Bed form characteristics in a live bed alluvial channel

Transcription

1 Scientia Iranica A (2014) 21(6), 1773{1780 Sarif University of Tecnology Scientia Iranica Transactions A: Civil Engineering Bed form caracteristics in a live bed alluvial cannel H. Heydari, A.R. Zarrati and M. Karimaee Tabarestani Department of Civil and Environmental Engineering, Amirkabir University of Tecnology, No. 424, Hafez Ave., Teran, P.O. Box 15914, Iran. Received 30 January 2013; received in revised form 15 June 2013; accepted 15 April 2014 KEYWORDS Abstract. Bed forms are generated in alluvial streams due to mutual interaction between 1. Introduction directly by dividing te ydraulic radius into two parts; one due to grain rougness, and te oter due to bed forms. Among te variety of possible bed forms in an alluvial stream, dunes are te most important feature and muc attention as been paid to tem in te literature [1,3-6] Tis feature is more frequently encountered in alluvial streams, wic ave large dimensions and, consequently, resistance to ow (Figure 1). Te ow over a dune is caracterized by a circulating zone, wose lengt depends on dune eigt, and a long fetc of attaced ow up to te dune crest [7]. Te triangular sections of te dunes are not symmetric. Te upstream face is inclined at about 10 to 20 degrees and te downstream face is at an angle of about 30 to 40 degrees to te orizontal. Tese bed forms are not static and gradually move forward wit time, of course at a very slow and creeping velocity muc less tan tat of te ow (Figure 1). Extensive researc as been undertaken in te past by various investigators into te prediction of bed Bed form; Live bed condition; Flow intensity; Dune celerity; Bed rougness. ow and erodible bed material. Among te variety of possible bed forms, dunes are te most important feature and muc attention as been paid to tem in te literature. In te present study, an experimental approac was carried out to investigate te geometry of dunes and teir celerity in an erodible sand bed. Te tests were conducted under live bed conditions in an experimental ume capable of re-circulating bot water and sediment. Present experiments sowed tat te Sields number ad a considerable e ect on dune eigt and celerity, wile te e ect of tis parameter on te dune lengt was not signi cant. Furtermore, dimensional analysis is used to present te relationsips between dune eigt and lengt, as well as celerity. Tese relationsips were also compared wit previous empirical equations and experimental data, wic sowed teir acceptable accuracy. Bed rougness related to bed forms was also analyzed based on all available experimental and eld data. Results demonstrated tat by increasing te Sields number, te ratio of Manning coe cient, related to bed forms, to total Manning coe cient increased wit a logaritmic trend Sarif University of Tecnology. All rigts reserved. In an alluvial stream, te mobile bed formed by sand is seldom at, and te streambed is usually covered by periodic bed deformations, known as bed forms. Tese bed forms cange in type and size depending on ow conditions. Bed forms initiate wit ripples at low sear stress, wit progressive development of dunes, wased-out dunes (transition), at bed, antidunes, and standing waves, wit increasing sear stress or velocity [1]. Te prediction of bed form geometry is an essential component for estimating overall ow resistance and water levels during oods in rivers. Te Einstein and Barbarossa [2] relationsip was te rst to consider te rule of bed forms in total bed friction *. Corresponding autor. Tel.: ; Fax: addresses: H. Heydari@gmail.com (H. Heydari); Zarrati@aut.ac.ir (A.R. Zarrati); M.Karimaee@aut.ac.ir (M. Karimaee Tabarestani)

