Measurements in a water channel for studying environmental problems Part I. Fabien ANSELMET

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1 Measurements in a water channel for studying environmental problems Part I Fabien ANSELMET IRPHE - Marseille With : M. Amielh, O. Boiron, (IRPHE) L. Pietri, A. Petroff, F. Ternat, P. Boyer, M.A. Gonze, (CEA/IRSN, Cadarache) A. Mailliat 1

2 Introduction Water channel characteristic properties Cohesive sediment properties Aerosol dry deposition on vegetative canopies 2

3 Introduction Water channel main advantages: - large Reynolds numbers - similitude with wind tunnels easily achieved (especially for turbulent boundary layers: δ/x, Cf = f(rex=u e X/ν)) - flow visualisations and LDV/PIV measurements easily performed but non negligible acceleration effect when channel is long (several to ten meters or more) 3

4 Water channel characteristic properties 4

5 Previous sediment experiments in the COM water channel Sediment samples Water volume 2 to 4 m 3 Wall stress (N/m2) 5

6 External velocity : U e U e Water height : h Boundary layer thickness : δ Y X Wall friction : C f, or u* Development length : X Spanwise dimension : B u* = U e 6 C 2 f

7 Re x = U e.x / ν δ/x = 0.38(Re x ) -1/5 C f = 0.059(Re x ) -1/5 Wall stresses τ p (=ρu* 2 ) 2 Nm -2 U e 1m/s X 1 m δ 3 cm 7

8 Estimated boundary Epaisseur conche layer limite thicknesses turbulente (δ) 0,25 0,2 épaisseur couche lim. en m 0,15 0,1 à 8m cond. D'entrée à 7m cond. D'entrée à 6m cond. D'entrée à 5m cond. D'entrée à 4m cond. D'entrée à 3m cond. D'entrée à 2m cond. D'entrée à 1m cond. D'entrée 0, ,2 0,4 0,6 0,8 1 1,2 Ecoulement m/s 8

9 The two sections where sediment samples can be inserted 8 m 13.5 m B = 60 cm, 10 cm < h < 50 cm, 0.1 m/s < U b < 1 m/s 9

10 The water channel HERODE (built in 2003) 10

11 80 U (cm/s) m 3 /h, X=550 cm 100m 3 /h, X=550 cm 150 m 3 /h, X=550 cm 200 m 3 /h, X=550 cm 230 m 3 /h, X=550 cm (cannot be used) 20 PIV velocity profiles Y (cm) 11

12 Bulk velocity : U b S Dh = 4 P Side a for a square duct Diameter D for a circular pipe Present experimental data : < Re Dh < PIV, X = 20 cm PIV, X = 70 cm PIV, X = 550 cm Melling (1976), Re Dh =42000 Gessner et al. (1979), Re Dh = U e /U b Present Fluent computations (h=16 cm): U b = 0.20 m/s U b = 0.30 m/s U b = 0.45 m/s U b = 0.60 m/s U b = 0.75 m/s X/D h Any guideline for quantifying this acceleration effect? 12

13 From Demuren and Rodi, JFM,

14 For laminar conditions only, from White, Viscous Fluid Flow,

15 Data for open channels : only by Kirgöz and Ardichoglu (1997) L/h = Re/Fr For HERODE (h=16 cm) : L 4 m : wrong!!! 15 Our measurements for δ/x (with δ=h) suggest L 11 m

16 Need for a systematic study of the development region of pipe, duct and open channel flows 3D Fluent computations : 2 mesh sizes: 160x32x60 (8/24 m, cm) 400x60x60 (40 m, 30 cm) (+ circular pipe) 2 conditions for the «free surface»: zero friction (open channel) symmetry (square duct) V, y U, x Free surface k-ε standard model : 3 u (u rms / U b = 1%, l rms = 1cm : inlet) Lengths : 8 m (stretched to 24 m) and 40 m ½ span (B) : 30 cm (with symmetry on the axis) 3 depths (h) : 16 cm, 21 cm, 30 cm 5 velocities : 20, 30, 45, 60 and 75 cm/s ε Lateral wall Outlet 16

17 17

18 18

Duct, d = 2h = 32 cm (small mesh) 1.35 1.30 1.25 Present computations : U b = 0.20 m/s U b = 0.

