Image-based river discharge estimation by merging heterogeneous data with information entropy theory

An information entropy based approach for the discharge measurements is evaluated for the gaging of the Isère river at the Grenoble university campus. Over a four month period, six discharge measurements were made using a vessel-mounted aDcp. Simultaneously, particle tracking velocimetry (PTV) from video images was used to estimate surface velocities. The surface velocities are projected along the regularly surveyed river section of the Isère-Campus gaging station. The vertical velocity profile at each stream-wise location is approximated by a 1D entropy profile. Information entropy 1D velocity vertical profile depends on two parameters which are fitted using aDcp and surface velocity measurements. The inclusion of the surface velocities reduces the dispersion of the estimated entropy parameters. The measurements show that the two parameters are linearly related with a slope that is stage dependent and thus, surface velocity dependent. From there, the information entropy theory for 1D velocity distribution offers a protocol by which surface velocities only are used to compute the discharges. The protocol is calibrated with both aDcp and surface velocity measurements. It is finally validated with several events during which only surface velocities are measured. For the high water flood event the estimated discharge falls within 2% of the one estimated with the rating curve of the gaging station.     

Prediction of stage–discharge curves in open-channels using a fixed-point velocity measurement

The single-point measurement method for discharge estimation, which was first introduced by Maghrebi, can be implemented to obtain the discharge at different stages of a river during a flood event. As an advantage of this method, discharge can be estimated automatically with a fixed measurement location in the river section or on the water surface, which is associated with minimum energy and cost consumptions. For the proposed model, we determine the isovel contours in a normalized form for the cross section of the flow. To do so, we need to apply the field or experimental data, concerning the cross sectional geometry at different stages and its roughness variation along the wetted perimeter to the model. Then we collect the data of the single fixed-point of velocity measurement at the flow section using a velocity current meter. To validate the method, it is applied to a flume with different cases of roughened walls. The obtained results of stage–discharge curves using the single point of measurement in comparison to the observed experimental ones show that this method can quickly and accurately estimate the flood discharges. The maximum deviation between the observed and calculated discharges for most of observations is less than 5%.     

Discharge prediction in flow measurement flumes with different downstream transition slopes

Experimental testing of 9 different rectangular compound cross-section flow measurement flumes with different downstream slopes was conducted to yield the coefficient of discharge and the approach velocity coefficient. The aim of the experimental research was the determination of stage–discharge relationship in compound cross-section flow measurement flumes with different downstream slopes. One empirical predictive model for each of the coefficient of discharge and the approach velocity coefficient for the 9 cross-sections have been derived using one dimensionless parameter for the coefficient of discharge and another one dimensionless parameter for the approach velocity coefficient as the single independent variable. This approach is preferred as it allows the estimation of discharge by only measuring the water depth at the head measurement section. All obtained predictive models statistics have indicated the high reliability of the derived models in estimating discharge in an open channel flume of a rectangular compound cross-section using the predicted coefficients.     

Estimating discharge in drainage channels through measurements of surface velocity alone: A case study

In the scientific literature it is possible to find at least two methods for estimating discharge in an open channel which represent a valid alternative to the Velocity-Area method; both offer a considerable advantage in that they are simple to apply and require knowledge solely of the channel bathymetry and maximum surface velocity. The first method is based on the entropy concept introduced into hydraulics by Chiu in the 1990s, whilst the second is focused on the reconstruction of dimensionless isovels in the channel cross-section.Both the methods have been extensively described in previous works and validated for medium/large-sized cross-sections where surface measurements are taken by current-meter or Acoustic Doppler Current Profiler (ADCP) sensor. In this technical paper, they are instead applied to a water drainage channel in a reclamation territory characterized by a very low velocity which required a particular measuring technique, called “total station”. This technique demonstrated to be reliable in situations where the velocity is very low and cannot be measured with other “no-contact” techniques, such as those based on the Doppler method, which are normally used when the use of current meters is not possible.     

Application of surface velocimetry in estimating rating curves in compound channels

Discharge estimation in natural rivers with geometrically irregular cross-sections and roughness differences between different parts of the wetted perimeter is complex. Therefore a compound channel can be used as a model of these rivers. Although assesing the behavior of rating curves in compound channels is very difficult and time-consuming, taking photographs of a floating object with a specified time interval is a method by which the velocity of the water surface can be estimated. The flow rate is first calculated using the isovels passing through the measured surface velocity. Then, the estimated discharge at a water level is applied to evaluate the rating curve. A compound channel model is built in the laboratory to carry out this experiment, and then the experimental results are obtained from rating curves. For the first time this paper uses surface water velocityto estimate the discharge and rating curve based on the SPM method introduced in 2003 and 2017, respectively. Also, an experimental setup consisting of a compound channel with a two-stage floodplain is another innovative feature of the current work that has not been previously explored. The results of discharge estimation based on the isovels and surface velocity show that the average error does not exceed 12%. Finally, the average statistical parameters of MAPE and NRMSE are obtained 6.4% and 0.045, respectively, for the estimated rating curve using the available data.     

