Wednesday, November 28, 2012

Mechanism of Efficient Sediment Transport by Hyperconcentrated Flow in the Lower Yellow River (Part II)

1. Friction Characteristics of Hyperconcentrated Flow

The magnitude of sediment transport capacity of flow is mainly determined by the hydrodynamic condition (Qi et al., 2002). It is found that in turbulent region, the friction characteristics of hyperconcentrated flow are the same as those of the clear water flowwhich can be calculated with Manning’s formula. As shown in Table 1, while sediment concentration ranges from 55 to 843 kg/m3, Manning’s coefficients of hyperconcentrated flow (S >= 200 kg/m3) and low sediment-laden flow (S < 200 kg/m3) at Xiaolangdi Station (Figure 1) on the lower Yellow River are almost the same. The average Manning’s n value for hyperconcentrated flow is 0.041, and 0.039 for low sediment-laden flow. The value of Manning’s coefficient of hyperconcentrated flow is a little bit higher, which is mainly caused by the velocity measurement device itself. 

Table 1 Comparison of Manning’s Coefficients between Hyperconcentrated Flow and Low Sediment-laden Flow at Xiaolangdi Station

Hyperconcentrated Flow (S >= 200 kg/m3)
Low Sediment-laden Flow (S < 200 kg/m3)
Date
Q
(m3/s)
S
(kg/m3)
H
(m)
V
(m/s)
n
Date
Q
(m3/s)
S
(kg/m3)
H
(m)
V
(m/s)
n
08/07/77
5,240
268
7.5
2.93
0.036
08/01/82
7,450
56.5
8.1
3.48
0.038
08/07/77
5,120
324
7.5
2.74
0.041
08/01/82
7,220
56.5
7.4
3.66
0.036
08/07/77
6,910
592
8.6
3.1
0.043
08/01/82
6,230
56.5
7.1
3.35
0.038
08/07/77
9,720
843
9.7
3.87
0.042
08/02/82
9,400
55
8.6
4.05
0.036
08/08/77
6,550
356
8.9
2.91
0.049
08/02/82
9,290
55
9.2
3.76
0.041
08/08/77
4,950
405
7.6
2.43
0.045
08/02/82
7,710
55
8.6
3.4
0.039
08/28/73
3,110
440
7.2
2.19
0.041
08/02/82
5,150
69.1
7.9
3.03
0.038
08/28/73
3,520
508
7.8
2.39
0.037
08/03/82
5,660
91.1
7.6
2.84
0.041
08/28/73
2,880
324
7.8
2.32
0.036
08/03/82
4,790
99.6
7
2.72
0.037
09/02/73
4,150
313
7.7
2.53
0.040
08/04/82
4,150
82
7.1
2.37
0.041

 
 
 
 
 
08/04/82
3,550
82
6.6
2.29
0.040

 
 
 
 
 
08/05/82
2,970
66.4
7.2
2.01
0.043
Average 
0.041
Average 
0.039
Note: in this table, Q, S, H, V and n stand for discharge (m3/s), sediment concentration  (kg/m3), average water depth (m), flow velocity (m/s) and Manning’s coefficient. Dates are expressed in MM/DD/YY notation.

2. Effect of Sediment Concentration on Its Vertical Distribution

The increase in sediment concentration and fine particle content results in the increase of flow viscosity and specific weight, and consequently decreases of particle fall velocity. In some cases even mud flow is formed. Based on 96 sets of field data collected from 9 stations along the main stream and tributaries, namely, Huayuankou, Jiahetan, Gaocun, Sunkou, Aishan, Luokou of the lower Yellow River (Figure 1), and Huaxian, Huayin of lower Weihe River (tributary), and Chaoyi of Beiluohe River (tributary), the vertical sediment concentration profile was studied by comparing value of Ks with the cross sectional average sediment concentrations S. Here Ks is the ratio of sediment concentration at the relative depth 0.2h to that at 0.8h (measured from free surface), e.g. Ks = S0.2 / S0.8, when median sediment grain size d50 is 0.03 - 0.10 mm. As shown in Figure 2, when the average sediment concentration is lower than 200 kg/m3, even with Froude’s number (Fr) higher than 0.2, the sediment concentration is not uniformly distributed in the vertical direction, where Ks is around 0.4 to 0.8. When the average sediment concentration is higher than 300 kg/m3, the sediment concentration becomes more uniform in the vertical direction, where Ks is around 0.9 to 1.0.
 Figure 2 Relationship between Sediment Concentration Ratio (Ks) and Sediment Concentration (S)

The effect of changes in rheological characteristics of fluid on sediment transport can be analyzed as followings. The ratio of fall velocity of a particle in clear water to that in sediment-water mixture (or muddy-water) can be written with Stokes equation: 
Where ω0 and ωs are particle fall velocities in clear water and in sediment water, respectively. γs and γm are the specific weights of sediment particles and sediment water. μr is the ratio of the viscosity of sediment water over clear water. With the increase of sediment concentration, μr also increases, which means fall velocity of particles decreases dramatically in sediment water. When d50 = 0.036 mm and percentage of sediment with grain size finer than 0.01 mm is 20% (equivalent to the average sediment gradient of the Yellow River),  calculated values of mr and w0/ws corresponding to the long term average sediment and field observed sediment of lower Yellow River are listed in Table 2.

Table 2 Impact of Sediment Concentration on Fall Velocity

S (kg/m3)
0
100
200
300
400
500
600
700
800
Notes
mr
1.0
1.49
2.08
2.74
3.48
4.32
5.40
6.93
9.33
Average Sediment Data
mr
1.0
1.50
2.0
2.4
3.0
4.0
4.50
6.50
8.50
Observed Sediment Data
w0/ws
1.0
1.55
2.25
3.09
4.10
5.32
6.97
9.38
13.4


As shown in Table 2, with the increase of sediment concentration, w0/ws increases continuously, and the fall velocity decreases significantly. When the sediment concentration is 300 kg/m3, the fall velocity in muddy water is only one-third of that in clear water. When the sediment concentration increases to 700 kg/m3, the fall velocity in muddy water is only one-tenth of that in clear water. The above result is in good agreement with the vertical sediment concentration distribution shown in Figure 2. Both indicate that fall velocity decreases with the increasing sediment concentration, and the vertical sediment distribution also becomes more uniform, which makes the sediment particles easier to be transported.

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