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超重力热湍流输运与湍流脉动统计特性的研究

Heat transport and statistical properties of turbulent fluctuations in supergravitational thermal turbulence

作者:王东璞
  • 学号
    2018******
  • 学位
    博士
  • 电子邮箱
    wdp******.cn
  • 答辩日期
    2023.05.20
  • 导师
    孙超
  • 学科名
    动力工程及工程热物理
  • 页码
    164
  • 保密级别
    公开
  • 培养单位
    014 能动系
  • 中文关键词
    热湍流,超重力,终极传热区间,纬向流,能量级串
  • 英文关键词
    Thermal turbulence, Supergravity, Ultimate regime, Zonal flow, Energy cascade

摘要

浮力驱动下的热湍流在自然界和工业生产过程中广泛存在,如地幔和地核、大气层、海洋中的对流、发电站对流换热过程,在极高的浮力驱动强度下,努塞尔数(反映热输运效率)与瑞利数(反映浮力驱动强度)的依赖关系可能进入“终极(渐近)传热区间”,同时极高浮力下的温度场可能不遵循被动标量统计规律,因此许多研究者试图提高瑞利数,并研究高浮力驱动强度条件下的热湍流。本文采用超重力驱动方式,通过极大增加有效重力这一新方法来增大瑞利数,研究湍流终极传热区间的存在性,同时探索了高浮力条件下的大尺度湍流动力学特征和小尺度湍流脉动统计特性。 本文利用最高达100倍等效地球重力的超重力热湍流实验和直接数值模拟,观察到在超过一个量级区间的瑞利数范围内,与终极区间理论预测的标度律相符的结果。此外,我们还发现了流态转变的其它直接证据,包括剪切雷诺数达到了湍流转捩临界值及出现对数型湍流边界层的速度型。通过对超重力热湍流边界层的理论受力分析,发现科氏力效应促进了边界层在较低瑞利数下即发生“层流-湍流转捩”,从而导致传热规律由经典区间标度律过渡到终极态标度律。 在超重力热湍流实验和模拟中均意外地发现了大尺度对流涡相对旋转系统的周向更快的转动,即纬向流,通过改变半径比发现该对称性破缺现象与内外圆柱曲率不同及科氏力有关,环形对流区域中的非对称的平均温度场导致了冷热羽流的非对称偏转,热羽流撞击冷羽流,从而形成与系统旋转方向相同的纬向流。通过研究大尺度对流涡的进动频率和时空平均的周向速度等反映纬向流强度的统计量,发现半径比越小,纬向流越强,证明了曲率效应是纬向流形成的一个重要因素。 对湍流脉动的统计分析发现,在比纬向流相关的Rhines尺度小约半个数量级的尺度区间,温度脉动能谱随频率的依赖关系近似遵循纬向流相速度与湍流流动特征速度相平衡的-5次方Rhines标度律,温度脉动的自相关函数显示纬向流的周期性显著,且周期显著高于羽流运动的特征时间尺度。而在大于浮力相关的Bolgiano尺度区间,能谱和结构函数与波数的依赖关系近似服从浮力输运与惯性力做功相平衡的Bolgiano-Obukhov标度律,随着瑞利数增大,不同区域的温度脉动的概率密度函数均呈现更长尾的分布特征。超重力热湍流中由于曲率效应形成的纬向流和高离心浮力作用可能影响了能量级串过程。

Buoyancy-driven thermal turbulence ubiquitously occurs in nature and in many industrial processes. Examples include the convective flows in the Earth‘s mantle and outer core, in the atmospheric motion, in the ocean, and in the process of convective heat transport in power plants. As the buoyancy-driven strength is extremely high, the dependence of Nusselt number (reflecting heat transport efficiency) and Rayleigh number (reflecting buoyancy-driven strength) may reach ``ultimate (asymptotic) regime‘‘, and the temperature field may not follow the statistical properties of passive scalar fields. So many researchers have attempted to increase the Rayleigh number and study the thermal turbulence with the condition of high buoyancy-driven strength. In this thesis, the novel supergravitational thermal turbulence is adopted to increase the Rayleigh number by significantly increasing the effective gravity. The main issues that this thesis has studied and explored include the existence of the ultimate scaling in thermal turbulence, the large-scale properties of turbulent dynamics, and the statistical properties of small-scale turbulent fluctuations under the condition of large buoyancy force. By exploiting the laboratory experiments with the largest supergravity cases reaching 100 times effective Earth‘s gravity and the direct numerical simulation, a scaling of Nusselt number and Rayleigh number for more than a decade of Rayleigh number is observed, and the scaling is consistent with the theory of ultimate scaling.In addition, some other direct evidences for the transition of the flow dynamics are found, including the shear Reynolds number reaching the critical value for the onset of the turbulent boundary layer and the transition of the velocity boundary layer towards the turbulent boundary layer with logarithmic range. Through the theoretical analysis of the dominated forces in the boundary layer of supergravitational thermal turbulence, the effect of the Coriolis force facilitates the early transition of the boundary layer from laminar to turbulent at a relatively low Rayleigh number and thus results in the transition of the heat transfer law from classical regime to ultimate regime.Surprisingly, it is found both in the experiments and simulations that the convective rolls revolve around the rotating center in the prograde direction in the rotating reference frame, signifying the emergence of the so-called zonal flow. By changing the radius ratio, it is found that this symmetry-breaking phenomenon is related to the different curvatures of the inner and outer cylinders and the effects of the Coriolis force. The asymmetric mean temperature field in the annular flow region leads to the asymmetric deflection of the cold and warm plumes, and the warm plumes impact on the cold plumes. Consequently, the prograde zonal flow is generated. By studying the statistical quantities including the drift frequency of the convection rolls and the space- and time-averaged azimuthal velocity, which reflects the strength of the zonal flow, it is found that the smaller the radius ratio is, the stronger the zonal flow becomes, which confirms that the curvature effect is an important reason for the generation of zonal flow. The statistical analysis of turbulent fluctuations shows that in the range around half of a decade smaller than the Rhines scale which is related to zonal flow, the thermal power spectra versus frequency follow Rhines-like scaling law with the scaling exponent `-5‘, which assumes a balance between the phase speed of zonal flow and the characteristic velocity of the turbulent flow. The autocorrelation function of the temperature fluctuations reveals that the periodicity of zonal flow is obvious, and the period is significantly longer than the characteristic time scale of the movement of plumes. In the range larger than the Bolgiano scale which is related to the buoyancy force, the power spectra and structure functions versus wavenumber follow BO59 scaling which assumes a balance between the energy fed by the buoyancy and inertial force. It is found that the probability density functions of temperature fluctuations in different regions follow a distribution with a relatively long tail at a high Rayleigh number. The energy cascade in supergravitational thermal turbulence may be affected by the zonal flow generated by the curvature effect and the large centrifugal buoyancy.