A thermal LBM-LES model in body-fitted coordinates: Flow and heat transfer around a circular cylinder in a wide Reynolds number range

In order to apply the lattice Boltzmann method (LBM) for modeling passive heat transfer at high Reynolds numbers, a number of models were proposed by introducing the large eddy simulation (LES) into the LBM framework to improve numerical stability. Our study finds that the generalized form of interpolation-supplemented LBM (GILBM), likewise, can locally modify the dimensionless relaxation time, thus enhancing the numerical stability at high Reynolds numbers. Given additional advantages of the GILBM in dealing with complicated geometries and improving computing accuracy, a thermal LBM-LES model in body-fitted coordinates is established in this paper. Numerical validation is performed by investigating the flow and heat transfer around a circular cylinder over a wide range of Reynolds numbers. The obtained results agree well with both experimental and numerical data in the previous work. Meanwhile, the effects of Reynolds number and Prandtl number on thermodynamic features of flow past a circular cylinder are revealed. It is found out that when the Reynolds number exceeds the critical value, the local Nusselt number fluctuates rapidly in a specific region of the rear cylinder surface affected by the Prandtl number. In the near-wake region, the temperature field exhibits significant dependence on the Prandtl number at moderate Reynolds numbers, while such effects turn to be slight at high Reynolds numbers.     

Forced convection heat transfer from an equilateral triangular cylinder at low Reynolds numbers

An unsteady two-dimensional numerical simulation is performed to investigate the forced convection heat transfer for flow past a long heated equilateral triangular cylinder in an unconfined medium for the low Reynolds number laminar regime. The Reynolds number considered in this study ranges from 50 to 250 with three different values of Prandtl number (Pr?=?0.71, 7 and 100). Fictitious confining boundaries are chosen on the lateral sides of the computational domain that makes the blockage ratio β?=?5?% in order to make the problem computationally feasible. An unstructured triangular mesh is used for the computational domain discretization and the simulation is carried out with the commercial CFD solver Fluent. The flow and heat transfer characteristics are analyzed with the streamline and isotherm patterns at various Reynolds numbers. The dimensionless frequency of vortex shedding (Strouhal number), drag coefficient and Nusselt numbers are presented and discussed. The results obtained are in good agreement with the available results in the literature.     

A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder

Forced convection heat transfer from an unconfined circular cylinder in the steady cross-flow regime has been studied using a finite volume method (FVM) implemented on a Cartesian grid system in the range as 10 ≤ Re ≤ 45 and 0.7 ≤ Pr ≤ 400. The numerical results are used to develop simple correlations for Nusselt number as a function of the pertinent dimensionless variables. In addition to average Nusselt number, the effects of Re, Pr and thermal boundary conditions on the temperature field near the cylinder and on the local Nusselt number distributions have also been presented to provide further physical insights into the nature of the flow. The rate of heat transfer increases with an increase in the Reynolds and/or Prandtl numbers. The uniform heat flux condition always shows higher value of heat transfer coefficient than the constant wall temperature at the surface of the cylinder for the same Reynolds and Prandtl numbers. The maximum difference between the two values is around 15–20%.     

Heat convection from a cylinder performing steady rotation or rotary oscillation – Part I: Steady rotation

In this paper, the problem of laminar, two dimensional heat convection from a circular cylinder performing steady rotation is investigated. The cylinder is␣placed with its axis horizontal in a quiescent fluid of infinite extent. Because of viscous dissipation, the flow process is confined to the region adjacent to the cylinder and is mainly driven by shear and buoyancy forces. The study is based on the solution of the full conservation equations of mass, momentum and energy for Rayleigh numbers up to 10⁴ and Reynolds numbers (based on surface velocity) up to 400 while Prandtl number ranges between 0.7 and 7.0. For the range of parameters considered, the study revealed that the rate of heat transfer increases with the increase of Rayleigh number and decreases with the increase of speed of rotation. The increase of Prandtl number resulted in an appreciable increase in the average Nusselt number only at low Reynolds numbers. The effect of Prandtl number at high Reynolds number is negligibly small. The resulting flow field in all cases is steady with no vortex shedding. The streamlines and isotherms are plotted for a number of cases to show the details of the velocity and thermal fields. Received on 15 December 1997     

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.     

