On the weak turbulent motions of an isothermal dry granular dense flow with incompressible grains: part II. Complete closure models and numerical simulations

The complete thermodynamically consistent turbulent closure models of isochoric and isothermal dry granular dense flows with incompressible grains and weak turbulent intensity are established on the basis of a linearized theory with respect to the granular coldness for the dynamic responses of the closure conditions. The models are applied to study a gravity-driven stationary turbulent flow down an inclined moving plane, and the numerical simulations are compared with the experimental outcomes. It shows that while the mean velocity decreases monotonically from its boundary value on the moving plane toward the free surface, the mean porosity and granular coldness display more “exponential-like” increasing/decreasing tendencies. Of particular interest is that the granular coldness evolves from its maximum value on the moving plane toward its minimum value on the free surface, leading to the turbulent dissipation evolving in a similar manner, while the turbulent kinetic energy demonstrate a reverse tendency. The obtained results show good agreements to the experimental outcomes and are similar to the characteristics of conventional Newtonian fluids in turbulent shear flows.     

Understanding the turbulent structure of the atmospheric boundary layer: A diagnostic approach

In this paper, we have attempted a diagnostic study of the turbulence characteristics of the ABL by means of two one-dimensional models. The first model uses a first order non-local closure, based on the Transilient Turbulence Theory, for parameterizing turbulent fluxes. while the second model uses second order local closure for parameterizing these. The models have been applied to conduct case studies using the Kytoon data taken at Kharagpur, during 17th–21st June, 1990, as part of the MONTBLEX programme. Our findings bring out various interesting features regarding the non-local and local turbulent statistics such as kinematic fluxes, turbulence kinetic energy, vertical velocity variance, the contribution of the eddies of various sizes to the fluxes at different level and the mixing lengths. The one-dimensional anisotropy of the turbulent eddies has been revealed by the findings from the transilient model. The vertical variation of the turbulence kinetic energy, as computed directly by the second order model, is found to be strongly correlated with the vertical velocity variance. In particular, for stably stratified boundary layers, identification of two distinct zones of the turbulence kinetic energy and corresponding vertical velocity maxima is possible, which has been interpreted as positive evidence of patchy turbulence in the boundary layer.     

几种紊流模型在底坎紊流分离流计算中的对比

利用标准模型κ-ε、重整群κ-ε模型和v2f三种不同的紊流模型,在同位网格系统基础上,采用了有限控制体积离散方程,数值模拟了底坎所形成紊流分离流。计算结果表明,所选用的3种模型虽大致都能模拟出底坎分离流的流动特性,如前后角涡、回流型态等,但在主涡心位置、回流长度、水头损失和流速分布等方面3种模型计算结果有所差异,其中v2f模型所计算的结果同试验和大涡模拟的结果值更趋一致。结果表明,v2f模型具有更精确模拟底坎所形成的紊流分离流方面的优势。     

Interaction of a normal shock wave with a compressible turbulent flow

A speckle photographic method, which is sensitive to changes of gradients in fluid density, is applied for analyzing a compressible turbulent air flow with density fluctuations. Spatial correlation coefficients, turbulent length scales, and energy spectra are determined under the assumption of homogeneous isotropic turbulence. The experiments are performed in a shock tube where the flow is passed through a turbulence grid. Measurements are taken before and after the turbulent regime interacts with the normal shock wave reflected from the tube's end wall. Amplification of the turbulence intensity by the shock interaction process is verified quantitatively and is shown to be restricted to the lower wave numbers in the spectrum.A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, Oct. 17–19, 1988.To Professor Dr.-Ing. Klaus Gersten on the occasion of his 60th birthday     

宽窄相间河道水流紊动特性试验研究

为了探索宽窄相间河道的水流紊动特性，以西南地区宝兴河上游宽窄相间河段为研究对象，基于室内概化模型试验，采用多普勒声学流速仪（ADV）测量了室内模型典型断面上的三维瞬时流速，分析典型断面上的纵向时均流速、紊动强度、雷诺切应力和紊动能的分布规律。试验结果显示：宽窄相间水槽中，扩散段边壁的紊动强度大于中心区域的紊动强度，最大值位于0.2倍水深处；扩散段两侧坡脚处紊动能最大；侧壁区的平面和立面雷诺切应力最大值出现在扩散段内，中心区域最大雷诺切应力位于两槽间的中间断面处；扩散段内水流紊乱，两侧出现旋涡和涡脱，易造成侧壁侵蚀加强，引起河道拓宽。深入分析了宽窄相间河道水流的紊动特性，可为山区河流治理和自然灾害防治提供参考。     

