EFFECTS OF FREE STREAM VELOCITY ON TURBULENT NATURAL CONVECTION FLOW OVER A VERTICAL FORWARD-FACING STEP

Measurements of heat transfer and fluid flow of turbulent boundary-layer air flow in natural and mixed convection over an isothermal two-dimensional, vertical forward-facing step are reported. The upstream and downstream walls and the step itself were heated to a uniform and constant temperature. Air velocity and temperature distributions and their turbulent fluctuations are measured simultaneously using a two-component laser-Doppler velocimeter (LDV) and a cold wire anemometer, respectively. The present study treats buoyancy-dominated mixed convection over a vertical forward-facing step and examines the effect of a small free stream velocity on turbulent natural convection. The experiment was carried out for a step height of 22 mm, for a range of free stream air velocities 0 m/s ? u_∞ ? 0.55 m/s (corresponding to a range of Reynolds numbers of 0 ? Re\abinf{s} ? 712), and a temperature difference, ΔT, of 30°C between the heated walls and the free stream air (corresponding to a local Grashof number Gr_xi = 6.45 × 10¹⁰). It was found that the reattachment length increases while the heat transfer rate from the downstream heated wall decreases as the small free stream velocity increases.     

Rotating turbulent Rayleigh–Bénard convection subject to harmonically forced flow reversals

The characteristics of turbulent flow in a cylindrical Rayleigh–Bénard convection cell which can be modified considerably in case rotation is included in the dynamics. By incorporating the additional effects of an Euler force, i.e., effects induced by non-constant rotation rates, a remarkably strong intensification of the heat transfer efficiency can be achieved. We consider turbulent convection at Rayleigh number Ra = 10⁹ and Prandtl number σ = 6.4 under a harmonically varying rotation, allowing complete reversals of the direction of the externally imposed rotation in the course of time. The dimensionless amplitude of the oscillation is taken as 1/Ro^* = 1 while various modulation frequencies 0.1 ≤ Ro_ω ≤ 1 are applied. Both slow and fast flow-structuring and heat transfer intensification are induced due to the forced flow reversals. Depending on the magnitude of the Euler force, increases in the Nusselt number of up to 400% were observed, compared to the case of constant or no rotation. It is shown that a large thermal flow structure accumulates all along the centreline of the cylinder, which is responsible for the strongly increased heat transfer. This dynamic thermal flow structure develops quite gradually, requiring many periods of modulated flow reversals. In the course of time, the Nusselt number increases in an oscillatory fashion up to a point of global instability, after which a very rapid and striking collapse of the thermal columnar structure is seen. Following such a collapse is another, quite similar episode of gradual accumulation of the next thermal column. We perform direct numerical simulation of the incompressible Navier–Stokes equations to study this system. Both the flow structures and the corresponding heat transfer characteristics are discussed at a range of modulation frequencies. We give an overview of typical time scales of the system response.     

竖直圆管中超临界压力CO2对流换热实验研究

本文对超临界压力CO2在竖直加热圆管内的对流换热进行了实验研究,比较了不同流向、不同热流密度等对流动和换热的影响。实验结果表明,管内径为2mm时,在低进口Re条件下,由于浮升力影响导致层流向湍流提前转变, 对流换热增强;与向上流动相比,向下流动更易由层流转变为湍流;向下流动的换热要强于向上流动,表明浮升力对换热有很大影响。对于管内径为0．27 mm的微细圆管,当进口Re高于104时,浮升力的影响可以忽略,对流换热系数的变化完全由物性的变化尤其是cp的变化导致。     

EFFECTS OF FREE-STREAM VELOCITY ON TURBULENT NATURAL-CONVECTION FLOW ALONG A VERTICAL PLATE

A detailed measurement of heat transfer and fluid flow of turbulent boundary-layer air flow in natural and mixed convection adjacent to an isothermal vertical flat plate are reported. A cold-wire anemometer and laser Doppler velocimeter were used, respectively, to measure simultaneously the time-mean turbulent temperature and velocity distributions and their turbulent fluctuations. In this experimental study, measurements of the flow and thermal fields were carried out at one streamwise location, x     

