Supercritical Flow Measurement Using a Small Parshall Flume

An experimental program was conducted to determine if a Parshall flume, developed to accurately measure open-channel subcritical flow, could also be used to measure discharge in a supercritical flow regime. Fifteen experimental configurations were tested using two small Parshall flumes [6-in. (15.2-cm) and 9-in. (22.9-cm) crest width] with varying approach channel slopes, approach channel roughness, and flume convergence. It was determined that a single Parshall flume can be used to measure flow (within ±5%) for both supercritical and subcritical flow regimes for a specified range of flows. The original Parshall flume equation was then modified to incorporate crest width, channel slope, channel roughness, and convergence in the prediction algorithm. Unique expressions were developed for both supercritical and subcritical flow regimes to estimate the discharge. A single expression does not appear feasible for accurate discharge measurement for both flow regimes in a Parshall flume at this time.     

Benchmark of Discharge Calibration Methods for Submerged Sluice Gates

Real accuracy of several calibration methods for sluice gates working in the submerged orifice flow condition was determined considering water discharge from water levels and gate openings. Data were taken from three gates of the same laboratory canal covering a large operational range. Using accurate hydraulic data, most of the methods produce errors of up to ±10%. However, errors can rise up to ±40% with methods using typically recommended calibration values or constant discharge coefficients. The best results were obtained by a method based on dimensional analysis and the incomplete self-similarity theory proposed recently in the literature. Calibration with field data, in this case, produced errors not higher than ±3%. On the other side, when the gate discharge data are not available, the use of a contraction value of 0.611 within a good theoretical formulation gives very good results.     

Some new aspects on inclusion separation in tundishes

The removal of non‐metallic inclusions due to buoyancy forces in tundishes in continuous casting systems is considered. The maximal theoretical removal rate is determined by the flow rate through the tundish, the magnitude of the tundish fluid surface area and the particle terminal rising velocity, depending on the particle size. Two reasons, why the particle separation is worse than the maximal possible one are an unsuitable fluid flow pattern and the turbulent particle diffusion. An analytical discussion of simple flow patterns (parallel flow with different velocity profiles, dead regions, swirling flows) and diffusion shows how they influence the particle removal. Using these simple considerations, it is demonstrated that the often used RTD (residence time distribution)‐curves are inappropriate to estimate the particle separation in tundishes; only the direct measurement and CFD‐simulation of particle removal should be used. The common CFD‐methods are affected with numerical errors such as numerical diffusion for particle concentration simulations with finite volume methods and interpolation errors for particle trajectory calculations. These errors influence significantly the calculated particle removal curves; they are non‐systematic and difficult to quantify.     

Flow in Open-Channel Embayments

This study investigates flows in a square and a rectangular embayment located on the side bank of an open channel. It is found that the main flow of the open channel induces a circulatory flow in the square and rectangular embayment and the center of the circulatory flow is shifted downstream in comparison with the center of the embayment. A solution of the shallow water equations solved using the method of variation yields results of the 95% confidence intervals within 10% of mean errors between the observed and computed nondimensional velocities.     

Modeling Depth-Averaged Velocity and Boundary Shear in Trapezoidal Channels with Secondary Flows

The Shiono and Knight method (SKM) offers a new approach to calculating the lateral distributions of depth-averaged velocity and boundary shear stress for flows in straight prismatic channels. It accounts for bed shear, lateral shear, and secondary flow effects via 3 coefficients—f,λ, and Γ—thus incorporating some key 3D flow feature into a lateral distribution model for streamwise motion. The SKM incorporates the effects of secondary flows by specifying an appropriate value for the Γ parameter depending on the sense of direction of the secondary flows, commensurate with the derivative of the term Hρ(UV)d. The values of the transverse velocities, V, have been shown to be consistent with observation. A wide range of boundary shear stress data for trapezoidal channels from different sources has been used to validate the model. The accuracy of the predictions is good, despite the simplicity of the model, although some calibration problems remain. The SKM thus offers an alternative methodology to the more traditional computational fluid dynamics (CFD) approach, giving velocities and boundary shear stress for practical problems, but at much less computational effort than CFD.     

