Numerical Investigation of Flow and Heat Transfer Characteristics of Two Tandem Circular Cylinders of Different Diameters

Unsteady laminar flow and heat transfer characteristics from a downstream cylinder of two tandem circular cylinders of different in diameters are numerically investigated. The working fluid is air, and the downstream cylinder is isothermal while the upstream cylinder is kept adiabatic. Two-dimensional numerical simulations are carried out for Reynolds numbers of 100 and 200. The ratio of the upstream to downstream cylinder diameters (diameter ratio) and the ratio of the gap distance to the downstream cylinder diameter (gap ratio) are considered in the range of 0.3 to 2 and 0.5 to 4, respectively. Numerical solutions are obtained using the FLUENT® software. The flow parameters such as the rms lift/drag coefficients and Strouhal numbers are computed and analyzed for the diameter ratio and gap ratio intervals investigated. The iso-vorticity lines and isotherms are also generated to understand, identify and analyze the flow and heat transport characteristics. Four basic flow structures are observed and classified as (i) over-shoot, (ii) symmetric-reattachment, (iii) front-side reattachment and (iv) co-shedding flow. The critical spacing, which marks the minimum gap spacing for the vortex formation to begin, depends on the diameter ratio and Reynolds number, and it decreases with increasing Reynolds number. The convective heat transfer phenomenon is observed to be strongly influenced by diameter ratio, gap ratio and Reynolds number. The mean and the local Nusselt number along the perimeter of isothermal cylinder are computed and discussed in connection with the flow characteristics.     

A Numerical Study of Fluid Flow and Heat Transfer around a Square Cylinder at Incidence using Unstructured Grids

A numerical investigation of flow and heat transfer around a square cylinder at incidence (α = 0° ? 45°) is presented for a range of Reynolds numbers ( Re = 60 ? 150). A finite-volume code suitable for unstructured grids has been developed to simulate the flow. The unstructured grid has been generated using the Delaunay triangulation algorithm. A modified pressure-velocity correction scheme with semi-explicit time-stepping is implemented to solve the Navier-Stokes equations. Collocated grid arrangement has been used for the dependent variables. Convective terms have been discretized using a second order upwind least squares scheme. The formation of Karman vortex street has been captured and the Strouhal number associated with the wake has been determined. The dependence of Strouhal number, force coefficients (drag and lift), moment coefficient and average Nusselt number on Reynolds number, and angle of incidence for a fixed blockage ratio has been reported and analyzed.     

低雷诺数下不同顶角三棱柱体绕流受力和尾涡脱落机制

为研究三棱柱体绕流特性,采用直接数值模拟方法,对雷诺数为100时顶角为15°~165°的三棱柱的二维绕流问题进行了数值模拟,并与经典的圆柱绕流进行对比分析。结果表明,随着顶角度数的增大,三棱柱体受到的时均阻力不断增大,而升力均方值先增大后减小,在顶角为60°时达到最大值(0.31);随着顶角度数的增大,尾涡强度逐渐增大,泄涡频率先增大后减小,在顶角为60°时,泄涡频率最大;前尾涡脱落产生的中心点与鞍点随新尾涡的产生依次消失,而新的尾涡的中心点与鞍点同时逐渐形成。     

Investigation of gas-solid two-phase flow across circular cylinders with discrete vortex method

In present paper, a Lagrangian–Lagrangian model is proposed to study gas-solid two-phase flow across single cylinder and two tandem cylinders at high Reynolds number. In this model, the single-phase flow is simulated by discrete vortex method and the particle trajectories are tracked by particle motion equation. A sub-cycle is introduced to adjust time-step in the particle collision model, through which the simulation of two phases is coupled. Validated by the comparison of the particle trajectory in Rankine vortex with literature, this model is used to study single-phase flow across single cylinder and cylinders with different arrangements firstly to get transient flow field and drag coefficients. Then, gas-solid two-phase flow across cylinders with different arrangement is studied and particle distribution is obtained under different Stokes number for horizontal and vertical particle transport cases. The settlement, entrainment and aggregation of solid particles moving with the large-scale coherent vortex structure in the wake of single cylinder and between two cylinders are numerically investigated, and the effects of St number on the distribution of solid particles are obtained.     

Triggering Vortex Shedding by Superimposed Thermal Buoyancy Around Bluff Obstacles in Cross-Flow at Low Reynolds Numbers

Influences of superimposed thermal buoyancy on the initiation of vortex shedding process behind bluff obstacles (such as circular and square cylinders in 2-D) in cross-flow at low Reynolds numbers (10 ≤ Re ≤ 40) are discussed. The flow which is steady and separated at this Reynolds number range eventually becomes unsteady periodic with the introduction of thermal buoyancy. The aim here is to numerically predict the critical value of the buoyancy parameter (Richardson number, Ri) for the onset of vortex shedding. The critical Ri is found to have a decreasing tendency for both types of cylinder geometries with increasing Re.     