Application of large scale PIV in river surface turbulence measurements and water depth estimation

Large-Scale Particle Image Velocimetry (LSPIV) has emerged as a reliable technology to measure river surface flow velocity distribution and can be applied to estimate river discharge. Fewer studies have explored the capability of surface turbulence measurements using LSPIV. In this paper, LSPIV is applied to evaluate statistics of surface turbulence of a natural river. Turbulence measurements including velocity fluctuation, velocity spectra and the dissipation rate of turbulent kinetic energy (TKE) are validated by comparing with those measured by an Acoustic Doppler Velocimeter (ADV). Traditionally, estimation of stream discharge through LSPIV needs a secondary measurement to determine river bathymetry and water depth. A new method is presented here to demonstrate that for a fully developed and channel-controlled flow, the cross section geometry can be estimated from the combined measurements of surface mean velocity and the dissipation rate, following the Manning-Strickler formula. Therefore, river discharge can be estimated with LSPIV along with a calibrated Manning's roughness, without additional bathymetry survey. The proposed new method is applied to measure discharge in Milwaukee River (Milwaukee, Wisconsin, U.S.A.), which agreed well with data obtained from a nearby streamgage station.     

Estimation of one-dimensional velocity distribution by measuring velocity at two points

The measurement of the velocity distribution and discharge in the open channels has always been an important issue in hydraulics. Unfortunately, flow measurement in the open channel is often expensive and sometimes produces poor results. There are many empirical methods to estimate the velocity distribution in a conduit, however, these methods are often applicable only to a narrow range of open channel conditions. In this paper, considering velocity as a random parameter, one-dimensional velocity distribution in open-channel has been derived based on the entropy concept and the principle of maximum entropy (POME). The entropy indexes (M, G, λ₂ and λ_*) are important parameters in entropy method to estimate velocity distribution and discharge in a conduit. A new approach is presented in this work for estimating the entropy parameters based on two-point velocity measurements. The approach for estimating the entropy parameters is tested for laboratory observations and velocity distribution and discharge are determined using Shannon, Renyi and Tsallis entropy methods. The present approach has shown good agreement with measured data. Also, the results showed that Tsallis entropy method is more accurate than other forms of entropy and the calculated values of NRMSE for estimated velocity profile and discharge are 7.86 and 8.8% respectively, showing a good simulation.     

Flow measurement using free over-fall in generalized trapezoidal channels based on one velocity point method

A free over-fall offers the possibility of being used as a flow measuring device in hydraulic structures with a single depth measurement of the end section. Due to its practical importance, considerable attention has been paid to investigate free over-falls for different channel cross-sections using various approaches. This paper presents a new theoretical approach for computing the end depth ratio (EDR) relationship for the generalized trapezoidal channel cross-sections at free over-falls in sub critical flow regimes from which the end depth discharge (EDD) can be computed. The generalized trapezoidal channel is a geometric shape that is defined mathematically with a single equation where five widely known prismatic channel cross-sectional shapes can be generated (trapezoidal, inverted triangular (Δ), rectangular, parabolic, and triangular). This suggested theoretical approach uses one velocity point at the geometric center of the end section based on the energy and the continuity equations. Relevant experimental and theoretical results were utilized in order to examine the suggested method through the statistical measuring indices (percentage difference and the correlation coefficient (R²)). The computed results show very close agreements with the earlier works. Furthermore, simple equations are also generated using the regression curve fitting technique in order to estimate the direct discharges (Q) using the end depth (y_e) for each of the above mentioned channel cross-sections.     

Robot's Emotion Decision by Energy and Entropy Concepts

This study is to introduce concepts of energy and entropy to describe a robnot's emotion decision.It chooses the dimensinal approach based on factors of pleasure and arousal for the merit of the interpolation between emotions.Especially,Circumplex model which has also two axes:pleasure and arousal is used.Besides,the model indicates how emotions are distributed in the two-dimensional plane.Then by the definition of psychodynamicsthe energy states (mental energy and physical energy) are matched to pleasure and arousal respectively that are the basis of Circumplex model.The mental energy is updated by the result of Prospect theory which measures the value of gain and loss as pleasure factor.And the physical energy is updated by the result of hedonic scaling which measures levels of arousal from pleasure computed by Prospect theory,and the result of intensity of stimuli.Then the energy states are fed by entropy.The feedback loop by entropy satisfies the 2nd law of thermodynamics.The energy states generated by stimuli and fed by entropy take a position in the plane of Circumplex model.Then distances between the current position and other emotions are computed to get a level of each emotion,proportional to the inverse of the distance.     