Determination of forced convection parameters by interferometric imaging of the concentration field during growth of KDP crystals

Growth of a potassium dihydrogen phosphate (KDP) crystal from its aqueous solution has been considered under forced convection conditions. The KDP crystal is grown in a conventional top hanging geometry. Forced convection conditions are created by rotating the crystal about a vertical axis. The rotational RPM is varied in a cycle, creating an accelerated rotation (AR) paradigm. The effect of varying the rotational RPM on the concentration field around the crystal was investigated. Mach-Zehnder interferometry was adopted as an optical technique to image the evolving concentration fields. Six different experiments were performed to obtain the specific set of time periods and rotation rates of the acceleration cycle that result in a uniform concentration field around the growing crystal. The Reynolds number, an index of the strength of forced convection, was optimized through the experiments. The optimized parameters of the accelerated rotation cycle were found to be as follows: maximum rotation rate of 32 RPM, spin up period=40 s, spin down period=40 s, steady period=40 s, and stationary period=40 s. The parametric study further revealed that concentration was highly sensitive to the maximum rotation rate adopted during the AR cycle. It did not depend crucially on the time periods that could be varied by as much as ±25% around the respective average values. Finally, a KDP crystal was grown using the optimized forced convection parameters and the crystal quality was found to be good.     

Drifting convection cells in rotating fluid layers heated from below

It is shown that hexagonal convection cells in a rotating horizontal fluid layer heated from below will in general exhibit a drift in contrast to convection rolls except in the case of a vertical axis of rotation. The direction of the drift is prograde (retrograde) for cells with rising (descending) motion in the center of the convection cell. In addition a mean flow generated by convection is derived. An application to solar convection is discussed.     

Turbulent convective heat transfer in an inclined tube filled with sodium

Turbulent free convection of liquid sodium in a straight thermally insulated tube with a length equal to 20 diameters and with end heat exchangers ensuring a fixed temperature drop is investigated experimentally. The experiments are performed for a fixed Rayleigh number Ra = 2.4 × 10⁶ and various angles of inclination of the tube relative to the vertical. A strong dependence of the power transferred along the tube on the angle of inclination is revealed: the Nusselt number in the angular range under investigation changes by an order of magnitude with a maximum at the angle of 65° with the vertical. The characteristics of large-scale circulation and turbulent temperature pulsations show that convective heat transfer is mainly determined by the velocity of large-scale circulation of sodium. Turbulent pulsations are maximal for small angles of inclination (α = 20°–30°) and reduce the heat flux along the channel, although in the limit of small angles (vertical tube), there is no large-scale circulation, and the convective heat flux, which is an order of magnitude larger than the molecular heat flux, is ensured only by small scale (turbulent) flow.     

Sloping convection in a rotating fluid

Laboratory experiments on thermal convection in a fluid which rotates about a vertical axis and is subject to a horizontal temperature gradient show that when the rotation rate Ω exceeds a certain critical value Ω_R (which depends on the acceleration of gravity, the shape and dimensions of the apparatus, the physical properties of the fluid and the distribution and intensity of the applied differential heating) Coriolis forces inhibit overturning motion in meridian planes and promote a completely different type of flow which has been termed ‘sloping convection’ or ‘baroclinic waves’. The motion is then non-axisymmetric and largely confined to meandering ‘jet streams’, with trajectories of individual fluid elements inclined at only very small (though essentially non-zero) angles to the horizontal. The kinetic energy of the waves derives from the interaction of slight vertical motions with the potential energy field maintained by differential heating, and it is dissipated by friction arising largely in boundary layers on the walls of the apparatus.

Provided that Ω, though greater than Ω_R, does not exceed a second critical value Ω_I, the waves are characterized by great regularity; they are either steady or undergo periodic ‘vacillation’ in their amplitude, shape and other properties. The azimuthal wavelength decreases with increasing Ω until at Ω=Ω_I it reaches a sufficiently low value, ～1.5 times the radial dimension of the wave, for nonlinear processes to overcome various constraints associated with the anisotropy of the flow, thereby rendering the main baroclinic wave barotropically unstable by transferring kinetic energy to larger as well as smaller scales of motions.

