Estimation of Power Spectra of Acoustic-Doppler Velocimetry Data Contaminated with Intermittent Spikes

Spectral analysis of velocity signals recorded by acoustic Doppler velocimetry (ADV) and contaminated with intermittent spikes remains a challenging task. In this paper, we propose a new method for reconstructing contaminated time series which integrates two previously developed techniques for detecting and replacing spurious spikes. The spikes are first detected using a modified version of the universal phase-space-thresholding technique and subsequently replaced by the last valid data points. The accuracy of the new approach is evaluated by applying it to identify and remove spikes and reconstruct the spectra of two clean data sets which are artificially contaminated with random spikes: (1) high-quality hot-wire measurement and (2) numerically simulated velocity time series with bimodal probability density distribution. The technique is also applied to reconstruct the spectra obtained from intentionally contaminated ADV measurements and compare them with ADV spectra at the same point in the flow obtained using proper ADV settings. Special emphasis is placed on testing the ability of the technique to reproduce realistic power spectra in flows with rich coherent dynamics. The results show that the power spectra of the reconstructed time series contain a filtered white noise caused by the steps in the reconstruction technique using the last valid data point. We show that even for a severely contaminated time series, the proposed method can accurately recover the power spectra up to the frequency corresponding to the half the mean sampling rate of the valid data points.     

Investigation of the Gas‐Liquid Flow in a Stopper‐Rod Controlled SEN

The behaviour of two‐phase gas‐liquid flows in a stopper‐rod controlled submerged entry nozzle (SEN) is investigated in water model experiments. The observed two‐phase flow patterns can be classified into either bubble coring or bubbly slug. The scaling of the two‐phase flows by means of similarity parameters is discussed. In the experiments, it is found that the liquid flow rates depend strongly on the two‐phase flow patterns. Additionally, the influence of swirl on the flow patterns is investigated in detail. It is shown that swirl has a marked impact on the transition from bubble coring to bubbly slug. Finally, an estimation of the two‐phase argon‐steel flow patterns in industrialscale SEN flows is given.     

ADV Measurements around a Cluster Microform in a Shallow Mountain Stream

A field study was conducted to examine the turbulent properties of the flow around a naturally formed cluster bedform. This was carried out on a mountain river using a 3D acoustic Doppler velocimeter (ADV). Concurrent with this objective, the ability of the ADV to make measurements in a shallow flow over a cobble bed (ho/d84 = 1.75) was examined. ADV measurements in natural clear-water shallow flows around obstacles are inherently difficult to obtain due to (1) signal interference between the acoustic reflections from the boundary and the ADV sample volume; (2) regions of high turbulent intensity, such as in local detached shear layers; and (3) low concentrations of suspended particles passing through the ADV sampling volume. These processes result in velocity time series that contain a significant amount of spikes, lower-than-average signal-to-noise ratios, and lower than average correlation values. A filtering process that optimized the removal of bad points while retaining a sufficient number of points to describe the velocity time series histogram was developed. In general, flow over the study section can be described by an inner roughness layer dominated by large roughness and detached flow, and an outer flow that exhibits a form of log scaling. It was found that the cluster acts to locally modify this structure by shifting the elevation of the roughness layer and the zone of primary production and dissipation of turbulent energy up towards the center of the water column. Mean and turbulent statistics, energy distributions, spectral properties, and a quadrant analysis are presented to characterize the flow around the cluster.     

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.     

Fluctuations of Suspended Sediment Concentration and Turbulent Sediment Fluxes in an Open-Channel Flow

A complex problem of turbulent-sediment interactions in an open-channel flow is approached experimentally, using specially designed field experiments in an irrigation canal. The experimental design included synchronous measurements of instantaneous three-dimensional (3D) velocities and suspended sediment concentration using acoustic Doppler velocimeters (ADV) and a water sampling system. Various statistical measures of sediment concentration fluctuations, turbulent sediment fluxes, and diffusion coefficients for fluid momentum and sediment are considered. Statistics, fractal behavior, and contributions of bursting events to vertical fluxes of fluid momentum and sediment are evaluated using quadrant analysis. It has been found that both turbulence and sediment events are organized in fractal clusters which introduce additional characteristic time and spatial scales into the problem and should be further explored. It is also shown that Barenblatt’s theory of sediment-laden flows appears to be a good approximation of experimental data.     

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.     

Evaluation of Flow Resistance in Smooth Rectangular Open Channels with Modified Prandtl Friction Law

Flow resistance in open channels is usually estimated by applying the approach that is developed originally for pipe flows. Such estimates may be useful for engineering applications but always differ from measurements to some extent. This paper first summarizes empirical approaches that have been proposed in the literature to reconcile the resistance difference. These include various modifications of the pipe friction for applications to rectangular ducts and open channel flows. An improved friction equation is then derived for evaluating flow resistance of smooth rectangular open channels. Comparisons are made with experimental data reported by previous researchers and those collected in the present study. It is shown that the new proposed equation is applicable for both narrow and wide channels and is more accurate than those available in the literature.     

