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.     

Laminar Flow and Heat Transfer Phenomena Across a Confined Semicircular Bluff Body at Low Reynolds Numbers

The present study is concerned with the simulation of incompressible Newtonian fluid flow and heat transfer over a long semicircular bluff body in a channel at low Reynolds numbers. In particular, wall effects on the forced convection from a (heated) semicircular cylinder confined in a horizontal channel are investigated for Reynolds number = 1–40 and blockage ratio = 16.67–50% for air as the working fluid. Flow and thermal fields are found steady for the preceding range of settings. The onset of flow separation increases as the wall confinement increases. The size of the recirculation zone downstream of a semicircular cylinder is seen to increase almost linearly with Reynolds number for a fixed blockage ratio, but it decreases with increasing blockage ratio for a fixed Reynolds number. As expected, total drag coefficient and its components decrease with increasing value of Reynolds number. However, with increasing blockage ratio, the values of these drag coefficients increase. On the basis of equal projected area, the total drag coefficient for the present flow system is found to be greater than the corresponding drag in the case of the unconfined semicircular cylinder. Similarly, the overall drag in the case of a confined semicircular cylinder is found to be greater than that of a confined circular cylinder for the appropriate range of dimensionless control parameters. The maximum augmentation in heat transfer for blockage ratios of 25% and 50% is found to be approximately 16% and 51% with respect to the corresponding value at the blockage ratio of 16.67% at Reynolds number = 1. Finally, the correlations of wake length, drag coefficient, and average Nusselt number are obtained.     

Convective Transport Around a Rotating Square Cylinder at Moderate Reynolds Numbers

Two-dimensional numerical simulation is performed to analyze the thermofluidic transport around a rotating square cylinder in an unconfined medium. The convective transport originates as a consequence of the interaction between a uniform free-stream flow and the flow evolving due to the rotation of the sharp-edged body. A finite volume-based method and a body-fitted grid system along with the moving boundaries are used to obtain the numerical solution of the incompressible Navier–Stokes and energy equations. The Reynolds number based on the free-stream flow is considered in the range 10 ≤ Re ≤ 200, and the dimensionless rotational speed of the cylinder is kept 0 ≤ Ω ≤ 5. Depending on the Reynolds number and the rotational speed of the cylinder, the transport characteristics change. For the range 10 ≤ Re < 50, the flow remains steady irrespective of the rotational speed. In the range 50 ≤ Re ≤ 200, regular low-frequency Kármán vortex shedding (VS) is observed up to a critical rate of rotation (Ω_cr ). Beyond Ω_cr , the global convective transport shows a steady nature. The rotating circular cylinder also shows likewise degeneration of Kármán VS at some critical rotational speed. However, the heat transfer behavior varies significantly with a rotating circular cylinder. Such thermofluidic transport around a spinning square in an unconfined free-stream flow is reported for the first time.     

低压涡轮低雷诺数条件下气动性能分析

对某型航空发动机低压涡轮末级进行了数值计算,对比分析了不同雷诺数条件下该级涡轮的气动性能。通过计算分析低雷诺数条件对压力场和损失系数的影响,可以看出,与高雷诺数条件相比,在低雷诺数条件下,低压涡轮效率明显降低,损失增大,扩压段增加,横向压力梯度增加,附面层增厚。雷诺数的降低,导致黏性力增加,在静叶片吸力面出现分离区,而且随着雷诺数的降低,分离区加大。     

Wall‐Confined Flow and Heat Transfer Around a Square Cylinder at Low Reynolds and Hartmann Numbers

