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1

Theoretical description of PIV measurement errors

Cameron Stuart Murray

Acta Geophysica

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2022

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Vol. 70, no 5

2379--2387

EN

Expressions for particle image velocimetry (PIV) mean error and error variance are derived for iterative deformation method algorithms. The analytical expressions explicitly account for the role of in- and out-of-plane displacements, displacement gradients, particle image diameter, fill factor of the imaging sensor, image noise, light sheet intensity distribution, seeding particle concentration, the interpolation function used to deform PIV images, and the interrogation window size and weighting window. The newly derived analytical expressions show good agreement with errors estimated using synthetic image sets.

2

Numerical study on two dimensional distribution of streamwise velocity in open channel turbulent flows with secondary current effect

Mohan S., Kundu S., Ghoshal K., Kumar J.

Archives of Mechanics

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2021

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Vol. 73, nr 2

175--200

EN

For studying mechanism of sediment transport in river flows, open channel flow is a prototype. Flow has always three components of velocity for all types of channel geometry and for a time independent uniform flow along streamwise or main flow direction, all the components of velocity are functions of lateral and vertical coordinates. The present study investigates the two dimensional distribution of streamwise (or longitudinal) velocity starting from the Reynolds averaged Navier–Stokes equation for a turbulent open channel flow which is steady and uniform along the main flow direction. Secondary flows both along the vertically upward direction and along the lateral direction are considered which are also taken as functions of lateral and vertical coordinates. Inclusion of the secondary current brings the effect of dip phenomenon in the model. The resulting second order partial differential equation is solved numerically. The model is validated for all the cross-sectional, transverse and centreline velocity distribution by comparing with existing relevant set of experimental data and also with an existing model. Comparison results show good agreement with data as well as with the previous model proving the efficiency of the model. It is found that the transverse velocity distribution depends on the formation of circular vortex in the cross-sectional plane and becomes periodic as the number of circular vortex increases for increasing aspect ratios.

3

The application of cumulants to flow routing

Romanowicz Renata J., Doroszkiewicz Joanna

Meteorology Hydrology and Water Management. Research and Operational Applications

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2019

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Vol. 7, Iss. 1

15--21

EN

This paper aims to fill a gap between present and past research approaches to modelling flow in open channels. In particular, a history of the analytical solutions of a linearized St. Venant equation is presented. A solution of the linearized St. Venant equation, describing the response of a river channel to a single impulse forcing, the so called Instantaneous Unit Hydrograph (IUH), can be described using cumulants, defined as the moments of a logarithm of a variable. A comparison of analytical and numerical solutions of flood wave propagation under various flow conditions is given. The river reach of Biała Tarnowska is used as an illustration of both approaches. A practical application of simplified solutions to the emulator of a flood wave propagation is suggested showing a link between theory and practice.

4

Numerical Modelling of Fish Passage with Turning Pools

Maniecki Ł.

Archives of Hydro-Engineering and Environmental Mechanics

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2018

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Vol. 65, nr 1

41--66

EN

An assessment of operating conditions in a baffled fish passage with pool dimensions of 2:2 3:0 m, and 180 horizontally turning pools, was carried out using numerical computations and a site survey of water flow velocity distribution. Velocity was measured with a PMS electromagnetic flowmeter and a hydrometric current meter in representative cross-sections of the fish passage in the pool centres and in the baffle barrier cross-section area. Numerical computations were also performed for two alternative baffle locations in the fishway. One reflected the actual conditions, and the other was an alternative arrangement designed to improve hydraulic conditions for fish migration. The numerical model used the Large Eddy Simulation (LES) method, which makes it possible to detect large vortexes. The study pays close attention to the velocity field analysis as well as the distribution and sizes of vortexes in the turning pool of the culvert. The results of numerical computations and the site survey show high consistency, and the proposed baffle placement modification significantly improves flow conditions, especially in the entry section of the passage.

5

Reinvestigation on Mixing Length in an Open Channel Turbulent Flow

Kundu S., Kumbhakar M., Ghoshal K.

Acta Geophysica

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2018

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Vol. 66, no. 1

93--107

EN

The present study proposes a model on vertical distribution of streamwise velocity in an open channel turbulent flow through a newly proposed mixing length, which is derived for both clear water and sedimentladen turbulent flows. The analysis is based on a theoretical consideration which explores the effect of density stratification on the streamwise velocity profile. The derivation of mixing length makes use of the diffusion equation where both the sediment diffusivity and momentum diffusivity are taken as a function of height from the channel bed. The damping factor present in the mixing length of sediment-fluid mixture contains velocity and concentration gradients. This factor is capable of describing the dip-phenomenon of velocity distribution. From the existing experimental data of velocity, the mixing length data are calculated. The pattern shows that mixing length increases from bed to the dip-position, having a larger value at dip-position and then decreases up to the water surface with a zero value thereat. The present model agrees well with these data sets and this behavior cannot be described by any other existing model. Finally, the proposed mixing length model is applied to find the velocity distribution in wide and narrow open channels.The derived velocity distribution is compared with laboratory channel data of velocity, and the comparison shows good agreement.