Formation of vortex street and vortex pair from a circular cylinder oscillating in water

The flow around a circular cylinder undergoing sinusoidal oscillating movement in still water is investigated by phase-locked PIV measurements. The pattern and development of large-scale vortex structures in the flow are studied from the velocity vectors and vorticity contours obtained at eight successive phases of an oscillating cycle. Experiments are performed at three Keulegan–Carpenter numbers; KC=12, 6.28 and 4.25. Results at KC=12 reveal the mechanism of vortex formation and the development of the shed vortices into a vortex street at a lateral direction to the line of cylinder movement. The role of a biased flow stream and the length of the cylinder stroke in the formation of the vortex street are discussed. At the lower KC numbers, a symmetric pair of vortices is found attached to the leeward face of the cylinder. The vortex pair exhibits an increasing degree of asymmetry when KC increases from 4.25 to 6.28. An explanation in terms of the length of the cylinder strokes and the degree of flow asymmetry is offered for the transition of flow regimes from a vortex pair to a vortex street. The present results are compared with the observations made in previous experimental and numerical studies in the literature.     

Transition phenomena in the wake of an inclined square cylinder

The division of flow regimes in a square cylinder wake at various angles of attack (α) is studied. This study provides evidence of the existence of modes A and B instabilities in the wake of an inclined square cylinder. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the Strouhal number versus Reynolds number curves. The spectra and time traces of wake streamwise velocity were observed to display three distinct patterns in different flow regimes. Streamwise vortices with different wavelengths at various Reynolds numbers were visualized. A PIV technique was employed to quantitatively measure the parameters of wake vortices. The wavelengths of the streamwise vortices in the modes A and B regimes were measured by using the auto-correlation method. From the present investigation, the square cylinder wake at various angles of attack undergoes a similar transition path to that of a circular cylinder, although various quantitative parameters measured which include the critical Reynolds numbers, spanwise wavelength of secondary vortices, and the circulation and vorticity of wake vortices all show an α dependence.     

Numerical investigation of flow and combined natural-forced convection from an isothermal square cylinder in cross flow

Unsteady flow and heat transfer from a horizontal isothermal square cylinder is studied numerically using a three-dimensional computational model to investigate the influence of buoyancy on the forced flow and heat transfer characteristics. The numerical model is based on a horizontal square cylinder subjected to laminar fluid flow in an unconfined channel. The governing equations in 3D form are solved using a fractional step method based on the finite difference discretization in addition to a Crank–Nicholson scheme employed to the convective and the viscous terms. Two working fluids–air (Pr = 0.7) and water (Pr = 7)–are considered, and the flow and heat transfer simulations were carried out for the Reynolds and Richardson numbers in the intervals 55 ≤ Re ≤ 250 and 0 ≤ Ri ≤ 2, respectively. The flow characteristics such as time-averaged drag/lift, rms drag/rms lift coefficients as well as Strouhal number were computed. The heat transfer from the cylinder is assessed by mean Nusselt number (and rms Nusselt number) over the total heated cylinder walls. As the buoyancy increases, the mass and the velocity of the fluid flowing underneath the cylinder increases. The fluid is injected into the near wake region with an upward motion which significantly alters the flow field in the downstream as well as upstream regions. The effects of Reynolds, Richardson and Prandtl numbers on the flow field and temperature distributions are discussed in detail. It is shown that the flow and heat transfer characteristics are influenced more for air than water. To fill the void in the literature, useful empirical correlations of practical importance are derived for pure forced and pure natural as well as mixed convection. The mixed convection correlations, in terms of the ratio of pure forced convection, are also developed, and their implications are discussed.     

Forced Convection Heat Transfer from a Finite-Height Cylinder

This paper presents a large eddy simulation of forced convection heat transfer in the flow around a surface-mounted finite-height circular cylinder. The study was carried out for a cylinder with height-to-diameter ratio of 2.5, a Reynolds number based on the cylinder diameter of 44 000 and a Prandtl number of 1. Only the surface of the cylinder is heated while the bottom wall and the inflow are kept at a lower fixed temperature. The approach flow boundary layer had a thickness of about 10% of the cylinder height. Local and averaged heat transfer coefficients are presented. The heat transfer coefficient is strongly affected by the free-end of the cylinder. As a result of the flow over the top being downwashed behind the cylinder, a vortex-shedding process does not occur in the upper part, leading to a lower value of the local heat transfer coefficient in that region. In the lower region, vortex-shedding takes place leading to higher values of the local heat transfer coefficient. The circumferentially averaged heat transfer coefficient is 20 % higher near the ground than near the top of the cylinder. The spreading and dilution of the mean temperature field in the wake of the cylinder are also discussed.     

