. The concepts of shear stress and power loss of water-flow were introduced to
deduce the expression for G in previous studies, i.e. the power loss of water-flow in per unit
volume is
Zhang Hongyi
Beijing University of Aeronautics and Astronautics, Beijing, China,100083
Zhang Hongwu
Tsinghua University,Beijing, China,100084
Li Yuanfa, Zhang Junhua, Li Shuxia
Yellow River Institute of Hydraulic Research, Zhengzhou, China, 450003
Abstract: A new formula for evaluating the mean velocity gradient G of high turbidity water flow in pipes is set up based on the mixing length theory of turbulent flows, which is proved valid for the hyper-concentrated turbulent flow in pipes. A test study is conducted to investigate the flocculation of high turbidity water flow in pipes. It is found that the optimum value of mixing reaction extent GT is 60~120.
Keywords: high turbidity water, flocculation in pipes, mixing extent, test study
With the development of Chinese economy, the water demand of industries and cities in the Yellow River basin has been increasing (Zhao, 1996; Xi, 1996), and the Yellow River is becoming an important water source of the industries and cities along the river. Due to the loose flocculent structure and small floc size, the sediment in high turbidity water of the Yellow River settles down very slowly during the natural settling process. In order to improve the water quality, a certain quantity of flocculating agent is usually added to the water to accelerate the sediment settling while the hyper-concentrated water with finer particles flows into a settling basin.
In the design of water supply and sewerage works, the mean velocity gradient G of the turbulent water-flow is often adopted to represent the intensity of mixing reaction, so the product of GT (T denotes the time of mixing reaction) can reflect the magnitude of mixing reaction extent. Many researchers studied the value of GT and several formulas for calculating G have been published (Camp.T.R, 1943; Li, 1986). Although the high turbidity water flow in pipes is turbulent and the turbulent stress is much larger than the laminar shear stress, the present formulas for evaluating the mean velocity gradient G were all derived under the laminar flow conditions.
In
view of the existing problems, a new formula for evaluating the mean velocity
gradient G of high turbidity
water-flow in pipes is established based upon Prandtl’s mixing length theory
for turbulent flows. A test study on flocculation in pipes is conducted and the
optimum values for GT and G
are obtained from the test results.
As we known that the mean velocity gradient is
applied to represent the mixing reaction intensity G, so G can be expressed as
. The concepts of shear stress and power loss of water-flow were introduced to
deduce the expression for G in previous studies, i.e. the power loss of water-flow in per unit
volume is
(1)
For laminar flow (Xu,
1996):
(2)
Substituting Eq. (2)
into Eq. (1) yields
And
(3)
Let
(4)
where W is the volume of water stirred in settling basin, W=QT; μ is the dynamic viscosity of water; P1 is the power loss of water-flow in mixing or reacting device.
When mixing or reacting device is used, P1 is determined by the head loss △h, namely P1=γQ△h,
and substituting P1 into Eq.
(4), one obtains
, substituting
into Eq. (3), one gets the commonly used formula:
(5)
where i is hydraulic slope. It can be found from the above derivation that the following simplifications are needed to modify:
(1) The turbulent high turbidity water-flow in pipes is treated as laminar flow;
(2) Po is a physical parameter at a point in Eq. (1), but in Eq. (4) it is defined as mean value of water body.
Under the turbulent flow conditions, τ=
τ2
with very small viscous stressτ1.
For flow in pipes
(6)
where l is called mixing length, and can be written as follows(Zhang,
1994):
(7)
In which r0 represents pipe radius; cn is vortex coefficient related to volume sediment concentration Sv (Zhang, 1994):
Substituting Eq. (7)
into Eq. (6) and let
and
, one gets:
(8)
In
Eq. (8), u* stands for
friction velocity and expressed by:
(9)
Because the value of
is negative, we take the absolute
value and have
(10)
Average
the value of
along vertical
direction
(11)
Integrating
Eq. (11), we obtain the new formula for calculating G:
(12)
The value of G estimated by Eq. (12) differs greatly from that by Eq. (5), in order to find out the optimum value of GT for flocculation of high turbidity water in pipes, a relationship between flocculation effects and GT values is depicted in Fig. 1 by adopting Eq. (12) and test data (Li, 1986). In this Figure, u at vertical coordinate represents settling velocity after high turbidity water was flocculated in pipes, u0 is the settling velocity of mixing reaction by hand in still water. The larger the ratio of u/u0, the larger the floc size in pipes will be, so the ratio u/u0 can used as the index of flocculating effects. We can see clearly from the figure that the optimum values of GT is within 60-100.