6

Time-averaged Turbulent Flow Characteristics over a Highly Spatially Heterogeneous Gravel-Bed

Sarkar S.

Acta Geophysica

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2016

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Vol. 64, no. 5

1797--1824

EN

The present study focuses on the time-averaged turbulence characteristics over a highly spatially-heterogeneous gravel-bed. The timeaveraged streamwise velocity, Reynolds shear and normal stresses, turbulent kinetic energy, higher-order moments of velocity fluctuations, length scales, and the turbulent bursting were measured over a gravel-bed with an array of larger gravels. It was observed that the turbulence characteristics do not vary significantly above the crest level of the array as compared to those below the array. The nondimensional streamwise velocity decreases considerably with a decrease in depth below the array. Below the array, the Reynolds shear stress (RSS) deviates from the gravity-law of RSS distributions. Turbulence intensities reduce below the crest level of the gravel-bed. The third-order moments of velocity fluctuations increase below the crest level of the gravel-bed and give a clear indication of sweeps as the predominating event which were further verified with the quadrant analysis plots. The turbulent length scales values change significantly below the crest level of the gravel-bed.

7

Scour Downstream of Grade Control Structures under the Influence of Upward Seepage

Shafai-Bejestan M., Nabavi S. M. R., Dey S.

Acta Geophysica

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2016

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Vol. 64, no. 3

694--710

EN

The installation of free falling jet grade control structures has become a popular choice for river bed stabilization. However, the formation and development of scour downstream of the structure may lead to failure of the structure itself. The current approaches to scour depth prediction are generally based on studies conducted with the absence of upward seepage. In the present study, the effects of upward seepage on the scour depth were investigated. A total of 78 tests without and with the application of upward seepage were carried out using three different sediment sizes, three different tailwater depths, four different flow discharges, and four different upward seepage flow discharge rates. In some tests, the three-dimensional components of the flow velocity within the scour hole were measured for both the cases with and without upward seepage. The scour depth measured for the no-seepage results compared well with the most accurate relationship found in the literature. It was found that generally the upward seepage reduced the downward velocity components near the bed, which led to a decrease in the maximum scour depth. A maximum scour depth reduction of 49% was found for a minimum tailwater depth, small sediment size, and high flow discharge. A decay of the downward velocity vector within the jet impingement was found due to the upward seepage flow velocity. The well known equation of D’Agostino and Ferro was modified to account for the effect of upward seepage, which satisfactorily predicted the experimental scour depth, with a reasonable average error of 10.7%.

8

Koncepcja stanowiska do badania wypływu zanieczyszczeń z kanałów burzowych

Rząsa M. R., Boguniewicz-Zabłocka J.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

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2015

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Nr 47

155--158

PL

Pomiary przepływu mieszaniny polidyspersyjnej są jednymi z najtrudniejszych do zrealizowania w warunkach technicznych. W artykule opisano koncepcję systemu pomiarowego, który umożliwi obserwację przepływającej mieszaniny oraz wyznaczenia podstawowych parametrów jej ruchu. W pracy zaproponowano sposób opisu wydmy przesuwającego się piasku. Wymiary wydmy zdefiniowano za pomocą czterech charakterystycznych wymiarów. Zaproponowano stanowisko laboratoryjne umożliwiające badanie przepływu mieszaniny w kanale otwartym przy różnym nachyleniu kanału i różnym składzie granulometrycznym frakcji stałej. Stanowisko wyposażono w system rejestracji obrazu. Obrazy zarejestrowane kamerą poddawane są procesowi komputerowej analizy obrazu i na tej podstawie możliwe jest określenie podstawowych parametrów ruchu mieszaniny. Praca zawiera opis koncepcji stanowiska laboratoryjnego oraz ideę metody analizy obrazu.