Numerical/experimental investigations on reducing drag penalty of passive vortex generators on a NACA 4415 airfoil

A study emphasizing the effects of passive vortex generators (VGs) on aerodynamic characteristics of a NACA 4415 airfoil is presented. Both experimental and numerical works have been carried out on an array of VGs attached to a NACA 4415 airfoil. Lift and drag measurements are made at various angles of attack by using three‐axis component balance system. On the numerical side, Reynolds‐averaged Navier‐Stokes (RANS) equations have been solved with ANSYS FLUENT 14.5 commercial code with fully structured mesh and three turbulence models (realizable k‐ε, k‐ω shear stress transport [SST] and the Spalart‐Allmaras model) at Reynolds number Re = 2 × 10⁵. Parametric studies have been conducted to find out optimal configurations with respect to span‐wise separation distance between VGs, along with their location along the chord. A very good agreement has been obtained between experimental and computational results indicating that this optimized configuration is robust for the considered parameters. It turns out that increasing the span‐wise separation length increases the aerodynamic performances (lift‐to‐drag ratio) at low attack angles for which low parasitic drag is achieved but conversely degrades it at higher ones. For the stream‐wise location along the chord, upstream position of VGs degrades the lift‐to‐drag ratio at low attack angles and conversely improves it at higher ones.     

Effect of Thermal Buoyancy on Fluid Flow and Heat Transfer Across a Semicircular Cylinder in Cross-Flow at Low Reynolds Numbers

The influence of superimposed thermal buoyancy on hydrodynamic and thermal transport across a semicircular cylinder is investigated through numerical simulation. The cylinder is fixed in an unconfined medium and interacted with an incompressible and uniform incoming flow. Two different orientations of the cylinder are considered: one when the curved surface is exposed to the incoming flow and the other when the flat surface is facing the flow. The flow Reynolds number is varied from 50 to 150, keeping the Prandtl number fixed (Pr = 0.71). The effect of superimposed thermal buoyancy is brought about by varying the Richardson number in the range 0 ≤ Ri ≤ 2. The unsteady two-dimensional governing equations are solved by deploying a finite volume method based on the PISO (Pressure Implicit with Splitting of Operator) algorithm. The flow and heat transfer characteristics are analyzed with the streamline and isotherm patterns at various Reynolds and Richardson numbers. The dimensionless frequency of vortex shedding (Strouhal number), drag, lift and pressure coefficients, and Nusselt numbers are presented and discussed. Substantial differences in the global flow and heat transfer quantities are observed for the two different configurations of the obstacle chosen in the study. Additionally, intriguing effects of thermal buoyancy can be witnessed. It is established that heat transfer rate differs significantly under the superimposed thermal buoyancy condition for the two different orientations of the obstacle.     

Momentum and Heat Transfer Characteristics for the Flow of Power-Law Fluids over a Semicircular Cylinder

In this study, the two-dimensional steady flow of power-law fluids past a semicircular cylinder (flat face oriented upstream) has been investigated numerically. The governing equations (continuity, momentum, and energy) have been solved in the steady symmetric flow regime over the range of the Reynolds number (0.01 ≤ Re ≤ 25), power-law index (0.2 ≤ n ≤ 1.8), and Prandtl number (0.72 ≤ Pr ≤ 100). Extensive new results reported here endeavor to elucidate the role of power-law index (0.2 ≤ n ≤ 1.8) on the critical Reynolds number denoting the onset of flow separation (Re ^c ) and of vortex shedding (Re _c ). In shear-thinning fluids, both of these transitions are seen to be delayed than that in Newtonian and shear-thickening fluids. Furthermore, the influence of the Reynolds and Prandtl numbers, power-law index on drag phenomenon, and heat characteristics of semicircular cylinder have been studied in the steady flow regime. Finally, the present numerical values of the critical Reynolds numbers and the average Nusselt number have been correlated by simple forms which are convenient for interpolating these results for the intermediate values of the governing parameters in a new application.     

The Effects of Reynolds and Prandtl Numbers on Flow and Heat Transfer Across Tandem Square Cylinders in the Steady Flow Regime

The effects of Reynolds and Prandtl numbers on the fluid flow and heat transfer characteristics over two equal isothermal square cylinders placed in a tandem arrangement in cross flow have been investigated in this article. The spacing between the cylinders is fixed with four widths of the cylinder. The numerical results are presented for the range of conditions as 1 ≤ Re ≤ 30 and 0.7 ≤ Pr ≤ 1000 for three different blockage parameters B = 0.05, 0.25, and 0.5. Numerical simulations are performed with a finite volume code based on the PISO algorithm in a collocated grid system. The representative streamlines and isotherm patterns are presented and discussed. In addition, the overall drag coefficient and average Nusselt number are determined to elucidate the role of Reynolds and Prandtl numbers on flow and heat transfer. It is found that the flow is completely steady for the chosen ranges of the parameters.     