The test device is shown in Fig. 2. The test procedure is as follows: firstly choose Yellow River sediment with a certain size distributions and mix the sediment evenly with tap water in slurry agitating tank, then send sediment into the test pipe by a slurry pump. The material of the rigid plastic test pipe is white polyvinyl chloride, its roughness n after calibration is 0.0095. Various flow velocities in the pipe can be reached by controlling the discharge in pipe via an electric magnetic flow meter. Polypropylene amide was used as flocculating agent in the test study, its molecular weight is 4,500,000 and drugging content 0.002. The drugging quantity is controlled by a rotary flow meter. To avoid the impact of valve at entrance on flow in the pipe, drugging point should be located at a place 50 times of pipe diameter downstream of the valve. When the stability of inlet water discharge and drugging quantity is all reached, sampling is made one by one at various sampling holes downstream of the drugging point. and carry out settling observation in still water in settling tube to determine the settling velocity of muddy water surface. The quicker the settling velocity of muddy water surface , the better the flocculation effects is.
The sediment prepared for the test is taken from the floodplain at Huayuankou of the Yellow River. The same sediment size distribution, concentration and drugging quantity are adopted in the tests to make their results comparable well. Table 1 shows the sediment size distribution used in the tests.
Table 1 Sediment size distribution for flocculation tests in pipes (d50=0.034mm)
|
Size (mm) |
0.100 |
0.075 |
0.050 |
0.025 |
0.010 |
0.005 |
|
Percentage (%) of sediment weight which is finer than a certain size |
100 |
89.4 |
77.2 |
33.2 |
14.5 |
9.9 |
Eq. (12) demonstrates that the mixing reaction intensity is a fixed value when the sediment concentration, pipe diameter and water-flow velocity are fixed. Sampling at different distance downstream the drugging point, different mixing reaction time T could be observed. The tests are carried out under the conditions of pipe diameter D = 10.5, 7.0, 4.5mm respectively, sediment concentration is 90kg/m3, drugging quantities are all the same 8mg/L, and water temperature is 19.7℃. Relationships of settling velocity u of muddy water surface with GT are illustrated in Fig. 3(a), Fig. 3(b) and Fig. 3(c). It is known from the figure that with increasing in GT values, settling velocity of muddy water surface increases firstly and then decreases and tends to a stable value. It basically conforms to Li’s results (Li, 1986) and some differences exist only in the optimum GT value range of flocculation of high turbidity water in pipes. The optimum GT values can be found in the range of about 60-120 from Figure.3 and the Eq. (12) is accurate in view of the test results.
It is pointed out that G values greatly affect the flocculation effects in high turbidity water in pipes, the effects could be lowered with too big or too small G values (Zhang, 1983; Fu,1994). The reason is that mixing extent between flocculating agent and sediment particles is not sufficient when G values are too small, conversely, flocs formed could be broken again when GT surpasses a critical value. Therefore, it is very important to select a reasonable G value. Relationship of G values with muddy water surfaces is displayed in Fig. 4 through the test results of flocculation in high turbidity water in pipes. It can be concluded that a maximum value of settling velocity of muddy water surface exists with changes of G values, and the optimum value of G is about 25S-1 .
Fig. 4 Relationship of flocculation effects in high turbidity water in pipes with G values
A test study is conducted to investigate the flocculation of high turbidity water in pipes. It is found from the test results that the optimum value of mixing reaction extent GT is 60~120.
References
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