Sediment Transport in Shallow Overland Flow

Transcription

1 Sediment Tranport in Shallow Overland Flow M.J.M. Römken USDA-ARS National Sedimentation Laboratory Oxford, MS M.R. Suryadevara Department of Civil Engineering Univerity of Miiippi Univerity, MS S. N. Praad Department of Civil Engineering Univerity of Miiippi Univerity, MS ISELE 11 Anchorage, Sept. 19-1, 11. 1

2 Overview 1. Introduction. Synopi of in-houe ediment movement reearch at the grain level. 3. Drag Reduction Analyi 4. Concluion

3 Introduction Numerou Sediment tranport tudie in channel flow motly coare ize material and ubcritical flow. Relative few ediment tranport tudie in hallow overland flow motly aggregated material and uper-critical flow. 3

4 Shallow overland flow - Experimental Micrometer Fibre-optic cable 1 Optical probe Reflective Solid granule tape Channel bottom Optical probe meaurement location Hopper Feeder Intermediate water tank Surge tank Rotameter Rotary ampler Inclined channel Travere mechanim Valve Schematic Diagram of Experimental Set-up 4

5 Meandering development: Medium and 5 cm t = ec t = 1 ec t = 446 ec t = 664 ec (a) (b) (c) (d) u t = 7 ec (1.3 min) t = 87 ec t = 11 ec 63.5cm (h) (e) (f) (g) Fig. (a) (g): Meander formation and it development (all the figure correpond to the ame cale (camera placed at a fixed location). Particle ize, d = 6 85 μm. Water flow rate, q l = 15.7 l/min (Fr l = 1.45); olid feed rate i contant, m = g/min. Fig. (h) Fully developed meander tructure (m t = 1. g/min). 5

6 Obervation Tranport mode 1 cm 1 m Figure : Sediment tranport rate in relation to ediment addition rate. Coare and (d = 1-14 m) water flow rate q l = 15.7 l/min (Fr l = 1.45) 6

7 Tranport rate v olid concentration 14 1 II II 1 m t, g/min 8 6 I I III III 4 Coare Sand Medium Sand Figure : Tranport rate-concentration curve for and tranport in hallow tream. Flow rate, 1.6 l/min. Label I, II, and III repreent altation, ediment wave (tripe), and ediment wave (meander) repectively. 7

8 Velocity v. Concentration Meaurement.5.4 gla bead (dm = 8 m) medium and (dm = 75 m) coare and (dm = 1 m).36.3 gla bead (dm = 8 m) medium and (dm = 75 m) coare and ( dm = 1 m) u, m/.3. u, m/ Frl = Frl = Fig : Meaured velocity v. concentration relationhip for gla bead, coare and medium ized and for two hydraulic regime (Fr l = 1.9 and Fr l = 1.45) 8

9 Analyi Baed on olution of the conervation of ma and momentum equation. For thi cae with water and relative large ize particle a two-layered flow ytem wa aumed to exit. A chematic of thi tranport model i given: y H-h h x z H water ediment Fig: Sediment tranport in water over an inclined channel - unit width diperive tre in the ediment - unit width tractive hydro-dynamic tre on the ediment h - altation height H - water depth (flow) - bed lope and x,y,z are coordinate 9

10 1. Differential equation Analyi Sediment tranport relationhip of olid concentration () a a function of the moving patial co-ordinate X = (x-ct) 3 (u c) d 5h dx d whg d d dx 1 d dx g1 1 3 in h d.5 3 (1) 1

11 6 (1 ) h 48 d 3 q C Analyi. Critical olid concentration A imple criteria for the tranition of grain proce from altation to trip mode i obtained from equation (1) by etting the coefficient of (d/dx) to zero. Then, the critical linear olid fraction c i implicitly given by, m w q m Sediment ma flow rate per unit width of the channel. U () 11

12 Particle velocity v concentration 3 u 1.7 C m C U α h / d (3) u particle velocity; C m Coefficient for the particle matrix (Eame et al., 4) ; C maximum poible volumetric concentration ; U free tream velocity of water ; - linear particle concentration ; h altation height ; d particle diameter Eame, I., J. C. R. Hunt, S. E. Belcher. 4. Invicid mean flow through and around group of bodie. J. Fluid Mech. 515:

13 Boundary Effect Conceptual Model of Particle Impact Mechanic U u 1 uv 1 v1 v uv u h Impact pule t t 1 Fdt t = t 1 Impule component: It mu1 I mv Relationhip : n 1 u v I t = t m uv1 uv with n m u1 u v 1 gh.5 ; I t.5i n Large oblique impact. t = t 1 u 1 = u t = t u = u t = e t u e t = coefficient of retitution Reult : h e t u Praad, S.N., M.R. Suryadevara, M.J.M. Römken. 9. Grain tranport mechanic in hallow overland flow. Ecohydrology (3): (4) 13

14 Boundary effect Aume u = (u +u t )/, then h = 8.6 x 1 [(1-e t )/(1+e t )] u (5) Which upon ubtitution in the particle velocity linear concentration relationhip yield u 1.13x1 C m C 4 d 1.5 U 1 1 e e t t (6) 14

15 A number of interaction were conidered : particle fluid interaction (Bagnold diperive preure); particle boundary impact (grain mechanic). Particle-particle interaction (colliion). However, not conidered i the particle particle interaction at low concentration that lead to drag reduction. That may be important in the formation of cluter and ediment wave. 15

16 Can we in edimentary fluid mechanic learn omething from fih and bird? Bird migration. A location in Irael. Photo Courtey : C. I. Cohen. Bird flock Vee formation. Location in Denmark. Photo Courtey : A. Filippone. Tropical under water life. Photo Courtey 16 : Kevin Crane.

17 Saltating coare and (a) (b) (c) (d) (a) u 5cm 5cm 5cm 5cm.4.3 (e) mt = 6. g/min.1.8 (f) mt = 55.3 g/min t, ec Fig : Saltating flow of coare and particle (d mean = 1 µm) with increaing ediment tranport rate and a water flow rate of 1.6 l/min (Fr l = 1.9). Typical photograph [fig (a)-(d)] of altating grain for four tranport rate m t = 6. g/min, 11.8 g/min, 38.1 g/min & 55.3 g/min repectively. Fig (e) & (f) repreent change in the planar concentration with time for fig. (a) & 17 (d), repectively. t, ec

18 Drag quantification Free urface Spherical particle u f u p Bottom wall u uf up u - lip velocity, u f - fluid velocity at the elevation of the particle. u p particle velocity. (1) Drag force on a particle, F C D D u Where C D i the coefficient of drag. () 18

19 Drag quantification Oceen expreion for tream function to account for the inertial effect of fluid motion (Thi may be of importance for the Reynold number in the wake region away from the particle center) u d 3R ψ (r 1) in θ r r 1 3R 1 1 r coθ (3) Drag force following correction : D 3πu d (4) Where, - Coefficient of vicoity 19

20 Drag quantification Velocity ditribution in wake region u r 1 ψ u d d. 3 r.inθ θ 4r 4r (5) Drag of lead particle F C F D1 D C D D u Drag of following particle Net drag effect << 1 F D u u CDu α (6) (7) (8)

21 F F DN C D u Drag quantification Net drag effect for multiple particle On the third particle 9 1 F D3 CDu 1 1 α (9) 16 On the N th particle π 6 DN CDu α N α Net drag on uniform paced particle Drag reduction coefficient k F 3π DN 1 α CDu 3 (1) (11) (1) 1

22 Concluion All evidence point out that edimentary fluid mechanic eem to play a much larger role in ediment tranport problem than o far ha been aumed.