An Experimental Study of the Drag Force on a Cylinder Exposed to an Argon Thermal Plasma Cross Flow

Experimental data are presented concerning the drag force on a cylinder exposed to an argon plasma cross flow with temperatures about 10~4 K and velocities about 10~2m/s. Using a method of sweeping a cylindrical probe across an argon plasma jet, the total drag force on the cylinder can be measured as a function of the lateral distance of cylindrical probe with respect to the plasma-jet axis. Through the Abel inversion, the drag force for per unit of cylinder length and thus the drag coefficient of cylinder have been measured under plasma conditions and compared with the values obtained from the standard drag curve of the cylinder in an isothermal flow. Experimental results show that the measured drag forces are always less than their counterparts read from the standard drag curve with the same Reynolds numbers based on the oncoming plasma properties. The drag force on the cylinder exoposed to a thermal plasma flow is shown to be approximately proportional to the square root of cylinder diameter in the present experiment and it increases slightly with increasing surface temperature of the cylinder. It is also shown that applying a voltage between the drag probe and the anode of the plasma jet generator has little effect on the drag force of cylinder under the experimental conditions. The drag force on a cylinder with finite length exposed to an argon plasma with the axis parallel to the plasma jet is independent of ratio of cylinder length to its dismeter L/d for the cases when L/d≤1.     

Experimental and computational analysis of stall cells on rectangular wings

The present paper is the second part of a combined (experimental and computational) study on stall cells (SCs) on a rectangular wing. In the first part, tuft data were used in order to geometrically characterize a stabilized SC resulting from a localized spanwise disturbance introduced by a zigzag tape. Here, pressure measurements on the model and in the wake and aerodynamic polars at midspan are reported. The wing model had an aspect ratio value of 2, the Reynolds number was 10⁶ and the range of angles of attack (α) was from ?6^° to 16^°. Experimental results confirm previous findings. Furthermore, two‐dimensional and three‐dimensional Reynolds Averaged Navier‐Stokes RANS simulations are used in order to better understand the structure of SCs. 3D simulations reproduce the experimental data with a 3° delay in α and permit a qualitative analysis. It is found that the SC vortices start normal to the wing surface and extend downstream in the wake; the evolution of the SC vortices in the wake is in strong interaction with the separation line vortex and the trailing edge line vortex; as the SC vortex develops downstream in the wake, its centreline is contracted towards the SC centre; the wing wake is pushed upstream at the centre of the SC and downstream at the sides by the SC vortices; spanwise lift and drag distributions always attain their minimum at the SC centre. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimization of the angle of attack of delta-winglet vortex generators in a plate-fin-and-tube heat exchanger

Delta-winglet vortex generators (VGs) are known to enhance the heat transfer between the energy-carrying fluid and the heat transfer surfaces in plate-fin-and-tube banks. In this study optimal angles of attack of the delta-winglets are investigated based on the Pareto optimal strategy. The optimization process combines a CFD analysis, genetic algorithms and the response surface methodology. The angle of attack of a pair a delta-winglet-type VGs mounted behind each tube is varied between β = ?90° and +90°. Three circular tube rows with inline and staggered tube arrangements are investigated for Reynolds numbers from 200 to 1200 (based on the inlet height and inlet velocity). The flow structure and heat transfer behavior is analyzed in detail for certain cases and the staggered and the inline tube arrangements are compared. Finally, for each of these arrangements the optimal sets of angles of attack for different Reynolds numbers are presented.     

大尺度展向波形圆柱绕流流场结构的数值研究

针对大尺度展向波形圆柱绕流的减阻特性，通过大涡模拟（LES）研究波形振幅对圆柱体绕流流场结构的影响，获得波形圆柱体绕流气动性能曲线、尾迹时均流速分布和非定常涡量场分布，最后与直圆柱绕流的流场结构进行对比分析。结果表明，波形圆柱绕流的平均阻力系数小于直圆柱体绕流，流向涡的形成改变了圆柱近尾迹区的流场结构，因此，波形圆柱体尾迹涡系表现得更为紧凑，尾迹涡流得到拉伸与破裂。在亚临界雷诺数为3000时，最大阻力系数减少18.3%，最优振幅比为0.152；且波形圆柱体的升力波动大大减少，甚至得到抑制。由于波形表面会形成更稳定的三维自由剪切层，这样的自由剪切层在下游位置卷起漩涡，大大地改变了圆柱周围的流场结构。研究表明振幅比在确定波形圆柱后面的三维涡旋结构中起着至关重要的作用，并对升力波动和流动阻力的降低有着显著的影响。     

