Flow resistance law under suspended sediment laden conditions

The uniform flow resistance equation, in the form due to Manning or Darcy-Weisbach, is widely applied to establish the stage-discharge relationship of a river cross-section. The application of this equation, namely the slope-area method, allows to indirectly measure the corresponding river discharge by measurements of bed slope, water level, cross-section area, wetted perimeter and an estimate of channel roughness. In this paper, a recently deduced flow resistance equation for open channel flow was tested during conditions of suspended sediment-laden flow. First, the flow resistance equation was determined by dimensional analysis and by applying the condition of incomplete self-similarity for the flow velocity profile. Then the analysis was developed by the following steps: (i) for sediment-laden flows characterized by known values of mean diameter and concentration of suspended sediments, a relationship (Eq. (28)) between the Γ function of the velocity profile, the channel slope and the Froude number was calibrated by the available measurements; and (ii) a relationship for estimating the Γ function (Eq. (29)) which also takes into account the mean concentration of suspended particles was also established. The theoretical flow resistance law (Eq. (26)) coupled with the relationship for estimating the Γ function (Eq. (28) or Eq. (29)), which is characterized by the applicability of a wide range of flow conditions, allowed to estimate the Darcy-Weisbach friction factor for flows with suspended-load. The analysis showed that for large-size mixtures the Darcy-Weisbach friction factor can be accurately estimated neglecting the effect of mean concentration of suspended sediments while for small-size mixtures the friction factor decreases when the mean sediment concentration increases.     

Flow resistance due to shrubs and woody vegetation

In this paper, a theoretical open channel flow resistance equation was verified using flow depth and discharge measurements carried out by Freeman et al. in a large channel, 2.44 m wide, for ten different types of uniform-sized plants (shrubs and woody vegetation). The plants, which are broadleaf deciduous vegetation commonly found in floodplains and riparian zones, were placed in staggered rows inside the channel whose bed was constructed to accept plants with their root systems. For each species, the available measurements were carried out by Freeman et al. with plants having different values of plant density, height, and bending stiffness. The available literature database (87 measurements) was divided into two groups which were separately used to calibrate and test the theoretical approach. In particular, 46 measurements were used to calibrate the relationship between the scale factor Γ of the velocity profile, the Froude number, and the channel slope. This relationship was calibrated using the entire available dataset or varying the scaling coefficient a with the investigated vegetation type. The measured values of the Darcy-Weisbach friction factor, obtained by the measured flow velocity, water depth and slope values, were compared with those calculated by the theoretical flow resistance law, coupled with the relationship for estimating the Γ function having a scaling coefficient different for each investigated vegetation type. This comparison allowed to demonstrate that an accurate estimate of the Darcy-Weisbach friction factor (errors less than or equal to ±10% for 87% of the investigated cases) can be obtained. However, for the investigated vegetation species, that are characterized by a large range of bending stiffness, also a mean value of the scaling coefficient a equal to 0.3283 allows an accurate estimate of the Darcy-Weisbach friction factor.     

Application of the sampling moiré method to shallow open-channel flows with circular roughness elements

This research presents an application of the sampling moiré method, a novel technique originally developed for measuring slight deformation of a static object such as a plate, to fluctuating free water surface in rough open channel flows. The method was used to capture the two-dimensional water surface deformation at a high sampling rate by dyeing the color of water white. The target flow was a very shallow subcritical flow with a depth of 1.5 times the height of the roughness. As a result, a series of instantaneous water surface profiles with non-uniform rough planes were successfully measured at a sampling rate of 100 Hz.It has become clear that the effect of dispersive gravity waves traveling on the water surface is greater than that of non-dispersive waves driven by the turbulence, and that this feature becomes more pronounced as the Froude number increases in such shallow flow conditions. Furthermore, it was experimentally and theoretically verified that the intensity of water surface fluctuation increases with the square of the Froude number. The decomposition of surface fluctuations due to gravity waves and subsurface turbulence using the wavenumber frequency spectrum revealed that the effects of subsurface turbulence are about 20%. This is much less than the contribution from gravity waves in very shallow flows as in this experiment.     

