DISTRIBUTION OF THE HYDRAULIC PARAMETERS AT RIVER BENDS

Transcription

1 DISTRIBUTION OF THE HYDRAULIC PARAMETERS AT RIVER BENDS Isa Issa Oran *, Riyad Hassan Al-Anbari ** and Walaa Khalil Ali *** * Assist. Professor, Foundation of Technical Education ** Assist. Professor, University of Technology, Baghdad, Iraq *** Lecturer, University of Technology, Baghdad, Iraq ABSTRACT In this research, an analytical study was done to indicate the hydraulic paraeters distribution of different bends at the canal of Great Al-Mussayab project. This paper stated that the distribution of the circulation constant, super elevation and the peak values of shear stress associated with the core of the axiu velocity. It was found that the value of shear stress causes the weakening of bank aterial. That eans the flow velocity could transport soe fallen bank aterial downstrea. Also the distribution of Reynolds nuber along the cross section of canal has peak values associated with the greatest depth of the flow. At high discharge, values of Reynolds nuber give noral distribution, while the shear stress becoes less unifor coparing with the distribution at low discharge. It was found that the influence of turbulent energy and eddy viscosity are sall and not varied greatly along the flow section of different discharges. 1- INTRODUCTION A natural eandering strea can represent one of the ost coplex fluid flow situation encountered in the environent. Not only is the flow turbulent and strongly three diensional but its irregular topography and bathyetry are ingeneral subject to constant changes as a result of erosion sedient transport and deposition processes [1]. In straight channels, the velocity distribution and shear stresses are syetrical about the channel centerline. The proble of designing the stable channel is thus can be siplified. On the other hand, when a bend is encountered the presence of secondary current and other hydraulic paraeters such as shear stress and Reynolds nuber generate the well known helicoidally flow patterns [,3]. This phenoenon causes excess local scouring near the outer bank of river bend and deposition of aterial towards the inner bank iediately downstrea of the bend.

2 In the bend, because the priary velocity changes with the depth, the centrifugal force acting on the flow has different effects at different depths [4,5]. Therefore, shear stresses becoe skewed and induced currents which directly affected on the stability of river bank. In recent years, several investigators [6,7,8,9] have considered this proble. They obtained the stable section of channel at the bends and developed atheatical odels to predict the effect of stresses on the stability of the channel bend. The actual failure echanis at river bends is closely related to the engineering properties of bank aterials. However, in attepting to stabilize an eroding bank, it is iportant to appreciate the need to protect the basal area fro erosion. Therefore, this paper indicated the distribution of hydraulic paraeters at cross-section of river bends. - THEORETICAL ANALYSIS -1 Boundary Shear Stress Distribution The agnitude of boundary shear stress depends on the velocity gradients closed to the bed of channel. These stresses exerted by the flowing water which ay resulting in the deforation or scouring of the bed and banks of river [], and as follows: dv τ o = k (1) dy Where τ o is the boundary shear stress N/ k is the eddy viscosity of flow (dynaic viscosity) kg/.s dv dy is the velocity gradient /s. The average boundary shear can be calculated by: τ o = ρ w g R S () Where ρ w is the density of water kg/ 3 R is the hydraulic radius S is the slope of total energy grade line / g is the gravitational acceleration /s

3 For the present research, the average boundary shear stress is calculated by using the following equation [10]: V V 1 τ o = ρ w (3) (.3 / k1 ) log d / d1 where V 1, V are the ean velocity in the x-direction at heights of d 1, d easured fro the bed of channel, k 1 von Karan constant (k 1 = 0.4). - Turbulent Energy Eddy Viscosity and Reynolds Nuber of Flow These paraeters have iportant effects on the stability of river banks. They can be deterined by the following equations [11]: T e = 1.05V (4) * 3 E = V / kd (5) * R e = Vd / γ (6) where T e is the turbulent energy rate, E is the dissipation rate of eddy viscosity, R e is the Reynolds nuber, V * is the shear velocity and γ is the kineatic viscosity. -3 Super Elevation and Circulation Constant The centrifugal force of flow deflects the particles of water fro straight line otion. It is responsible for the super elevation and circulation constant [10]. To deterine these paraeters, the following equations were suggested [5]: Y = V T / (7) gm r C = M r V (8) Also, the above equations were siplified with good accuracy [1], and as follows: Y = V (9) 0.03 C = 4.4V T (10) where Y is the super elevation of flow C is the circulation constant V is the average velocity of flow at the bend /s T is the top of cross-sectional flow