2 1774 H. Heydari et al./scientia Iranica, Transactions A: Civil Engineering 21 (2014) 1773{1780 Table 1. Empirical equation for predicting dune dimensions. Equation No. Reference Dune lengt Dune eigt 1 Allen (1978) For < 0:15 Log() = 1:0517 Log() +1:1534 For 0:15 Log() = 1:3543 Log() +1:4553 Log() = 1:2091 Log() 1: Yalin (1964) = 5 n = c 3 Van Rijn (1984) = 7:3 0 = 0:11(d50=)0:3 (1 e 0:5T )(25 T ) 4 Julien and Klaassen (1995) = 6:25 = 2:5 d 50 Note: is dune lengt; is dune eigt; is ow dept; 0 and c are available and criticcal sear stress, respectively, and T is transport stage parameter dened as ( 0 c )= c. 0:3 Figure 1. Scematic view of dune caracteristics and migration. form geometry, specically, dunes in alluvial cannels, using eld [6] or experimental data [8,9,10], or bot [5]. Table 1 summarizes some dierent equations for estimation of dune dimensions. Eac of tese contributions is applicable to problems similar to te specic pysical conditions under wic te empirical equations were developed. Signicant early contributions, in tis respect, were made by Yalin [3], Ranga Raju and Soni [4], and Allen [11] wo developed dune eigt relationsips as a function of bed sear stress and oter variables. Van Rijn [5] analyzed a large number of experimental and eld data to develop a relationsip for dune dimensions as a function of ow dept, sediment size and a transport stage parameter (function of sear stress and critical sear stress). However, Julien and Klaassen [6] suggested tat te Van Rijn [5] approac underestimates te dune eigt in large rivers. Tey found tat dune caracteristics are independent of transport stage parameters for large rivers and are only a function of relative particle diameter. Tey also modied te Van Rijn [5] metod and presented new relationsips for dune caracteristics. Karim [1] proposed a new metod for predicting relative dune eigt in a sand-bed stream based on te concept of relating energy loss due to form drag to te ead loss across a sudden expansion in open cannel ows. Tere is no study in te literature on dune celerity. Basically, two approaces are suggested to estimate te bed rougness in alluvial streams: 1) metods based on bed forms and grain related parameters, suc as bed form lengt and eigt and material size [5], and 2) metods based on integral parameters, suc as mean ow dept and velocity and bed-material size [12]. However, since te rst metod conforms to te pysics of te penomenon, it is more universal and popular. According to tis metod, te bed sear stress () in an alluvial stream can be divided into two parts: i) sear stress due to grain rougness or skin friction ( 0 ), and ii) form related bed sear stress ( 00 ) [13]. Te latter is related to te dierence in pressure distribution between upstream and downstream of te bed form crest. Results of previous relationsips for dune caracteristics and bed resistance related to bed forms dier drastically from eac oter. Tis may be due to te complexity of te underlying pysical process, wic can be attributed to several factors, e.g., a large number of governing variables and interaction between tem, te 3D nature of bed form development and te lag in bed form adjustment in response to canging ow conditions [1]. Terefore, additional researc is needed and more data is required for te accurate formulation of tis complex process. Te main scope of te present work is to study, experimentally, dune caracteristics and teir eect on ow resistance. In addition, te celerity of dunes, wic ad not been addressed by

3 H. Heydari et al./scientia Iranica, Transactions A: Civil Engineering 21 (2014) 1773{ previous studies, is also investigated and a relationsip is suggested for it. An approac for estimating bed rougness is also presented. 