This article discusses the results obtained through a two‐dimensional numerical simulation following a finite volume approach on the forced convection heat transfer for the hydromagnetic flow around a square cylinder at low Reynolds and Hartmann numbers. The magnetohydrodynamic (MHD) flow of a viscous incompressible and electrically conducting fluid is assumed to take place in a rectangular channel subjected to externally imposed magnetic fields and the cylinder is fixed within the channel. The magnetic fields may be applied either along the streamwise or transverse directions. Simulations are performed for the range of kinetic Reynolds number 10 ≤ Re ≤ 60 with Hartmann number 0 ≤ Ha ≤ 15 and for different thermal Prandtl numbers, Pr = 0.02 (liquid metal), 0.71 (air), and 7 (water) for a blockage ratio β = 0.25. A steady flow can be expected for the above range of conditions. Besides the channel wall, the magnetic field imparts additional stability to the flow as a consequence of which the recirculation region behind the obstacle reduces with increasing magnetic field strength for a particular Re. The critical Hartmann numbers for the complete suppression of flow separation in the case of a transversely applied magnetic field are computed. The rate of heat transfer is found almost invariant at low Re whereas it increases moderately for higher Re with the applied magnetic field. The heat transfer increases in general with the Reynolds number for all Hartmann numbers. Finally, the influence of obstacle shape on the thermohydrodynamic quantities is noted. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 459–475, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21091     

较大雷诺数下方柱绕流的数值模拟

基于k-ω SST模型和γ-Re_θ转捩模型,分析了雷诺数为1.4×10~4和2.2×10~4时二维方柱的流场特征,计算方柱的阻力系数和斯特劳哈尔数Sr,并对方柱平均流场的速度剖面进行分析,综合考虑不同湍流模型的计算成本及计算精度.结果表明:γ-Re_θ转捩模型比k-ω SST模型计算结果更加精确且所需计算成本较小;γ-Re_θ转捩模型能较好地预测方柱尾缘近壁回流区的位置和大小,且能较好地观测流场在方柱尾缘的再附着现象;在求解实际大雷诺数工程问题中γ-Re_θ转捩模型为优秀的湍流模型.     

Cooled Vortex Street Generated by Cooling a Cylinder at Low Reynolds Number: Effects of Reynolds Number Difference on Cooled Wake and Cooled Vortex Street

First, the dominant action in the cooled wakes in mercury and water at the Reynolds number Re = 22 and 44 is discussed. Next, the cooled wake at Re = 22 is numerically simulated and is compared with the previous results at Re = 44. Finally, effects of Re on the cooled wake and the cooled vortex street are elucidated, and are found to be extremely powerful as follows.

• 1. The dominant action can be determined at different fluids and different Re. Here, the vorticity and the temperature are relating with each other.

• a. “Table of diffusion intensity order” is invented. By obtaining and using this table, the dominant action can be determined automatically.

• b. The kinds of the dominant action are the advection and the diffusion in the vorticity and the temperature.

• c. In mercury and water at Re = 44 and 22, the dominant action is the vorticity diffusion at the low Re, the vorticity advection at the high Re, the temperature diffusion at the low Peclet number Pe, and the temperature advection at the high Pe.

• d. The dominant action in air at Re = 44 is between the dominant action in mercury and water at Re = 44. The dominant action in air at Re = 22 is the same as the dominant action in mercury at Re = 22.

• e. By using the dominant action, the wake variations and item 2 below, i.e., the characteristics of the cooled wake behavior, can be explained.

• 2. When Re is decreased, the following occurs and its cause is elucidated.

• f. In the cooled wake, the Karman vortex street does not occur, but the cooled vortex street with g below occurs.

• g. The vortex spiral size is not changed in mercury but is increased in water.

• h. The following is decreased in mercury but is increased in water. The range of the absolute Richardson number|Ri|generating the cooled vortex street, the spiral degree in the cooled vortex, the critical|Ri| for the symmetric wake onset, and the reciprocal of the temperature wake area.

     

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.     

Effect of Side Ratio and Aiding/Opposing Buoyancy on the Aerodynamic and Heat Transfer Characteristics around a Rectangular Cylinder at Low Reynolds Numbers

A numerical investigation is carried out to understand the effect of side ratio, as well as aiding/opposing buoyancy on the aerodynamic and heat transfer characteristics around a rectangular cylinder in the vertical unconfined configuration. The representative vortex structures and isotherms patterns are presented and discussed. A correlation between the critical Richardson number for the buoyancy-induced breakdown of Kármán vortex street and the side ratio of the cylinder is obtained. The influence of side ratio and buoyancy on Strouhal number, drag and lift coefficient, the recirculation length, and heat transfer from the cylinder is also investigated.     