4 M r is the radius of bend 3- FIELD MEASUREMENTS The easureents of hydraulic paraeters were carried out on selected reaches of the great Mussayab canal, Fig. (1). Various types of river bends (3 bends) were chosen for this study. The cross section of canal was divided into a liited nuber of verticals (10-1). The flow velocity profile for each vertical ade at different depths of flow. Points of velocity easureent located between the upper part at 10 c below the water surface, and the lower part at 10% of the total depth above the bed, Table (1). Baghdad Euphrates River Tigris River Bend Location City Al-Mussayb City Al-Hindiya Barrages 1 3 Hilla Great Al-Mussayab Canal Fig. (1) Location Map of Great Al-Mussayab Canal (The Studied Area) Table (1) Paraeters of Flow for Different Bends on Great Al-Mussayab Canal Bend No Angle eandering (degrees) Radius of curvature () Water surface slope Hydraulic depth () Width () Cross sectional area ( ) Mean velocity (/s) Discharge ( 3 /s)

5 4- RESULTS AND DISCUSSION 4-1 Velocity Distribution of Flow By analyzing the field easureents at various bends on Great Al-Mussayab Canal Figs. (, 3, 4-c) and other bends which reebered in other papers [7,8], it was found that the (V = 0.94V), (d = 0.94d) and (R = 0.94R). These analyses were conducted by assuing that the discharge of flow is the sae in straight and bend section of the canal; where V, d, R are the averages of velocity, hydraulic depth and hydraulic radius at the bend section respectively. Also, this research paper indicates that the core of axiu velocity of flow was located near the inner side of the bend (about 30% of the canal ). The flow lines of velocity distribution at each section especially with high discharges igrate towards the outer side of bend. Also, the variation of flow lines unifority increases at this place. 4- Boundary Shear Distribution Shear stress was calculated by analyzing the velocity gradient which is very close to the bed. It was obtained by using Eq. (4), and the distribution of shear stress at each section is shown in Figs. (, 3, 4-b). Peak values of shear stress occur in regions where the flow velocity is high. While, low values of shear stress occur at zones of low velocity, these zones are found near the inside and outside of the bend. As discharge increases to the axiu values, the distribution of shear stress becoes less unifor copared with this distribution at low discharges. High values of shear stress are the product of convergence of secondary circulations which caused the weakening of bank aterial, and decreased its strength against shear failure. 4-3 Super Elevation and Circulation Constant Figures (, 3, 4-c,d) show that the super elevation and circulation constant have peak values associated with the core of axiu velocity. The distribution of these paraeters at different depths of flow gives noral shape. In bend, because the flow velocity changes with the depth, the centrifugal force acting has different effects. Therefore, shear stress becoes skewed, and igrates towards the outer side of the bend and away fro the centre of channel. This skewness induced strong secondary circulation.

6 N/ (b) (b) (c) (c) (d) (d) (e) (e) (f) (f) (g) (g) Reynolds Nuber The dissipation Rate Turbulent Energy eddy viscosity Rate Super elevation Circulation constant Bed shear stress Depth of flow Fig. () (a) Pattern of Long Strea Isovels at Bend (1) (b,c,d,f,g) Distribution of Different Hydraulic Paraeters at Bend (1)

7 (b) (c) (c) (d) (d) Circulation constant (b) Super elevation N/ The dissipation Rate Turbulent Energy Rate eddy viscosity Bed shear stress Depth of flow (e) Reynolds Nuber (f) Fig. (3) (g) (e) (f) (g) (a) Pattern of Long Strea Isovels at Bend () (b,c,d,f,g) Distribution of Different Hydraulic Paraeters at Bend ()