2. Experimental setup Experiments were conducted in a orizontal ume, wit an erodible bed 14 m long, 0.75 m wide and 0.6 m deep, at te ydraulic laboratory of Amirkabir University of Tecnology, Iran. Water and sediment were circulated in te cannel by a centrifugal pump wit maximum capacity of 120 (Lit/s) and a sludge pump wit maximum capacity of 5 (Lit/s), respectively. Te ow rate in te ume was controlled and preset by a speed control unit attaced to te pump system. An electrical ow-meter was installed in te supply conduit to measure te water discarge troug te cannel. Figure 1 sows te longitudinal prole of te laboratory ume and its dierent components. Te cannel bed was lled wit uniform sand about 20 cm tick, wit d 10 = 0:65 mm, d 50 = 0:85 mm, as median bed material size, d 90 = 1:05 mm, and a density of 2650 (kg/m 3 ), starting at a distance 2 m downstream of te entrance. Te geometric p standard deviation of sediment grading, g = d 84 =d 16, was 1.22, were d a is te size of sediment for wic a percentage of material by weigt is ner, implying tat te sample is uniform. In order to reduce te ow disturbance and turbulence, a oneycomb (ow straigtener) was used at te upstream section of te cannel). Velocity proles measured by ADV (Acoustic Doppler Velocitimeter), wen te ume bed was xed, sowed tat te ow was fully developed after 5 m from te ume intake. All experiments were conducted under live bed conditions (u =u c > 1; were u is bed sear velocity and u c is critical sear velocity for te bed material). Te range of ow intensity (u =u c ) was between 1.2 to 4.7. Te ow regime in all experiments was subcritical wit maximum Froude number of 0.8. Sear velocity (u) in te cannel was determined by calculating te water surface prole and te slope of te energy line. Tereby, te water dept at upstream and downstream of te cannel was measured by a point gage wit accuracy of 0:1 mm after te bed form caracteristics in te cannel were developed, and similar wit time. To calculate water surface prole, a value for Cezy coecient was initially assumed. Ten, te calculated water surface elevation upstream of te ume was compared wit te measurement results and, if dierent, te bed rougness coecient was sligtly modied. However, at iger ow intensities (u =u c 2:35), wit large dunes, te water surface was undulated and accurate measurements were not possible. From experiments in ow intensity lower tan 2 (u =u c < 2), it was concluded tat te measured Cezy coecient for te ow conforms well to te empirical equation presented by Van Rijn [13], wic is: C = 18Log 12R 3d :1(1 e = ) ; (1) were C is Cezy coecient, R is ydraulic radius, is dune lengt, is dune eigt and d 90 is te size of sediment for wic 90% of te material by weigt is ner. Terefore, at iger ow intensities, te Van Rijn [13] equation was used for te estimation of te Cezy coecient. Sear velocity was ten calculated from te Cezy coecient. In addition, critical sear velocity (u c ) was found by te Sields' diagram, knowing te bed sear velocity. In eac experiment, after lling te cannel wit water and adjusting te downstream tailgate for te desired ow dept, te ow and sludge pumps were turned on. Te ow discarge was gradually increased to te considered value. Initially, te bed was in a nonequilibrium condition and was degraded by te ow. Te transported sediment was ten deposited in te reservoir at te downstream end of te cannel and was pumped continuously by te sludge pump to te cannel inlet (Figure 2). Gradually te bed forms were developed in te cannel and migrated downstream wit increasing dimensions, temporally. However, after a couple of ours, te bed forms (dune wave) reaced equilibrium condition, were teir lengt and eigt were similar along te cannel. Te longest time for development of dunes was about 5 ours for te smallest ow intensity, wic was decreased by increasing ow intensity. After te equilibrium state was reaced, te dimensions of dunes and teir celerity were measured by plastic rulers attaced to te ume side walls, bot orizontally and vertically. Eac experiment was repeated at least twice for verication. Figure 3 sows te dune under equilibrium condition. 3. Dimensional analysis Important parameters tat aect dune dimensions, including its lengt, eigt, and also dune celerity in a steady and quasi-uniform ow, can be expressed as [5,10]: G = f (; d 50 ; u; ; s ; ; g) ; (2) Figure 2. Side view of laboratory ume and its dierent components.

