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1

Analysis of time-averaged secondary flow cells in wide and narrow straight open channels with lateral bed deformation

Chattopadhyay T., Kundu S.

Archives of Mechanics

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2023

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Vol. 75, nr 1-2

169--211

EN

The usual cellular pattern of the time averaged secondary flow circulation in the central section of wide open channels shows a distorted (laterally or vertically) structure due to the changes in bed configurations along lateral direction. The structures of these secondary circulations (under different bed configurations) are crucial for different types of hydraulic modeling. This study presents mathematical models of the time averaged secondary velocities (lateral and vertical components) for a turbulence-induced secondary current at the central section of a wide open-channel flow under different types of elevated and non-elevated bed conditions. Starting with the Reynolds Averaged Navier-Stokes equation and using the continuity equation, at first the governing equation of secondary flow velocity is obtained including the effects of the eddy viscosity and viscosity of the fluid. The model equations is solved using a separation of the variable technique imposing the bed perturbation condition. Full analytical solutions are achieved through mathematical analysis using suitable boundary conditions consistent with experimental observations. Initially the models are derived for a non-elevated bedforms comprised of alternating equal widths of smooth and rough bed strips. These models are modified further for bedforms with unequal widths of rough and smooth bed strips and elevated periodic bed structures. Four different types of elevated bed configurations are investigated and a general approach is suggested for other types of bed forms. All the proposed models are validated with existing experimental results to ensure the applicability and in each cases, improved results are observed. Obtained results show that the centre of circulation of the cellular structure occurs above the junction of the rough and smooth bed strips (consistent with experimental observations) and it gradually shifts towards the smooth strip, when the length of the rough bed strip is increased. The shifting as a function shows a non-linear pattern with the length of the rough bed strip. A least-square model is proposed to identify the circulation center as a function of the ratio of rough to smooth bed strips. It is also found that the vertically distorted secondary cells are generated when the bed slope strictly increase/decrease throughout the length of the one whole circulation. Finally, all the proposed models are compared with an existing model and an error analysis is done. Results of error analysis show that the present study can be more suitable as it yields improved results.

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

International comparison of AC current ratio standards

Draxler K., Styblikova R., Lobjanidze N.

Przegląd Elektrotechniczny

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2010

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R. 86, nr 9

252-256

EN

This paper presents the results of an international comparison of AC current ratio standards between the Czech Metrology Institute (CMI) and the Georgian National Agency for Standards, Technical Regulation and Metrology (GEOSTM). Ratio errors and phase displacements were measured in the range (5 up to 2 000) A at 50 Hz mains frequency. Two GEOSTM 2-stage standard current transformers were used as transfer standards. These transformers were designed and developed at GEOSTM Tbilisi, Georgia.

PL

W artykule przedstawiono międzynarodowe porównanie wzorców stosunku prądów AC wykonanych przez Czeski Instytut Metrologii CMI i Gruzińską Narodową Agencję Wzorców, Norm i Metrologii GEOSTIM. Zbadano błąd stosunku oraz fazy w zakresie 5 - 2000 A przy częstotliwości 50 Hz. Wykorzystano wzorce Instytutu gruzińskiego. Transformatory zostały opracowane w GEOSTM.