Field Calibration of Submerged Sluice Gates in Irrigation Canals

Four rectangular sluice gates were calibrated for submerged-flow conditions using nearly 16,000 field-measured data points on Canal B of the B-XII irrigation scheme in Lebrija, Spain. Water depth and gate opening values were measured using acoustic sensors at each of the gate structures, and the data were recorded on electronic data loggers. Several gate calibration equations were tested and it was found that the rectangular sluice gates can be used for accurate flow measurement. The Energy-Momentum (E-M) equations proved to be sound. The calibration of the contraction coefficient, to be used in the energy equation, allowed good estimations of the discharge for three of the four gates studied. The gate for which the E-M method did not perform satisfactorily was located at the head of the canal with a unique nonsymmetric approach flow condition. Alternatively, we investigated the performance of the conventional discharge equation. The variation of the discharge coefficient, Cd, with the head differential, Δh, and the vertical gate opening, w, suggests that Cd be expressed as a function of these two variables. For the sluice gates considered in this study, the best empirical fit was obtained by expressing Cd as a parabolic function of w, although an exponential expression tested previously by other writers also produced satisfactory results. The greatest uncertainty in the variables considered in this study was in the calculated coefficient of discharge, and based on the uncertainty analysis, it is possible to quantify the uncertainty in the estimated discharge through a calibrated sluice gate. The discharge uncertainty in each of the four gates in this study decreases with increasing gate opening, and it decreases slightly with increasing head differentials.     

Method of Solution of Nonuniform Flow with the Presence of Rectangular Side Weir

An iterative step method for solving the nonlinear ordinary differential equation, governing spatially varied flows with decreasing discharge, like the flow over side weirs, is developed. In the procedure, starting at a known flow depth and discharge in the control section, the analytical integration of the dynamic equation with bed and friction slope is carried out. The specific energy, the weir coefficient and the velocity distribution coefficient are considered as local variables, then for the explicit integration, the respective average values along the short side weir elements are assumed. The water surface profiles and the discharges for flow over side weirs, obtained with the proposed relation and valid for rectangular channels, are compared with experimental data for subcritical and supercritical flow conditions. The validation of the method is accomplished by the comparison with the solution obtained by De Marchi’s classical hypothesis, about the specific energy, which is constant along a side weir. In addition, the influence of the coefficient velocity distribution is considered.     

Use of Brink Depth in Discharge Measurement

The behavior of free surface flow at a rectangular free overfall is studied experimentally to obtain a relation between the brink depth and the flow rate. A series of experiments were conducted in a tilting flume with wide range of flow rates covering subcritical, critical, supercritical regimes, and two different roughnesses in order to develop a relationship between the discharge and the brink depth. An equation is proposed to determine the flow rate using the brink depth for a channel of known roughness and bed slope.     

Shear Stress Distribution in Partially Filled Pipes

Boundary shear stresses have been calculated for circular pipes with a flat sediment bed using computational fluid dynamics (CFD). First of all, CFD simulations were carried out for rectangular channels in order to check the software package for its ability to reproduce experimental (literature) results. The influence of the applied turbulence model (isotropic or anisotropic) was also studied for rectangular channels. The simulations for circular pipes, using an isotropic turbulence model, were done for different filling ratios, mean flow velocities, and roughness heights. For validation, the numerical results were compared with former experimental work. With the help of the detailed shear stress distribution, sediment transport can be calculated more accurately than using the global shear stress, as is traditionally done. This method was applied to a simple flume experiment, subjected to a triangular inflow hydrograph, and the comparison with the traditional approach was made.     

Near-Transducer Errors in ADCP Measurements: Experimental Findings

Acoustic Doppler current profilers (ADCPs) are not able to accurately determine velocity near their transducers and near the bed. These limitations have restricted the use of ADCPs to flow depths that are large enough to allow acquisition of few directly measured velocity data that can be subsequently used to accurately estimate vertical velocity profiles and flow discharge in cross sections. While the causes that make ADCPs unable to collect data in the near-bed region are relatively well documented, the causes of near-transducer errors have not yet been fully understood and are only partly documented. We present results from an experimental study aimed at characterizing the systematic errors due to the combined effect of acoustic interference and instrument-induced flow disturbance near a Janus-configured ADCP. The study comprises: (1) concurrent measurements with an ADCP and an acoustic Doppler velocimeter (ADV) under the ADCP; (2) measurements of the flow disturbance produced by the ADCP in the vertical and horizontal planes; and (3) ADV measurements along the path of the acoustic beams ensonified by the ADCP during a measurement. Results suggest that ADCPs bias low the velocity profiles with respect to the undisturbed velocity profiles, mostly because of the flow disturbance induced by the ADCP, with acoustic effects playing a secondary role. For the range of flows we studied, both undisturbed and disturbed profiles exhibit similar shapes when plotted in dimensionless form, with the bulk flow velocity and the ADCP diameter (D) as characteristic scales. The differences between the undisturbed and the ADCP-disturbed profiles extend up to a distance of about 1.5D from the ADCP, except for the profiles measured at locations where the flow depth is close to D for which the boundary layer induced by the ADCP interacts with the one induced by the flume bed.     