宽窄相间河道水流紊动特性试验研究

为了探索宽窄相间河道的水流紊动特性,以西南地区宝兴河上游宽窄相间河段为研究对象,基于室内概化模型试验,采用多普勒声学流速仪(ADV)测量了室内模型典型断面上的三维瞬时流速,分析典型断面上的纵向时均流速、紊动强度、雷诺切应力和紊动能的分布规律。试验结果显示:宽窄相间水槽中,扩散段边壁的紊动强度大于中心区域的紊动强度,最大值位于0.2倍水深处;扩散段两侧坡脚处紊动能最大;侧壁区的平面和立面雷诺切应力最大值出现在扩散段内,中心区域最大雷诺切应力位于两槽间的中间断面处;扩散段内水流紊乱,两侧出现旋涡和涡脱,易造成侧壁侵蚀加强,引起河道拓宽。深入分析了宽窄相间河道水流的紊动特性,可为山区河流治理和自然灾害防治提供参考。     

Statistical properties of the atmospheric turbulent boundary layer over steep surface waves

A new method of digital optical anemometry (Particle Image Velocimetry, PIV) of turbulent flows is suggested and implemented in the laboratory; it is based on the use of continuous laser radiation and high-speed video photography, providing continuous statistical ensembles of flow velocity fields. Application of the method to the study of wind field over waves has allowed us to perform, for the first time, direct measurements of velocity fields, averaged over turbulent pulsations induced by waves in the air flow. The experiments demonstrated that the velocity fields, averaged over the turbulent pulsations, are nonseparated even in the case of steep and breaking waves, when separation of the flow from the wave crests in the instantaneous fields is observed. Based on comparison with the experimental data, it is shown that the average wind fields over waves are described well quantitatively in the framework of semiempirical closure models of turbulence.     

Limitations and improvements of the energy balance closure with reference to experimental data measured over a maize field

The use of energy fluxes data to validate land surface models requires that energy balance closure conservation is satisfied, but usually this condition is not verified when the available energy is bigger than the sum of turbulent vertical fluxes. In this work, a comprehensive evaluation of energy balance closure problems is performed on a 2012 data set from Livraga obtained by a micrometeorological eddy covariance station located in a maize field in the Po Valley. Energy balance closure is calculated by statistical regression of turbulent energy fluxes and soil heat flux against available energy. Generally, the results indicate a lack of closure with a mean imbalance in the order of 20%. Storage terms are the main reason for the unclosed energy balance but also the turbulent mixing conditions play a fundamental role in reliable turbulent flux estimations. Recently introduced in literature, the energy balance problem has been studied as a scale problem. A representative source area for each flux of the energy balance has been analyzed and the closure has been performed in function of turbulent flux footprint areas. Surface heterogeneity and seasonality effects have been studied to understand the influence of canopy growth on the energy balance closure. High frequency data have been used to calculate co-spectral and ogive functions, which suggest that an averaging period of 30 min may miss temporal scales that contribute to the turbulent fluxes. Finally, latent and sensible heat random error estimations are computed to give information about the measurement system and turbulence transport deficiencies.     

滩地植被化明渠中横向水平射流特性试验研究

运用Micro ADV测速系统,对3种工况下滩地植被化的复式断面横流环境中三维圆形水平射流的特性进行了试验研究.试验测得的射流典型横断面速度场及湍动能的成果表明,射流与来流的相互作用表现出明显的分叉现象,其分叉半角为5.71°;复式断面二次流具有加速射流分叉的作用,滩地植被具有减缓射流分叉的效应.对射流出口平面的速度场及湍动能的分析表明,射流轨迹曲线的弯曲程度、射流中心线的位置主要取决于射流与来流流速比.流动横断面流速和湍动能特性表明,射流在整个流场中是各向异性的.     

春末黄土高原半干旱区地表能量闭合的观测研究

利用兰州大学半干旱气候与环境监测站的连续观测数据,分析了该站的数据质量情况和黄土高原半干旱区的近地层湍流通量特征及地表能量平衡能量闭合状况.结果表明:兰州大学半干旱气候与环境监测站(SACOL)湍流通量的平均时间取30min为宜.该站利用EdiRe获得的湍流通量较TK2和CR5000数据自动记录器输出的湍流通量结果要好.黄土高原半干旱区近地层湍流能量与地表含水量状况明显相关,地表干燥时感热通量处于主导地位,接近于干旱区的特征;地表湿润时感热通量和潜热通量则相当,接近于湿润地区的特征.地表能量平衡分析表明,兰州大学黄土高原半干旱环境监测站观测的地表能量闭合度高达85%,与已有的观测相比,能量闭合情况属于较好水平.     