Application of video imagery techniques for low cost measurement of water surface velocity in open channels

Developments in digital video recording technology make the video imagery tools more popular for velocity measurement in water flows. This has especially been of large interest due to its inherent advantage of non-contact nature which is quite handy in extreme flow conditions. Particle Image Velocimetry (PIV), Particle Tracking Velocimetry (PTV) and Large Scale Particle Tracking Velocimetry (LSPTV) are applied to free surface channel flow for water surface velocity measurement. Experiments are conducted to measure either a single point velocity applying PTV or velocity profiles across the channel width applying PIV on the water surface in a rectang typical velocities of nearly 1 andular tilting flume for various flow conditions. Technical issues regarding tracer particle size and type, travel distance, lighting, recording speed, camera position, image distortion and state of flow are discussed. Measured data is compared to computational results obtained from a numerical model involving a non-linear turbulence model capable of predicting turbulence driven secondary flows. Confirmation of reasonable match between computational and experimental results whereby applying mutual collaboration of them for discharge measurement has been attested. In addition to discharge, boundary roughness has also been predicted as an outcome of the numerical solution.     

A new visualisation and measurement technology for water continuous multiphase flows

This paper reports the performance of a research prototype of a new multiphase flow instrument to non-invasively measure the phase flow rates, with the capability to rapidly image the flow distributions of two- and three-phase (gas and/or oil in water) flows. The research prototype is based on the novel concepts of combining vector Electrical Impedance Tomography (EIT) sensor (for measuring dispersed-phase velocity and fraction) with an electromagnetic flow metre (EMF, for measuring continuous-phase velocity with the EIT input) and a gradiomanometer flow-mixture density metre (FDM), in addition to on-line water conductivity, temperature and absolute pressure measurements. EIT–EMF–FDM data fusion embedded in the research prototype, including online calibration/compensation of conductivity change due to the change of fluids' temperature or ionic concentration, enables the determination of mean concentration, mean velocity and hence the mean flow rate of each individual phase based on the measurement of dispersed-phase distributions and velocity profiles. Results from first flow-loop experiments conducted at Schlumberger Gould Research (SGR) will be described. The performance of the research prototype in flow-rate measurements are evaluated by comparison with the flow-loop references. The results indicate that optimum performance of the research prototype for three-phase flows is confined within the measuring envelope 45–100% Water-in-Liquid Ratio (WLR) and 0–45% Gas Volume Fraction (GVF). Within the scope of this joint research project funded by the UK Engineering & Physical Sciences Research Council (EPSRC), only vertical flows with a conductive continuous liquid phase will be addressed.     

Discharge equation of semi-circular side weirs: An experimental study

Side weirs are diverting structures and usually used for diverting and controlling the water flow into the side open channel. The present study deals with an experimental study regarding the hydraulic performance of side weirs with semi-circular vertical sections along the main channel. As flow depth of the main channel increases the top flow width of the semi-circular side weir (SCSW) increases which is an advantage when high discharge enters the main channel and should be immediately diverted for safety reasons. In this study, the flow discharge of semi-circular sharp-crested side weirs and their affecting parameters are investigated. To investigate the hydraulic behavior and geometric characteristics of the SCSWs, a comprehensive laboratory study including 155 tests (for three weir diameters 0.25, 0.30 and 0.40 m) was conducted in a physical model under subcritical flow conditions. Flow discharge of the SCSW was investigated in relation to height, diameter and flow head of side weir, also approach Froude number (Froude number at upstream end of the side weir) and main channel width. Three different discharge models were developed based on; purely dimensional analysis technique, classical weir equation with linear water surface and classical weir equation with horizontal water surface profile (conventional weir theory along with dimensional analysis technique). The presented mathematical discharge models enable estimation of discharge along the SCSW with acceptable accuracy (best model has an average error of 1.87% with a maximum error of 6.31%) compared with the measured data under subcritical flow conditions. Additionally, a relationship was proposed for computing the limiting flow depth at the downstream end of the SCSW. Experimental results confirm that the proposed relationship well explains the behavior of flow over the SCSW regarding the downstream flow conditions.     

