格子Boltzmann方法分析加热尺寸和瑞利数对可变形开口腔内自然对流的影响

采用格子Boltzmann方法对可变形腔体内自然对流问题进行数值研究，给出平均努赛尔数的经验关系式.腔体左壁加热长度分为左壁面的整个区域（H）和左壁面的中间区域（0.5H）两种情况，右壁向外界环境开放，上下边界绝热且可以上下移动，以此调节右出口尺寸.主要研究瑞利数（10⁴ ≤ Ra ≤ 10⁶），右出口尺寸（1.0H ≤ L ≤ 2.0H），左壁加热尺寸（L_h=0.5H或L_h=H）对腔体内等温线、流线、局部努塞尔数和平均努赛尔数的影响.结果表明：腔体内换热随着瑞利数的增大越来越强烈，表现为椭圆形准静止区域更加靠近上绝热壁，且热分层厚度逐渐变小，平均努赛尔数增加.而右出口尺寸的增加，对于两种加热尺寸下腔内的换热效果有不同程度影响，其中与加热尺寸为左壁面的全部区域L_h=H相比，加热尺寸为左壁面的中间情况L_h=0.5H时，右侧开口尺寸的增加对换热效果的影响不显著.此外，左壁加热尺寸为0.5H时显示出比加热尺寸为H时更高的平均传热效率.最后，针对不同的加热尺寸，提出加热面平均努赛尔数与Ra数及右壁面开口尺寸L^*之间函数关系的经验预测，拟合效果满足工程实践与设计需要.     

AN EMPIRICAL CORRELATION FOR NATURAL CONVECTION FROM CONFINED ELLIPTIC TUBE

An experimental study was conducted to obtain a correlation for free convection heat transfer from isothermal elliptic tubes of minor to major axis ratios of ∈ = 0.53, 0.67, 0.8, and 1 confined between two adiabatic walls. Local and average Nusselt numbers were determined for several different tube axis ratios, Rayleigh numbers, and wall spacings by means of the Mach-Zehnder Interferometery (MZI) technique. For each tube axis ratio, the Rayleigh number varied from 1,000–2,750 and the wall spacing to tube minor axis ratio from 1.25–∞. For all the tube axis ratios, the periphery and length of the tubes were kept constant. Experimental data are presented with a correlation which gives the average Nusselt number as a function of the tube axis ratio, Rayleigh number, and wall spacing to tube minor axis ratio. As the tube axis ratio decreases the average heat transfer coefficient increases. Also, for a constant Rayleigh number and tube axis ratio there is an optimum wall spacing which maximizes the heat transferred from the tube.     

Experimental Analysis of Gas Micro-Convection Through Commercial Microtubes

In this article, an experimental campaign devoted to analyzing the forced micro-convection features of heated gas flows through commercial stainless-steel microtubes having inner diameters of 172 μm and 750 μm is described. The experimental results obtained by heating the microtubes with an imposed uniform heat flux (H-boundary condition) at the external wall, in terms of Nusselt numbers, are compared to the predictions of the classical correlations validated for conventional pipes and to the correlations proposed for gas flows through microtubes under laminar and transitional conditions (100 < Re < 4,000). The cross-sections of the tested microtubes enabled the analysis of the effects of wall axial heat conduction on the Nusselt number. It was observed that the Nusselt number is strongly dependent on the Reynolds number in the laminar regime, and this fact is explained in the article with the effects of wall axial heat conduction and the difficulties in the experimental determination of the right exit bulk temperature of the gas flow, which cannot be ignored in the thermal analysis. The agreement between the Gnielinski correlation and the experimental Nusselt number is poor, especially for low Reynolds numbers, if one uses the average gas bulk temperature, obtained as the arithmetic mean between the inlet and outlet gas bulk temperature, in the definition of the experimental Nusselt number. On the contrary, the agreement with the Gnielinski correlation improves if the local wall-gas temperature difference near the exit of the microtube is used instead. The experimental results presented in the article demonstrate that the criteria for the design of accurate micro-convection tests can be quite different from those for the analysis of forced convection through conventional pipes.     

