Buoyancy-induced flow and convective heat transfer in an inclined arc-shape enclosure

Numerical and experimental investigations have been conducted to study the flow and heat transfer characteristics for the buoyancy-induced flow inside an inclined arc-shape enclosure. Mathematical model in form of a stream function-vorticity formulation representing the laws of conservation in mass, momentum, and energy is expressed in a curvilinear coordinate frame and solved by a finite-volume discretization method. Heat transfer and flow pattern are predicted at various Grashof numbers and inclination angles. Meanwhile, an experimental system is developed and a flow-visualization technique using smoke is employed to observe the flow pattern. Results show that only when the Grashof number is higher than 10⁵, the increase in natural convection heat transfer becomes appreciable. Both the strength and the pattern of the buoyancy-induced vortex are found to be greatly dependent on the inclination angle. The range of the Grashof number considered in this study is up to 10⁷ and the inclination angle is varied from 0 to π.     

Numerical and experimental study of turbulent impinging twin-jet flow

The two dimensional impinging circular twin-jet flow with no-cross flow is studied numerically and experimentally. The theoretical predications are carried out through numerical procedure based on finite volume method to solve the governing mass, momentum, turbulent kinetic energy and turbulent kinetic energy dissipation rate. The parameters studied were jet Reynolds number (9.5 × 10⁴  Re  22.4 × 10⁴), nozzle to plate spacing (3  h/d  12), nozzle to nozzle centerline spacing (l/d = 3, 5 and 8) and jet angle (0°  θ  20°). It is concluded that the stagnation primary point moves away in the radial main flow direction by increasing the jet angle. This shift becomes stronger by increasing the nozzle to nozzle centerline spacing (l/d). A secondary stagnation point is set up between two jets. The value of pressure at this point decreases by decreasing Reynolds number and/or increasing the jet angle.

The sub atmospheric region occurs on the impingement plate. It increases strongly by increasing Reynolds number and decreases as the jet angle and/or a nozzle to plate spacing increases. The spreading of jet decreases by increasing nozzle to plate spacing. The intensity of re-circulation zone between two jets decreases by increasing of h/d and jet angle. The increase of turbulence kinetic energy occurs within high gradient velocity.     

Lattice Boltzmann simulation of natural convection in open end cavity with inclined hot wall

Natural convection in an open end cavity with a hot inclined wall is simulated based on the lattice Boltzmann method (LBM). The physics of flow and energy transfer in open end cavities are addressed when the hot wall is inclined. The combination of the two topics (open cavity and inclined walls) is the main novelty of the present study. The effects of the angle of the hot inclined wall on the flow field and heat transfer are thoroughly investigated. The Prandtl number is fixed to 0.71 (air). The Rayleigh number and the angle of the hot inclined wall are varied in the range of 10⁴ to 10⁶ and 60? to 85?, respectively. The results are presented for two different aspect ratios, i.e., A = 1 and 2. The results obtained with the LBM are also compared with those of the finite volume method (FVM). The predicted results of the LBM conform to those of the FVM. The results show that by increasing the angle of the hot inclined wall and the aspect ratio of the cavity, the average Nusselt number decreases. The trend of the local Nusselt number on the inclined wall is also discussed.     

Shroud heat transfer measurements inside a heated multiple rotating cavity with axial throughflow

Experimental measurements of heat transfer are made from the inner peripheral surface of a rotating test rig designed to be similar to a gas turbine high pressure compressor internal air system. The test rig comprises a number of annular discs sealed at their periphery by a shroud. An axial throughflow of cooling air enters the test rig and flows through the annular section between the disc bores and a central shaft. Tests were carried out for the following range of rotational speeds and axial throughflow rates: 540 < N_R < 10,800 rev/min and (corresponding to the range of rotational and axial Reynolds numbers 4 × 10⁵ < Re < 7.7 × 10⁶ and 3.3 × 10⁴ < Re_z < 2.2 × 10⁵).

The shroud Nusselt numbers are found to depend on the shroud Grashof number. They are relatively insensitive to changes in axial Reynolds number and two geometrically similar cavities give similar values of Nusselt number. The heat transfer from the shroud is governed by the mechanism of free convection. It is recommended that a modified form of a correlation for Rayleigh–Bénard convection in a gravitational force field be used, with appropriate modification, to predict shroud heat transfer.     