EN

A storm water system with open channels for the discharge of rainwater exists in most urbanised areas. The flow in these kind of channels is generally multiphase flow, in which there are solids and liquids and in some places there may be an additional gas phase. Therefore the ability to describe such flow is reduces to the description of the motion of the polydisperse mixture. Polydisperse mixture flow measurements are among the most difficult to achieve in technical terms. The article describes the concept of a measurement system that allows observation of the poly-dispersed flow and determine the basic parameters of its motion. Concept of experimental laboratory set-up was proposed to measure the parameters of the polydispersed mixture flow process in open channel with different slope of the channel and various granulometry of the solid fraction. In this work description of sand dunes with four typical parameters was proposed. A digital camera is used to interrogate the flow. Images recorded on the camera will be subjected to a process of image analysis, and from this the basic parameters of the movement are determined. The work includes a description of the experimental set-up with the idea of image analysis methods.

9

A large eddy based lattice-Boltzmann simulation of velocity distribution in an open channel flow with rigid and flexible vegetation

Gac J.

Acta Geophysica

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2014

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Vol. 62, no. 1

180--198

EN

The large eddy simulation method, based on a lattice-Boltzmann algorithm, was used to compute the vertical velocity profile in an open channel flow with submerged and emerged vegetation. The numerical method is characterized by the relatively short time of computation and low complexity. On the other hand, it allows a more realistic description of the vegetation properties relative to the methods commonly used in 1-D numerical models. For the proper conditions, the method developed in this work gives results similar to other numerical methods. These results are also in good agreement with the experimental data presented in other papers.

10

Lax-Wendroff and McCormack Schemes for Numerical Simulation of Unsteady Gradually and Rapidly Varied Open Channel Flow

Machalińska-Murawska J., Szydłowski M.

Archives of Hydro-Engineering and Environmental Mechanics

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2013

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Vol. 60, nr 1-4

51--62

EN

Two explicit schemes of the finite difference method are presented and analyzed in the paper. The applicability of the Lax-Wendroff and McCormack schemes for modeling unsteady rapidly and gradually varied open channel flow is investigated. For simulation of the transcritical flow the original and improved McCormack scheme is used. The schemes are used for numerical solution of one dimensional Saint-Venant equations describing free surface water flow. Two numerical simulations of flow with different hydraulic characteristics were performed – the first one for the extreme flow of the dam-break type and the second one for the simplified flood wave propagation problem. The computational results are compared to each other and to arbitrary solutions.

11

Green’s function of the linearized Saint-Venant equations in laminar and turbulent flows

Di Cristo C., Iervolino M., Vacca A.

Acta Geophysica

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2012

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Vol. 60, no. 1

173-190

EN

In the present paper, an analytical expression of the Green’s function of linearized Saint-Venant equations (LSVEs) for shallow water waves is provided and applied to analyse the propagation of a perturbation superposed to a uniform flow. Independently of the kinematic character of the base flow, i.e., subcritical or supercritical uniform flow, the effects of a non-uniform vertical velocity profile and a non-constant resistance coefficient are accounted for. The use of the Darcy-Weisbach friction law allows a unified treatment of both laminar and turbulent conditions. The influence on the wave evolution of the wall roughness and the fluid viscosity are finally discussed, showing that in turbulent regime the assumption of constant friction coefficient may lead to an underestimation of both amplification and damping factors on the wave fronts, especially at low Reynolds numbers. This conclusion has to be accounted for, particularly in describing hyper-concentrated suspensions or other kinds of Newtonian mixtures, for which the high values of the kinematic viscosity may lead to relatively low Reynolds numbers.

12

Numerical Simulation of Open Channel Flow between Bridge Piers

Szydłowski M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2011

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Vol. 15, No 3-4

271-282

EN

Free-surface flow in the vicinity of bridge piers on a fixed channel bed is a classical problem of open-channel hydraulics. This problem is usually analyzed using one-dimensional hydraulic models for steady-flow problems. The aim of this paper is to present a two-dimensional numerical simulation of water flow around obstacles, such as cylinders, which can act as a simplified model of real piers. The depth-averaged Navier-Stokes equations describing unsteady free-surface flow are solved using an explicit scheme of the finite-volume method. The numerical solution prepared for the simulations of unsteady free-surface flows was used here to analyze the case of steady flow. A numerical simulation of flow in the channel with the obstruction was performed for two different inflow discharges determining, respectively, the subcritical and supercritical flow in the cross-section of a channel constriction. In the second simulation, a hydraulic jump was observed downstream of the bridge section. The numerical results were compared with measurements. Water surface profiles were measured for both discharges in the hydraulic laboratory of the Faculty of Civil and Environmental Engineering at Gdansk University of Technology (GUT). Comparisons with laboratory data showed that the proposed approach constitutes a sufficiently accurate and reliable technique for predicting basic flow parameters. The method of two-dimensional modeling of flow in a river channel between bridge piers can be also integrated with the simulation of unsteady flood wave propagation, ensuring a uniform approach to the problem of flood modeling in river valleys. Moreover, a two-dimensional simulation yields detailed information about flow structure near the obstruction, which can be used to better elucidate debris transport and river bed deformation processes.