旋转单斜丝热线测量叶轮机出口流场

结合热线测量的一般方法及周期性采样平均技术，推导出旋转单丝斜探头测量叶轮机出口周期性三维流场的方法，借助于Matlab的程序实现非线性L-M最小二乘法求解三维速度平均量。采用上述方法成功测量了T35轴流通风机出口周期性三维流场。     

Application of LSPIV to measure supercritical flow in steep channels with low relative submergence

Measuring flow discharge has always been one of the most important concerns of water experts. To measure discharge in streams using velocity-area method it is necessary to quantify average velocity of the flow. It is not feasible to measure velocity by contact approaches like current meters under certain conditions such as in flood periods or for very shallow flows. Flow surface image velocimetry methods as non-intrusive solutions have recently been widely utilized to measure discharge in open channels. One of these methods is a variety of PIV method named LSPIV which has been very popular due to the elimination of laser application. In this study, LSPIV was used to measure 2D velocity field over the surface of steep supercritical flow. The obtained surface velocity data were used to calculate Velocity Index (VI) which is multiplied by surface velocity to convert it to mean velocity and subsequently flow discharge. Also, a few relations were proposed to calculate the VI according to the slope and relative submergence. Since, Velocity Index has been so far mostly studied for subcritical conditions, results of this study may be applied for measuring supercritical flows. Eventually, the proposed method was verified to be used for discharge measurement and was proven quite precise in this regard.     

Discharging capacity of rectangular side weirs in straight open channels

A side weir is a hydraulic control structure used in irrigation and drainage systems and combined sewer systems. A comprehensive laboratory study, including 843 tests for the discharge coefficient of a sharp-crested rectangular side weir in a straight channel, was conducted in a large physical model under subcritical flow conditions. The discharge coefficient is a function of the upstream Froude number, the ratios of weir length to channel width, weir length to flow depth, and weir height to flow depth. An equation was developed considering all dimensional parameters for discharge coefficient of the sharp-crested rectangular side weir. The average error of the proposed equation is 4.54%. The present study data were compared with ten different discharge coefficient equations developed by several researchers. The study also presents water surface profile and surface velocity streamlines.     

Flow over trapezoidal side weir

In this paper, the hydraulic characteristics of a sharp crested trapezoidal side weir have been experimentally and theoretically investigated. It was found that the DeMarchi coefficient of discharge for a sharp crested trapezoidal side weir in subcritical flow is related to the main channel Froude number, the side slope of weir, ratio of weir height to upstream depth of flow and ratio of weir length to upstream depth of flow. Suitable equations for the discharge coefficient are also obtained.     

Dissipative scaling of step-pool features

This paper focuses on the dissipative similarity of step-pool units at rill, flume and stream scale. This investigation is carried out using recent advances in open channel flow resistance, applications of close-range photogrammetry to rill erosion, available published data on step-pool features in flumes and streams and a new dataset of measurements in fixed bed step-pool rills. A theoretically-based equation for calculating the Darcy-Weisbach friction factor obtained by integration of a power velocity profile is presented. The scale factor Γ of this power velocity profile, which is included in the flow resistance equation, was previously calibrated (Eq. 10) for mobile bed rills with step-pool units. At first, in this investigation an additional test of this flow resistance equation is developed using measurements carried out in fixed bed rills with step-pool features. In particular, the proposed Γ function is tested using the measurements carried out in 63 fixed bed rill reaches incised on a 24 and 26% sloped plot. This test shows that the effect of sediment transport on the flow resistance law can be considered negligible as compared to the effect of the form-induced dissipative mechanisms due to the presence of step-pools structures. Then, using measurements carried out in 61 flume experimental runs and 109 reaches of step-pool streams, this investigation demonstrates that the Γ function for flume and stream conditions can be obtained scaling that (Eq. 10) determined for step-pool rills. The Darcy-Weisbach friction factor values measured in flumes and streams are, on average, higher than those related to rills. Finally, the application of the theoretical equation for calculating the Darcy-Weisbach friction factor for flume and stream conditions requires Γ, estimated by Eq. (10), to be multiplied by a specific scale factor.     

Experimental study and numerical simulation of flow over the inclined airfoil-shaped weir in rectangular channel

In order to find an integrated flow measurement and control facility with stable outflow form, a series of experiments and numerical simulations were performed for the inclined airfoil-shaped weir. Based on the experimental and simulated data, the stage-discharge relationship was deduced by using dimensional analysis and incomplete self-similarity theory. And two flow measurement formulas with inclination angle of 0°–45° were obtained through different fitting schemes. The variation law of discharge ratio with inclination angle and the accuracy comparison of flow measurement formulas were analyzed. Moreover, the Froude number, critical submergence degree, head loss and velocity distribution of the flow field over the weir were studied. The results show that streamlined airfoil improves the stability of flow behind the weir. The average relative error of the free water surface line data between experiments and simulations is 5.05%, which indicates the reliability of the numerical simulation. The discharge ratio proposed in the fitting scheme I takes the 25° inclination angle as the limit, which increases slightly at first and then decreases gradually, and the flow measurement relative errors of the two fitting formulas are all within ±7%. The average Froude number of the upstream reference section at each inclination angle is less than 0.25, the critical submergence range is between 0.87 and 0.96, and the relative head loss ranges from 3.54% to 12.16%, so as to ensure the accuracy of flow measurement.     