明渠恒定紊流的总流控制方程与能量损失特性

为进一步深化对明渠总流控制方程的认识,探究总流能量损失的构成与分布特点,通过理论分析,在黏性流体力学理论的框架下构建了描述明渠恒定紊流总体特性的总流积分模型与总流微分模型的控制方程,其模型参数能直接通过流动统计特征量在过流断面上的分布来获取,由此实现明渠流的流场特性描述与总流描述的统一,并得到了总流能量损失的显示表达式。同时指出,总流能量损失由黏性耗散与维持紊动两部分构成,在矩形明渠恒定均匀流紊流的分类能量损失构成中,壁面上以黏性耗散部分为主,维持紊动部分的能量损失密度随着离开壁面距离的增加而快速增加,且随着雷诺数的增大,其增加速度也越快。     

明渠恒定紊流的总流控制方程与能量损失特性

为进一步深化对明渠总流控制方程的认识,探究总流能量损失的构成与分布特点,通过理论分析,在黏性流体力学理论的框架下构建了描述明渠恒定紊流总体特性的总流积分模型与总流微分模型的控制方程,其模型参数能直接通过流动统计特征量在过流断面上的分布来获取,由此实现明渠流的流场特性描述与总流描述的统一,并得到了总流能量损失的显示表达式。同时指出,总流能量损失由黏性耗散与维持紊动两部分构成,在矩形明渠恒定均匀流紊流的分类能量损失构成中,壁面上以黏性耗散部分为主,维持紊动部分的能量损失密度随着离开壁面距离的增加而快速增加,且随着雷诺数的增大,其增加速度也越快。     

横流环境湍射流涡动力学特性数值模拟

采用三维湍流模型及其混合有限分析解法进行横流中湍射流这一复杂三维流动的研究。在利用实验数据对模型及其计算方法验证的基础上,对多种喷口形式和流速比工况下的流速场和涡量场进行了数值计算,模拟得到了其旋涡结构发展演化特性。在射流初始阶段,横流在射流背流面形成绕流分离旋涡,其结构与射流喷口形式和流速比有关。射流主轴沿流向布置的窄缝射流产生的旋涡最为特殊和复杂,在喷口侧面存在4个分离点,从而形成4个旋涡。在射流远区,流动主要由反向旋转涡对所控制,并诱导出二次涡对。分析得出了射流喷口形式及流速比对反向旋转涡对涡核位置和旋转强度的影响。     

From solid to granular gases: the steady state for granular materials

This paper aims at extending the well‐known critical state concept, associated with quasi‐static conditions, by accounting for the role played by the strain rate when focusing on the steady, simple shear flow of a dry assembly of identical, inelastic, soft spheres. An additional state variable for the system, the granular temperature, is accounted for. The granular temperature is related to the particle velocity fluctuations and measures the agitation of the system. This state variable, as is in the context of kinetic theories of granular gases, is assumed to govern the response of the material at large strain rates and low concentrations. The stresses of the system are associated with enduring, frictional contacts among particles involved in force chains and nearly instantaneous collisions. When the first mechanism prevails, the material behaves like a solid, and constitutive models of soil mechanics hold, whereas when inelastic collisions dominate, the material flows like a granular gas, and kinetic theories apply. Considering a pressure‐imposed flow, at large values of the normal stress and small values of the shear rate, the theory predicts a nonmonotonic shear rate dependence of the stress ratio at the steady state, which is likely to govern the evolution of landslides. Copyright © 2013 John Wiley & Sons, Ltd.     

弯曲槽道边壁振动情况下湍流特性的大涡模拟

为了更好地理解透平机械流道内能量耗散的机理和湍流结构变化,利用大涡数值模拟方法,数值试验了时、空做正弦振动的壁面所围成的弯曲槽道内的湍流流动。研究了6种不同的振动参数下,槽道内压力分布、近壁涡量以及其它相关湍流统计量的分布特性。计算结果表明,受展向壁面振动的影响,近壁区速度梯度增加,粘性底层变薄,湍流强度增加,能量耗散加大。该研究还发现壁面展向振动而引起的能量耗散主要依赖于近壁区粘性底层的展向涡量大小。     

石梁河水库消力池强紊动水流的数值模拟

采用半隐式的控制体积法离散紊流控制方程,考虑曲率修正的双方程紊流模型封闭雷诺应力,引入通度和体积函数的概念,数值模拟了石梁河水库工程改建后两级消力池的泄流过程.计算结果给出了自由表面的演变过程及其相互碰撞、重叠的消力池水流特征,断面流速、压力分布及自由水面位置与物理模型试验结果吻合良好.     

