Effect of Froude similitude deviation on curved channel simulations: A case study in the Middle Yangtze River

Froude similitude and friction similitude are the two crucial similarity conditions that are often used in physical-scale modeling of rivers.However,models often deviate from Froude similitude when dealing with real-world situations.This study developed several fixed-bed river models with various curvatures to determine the effect of Froude similitude deviation on curved channel modeling.Models were constructed according to the characteristics of the Middle Yangtze River.Differences in longitudinal slope,transverse slope,and main stream line location were measured by varying Froude similitude deviation.The deviations of longitudinal slope and velocity were negligible because friction similitude was accounted for.The transverse slope varied significantly with the Froude similitude deviation,and the main stream line varied with the curvature and Froude similitude deviation.Formulae were derived to estimate the slope deviation.These analyses helped to clarify the feasibility of the method of Froude similitude deviation for curved channels.

基于面积型Froude数的河型判数与黄河河道最大输沙流量及河槽宽深尺度

Froude数同水流强度和水流能量关系密切,水深型Froude数不适用于黄河沙质河段,面积型Froude数在判断复杂河流水流相对强度、河床冲淤与稳定程度等方面都有较大价值。本文以此为基础研究面积型Froude数在河型判别的应用,利用不同河型临界关系式,得到整治流量或整治河宽计算式,以及均衡条件下的河床形态公式。根据黄河模型小河造床过程,得到主槽最大输沙或相对稳定状态下,断面单位能量与河相系数关系方程,进一步研究了最大输沙流量对应的主河槽宽深尺度的计算。

Froude摆系统的全局有限时间同步

基于广义线性状态误差反馈控制器,构造了2个Froude摆系统的主从有限时间同步框架,并将2个Froude摆系统的全局有限时间同步问题转化为主-从系统的误差系统的全局有限时间稳定性问题;然后,应用有限时间稳定性理论证明了2个Froude摆系统实现全局有限时间同步的判据并进行了优化,同时估算了同步时间;最后,通过计算机仿真验证了所得判据的有效性。

受地求旋转作用的小Froude数过山气流

在小Ｆｒｏｕｄｅ数的过山气流中，常在迎风坡上出现流阻塞，北风坡之上出现波碎碎区。因此，即使上游Ｒｏｓｓｂｙ数很大，在这两个局地的滞流区域内Ｒｏｓｂｙ数仍很小，柯氏力作用很重要。本文分别就无地表摩擦和有地表摩擦两种他地求旋转对小Ｆｒｏｕｄｅ数过山气流的作用。结果表明：地球旋转作用使得过山气流周期振汇，有利于背风坡上强下坡风和波破碎现象的出现，抑制迎风坡上气流阻塞的发生。而且对于存在地表摩擦作用情形，

层结大气中Froude数对过山气流的影响

本文建立了一个层结大气中二维过山气流模式，对层结大气的Froude数对过山气流的影响进行了数值研究，通过地形上空流场、位温场以及平行于山脉的风场的分析。探讨了Froude数影响地形上空大气运动的一些规律。

Application of Froude dynamic similitude in anaerobic baffled reactors to prediction of hydrodynamic characteristics of a prototype reactorusing a model reactor

An anaerobic baffled reactor is a system developed in recent decades and has been used as part of the treatment of high-strength wastewater. Since the function of this system is based on its hydrodynamic features, hydrodynamics and the regime of the flow through the reactor are crucial. In this study, a prototype reactor with eight chambers, which had a total volume of 48 L, and a model reactor, whose dimensions were half of those of the prototype reactor, were used. The Froude dynamic similitude in these reactors was investigated. The results show that the curve dimensionless variances were 0.089 and 0.096 for the prototype and model reactors, respectively, the short-circuiting indices were 0.483 and 0.489 for the prototype and model reactors, respectively, the effective volume and short-circuiting index measurement errors were both 1%, the hydraulic efficiency error was 2%, and the Peclet and dispersion number errors were both 7%. Most of the compared indices were close to one another in value. Therefore, the model reactor can be used based on the Froude dynamic similitude to determine hydrodynamic charac-teristics of a baffled reactor at a full scale.