Numerical Investigation of the Air-Side Thermal Hydraulic Performance of a Louvered-Fin and Flat-Tube Heat Exchanger at Low Reynolds Numbers

In this study, the air-side heat transfer and fluid flow characteristics of a louvered-fin and flat-tube type heat exchanger used in the household refrigerators were investigated numerically. Louver angles of 20°, 24°, 28°, and 32° and fin pitches of 1.50, 2.00, and 2.50 mm were tested. To represent domestic refrigeration systems, the simulations were conducted for low Reynolds numbers, between 223 and 573. The results were evaluated using the volume goodness factor for the air side. The best performance was obtained with louver angle of 20° and fin pitch of 1.50 mm at Reynolds number of 229 over the investigated cases. It was demonstrated that the Colburn j-factor, friction factor, Stanton number, and volume goodness factor did not change linearly with respect to the parameters considered.     

Heat-Mass Transfer and Friction Characteristics of Profiled Pins at Low Reynolds Numbers in Minichannels

Three pin fin array geometries (T60, T90, and T120) are investigated at low Reynolds numbers, Re _D  < 350, in a channel. The number in T60, T90, and T120 denotes the angle made by the pin surface with the end wall. Results show that the T120 pin is the most effective in facilitating momentum transport along the height of the pin and mitigates the undesired effect of low momentum and recirculating wakes. Additionally, pin T120 causes localized flow acceleration between pins near the end wall, which results in high heat transfer coefficients at the end wall. Overall, T120 has the highest heat transfer (augmentation ratio 2.9 at Re _D  = 325), without any increase in friction factor (augmentation ratio 8.3 at Re _D  = 325) from the baseline configuration of T90. However, T120 results in a large reduction in end-wall surface area, which reduces overall conductance, and in this respect T60 is superior in the range Re _D  < 150. A performance study of conductance under the constraint of the same pumping power in an equivalent plane channel shows that the profiled geometries T60 and T120 augment conductance between 40% and 250% over an equivalent channel.     

Unsteady Forced Convection Heat Transfer Over a Semicircular Cylinder at Low Reynolds Numbers

An unsteady two-dimensional numerical simulation is performed to investigate the laminar forced convection heat transfer for flow past a semicircular cylinder in an unconfined medium. The Reynolds number considered in this study ranges from 50 to 150 with a fixed Prandtl number (Pr = 0.71). Two different configurations of the semicircular cylinder are considered; one when the curved surface facing the flow and the other when the flat surface facing the flow. Fictitious confining boundaries are chosen on the lateral sides of the computational domain that makes the blockage ratio B = 5% in order to make the problem computationally feasible. A finite volume-based technique is used for the numerical computation. 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. Substantial differences in the global flow and heat transfer quantities are observed for the two different configurations of the obstacle chosen in the study. It is observed that the heat transfer rate is enhanced substantially when the curved surface is facing the flow in comparison to the case when the flat surface is facing the flow.     

Mixed Convection Heat Transfer From an Equilateral Triangular Cylinder in Cross Flow at Low Reynolds Numbers

A two-dimensional numerical study is undertaken to investigate the influences of cross buoyancy on the vortex shedding phenomena behind a long heated equilateral triangular cylinder for the low-Reynolds-number laminar regime. The flow is considered in an unbounded medium; however, fictitious confining boundaries are chosen on the lateral sides to make the problem computationally feasible. Numerical calculations are performed by using a finite-volume method based on the pressure-implicit with splitting of operators algorithm in a collocated grid system. The range of Reynolds number is chosen to be 10–100 with a fixed Prandtl number, 0.71. The mixed convection effect is studied for the Richardson number range of 0–1. The effects of superimposed thermal buoyancy on flow and isotherm patterns are presented and discussed. The global flow and heat transfer quantities such as the overall drag and lift coefficients, local and surface average Nusselt numbers, and Strouhal number are calculated and discussed for various Reynolds and Richardson numbers.     