Simulation of Transcritical Flow in Pipe/Channel Networks

Using finite difference methods in conjunction with the reduced momentum equation and applying boundary condition structure inherent to subcritical flow to all regimes, is an approach that enables efficient numerical simulation of supercritical and transcritical flows in pipe/channel systems. However, as well as certain errors within a single channel due to incomplete equations, this technique also may introduce unwanted effects propagating across a network in both upstream and downstream directions. These may include: unrealistic backwater effects due to improper boundary conditions, nonamplifying oscillations due to jerky jump movement, and other computational instabilities. Practical implications of these are analyzed in detail and are illustrated using a set of examples. Sensitivity analyzes and comparisons with analytical solutions and laboratory experiments are made. The measures to reduce the inaccuracies inevitable in simulation of transcritical flows are discussed.     

Direct Integration of the Equation of Gradually Varied Flow

The steady flow in open channels, when the depth of the flow varies gradually with distance, is governed by the classic gradually-varied-flow equation. The solution of this ordinary differential equation allows the tracing of the longitudinal profiles of the water surface of the flow. In this note, a relation obtained by direct integration is proposed for a wide rectangular channel, when Manning’s formula is used for the computation of the energy slope. Then the profiles for subcritical and supercritical flow in a mild and steep channel are presented and a comparison with the Bresse solution, relative to the same channels, is carried out.     

New Method for Estimation of Discharge

A new technique for drawing isovel patterns in an open or closed channel is presented. It is assumed that the velocity at each arbitrary point in the conduit is affected by the hydraulic characteristics of the boundary. While any velocity profile can be applied to the model, a power-law formula is used here. In addition to the isovels patterns, the energy and momentum correction factors (α and β), the ratio of mean to maximum velocity (V/umax), and the position of the maximum velocity are calculated. To examine the results obtained, the model was applied to a pipe with a circular cross section. A comparison between the profiles of the proposed model and the available power-law profile indicated that the two profiles were coincident with each other over the majority of the cross section. Furthermore, the predicted isovels were compared with velocity measurements in the main flow direction obtained along the centerline and lateral direction of a rectangular flume. The estimated discharge, based on measured points on the upper half of the flow depth away from the boundaries was within ±7% of the measured and much better in comparison to the prediction of one- and two-point methods. The prediction of the depth-averaged velocity values for the River Severn in the United Kingdom shows a good agreement with the measured data and the best analytical results obtained by the depth-averaged Navier–Stokes equations.     

Experimental Study of 3D Pump-Intake Flows with and without Cross Flow

Detailed measurements of three-dimensional turbulent flows within a rectangular single-pump bay area of a right-angle water intake model with and without cross flow were obtained using an acoustic Doppler velocimeter (ADV) in order to elucidate swirling flow characteristics within the pump sump. Without cross flow, the pump-approach flow distributions were characterized by nearly uniform streamwise velocities in the pump bay and weak free-surface vortices near the pump column. With cross flow, the three-dimensional mean velocity measurements revealed the existence of a large recirculation zone upstream of the pump column such that strong streamwise velocities were present at higher depths and near the left sidewall, while the reverse current concentrated at lower depths along the right sidewall. Flow patterns in the latter case were also characterized by strong free-surface vortices in the vicinity of the pump column and a strong floor-attached subsurface vortex underneath the pump bell. Uncertainty analysis for ADV velocity measurements showed good quality data, with uncertainty in mean velocities varying from 2.5 to 6.4%. These experimental data were utilized in validating inviscid numerical solutions.     