13

Experimental Analysis of Relations Between Coherent Turbulent Structures and Formation of Bedforms

Termini D., Sammartano V.

Archives of Hydro-Engineering and Environmental Mechanics

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2008

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Vol. 55, nr 3-4

125-143

EN

The present paper describes an experimental investigation on the interactions between flow turbulence and sediment motion. During the experiments, detailed measurements of flow velocity components were carried out using an Acoustic Doppler Velocimeter (ADV). The occurrence of turbulent events (inward interaction, ejection, sweep and burst) was verified through conditioned quadrant analysis. The quantitative information on the spatial and temporal evolution of turbulent events was obtained through space-time correlations of the conditioned data. As the primary objective was to analyse how turbulent structures influence formation of bedforms, the spatial scale of turbulent event evolution has been compared with the wavelength of bed-forms (alternate bars) observed on the bed. The analysis has essentially highlighted that such spatial scale compares well with the wavelength of the bars.

14

Hydraulic Loss Coefficients in 1D Flows

Sawicki J. M.

Archives of Hydro-Engineering and Environmental Mechanics

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2007

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Vol. 54, nr 2

95-116

EN

Determination of hydraulic losses is a very important problem, both from the cognitive and practical points of view. For the uniform and steady fluid streams these losses are described by the well known algebraic expressions, containing some experimental coefficients. In technical practice it is commonly assumed, that these coefficients can be applied also for more complex kinds of flow (non-uniform and even unsteady). However, the problem analysis shows that the proper level of conformity between the results of calculations and measurements can be obtained only after a considerable enlargement of the loss coefficient. Investigation of available characteristics of non-uniform and unsteady 1D velocity fields, presented in this article, leads to the conclusion that this enlargement is physically justified and in some cases it is possible to determine correction factors, which enable recalculation of "basic" coefficients into their new values, suitable for more complex models of 1D flows.

15

Zastosowanie programu HEC-RAS do modelowania przepływu wielkich wód w rzece Widawie

Chmielewska I.

Przegląd Naukowy Inżynieria i Kształtowanie Środowiska

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2005

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Vol. 14, No. 1

39--48

EN

This report contains results from modeling computation of flood discharge in the W idawa River within the city area of Wrocław. Calculations were performed with the use of HEC-RAS ver.3.1.1. application program. The following initial data were entered to model: situation channel chart, geometrie data of cross-sections, geometrie data of hydrotechnical and communication structures, flow non-effective areas, contraction and expansion coefficient, Manning’s roughness coefficients for channel and overbanks. Calculations were carried out for stationary flow conditions. After accomplishing entering the above initial data, simulations were carried out and the results were used for preparing flood risk zones charts.

16

A turbulence model for 3-d flows with anisotropic structure of turbulence

Czernuszenko W., Rylov A.

Archives of Hydro-Engineering and Environmental Mechanics

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2005

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Vol. 52, nr 4

303-320

EN

A new turbulence model for flows in open channels with compound cross-sections is presented. The structure of turbulence in these channels can be anisotropic. This structure is described by the turbulent stress tensor that is presented here as the sum of two tensors, namely, normal and shear stress tensors. The normal and shear turbulent stresses are expressed by the turbulence intensities and the mixing length tensor (MLT), respectively. The turbulence intensities can be learned from measurements or another suitable approaches. One such approach that allows calculating the main component of the normal stresses is presented in the paper. The components of MLT are defined based on a new concept of generic mixing length (GML). The generic mixing length is assumed to depend on both distances; from the nearest wall and from the water surface. To demonstrate how the new model works the basic hydrodynamic equations (parabolic approximation of Reynolds equations) together with the turbulence model are solved. The well-known Patankar and Spalding (1972) algorithm was used when solving these equations. A series of numerical simulations were performed for different components of MLT and different channel geometries.

17

Flow turbulence over mobile gravel-bed: spectral scaling and coherent structures

Nikora V.

Acta Geophysica Polonica

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2005

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Vol. 53, nr 4

539-552

EN

The turbulence structure of high Reynolds number, quasi-2-D flow with a weakly mobile gravel bed is considered, with particular focus on velocity spectra and bursting events from quadrant analysis. A four-range scaling model for velocity auto-spectra and co-spectra is discussed and tested. It is suggested that eddy clusters revealed using quadrant analysis contribute to the energy production, low wave -number region in velocity spectra, while individual bursting events contribute to the "-1" scaling region of intermediate wave numbers where energy production and cascade energy transfer co-exist. Possible relations between spectral scaling and coherent structures are briefly discussed.