磁场对多孔介质方腔内空气热磁对流的影响

数值分析了微重力下圆形载流线圈倾斜时多孔介质方腔内空气热磁对流. 磁场计算采用毕奥--萨伐定律求解; 动量方程与能量方程分别采用达西模型与局部热非平衡模型求解. 计算结果表明随着磁场力数\gamma 数和Da数的增加, 方腔内对流变得越来越强. 线圈倾斜角x_{\rm euler}从0^\circ到90^\circ变化时, 对流结果关于x_{\rm euler}=45^\circ呈现对称分布. Nu_{\rm m}数随线圈倾斜角的改变而变化且每个工况下局部最大Nu_{\rm m}数出现在x_{\rm euler}=45^\circ. 局部最小Nu_{\rm m}数出现在x_{\rm euler}=0^\circ, 90^\circ.      

Fully developed mixed convection in horizontal and inclined tubes with uniform heat flux using nanofluid

Fully developed laminar mixed convection of a nanofluid consists of water and Al₂O₃ in horizontal and inclined tubes has been studied numerically. Three-dimensional elliptic governing equations have been solved to investigate the flow behaviors over a wide range of the Grashof and Reynolds numbers. Comparisons with previously published experimental and numerical works on mixed convection in a horizontal and inclined tube are performed and good agreements between the results are observed. Effects of nanoparticles concentration and tube inclinations on the hydrodynamics and thermal parameters are presented and discussed. It is shown that the nanoparticles concentration does not have significant effects on the hydrodynamics parameters. Heat transfer coefficient increases by 15% at 4 Vol.% Al₂O₃. Skin friction coefficient continually increases with the tube inclination, but the heat transfer coefficient reaches a maximum at the inclination angle of 45°.     

Experimental investigation of inclined liquid water jet flow onto vertically located superhydrophobic surfaces

In this study, the behaviour of an inclined water jet, which is impinged onto hydrophobic and superhydrophobic surfaces, has been investigated experimentally. Water jet was impinged with different inclination angles (15°–45°) onto five different hydrophobic surfaces made of rough polymer, which were held vertically. The water contact angles on these surfaces were measured as 102°, 112°, 123°, 145° and 167° showing that the last surface was superhydrophobic. Two different nozzles with 1.75 and 4 mm in diameters were used to create the water jet. Water jet velocity was within the range of 0.5–5 m/s, thus the Weber number varied from 5 to 650 and Reynolds number from 500 to 8,000 during the experiments. Hydrophobic surfaces reflected the liquid jet depending on the surface contact angle, jet inclination angle and the Weber number. The variation of the reflection angle with the Weber number showed a maximum value for a constant jet angle. The maximum value of the reflection angle was nearly equal to half of the jet angle. It was determined that the viscous drag decreases as the contact angle of the hydrophobic surface increases. The drag force on the wall is reduced dramatically with superhydrophobic surfaces. The amount of reduction of the average shear stress on the wall was about 40%, when the contact angle of the surface was increased from 145° to 167°. The area of the spreading water layer decreased as the contact angle of the surface increased and as the jet inclination angle, Weber number and Reynolds number decreased.     

细长锥边界层绊线转捩风洞自由飞试验

通过在半锥角θ_c=10°细长锥面上布置一定数量的人工绊线,促使细长锥表面边界层在相应轴向位置上发生层流向湍流转变的固定转捩,采用运动自由度不受约束的风洞自由飞试验技术研究边界层转捩对高超声速细长锥再入体无控自由飞行下的运动特性和气动特性影响规律,并与以往无人工绊线的细长锥风洞自由飞试验结果作对比.试验马赫数Ma=5.0,通过改变风洞前室总压P_0实现两个雷诺数的模拟,以模型长为特征尺寸自由流雷诺数分别为0.84×10~6和1.68×10~6.结果表明:当自由流雷诺数Re=0.84×10~6时,人工绊线尚不足以促使边界层发生转捩,有绊线的细长锥气动特性与无绊线基本一致,动稳定导数大于零;当自由流雷诺数Re=1.68×10~6时,人工绊线促使边界层发生固定转捩,细长锥的动稳定导数小于零,细长锥自由飞行动稳定.     