含不同形状内热源的圆管内纳米流体自然对流及换热数值研究

采用格子玻尔兹曼方法对有三种恒温热源（圆形、三角形、方形）参与的圆管内纳米流体（铜-水）自然对流进行数值研究。主要研究瑞利（Ra）数,纳米颗粒体积分数以及热源几何形状等控制参数对纳米流体的流动与传热的影响。结果发现纳米颗粒体积分数的增加有利于强化传热,且在Ra数较小时,平均努塞尔（Nu）数增加的幅度要优于Ra数较大的情况。在所研究的控制参数范围内,方形热源的平均Nu数最大。根据数值结果给出不同热源表面的平均Nu数、纳米颗粒体积分数、Ra数三者之间的函数关系式,该函数关系可为此类工程的设计提供理论指导。     

格子Boltzmann方法模拟填充纳米流体三角形腔内的自然对流

采用格子Boltzmann方法研究填充水-氧化铝纳米流体的等腰直角三角形腔体中的自然对流。讨论瑞利数、颗粒体积分数、热源位置等因素对对流换热的影响,以及不同纳米流体模型对模拟结果的影响。结果表明：在低瑞利数下,随着热源在左壁面向上移动,换热效率逐渐增加。而在高瑞利数（Ra=10⁶）时,观察到相反的现象;采用单相纳米流体模型,模拟表明热壁面平均努塞尔数比率随着体积分数的增加近似线性增加。采用改进的纳米流体模型,结果显示平均努塞尔数比率随着体积分数的增加而增大,但是平均努塞尔数比率的变化斜率逐渐减小。改进模型模拟的换热效率比单相模型高,这是因为改进模型考虑了粒子间作用力及换热,更符合实际情况。     

微针肋内潜热型功能热流体换热特性研究

引入潜热型功能热流体替换现有传统工质冷却大功率激光器,实验研究了潜热型功能热流体与传统工质去离子水在高4 mm、宽2 mm、间距1 mm的微针肋内的层流流动换热特性。结果表明:在雷诺数Re为625~1125范围内,潜热型功能热流体均表现出比水更好的冷却性能及更低的壁面温度,且存在最佳的质量分数值;相同工况下,潜热型功能热流体平均努谢尔数Nu大于去离子水,平均努谢尔数Nu随着雷诺数Re的增加而增加。拟合了平均努谢尔数与流体雷诺数、普朗特数、质量分数的经验的关系式,最大偏差为16.9%,可以较好反映潜热型功能热流体的换热特性;潜热型功能热流体沿着流动长度的方向存在一个稳定的局部换热强化区,且强化换热存在最佳的长度。     

单面加热方管混合对流换热特性实验研究

本文对单壁面加热水平方管通道内混合对流换热进行了实验研究,其中加热面分别为底面、侧面、顶面,Re=1514～3028,Gr~*=2.06×10~6～8.22×10~6;通过对加热面温度进行曲线拟合减小壁面温度测量误差,得到考虑轴向导热的局部Nusselt数的变化规律。实验结果表明侧面加热和底面加热时,局部Nusselt数要明显高于顶面加热的情况;局部Nusselt数在管道前段受Re的影响较大,在后段受Gr~*的影响较大。     

壁面轴向导热对微细管内对流换热的影响

本文通过数值解析的方法研究了考虑壁面轴向导热时微细管内的对流换热。结果表明,当管外为对流换热边界条件时,管内充分发展对流换热的Nu依然在3.66～4.36之间。但若忽略壁面轴向导热,采用一维热阻模型整理微细管内对流换热的实验数据将会导致错误的结论。     

An experimental study on convective heat transfer performance of steam and air flow in V-shaped rib roughened channels

An experimental study on heat transfer characteristics of steam and air flows in a V-shaped ribbed channels was conducted. The effects of Reynolds numbers and rib angles on heat transfer of steam and air were obtained. The area-averaged Nusselt numbers of steam flow at a Reynolds number of 12,000 were 13.9%, 20.6%, 27.1%, and 27.9% higher than those of air flow for rib angles of 90°, 75°, 60°, and 45°, respectively. The correlations for Nusselt number in terms of Reynolds number and rib angle for steam and air in V-shaped ribbed channels were developed.     

交叉三角形波纹板流道在过渡流状态下的传热与阻力特性

交叉三角形波纹板流道中流动常处于过渡态。本文研究了交叉波纹板中的周期性完全发展流动及热传递。利用周期性降低几何流道的复杂性以及简化模拟对象。为了模拟这个拓扑结构中的过渡流,利用了已经验证的低雷诺数k-ε,湍流模型来说明流动中的湍流流动。得到了三维复杂计算区的温度、速度以及湍流场。计算了在恒壁温和恒热流密度两种边界条件下的摩擦系数和平均Nusselt数及其与雷诺数的关系。湍流中心从上层壁面的波纹处移向下层壁面的波纹处并逐步增强。     

Natural Convection of Temperature-Sensitive Magnetic Fluids in Porous Media

In this article, natural convection of a temperature-sensitive magnetic fluid in a porous media is studied numerically by using lattice Boltzmann method. Results show that the heat transfer decreases when the ball numbers increase. When the magnetic field is increased, the heat transfer is enhanced; however, the average wall Nusselt number increases at small ball numbers but decreases at large ball numbers due to the induced flow being more likely confined near the bottom walls with a high number of obstacles.     

