Numerical simulation of laminar flow and heat transfer over banks of staggered cylinders

A study is conducted to investigate forced convective flow and heat transfer over a bank of staggered cylinders. Using a novel numerical formulation based on a non‐orthogonal collocated grid in a physical plane, the effects of Reynolds number and cylinder spacing on the flow and heat transfer behaviour are systematically studied. It is observed that both the Reynolds number and cylinder spacing influence the recirculatory vortex formation and growth in the region between the cylinders; in turn, the rates of heat transfer between the fluid and the staggered cylinders are affected. As the cylinder spacing decreases, the size and length of eddies reduce. For sufficiently small spacings, eddy formation is completely suppressed even at high Reynolds number. Pressure drop and Nusselt number predictions based on numerical study are in excellent agreement with available correlations. The study provides useful insight on the detailed flow and heat transfer phenomena for the case of a bank of staggered cylinders. Copyright © 2002 John Wiley & Sons, Ltd.     

Vortex Induced Vibrations of a Pair of Cylinders at Reynolds Number 1000

Vortex induced vibrations of two equal-sized cylinders in tandem and staggered arrangement placed in uniform incompressible flow is studied. A stabilized finite element formulation is utilized to solve the governing equations. The Reynolds number for these 2D simulations is 1000. The cylinders are separated by 5.5 times the cylinder diameter in the streamwise direction. For the staggered arrangement, the cross-flow spacing between the two cylinders is 0.7 times the cylinder diameter. In this arrangement, the downstream cylinder lies in the wake of the upstream one and therefore experiences an unsteady inflow. The wake looses its temporal periodicity, beyond a few diameters downstream of the front cylinder. The upstream cylinder responds as an isolated single cylinder while the downstream one undergoes disorganized motion. Soft-lock-in is observed in almost all the cases.     

Identification of flow regimes around two staggered square cylinders by a numerical study

The flow over two square cylinders in staggered arrangement is simulated numerically at a fixed Reynolds number (\(Re =150\)) for different gap spacing between cylinders from 0.1 to 6 times a cylinder side to understand the flow structures. The non-inclined square cylinders are located on a line with a staggered angle of \(45^{\circ }\) to the oncoming velocity vector. All numerical simulations are carried out with a finite-volume code based on a collocated grid arrangement. The effects of vortex shedding on the various features of the flow field are numerically visualized using different flow contours such as \(\lambda _{2}\) criterion, vorticity, pressure and magnitudes of velocity to distinguish the distinctive flow patterns. By changing the gap spacing between cylinders, five different flow regimes are identified and classified as single body, periodic gap flow, aperiodic, modulated periodic and synchronized vortex shedding regimes. This study revealed that the observed multiple frequencies in global forces of the downstream cylinder in the modulated periodic regime are more properly associated with differences in vortex shedding frequencies of individual cylinders than individual shear layers reported in some previous works; particularly, both shear layers from the downstream cylinder often shed vortices at the same multiple frequencies. The maximum Strouhal number for the upstream cylinder is also identified at \({G}^{*}=1\) for aperiodic flow pattern. Furthermore, for most cases studied, the downstream cylinder experiences larger drag force than the upstream cylinder.     

基于浸入边界-格子Boltzmann通量求解法的椭圆柱流动特性分析

基于浸入边界-格子Boltzmann通量求解法,开展了雷诺数Re=100不同几何参数下单椭圆柱及串列双椭圆柱绕流流场与受力特性对比研究。结果表明,随长短轴比值的增加,单椭圆柱绕流阻力系数先减小后缓慢上升,最大升力系数则随长短轴比值的增大而减小;尾迹流动状态从周期性脱落涡到稳定对称涡。间距是影响串列圆柱及椭圆柱流场流动状态的主要因素,间距较小时,串列圆柱绕流呈周期性脱落涡状态,而椭圆柱则为稳定流动;随着间距增加,上下游圆柱及椭圆柱尾迹均出现卡门涡街现象,且串列椭圆柱临界间距大于串列圆柱。串列椭圆柱阻力的变化规律与圆柱的基本相同,上游平均阻力大于下游阻力;上游椭圆柱阻力随着间距的变大先减小,下游随间距的变大而增加,当间距达到临界间距时上下游阻力跃升,随后出现小幅度波动再逐渐增加,并趋近于相同长短轴比值下单柱体绕流的阻力。     