基于改进Froude数的太子河流域河相形态分析

文章针对水深型Froude数计算局限,采用基于面积型Froude数对其进行改进,并以太子河为例,对典型断面河相形态进行分析。分析结果表明:相比于水深型Froude数,改进的Froude数更适合于河相形态的分析,太子河流域典型断面河相系数沿程递减趋势明显。河道主槽流量与河相系数呈现强相关性,流量越高其河相系数相对越大。文章研究成果为太子河流域河道形态演变分析提供参考和借鉴。

Investigation of solids segregation of binary mixtures in a rotating drum at various Froude numbers

To investigate the effect of the Froude number(Fr)on solid segregation in a rotating drum,a two dimensional mathematical modelling on solids behaviour in horizontally oriented rotating drums operated in rolling,cascading and cataracting modes has been carried out by using Euler-Euler multi-fluid model in Fluent6.2 environment.Small particles and big particles are used in the work as binary mixtures to investigate segregation characteristics.The effect of Froude number(rotating velocity)on the flow field is investigated.It is found that the model captures the main features of solids motion and segregation in the drum and numerical results agree well with limited experimental data for solid velocity.

分数阶Froude摆系统的混沌同步

以Lyapunov稳定性理论和分数阶微积分为理论基础,研究了分数阶Froude摆系统的同步问题,给出了实现系统同步的方案。在该方案下,适当地选取控制律,可以使分数阶Froude摆系统的主从系统取得混沌同步,给出的数值仿真表明可行性和有效性。

基于面积型Froude数的浑河流域河相系数计算及沿程关系探讨

针对水深型Froude数对于河相系数计算不适用的问题,采用面积型Froude数对浑河流域河相系数进行计算,定量分析其Froude数分布,并探讨不同河型下整治流量和对应宽度的范围。结果表明:面积型Froude数与水流强度及水能具有强相关性,与河相系数呈现反相关性,相关程度高于0.7。随着流量的增加,河相系数沿程递增,且随流量呈现指数变化。

复杂河流面积型Froude数新形式及其应用

通过回顾Froude数的提出与发展,探讨了其中流体特征长度的选取问题,认为水深型Froude数在复杂河流计算中具有局限性.鉴于断面几何形态直接影响水流特性,提出了面积型Froude数的形式,可用于流态判断,具有普遍适用性.分析表明,面积型Froude数可正确计算冲积河流复式断面中滩地、河槽及全断面水流相对强度大小.进一步通过实测资料比较及理论分析,阐述了面积型Froude数在判断复杂河流河床稳定性、划分河型、描述水力摩阻特性、完善河工变态模型相似理论等方面具有应用价值.

Study of a Hydraulic Jump in an Asymmetric Trapezoidal Channel with Different Sluice Gates

In this study,the main properties of the hydraulic jump in an asymmetric trapezoidal flume are analyzed experimentally,including the so-called sequent depths,characteristic lengths,and efficiency.In particular,an asymmetric trapezoidal flume with a length of 7 m and a width of 0.304 m is considered,with the bottom of the flume transversely inclined at an angle of m=0.296 and vertical lateral sides.The corresponding inflow Froude number is allowed to range in the interval(1.40<F1<6.11).The properties of this jump are compared to those of hydraulic jumps in channels with other types of cross-sections.A relationship for calculating hydraulic jump efficiency is proposed for the considered flume.For F1>5,the hydraulic jump is found to be more effective than that occurring in triangular and symmetric trapezoidal channels.Also,when■mes>8 and■>5,the hydraulic jump in the asymmetrical trapezoidal channel downstream of a parallelogram sluice gate is completely formed as opposed to the situation where a triangular sluice is considered.

