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 flow，which 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 K_s with the cross sectional average sediment concentrations S. Here K_s is the ratio of sediment concentration at the relative depth 0.2h to that at 0.8h (measured from free surface), e.g. K_s = S_0.2 / S_0.8, 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 K_s 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 K_s is around 0.9 to 1.0.

 Figure 2 Relationship between Sediment Concentration Ratio (K_s) 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 ω_s are particle fall velocities in clear water and in sediment water, respectively. γ_s and γ_m are the specific weights of sediment particles and sediment water. μ_r is the ratio of the viscosity of sediment water over clear water. With the increase of sediment concentration, μ_r 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 m_r and w₀/w_s 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/w_s 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.