Analysis of three-dimensional extrusion of sections through curved dies by conformal transformation

A new method of analysis is proposed for the extrusion of arbitrarily shaped sections through curved die profiles. A kinematically admissible velocity field is found by deriving the equation of a stream line. Conformal transformation of a unit circle onto a section is utilized in the derivation. The upper-bound method is then applied to determine the extrusion pressure for the rigid-perfectly plastic material. The redundant work relating to the velocity discontinuities at the entrance and the exit is included in the formulation. The general formulation for an arbitrary cross section is obtained by use of conformal transformation. The upper-bound pressure for extrusion through curved die profiles is computed for a complex section with a curved boundary. Two curved die profiles widely used are chosen to compare the effects of die profiles. From the derived velocity field, the upper-bound extrusion pressures are also computed for the extrusion of regular polygons and rectangles of various aspect ratios. The effects of sectional shape, die profile and interfacial friction at the die surface are discussed.     

ANALYSIS OF SPARK PROFILES DURING EDM PROCESS

A fundamental study of electro discharge machining (EDM) based on the physics of an arc and heat transfer theory has been carried out. The field equations for electric potential and temperature in the spark region are simultaneously solved by employing the finite element method. Using the criterion of constant current at any cross section of a spark, the arc radii at different cross sections are corrected until convergence. The final spark shape obtained is noncylindrical, and has different radii at different cross sections. Also, the percent of heat input absorbed by cathode, anode, and dielectric has been calculated. The computed relative electrode wear has been compared with experimental results.     

ANALYSIS OF SPARK PROFILES DURING EDM PROCESS

Abstract

A fundamental study of electro discharge machining (EDM) based on the physics of an arc and heat transfer theory has been carried out. The field equations for electric potential and temperature in the spark region are simultaneously solved by employing the finite element method. Using the criterion of constant current at any cross section of a spark, the arc radii at different cross sections are corrected until convergence. The final spark shape obtained is noncylindrical, and has different radii at different cross sections. Also, the percent of heat input absorbed by cathode, anode, and dielectric has been calculated. The computed relative electrode wear has been compared with experimental results.     

Prediction of the key parameters of free over-fall flows within the generalized circular cross-section with varying flat bases

Free over-fall occurring due to the sudden bed drop at the channel end that referred as the brink, facilitates the determination of the flow amount (discharge) by only trailing the value of the water depth at that section. This paper mainly focuses on a new theoretical approach that analysis the free over-fall within a channel of circular cross-section with flat base at different elevation levels by applying the continuity and the energy equations based on one velocity point method. The hydraulic behaviors of the circular cross-section especially having different elevation of the flat base have been investigated in sub-critical flow regime to obtain the end depth ratio (EDR) from which the end depth discharge (EDD) values are computed. The non-horizontal free surface profile at the upstream of the end section due to the accelerated flow velocity is also computed based on the extended energy equation. Subsequently, due to its practical importance direct equations for the free surface profile are provided for each channel cross-section for different values of the non-dimensional critical depth. Furthermore, in order to ease the use of the solution for practitioner in this field, the generalized unique relationships for the EDR, the non-dimensional discharge, and the free surface profile are presented, since there is no direct general equation for all the derivatives of the circular channel as a single solution in the previous studies due to its complexity. Even, relevant experimental and theoretical studies are used to obtain more robust assessment of the applied approach.     

Numerical Simulation of Unsteady Discharge Flow with Fluctuation in Positive Discharge Blower

The operating performance of positive discharge blower/s markedly influenced by the pulsation of the discharge flow, but difficult to be measured with experimental methods. The internal and discharge flow of positive discharge blower with involute type three-lobe are numerically investigated, both in air cooling and countercurrent cooling conditions by means of computational fluid dynamics (CFD). The unsteady compressible flow equations are solved using RNG κ-ε turbulent model. The finite difference method and the second order upwind difference scheme are applied into discrete equations. In the numerical simulation, the dynamic mesh techniques are used to approach the rotating displacement of cell cubage and the alterability of inlet, outlet flow area. The non-uniform mesh is applied to the rotor-stator coupled area. The reliability of the numerical method is verified by simulating the inner flow and comparing with the semi-empirical theory. The flow flux curves and the distributing of velocity vector showed obvious vortex motion in all the discharge process, both in air cooling and countercurrent cooling conditions. These vortexes with different positions, intension and numbers at different rotating angles have remarkable influences on the discharge flux. For air cooling, the vortex produced a second pulsation with big-amplitude in a cycle, and led to the early appearance of maximum of backflow. For countercurrent cooling, the frequency of pulsation increased due to the pre-inflow, but the hackflow at the outlet is prevented, also the pulsation strength has greatly decreased.     