8 Q=73/s N/ Bed shear stress Depth of flow (b) (c) Top (c) Top (c) (c)top Top (d) Top (d) (d) Top (d) Top (e)top (e) (e) (e) TopTop (f)(f) Top Top Top (f)(f) Top (g) (g) Reynolds Reynolds Nuber Nuber Super Super elevation elevation (b) TheThe dissipation Rate dissipation Rate Turbulent TurbulentEnergy Energy Rate eddy viscosity eddy viscosity Rate Circulation Circulation constant constant (b) (b)top Top Fig. (4) (a) Pattern of Long strea Isovels at Bend (3) (b,c,d,f,g) Distribution of Different Hydraulic Paraeters at Bend (3)

9 4-4 Turbulent Energy and Eddy Viscosity Figures (, 3, 4-e,f) indicate that the distributions of turbulent energy and eddy viscosity have peak values associated with the core of axiu velocity. These distributions take the siilar shape of shear stress distribution. It was found that the effects of turbulent energy and eddy viscosity are sall, and not varied greatly along the section of flow at different discharges. 4-5 Reynolds Nuber Figures (, 3, 4-g) show that the distribution of R e has peak values associated with the greatest depth at each section of flow. It is not related to the core of axiu velocity. At high discharge, the values of R e give noral distribution, while the distribution of shear stress becoes ore unifor as R e decreases. 5- CONCLUSIONS This research paper indicated the distribution of hydraulic paraeters at cross-section of river bends, and its conclusions are as follows: a- The rate of flow velocity in straight section to the bend at the sae canal is equal to b- The core of axiu velocity is located near the inner side of the bend with distance about 30% of canal. c- The values of shear stress cause the weakening of bank aterial, and that eans the flow velocity can transport soe fallen bank aterials down strea. d- Peak values of shear stress occur in regions where the flow velocity is high. e- As discharge increases to axiu values, the distribution of shear stress becoes less unifor copared with this distribution at low discharge. f- The distribution of Reynolds Nuber values has peak values associated with the greatest depth of flow. It is not related to the core of axiu velocity. g- The distribution of shear stress becoes ore unifor as Reynolds nuber decreases. h- The distributions of shear stress, super elevation, and circulation constant have peak values associated with the core of axiu velocity. i- At different bends, values of turbulent energy and eddy viscosity are sall and not varied greatly along the flow section at different discharges. REFERENCES 1. Leschziner, M.A. "Calculation of Strongly Curved Open Channel Flow" J. of the Hydraulics Div., ASCE, Vol. 108, HY10, pp , Nouh, M.A. "Shear Stress Distribution in Stable Bends" J. of the Hydraulics Div., ASCE, Vol. 105, HY10, pp , 1979.

10 3. U.S. Ary Corps of Engineers, Massachusetts Estuaries Project "Hydrodynaic Modeling of the Popponesset Bay Estuarine Syste Using RMA Model" USA, Arceent, G.J. and V. Schreider "Guides for Selecting Manning's Roughness Coefficient for Natural Channels and Flood Plains", U.S.G.S., Water Supply Paper 339, USA, Rijn, L.C. "Handbook of Sedient Transport by Currents and Waves" Delft Hydraulic Lab. Counication, Delft, The Netherlands, Young, D.L. and Y. Wang "Three Diensional Transient Shallow Water Flow Siulation Using a Boundary Integral Equation Model" J. of the Hydraulic Research, Vol. 40, No. 4, p. 4, Yen, C. L. "Bed Topography Effect on Flow in a Meander" J. of the Hydraulics Div., Vol. 96, HY1, p. 71, England, F. "Flow and Bed Topography in Channel Bends" J. of the Hydraulics Div., ASCE, Vol. 100, HY11, pp , Rastogi, A.K. "Predictions of Heat and Mass Transfer in Open Channels" J. of the Hydraulics Div., ASCE, Vol. 104, HY3, p. 84, Chow, V. "Open Channel Hydraulics" Int. St. Ed., 0 th ed., Noat, D. "Calculation of Secondary Currents in Channel Flows" J. of the Hydraulics Div., ASCE, Vol. 108, HY8, p. 141,