19 Duct, d = 2h = 32 cm (small mesh) Present computations : U b = 0.20 m/s U b = 0.30 m/s U b = 0.45 m/s U b = 0.60 m/s U b = 0.75 m/s 1.20 U e /U b X/D h or X/d 19

20 Duct, d = 2h = 32 cm (small mesh) 1.0 U/U e Present computations : 0.20 m/s 0.30 m/s 0.45 m/s 0.60 m/s 0.75 m/s Power law with 1/n = 1/6 Power law with 1/n = 1/8 Power law with 1/n = 1/ y/δ 20

21 Duct, d = 2h = 60 cm (small mesh) 1.0 U/U e Present computations : 0.20 m/s 0.30 m/s 0.45 m/s 0.60 m/s 0.75 m/s Power law with 1/n = 1/6 Power law with 1/n = 1/8 Power law with 1/n = 1/ y/δ 21

22 Duct, d = 2h = 32 cm (small mesh) U U + = (1/0.41)ln(y + )+5.25 Present computations : 0.20 m/s, u * =0.010 m/s 0.30 m/s, u * =0.014 m/s 0.45 m/s, u * =0.020 m/s 0.60 m/s, u * =0.026 m/s 0.75 m/s, u * =0.032 m/s y + 22

23 Duct, d = 2h = 60 cm (small mesh) U U + = (1/0.41)ln(y + )+5.25 Present computations : 0.20 m/s, u * = m/s 0.30 m/s, u * = m/s 0.45 m/s, u * = m/s 0.60 m/s, u * = m/s 0.75 m/s, u * = m/s y + 23

24 Schematic iso-velocity lines (experiments) δ δ h δ 1 δ 1 δ 1 δ B S Bh Dh = 4 ( = 4 ) P B+ 2h U With : δ 1 = (1 )dy U 0 e For a velocity profile U/Ue (y/δ) 1/n, 24 δ 1 = δ/ (n+1) δ

25 Circular pipes, D = 16 cm ( ) and D = 30 cm ( ) 10-2 δ 1 /X 10-3 Slope δ 1 /X=(0.38/8)Re x -1/5 Present computations : 0.20 m/s 0.45 m/s 0.75 m/s Re x 25

26 Square duct, d = 60 cm ( ) and open channel h = 30 cm ( ) 10-2 δ 1 /X 10-3 δ 1 /X=(0.38/8)Re x -1/5 Present computations : 0.20 m/s 0.45 m/s 0.75 m/s Slope Re x 26

27 Influence of the acceleration? δ dθ U U δ1 Cf = 2, with θ= (1 )dy and H 1 2 / n 1.3 dx = + U 0 e Ue θ Slope for C f = Slope for δ 1. (1/5).(n)/((n+1)(n+2)) if du e /dx negligible ( (1/5).(7/72) with 1/n=1/7) dθ H+ 2 dp but C = 2 2θ otherwise dx ρ U dx f 2 e 27

28 Circular pipes, D = 16 cm ( ) and D = 30 cm ( ) Square duct, d = 60 cm ( ) and open channel h = 30 cm ( ) C f 10-3 C f =0.059 Re x -1/5 Present computations : 0.20 m/s 0.45 m/s 0.75 m/s Re x 28

29 Circular pipes, D = 16 cm ( ) and D = 30 cm ( ) Square duct, d = 60 cm ( ) and open channel h = 30 cm ( ) Present computations : 0.20 m/s 0.45 m/s 0.75 m/s Asymptotic value (dp/dx = cste, θ = cste) Cf nd term in C f evolution law X/D h 29