4 1776 H. Heydari et al./scientia Iranica, Transactions A: Civil Engineering 21 (2014) 1773{1780 Exp. number Flow dept (m) Discarge (m 3 /s) d 50 (mm) u (m/s) Table 2. Results of experiments. u =u c Sields number () Sediment Reynolds number (Re*) Dune eigt (cm) Dune lengt (cm) Dune celerity (cm/s) Investigation Present study Colman et al. (2005) [14] Tallebbydokti et al. (2006) [10] Guy et al. (1966) from Karim (1999) [1] Reynolds number (Re*) and Sields parameter (), respectively. Figure 3. Dune waves in equilibrium condition. were is ow dept, d 50 is te median diameter of te bed sediment, u is friction velocity, and s are uid and sediment density, is uid dynamic viscosity, and g is gravitational acceleration. Te parameter, G, in te above equation stands for dune lengt (), its eigt () or its celerity (V d ). By applying Buckingam teory wit repeatable variables of, d 50 and g, Eq. (2) can be written as: G = f ; u d 50 u 2 ; ; (3) d 50 d 50 g were G is a dimensionless parameter and is dened as dune eective lengt (=d 50 ) or dune eective p eigt (=) or dune eective celerity, V s = V d = g:d 50 : =, were is te dierence between sediment and ow densities. Te rst parameter in te rigt and side of Eq. (3) is relative bed rougness. Te second and tird parameters are dened as particles 4. Results 4.1. Dune caracteristics Experiments were conducted wit dierent ow depts and discarge, so tat te Sields number was increased up to Table 2 summarizes all experiments conducted in te present study, and te measurement results. In addition to te present work, experimental and eld data for dune dimensions under a wide range of ow conditions and sediment sizes presented by previous investigations are also sown in Table 2. Figure 4 sows te variations of dune dierent caracteristics wit Sields number, and no correlation can be observed between te dune eective lengt (=d 50 ) and. Neverteless, present experiments sow tat Sields number is important on dune eigt (=). For example, by increasing about 15 times, te dune eective eigt (=) is increased 3.5 times (Figure 4(b)). An interesting conclusion from tis gure is tat te increasing rate of dune relative eigt decreased at iger Sields number (), i.e. > 0:4. Tis may be due to te cange in te ow regime, as te eigt of dunes in te low ow regime decreased in te ig ow regime, were te dune crest is wased away towards transition. Finally, as sown in Figure 4(c), by increasing te Sields number, dunes eective celerity (V s ) increased

5 H. Heydari et al./scientia Iranica, Transactions A: Civil Engineering 21 (2014) 1773{ Figure 5. Comparison of measured and calculated relative dune eigt. Figure 4. Variations of dune dimensions and celerity wit Sields number: a) Dune relative lengt; b) dune relative eigt; and c) dimensionless celerity of dunes. considerably. From experiments, by increasing from to 0.68 (for about 15 times), parameter V s increased about 35.7 times. Tis sows te substantial eect of ow velocity and bed sear stress on te celerity of te dunes. Based on te present experimental data and Eq. (2), te following equations were derived for dune caracteristics: =0:05 d50 0:15 u 0:7 d 50 u 2 0:1 ; d 50 g (4) = 4:8 ; (5) V s =0:05 d50 0:95 u 1:1 d 50 u 2 0:3 : d 50 g (6) Te regression coecients for Eqs. (4) and (5) are about R 2 = 0:96, and, for Eq. (6), is about R 2 = 0:93. Figure 6. Comparison of measured and calculated dune lengt. Eq. (5) sows tat te most eective parameter on dune lengt is te ow dept. Tis is in agreement wit previous studies (see Table 1). Figures 5 to 7 sow a comparison of Eqs. (4) to (6) predictions wit te present experimental data. Te 45 line and te dased lines in tese gures sow complete agreement and error bounds of prediction, respectively. Furtermore, Figures 8 and 9 sow te comparison of Eqs. (3) and (4) wit previous empirical equations using all existing data presented in Table 2. As sown in Figure 8, nearly all clouds of experimental data for dune lengt are between te two lines of empirical equations presented by Allen [11] and Van Rijn [5]. However, te results of Eq. (4) are nearly in te middle of te regions between tese two lines. Figure 9 compares te prediction of dierent empirical equations for dune eective eigt wit all available experimental data. Te line of best agreement is also sown in tis gure. Te range of eac equation prediction is sown by a polygon in tis gure.

