influence on the rate of heat transfer. In the limiting case of the Newtonian fluid behaviour ( n = 1 ), the present predictions are in excellent agreement with the scant experimental results available in the literature.

Momentum and heat transfer from a square cylinder in power-law fluids

Numerical solutions are sought, using FLUENT, to the mass, momentum and thermal energy equations for the 2-D flow of power-law fluids over a cylinder of square cross-section. The major thrust of this work is to delineate the values of the Reynolds number denoting the onset of flow separation and the limits of the steady flow regime for both shear-thinning and shear-thickening type fluids. Extensive results are reported on streamline and vorticity contours over wide ranges of power-law index (0.2–1.4) corroborating the occurrence of these two transitions. Having established the limits of the steady flow regime, drag and Nusselt number results are obtained in this regime as functions of the Reynolds number (0.1–40), of Prandtl number (0.7–100) for highly shear-thinning fluids (power-law index < 0.5) thereby extending the range of currently available results to that encountered in practical applications. The Nusselt number shows positive dependence on both the Reynolds and Prandtl numbers. Also, shear-thinning characteristics can augment the rate of heat transfer by up to 100% under appropriate conditions.

Influence of Buoyancy on Vortex Shedding and Heat Transfer from a Square Cylinder in Proximity to a Wall

The flow and heat transfer past a heated cylinder of square cross section mounted horizontally above a plane wall and subjected to a uniform shear flow is considered. The flow field is considered for a moderate range of Reynolds number (based on the incident stream at the cylinder upstream face and the height of the cylinder) and Grashof number at cylinder-to-wall gap height 0.5 times the cylinder height. The flow field and heat transfer are computed through a pressure-correction-based iterative algorithm with the QUICK scheme in convective terms. The code is tested for accuracy by comparing with published results for certain values of the flow parameters. We examine the combined effects of buoyancy and shear flow on the vortex shedding behind the cylinder in close proximity to a plane wall. A boundary layer develops along the wall, and this interacts with the shear layer formed along the two sides of the cylinder. The role of the thermally induced baroclinic vorticity production term on the vortex shedding is examined. Our results show that the breakdown of vortex shedding takes place beyond certain values of Richardson number (which depends on the Reynolds number). The dependence of the average rate of heat transfer from the surface of the cylinder on Reynolds number and Grashof number is also investigated.