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.     

Flow field and heat transfer of a two‐dimensional impinging jet disturbed by an elastically suspended circular cylinder

The flow field around a circular cylinder elastically suspended with a cantilever‐type plate spring in the jet impingement region was visualized to investigate the mechanism of the impingement heat transfer. The impingement distance H was kept constant at 3 or 5 times as large as the jet slot width, h = 15 mm.The Reynolds number was fixed at 10,000, or 5000 in the case of flow visualization. The self‐induced periodic swing motion of the cylinder across the jet axis was caused by the interaction between the jet and the elastically suspended cylinder. It was found that this swing motion has direct effects on the flow and heat transfer characteristics of the stagnation region. The ensemble‐averaged values of the flow velocity and its fluctuations depended on the cylinder diameter and the impingement distance. The local Nusselt number in the case of H/h = 3 with the oscillating cylinder of the smallest diameter D = 4 mm was increased to 1.15 times as large as that without the cylinder. The interesting patterns of the intermittency function defined with a certain threshold level of turbulence intensity were obtained under the above experimental conditions. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 313–330, 2001     

Heat transfer around a circular cylinder in separated air flow

An experimental study has been conducted to determine the heat transfer characteristics around a circular cylinder attached to the separated flow of air shed from a fence. The fence was located vertically to the flow with a height of H = 40 mm. d/H was constant at 0.638, where d is the cylinder diameter of 25.5 mm. X/H were 0.50 and 0.775 and Y/H ranged from 0.525 to 1.50, where X and Y are, respectively, the distances between the axis of the cylinder and the front face of the fence, and the bottom wall of the test section. The Reynolds number based on the cylinder diameter and the velocity of the undisturbed flow ranged from 1.9 × 10⁴ to 6.0 × 10⁴. It was found that the maximum local Nusselt number changes drastically in the vicinity of Y/H = 1.0–1.11 and that the maximum mean Nusselt number occurs in the neighborhood of Y/H = 1.24–1.43 for X/H = 0.50 and 1.3–1.4 for X/H = 0.775. © 1999 Scripta Technica, Heat Trans Asian Res, 28(3): 211–226, 1999     

Heat transfer enhancement of round impinging jet by orifice nozzle (Effects of contraction area ratio)

The effects of the nozzle contraction ratio on the flow and heat transfer characteristics of an orifice impinging jet were investigated in this experiment. The nozzle diameter was d_o=10.0 mm=const., and the contraction area ratio CR=(d_o/d_i)², where d_i is the inner pipe diameter was varied from CR=1.00 to 0.11 and the nozzle‐plate distance was varied from H/d_o=2.0 to 5.0. The nozzle Reynolds number was Re=1.5×10⁴=const. The flow characteristics were clarified by measuring the pressure and velocity distributions on the plate and flow visualization. The Nusselt number obtained from measuring the temperature distribution on the plate of an orifice impinging jet with a CR of 0.11 and 0.69 were respectively larger by 19% and 9% than those of a pipe impinging jet (CR=1.00), because the centerline velocity of the orifice jet was larger than that of the pipe jet. Under the same operation power, an orifice impinging jet has improved heat transfer characteristics. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20225     

Momentum and heat transfer characteristics of a thin circular disk in Bingham plastic fluids

The laminar forced convection momentum and heat transfer aspects of a circular disk oriented normal to the flow and maintained at a constant flux or a constant temperature condition in a stream of a Bingham plastic fluid are studied over wide ranges of parameters as follows: Reynolds number, Re?≤?150; Prandtl number, 1 ≤Pr?≤?100; Bingham number, Bn?≤?100, and thickness-to-diameter ratio, 0.01?≤?(t/d)?≤?0.075. The new results on hydrodynamics are analyzed in terms of streamline plots, recirculation length, morphology of yielded/unyielded regions, and drag coefficient, and on heat transfer aspects in terms of isotherm contours, local and average Nusselt number. The flow domain is spanned by the simultaneous existence of the yielded and unyielded sub-regions, depending upon the relative strengths of the fluid inertia (Re) and yield stress (Bn). All else being equal, the rate of heat transfer is higher for an isothermal disk than that for the isoflux condition. Both the drag and average Nusselt number bear a positive dependence on the Bingham number. The drag is influenced only slightly (～5%) by thickness (t/d); however, the heat transfer can increase on this count by up to 15% under appropriate conditions. Finally, the present numerical results on drag and Nusselt number (in terms of j_H-factor) have been correlated via simple empirical equations using the modified definitions of the Reynolds (Re^*) and Prandtl number (Pr^*), thereby enabling a priori estimation of drag and heat transfer in a new application.     