光电非接触式表面流速测量

针对水工物理模型试验中尚无简单易行的表面流速测量方法,提出了一种新型光电非接触式表面流速直接测量法。在对光束入射水体后散射光强度公式进行推导的基础上,根据水体浅层泥沙浓度的统计继承效应,得出了经上下游浅层泥沙调制的散射光强成相关特性的结论。根据上下游散射光的相关特性,推导了流速测量公式,并分析了上下游测量间距、水流流速、采样率对测量结果的影响。搭建了实验系统,在6种不同标定流速下,分析了不同含沙量对测量精度的影响。实验结果表明,在0～50kg/m36种不同含沙量情况下,实测流速与标定流速的一致性均较好,但水体在10～50kg/m3适量含沙情况下,测量精度较不含沙情况有所提高,测量绝对误差均小于0.1m/s,相对误差能控制在8%以内。     

A new correlation of wet gas flow for low pressure with a vertically mounted Venturi meter

Wet gas metering has become an increasingly important technique for many industries. However, the over-reading phenomenon reduces the accuracy of Differential Pressure meters. This research fills the vacancy of correlations and presents a new correlation for low pressure between 0.82 and 1.52 MPa with a vertically mounted Venturi meter to calculate the over-reading coefficient accurately. Based on the correlational analysis, the over-reading coefficient is a function of the Lockhart-Martinelli parameter, density ratio, and gas Froude number. The constant coefficients in this correlation are obtained by nonlinear regression. Effect of low gas velocity with gas Froude number under 1.5 is taken into consideration as well. The average relative error is 1.9% and the root mean square error is 3.0%. Furthermore, a new method to calculate the over-reading coefficient for industrial applications is put forward due to the difficulties of online measurements of the Lockhart-Martinelli parameter which is substituted with the void fraction. The void fraction is calculated by an empirical correlation using quality and an approximate algorithm is utilized to obtain gas Froude number. For this new method, the average relative error is 2.3% and the root mean square error is 3.7%. This quality-based method will be helpful to resolve the limited applicability of gamma-ray attenuation for wet gas flow metering in industry regarding vertical low pressure conditions.     

Research the wet gas flow measurement based on dual-throttle device

In this paper a novel flow measurement device composed of a long throat Venturi tube and a V-cone was proposed to deal with the wet gas flow measurement without separation, and a new metering method was put forward based on the triple differential pressures. The correlations were based on the gas densiometric Froude number, gas–liquid density ratio, and the differential pressure ratios, which were then compared and validated by the laboratory and field tests. The laboratory test results showed that the uncertainty of relative errors for the gas and liquid flow rates were less than 3% and 6%, respectively. The field test results showed that the uncertainty of relative errors for the gas flow rates before correction varied from 5.53% to 11.57%. After correction the uncertainty of relative errors for gas flow rate varied from 1.37% to 3.22% and full-scale error for liquid flow rate was less than ±10%.     

An investigation into the effects of installation on the performance of insertion flowmeters

An electromagnetic and a turbine insertion flowmeter were tested in three different flow conditions inside a 0.590-m bore pipe inserted in the National Engineering Laboratory (NEL) large water flow measurement facility. The results were compared with velocity measurements obtained from a laser Doppler velocimeter (LDV). The advantage of using such a reference measurement is that LDV is non-intrusive and does not affect the velocity profile itself.Of the meters tested, one was supplied with a whole meter calibration factor and the other was supplied with a calibration factor for the D/2 position.For both meters, application of the respective manufacturer's blockage correction improved the velocity measurements, reducing the differences between the LDV and corrected insertion meter measurements and the difference between the integrated insertion meter measurements and the gravimetric measurements.Swirling and skew flow profiles were generated by the installation of the NEL designed swirl generator and flow disturber, respectively. Neither of these disturbed profiles affected the performance of either of the meters in terms of accuracy of measurement compared with the LDV readings. The profiles themselves, however, changed the velocities at the D/8 and 7D/8 points, making single point estimates of the mean velocity inappropriate. A complete 13-point traverse, integrated using the method of cubics as described in BS 1042 [1] (Section 2.3: Measurement of fluid flow in closed conduits, 1992), gave acceptable estimates of mean velocity in both swirling and skew flow for both probes.     