Power‐law flow and heat transfer over an inclined square bluff body: effect of blockage ratio

Flow and heat transfer of non‐Newtonian power‐law fluids over an inclined square cylinder placed inside a channel are studied numerically at low Reynolds numbers. In particular, calculations are carried out for Reynolds number (Re) = 1–40; power‐law index (n) = 0.4–1 and blockage ratio (β) = 12.5–50% at a Prandtl number (Pr) = 50. An increase in blockage ratio results in an increase in the total drag coefficient and decrease in the wake length. The Strouhal number and the root mean square value of the lift coefficient increase with the increasing Reynolds number for the fixed values of blockage ratio and power‐law index. The average Nusselt number increases with power‐law index and/or blockage ratio. The maximum enhancement in heat transfer is approximately 49, 41, and 35% for the values of blockages of 50, 25, and 12.5%, respectively, as compared to the corresponding Newtonian value. The average Nusselt number for the inclined square cylinder (at α = 45^°) is always greater than the average Nusselt number for the regular square cylinder (at α = 0). Finally, simple expressions of drag and Nusselt number have been established for the above range of settings. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 167‐196, 2014; Published online 20 June 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21071     

Airfoil wind tunnel correction for angles of attack from −180° to 180°

Wind tunnel corrections are investigated for two‐dimensional low‐speed wind tunnel tests that are performed for three similar airfoils for angles of attack ranging from ?180° to 180° at Re = 0.75 × 10⁶. Aided by the Blasius theorem, wind tunnel corrections are deduced for the lift, drag and pitching moment of the airfoil at high angles of attack. The wall pressure signature method is applied to determine the strengths of the equivalent singularities. The tunnel wall‐induced force and pitching moment are obtained by calculating the force and moment exerted on the equivalent singularities. The maximum correction for drag is determined to be about 50%. The corrected forces and pitching moments for three similar airfoils are coincident with one another. A method to determine an optimum singularities distribution range is presented. The results indicate that the correction method in the paper is effective for airfoil testing at high angles of attack. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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

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

Mixed Convection Heat Transfer from an In-Line Row of Square Cylinders in Cross-Flow at Low Reynolds Number

This article presents a two-dimensional numerical study on the unsteady laminar mixed convection heat transfer from a row of five in-line isothermal square cylinders placed in an unconfined medium and subjected to cross-flow of a Newtonian fluid at low Reynolds number (Re = 125). The hydrodynamic and thermal transport phenomena are captured for the separation ratios (spacing to cylinder size ratio, s/d) of 0.5, 1, 1.5, 2, 3, and 4. The mixed convection heat transfer is studied for Richardson numbers (Ri) ranging from 0 to 3 with a fixed Prandtl number (Pr = 0.71). Numerical calculations are performed by using a PISO algorithm-based finite volume solver in a collocated grid system. The instantaneous vorticity fields along with the isotherm patterns are systematically presented and discussed for different separation ratios and Richardson numbers. Depending on the engineering application, the temperature difference between the surface and the free stream could vary to make buoyancy of primary importance, entailing major modification of the flow field. Additionally, the instantaneous and mean drag and lift coefficients, Strouhal numbers, and mean Nusselt numbers are determined and discussed.     

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

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

Computational study of thermal buoyancy from two confined cylinders within a square enclosure wifth single inlet and outlet ports

This article is devoted to investigating the mixed convection arising from two equally hot circular cylinders embedded in a square cavity of adiabatic surfaces. This cavity is filled with an incompressible fluid and contains single entry and outlet orifices. The heated cylinders are assumed to be arranged side-by-side with a fixed gap within the square cavity. Based on some simplifying assumptions, the nonlinear governing equations that express the principle of conservation of mass, momentum, and energy are obtained and numerically solved using a Computational fluid dynamics package ANSYS-CFX with finite volume technique. Pertinent results showing the roles of embedded parameters such as Richardson number (Ri = 0 to 1) and Reynolds number (Re = 1 to 40) at Prandtl number (Pr = 1) on the overall fluid flow and temperature patterns are graphically depicted in the form of representative streamlines and isotherms. The values of average Nusselt number and total drag coefficient (C_D) for both representative cylinders are also computed and discussed. Generally, an increase in buoyancy force augments the effectiveness of heat transfer only of the down cylinder. Also, a rise in Re and/or Ri numbers augment the flow instability.