30 Circular pipes, D = 16 cm ( ) and D = 30 cm ( ) Rectangular duct, d = 32 cm ( ) and open channel h = 16 cm ( ) Square duct, d = 60 cm ( ) and open channel h = 30 cm ( ) Present computations : 0.20 m/s 0.45 m/s 0.75 m/s 1.20 U e /U b X/D h 30

31 Circular pipe, D = D h = 0.16 m Square duct, d = D h = 0.60 m 1.20 U e /U b Present computations : 0.20 m/s 0.30 m/s 0.45 m/s 0.60 m/s 0.75 m/s x x x10 7 U b X/ν 31

32 Slope U e /U b Present computations : 0.20 m/s 0.45 m/s 0.75 m/s (X/D h )/(U b X/ν) 1/5 32

33 Slope U e /U b Present computations : 0.20 m/s 0.45 m/s 0.75 m/s δ 1th /D h with δ 1th = (0.38/8) x (Re x ) -1/5 (direct consequence of the flow rate conservation, π 2 π 2 Ue 1 pipe flow : Ub D h = U e (D h - 2 δ 1), = 1+ 4 δ1/dh ) 4 4 U (1-2 δ /D ) b 1 h 2 33

34 Slope U e /U b Present computations : 0.20 m/s 0.45 m/s 0.75 m/s (X/D h )/(U b X/ν) 1/5 1/5 5 5 h b e h b e (X/D )/(U X/ ν ) = C, (L /D ) = C U L / ν 5/4 1/4 5/4 1/4 e h = b h ν = L/D C (UD/) C (Re), L e /D h = 1.3 (Re) 1/4 or 2.0 (Re) 34 1/4

35 Szablewski (1953) : pipe flows, Kirgöz and Ardichoglu (1997) : open channel flows, L e /D h Published relation : 4.4 Re 1/6 Published relation : 1.6 Re 1/4 Present results : 1.3 Re 1/4 Present results : 2.0 Re 1/ Re 35

36 Circular pipes, D = 16 cm ( ) and D = 30 cm ( ) 10-2 δ 1 /X 10-3 Present computations : 0.20 m/s 0.45 m/s 0.75 m/s (X/D h )/(U b X/ν) 1/5 36

37 Square duct, d = 60 cm ( ) and open channel h = 30 cm ( ) 10-2 δ 1 /X 10-3 Present computations : 0.20 m/s 0.45 m/s 0.75 m/s (X/D h )/(U b X/ν) 1/5 37

38 Compilation of square duct data by Demuren and Rodi (1984), Open channel data measured by Nezu and Rodi (1986), x10-3 8x10-3 7x10-3 6x10-3 5x10-3 Cf asympt 4x10-3 3x10-3 2x10-3 Prandtl relation for circular pipes Present computations : Circular pipe Square duct Open channel Re Asymptotic values in the developed region 38

39 Compilation of pipe flow data by Coantic (1966), Compilation of plane channel data by Dean (1978), Compilation of square duct data by Demuren and Rodi (1984), Open channel data measured by Nezu and Rodi (1986), Present computations : Circular pipe Square duct Open channel (U e ) asympt /U b Re 39

40 Similarities / differences with laminar conditions Schmidt & Zeldin's data (1969) Circular pipes : Re D =100, 500, 1000 Plane channels : Re d =100, 500, K Data reported by Sparrow et al. (1964) : 0.4 pipe, Targ's data pipe, Sparrow's data 0.2 channel, Targ's data channel, Sparrow's data (X/D)/(U b D/ν) or (X/d)/(U b d/ν) Laminar flows seem to display weaker universal behaviour : role of (specific) instabilities for pipe flows? 40

41 Re = 100 Re = 500 Pipes U e /U b Re = 1000 Channels X/D h 41

42 Results obtained by Sparrow et al. (1964) : circular pipe plane channel 1.8 U e /U b Slope δ 1 /D h 42

43 δ 1 /X δ 1 /X=1.72Re x -1/2 δ 1 /X=1.15Re x -1/2 δ 1 /X=600Re x -1 Sparrow et al. (1964) : circular pipe plane channel Re x (δ 1 ) asympt = δ/3 = d/6, Re =