Numerical study of mixed convective heat transfer in a lid‐driven enclosure with rotating cylinders

A numerical simulation is performed to characterize the mixed convective transport in a three‐dimensional square lid‐driven enclosure with two rotating cylinders. The top wall is moving in the positive x‐direction, and the bottom wall is at a higher fixed temperature compared with all other isothermal walls. Both cylinders are rotating in its own plane about their centroidal axis. On the basis of rotation of both cylinders in clockwise or counter‐clockwise directions, four rotational models are studied. Various controlling parameters considered in the present study are Grashof number (10 ³ < Gr < 10 ⁵), rotating speed of the cylinder (5 < ω < 50), and the Reynolds number based on top wall movement is fixed to 100. The effect of cylinder rotation on the heat transfer of bottom wall is reported with the help of streamlines, contour plots of z‐component of vorticity, averaged and local Nusselt number, ratios of secondary flow and drag coefficient. It is observed that the heat transfer at the bottom wall is substantially dependent on the rotational model and rotational speed of the cylinder.     

Heat transfer on a horizontal rotating cylinder near a flat plate in a cross‐flow

An experimental study of heat transfer on a horizontal rotating cylinder near a flat plate was performed. The cylinder and plate were set in a cross‐flow. Temperature distribution and coefficients of local heat transfer were measured by a Mach–Zehnder interferometer. Flow visualization was made using smoke. Rotating Reynolds numbers (Re_r) and cross‐flow Reynolds numbers (Re_d) were varied from 0 to 2000. The spaces between cylinder and plate were varied from 1 × 10^?3 m to 5 × 10^?3 m. The rotating direction of cylinder was changed clockwise or counterclockwise. The following results are obtained: When the space between the rotating cylinder and flat plate is the same as the displacement thickness on the plate, the heat transfer on the cylinder near the plate has the best performance. We have procured the empirical equation of heat transfer from a rotating cylinder near the flat plate in the cross‐flow. 8 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20329     

Free Convection Heat Transfer from a Confined Horizontal Elliptic Cylinder

The laminar free convection heat transfer from an isothermal horizontal cylinder of elliptical cross-section confined between two adiabatic walls is investigated by the Mach-Zehnder interferometry technique. The ellipse major axis is vertical, and the minor to major axis ratio is kept constant to 0.53. This paper focuses on the effect of wall spacing and Rayleigh number variation on the local and average free convection heat transfer coefficient from the cylinder surface. The local and average Nusselt numbers were determined for the Rayleigh number range of 9 × 10 ² to 3.2 × 10 ³ and wall spacing to cylinder minor axis ratios of 1.9, 2.3, 2.67, 3.17, 3.8, 4.6, 6.12, 8, 13, ∞. Results are indicated with a single correlation that gives the average Nusselt number as a function of the ratio of the wall spacing to cylinder minor axis and the Rayleigh number. There is an optimum distance between the walls in which the Nusselt number is maximum. The experiment was also carried out on a cylinder of circular cross-section with the same periphery and length of the elliptic cylinder to allow a comparison with the results of other research.     