Effect of flow diverters on free convection heat transfer from a pair of vertical arrays of isothermal cylinders

Laminar free convection heat transfer from two vertical arrays of five isothermal cylinders separated by flow diverters is studied experimentally using a Mach-Zehnder interferometer. The width of flow diverters is kept constant to two-cylinder diameters and the cylinders vertical center-to-center spacing is equal to three-cylinder diameter. Effect of the ratio of the horizontal spacing between two cylinder arrays to their diameter (S_h/D) on heat transfer from the cylinders is investigated for various Rayleigh numbers. The experiments are performed for S_h/D = 2-4, and the Rayleigh number based on the cylinder diameter ranging from 10³ to 3 × 10³. It is observed that for small S_h/D ratios, the flow diverters have a negative effect on the total rate of heat transfer from the arrays; while by increasing the horizontal center to center spacing, they tend to enhance the overall cooling rate of the array. Moreover, increasing Ra and S_h/D generally results in a higher average Nusselt number for each cylinder in the array.     

Forced‐convection heat transfer from tandem square cylinders in cross flow at low Reynolds numbers

This paper presents the results of a numerical study on the flow characteristics and heat transfer over two equal square cylinders in a tandem arrangement. Spacing between the cylinders is five widths of the cylinder and the Reynolds number ranges from 1 to 200, Pr=0.71. Both steady and unsteady incompressible laminar flow in the 2D regime are performed with a finite volume code based on the SIMPLEC algorithm and non‐staggered grid. A study of the effects of spatial resolution and blockage on the results is provided. In this study, the instantaneous and mean streamlines, vorticity and isotherm patterns for different Reynolds numbers are presented and discussed. In addition, the global quantities such as pressure and viscous drag coefficients, RMS lift and drag coefficients, recirculation length, Strouhal number and Nusselt number are determined and discussed for various Reynolds numbers. Copyright © 2008 John Wiley & Sons, Ltd.     

Thermal study of an array of inline horizontal cylinders below a nearly adiabatic ceiling

Steady state two-dimensional free convection heat transfer from a horizontal, isothermal cylinder in a horizontal array of cylinders consists of three isothermal cylinders, located underneath a nearly adiabatic ceiling is studied experimentally. A Mach–Zehnder interferometer is used to determine thermal field and smoke test is made to visualize flow field. Effects of the cylinders spacing to its diameter (S/D), and cylinder distance from ceiling to its diameter (L/D) on heat transfer from the centered cylinder are investigated for Rayleigh numbers from 1500 to 6000. Experiments are performed for an inline array configuration of horizontal cylinders of diameters D = 13 mm. Results indicate that due to the nearly adiabatic ceiling and neighboring cylinders, thermal plume resulted from the centered cylinder separates from cylinder surface even for high L/D values and forming recirculation regions. By decreasing the space ratio S/D, the recirculation flow strength increases. Also, by decreasing S/D, boundary layers of neighboring cylinders combine and form a developing flow between cylinders. The strength of developing flow depends on the cylinders Rayleigh number and S/D ratio. Due to the developing flow between cylinders, the vortex flow on the top of the centered cylinder appears for all L/D ratios and this vortex influences the value of local Nusselt number distribution around the cylinder.Variation of average Nusselt number of the centered cylinder depends highly on L/D and the trend with S/D depends on the value of Rayleigh number.     