Experimental and numerical study on flow characteristics and heat transfer of an oscillating jet in a channel

A fluidic oscillator can produce self-induced and self-sustaining oscillating jet by fluid supply without moving parts. This device has attracted research interest in heat and mass transfer enhancement in recent years. In the current study, a double-feedback fluidic oscillator was numerically investigated based on three-dimensional unsteady Reynolds-averaged Navier-Stokes equations (3D-URANS) while the operating fluid is an incompressible flow. Then, the results were validated with experimental data by two-dimensional time-resolved particle image velocimetry (2D-TR-PIV) and thermographic phosphor thermometry (TPT) for the velocity and temperature field, respectively. A grid sensitivity study was done by comparison of instantaneous and time-averaged flow fields. Additionally, the proper orthogonal decomposition (POD) method was used to find the phase information of the oscillating jet, and fast Fourier transform (FFT) analysis was used to find the frequency of the oscillating jet to validate the numerical results. The effect of the working fluid was also studied. Finally, in order to determine the effect of the Reynolds number on heat transfer enhancement, the Q-criterion was calculated to provide detailed insight into the oscillating mechanism. The results show that the non-dimensional frequency of oscillation is independent of either the working fluid or mass flow rate. Additionally, for a given fluid, increasing Re causes strong vortices and increases the frequency of oscillation. However, the convection heat transfer did not change significantly when varying the mass flow rate because the convection velocity of vortices increases as the mass flow rate is enhanced. A comparison with a free jet reveals that the oscillating jet in a channel is useful in terms of covering a larger area.     

A numerical simulation of combined radiation and natural convection heat transfer in a square enclosure heated by a centric circular cylinder

A numerical simulation of combined natural convection and radiation in a square enclosure heated by a centric circular cylinder and filled with absorbing-emitting medium is presented. The ideal gas law and the discrete ordinates method are used to model the density changes due to temperature differences and the radiation heat transfer correspondingly. The influence of Rayleigh number, optical thickness and temperature difference on flow and temperature fields along with the natural convection, radiation and total Nusselt number at the source surfaces is studied. The results reveal that the radiation heat transfer as well as the optical thickness of the fluid has a distinct effect on the fluid flow phenomena, especially at high Rayleigh number. The heat transfer and so the Nusselt number decreases with increase in optical thickness, while increases greatly with increase in temperature difference. The variation in radiation heat transfer with optical thickness and temperature difference is much more obvious as comparison with convection heat transfer.     

Numerical Simulation of Forced Convective Heat Transfer Past a Square Diamond-Shaped Porous Cylinder

Fluid flow and heat transfer around and through a porous cylinder is an important issue in engineering applications. In this paper a numerical study is carried out for simulating the fluid flow and forced convection heat transfer around and through a square diamond-shaped porous cylinder. The flow is two-dimensional, steady, and laminar. Conservation laws of mass, momentum, and heat transport equations are applied in the clear region and Darcy–Brinkman–Forchheimer model for simulating the flow in the porous medium has been used. Equations with the relevant boundary conditions are numerically solved using a finite volume approach. In this study, Reynolds and Darcy numbers are varied within the ranges of $1<Re<45$ and $10^{-6}<Da<10^{- 2}$ , respectively. The porosity $(\varepsilon )$ is 0.5. This paper presents the effect of Reynolds and Darcy numbers on the flow structure and heat transfer characteristics. Finally, these parameters are compared among solid and porous cylinder. It was found that the drag coefficient decreases and flow separation from the cylinder is delayed with increasing Darcy number. Also the size of the thermal plume decreases by decreasing Darcy number.     

Characterization of long time fluctuations of forces exerted on an oscillating circular cylinder at KC=10

Flow dynamics, in-line and transverse forces exerted on an oscillating circular cylinder in a fluid initially at rest are studied by numerical resolution of the two-dimensional Navier-Stokes equations. The Keulegan-Carpenter number is held constant at KC=10 and Re is increased from 40 to 500. For the different flow regimes, links between flow spatio-temporal symmetries and force histories are established. Besides simulations of long duration show that in two ranges of Re, forces exhibit low frequency fluctuations compared to the cylinder oscillation frequency. Such observations have been only mentioned in the literature and are more deeply examined here. In both ranges, force fluctuations correspond to oscillations of the front and rear stagnation points on the cylinder surface. However, they occur in flow regimes whose basic patterns (V-shaped mode or diagonal mode) have different symmetry features, inducing two distinct behaviors. For 80≤Re≤100, fluctuations are related to a spectral broadening of the harmonics and to a permutation between three vortex patterns (V-shaped, transverse and oblique modes). In the second range 150≤Re≤280, amplitude fluctuations are correlated to the appearance of low frequency peaks interacting with harmonics of the cylinder frequency. Fluctuations are then a combination of a wavy fluctuation and an amplitude modulation. The carrier frequency corresponding to the wavy fluctuation depends on Re and is related to a fluid characteristic time; the modulation frequency is independent of Re and equal to 1/4 of the cylinder oscillation frequency.     

Experimental investigation on heat transfer enhancement from a heated circular cylinder with constant heat input power in turbulent pulsating crossflows

Experiments were carried out to study the heat transfer performance of a heated circular cylinder in turbulent pulsating crossflows. For a single heated circular cylinder, heat transfer enhancement factors up to 1.26 were observed in the studied parameter range. Two empirical correlations with different deviations were developed. The heat transfer enhancement factor was found to decrease with Strouhal number and Reynolds number, but increase in trend with the ratio of pulsating to steady Reynolds number.     