6 1778 H. Heydari et al./scientia Iranica, Transactions A: Civil Engineering 21 (2014) 1773{1780 Obviously, te closer tis polygon is to te line of perfect agreement, te more accurate te equation is. As sown in tis gure, te lowest and igest polygons (under prediction and over prediction) are related to te empirical equations presented by Allen [11] and Julien and Klaassen [6], respectively. However, te data region of Eq. (4) is between tem and encompasses data regions for te equations presented by Julien and Klaassen [6], VanRijn [5] and Yalin [3] Bed rougness In a uniform ow, te bed sear stress () can be correlated to te square of te mean velocity wit te following relationsip: = 1 8 fv 2 ; (7) were f is te Darcy-Weisbac rougness coecient. Te following relationsip can be written for total rougness coecient in a live bed alluvial stream [13]: f = f 0 + f 00 ; (8) Figure 7. Comparison of measured and calculated dune celerity. were f 0 and f 00 are rougness coecients related to grains and bed forms, respectively. Based on te relationsip between te Darcy-Weisbac rougness coecient and te Manning rougness coecient, neglecting te eect of ydraulic radius on Manning coecient, one can write: n 2 = n 02 + n 002 : (9) Te Manning coecient related to grains in a plane bed (n 0 ) can be estimated from [13]: Figure 8. Comparison of dierent equations in predicting dune lengt. n 0 = R Log 12R d :3 u ; (10) were R is ydraulic radius and is te kinematic viscosity of water. By estimating total Manning coecient (n) from te Manning equation and also te Manning coecient related to grains (n 0 ) from Eq. (10), one can predict te Manning coecient related to bed forms (n 00 ) from Eq. (9). Analyzing experimental data sowed tat te ratio of n 00 =n is between 0.5 and 0.92 Figure 9. Comparison of dierent equations in predicting relative dune eigt considering all available data. Figure 10. Variation of n 00 =n calculated by log. law wit Sields number.

7 H. Heydari et al./scientia Iranica, Transactions A: Civil Engineering 21 (2014) 1773{ for Sields number between to 1.16, equivalent to Froude number (F ) between 0.24 and 0.76 (Figure 10). By regression analysis, including all data in Table 2, te following logaritmic relationsip was developed for te relative Manning coecient related to te bed form as: n 00 n = 0:11Ln + 0:88: (11) 5. Conclusion An experimental study was carried out to investigate dune caracteristics in sand beds. Te experiments were conducted in a water and sediment recirculating ume. Te ow and deposited sediment in te reservoir at te downstream of te ume were pumped to its upstream inlet. Experiments were performed under live bed conditions, wit a ow intensity parameter (u =u c ) range of 1.2 to 4.7. Eac test was continued until equilibrium condition was acieved, were te bed features (dune wave) were similar in lengt and eigt along te cannel. Under tis condition, dune dimensions, including eigt and lengt, as well as celerity, were recorded. Present experiments sowed tat te Sields number as a considerable eect on dune eigt and celerity. For example, by increasing te Sields number from to 0.68, te dune eective eigt and its eective celerity increased by 3.5 and 35.7 times, respectively. However, te eect of tis parameter on dune lengt was negligible. Based on dimensional analysis and experimental data, empirical equations were developed for dune caracteristics by regression analysis. Comparison of te present relationsip wit te available experimental and eld data, as well as empirical equations presented by previous investigations, sowed an acceptable accuracy. Furtermore, in addition to dune caracteristics, bed rougness related to bed forms was analyzed based on all available experimental and eld data. Results of tis part sowed tat by increasing te Sields number from to 1.16, te ratio of Manning coecient, related to dune eigt, to total Manning coecient