Heat transfer characteristics from in-line arrays of free impinging jets

An experimental investigation of the convective heat transfer on a flat surface in a multiple-jet system is described. A thin metal sheet was heated electrically and cooled from one side. On the other black coated side the temperature field was measured using an IR camera. Varied parameters were the jet Reynolds number in the range from 1,400 to 41,400, the normalized distance nozzle to sheet H/d from 1 to 10, and the normalized nozzle spacing S/d from 2 to 10. A geometrical arrangement of nine nozzle in-line arrays was tested. The results show that the multiple-jet system enhances the local and average heat transfer in comparison with that of a single nozzle. A maximum of the heat transfer was found for the normalized spacing S/d = 6.0. The normalized distance H/d has nearly no effect on the heat transfer in the range 2 ≤ H/d ≤ 4. The maximum average Nusselt number was correlated as a function of the jet Reynolds number      

Unsteady mixed convection heat transfer from tandem square cylinders in cross flow at low Reynolds numbers

A two-dimensional numerical study is carried out to understand the influence of cross buoyancy on the vortex shedding processes behind two equal isothermal square cylinders placed in a tandem arrangement at low Reynolds numbers. The spacing between the cylinders is fixed with five widths of the cylinder dimension. The flow is considered in an unbounded medium, however, fictitious confining boundaries are chosen to make the problem computationally feasible. Numerical calculations are performed by using a finite volume method based on the PISO algorithm in a collocated grid system. The range of Reynolds number is chosen to be 50–150. The flow is unsteady laminar and two-dimensional in this Reynolds number range. The mixed convection effect is studied for Richardson number range of 0–2 and the Prandtl number is chosen constant as 0.71. The effect of superimposed thermal buoyancy on flow and isotherm patterns are presented and discussed. The global flow and heat transfer quantities such as overall drag and lift coefficients, local and surface average Nusselt numbers and Strouhal number are calculated and discussed for various Reynolds and Richardson numbers.     

Numerical study of self-sustained oscillatory flows and heat transfer in channels with a tandem of transverse vortex generators

A numerical investigation was conducted into channel flows with a tandem of transverse vortex generators in the form of rectangular cylinders. The oscillatory behavior of the flow is studied. Data for heat transfer and flow losses are presented for 100≤Re≤400 and cylinder separation distances 1≤S/H≤4. The results are obtained by numerical solution of the full Navier-Stokes equations and the energy equation. Self-sustained flow oscillations are found for Re>100. Alternate and dynamic shedding of large vortex structures from the cylinders is observed by visualization of the numerically determined flow field. A heat transfer enhancement up to a factor 1.78 compared to plane channel flow is observed. Received on 16 July 1997     

Lattice Boltzmann simulation of heat transfer and fluid flow in a microchannel with nanofluids

Mathematical modeling is performed to simulate forced convection flow of 47 nm- Al₂O₃/water nanofluids in a microchannel using the lattice Boltzmann method (LBM). Single channel flow and conjugate heat transfer problem are taken into consideration and the heat transfer rate using a nanofluid is examined. Simulations are conducted at low Reynolds numbers (2 ≤ Re ≤ 16). The computed average Nusselt number, which is associated with the thermal conductivity of nanofluid, is in the range of 0.6 ￡ [`(Nu)] ￡ 13 0.6 \le \overline{Nu} \le 13 . Results indicate that the average Nusselt number increases with the increase of Reynolds number and particle volume concentration. The fluid temperature distribution is more uniform with the use of nanofluid than that of pure water. Furthermore, great deviations of computed Nusselt numbers using different models associated with the physical properties of a nanofluid are revealed. The results of LBM agree well with the classical CFD method for predictions of flow and heat transfer in a single channel and a microchannel heat sink concerning the conjugate heat transfer problem, and consequently LBM is robust and promising for practical applications.     