Characteristics of Horseshoe Vortex in Developing Scour Holes at Piers

The outcome of an experimental study on the turbulent horseshoe vortex flow within the developing (intermediate stages and equilibrium) scour holes at cylindrical piers measured by an acoustic Doppler velocimeter (ADV) are presented. Since the primary objective was to analyze the evolution of the turbulent flow characteristics of a horseshoe vortex within a developing scour hole, the flow zone downstream of the pier was beyond the scope of the investigation. Experiments were conducted for the approaching flow having undisturbed flow depth ( = 0.25?m) greater than twice the pier diameter and the depth-averaged approaching flow velocity ( = 0.357?m/s) about 95% of the critical velocity of the uniform bed sand that had a median diameter of 0.81?mm. The flow measurements by the ADV were taken within the intermediate (having depths of 0.25, 0.5, and 0.75 times the equilibrium scour depth) and equilibrium scour holes (frozen by spraying glue) at a circular pier of diameter 0.12?m. In order to have a comparative study, the ADV measurements within an equilibrium scour hole at a square pier (side facing the approaching flow) of sides equaling the diameter of the circular pier were also taken. The contours of the time-averaged velocities, turbulence intensities, and Reynolds stresses at different azimuthal planes (0, 45, and 90°) are presented. Vector plots of the flow field at azimuthal planes reveal the evolution of the characteristics of the horseshoe vortex flow associated with a downflow from intermediate stages to equilibrium condition of scour holes. The bed-shear stresses are determined from the Reynolds stress distributions. The flow characteristics of the horseshoe vortex are discussed from the point of view of the similarity with the velocity and turbulence characteristic scales. The imperative observation is that the flow and turbulence intensities in the horseshoe vortex flow in a developing scour hole are reasonably similar.     

Nonhydrostatic Three-Dimensional Method for Hydraulic Flow Simulation. II: Validation and Application

A three-dimensional computational method, without the use of hydrostatic assumption, is developed to solve fluid flows for hydraulic applications. Numerical algorithms and verification of the nonhydrostatic model are described in our companion paper. The model employs unstructured grid technology with arbitrarily shaped cells, offering the potential to unify many grid topologies into a single formulation. Herein, the model is applied to two practical steady hydraulic flows to provide further validation of the model and demonstrate its use in practical flows. The flows in a hydroturbine draft tube and in the forebay of Rocky Reach Dam for the fish passage facility design are simulated. Comparisons with experimental data in the former and physical and field measurements in the latter establish the scope of the model.     

Numerical Calculation of Turbulence Structure in Depth-Varying Unsteady Open-Channel Flows

Unsteady depth-varying open-channel flows are really observed in flood rivers. Owing to highly accurate laser Doppler anemometers (LDA), some valuable experimental databases of depth-varying unsteady open-channel flows are now available. However, these LDA measurements are more difficult to conduct in open-channel flows at higher unsteadiness, in comparison with unsteady wall-bounded flows such as oscillatory boundary layers and duct flows. Therefore, in this study, a low-Reynolds-number k–ε model involved with a function of unsteadiness effect was developed and some numerical calculations were conducted using the volume of fluid method as a free-surface condition. The present calculated values were in good agreement with the existing LDA data in the whole flow depth from the wall to the time-dependent free surface. These values were also compared with those of unsteady wall-bounded flows. The present calculations were able to predict the distributions of turbulence generation and its dissipation, and consequently the unsteadiness effect on turbulence structure was discussed on the basis of the outer-variable unsteadiness parameter α, which is correlated with the inner-variable unsteadiness parameter ω+ in unsteady wall-bounded flows.     

Ultrasonic Lift Measurement Technique for Flow-Induced Structural Vibrations

Deficiencies exist in our current ability to measure lift forces in wind-tunnel experiments on vibrating structures in a fluid flow. The ultrasonic lift measurement (ULM) technique has been previously developed to measure time-averaged fluid circulation and lift on stationary structures. The ULM technique is based on measuring transit times of acoustic pulses along paths enclosing the structure. A quasi-steady method based on the Kutta–Joukowski theorem has been used in the past to convert fluid circulation to lift values in ULM studies. In this paper, the largely unstudied extension of the ULM technique to measure unsteady lift forces in flows involving structural vibration is considered. Analytic methods are developed that can be used to properly convert the instantaneous circulation measurements (attainable from ULM experiments) to lift values. These unsteady methods are validated by using numerical simulations of flows over flat plates undergoing oscillating motion. It is shown that the addition of unsteady terms provides a method with improved accuracy over the previous quasi-steady assumption. The methods are also applied to ULM data from an oscillating airfoil experiment in a preliminary study.     