Theoretical investigations of sloping convection have their origin in ideas concerning the large-scale mid-latitude circulation of the Earth's atmosphere, modern work on which includes important studies based on numerical models. Conditions favouring sloping convection should be fairly common in natural systems and the process is expected to underlie various phenomena of interest to oceanographers, geophysicists, planetary scientists and astronomers.     

Azimuthal symmetry, flow dynamics, and heat transport in turbulent thermal convection in a cylinder with an aspect ratio of 0.5

We report an experimental study of flow dynamics and structure in turbulent thermal convection. Flow visualization, together with particle image velocimetry (PIV) measurement, reveal that the instantaneous flow structure consists of an elliptical circulatory roll and two smaller counterrotating rolls, and that the azimuthal motion of the quasi-2D instantaneous flow structure produces a time-averaged 3D flow pattern featuring two toroidal rings near the top and bottom plates, respectively. The apparently stochastic azimuthal motion of the flow structure, which generates a net rotation on average, is found to possess the characters of a Brownian ratchet. Using an artificially generated flow mode, we are able to produce a bimodal-Nu behavior and thus demonstrate that different flow states can indeed produce different global heat transport in a turbulent convection system.     

湍流热对流的高效并行直接求解方法

结合泊松方程直接求解的PDD算法,创建二维湍流热对流DNS模拟的并行直接求解方法（PDM-DNS）.在"天河二号"超级计算机上完成高Ra数湍流热对流大规模DNS计算,计算效果令人惊喜,实现了一年前难以达到的计算规模.高分辨率的湍流热对流计算结果显示,不同高Ra数的湍流热对流流动状态完全不同.为高Ra数湍流热对流大规模并行计算和数值模拟研究提供了有价值的计算方法.     

Numerical investigation of using various electrode arrangements for amplifying the EHD enhanced heat transfer in a smooth channel

Forced convection heat transfer enhancement with electrohydrodynamic (EHD) technique of turbulent flow inside a smooth channel has been numerically investigated. A two dimensional numerical approach has been chosen to evaluate the local and average heat transfer coefficient. In addition, the swirling flow pattern in the presence of an electric field has been studied. To achieve higher enhancement while using multiple electrodes, variety of electrode arrangements have been examined for specified values of Reynolds number, applied voltage, and wire radius. The results demonstrate that different electrode arrangements cause significant improvement of the heat transfer coefficient.     

The turbulent/nonturbulent interface in penetrative convection

The effect of buoyancy on the turbulent/nonturbulent interface (TNTI) and viscous superlayer are studied by performing direct numerical simulation of penetrative convection. In this flow, rising turbulent thermals alternate with unmixed fluid entrained from above, forming a TNTI between the turbulent and irrotational flow regions. We detect the TNTI using a broad range of enstrophy iso-levels, from the very low levels of the outer fringes of the turbulent flow region to high levels located in the turbulent flow region. We study the local entrainment velocity v_n by which the TNTI propagates outwards relative to the fluid flow while entraining unmixed fluid into the turbulent region. The relative entrainment velocity is decomposed into a viscous, an inertial and a baroclinic torque term, respectively. For low enstrophy levels we find a viscous superlayer (VSL) where viscous diffusion dominates, while inertial and baroclinic torque terms are small. It is only for higher iso-levels in the buffer region of the TNTI, which extends from the edge of the VSL to the threshold for which v_n = 0, that the inertial enstrophy production term plays a significant role. Penetrative convection does not feature a turbulent core where v_n > 0 (i.e. inward moving enstrophy isosurfaces) that has been previously identified in other entraining flows such as jets or gravity currents. Surprisingly, the baroclinic torque remains inactive throughout the whole range of enstrophy iso-levels. The smallness of the baroclinic torque against viscous effects in the TNTI is supported by a dimensional argument which predicts that at high Reynolds number the baroclinic torque term will be negligible.     