increased from 0.5 to An empirical equation was also developed for te Manning coecient related to bed forms. Abbreviations V d V s Dune lengt Dune eigt Dune celerity Dimensionless dune celerity Flow dept 0 c T g d a u u c C R s g Re f f 0 f 00 n n 0 n 00 F References Available sear stress Critical sear stress Transport stage parameter Geometric standard deviation of sediment grading Size of sediment for wic a percent of material by weigt are ner Bed sear velocity Critical sear velocity for te bed material Cezy coecient Hydraulic radius Fluid density Sediment density Fluid dynamic viscosity Kinematic viscosity of water Gravitational acceleration Sediment Reynolds number Sields parameter Darcy-Weisbac rougness coecient Darcy-Weisbac rougness coecient related to grains Darcy-Weisbac rougness related to bed forms Manning rougness coecient Manning rougness coecient related to grains Manning rougness coecient related to bed forms Froude number 1. Karim, F. \Bed-form geometry in sand-bed ows", J. of Hyd. Eng., 125(12), pp (1999). 2. Einstein, H.A. and Barbarossa, N.L. \River cannel rougness", Trans. ASCE, 117, pp (1952). 3. Yalin, M.S. \Geometrical properties of sand waves", J. of Hyd. Div., 90(5), pp (1964). 4. RangaRaju, K.G. and Soni, J.P. \Geometry of ripples and dunes in alluvial cannels", J. of Hyd. Res., 14(3), pp (1976). 5. Van Rijn, L.C. \Sediment transport, Part III: Bed forms and alluvial tougness", J. of Hyd. Eng., 110(12), pp (1984). 6. Julien, P.Y. and Klaassen, G.J. \Sand-dune geometry of largerivers during oods", J. of Hyd. Eng., 121(9), pp (1995). 7. Yoon, J.Y. and Patel, V.C. \Numerical model of turbulent ow over sand dune", J. of Hyd. Eng., 122(1), pp (1996).

8 1780 H. Heydari et al./scientia Iranica, Transactions A: Civil Engineering 21 (2014) 1773{ Kennedy, J.F. and Odgaard, A.J., An Informal Monograp on Riverine Sand Dunes, IIHR Ltd. Distribution Rep. No. 169, Iowa Institute of Hydraulic Researc, University of Iowa, Iowa City, Iowa (1990). 9. Sen, H.W., Felman, H.M. and Mendoza, C. \Bed form resistancein open cannel ows", J. of Hyd. Eng., 116(6), pp (1990). 10. Talebbydokty, N., Hekmatzade, A.A. and Raksanderoo, G.R. \Experimental modeling of dune bed form in a sand-bed cannel", Iranian J. of Sci. & Tec., 30(B4), pp (2006). 11. Allen, J.R.L. \Computational metods for dune timelag: Calculations using Stein's rule for dune eigt", Sed. Geo., 20(3), pp (1978). 12. Wite, W., Paris, E. and Bettess, R. \A new general metod for predicting te frictional caracteristics of alluvial streams", H.R.S. Wallingford, Report No. IT 187, England (1979). 13. Van Rijn, L.C., Principles of Sediment Transport in Rivers, Estuaries and Coastal Seas, Aqua publication, Te Neterlands (1993). 14. Coleman, S.E., Zang, M.H. and Clune, T.M. \Sediment-wave development in subcritical water ow", J. of Hyd. Eng., 131(2), pp (2005). Biograpies Hossein Heydari received is BS degree in Water Engineering from Mazandaran University, Sary, Iran, and is MS degree in Hydraulic Engineering from Amirkabir University of Tecnology, Teran, Iran. He is currently working as a consulting engineer. Amir R. Zarrati obtained a BS degree in Civil Engineering from Amirkabir University of Tecnology, Teran, Iran, an MS degree in Hydraulic Engineering from te University of Newcastle upon Tyne, UK, and a PD degree from Imperial College of Science and Tecnology, London, UK, in Dr Zarrati is currently Faculty Member and Professor of Hydraulic Engineering at Amirkabir University of Tecnology, Iran, and is involved in teacing and researc in various elds of Hydraulic Engineering. Mojtaba Karimaee Tabarestani received is BS degree in Civil Engineering from Mazandaran University, Babol, Iran (Nosirvani Institute of Tecnology) and is MS degree in Hydraulic Engineering from Amirkabir University of Tecnology, Teran, Iran, were e is currently a PD degree student of Hydraulic Engineering.