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.     

Flow and heat transfer performance of a mini-channel radiator with cylinder disturbed flow

Mini-channel heat sinks have relatively low Nusselt number due to small Reynolds number. For heat transfer enhancement purpose, a mini-channel radiator with cylinder disturbed flow was proposed. The disturbed flow was created by a circular cylinder placed horizontally in front of channels entrance. The performance of heat transfer and pressure drop with/without disturbed flow was studied experimentally. It was found that the friction factor of mini-channel flow was larger than that of the macro-channel flow due to larger surface roughness, and the pressure drop caused by cylinder disturbed flow was less than 5%. It also concluded that the average Nusselt number increases with augment of Reynolds and Prandtl number. The Nusselt number correlations as the function of the Reynolds and Prandtl number were given for evaluation the heat removal performance of similar heat radiators. There is an inflexion point in the empirical formulas when the channel length equals to the thermal entrance length. For the mini-channels heat radiators with disturbed flow, the inflexion Reynolds number is larger than that of without disturbed flow. Due to the flow pulsing caused by circular cylinder placed in front of channels entrance, the thermal entrance length increases. On the other hand, for both mini-channels with or without disturbed flow, the thermal resistance increases with the decrease of pressure drop.     

Fluid flow due to combined convection in lid-driven enclosure having a circular body

The present work is aimed to study mixed convection heat transfer characteristics for a lid-driven air flow within a square enclosure having a circular body. Flows are driven by the left lid, which slides in its own plane constant velocity. This wall is isothermal and it moves up or down in y direction while the other walls remain stationary. The horizontal walls are adiabatic. The cavity is differentially heated and the left wall is maintained at a higher temperature than the right wall. Three different temperature boundary conditions were applied for the inner cylinder as adiabatic, isothermal or conductive. The computation is carried out for wide ranges of Richardson numbers, diameter of inner cylinder and center and location of the inner cylinder. It was found that the most effective parameter on flow field and temperature distribution is the orientation of the moving lid. The circular body can be a control parameter for heat and fluid flow. An interesting obtained result that the thermal conductivity becomes insignificant for small values of diameter of the circular body.     

Numerical Analysis of Secondary Flows Around An Oscillating Cylinder

This paper considers methods for controlling secondary flows near an oscillating circular cylinder by changing two process control parameters: the dimensionless amplitude and the vibrational Reynolds number. A direct numerical modeling study is performed. It is shown that by varying the indicated parameters in a relatively small range, it is possible not only to intensify mass transfer processes, but also to change the direction of the main secondary flows.     

Heat transfer and flow behavior around four staggered elliptic cylinders in cross flow

Experimental and numerical studies were carried out to investigate forced convection heat transfer and flow features around the downstream elliptic cylinder in four staggered cylinders in cross flow. The elliptic cylinders examined had an axis ratio (b/c) of 1:2, and they were arranged with zero angle of attack to the upstream flow. The present heat transfer measurements were obtained by heating only the downstream elliptic cylinder (test cylinder) under the condition of constant heat flux. The testing fluid was air and the Reynolds number based on the major axis length (c) was ranged from 4,000 to 45,570. The tested longitudinal spacing ratio (S_x/c) and the transversal spacing ratio (S_y/b) were in the ranges of 1.5 ≤ S_x/c ≤ 4.0 and 1.5 ≤ S_y/b ≤ 4.0, respectively. The air flow pattern and temperature fields around the four staggered elliptic cylinders were predicted by using CFD software package. Also, a flow visualization study was made to show the flow features around the elliptic cylinders. It was observed that Nu_m of the downstream elliptic cylinder in four staggered cylinders was higher than that of three in-line cylinders for all tested spacing ratios and Reynolds numbers except for Re = 4,000. It was clear that, at lower Reynolds number values (Re < 14,100), the average Nusselt number of the downstream elliptic cylinder in three staggered arrangement was higher than that of the downstream cylinder in four staggered arrangement for all tested spacing ratios. On the other hand, at Re > 14,100, the tested elliptic cylinder in four staggered arrangement had the higher values of the average Nusselt number. Moreover, in four staggered arrangement, the maximum average Nusselt number enhancement ratio (average Nusselt number of the tested downstream cylinder/average Nusselt number of a single elliptic cylinder) was found to be about 2.0, and was obtained for spacing ratios of S_x/c = 2.5, S_y/b = 2.5 and at Re = 32,000. Finally, the average Nusselt number of the tested cylinder in four staggered arrangement was correlated in terms of Reynolds number and cylinder spacing ratios.     

Convective heat transfer from two rotating circular cylinders in tandem arrangement by using lattice Boltzmann method

The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.