Series solutions for turbulent plumes evolving in a natural environment

Closed form solutions to the boundary layer equations for turbulent point and line thermal plumes evolving in natural convection have been obtained in the form of power series for the case when the turbulent viscosity is assumed to be proportional to the vertical height above the source. The initial values needed to generate the coefficients of the power series for different turbulent Prandtl number have been obtained numerically. To compliment these values the constants of proportionality between the turbulent viscosity and the height were determined using different methodologies including analysis of experimental data, computational fluid dynamics and numerical considerations. Evaluation of the results is primarily carried out by comparison to experimentally determined profiles of the temperature and velocity that are found in the literature. The best agreement was obtained when the Reynolds analogy—giving the turbulent Prandtl number as unity—was adopted. While the range of validity of the power series is limited, its radius of convergence can be extended using a suitable transformation.     

Application of the wavelet transform in the laminar turbulent transition for a flow in a mixed convection phenomenon

The aim of this paper is to show the effect of secondary flows caused by natural convection on the laminar-turbulent hydrodynamic transition. It is not a question of measuring a critical threshold value of Reynolds number of transition but only to estimate the degree of turbulence in the transition regime, i.e. weak turbulence in the case of superposition (mixed convection) or not (forced convection) of secondary flows on the forced flow. This is possible thanks to the application of the wavelet transform. The calculation of the H?lder exponent, associated with the maximum value of the singularity spectrum for two configurations, vertical (forced convection) and horizontal (mixed convection) allows the degree of turbulence to be measured in both cases. The variation of the H?lder exponent versus the Reynolds number has enabled it to be shown that the secondary flows stabilise the main flow and stifle the beginnings of the turbulence during the regime of transition to turbulence; these kinds of results have also been shown in literature. Generally, large-sized secondary flows (for example Dean's flows) stabilise the turbulence. Our work confirms this, through an experiment carried out in identical conditions for mixed convection (horizontal flow) and forced convection (vertical flow). Received 30 March 1998 and Received in final form 28 April 1999     

湍流热对流大尺度环流反转时的角涡特性

本文采用DNS方法计算二维方腔Rayleigh–Bénard热对流.在软湍流区热对流场呈现大尺度环流和两个反向转动的角涡,并出现了大尺度环流的反转现象.连续的温度等值线和流线图清晰地描述了反转现象的全过程.在反转过程中,角涡的大小尺度变化起到重要的作用.对角涡大小尺度变化的分析发现,在反转现象中其角涡尺度随时间的变化出现剧烈的振荡,而没有反转现象的热对流场中角涡尺度变化只有小幅的脉动.对反转过程前后的角涡大小尺度、典型位置速度及角点附近温度等流动特性进行了探讨和分析,发现反转是在瞬间完成的,角涡内速度脉动较小、温度较高,反转前角涡尺度与角涡侧壁垂向速度变化具有同步性.     

Plume dynamics in quasi-2D turbulent convection

We have studied turbulent convection in a vertical thin (Hele-Shaw) cell at very high Rayleigh numbers (up to 7x10(4) times the value for convective onset) through experiment, simulation, and analysis. Experimentally, convection is driven by an imposed concentration gradient in an isothermal cell. Model equations treat the fields in two dimensions, with the reduced dimension exerting its influence through a linear wall friction. Linear stability analysis of these equations demonstrates that as the thickness of the cell tends to zero, the critical Rayleigh number and wave number for convective onset do not depend on the velocity conditions at the top and bottom boundaries (i.e., no-slip or stress-free). At finite cell thickness delta, however, solutions with different boundary conditions behave differently. We simulate the model equations numerically for both types of boundary conditions. Time sequences of the full concentration fields from experiment and simulation display a large number of solutal plumes that are born in thin concentration boundary layers, merge to form vertical channels, and sometimes split at their tips via a Rayleigh-Taylor instability. Power spectra of the concentration field reveal scaling regions with slopes that depend on the Rayleigh number. We examine the scaling of nondimensional heat flux (the Nusselt number, Nu) and rms vertical velocity (the Peclet number, Pe) with the Rayleigh number (Ra(*)) for the simulations. Both no-slip and stress-free solutions exhibit the scaling NuRa(*) approximately Pe(2) that we develop from simple arguments involving dynamics in the interior, away from cell boundaries. In addition, for stress-free solutions a second relation, Nu approximately nPe, is dictated by stagnation-point flows occurring at the horizontal boundaries; n is the number of plumes per unit length. No-slip solutions exhibit no such organization of the boundary flow and the results appear to agree with Priestley's prediction of Nu approximately Ra(1/3). (c) 1997 American Institute of Physics.     