MHD natural convective flow through a porous medium in a square cavity filled with liquid gallium

This article contains a computational study of free convective flow through a square enclosure filled with liquid gallium saturated porous medium in the presence of a uniform inclined magnetic field. Lower boundary of enclosure is considered to be heated uniformly, upper horizontal boundary is taken insulated, left wall of the cavity is heated linearly, and right wall is heated linearly or taken cold. Navier–Stokes equations governing the flow problem are first exposed to penalty method to eliminate the pressure terms and then Galerkin FEM is employed to solve reduced equations. Grid independent results are achieved and shown in tabular form for numerous ranges of physical flow parameters. To ensure the accuracy of developed code, computed results are compared with those available in earlier studies through figures. It is found that the strength of streamlines circulation is increased due to increase in Darcy number while imposition of vertical magnetic field instead of horizontal magnetic field causes slow rate of increase in strength of streamlines circulation. Whereas, in the case of linearly heated right wall, the average Nusselt number is an increasing function of the Darcy number, and vertical magnetic field causes higher values for average Nusselt number as compared to horizontal magnetic field along bottom and side walls of cavity. Contrarily, in the case of cold right wall, the horizontal magnetic field results in higher values of average Nusselt number as compared to the vertical magnetic field case, and the average Nusselt number reduces as we move along lower and right boundary while increases along left wall with increase in distance.     

Laminar Heat Transfer Augmentation through A Square Duct and Circular Tube Fitted with Twisted Tapes

Experimental studies on friction factor and heat transfer characteristics for the laminar flow of ethylene glycol in a square duct fitted with twisted tapes of different twist ratios under nearly uniform wall temperature conditions are reported in this article. The Nusselt numbers were found to be 5.44–7.49 and 2.46–4.87 times that of plain square duct forced convection values based on constant flow rate and constant pumping power criteria, respectively, for y = 2.66. The augmented friction factor and Nusselt number for a square duct is about 1.9 and 2.10 times higher than that for an augmented circular tube.     

A numerical study of laminar natural convective heat transfer inside a closed cavity with different aspect ratio

Two-dimensional steady-state laminar natural convection was studied numerically for differentially heated air-filled closed cavity with adiabatic top and bottom walls. The temperature of the left heated wall and cooled right wall was assumed to be constant. The governing equations were iteratively solved using the control volume approach. In this paper, the effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively.Variations of the maximum stream function and the average heat transfer coefficient were also shown. The average Nusselt number and was correlated to the Rayleigh number based on curve fitting for each aspect ratio. The investigation covered the range 10⁴ ≤ RA ≤ 10⁷ and is done at Prandtl number equal to 0.693. The result shows the average Nusselt number is the increasing function of Rayleigh number. As the aspect ratio increases, Nusselt number decreases along the hot wall of the cavity. As Rayleigh number increases, Nusselt number increases. Result indicates that at constant aspect ratio, with increase in Rayleigh number the heat transfer rate increases.     

Experimental Investigation of Transient Forced Convection of Liquid Methane in a Channel at High Heat Flux Conditions

Transient heat transfer of liquid methane under forced convection in a 1.8 mm × 1.8 mm asymmetrically heated square channel was investigated. This study is aimed at understanding the heat transfer behavior of cryogenic propellant in cooling channels of a regeneratively cooled rocket engine at the start-up condition. To simulate high heat load conditions representative of regeneratively cooled rocket engines, a high heat flux test facility with cryogenic liquid handing capabilities was developed at the Center for Space Exploration Technology Research. The time history of inlet and outlet fluid temperatures and test section channel wall temperatures were measured at high heat flux conditions (from 1.19 to 3.80 MW/m²) and a Reynolds number (Re) range of 1.88 × 10⁵ to 3.45 × 10⁵. The measured wall temperature data point toward possible film boiling within the test section during certain tests, particularly with higher heat fluxes and lower Reynolds number conditions that resulted in higher wall temperatures. The transient average Nusselt numbers (Nu_L) of the channel obtained from the experimental measurements are lower than those calculated from the Sieder–Tate correlation (Nu_O); however, the ratio (Nu_L/Nu_O) increases with the increase in Reynolds number. The ratio is around 0.25 at the lower end of Re and then increases to 0.7 at the maximum Re studied in the present investigation.     