Unsteady incompressible flows past two cylinders in tandem and staggered arrangements

A stabilized finite element formulation is employed to study incompressible flows past a pair of cylinders at Reynolds numbers 100 and 1000 in tandem and staggered arrangements. Computations are carried out for three sets of cylinder arrangements. In the first two cases the cylinders are arranged in tandem and the distance between their centres is 2·5 and 5·5 diameters. The third case involves the two cylinders in staggered arrangement. The distance between their centres along the flow direction is 5·5 diameters, while it is 0·7 diameter in the transverse direction. The results are compared with flows past a single cylinder at corresponding Reynolds numbers and with experimental observations by other researchers. It is observed that the qualitative nature of the flow depends strongly on the arrangement of cylinders and the Reynolds number. In all cases, when the flow becomes unsteady, the downstream cylinder, which lies in the wake of the upstream one, experiences very large unsteady forces that may lead to wake-induced flutter. The Strouhal number, based on the dominant frequency in the time history of the lift coefficient, for both cylinders attains the same value. In some cases, even though the near wake of the two cylinders shows temporal periodicity, the far wake does not. © 1997 John Wiley & Sons, Ltd.     

Heat transfer and friction factor of turbulent flow through a horizontal semi-circular duct

Forced convection heat transfer and pressure drop characteristics of air flow inside a horizontal semi-circular duct are investigated experimentally. The experiments are carried out on a semi-circular duct of 23 mm inner radius, 2 mm thickness, and 2,000 mm length within a range of Reynolds number (8,242 ≤ Re ≤ 57,794)., under uniform wall heat flux conditions. The friction factor is determined by measuring the axial static pressure at different selected axial stations along the semi-circular duct. The variations of surface and mean air temperatures, local heat transfer coefficient, local Nusselt number, and the friction factor with the axial dimensionless distance are presented. It is observed that, for a given value of Reynolds number, each of the local heat transfer coefficient and the friction factor has a relatively high value near the entrance of the semi-circular duct then it decreases with increasing the dimensionless axial distance until it approaches a nearly constant value at the fully developed region. Also, it is found that, with increasing the Reynolds number the average heat transfer coefficient is increased and the friction factor is decreased. Moreover, empirical correlations for the heat transfer coefficient and friction factor as a function of the Reynolds number are obtained.     

3D Numerical heat transfer and fluid flow analysis in plate-fin and tube heat exchangers with electrohydrodynamic enhancement

Three-dimensional laminar fluid flow and heat transfer over a four-row plate-fin and tube heat exchanger with electrohydrodynamic (EHD) wire electrodes are studied numerically. The effects of different electrode arrangements (square and diagonal), tube pitch arrangements (in-line and staggered) and applied voltage (V_E=0–16 kV) are investigated in detail for the Reynolds number range (based on the fin spacing and frontal velocity) ranging from 100 to 1,000. It is found that the EHD enhancement is more effective for lower Re and higher applied voltage. The case of staggered tube pitch with square wire electrode arrangement gives the best heat transfer augmentation. For V_E=16 kV and Re = 100, this study identifies a maximum improvement of 218% in the average Nusselt number and a reduction in fin area of 56% as compared that without EHD enhancement.     

Finite-element analysis of fluid flow and heat transfer for staggered bundles of cylinders in cross flow

The two-dimensional Navier-Stokes equations and the energy equation governing steady laminar incompressible flow are solved by a penalty finite-element model for flow across finite depth, five-row deep, staggered bundles of cylinders. Pitch to diameter ratios of 1·5 and 2·0 are considered for cylinders in equilateral triangular and square arrangements. Reynolds numbers studied range from 100 to 400, and a Prandtl number of 0·7 is used. Velocity vector fields, streamline patterns, vorticity, pressure and temperature contours, local and average Nusselt numbers, pressure and shear stress distributions around the cylinder walls and drag coefficients are presented. The results obtained agree well with available experimental and numerical data.     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

Finite element solutions of laminar flow and heat transfer of air in a staggered and an in-line tube bank

A finite element method is used to solve the full Navier-Stokes and energy equations for the problems of laminar flow and heat transfer characteristics of air around three isothermal heated horizontal cylinders in a staggered tube bank and around four isothermal heated horizontal cylinders in an in line tube bank. The variations of surface shear stress, pressure and Nusselt number are obtained over the entire cylinder surface, including the zone beyond the separation point. The predicted values of total drag, pressure drag and friction drag coefficients, average Nusselt number, and the plots of velocity flow fields and isotherms are also presented.     