直拉法晶体生长过程非稳态流体热流耦合

为了改善复杂对流形态下的晶体生长品质, 提出了一种改进的格子Boltzmann方法研究非稳态熔体流动和传热的耦合性质. 该方法基于不可压缩轴对称D2Q9模型, 构建了包含旋转惯性力和热浮力等外力项的演化关系, 实现了对轴对称旋转流体的速度、温度和旋转角速度的计算与分析. 结果表明, 非稳态熔体中的流、热耦合性质与格拉斯霍夫数和雷诺数的相互作用有关; 通过调节高雷诺数, 可有效抑制熔体中的自然对流, 改善温度分布, 有助于提高单晶的品质. 数值计算结果与实际硅单晶生长试验均证明了所提方法的正确性及有效性.     

Large-eddy simulation of plane channel flow with Vreman's model

In this paper, large-eddy simulations of Vreman's model (VM) have been carried out to investigate its performances in a temporal transitional channel flow and in high Reynolds number turbulent channel flows. As a preliminary work, it is found that cubic root of the cell volume is the best choice of filter width for both VM and dynamic VM based on Germano identity (DVM), according to comparative studies and a-posteriori analyses at Re_τ = 590. VM and DVM are then used to simulate the temporal laminar–turbulent transitional channel flow, and the results turn out that VM and DVM are capable to simulate this temporal transient flow. In simulating high Reynolds number turbulent channel flows with a relatively coarse grid resolution, DVM itself shares the same weakness as the dynamic Smagorinsky model, while it can successfully predict the mean velocity profile and skin friction coefficient when it is coupled with the constrained large eddy simulation methodology. The coupling highly promotes the capability of Vreman's model, offering a new promising approach to simulate high Reynolds number wall-bounded turbulent flows.     

数值分析环形池硅熔体旋转-热毛细对流及其稳定性

数值模拟了内半径20 mm、外半径40 mm、深5 mm环形池内硅熔体在旋转和热毛细力共同驱动下的热对流,通过线性稳定性分析确定了旋转-热毛细对流失稳的临界Marangoni数等临界条件。研究结果表明,液池低速旋转会降低轴对称热毛细对流的稳定性,而较高速度的旋转能增强热毛细对流的稳定性。临界条件下旋转-热毛细对流耗散结构波纹的传播方向与液池的旋转方向相同,临界周向波数随旋转速度的增加而增加。在较大的旋转速度下,液池底部出现涡胞,底部涡胞对热毛细对流的稳定性具有削弱作用。     

不同光线入射角度下超声速湍流边界层气动光学效应的实验研究

利用基于纳米粒子的平面激光散射技术获取超声速(Ma=3.0)湍流边界层的密度分布,采用光线追迹方法计算其对应的光程差分布,并结合边界层气动光学相似律验证实验结果的可靠性.着重研究了光线入射角度对超声速湍流边界层气动光学效应的影响,并对其内在机理进行了分析.研究表明,气动光学效应对光线入射角度的依赖性源于光线在流场中的传输路径,传输路径的不同导致了光线在流场中的传输距离以及对应密度脉动互相关结果的差异.光线倾斜入射导致其在流场中传输距离增长,进而气动光学效应出现恶化.光线入射方向与壁面垂直方向之间的夹角越大,气动光学效应越显著,而且不同时刻的差异性增加,气动光学效应校正的难度增加.超声速湍流边界层中大量具有特定方向的涡结构导致了湍流边界层气动光学效应的各向异性.当光线倾斜向下游入射时,光线传播方向与流场中的涡结构具有较好的一致性,体现为此方向上密度脉动互相关系数较大,故气动光学效应比较严重.而当光线倾斜向上游入射时,相关系数较小,故气动光学效应较弱.