Numerical Investigation of Convective Heat Transfer in Unsteady Laminar Flow Over a Square Cylinder in a Channel

Unsteady laminar flow past a heated square cylinder mounted inside a plane channel was investigated numerically. The blockage ratio was chosen as 1/8 and the Reynolds number based on the mean flow velocity and chord length of the square cylinder was selected as less than 200, for which the two-dimensional behavior of the flow is assured. The time-averaged Nusselt number as well as some integral parameters such as drag coefficient, recirculation length, and Strouhal number were obtained and compared with literature. Results show a nearly linear increase in recirculation length and decrease in drag coefficient with increasing Reynolds number for the steady flow regime. There is an increase in the total Nusselt number and drag coefficient with a Reynolds number for unsteady flow regime, where vortex shedding is observed from the cylinder. A correlation was obtained for the variation of the total Nusselt number with the Reynolds number.     

Optimal smoothing length scale for actuator line models of wind turbine blades based on Gaussian body force distribution

The actuator line model (ALM) is a commonly used method to represent lifting surfaces such as wind turbine blades within large‐eddy simulations (LES). In the ALM, the lift and drag forces are replaced by an imposed body force that is typically smoothed over several grid points using a Gaussian kernel with some prescribed smoothing width ε. To date, the choice of ε has most often been based on numerical considerations related to the grid spacing used in LES. However, especially for finely resolved LES with grid spacings on the order of or smaller than the chord length of the blade, the best choice of ε is not known. In this work, a theoretical approach is followed to determine the most suitable value of ε, based on an analytical solution to the linearized inviscid flow response to a Gaussian force. We find that the optimal smoothing width ε^opt is on the order of 14%‐25% of the chord length of the blade, and the center of force is located at about 13%‐26% downstream of the leading edge of the blade for the cases considered. These optimal values do not depend on angle of attack and depend only weakly on the type of lifting surface. It is then shown that an even more realistic velocity field can be induced by a 2‐D elliptical Gaussian lift‐force kernel. Some results are also provided regarding drag force representation. Copyright © 2017 John Wiley & Sons, Ltd.     

Effects of surrounding gas on the long laminar argon plasma jet characteristics

Comparative study is performed concerning the characteristics of long laminar argon plasma jets issuing into argon or into air surroundings. It is shown that when argon, instead of air, is used as the surrounding gas, besides pure argon atmosphere can be formed, the mass flow rate of surrounding gas entrained into the plasma jet and the length of jet high-temperature region increase but the gas specific enthalpy decreases in the downstream region of the plasma jet.     

Fluid flow and heat transfer characteristics of cone orifice jet (effects of cone angle)

The use of a jet from an orifice nozzle with a saddle‐backed‐shape velocity profile and a contracted flow at the nozzle exit may improve the heat transfer characteristics on an impingement plate because of its larger centerline velocity. However, it requires more power to operate than a common nozzle because of its higher flow resistance. We therefore initially considered the use of a cone orifice nozzle to obtain better heat transfer performance as well as to decrease the flow resistance. We examined the effects of the cone angle α on the cone orifice free jet flow and heat transfer characteristics of the impinging jet. We compared two nozzles: a pipe nozzle and a quadrant nozzle. The first one provides a velocity profile of a fully developed turbulent pipe flow, and the second has a uniform velocity profile at the nozzle exit. We observed a significant enhancement of the heat transfer characteristics of the cone orifice jets at Re=1.5×10⁴. Using the cone orifice impinging jets enhanced the heat transfer rates as compared to the quadrant jet, even when the jets were supplied with the same operational power as the pipe jet. For instance, a maximum enhancement up to approximately 22% at r/d_o?0.5 is observed for α=15^°. In addition, an increase of approximately 7% is attained as compared to when the pipe jet was used. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20243     

Heat transfer of combined forced and natural convection from horizontal cylinder to air

Experimental investigations have been carried out for combined convective flows of air induced around uniformly heated, horizontal cylinders. Three cases of aiding, opposing, and cross flows were examined. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers of Re_d=50 to 900 and Ra_d^*=5×10⁴ to 3×10⁶. The flow fields around the cylinders were visualized with smoke. The results showed that separation points gradually shift from those of the forced convection to the top edge of the cylinder with increasing wall heat fluxes. The local heat transfer coefficients of the cylinders were also measured. Although the local coefficients show complex variations with the forced flow velocities and the wall heat fluxes, the overall coefficients become higher than those estimated from pure forced and natural convections throughout the cases of aiding, opposing, and cross flows. Moreover, it was confirmed that the overall Nusselt numbers as well as the separation points can be predicted with the non‐dimensional parameter (Gr_d^*/Nu_dRe_d²). © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(8): 474–488, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20180     