Mixed Convection Heat Transfer from Tandem Square Cylinders in a Vertical Channel at Low Reynolds Numbers

The fluid flow and heat transfer characteristics around two isothermal square cylinders arranged in a tandem configuration with respect to the incoming flow within an insulated vertical channel at low Reynolds number range (1 ≤ Re ≤ 30) are estimated in this article. Spacing between the cylinders (S) is fixed at four widths of the cylinder dimension (d) and, the blockage parameter (B) is set to 0.25. The buoyancy-aided/opposed convection is examined for the Richardson number (Ri) ranges from ?1 to 1 with a fixed Prandtl number (Pr) of 0.7. The transient numerical simulation for this two-dimensional, incompressible, laminar flow and heat transfer problem is carried out by a finite volume code based on the PISO algorithm in a collocated grid system. The results suggest that the flow remains steady for the entire range of parameters chosen in this study. The representative streamlines, vorticity, and isotherm patterns are presented to interpret the flow and thermal transport visualization. Additionally, the time average drag coefficient (C _D ) as well as time and surface average Nusselt number (Nu) for the upstream and downstream cylinders are determined to elucidate the effects of Re and Ri on flow and heat transfer phenomena.     

Numerical Computation of a New Vortex (A Cooled Vortex Street) and its Generation Mechanism in a Cooled Circular Cylinder Wake at Low Reynolds Number

A strongly cooled, circular cylinder wake with an upward main stream of air at low Reynolds number Re, i.e., 15 ≦ Re ≦ 44, is analyzed numerically, and is elucidated as follows. (1) A new vortex street, i.e., a “cooled vortex street,” is discovered, develops in the range of computed Re, i.e., 15 ≦ Re ≦ 44, has strong asymmetry, and is extremely different from the Karman vortex. (2) The vortex street occurring in the cooled wake is either the Karman vortex street or the cooled vortex street. No vortex street except these vortex streets ever occurs in a wake. (3) The critical Reynolds number Re_c, i.e., the minimum Re occurring in the Karman vortex street by cooling a cylinder, is nearly 24. When the isothermal wake is cooled weakly, the Karman vortex street certainly develops at Re > 24, but never occurs at any cooling rate at Re < 24.

The generation mechanism of the cooled vortex street is elucidated by employing the computed vorticity and temperature distributions as follows. (1) With an extreme increase in the cooling rate, the wake vorticity is generated strongly by the temperature gradient, the absolute value of vorticity in shear layers becomes extremely large, and the shear layers are elongated remarkably. The angle between shear layers and the wake width increase remarkably. (2) As a result, shear layers roll up considerably, and their tips reach the midplane alternately. Extremely large-scale vorticity-concentrated tips are generated, and move to the downstream. Thus a stable wake, i.e., the cooled vortex street, is generated. That is, the stable rolling of shear layers is realized only in the Karman and the cooled vortex streets.     

Heat Transfer from Confined Contaminated Bubbles to Power‐Law Liquids at Low to Moderate Reynolds and Prandtl Numbers

In this work combined effects of the wall confinement and the power‐law fluid viscosity on the heat transfer phenomena of contaminated bubbles are reported through numerical investigations. In order to delineate the effect of insoluble surfactants the spherical stagnant cap model is adopted. The solver is thoroughly validated by comparing the present results with their literature counterparts. Further, extensive new results are reported on the isotherm contours and average Nusselt numbers of confined contaminated bubbles in the range of conditions: Reynolds number, Re: 0.1 to 200; Prandtl number, Pr: 1 to 1000; power‐law index, n: 0.2 to 1.6 and stagnant cap angle, α: 0 to 180°. Briefly, results are indicative of the following observations. The temperature contours are increasingly sucked towards the rear end of the bubble with the increase in Reynolds number and/or with the increase in Prandtl number and/or with the decrease in power‐law index and/or with the decrease in stagnant cap angle. At Re ≤ 1 and Pr ≤ 10, the average Nusselt number is almost independent of power‐law indices and the stagnant cap angle. For Pe > 10, regardless of values of the confinement ratio and Reynolds number, for α ≥ 60 the average Nusselt number decreases with an increasing stagnant cap angle whereas for α < 60 the effect of contamination is found to be insignificant. The increase in the average Nusselt number with an increasing confinement ratio would occur only at moderate to large values of Reynolds and Prandtl numbers regardless of the values of the power‐law index provided that α ≥ 60°.     