A simple model for estimation of dimensionless isovel contours in open channels

A simple model is proposed for predicting the dimensionless isovel contours in straight ducts and open channels. It is assumed that each element of the boundary influences the velocity at an arbitrary point in the cross section. Then, the total effect of the boundary can be obtained using integration along the wetted perimeter. In this paper, power and logarithmic laws are used, while any velocity profile can be applied in the model. The model is applied to calculate the normalized isovel contours in rectangular channels. Then they are used, in combination with a single-point velocity measurement at a cross section of the uniform flow, to estimate the discharge. The kinetic energy and momentum correction factors, and the ratio of maximum to mean velocity, are also calculated from isovel patterns. Calibration and validation of the model are carried out by comparing the results obtained with measurements of the velocity in the main flow direction along the centerline of a rectangular flume as well as in the transverse direction. Each point of measurement can be used to estimate the discharge. Then, the estimated discharge is compared with the actual measured one. Depending on the position of the measurement, the deviation of the calculated and measured discharges will be altered. Model predictions are well correlated with experimental data for rectangular open channels.     

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.     

Flume experiments for assessing the dye-tracing technique in rill flows

Flow velocity controls hillslope soil erosion and is a key hydrodynamic variable involved in sediment transport and deposition processes. The dye-tracer technique is one of the most applied methods for measuring velocity of shallow interrill and rill flow. The technique is based on the injection of a tracer in a specific point and the measurement of its speed to travel the known distance from the injection point to a given channel section. The dye-tracer technique requires that the measured surface flow velocity has to be corrected to obtain the mean flow velocity using a correction factor which is generally empirically deduced. The technique has two sources of uncertainties: i) the method applied for measuring the travel time of the dye-tracer and ii) the estimate of the correction factor, which is the ratio between the mean flow velocity and the surface velocity, in different flow conditions. In this paper the results of a wide experimental investigation, carried out using a fixed bed small flume simulating a rill channel, are presented. At first, the comparison between a chronometer-based (CB) and video-based (VB) technique was carried out for establishing the influence of the travel time measuring technique. For each experimental run, which was characterized by a sample of 20 measurements carried out with the same values of slope and discharge, the developed analysis showed that the empirical frequency distribution of the ratio between the single measurement and the sample mean (i.e., the average of 20 measurements) is more uniform for the VB technique than for the CB one. In any case, this sample mean was representative of surface flow velocity for both the CB and the VB technique. Furthermore, the mean value obtained by the CB measurements lightly underestimated (−1.7%) the corresponding mean obtained by the VB technique. Finally, the effects of slope (0.1–8.7%), flow Reynolds number (3462–10040), Froude number (1.44–5.17) on the correction factor are presented. The analysis demonstrated that the correction factor is independent of flow Reynolds number while a relationship with a Froude number, obtained by surface velocity measurement, or channel slope can be established.     

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.     

The measurement of discharge using a commercial digital video camera in irrigation canals

This paper presents measurements of the discharge by image techniques on the surface velocity field and water stage in irrigation canals. The velocity and stage gauge are obtained from a commercial digital video camera. The time series of the surface velocity and stage were collected simultaneously. Particle image velocimetry (PIV) was used to determine the surface velocities in the irrigation canal. PIV proceeds by using bubbles floating on the water surface as tracer particles, and making a cross-correlation analysis between two continuous images. The whole surface velocity distribution in the irrigation canals can be obtained. The water stage of the canal is obtained from the digital video camera images by making use of image segments to separate the stage gauge and the background. The discharge is computed by using the surface velocities and water stage via open channel velocity distribution theory. Comparing the discharge measured using image techniques with Parshall flume data shows that the differences are less then 5%. The results suggest that the image measurement techniques developed can be used in applications to estimate the discharge in irrigation canals effectively.     

Entropy analysis of flow and heat transfer caused by a moving plate with thermal radiation

This study examines the effects of thermal radiation on entropy generation in flow and heat transfer caused by a moving plate. The equations that govern the flow and heat transfer phenomenon are solved numerically. Velocity and temperature profiles are obtained for the parameters involved in the problem. The expressions for the entropy generation number and the Bejan number are obtained based on the profiles. Graphs for velocity, temperature, the entropy generation number, and the Bejan number are plotted and discussed qualitatively.