The effect of flow field and turbulence on heat transfer characteristics of confined circular and elliptic impinging jets

The flow field of confined circular and elliptic jets was studied experimentally with a Laser Doppler Anemometry (LDA) system. In addition, heat transfer characteristics were numerically investigated. Experiments were conducted with a circular jet and an elliptic jet of aspect ratio four, jet to target spacings of 2 and 6 jet diameters, and Reynolds number 10 000. The toroidal recirculation pattern was observed in the outflow region for both geometries at dimensionless jet to plate distance 2. Higher spreading rates in the minor axis direction of the elliptic jet have also been mapped. Along the target plate, different boundary layer profiles were obtained for circular and elliptic jets at H/d=2, but profiles became similar when dimensionless jet to plate distance was increased to 6. Positions of maximum radial and axial velocities and turbulence intensities have been determined for both geometries. For the confined circular and elliptic jet geometries, analysis of flow field measurements and numerical heat transfer results showed that inner peaks in local heat transfer closely relate to turbulence intensities in the jet and radial flow acceleration along the wall. Differences between the circular and elliptic jet, in terms of flow field and heat transfer characteristics, reduced with increase in the jet to plate distance.     

Simulation of mixed convection heat transfer in a horizontal channel with an open cavity containing a heated hollow cylinder

The objective of this paper is to numerically investigate the mixed convective flow and heat transfer controlled by a heated hollow cylinder inside an open cavity attached with a horizontal channel. All the boundaries of the channel and cavity are perfectly insulated while the inner surface of the cylinder is heated uniformly by heat flux q. The equations of conservation of mass, momentum, and energy were solved using adequate boundary conditions by Galarkin's weighted residual finite element technique. The solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been conducted for Ra = 10³–10⁵, Prandtl number Pr varying from 0.7 to 7 and ratio of solid to fluid thermal conductivities from 0.2 to 50. Results are presented in terms of streamlines, isotherms, heat transfer rate in terms of the average Nusselt number (Nu_av), drag force (D), and maximum bulk temperature (θ_max). © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21002     

Effects of jet plate size and plate spacing on the stagnation Nusselt number for a confined circular air jet impinging on a flat surface

This work deals with the effects of jet plate size and plate spacing (jet height) on the heat transfer characteristics for a confined circular air jet vertically impinging on a flat plate. The jet after impingement was restricted to flow in two opposite directions. A constant surface heat flux of 1000 W/m² was arranged. Totally 88 experiments were performed. Jet orifices individually with diameter of 1.5, 3, 6 and 9 mm were adopted. Jet Reynolds number (Re) was in the range 10,000–30,000 and plate spacing-to-jet diameter ratio (H/d) was in the range 1–6. Eleven jet plate width-to-jet diameter ratios (W/d = 4.17–41.7) and seven jet plate length-to-jet diameter ratios (L/d = 5.5–166.7) were individually considered. The measured data were correlated into a simple equation. It was found that the stagnation Nusselt number is proportional to the 0.638 power of the Re and inversely proportional to the 0.3 power of the H/d. The stagnation Nusselt number was also found to be a function of exp[−0.044(W/d) − 0.011(L/d)]. Through comparisons among the present obtained data and documented results, it may infer that, for a jet impingement, the impingement-plate heating condition and flow arrangement of the jet after impingement are two important factors affecting the dependence of the stagnation Nusselt number on H/d.     