倾斜隧道火灾烟气分层稳定性研究

隧道内的烟气分层特征对分析疏散和救援的难度以及制定有效的应急策略具有至关重要的作用。倾斜隧道中的烟气流动受到浮力和烟囱效应的共同影响,导致烟气的分布和运动规律与水平隧道存在显著差异。在倾斜隧道中,烟气分层稳定性受到多种因素的影响,且相关研究较少。本文采用数值模拟方法对倾斜角度为1%~15%的两端开口的倾斜隧道火灾烟气分布特性及其影响因素进行了研究。研究表明:Newman提出的判定烟气分层状态的临界无量纲温差在倾斜隧道火灾中仍然适用(坡度在1%~15%范围内)。倾斜隧道火灾发生后,火源与低端入口之间的烟气层始终能够保持稳定的烟气分层。而火源与下游出口之间的烟气层则随着烟囱效应的增强,稳定分层被破坏的区域不断扩大,并逐渐扩展至整个下游区域。火源功率和火源与下游出口之间的高差可直接影响隧道内的烟囱效应和烟气自身浮力,进而影响烟气分层状态。在此基础上,提出了用于预测倾斜隧道火灾烟气分层特性的计算模型,并确定了烟气分层区域1和区域2之间的临界Froude数为0.9。本文研究可为隧道火灾排烟及疏散设计提供指导。

Effects of Froude number and geometry on water entry of a 2-D ellipse

By using the finite volume method with volume of fluid model and global dynamic mesh technique, the effects of Froude number and geometry on the water entry process of a 2-D ellipse are investigated numerically. For the time history of the vertical force, the computational fluid dynamics（CFD） results match the experimental data much better than the classical potential-flow theories due to the consideration of the viscosity, turbulence, surface tension, gravity, and compressibility. The results show that the position of peak pressure on ellipse shifts from the spray root to the bottom of ellipse at a critical time. The critical time changes with the geometry and Froude number. By studying the vertical force, the ellipse water entry process can be divided into the initial and late stages based on the critical dimensionless time of about 0.1. The geometry of the ellipse plays a dominant role in the initial stage, while the Froude number is more important in the late stage of entry. The classical Wagner theory is extended to the ellipse water entry, and the predicted maximum value of vertical force coefficient in the initial stage is 4？a/b that matches the CFD results very well, where a and b are the horizontal axis and vertical axis of the ellipse parallel and perpendicular to the initial calm water surface, respectively.

Experimental investigation of the optimization of stilling basin with shallowwater cushion used for low Froude number energy dissipation

Energy dissipations induced by the hydraulic jump and the trajectory jet are the most widely known as the two dissipation modes at the downstream of flood discharging structures, which are often considered quite different even contradictory. However, such two energy dissipators can be used jointly and harmonically. In this paper, a new type of stilling basin with a shallow-water cushion and a triangular bottom deflector is proposed based on two different scale physical model tests of the flood discharging tunnel No.2 of Luding hydropower project. The experimental results show that the flow regime of the hydraulic jump in the presented stilling basin with bottom deflector enjoys a good and stable performance within a large range of flow rates and the energy dissipation rate is considerably high as compared to the conventional stilling basin even at a low Froude number. The results also indicate that the stilling basin with triangular bottom deflector has a better performance in improving the potential cavitation erosion according to the analysis of the pressure and the cavitation number compared to the trapezoidal one. The proposed new type of shallow-cushion stilling basin with a shallow-water cushion can be applied in similar energy dissipation projects with low Froude number and large range of flow rates.

Hydraulics of crest spillway with large unit discharge and low Froude number

With respect to the crest spillway with large unit discharge and low Froude number, the hydraulics of the slit-type energy dissipater at the outlet should be noticed due to the complicated flow regimes. In the present paper, some issues about hydraulic characteristics were experimentally investigated by means of five slit-type outlets and four tetrahedrons, including the flow choking, impact to river banks and jet trajectory. The main findings are as follows. The critical Froude number for the flow choking decreases with increasing outlet width of the slit-type energy dissipater. If the flow Froude number is expressed by the parameters just before this energy dissipater, the tetrahedron placed inside the side wall of the outlet could efficiently avoid the flow impact to the river bank of same side, and compared with the jet trajectory of the slit-type energy dissipater, the outlet with tetrahedron has different trajectory trend, i.e., the distance of the jet trajectory decreases with the increase of the water head due to special form of the outlet tetrahedron.