Theoretical modelling of gas-liquid two-phase flow in a vertical and straight pipe

This paper treats the theoretical analysis to obtain the flow characteristics of gas-liquid two-phase mixtures in a vertical and straight pipe. The system of equations governing the gas-liquid two-phase flow field is based upon the multifluid model. The transitions of the gas flow pattern from bubbly to slug flows as well as from slug to churn flows are introduced into the system of the above governing equations. In order to confirm the validity of the present theoretical model, the flow characteristics calculated on the basis of this model have been compared with experimental data measured by changing the pipe diameter and the submergence ratio. As a result, it has been found that the present theoretical model built up in this investigation gives good fit to the measured data. We believe that the simplicity of this pump can make it possible to transport molten iron/steel between different refining processes. But, we also note that the experiments have been performed on a cold model using an air-water system     

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.     

Shear Stress in Smooth Rectangular Open-Channel Flows

The average bed and sidewall shear stresses in smooth rectangular open-channel flows are determined after solving the continuity and momentum equations. The analysis shows that the shear stresses are function of three components: (1) gravitational; (2) secondary flows; and (3) interfacial shear stress. An analytical solution in terms of series expansion is obtained for the case of constant eddy viscosity without secondary currents. In comparison with laboratory measurements, it slightly overestimates the average bed shear stress measurements but underestimates the average sidewall shear stress by 17% when the width–depth ratio becomes large. A second approximation is formulated after introducing two empirical correction factors. The second approximation agrees very well (R2>0.99 and average relative error less than 6%) with experimental measurements over a wide range of width–depth ratios.     

Formulas for Friction Factor in Transitional Regimes

This note concerns variations of the friction factor in the two transitional regimes, one between laminar and turbulent flows and the other between fully smooth and fully rough turbulent flows. An interpolation approach is developed to derive a single explicit formula for computing the friction factor in all flow regimes. The results obtained for pipe flows give a better representation of Nikuradse’s experimental data, in comparison with other implicit formulas available in the literature. Certain modifications are also made for applying the obtained friction formula to open-channel flows.     

Efficient Approximation of Unsteady Friction Weighting Functions

A simple method is presented for evaluating wall shear stresses from known flow histories in unsteady pipe flows. The method builds on previous work by Trikha, but has two important differences. One of these enables the method to be used with much larger integration time steps than are acceptable with Trikha’s method. The other, a general procedure for determining approximations to weighting functions, enables it to be used at indefinitely small times (high frequencies). The method is applicable to both laminar and turbulent flows.     

Numerical and Experimental Study of Dividing Open-Channel Flows

Dividing flows in open channels are commonly encountered in hydraulic engineering systems. They are inherently three-dimensional (3D) in character. Past experimental studies were mostly limited to the collection of test data on the assumption that the flow was 1D or 2D. In the present experimental study, the flow is treated as 3D and test results are obtained for the flow characteristics of dividing flows in a 90°, sharp-edged, rectangular open-channel junction formed by channels of equal width. Depth measurements are made using point gauges, while velocity measurements are obtained using a Dantec laser Doppler anemometer over grids defined throughout the junction region. A 3D turbulence model is also developed to investigate the dividing open-channel flow characteristics. The predicted flow characteristics are validated using experimental data. Following proper model validation, the numerical model developed can yield design data pertaining to flow characteristics for different discharge and area ratios for other dividing flow configurations encountered in engineering practice. Energy and momentum coefficients based on the present 3D model yield more realistic energy losses and momentum transfers for dividing flow configurations. Data related to secondary flows provide information vital to bank stability, if the branch channel sides are erodible.     

Turbulent flow of liquid steel and argon bubbles in slide-gate tundish nozzles: Part I. model development and validation

The quality of continuous-cast steel is greatly affected by the flow pattern in the mold, which depends mainly on the jets flowing from the outlet ports in casting with submerged tundish nozzles. An Eulerian multiphase model using the finite-difference program CFX has been applied to study the three-dimensional (3-D) turbulent flow of liquid steel with argon bubbles in slide-gate tundish nozzles. Part I of this two-part article describes the model formulation, grid refinement, convergence strategies, and validation of this model. Equations to quantify average jet properties at the nozzle exit are presented. Most of the gas exits the upper portion of the nozzle port, while the main downward swirling flow contains very little gas. Particle-image velocimetry (PIV) measurements are performed on a 0.4-scale water model to determine the detailed nature of the swirling velocity profile exiting the nozzle. Predictions with the computational model agree well with the PIV measurements. The computational model is suitable for simulating dispersed bubbly flows, which exist for a wide range of practical gas injection rates. The model is used for extensive parametric studies of the effects of casting operation conditions and nozzle design, which are reported in Part II of this two-part article.     

Transcritical Flow due to Channel Contraction

The singular point is a physical phenomenon consistent with critical flow conditions, and, consequently, the real control section of a water surface profile. A general method to study the location, type, and water surface slope of a singular point is described. This method, in addition to improving the classic gradually-varied flow theory, can be used for the design of channel contractions involving transcritical flows, as in the case of chute spillways and inlets to river diversion tunnels. The method is explained in the case of a chute spillway and verified against experimental data recorded in a Venturi channel.     

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.