Effect of channel-confinement and aiding/opposing buoyancy on the two-dimensional laminar flow and heat transfer across a square cylinder

The effect of channel-confinement of various degree (blockage ratio of 10%, 30% and 50%) on the upward flow and heat transfer characteristics around a heated/cooled square cylinder is studied by considering the effect of aiding/opposing buoyancy at −1 Ri 1, for Re = 100 and Pr = 0.7. With increasing blockage ratio, the minimum heating (critical Ri) required for the suppression of vortex shedding decreases up to a certain blockage ratio (=30%), but thereafter increases. The influence of buoyancy and channel-confinement on the recirculation length, drag and lift coefficient, pumping power, Strouhal number and heat transfer from the cylinder, is also investigated.     

Modeling study on the characteristics of laminar and turbulent argon plasma jets impinging normally upon a flat plate in ambient air

Modeling study is performed to compare the flow and heat transfer characteristics of laminar and turbulent argon thermal-plasma jets impinging normally upon a flat plate in ambient air. The combined-diffusion-coefficient method and the turbulence-enhanced combined-diffusion-coefficient method are employed to treat the diffusion of argon in the argon–air mixture for the laminar and the turbulent cases, respectively. Modeling results presented include the flow, temperature and argon concentration fields, the air mass flow-rates entrained into the impinging plasma jets, and the distributions of the heat flux density on the plate surface. It is found that the formation of a radial wall jet on the plate surface appreciably enhances the mass flow rate of the ambient air entrained into the laminar or turbulent plasma impinging-jet. When the plate standoff distance is comparatively small, there exists a significant difference between the laminar and turbulent plasma impinging-jets in their flow fields due to the occurrence of a large closed recirculation vortex in the turbulent plasma impinging-jet, and no appreciable difference is found between the two types of jets in their maximum values and distributions of the heat flux density at the plate surface. At larger plate standoff distances, the effect of the plate on the jet flow fields only appears in the region near the plate, and the axial decaying-rates of the plasma temperature, axial velocity and argon mass fraction along the axis of the laminar plasma impinging-jet become appreciably less than their turbulent counterparts.     

Flow visualization in an annulus between co-axis rotating cylinders with a circular jet on stationary outer cylinder

This work experimentally investigated the effects of jet flow and flow outlet configuration on the fluid flow in an annulus between co-axis rotating cylinders. By using the incense and the laser light, smoke flow visualization in a rotating annulus can be obtained. Firstly, the flow behavior in a rotating annular without jet flow and flow outlet was investigated. When Taylor number (Ta) exceeded 1708, the well-known Taylor vortices were successfully observed. Subsequently, the flow characteristics in a rotating annular with a jet flow and various flow outlet configurations were investigated. The circle jet nozzle was located at the middle position of the stationary outer cylinder. In addition, two flow outlet configurations were employed. One was the model of single outlet at the right side of the annulus, the other was the model of double outlets at both side of the annulus. The jet Reynolds number (Re) was 1351. The Taylor number (Ta) varied from 545 to 24,217. When the impinging force and the inertia force from the jet flow interacted with the Coriolis force and the centrifugal force due to rotation, the fluid flow should become very complicated. The experimental results indicated that the rapid rotation broke the original stream line of the jet flow. On the other hand, when the jet flow turned 90° to be the axial flow, it would suppress the onset of Taylor vortices. Finally, fixing the Re and Ta, the model of single outlet more suppressed the onset of Taylor vortices than the model of double outlets did.     

Impingement heat transfer at a circular cylinder due to an offset or non-offset slot jet

Heat transfer coefficients were measured on a circular cylinder subjected to the crossflow impingement of a slot jet. In one set of experiments, the symmetry plane of the jet was aligned with the axis of the cylinder, while in other experiments the jet was offset from the cylinder. In addition to the offset, parametric variations were also made for the width of the jet-inducing slot, the distance between the slot and the cylinder, and the Reynolds number. Supplementary flow visualization experiments showed that even in the presence of offset, the jet impinged on the cylinder, although not at the cylinder apex as in the aligned case. It was found that the heat transfer coefficient increased with slot width and Reynolds number but decreased with slot-to-cylinder separation distance and offset. The effect of offset is accentuated for narrow slots and at small slot-to-cylinder separation distances. The largest measured offset-related reduction in the heat transfer coefficient was slightly in excess of 50%.