Calibration and Verification of a 2D Hydrodynamic Model for Simulating Flow around Emergent Bendway Weir Structures

The predictive capability of a two-dimensional (2D)-hydrodynamic model, the finite-element surface water modeling system (FESWMS), to describe adequately the flow characteristics around emergent bendway weir structures was evaluated. To examine FESWMS predictive capability, a sensitivity analysis was performed to identify the flow conditions and locations within the modeled reach, where FESWMS inputs for Manning’s n and eddy viscosity must be spatially distributed for to better represent the river bed flow roughness characteristics and regions where the flow is highly turbulent in nature. The sensitivity analysis showed that high flow conditions masked the impact of Manning’s n and eddy viscosity on the model outputs. Therefore, the model was calibrated under low flow conditions when the structures were emergent and had the largest impact on the flow pattern and model inputs. Detailed field measurements were performed under low flow conditions at the Raccoon River, Iowa for model calibration and verification. The model predictions were examined for both spatially averaged and distributed Manning’s n and eddy viscosity model input values within the study reach for an array of emergent structures. Spatially averaged model inputs for Manning’s n and eddy viscosity provided satisfactory flow depth predictions but poor velocity predictions. Estimated errors in the predicted values were less than 10% for flow depth and about 60% for flow velocity. Distributed Manning’s n and eddy viscosity model inputs, on the contrary, provided both satisfactory flow depth and velocity predictions. Further, distributed inputs were able to mimic closely the recirculation flow pattern in the wake region behind the bendway weir structures. Estimated errors in the predicted values were less than 10 and 25% for flow depth and velocity, respectively. Overall, in the case of distributed model inputs, FESWMS provided satisfactory results and allowed a closed depiction of the flow patterns around the emergent bendway weirs. These findings suggest that 2D models with spatially distributed values for Manning’s n and eddy viscosity can adequately replicate the velocity vector field around emergent structures and can be valuable tools to river managers, except in cases when detailed three-dimensional flow patterns are needed. The study was limited to the examined low flow conditions, and more field data, especially under high flow conditions, are necessary to generalize the findings of this study regarding the model prediction capabilities.     

Laminar Pipeline Flow of Wastewater Sludge: Computational Fluid Dynamics Approach

A computational fluid dynamics (CFD) technique applied to laminar flow of wastewater sludge in horizontal, circular pipes is presented. The technique employs the Crank-Nicolson finite difference method in conjunction with the variable secant method, an algorithm for determining the pressure gradient of the flow. Head loss (pressure drop) and velocity profile are predicted using the technique. Numerical predictions of head loss and velocity profile for several combinations of flows, pipe sizes, and sludge solids concentrations are compared to exact analytical values, derived from the theory of laminar flow of Bingham-plastic fluids. The predicted values are in good agreement with the exact values. Comparisons are also made to head loss values for municipal wastewater sludge from the literature. The CFD technique has several advantages over the analytical calculations, including ease of use, time efficiency, and the ability to readily change boundary conditions, flow geometry, and the rheological model for the shear stress.     

Three-Dimensional Simulation on the Water Flow Field and Suspended Solids Concentration in the Rectangular Sedimentation Tank

A 3D computational fluid dynamics model for describing the water flow and suspended solids (SS) concentration distribution in a rectangular sedimentation tank is presented. The interfacial momentum transfer, buoyant forces, and the effect of sediment-induced density currents are considered. A convection-diffusion equation, which is extended to incorporate the sedimentation of activated sludge in the field of gravity, governed the mass transfer in the clarifier. The double-exponential law is used to describe the dependence of the settling velocity on the concentration. The results show that during the dynamic settling process of the sludge, the mud surface rose slowly, and a period of time later, the mud surface kept stability and reached dynamic equilibrium in the tank. The distribution of velocity along the z axis in the rectangular tank is not uniform, and the surface return flow is found. The turbulent kinetic energy is larger and dropped drastically in the inlet zone, while in the settling zone the turbulent kinetic energy is relatively small. Density current is formed, and the clear water zone, flocculation zone, lamella zone, and compression zone are found. Furthermore, under certain operational conditions, the influence of inlet baffle length on SS settling in the rectangular sedimentation tank is discussed. The prediction by the present model for liquid flow and SS concentration is confirmed by the experimental measurement in a rectangular sedimentation tank in Sweden reported by Larsen in 1977.     