复合肋套管导热和对流耦合换热的数值模拟

在层流范围内,数值模拟了带均布纵肋同心套管内的三维导热和对流耦合换热。结果表明间壁温度沿管长变化 较大且分布呈非线性变化;在通道人口流体内部温度和速度分布呈现层流附面层特征,换热的入口段比例随Re增大而加 大,入口段换热的Nu也随Re增大而加大;换热的Nu随管长增加趋于不变。     

Lattice Boltzmann simulation of double diffusive natural convection in heterogeneously porous media of a fluid with temperature-dependent viscosity

Double diffusive natural convection inside a porous cavity with non-uniform porosity has been numerically studied. The cavity was filled with two parallel porous layers with different porosity. Considering the effects of temperature-dependent viscosity, simulations have been done via the Lattice Boltzmann method (LBM) at representative elementary volume (REV) scale. In this study, the effect of porosity, buoyancy ratio, the viscosity-variation number and thermal Rayleigh number on heat and mass transfer rates was investigated. The streamlines, isotherms, isoconcentrations, average Nusselt number and average Sherwood number curves of different parameters were discussed in detail. It was observed that the governing parameters has significant impact on the fluid flow, temperature and concentration distributions. In addition, the average Nusselt and Sherwood numbers are increase with an reduce in the viscosity-variation number. Further, as the absolute value of buoyancy ratio and thermal Rayleigh number increases, the effect of porosity and viscosity changes on the heat and mass transfer enhancement was augmented.     

Triple convective flow of micropolar nanofluids in double lid-driven enclosures partially filled with LTNE porous layer under effects of an inclined magnetic field

In this paper, free, forced and Marangoni convective flows within an open enclosure partially filled with a porous medium under impacts of an inclined magnetic field are investigated. The forced convection is due to the movement of the side walls, the free convection induces from the heated part in the bottom wall and the Marangoni convection is a responsible on the thermal interaction at the free surface (top wall). The flow domain is partially heated from below and partially filled by a porous medium. The local thermal non-equilibrium model (LTNEM) is used to represent the thermal field in the porous layer (bottom layer) while the two-phase model is used to simulated the micropolar nanofluid behavior. Two cases based on the direction of the movement of the side walls are considered, namely, assisting flow (downward lid motion) and opposing flow (upward lid motion). Numerical analysis based on the finite volume method is conducted and the obtained are presented in terms of the streamlines, isotherms, angular velocity, and the cup-mixing temperature θ_cup, the bulk-averaged temperature θ_ave and the average Nusselt numbers. The controlling parameters, in this situation, are the Darcy number Da, the Marangoni number Ma, the Nield number H, the vortex viscosity Δ, the Biot number Bi and the Hartmann number Ha. The results revealed that the increase in the Nield number enhances the cup-mixing temperature θ_cupand bulk-averaged temperature θ_ave regardless the direction of the side walls motion. Also, the average Nusselt number is boosted as the Marangoni number is grown.     

多孔介质方腔内混合对流格子Boltzmann模拟

采用格子Boltzmann方法,对多孔介质方腔内的混合对流现象进行研究.方腔内部中心有一发热圆,径宽比D/L=0.4,冷流体从方腔左下角入口流进,从方腔左上角出口流出,四周壁面绝热.在普朗特数Pr=0.71和格拉晓夫数Gr=1.4×10⁴时,分析理查德森数Ri和达西数Da对发热圆表面平均努赛尔数Nu的影响.结果表明：Ri数位于10^-3~10范围内,Nu随Ri的增大而减小.Da越大,Ri对Nu的影响越显著;Da数位于10^-5~10^-2范围内,强制对流占主导的情况下（Ri≤0.1）,Nu随着多孔介质的Da的增大而增大.自然对流占主导的情况下（Ri=10）,Nu对Da的变化不敏感.     

Heat transfer and force balance approaches in bubble dynamic study during subcooled flow boiling of water–ethanol mixture

In this paper, the subcooled flow boiling heat transfer coefficient of pure water, water–ethanol mixture and pure ethanol is determined experimentally in horizontal rectangular channels for various parameters like heat flux, mass flux and channel inlet temperatures. Flow visualization is carried out using high speed camera. The bubble departure diameter, growth period and waiting period of bubbles are determined. Correlations are developed for subcooled flow boiling Nusselt number of water–ethanol mixture based on force balance approach and heat transfer approach. The parameters considered for correlation are grouped as dimensionless numbers by Buckingham π-theorem. The significance of each dimensionless number on heat transfer coefficient is discussed. The correlations developed for subcooled flow boiling heat transfer coefficient are validated with the experimental data. They are found to be in good agreement with the experimental data. It is found that the correlation based on force balance approach predicts the subcooled flow boiling Nusselt number well when compared with that of heat transfer approach correlation.