Coherent and turbulent processes in the bistable regime around a tandem of cylinders including reattached flow dynamics by means of high-speed PIV

The turbulent flow around two cylinders in tandem at the sub-critical Reynolds number range of order of 10⁵ and pitch to diameter ratio of 3.7 is investigated by using time-resolved Particle Image Velocimetry (TRPIV) of 1 kHz and 8 kHz. The bi-stable flow regimes including a flow pattern I with a strong vortex shedding past the upstream and the downstream cylinder, as well as a flow pattern II corresponding to a weak alternating vortex shedding with reattachment past the upstream cylinder are investigated. The structure of this “reattachment regime” has been analyzed in association with the vortex dynamics past the downstream cylinder, by means of POD and phase-average decomposition. These elements allowed interconnection among all the measured PIV planes and hence analysis of the reattachment structure and the flow dynamics past both cylinders. The results highlight fundamental differences of the flow structure and dynamics around each cylinder and provide the ‘gap’ flow nature between the cylinders. Thanks to a high-speed camera of 8 kHz, the shear-layer vortices tracking has been possible downstream of the separation point and the quantification of their shedding frequency at the present high Reynolds number range has been achieved. This issue is important regarding fluid instabilities involved in the fluid–structure interaction of cylinder arrays in nuclear reactor systems, as well as acoustic noise generated from the tandem cylinders of a landing gear in aeronautics.     

Mixed convection cooling of a heated circular cylinder by laminar upward-directed slot jet impingement

An experimental and numerical study has been carried out to investigate the heat transfer characteristics of a horizontal circular cylinder exposed to a slot jet impingement of air. A square-edged nozzle is mounted parallel with the cylinder axis and jet flow impinges on the bottom of the cylinder. The study is focused on low Reynolds numbers ranging from 120 to 1,210, Grashof numbers up to Gr = 10Re ² and slot-to-cylinder spacing from 2 to 8 of the slot width. The flow field is greatly influenced by the slot exit velocity and the buoyancy force due to density change. A Mach–Zehnder Interferometer is used for measurement of local Nusselt number around the cylinder at 10° interval. It is observed that the average Nusselt number decreases with increasing the jet spacing and increases with rising the Reynolds number. A finite volume method utilizing a curvilinear coordinate transformation is used for numerical modeling. The numerical results show good agreement with the experimental results. The flow and thermal field are seen to be stable and symmetric around the cylinder over the range of parameters studied.     

URANS vs. experiments of flow induced motions of multiple circular cylinders with passive turbulence control

Two-dimensional Unsteady Reynolds-Average Navier–Stokes equations with the Spalart–Allmaras turbulence model are used to simulate the flow induced motions of multiple circular cylinders with passive turbulence control (PTC) in steady uniform flow. Four configurations with 1, 2, 3, and 4 cylinders in tandem are simulated and studied at a series of Reynolds numbers in the range of 30 000<Re<120 000. Simulation results are verified by experimental data measured in the Marine Renewable Energy Laboratory. Good agreement was observed between the values of vorticity, amplitude ratio, and frequency ratio predicted by numerical simulations and experimental measurements. The amplitude and frequency response show the initial and upper branches in vortex induced vibration (VIV), transition from VIV to galloping, and galloping branch for all PTC-cylinders. The maximum amplitude of 2.9 diameters for the first cylinder is achieved at Re=104 356 in the numerical results. Compared with the first cylinder, the VIV initial branch starts at higher Re for the downstream cylinders due to the presence of the upstream cylinder(s). 2P and 2P+2S vortex patterns are observed at Re=62 049 and Re=90 254 for the single PTC-cylinder. Furthermore, the shed vortices of the downstream cylinders are strongly disrupted and modified by the vortices shed from the upstream one in the cases of multiple PTC-cylinders.