CFD Predictions and Experimental Comparisons of Pressure Drop Effects of Turning Vanes in 90° Duct Elbows

This paper presents new results for numerical predictions of air flow and pressure distribution in two commonly used elbows: (1) 90° mitered duct elbows with turning vanes having 0.05 m radius, 0.038 m vane spacing and (2) 90° mitered duct elbows without turning vanes, in 0.2×0.2?m (8?in.×8?in.) duct cross section using the STAR-CD computational fluid dynamics (CFD) code. A k-ε turbulence model for high Reynolds number and k-ε Chen model were used for that purpose for comparative purposes. The simulation used 13 different Reynolds numbers chosen between the range of 1×105 and 2×106. To validate the CFD results, the results of two experimental papers using guided vanes were compared with simulated vane runs under the same condition. The first experimental study used a 0.6×0.6?m (24?in.×24?in.) square elbow with 0.05 m radius, 0.038 m vane spacing and air velocities at 2.54 m/s (500 fpm) and 25.4 m/s (5,000 fpm), the second experiment used a 0.81×0.2?m (32?in.×8?in.) rectangular elbow geometry with 0.05 m radius, 0.038 m vane spacing with air velocities from 10.16 m/s (2,000 fpm) to 13.97 m/s (2,750 fpm). For Reynolds numbers (1.00–2.00)×105 the pressure drop difference between vaned and unvaned elbows was found to be 35 Pa as compared to 145 Pa. The simulations also agreed reasonably well with published experimental results. For the 0.6×0.6?m (24?in.×24?in.) square elbow and 0.81×0.2?m (32?in.×8?in.) rectangular elbow with vanes, the difference in pressure drop was 3.9 and 4.1% respectively and indicates that CFD models can be used for predictive purposes in this important HVAC applications area.     

Turbulence Characteristics in Gradual Channel Transition

A field study was conducted to determine the effects of a channel transition on turbulence characteristics. Detailed three-dimensional (3D) flow measurements were collected at a cross section that is located downstream of a gradual channel expansion. These measurements were obtained via an acoustic doppler velocimeter and include the 3D velocity field, the mean local velocities, the turbulent intensities, the frictional characteristics of the flow, the secondary velocity along the transverse plane, and the instantaneous shear stress components in the streamwise and transverse directions. Analysis of the 3D flow data indicates that the turbulent flow on the outer bank of the channel is anisotropic. Such anisotropy of turbulence, which is attributed to the gradual expansion in the channel and bed roughness, yields the development of a secondary flow of Prandtl’s second kind as reported in 1952. In particular, it was found that turbulent intensities in the vertical and transverse directions on the outer bank section are different in magnitude creating turbulence anisotropy in the cross-sectional plane and secondary flows of the second kind. Turbulent intensities increase toward the free surface indicating the transfer of a higher-momentum flux from the channel bed to the free surface, which contradicts common wisdom. Results for the normalized stress components in the streamwise and transverse direction show similar behavior to the intensities. Moreover, the nonlinear distribution of stresses is indicative of the oscillatory nature of the flow induced by the secondary flows of Prandtl’s second kind. A similar behavior was found for flows in straight rectangular channels over different roughness. Finally, a comparison between the secondary current velocity with the mainstream velocity indicates that secondary flow of Prandtl’s second kind is present within the right half of the measured cross section.     

Field Testing of a Simple Flume (SMBF) for Flow Measurement in Open Channels

In this paper the stage–discharge relationship of a new flume named SMBF (Samani, Magallanex, Baiamonte, Ferro), originally proposed by Samani and Magallanez and tested by Baiamonte and Ferro, for measuring flow discharge in open channels is reviewed. The flume is obtained inserting two semicylinders in a rectangular cross section. The results of some experimental runs carried out using horizontal flumes characterized by different values of the contraction ratio (ranging from 0.17 to 0.81) are used for determining the two coefficients of the power stage–discharge equation. The stage–discharge equation is tested using flow measurements carried out in the period between December 2004 and March 2006 in the Sicilian experimental SPA1 basin. Field testing of the SMBF flume is developed using discharge measurements carried out by a Khafagi–Venturi flume placed in the field measurement channel.