44 Conclusion - Acceleration in the development region of pipe, duct and open channel flows is a unique linear function of δ 1 /D h - Development length L e is a function of (Re) 1/4 and not (Re) 1/6 ( as written in most monographs) - Acceleration scales as (X/D h )/(Re) 1/4 and not (X/D h )/(Re) ( as is the case for laminar flows) - Influence of secondary vortices in the corners is negligible for these flow features -k-ε model is sufficiently accurate for studying such properties of the development region We are now ready to use the water channel for studying specific problems associated with turbulent boundary layers. 44

45 Cohesive sediment properties (Fabien TERNAT s thesis, 2007) 45

46 - For pollutant transport/storage in rivers (radionuclide/metallic elements), fine cohesive particles are essential because of their affinity with such 46 positive ions.

47 Diffusion Sorption Transport Desorption Diffusion Deposit Sorption Desorption Diffusion Erosion Accumulating role of the bottom sediment Diagenesis Liquid mud Plastic mud Solid mud 47

48 - Very little is known about the properties of cohesive sediment : * erosion is modelled through threshold laws like Partheniades (1965) : τ ce is «much larger» for cohesive than for non-cohesive sediment, * β is generally considered equal to 1, * for non-cohesive sediment, Shields diagram allows to collapse all data Can we derive a «general» model to account for the cohesive effect? 48

49 * ce ρwuce τ Wallfriction θ (or τ *) = = = ( ρ ρ )gd ( ρ ρ )gd Buoyant weight s w s w 2 Particle Reynolds number, * ce * u d Re = ν 49

50 d = cste : θ = Re*2(ρ w ν2/((ρ s ρ w )gd3)) u* = cste : θ = Re*-1(ρ w u*3/((ρ s ρ w )gν)) 50

51 51

52 1) 2) 4) 3) 52

53 53

54 using : 54

55 Different sediment classes associated with increasing τ ce values 55

56 56

57 Shields/Soulsby Our domain of interest : Re* < 1 57

58 Balance between : The particle «moves» (rotation around the vertex I) if (Φ is a characteristic internal friction angle) 58

59 Erosion threshold : 59

60 For non cohesive sediment : 60

61 A modelling attempt of cohesion : using Van der Waals force For two particles : 61

62 For any particular cristal arrangement (simple cubic, centered cubic, ), the compaction factor is defined (as the ratio between the effective volume of particles and the total cristal volume) by :, with b = d + di, the distance between two particle centers. Thus :, with d i > 0 implying that c < c c (generally equal to π/6). 62

63 63

64 And, using the porosity n : (n = V w /V tot ) 64

65 If we now consider that the «small» and «big» particles are arranged like: 65

66 Then, with so that (with d i = K d s ). 66

67 If we also consider that the particle is only partially buried at the Interface water/sediment: then the actual contact surface is: so that C is given by: (for any d b /d s pair) 67

68 For a given size of «big» particles d b, the elementary cohesion force exerted by all smaller particles of size d s is then : (where s(d) is the granulometric spectrum). Then, the total cohesion force writes: 68

69 69

70 70

71 71

72 Finally, the global cohesion function acting within a sediment sample is: So that u* ce is finally obtained by fiding the zeros of the relation: (which is found to have only one positive real solution). 72

73 73

74 These porosity profiles are fitted according to Athy s law: 74

75 75 The eroded depth estimated from the suspended matter concentration in the water channel has to be corrected (on the basis of Athy s law).

76 76

77 Conclusion - The water channel HERODE allowed us to perform experiments on the erosion properties (τ ce, porosity, granulometry) of cohesive sediment - These results were used as a basis for developing a model of cohesion Future developments: - Test the cohesion model on other cohesive sediment (with different origins : different clay contents, different water salinities, different water ph values,., and different erosion modes also?) - Improve the water channel in order to have a better control of the eroded sediment height and of the fraction of saltating eroded matter 77

78 Thank you.. 78

Fundamental Concepts of Convection : Flow and Thermal Considerations. Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.

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