Heat Transfer in High Moisture Content Gas Flow Across a Cylinder at Moderate Reynolds Numbers

The average Nusselt number for the flow of a mixture of air and vapor across a tube was measured at moderate Reynolds numbers (2000–7000) for temperatures from 300 to 700°C and for humidity ratios from 0.22–0.54. Results are also presented for flow over a set of three tubes aligned perpendicular to the flow for the same range of conditions. The effects of humidity ratio and temperature on the convection coefficients were investigated to develop a modified Nusselt number correlation describing the heat transfer over the tubes. The results showed that the Nusselt number increased as the humidity ratio increased and that the increase was more than could be accounted for by typical models for the property variations of mixtures. The Nusselt number data were correlated with an equation that included both a Prandtl number ratio and a thermal conductivity ratio to correlate the multiple property variations due to both the large temperature variations and the large humidity variations. The exponent of the thermal conductivity ratio used in the modified correlation to correlate the additional effects of the property variations due to the large humidity variations was 0.073 for the entire data set, indicating the importance of the property variation due to the moisture content.     

Convective Transport Around Rows of Square Cylinders Arranged in a Staggered Fashion at Moderate Reynolds Number

The thermohydrodynamic interactions among multiple bodies fixed in an incident flow are analyzed through two-dimensional numerical computation. The bodies are identical in shape and size with square cross section and arranged in two rows in a staggered fashion within an unconfined domain. Simulation is carried out using a finite-volume-based method considering a uniform cross flow of air (Prandtl number, Pr =0.71) at a moderate Reynolds number (Re = 100). Apart from the Reynolds number, certain geometrical parameters such as the streamwise and transverse spacing of the objects may significantly influence the wake dynamics, vortex structure formation, and the associated thermal transport. Accordingly, both the dimensionless transverse spacing (S/d = 1, 3, and 5, with S and d the transverse spacing and cylinder size, respectively) and the nondimensional streamwise gap (L/d = 1, 3, and 5, with L being the streamwise gap) are varied to elucidate their roles in controlling the hydrodynamic and thermal transport. Even at such a moderate Reynolds number, the flow and thermal fields show chaotic behavior at smaller transverse spacing, this behavior being established through various chaos characterization tools. However, at larger spacing, the usual unsteady vortex dynamics persists. Shedding in the gap is inhibited at smaller streamwise spacing. Again, at larger spacing, the normal shedding characteristics continue. Average heat transfer from the cylinders is higher at smaller streamwise and transverse spacing.     

Numerical Study of Sphere Drag Coefficient in Turbulent Flow at Low Reynolds Number

The drag coefficient of a sphere immersed in turbulent air flow in the Reynolds number (Re = U _∞ d/ν _∞) range up to 250 and turbulence intensity (u _∞′/U _∞) up to 60% is computed numerically. Reynolds-averaged Navier-Stokes equations (RANS) are solved in Cartesian coordinates by using a blocked-off technique. To our knowledge, the present work is the first to employ the blocked-off technique for flow over a sphere. Closure for the turbulence stress term is accomplished by testing four different turbulence closure models. The main findings of the present investigation are that the laminar numerical data compare well with numerical and experimental published work. However, different turbulence closure models produce different trends in the range of Reynolds number up to Re = 100, and this difference is demarcated by the nonagreement between the turbulent predictions and the “standard” drag coefficient results. However, the results obtained using Menter's SST turbulence model show fair agreement with the well-known sphere “standard” drag over the range of test conditions explored here. Thus, the present results confirm recently published findings, which suggest that the free-stream turbulence intensity does not have a significant effect on the sphere mean drag.     

Steady Conjugate Heat Transfer from X-Ray or Laser-Heated Sphere in External Flow at Low Reynolds Number

ABSTRACT

A laser or an X-ray beam is used to heat a sphere that is immersed in uniform external flow. Temperature distributions as well as local and average convective heat transfer coefficients are calculated in order to evaluate the efficacy of cooling the solid sphere. The present work extends previous studies by: (1) applying a unique heat source imposed by irradiating the sphere with an intense X-ray energy beam; (2) performing the conjugate heat transfer analysis in fluid and solid domain; and (3) calculating the internal and surface temperature distribution. Absorption of the irradiation results in nonuniform heat generation, having an exponential spatial distribution of heat source. The limiting cases of heat source distribution are localized surface “laser” heating and near-uniform heat generation throughout the sphere. Key results are reported for two different source beam sizes (small and large) striking the sphere, with comparison to the solution for the isothermal wall boundary condition.