Dynamic behavior of frozen soil under uniaxial strain and stress conditions

The split Hopkinson pressure bar (SHPB) method is used to investigate the dynamic behavior of the artificial frozen soil under the nearly uniaxial strain and uniaxial stress conditions. The tests are conducted at the temperatures of −3^?C, −8^?C, −13^?C, −17^?C, −23^?C, and −28^?C and with the strain rates from 900 s⁻¹ to 1 500 s⁻¹. The nearly uniaxial stress-strain curves exhibit an elastic-plastic behavior, whereas the uniaxial stress-strain curves show a brittle behavior. The compressive strength of the frozen soil exhibits the positive strain rate and negative temperature sensitivity, and the final strain of the frozen soil shows the positive strain rate sensitivity. The strength of the frozen soil under the nearly uniaxial strain is greater than that under the uniaxial stress. After the negative confinement tests, the specimens are compressed, and the visible cracks are not observed. However, the specimens are catastrophically damaged after the uniaxial SHPB tests. A phenomenological model with the thermal sensitivity is established to describe the dynamic behavior of the confined frozen soil.     

Numerical investigation of natural convection inside an inclined parallel‐walled channel

Steady two‐dimensional natural convection in an inclined parallel‐walled channel was investigated numerically. The full elliptic forms of conservation equations were solved together and the velocity vectors, temperature contours and local and average Nusselt number distribution were obtained. The comparisons of local and average Nusselt number with published experimental and numerical results indicate very good agreement. Results are presented for a single aspect ratio, L/b=24, over the range of Rayleigh number of 3–1000 and angle of inclination 0–90°. The results indicate that the overall channel average Nusselt number is reduced as the inclination angle is increased. Significant reductions in the overall Nusselt number are exhibited at high angle of channel inclination. Copyright © 2005 John Wiley & Sons, Ltd.     

矩形倾斜腔体中的两种对流斑图和分区

为了研究矩形倾斜腔体中普朗特数Pr=0.72的流体对流斑图和分区,本文基于流体力学方程组进行了数值模拟。在相对瑞利数r=6.0的情况下,观察了倾角θ=10°和θ=60°时对流斑图随着时间的发展,发现系统存在单圈型对流和多圈型对流两种斑图。流线随着倾角的变化说明:随着倾角增加,对流圈数逐渐减少,对流波长逐渐增加,对流波数减小;然后,随着对流圈数显著地减少,系统由多圈型对流过渡到单圈型对流。根据模拟计算结果,给出了多圈型对流过渡到单圈型对流的临界倾角θc随着相对瑞利数r变化的关系曲线。对流在θ-r平面上分为两个区域:θ<θc时系统是单圈型对流,θ>θc时系统是多圈型对流。对流最大振幅A和努塞尔数Nu随着倾角θ的变化曲线被临界倾角θc分成两段,它们有不同的变化规律。因此,临界倾角也可以由对流最大振幅A或努塞尔数Nu的变化曲线来确定。     

Graphite dust resuspension in an HTR-10 steam generator

Graphite dust has an important effect on the safety of high-temperature gas-cooled reactors(HTR).The flow field in the steam generator was studied by the computational fluid dynamics(CFD) method,with the results indicating that the friction velocity in the windward and the leeward of the heat transfer tubes is relatively low and is higher at the sides.Further analysis of the resuspension of graphite dust indicates that the resuspension fraction reaches nearly zero for particles with a diameter less than 1 μm,whereas it will increases as the helium velocity in the steam generator increases for particle size larger than 1 μm.Moreover,the resuspension fraction increases as the particle size increases.The results also indicate that resuspension of the particles with sizes larger than 1 μm exhibited obvious differences in different parts of the steam generator.     