Quantifying velocity and turbulence structure in depositing sustained turbidity currents across breaks in slope

Two-dimensional experiments investigating sediment transport and turbulence structure in sustained turbidity currents that cross breaks in slope are presented as analogue illustrations for natural flows. The results suggest that in natural flows, turbulence generation at slope breaks may account for increased sand transport into basins and that the formation of a hydraulic jump may not be necessary to explain features such as the occurrence of submarine plunge pools and the deposition of coarser-grained beds in the bottomsets of Gilbert-type fan deltas. Experimental flows were generated on 0°, 3°, 6° and 9° slopes of equal length which terminated abruptly on a horizontal bed. Two-component velocities were measured on the slope, at the slope break and downstream of the slope break. Flows were depositional and non-uniform, visibly slowing and thickening with distance downstream. One-dimensional continuous wavelet transforms of velocity time series were used to produce time-period variance maps. Peaks in variance were tested against a background red-noise spectrum at the 95% level; a significant period banding occurs in the cross-wavelet transform at the slope break, attributed to increased formation of coherent flow structures (Kelvin–Helmholtz billows). Variance becomes distributed at progressively longer periods and the shape of the bed-normal-velocity spectral energy distribution changes with distance downstream. This is attributed to a shift towards larger turbulent structures caused by wake stretching. Mean velocity, Reynolds shear stress and turbulent kinetic energy profiles illustrate the mean distribution of turbulence through the currents. A turbulent kinetic energy transfer balance shows that flow non-uniformity arises through the transfer of mean streamwise slowing to mean bed-normal motion through the action of Reynolds normal stresses. Net turbulence production through the action of normal stresses is achieved on steeper slopes as turbulence dissipation due to mean bed-normal motion is limited. At the slope break, an imbalance between the production and dissipation of turbulence occurs because of the contrasting nature of the wall and free-shear boundaries at the bottom and top of the flows, respectively. A rapid reduction in mean streamwise velocity predominately affects the base of the flows and steeper proximal slope flows have to slow more at the break in slope. The increased turbulent kinetic energy, limited bed-normal motion and strong mixing imposed by steep proximal slopes means rapid slowing enhances turbulence production at the break in slope by focusing energy into coherent flow structures at a characteristic period. Thus, mean streamwise slowing is transferred into turbulence production at the slope break that causes increased transport of sediment and a decrease in deposit mass downstream of the slope break. The internal effects of flow non-uniformity therefore can be separated from the external influence of the slope break.     

初始裂隙对岩溶水紊流形成的影响

岩溶地区地下发育着大量的溶洞和地下河管道,地下水流状态既有层流也有紊流,而紊流是溶洞管道形成的重要条件。紊流的形成受到岩石初始裂隙的影响,初始裂隙的张开度、分布、走向、迹长、密度等因素都影响着裂隙发育过程中水流状态的变化。通过对不同统计特征的初始裂隙网络进行水流和溶蚀的数值模拟发现,以张开度标准差反映的裂隙网络非均匀性越强,模拟紊流出现的时间就越早;主要裂隙的存在使裂隙网络的非均性增强,主要裂隙与水力梯度总方向的角度越小,紊流出现的时间就越早;当裂隙平均迹长过小时会导致裂隙连通性较差,影响裂隙水流和溶蚀作用;裂隙密度,尤其是主要裂隙密度,对岩溶发育的影响较大。相对于次要裂隙,如果主要裂隙密度偏小,紊流形成时间会大大增加,甚至很难形成紊流。当初始裂隙张开度小于0.001 cm,增大水力梯度仍没有紊流发生,岩溶几乎不发育。      

Direct numerical simulation of a turbulent stably stratified air flow above a wavy water surface

The influence of the roughness of the underlaying water surface on turbulence is studied in a stably stratified boundary layer (SSBL). Direct numerical simulation (DNS) is conducted at various Reynolds (Re) and Richardson (Ri) numbers and the wave steepness ka. It is shown that, at constant Re, the stationary turbulent regime is set in at Ri below the threshold value Ri_c depending on Re. At Ri > Ri_c, in the absence of turbulent fluctuations near the wave water surface, three-dimensional quasiperiodical structures are identified and their threshold of origin depends on the steepness of the surface wave on the water surface. This regime is called a wave pumping regime. The formation of three-dimensional structures is explained by the development of parametric instability of the disturbances induced by the surface water in the air flow. The DNS results are quite consistent with prediction of the theoretical model of the SSBL flow, in which solutions for the disturbances of the fields of velocity and temperature in the wave pumping regime are found to be a solution of a two-dimensional linearized system with the heterogeneous boundary condition, which is caused by the presence of the surface wave. In addition to the turbulent fluctuations, the three-dimensional structures in the wave pumping regime provide for the transfer of impulse and heat, i.e., the increase in the roughness of the water–air boundary caused by the presence of waves intensifies the exchange in the SSBL.     

水动力学条件对复氧过程的影响研究

通过水槽实验对紊动水体复氧规律进行了研究.将氧通量理论应用于紊动水体复氧过程的研究,得到了紊动水体表面传质系数.数值模拟研究了实验流场分布和紊动特性,得出了紊动水体表面传质系数与流速和紊动动能的关系式.不同工况的实验资料验证表明了紊动复氧理论的合理性和可靠性.