A review of studies on estimating the discharge coefficient of flow control structures based on the soft computing models

The discharge coefficient (Cd) plays a vital role in the accurate design and safety of weirs, spillways, and dams. In the last decade, Soft Computing(SC) models, which showed excellent capabilities for non-linear mapping between parameters, were widely used to estimate the discharge coefficient of flow control structures. This study provides a comprehensive review of the application of SC models for estimating Cd of different flow control structures such as ogee spillways, orifices, side weirs, etc. In addition, the most common empirical relations which are obtained from laboratory experiments are discussed briefly. The findings revealed that weir length/flow depth ratio, weir length/channel width ratio, weir height/flow depth, and Froude number are widely used to estimate Cd in the side weirs. Besides, the ratio of orifice crest height to height of side orifice, the ratio of main channel width to length of side orifice, ratio of main channel width to height of side orifice, and ratio of the height of side orifice to upstream flow depth were extensively employed to calculate Cd of orifice structures. The common parameters for measuring Cd of labyrinth weirs are, discharge over a labyrinth cycle, weir height, channel width, apex constant, upstream head, discharge over the weir, effective length, convergence constant, sidewall angle, and Froude number. In the weir-gate structure, some factors such as contraction coefficient of the gate, head loss, and weir height are key parameters for the accurate evaluation of Cd. The trends of SC models, features of popular models, and the background of models are discussed briefly in this paper. Also, research gaps and possible directions for new studies are suggested.     

超声波气体流量计检测精度影响因素分析

在天然气的管道运输过程中,提高气体流量测量的精度是提高运输效率、避免安全事故发生的关键技术。利用流体力学仿真（CFD）方法建立组合双弯管及变径管道模型,定量计算修正系数,对双声道超声波流量计结构和安装位置对于管道内气体速度场的影响进行研究。通过仿真得出超声波流量计的最优声道位置,并结合实验验证了仿真结果的可信性。模拟结果表明,双弯管和变径管与超声波流量计的安装位置至少为10D才能保证流体充分流动;通过修正系数随雷诺数的变化情况得出双声道超声波流量计的最优声道位置为距管道截面中心0.25D处。研究结论对于不同性质气体的流量检测同样适用,为工业中气体运输检测精度的提高以及超声波流量计的优化提供了依据。     

Unsteady velocity profiling in bores and positive surges

In an open channel, steady flow conditions may be achieved when the discharge and boundary conditions remain constant for a reasonable period of time. The operation of any regulation device (e.g. gate) is associated with some unsteady surge motion. In the present study, new velocity profiling measurements were performed systematically under controlled flow conditions. Both steady and unsteady measurements were conducted in a relatively large laboratory facility. An ensemble-averaged technique was applied in unsteady flows to investigate positive surges. The experiments were repeated 25 (or 50) times for each controlled flow condition and the results were ensemble-averaged. The quality and accuracy of the Profiler data set were validated against data collected with an acoustic Doppler velocimeter, in both steady and unsteady rapidly-varied flows. A careful sensitivity analysis was conducted to test the appropriate number of runs. The results indicated that the selection of 25 runs was suitable for ensemble-averaging in rapidly-varied unsteady flows. Some instrumental error was observed however with the velocity profiler. Outside the boundary layer, the Profiler tended to produce errors in terms time-averaged velocity data and velocity fluctuations for a number of points in a profile. Overall, the study demonstrated that the propagation of positive surges is a highly unsteady turbulent process, and the performance of ADV Vectrino II Profiler in such an unsteady turbulent flow was satisfactory, provided that a careful validation was undertaken for all Profiler outputs.     

高精度质量检测在航空器叶轮五轴加工中的应用

以航空器叶轮五轴高速加工为基础,针对叶轮复杂三维扭曲流道空间曲面检测困难的问题,研究了在机检测和智能修正技术、三维扫描检测技术,并利用工业级蓝光三维检测系统,对航空器叶轮进行五轴加工和准确、高效、可靠的三维数字化高精度检测。结果表明,该方法可快速实现高精度三维全尺寸检测,提高了测量效率。