层状岩体力学特性模拟实验研究

对层状岩体变形特性和强度特性的正确认识,合理选取其变形和强度参数,是水电站等大型岩体工程论证与设计需要解决的关键问题.为此,利用模拟实验对层状岩体的变形特性和强度特性进行了研究,得到了模拟试样的变形模量和强度随试样所含节理数、轴向应力与节理面间的夹角和围压之间的变化关系.结果表明:当最大主应力与节理面间的夹角由0°增加...     

Motion of a spherical particle in a fluid forced vortex by DO M and DTM

In this study, coupled equations of the motion of a particle in a fluid forced vortex were investigated using the differential transformation method （DTM） with the Pad6 approximation and the differential quadrature method （DO_M）. The significant contribution of the work is the introduction of two new, fast and efficient solutions for a spherical particle in a forced vortex that are improvements over the previous numerical results in the literature. These methods represent approximations with a high degree of accuracy and minimal computational effort for studying the particle motion in a fluid forced vortex. In addition, the velocity profiles （angular and radial） and the position trajectory of a particle in a fluid forced vortex are described in the current study.     

Numerical simulation of MHD natural convection flow in a wavy cavity filled by a hybrid Cu-Al_2O_3-water nanofluid with discrete heating

We consider the combined effect of the magnetic field and heat transfer inside a square cavity containing a hybrid nanofluid(Cu-Al_2O_3-water). The upper and bottom walls of the cavity have a wavy shape. The temperature of the vertical walls is lower,the third part in the middle of the bottom wall is kept at a constant higher temperature,and the remaining parts of the bottom wall and the upper wall are thermally insulated.The magnetic field is applied under the angle γ, an opposite clockwise direction. For the numerical simulation, the finite element technique is employed. The ranges of the characteristics are as follows: the Rayleigh number(10~3≤Ra≤10~5), the Hartmann number(0≤Ha≤100), the nanoparticle hybrid concentration(?_(Al_2O_3),?_(Cu) = 0, 0.025, 0.05),the magnetic field orientation(0≤γ≤2π), and the Prandtl number P_r, the amplitude of wavy cavity A, and the number of waviness n are fixed at P_r = 7, A = 0.1, and n = 3, respectively. The comparison with a reported finding in the open literature is done,and the data are observed to be in very good agreement. The effects of the governing parameters on the energy transport and fluid flow parameters are studied. The results prove that the increment of the magnetic influence determines the decrease of the energy transference because the conduction motion dominates the fluid movement. When the Rayleigh number is raised, the Nusselt number is increased, too. For moderate Rayleigh numbers, the maximum ratio of the heat transfer takes place for the hybrid nanofluid and then the Cu-nanofluid, followed by the Al_2O_3-nanofluid. The nature of motion and energy transport parameters has been scrutinized.     

Fluid flow and heat transfer around circular cylinder – flat and curved plates combinations

Experimental studies were carried out to investigate the fluid flow and heat transfer around a heated circular cylinder which was placed at various distances of a wall boundary with different geometries (flat or curved plate) with subcritical Reynolds number ranging from 3.5×10³ to 10⁴. The effects of plate geometry (aspect ratio: W|H=1.0,1.5 and 2.0, and rim angle, φ=0°,60°,90°, and 120°) and gap ratio, (G|D=0.0,0.86,2.0,7.0,10.0) on the fluid flow and heat transfer characteristics (static pressure around cylinder surface, wake width, base pressure, pressure drag coefficients, velocity distribution, and both local and mean Nusselt numbers) were presented. Also flow visualization was carried out to illustrate the flow patterns around the cylinder at various gap ratios (G|D). It was found that the heat transfer and fluid flow characteristics are dependent on the plate geometry at all tested gap ratios, except for G|D=7.0 and 10.0, they are independent of the plate geometry.     