An Innovative Approach to Predicting Scour Depth Around Foundations Under Combined Waves and Currents in Large-Scale Tests Based on Small-Scale Tests

This study presents an innovative theoretical approach to predicting the scour depth around a foundation in large-scale model tests based on small-scale model tests under combined waves and currents.In the present approach,the hydrodynamic parameters were designed based on the Froude similitude criteria.To avoid the cohesive behavior,we scaled the sediment size based on the settling velocity similarity,i.e.,the suspended load similarity.Then,a series of different scale model tests was conducted to obtain the scour depth around the pile in combined waves and currents.The fitting formula of scour depth from the small-scale model tests was used to predict the results of large-scale tests.The accuracy of the present approach was validated by comparing the prediction values with experimental data of large-scale tests.Moreover,the correctness and accuracy of the present approach for foundations with complex shapes,e.g.,the tripod foundation,was further checked.The results indicated that the fitting line from small-scale model tests slightly overestimated the experimental data of large-scale model tests,and the errors can be accepted.In general,the present approach was applied to predict the maximum or equilibrium scour depth of the large-scale model tests around single piles and tripods.

不稳定分层大气边界层中沙尘暴的无黏模型研究

实验观测表明,沙尘暴发生之前的大气边界层常常是不稳定分层的。沙尘暴可被视为处于超高Reynolds数的颗粒两相湍流异重流。为了研究异重流坍塌阶段的主控机制,建立了一个无黏模型,发现在重流体或环境流体或两者均存在不稳定密度分层时,表征异重流头部速度的Froude数都会变小。对不同的开闸高度和不稳定分层情况的开闸式异重流进行了数值模拟。尽管在密度界面存在混合,但是模拟所得的头部速度与高度关系同无黏模型的预测相符。另外,野外观测到的沙尘暴头部速度增量同该模型的预测基本一致,显示在该类高Reynolds数湍流中无黏机制的贡献不容忽视。

水库浑水异重流潜入点判别条件

泥沙淤积是影响多沙河流水库寿命的一大难题,而异重流排沙是减少库区淤积的重要措施之一。异重流的潜入现象是异重流开始形成的直观标志,研究异重流潜入条件的判别方法有助于掌握异重流在库区内的演进规律。总结了水库异重流潜入条件的定性描述及定量计算方法,指出已有的潜入点判别公式的优缺点及适用范围,改进了描述异重流运动的动量方程,同时分析了异重流流速与含沙量沿垂线不均匀分布对动量传递的影响;在此基础上提出新的异重流潜入条件判别式,并用多组室内及野外实测资料对该判别条件进行率定与验证。分析结果表明,新的计算公式可用于判别小浪底库区异重流的潜入条件。

1000kV苏通大跨越输电塔线体系气弹模型的风洞试验研究

拟建的苏通大跨越输电线路是目前为止塔身最高、跨度最长的塔线体系,主要受风荷载控制。气弹模型的风洞试验是深入研究各种风致耦合振动现象的有效手段。由于风洞条件和模型材料的限制,模型设计需要放松输电塔的Froude数相似准则,采用Davenport提出的线模型等效设计方法。但这会引起塔线体系响应不匹配以及气动阻尼和质量不符合相似比等问题。通过增大输电线模型的刚度矩阵,不改变输电线模型垂度,推导输电线模型的精确气动力相似比等手段设计塔线体系气弹模型。将其放置于标定好的风场中,通过有限元分析梯度风对其的影响,测试单塔和塔线体系的风致响应,揭示位移、频率以及阻尼等塔线耦合的机理。试验结果表明：30o风向角时输电塔的位移响应最大;塔线耦合改变了输电塔的动力特性和风致响应分量;试验风速下的输电塔和导线均没有动力失稳。