Numerical computation of natural convection in an isosceles triangular cavity with a partially active base and filled with a Cu–water nanofluid

This paper discusses the results of a study related to natural convection cooling of a heat source located on the bottom wall of an inclined isosceles triangular enclosure filled with a Cu water-nanofluid. The right and left walls of the enclosure are both maintained cold at constant equal temperatures, while the remaining parts of the bottom wall are insulated. The study has been carried out for a Rayleigh number in the range 10⁴ ≤ Ra ≤ 10⁶, for a heat source length in the range 0.2 ≤ ε ≤0.8, for a solid volume fraction in the range 0 ≤ ?≤0.06 and for an inclination angle in the range 0° ≤ δ≤45°. Results are presented in the form of streamline contours, isotherms, maximum temperature at the heat source surface and average Nusselt number. It is noticed that the addition of Cu nanoparticles enhances the heat transfer rate and therefore cooling effectiveness for all values of Rayleigh number, especially at low values of Ra. The effect of the inclination angle becomes more noticeable as one increases the value of Ra. For high Rayleigh numbers, a critical value for the inclination angle of δ = 15° is found for which the heat source maximum temperature is highest.     

Conjugate natural convection from an array of discrete heat sources: part 2 — a numerical parametric study

Coupled conduction and natural convection transport within a discretely heated cavity have been investigated numerically. One vertical wall of the cavity is composed of discrete, isoflux heat sources mounted in a substrate of finite thermal conductivity. The opposite vertical wall and the horizontal walls are assumed to be isothermal and adiabatic, respectively. The governing steady-state partial differential equations for the fluid and solid region are solved simultaneously using a control volume formulation, coupled with an additive correction multigrid procedure that increases the convergence rate of the solution. The fluid Prandtl number and heater/fluid thermal conductivity ratio are fixed at 25 and 2350, respectively, corresponding to a dielectric fluid (FC-77) and heaters manufactured from silicon. With increasing modified Rayleigh number (10⁴ < Ra_Lz^* < 109), the cavity flow becomes more boundary layer-like along the vertical walls, and multiple fluid cells develop in the central region. Thermal spreading in the substrate increases with decreasing modified Rayleigh number and with increasing values of the substrate/fluid thermal conductivity ratio (10⁻¹ <- R_s ≤ 10³). For large R_s, the discrete heat sources lose their thermal identity, and the streamlines and isotherms resemble those associated with a differentially heated cavity. Thermal spreading in the substrate also has a significant effect on circulation in the cavity and on maximum surface temperatures.     

Aspect ratio effect on natural convection in water near its density maximum temperature

The effect of the aspect ratio on natural convection in water subjected to density inversion has been investigated in this study. Numerical simulations of the two-dimensional, steady state, incompressible flow in a rectangular enclosure with a variety of aspect ratios, ranging from 0.125 to 100, have been accomplished using a finite element model. Computations cover Rayleigh numbers from 10³ to 10⁶. Results reveal that the aspect ratio, A, the Rayleigh number, Ra, and the density distribution parameter, R, are the key parameters to determine the heat transfer and fluid flow characteristics for density inversion fluids in an enclosure. A new correlation for predicting the maximum mean Nusselt number is proposed in the form of , with the constants a and b depending on density distribution number R. It is demonstrated that the aspect ratio has a strong impact on flow patterns and temperature distributions in rectangular enclosures. The stream function ratio Ψ_inv/|Ψ_reg| is introduced to describe quantitatively the interaction between inversional and regular convection. For R=0.33, the density inversion enhancement is observed in the regime near A=3.     

Natural convection in an inclined enclosure containing internal energy sources and cooled from below

Natural convection in an inclined enclosure from below and containing internally heated fluid has been investigated using a finite difference calculation procedure. Results have been obtained for Rayleigh number values up to 10⁶ and for inclination angles of 30 and 60°. For internal Rayleigh numbers that are much larger than the external Rayleigh number, the flow rises in the interior and moves down both the hot and cold walls. On the other hand, if the external Rayleigh number has a larger magnitude, the flow moves upwards along the hot surface and downwards along the cold surface. For the latter situation, the inner core is multicellular in nature at large external Rayleigh numbers. The average heat flux ratio along the cold surface (convective heat flux/corresponding conduction heat flux) increases with increasing external Rayleigh number and decreasing internal ratio is non-monotonic in nature. The heat flux ratio along both surfaces is observed to be strongly dependent on the inclination angle at high external Rayleigh numbers. A maximum in the local heat flux along the cold surface is obtained in the vicinity of x/L = 1 where hot fluid, either from the interior or directly from the opposite hot wall, meets the surface. Along the hot wall, a maximum in the heat flux ra flo